CH 9 Solutions
112 Pages

CH 9 Solutions

Course: CHE 2450, Spring 2010

School: LSU

Word Count: 9441

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9 Solutions 44918 1/28/09 2:34 PM Page 815 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 91. Determine the mass and the location of the center of mass (x, y) of the uniform...

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Solutions 9 44918 1/28/09 2:34 PM Page 815 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 91. Determine the mass and the location of the center of mass (x, y) of the uniform parabolic-shaped rod. The mass per unit length of the rod is 2 kg> m. y y2 4x 4m x 4m 8 15 9 Solutions 44918 1/28/09 2:34 PM Page 816 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 92. The uniform rod is bent into the shape of a parabola and has a weight per unit length of 6 lb> ft. Determine the reactions at the fixed support A. y y2 3x 3 ft A x 3 ft 8 16 9 Solutions 44918 1/28/09 2:34 PM Page 817 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 93. Determine the distance x to the center of mass of the homogeneous rod bent into the shape shown. If the rod has a mass per unit length of 0.5 kg> m, determine the reactions at the fixed support O. y 1m 1m y2 O x3 x 8 17 9 Solutions 44918 1/28/09 2:34 PM Page 818 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. *94. Determine the mass and locate the center of mass (x, y) of the uniform rod. The mass per unit length of the rod is 3 kg> m. y y 4 x2 4m x 2m 8 18 9 Solutions 44918 1/28/09 2:34 PM Page 819 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 95. Determine the mass and the location of the center of mass x of the rod if its mass per unit length is m = m0(1 + x> L). y x L 8 19 9 Solutions 44918 1/28/09 2:34 PM Page 820 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 96. Determine the location (x, y) of the centroid of the wire. y 2 ft 4 ft y x2 x 97. Locate the centroid x of the circular rod. Express the answer in terms of the radius r and semiarc angle a. y r a C x a r x 8 20 9 Solutions 44918 1/28/09 2:34 PM Page 821 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. *98. Determine the area and the centroid (x, y) of the area. y 4m y2 4x x 4m 8 21 9 Solutions 44918 1/28/09 2:34 PM Page 822 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 99. Determine the area and the centroid (x, y) of the area. y 1m y2 x3 x 1m 8 22 9 Solutions 44918 1/28/09 2:34 PM Page 823 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 910. Determine the area and the centroid (x, y) of the area. y 3 ft y 1 x3 9 x 3 ft 8 23 9 Solutions 44918 1/28/09 2:34 PM Page 824 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 911. Determine the area and the centroid (x, y) of the area. y y2 2 ab 4ax x b 8 24 9 Solutions 44918 1/28/09 2:34 PM Page 825 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. *912. Locate the centroid x of the area. y y x1/ 2 2x5/ 3 x 2 ft 8 25 9 Solutions 44918 1/28/09 2:34 PM Page 826 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 913. Locate the centroid y of the area. y y x1/ 2 2x5/ 3 x 2 ft 8 26 9 Solutions 44918 1/28/09 2:34 PM Page 827 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 914. Determine the area and the centroid (x, y) of the area. y xy c2 x a b 8 27 9 Solutions 44918 1/28/09 2:34 PM Page 828 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 915. Determine the area and the centroid (x, y) of the area. y h y h x2 a2 x a 8 28 9 Solutions 44918 1/28/09 2:34 PM Page 829 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. *916. Locate the centroid (x, y) of the area. y 1 1 x2 4 y 1m x 2m 8 29 9 Solutions 44918 1/28/09 2:34 PM Page 830 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 917. Determine the area and the centroid (x, y) of the area. y h y h x2 a2 x a 8 30 9 Solutions 44918 1/28/09 2:34 PM Page 831 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 918. The plate is made of steel having a density of 7850 kg> m3. If the thickness of the plate is 10 mm, determine the horizontal and vertical components of reaction at the pin A and the tension in cable BC. y C y3 2m A B 2x x 4m 8 31 9 Solutions 44918 1/28/09 2:34 PM Page 832 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 919. Determine the location x to the centroid C of the upper portion of the cardioid, r = a(1 - cos u). r a (1 cos u) y C _ x r u x 8 32 9 Solutions 44918 1/28/09 2:34 PM Page 833 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. *920. The plate has a thickness of 0.5 in. and is made of steel having a specific weight of 490 lb> ft3. Determine the horizontal and vertical components of reaction at the pin A and the force in the cord at B. y B 3 ft y x2 3 x 3 ft A 8 33 9 Solutions 44918 1/28/09 2:34 PM Page 834 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 921. Locate the centroid x of the shaded area. y x2 ) 2a y 2k(x ka x a 922. Locate the centroid x of the area. y 0.5 in. 2 in. y 1 x 0.5 in. 2 in. x 8 34 9 Solutions 44918 1/28/09 2:34 PM Page 835 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 923. Locate the centroid y of the area. y 0.5 in. 2 in. y 1 x 0.5 in. 2 in. x *924. Locate the centroid (x, y) of the area. y y 9 ft 9 x2 x 3 ft 8 35 9 Solutions 44918 1/28/09 2:34 PM Page 836 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 925. Determine the area and the centroid (x, y) of the area. y y 3 ft x y x3 9 x 3 ft 8 36 9 Solutions 44918 1/28/09 2:34 PM Page 837 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 926. Locate the centroid x of the area. y y2 1m x y 1m x2 x 927. Locate the centroid y of the area. y y2 1m x y 1m x2 x 8 37 9 Solutions 44918 1/28/09 2:34 PM Page 838 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. *928. Locate the centroid x of the area. y y h xn an h x a 929. Locate the centroid y of the area. y y h xn an h x a 8 38 9 Solutions 44918 1/28/09 2:34 PM Page 839 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 930. The steel plate is 0.3 m thick and has a density of 7850 kg> m3. Determine the location of its center of mass. Also determine the horizontal and vertical reactions at the pin and the reaction at the roller support. Hint: The normal force at B is perpendicular to the tangent at B, which is found from tan u = dy> dx. y y2 2x 2m A x 2m B 2m 8 39 9 Solutions 44918 1/28/09 2:34 PM Page 840 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 931. Locate the centroid of the area. Hint: Choose elements of thickness dy and length [(2 - y) - y2]. y y2 1m x y x 2 x 1m 1m 8 40 9 Solutions 44918 1/28/09 2:34 PM Page 841 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. *932. Locate the centroid x of the area. y y2 4x 2 ft y 2x 1 ft x 933. Locate the centroid y of the area. y y2 4x 2 ft y 2x 1 ft x 8 41 9 Solutions 44918 1/28/09 2:34 PM Page 842 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 934. If the density at any point in the rectangular plate is defined by r = r0(1 + x> a), where r0 is a constant, determine the mass and locate the center of mass x of the plate. The plate has a thickness t. y b 2 x b 2 a 8 42 9 Solutions 44918 1/28/09 2:34 PM Page 843 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 935. Locate the centroid y of the homogeneous solid formed by revolving the shaded area about the y axis. z y2 (z a)2 a2 a y x 8 43 9 Solutions 44918 1/28/09 2:34 PM Page 844 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. *936. Locate the centroid z of the solid. z a a z 1 a (a y)2 y x 8 44 9 Solutions 44918 1/28/09 2:34 PM Page 845 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 937. Locate the centroid y of the homogeneous solid formed by revolving the shaded area about the y axis. z z2 1 y3 16 2m y x 4m 8 45 9 Solutions 44918 1/28/09 2:34 PM Page 846 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 938. Locate the centroid z of the homogeneous solid frustum of the paraboloid formed by revolving the shaded area about the z axis. z h2 (a a2 y2) z h 2 h 2 y a x 8 46 9 Solutions 44918 1/28/09 2:34 PM Page 847 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 939. Locate the centroid y of the homogeneous solid formed by revolving the shaded area about the y axis. z 5 ft z2 y2 9 4 ft y 3 ft x 8 47 9 Solutions 44918 1/28/09 2:34 PM Page 848 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. *940. Locate the center of mass y of the circular cone formed by revolving the shaded area about the y axis. The density at any point in the cone is defined by r = (r0 > h)y, where r0 is a constant. a z h z a y h a y x 8 48 9 Solutions 44918 1/28/09 2:34 PM Page 849 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 941. Determine the mass and locate the center of mass y of the hemisphere formed by revolving the shaded area about the y axis. The density at any point in the hemisphere can be defined by r = r0(1 + y> a), where r0 is a constant. z y2 z2 a2 r y x 8 49 9 Solutions 44918 1/28/09 2:34 PM Page 850 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 942. Determine the volume and locate the centroid (y, z) of the homogeneous conical wedge. z h a y h z x a y 8 50 9 Solutions 44918 1/28/09 2:34 PM Page 851 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 943. The hemisphere of radius r is made from a stack of very thin plates such that the density varies with height, r = kz, where k is a constant. Determine its mass and the distance z to the center of mass G. G z r x _ z y 8 51 9 Solutions 44918 1/28/09 2:34 PM Page 852 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. *944. Locate the centroid (x, y) of the uniform wire bent in the shape shown. y 100 mm 20 mm 150 mm x 50 mm 8 52 9 Solutions 44918 1/28/09 2:34 PM Page 853 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 945. Locate the centroid (x, y, z) of the wire. z 400 mm 200 mm y x 8 53 9 Solutions 44918 1/28/09 2:34 PM Page 854 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 946. Locate the centroid (x, y, z) of the wire. z 6 in. 4 in. x y 8 54 9 Solutions 44918 1/28/09 2:34 PM Page 855 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 947. Locate the centroid (x, y, z) of the wire which is bent in the shape shown. 2 in. z 4 in. 2 in. x y 8 55 9 Solutions 44918 1/28/09 2:34 PM Page 856 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. *948. The truss is made from seven members, each having a mass per unit length of 6 kg/m. Locate the position (x, y) of the center of mass. Neglect the mass of the gusset plates at the joints. y E D 3m A 3m B C 3m x 8 56 9 Solutions 44918 1/28/09 2:34 PM Page 857 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 949. Locate the centroid (x, y) of the wire. If the wire is suspended from A, determine the angle segment AB makes with the vertical when the wire is in equilibrium. y A 60 B 200 mm 200 mm C x 8 57 9 Solutions 44918 1/28/09 2:34 PM Page 858 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 950. Each of the three members of the frame has a mass per unit length of 6 kg/m. Locate the position (x, y) of the center of mass. Neglect the size of the pins at the joints and the thickness of the members. Also, calculate the reactions at the pin A and roller E. 6m y 4m C D 4m E B 7m A x 8 58 9 Solutions 44918 1/28/09 2:34 PM Page 859 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 951. Locate the centroid (x, y) of the cross-sectional area of the channel. y 1 in. 22 in. x 1 in. 9 in. 1 in. 8 59 9 Solutions 44918 1/28/09 2:34 PM Page 860 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. *952. Locate the centroid y of the cross-sectional area of the concrete beam. 12 in. 3 in. y 12 in. 27 in. 6 in. x 3 in. 3 in. 8 60 9 Solutions 44918 1/28/09 2:34 PM Page 861 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 953. Locate the centroid y of the cross-sectional area of the built-up beam. y 6 in. 1 in. 1 in. 6 in. 3 in. 1 in. 3 in. 1 in. x 8 61 9 Solutions 44918 1/28/09 2:34 PM Page 862 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 954. Locate the centroid y of the channels crosssectional area. 2 in. 4 in. 2 in. 12 in. 2 in. y C 955. Locate the distance y to the centroid of the members cross-sectional area. y 0.5 in. 0.5 in. 6 in. 1.5 in. 1 in. 3 in. 3 in. x 8 62 9 Solutions 44918 1/28/09 2:34 PM Page 863 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. *956. Locate the centroid y of the cross-sectional area of the built-up beam. 1.5 in. 1.5 in. y 4in. 4 in. 1.5 in. 3.5 in. 11.5 in. 1.5 in. x 8 63 9 Solutions 44918 1/28/09 2:34 PM Page 864 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 957. The gravity wall is made of concrete. Determine the location (x, y) of the center of mass G for the wall. y 1.2 m _ x G _ y 3m 0.4 m x 0.6 m 2.4 m 0.6 m 8 64 9 Solutions 44918 1/28/09 2:34 PM Page 865 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 958. Locate the centroid x of the composite area. y r0 x ri 8 65 9 Solutions 44918 1/28/09 2:34 PM Page 866 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 959. Locate the centroid (x, y) of the composite area. y 3 in. 4 in. 3 in. 3 in. x 8 66 9 Solutions 44918 1/28/09 2:34 PM Page 867 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. *960. Locate the centroid (x, y) of the composite area. y 3 ft 1.5 ft 3 ft 1 ft x 8 67 9 Solutions 44918 1/28/09 2:34 PM Page 868 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 961. Divide the plate into parts, and using the grid for measurement, determine approximately the location (x, y) of the centroid of the plate. y 200 mm 200 mm x 8 68 9 Solutions 44918 1/28/09 2:34 PM Page 869 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 962. To determine the location of the center of gravity of the automobile it is first placed in a level position, with the two wheels on one side resting on the scale platform P. In this position the scale records a reading of W1. Then, one side is elevated to a convenient height c as shown. The new reading on the scale is W2. If the automobile has a total weight of W, determine the location of its center of gravity G(x, y). y c x b G P W2 8 69 9 Solutions 44918 1/28/09 2:34 PM Page 870 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 963. Locate the centroid y of the cross-sectional area of the built-up beam. 150 mm y 150 mm 20 mm 200 mm 450 mm x 20 mm 8 70 9 Solutions 44918 1/28/09 2:34 PM Page 871 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. *964. Locate the centroid y of the cross-sectional area of the built-up beam. 200 mm 20 mm 50 mm 150 mm 10 mm 300 mm 20 mm y 200 mm 10 mm 20 mm x 8 71 9 Solutions 44918 1/28/09 2:34 PM Page 872 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 965. The composite plate is made from both steel (A) and brass (B) segments. Determine the mass and location 1x, y, z2 of its mass center G. Take rst = 7.85 Mg> m3 and rbr = 8.74 Mg> m3. A G z 225 mm 150 mm B 150 mm 30 mm x y 8 72 9 Solutions 44918 1/28/09 2:34 PM Page 873 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 966. The car rests on four scales and in this position the scale readings of both the front and rear tires are shown by FA and FB. When the rear wheels are elevated to a height of 3 ft above the front scales, the new readings of the front wheels are also recorded. Use this data to compute the location x and y to the center of gravity G of the car. The tires each have a diameter of 1.98 ft. G B _ x _ y A 9.40 ft FA 1959 lb 1129 lb 1168 lb 2297 lb FB 975 lb 984 lb 3.0 ft B G A FA 1269 lb 1307 lb 2576 lb 8 73 9 Solutions 44918 1/28/09 2:34 PM Page 874 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 967. Uniform blocks having a length L and mass m are stacked one on top of the other, with each block overhanging the other by a distance d, as shown. If the blocks are glued together, so that they will not topple over, determine the location x of the center of mass of a pile of n blocks. y 2d d x L 8 74 9 Solutions 44918 1/28/09 2:34 PM Page 875 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws they as currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. *968. Uniform blocks having a length L and mass m are stacked one on top of the other, with each block overhanging the other by a distance d, as shown. Show that the maximum number of blocks which can be stacked in this manner is n 6 L> d. y 2d d x L 8 75 9 Solutions 44918 1/28/09 2:34 PM Page 876 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 969. Locate the center of gravity (x, z) of the sheetmetal bracket if the material is homogeneous and has a constant thickness. If the bracket is resting on the horizontal xy plane shown, determine the maximum angle of tilt u which it can have before it falls over, i.e., begins to rotate about the y axis. z 60 mm 60 mm 20 mm 20 mm 10 mm dia. holes y 20 mm 80 mm 20 mm 60 mm u x 8 76 9 Solutions 44918 1/28/09 2:34 PM Page 877 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 970. Locate the center of mass for the compressor assembly. The locations of the centers of mass of the various components and their masses are indicated and tabulated in the figure. What are the vertical reactions at blocks A and B needed to support the platform? y 2 4 4.83 m 5 3 3.26 m x 1 3.68 m 3.15 m 1.20 m A 1.80 m 2.30 m 2.42 m 2.87 m B 1.19 m 1.64 m 1 Instrument panel 2 Filter system 3 Piping assembly 4 Liquid storage 5 Structural framework 230 kg 183 kg 120 kg 85 kg 468 kg 8 77 9 Solutions 44918 1/28/09 2:34 PM Page 878 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 971. Major floor loadings in a shop are caused by the weights of the objects shown. Each force acts through its respective center of gravity G. Locate the center of gravity (x, y) of all these components. z y 450 lb 1500 lb G1 9 ft 6 ft 12 ft 8 ft 4 ft 5 ft 3 ft x 7 ft 600 lb G3 G2 280 lb G4 8 78 9 Solutions 44918 1/28/09 2:34 PM Page 879 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. *972. Locate the center of mass (x, y, z) of the homogeneous block assembly. z 250 mm 200 mm x 100 mm 150 mm 150 mm 150 mm y 8 79 9 Solutions 44918 1/28/09 2:34 PM Page 880 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 973. Locate the center of mass z of the assembly. The hemisphere and the cone are made from materials having densities of 8 Mg> m3 and 4 Mg> m3, respectively. z 100 mm 300 mm x y 8 80 9 Solutions 44918 1/28/09 2:34 PM Page 881 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 974. Locate the center of mass z of the assembly. The cylinder and the cone are made from materials having densities of 5 Mg> m3 and 9 Mg> m3, respectively. z 0.4 m 0.6 m 0.2 m 0.8 m x y 8 81 9 Solutions 44918 1/28/09 2:34 PM Page 882 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 975. Locate the center of gravity (x, y, z) of the homogeneous block assembly having a hemispherical hole. z 3 in. 1 in. 2.5 in. 2.5 in. x 1 in. 2.25 in. 3 in. 2.25 in. y 8 82 9 Solutions 44918 1/28/09 2:34 PM Page 883 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. *976. Locate the center of gravity (x, y, z) of the assembly. The triangular and the rectangular blocks are made from materials having specific weights of 0.25 lb> in3 and 0.1 lb> in3, respectively. z 3 in. 1 in. 2.5 in. 2.5 in. x 1 in. 2.25 in. 3 in. 2.25 in. y 8 83 9 Solutions 44918 1/28/09 2:34 PM Page 884 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 977. Determine the distance x to the centroid of the solid which consists of a cylinder with a hole of length h = 50 mm bored into its base. 40 mm y 120 mm x 20 mm h 8 84 9 Solutions 44918 1/28/09 2:34 PM Page 885 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 978. Determine the distance h to which a hole must be bored into the cylinder so that the center of mass of the assembly is located at x = 64 mm. The material has a density of 8 Mg> m3. y 120 mm 40 mm x 20 mm h 8 85 9 Solutions 44918 1/28/09 2:34 PM Page 886 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 979. The assembly is made from a steel hemisphere, and an aluminum cylinder, rst = 7.80 Mg> m3, ral = 2.70 Mg> m3. Determine the mass center of the assembly if the height of the cylinder is h = 200 mm. z 80 mm G _ z h 160 mm y x 8 86 9 Solutions 44918 1/28/09 2:35 PM Page 887 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. *980. The assembly is made from a steel hemisphere, rst = 7.80 Mg> m3, and an aluminum cylinder, ral = 2.70 Mg> m3. Determine the height h of the cylinder so that the mass center of the assembly is located at z = 160 mm. _ z z 80 mm G h 160 mm y x 8 87 9 Solutions 44918 1/28/09 2:35 PM Page 888 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 981. The elevated water storage tank has a conical top and hemispherical bottom and is fabricated using thin steel plate. Determine how many square feet of plate is needed to fabricate the tank. 8 ft 6 ft 10 ft 8 ft 8 88 9 Solutions 44918 1/28/09 2:35 PM Page 889 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 982. The elevated water storage tank has a conical top and hemispherical bottom and is fabricated using thin steel plate. Determine the volume within the tank. 8 ft 6 ft 10 ft 8 ft 8 89 9 Solutions 44918 1/28/09 2:35 PM Page 890 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 983. Determine the volume of the solid formed by revolving the shaded area about the x axis using the second theorem of PappusGuldinus.The area and centroid y of the shaded area should first be obtained by using integration. y 4 ft y2 4x 4 ft x 8 90 9 Solutions 44918 1/28/09 2:35 PM Page 891 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. *984. Determine the surface area from A to B of the tank. B z 3m 1.5 m A 1m 985. Determine the volume within the thin-walled tank from A to B. z B 3m 1.5 m A 1m 8 91 9 Solutions 44918 1/28/09 2:35 PM Page 892 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 986. Determine the surface area of the roof of the structure if it is formed by rotating the parabola about the y axis. y y 16 (x2/16) 16 m x 16 m 8 92 9 Solutions 44918 1/28/09 2:35 PM Page 893 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 987. Determine the surface area of the solid formed by revolving the shaded area 360 about the z axis. z 0.75 in. 0.5 in. 0.75 in. 2 in. 1 in. 3 in. 8 93 9 Solutions 44918 1/28/09 2:35 PM Page 894 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. *988. Determine the volume of the solid formed by revolving the shaded area 360 about the z axis. z 0.75 in. 0.5 in. 0.75 in. 2 in. 1 in. 3 in. 989. Determine the volume of the solid formed by revolving the shaded area 360 about the z axis. z 75 mm 75 mm 75 mm 250 mm 75 mm 300 mm 8 94 9 Solutions 44918 1/28/09 2:35 PM Page 895 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 990. Determine the surface area and volume of the solid formed by revolving the shaded area 360 about the z axis. z 1 in. 2 in. 1 in. 8 95 9 Solutions 44918 1/28/09 2:35 PM Page 896 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 991. Determine the surface area and volume of the solid formed by revolving the shaded area 360 about the z axis. z 75 mm 50 mm 300 mm 400 mm 75 mm 50 mm *992. The process tank is used to store liquids during manufacturing. Estimate both the volume of the tank and its surface area. The tank has a flat top and a thin wall. 3m 3m 6m 4m 8 96 9 Solutions 44918 1/28/09 2:35 PM Page 897 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 993. The hopper is filled to its top with coal. Estimate the volume of coal if the voids (air space) are 35 percent of the volume of the hopper. z 1.5 m 4m 1.2 m 0.2 m 994. The thin-wall tank is fabricated from a hemisphere and cylindrical shell. Determine the vertical reactions that each of the four symmetrically placed legs exerts on the floor if the tank contains water which is 12 ft deep in the tank. The specific gravity of water is 62.4 lb> ft3. Neglect the weight of the tank. 8 ft water surface 6 ft 4 ft 8 ft 8 97 9 Solutions 44918 1/28/09 2:35 PM Page 898 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 995. Determine the approximate amount of paint needed to cover the outside surface of the open tank. Assume that a gallon of paint covers 400 ft2. water surface 8 ft 6 ft 4 ft 8 ft *996. Determine the surface area of the tank, which consists of a cylinder and hemispherical cap. 4m 8m 8 98 9 Solutions 44918 1/28/09 2:35 PM Page 899 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 997. Determine the volume of the thin-wall tank, which consists of a cylinder and hemispherical cap. 4m 8m 8 99 9 Solutions 44918 1/28/09 2:35 PM Page 900 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 998. The water tank AB has a hemispherical top and is fabricated from thin steel plate. Determine the volume within the tank. B 1.6 m 1.5 m 1.6 m A 0.2 m 9 00 9 Solutions 44918 1/28/09 2:35 PM Page 901 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 999. The water tank AB has a hemispherical roof and is fabricated from thin steel plate. If a liter of paint can cover 3 m2 of the tanks surface, determine how many liters are required to coat the surface of the tank from A to B. B 1.6 m 1.5 m 1.6 m A 0.2 m 9 01 9 Solutions 44918 1/28/09 2:35 PM Page 902 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. *9100. Determine the surface area and volume of the wheel formed by revolving the cross-sectional area 360 about the z axis. z 1 in. 1 in. 1.5 in. 2 in. 4 in. 9 02 9 Solutions 44918 1/28/09 2:35 PM Page 903 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 9101. Determine the outside surface area of the storage tank. 4 ft 15 ft 30 ft 9102. Determine the volume of the thin-wall storage tank. 4 ft 15 ft 30 ft 9 03 9 Solutions 44918 1/28/09 2:35 PM Page 904 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 9103. Determine the height h to which liquid should be poured into the conical paper cup so that it contacts half the surface area on the inside of the cup. 100 mm 150 mm h *9104. The tank is used to store a liquid having a specific weight of 80 lb> ft3. If it is filled to the top, determine the magnitude of the force the liquid exerts on each of its two sides ABDC and BDFE. C A 4 ft D B F 6 ft 6 ft E 12 ft 8 ft 9 04 9 Solutions 44918 1/28/09 2:35 PM Page 905 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 9105. The concrete gravity dam is held in place by its own weight. If the density of concrete is rc = 2.5 Mg> m3, and water has a density of rw = 1.0 Mg> m3, determine the smallest dimension d that will prevent the dam from overturning about its end A. 6m A d 9 05 9 Solutions 44918 1/28/09 2:35 PM Page 906 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 9106. The symmetric concrete gravity dam is held in place by its own weight. If the density of concrete is rc = 2.5 Mg> m3, and water has a density of rw = 1.0 Mg> m3, determine the smallest distance d at its base that will prevent the dam from overturning about its end A. The dam has a width of 8 m. 1.5 m 9m A d 9 06 9 Solutions 44918 1/28/09 2:35 PM Page 907 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 9107. The tank is used to store a liquid having a specific weight of 60 lb> ft3. If the tank is full, determine the magnitude of the hydrostatic force on plates CDEF and ABDC. z E D F C 1.5 ft x 1.5 ft A 1.5 ft 1.5 ft y 2 ft 2 ft 5 ft B 9 07 9 Solutions 44918 1/28/09 2:35 PM Page 908 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. *9108. The circular steel plate A is used to seal the opening on the water storage tank. Determine the magnitude of the resultant hydrostatic force that acts on it. The density of water is rw = 1 Mg> m3. 2m 45 1m A 1m B 0.5 m 0.5 m 1m 9 08 9 Solutions 44918 1/28/09 2:35 PM Page 909 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 9109. The elliptical steel plate B is used to seal the opening on the water storage tank. Determine the magnitude of the resultant hydrostatic force that acts on it. The density of water is rw = 1 Mg> m3. 2m 45 1m A 1m B 0.5 m 0.5 m 1m 9 09 9 Solutions 44918 1/28/09 2:35 PM Page 910 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 9110. Determine the magnitude of the hydrostatic force acting on the glass window if it is circular, A. The specific weight of seawater is gw = 63.6 lb> ft3. 4 ft 0.5 ft 1 ft A 0.5 ft B 1 ft 1 ft 9 10 9 Solutions 44918 1/28/09 2:35 PM Page 911 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 9111. Determine the magnitude and location of the resultant hydrostatic force acting on the glass window if it is elliptical, B. The specific weight of seawater is gw = 63.6 lb> ft3. 4 ft 0.5 ft 1 ft A 0.5 ft B 1 ft 1 ft 9 11 9 Solutions 44918 1/28/09 2:35 PM Page 912 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. *9112. Determine the magnitude of the hydrostatic force acting per foot of length on the seawall. gw = 62.4 lb> ft3. y y x 2 x2 8 ft 2 ft 9 12 9 Solutions 44918 1/28/09 2:35 PM Page 913 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 9113. If segment AB of gate ABC is long enough, the gate will be on the verge of opening. Determine the length L of this segment in order for this to occur. The gate is hinged at B and has a width of 1 m. The density of water is rw = 1 Mg> m3. 4m L A 2m C B 9 13 9 Solutions 44918 1/28/09 2:35 PM Page 914 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 9114. If L = 2 m, determine the force the gate ABC exerts on the smooth stopper at C. The gate is hinged at B, free at A, and is 1 m wide. The density of water is rw = 1 Mg> m3. A 4m L B 2m C 9 14 9 Solutions 44918 1/28/09 2:35 PM Page 915 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 9115. Determine the mass of the counterweight A if the 1-m-wide gate is on the verge of opening when the water is at the level shown. The gate is hinged at B and held by the smooth stop at C. The density of water is rw = 1 Mg> m3. 2m 1m B 45 C 2m A 9 15 9 Solutions 44918 1/28/09 2:35 PM Page 916 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. *9116. If the mass of the counterweight at A is 6500 kg, determine the force the gate exerts on the smooth stop at C. The gate is hinged at B and is 1-m wide. The density of water is rw = 1 Mg> m3. 2m 1m B 45 C 2m A 9 16 9 Solutions 44918 1/28/09 2:35 PM Page 917 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 9117. The concrete gravity dam is designed so that it is held in position by its own weight. Determine the factor of safety against overturning about point A if x = 2 m. The factor of safety is defined as the ratio of the stabilizing moment divided by the overturning moment. The densities of concrete and water are rconc = 2.40 Mg> m3 and rw = 1 Mg> m3, respectively. Assume that the dam does not slide. y x 3 x2 2 6m y A 2m x 9 17 9 Solutions 44918 1/28/09 2:35 PM Page 918 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 9 18 9 Solutions 44918 1/28/09 2:35 PM Page 919 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 9118. The concrete gravity dam is designed so that it is held in position by its own weight. Determine the minimum dimension x so that the factor of safety against overturning about point A of the dam is 2. The factor of safety is defined as the ratio of the stabilizing moment divided by the overturning moment. The densities of concrete and water are rconc = 2.40 Mg> m3 and rw = 1 Mg> m3, respectively. Assume that the dam does not slide. y x 3 x2 2 6m y A 2m x 9 19 9 Solutions 44918 1/28/09 2:35 PM Page 920 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 9 20 9 Solutions 44918 1/28/09 2:35 PM Page 921 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 9119. The underwater tunnel in the aquatic center is fabricated from a transparent polycarbonate material formed in the shape of a parabola. Determine the magnitude of the hydrostatic force that acts per meter length along the surface AB of the tunnel. The density of the water is rw = 1000 kg/m3. y 2m y 4 x 2 A 4m 2m 2m B x 9 21 9 Solutions 44918 1/28/09 2:35 PM Page 922 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. *9120. Locate the centroid x of the shaded area. y y x2 4 in. 1 in. x 1 in. 1 in. 9121. Locate the centroid y of the shaded area. y y x2 4 in. 1 in. x 1 in. 1 in. 9 22 9 Solutions 44918 1/28/09 2:35 PM Page 923 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 9122. area. Locate the centroid y of the beams cross-sectional 50 mm y 50 mm 75 mm 75 mm 25 mm 100 mm C y x 25 mm 25 mm 9123. Locate the centroid z of the solid. z y2 z a a 2 2a a y x 9 23 9 Solutions 44918 1/28/09 2:35 PM Page 924 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. *9124. The steel plate is 0.3 m thick and has a density of 7850 kg> m3. Determine the location of its center of mass. Also compute the reactions at the pin and roller support. y y2 2x 2m x A 2m y x B 2m 9125. Locate the centroid (x, y) of the area. y 3 in. 1 in. 6 in. 3 in. x 9 24 9 Solutions 44918 1/28/09 2:35 PM Page 925 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 9126. Determine the location (x, y) of the centroid for the structural shape. Neglect the thickness of the member. y 3 in. x 1.5 in. 1.5 in. 1 in. 1 in. 1.5 in. 1.5 in. 9127. Locate the centroid y of the shaded area. y a a x a a 2 a 2 9 25 9 Solutions 44918 1/28/09 2:35 PM Page 926 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. *9128. The load over the plate varies linearly along the sides of the plate such that p = 2 [x(4 - y)] kPa . Determine 3 the resultant force and its position (x , y ) on the plate. p 8 kPa 3m y x 4m 9129. The pressure loading on the plate is described by the function p = 5 - 240> (x + 1) + 3406 Pa. Determine the magnitude of the resultant force and coordinates of the point where the line of action of the force intersects the plate. 100 Pa y p 300 Pa 6m 5m x 9 26

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Capital BudgetingChapter 26McGraw-Hill/I rwinCopyright2010byTheMcGrawHillCompanies,Inc.Allrightsreserved.Capital Investment DecisionsOutcome is uncertain. Investment involves a long-term commitment.Capital budgeting: Analyzing alternative longterm i
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McGraw-Hill/IrwinCopyright 2011 by the McGraw-Hill Companies, Inc. All rights reserved.1 Environment and Theoretical Structure of Financial AccountingPowerPoint Authors: Susan Coomer Galbreath, Ph.D., CPA Charles W. Caldwell, D.B.A., CMA Jon A. Booker,
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2 Review of the Accounting ProcessPowerPoint Authors: Susan Coomer Galbreath, Ph.D., CPA Charles W. Caldwell, D.B.A., CMA Jon A. Booker, Ph.D., CPA, CIA Cynthia J. Rooney, Ph.D., CPAMcGraw-Hill/IrwinCopyright 2011 by the McGraw-Hill Companies, Inc. All
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4 The Income Statement and Statement of Cash FlowsPowerPoint Authors: Susan Coomer Galbreath, Ph.D., CPA Charles W. Caldwell, D.B.A., CMA Jon A. Booker, Ph.D., CPA, CIA Cynthia J. Rooney, Ph.D., CPAMcGraw-Hill/IrwinCopyright 2011 by the McGraw-Hill Com
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5 Income Measurement and Profitability AnalysisPowerPoint Authors: Susan Coomer Galbreath, Ph.D., CPA Charles W. Caldwell, D.B.A., CMA Jon A. Booker, Ph.D., CPA, CIA Cynthia J. Rooney, Ph.D., CPAMcGraw-Hill/IrwinCopyright 2011 by the McGraw-Hill Compan
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6 Time Value of Money ConceptsPowerPoint Authors: Susan Coomer Galbreath, Ph.D., CPA Charles W. Caldwell, D.B.A., CMA Jon A. Booker, Ph.D., CPA, CIA Cynthia J. Rooney, Ph.D., CPAMcGraw-Hill/IrwinCopyright 2011 by the McGraw-Hill Companies, Inc. All rig
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7 Cash and ReceivablesPowerPoint Authors: Susan Coomer Galbreath, Ph.D., CPA Charles W. Caldwell, D.B.A., CMA Jon A. Booker, Ph.D., CPA, CIA Cynthia J. Rooney, Ph.D., CPAMcGraw-Hill/IrwinCopyright 2011 by the McGraw-Hill Companies, Inc. All rights rese
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8 Inventories: MeasurementPowerPoint Authors: Susan Coomer Galbreath, Ph.D., CPA Charles W. Caldwell, D.B.A., CMA Jon A. Booker, Ph.D., CPA, CIA Cynthia J. Rooney, Ph.D., CPAMcGraw-Hill/IrwinCopyright 2011 by the McGraw-Hill Companies, Inc. All rights
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9 Inventories: Additional IssuesPowerPoint Authors: Susan Coomer Galbreath, Ph.D., CPA Charles W. Caldwell, D.B.A., CMA Jon A. Booker, Ph.D., CPA, CIA Cynthia J. Rooney, Ph.D., CPAMcGraw-Hill/IrwinCopyright 2011 by the McGraw-Hill Companies, Inc. All r
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10Property, Plant, and Equipment and Intangible Assets: Acquisition and DispositionPowerPoint Authors: Susan Coomer Galbreath, Ph.D., CPA Charles W. Caldwell, D.B.A., CMA Jon A. Booker, Ph.D., CPA, CIA Cynthia J. Rooney, Ph.D., CPAMcGraw-Hill/IrwinCop
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12 InvestmentsPowerPoint Authors: Susan Coomer Galbreath, Ph.D., CPA Charles W. Caldwell, D.B.A., CMA Jon A. Booker, Ph.D., CPA, CIA Cynthia J. Rooney, Ph.D., CPAMcGraw-Hill/IrwinCopyright 2011 by the McGraw-Hill Companies, Inc. All rights reserved.Na
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13 Current Liabilities and ContingenciesPowerPoint Authors: Susan Coomer Galbreath, Ph.D., CPA Charles W. Caldwell, D.B.A., CMA Jon A. Booker, Ph.D., CPA, CIA Cynthia J. Rooney, Ph.D., CPAMcGraw-Hill/IrwinCopyright 2011 by the McGraw-Hill Companies, In
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14 Bonds and Long-Term NotesPowerPoint Authors: Susan Coomer Galbreath, Ph.D., CPA Charles W. Caldwell, D.B.A., CMA Jon A. Booker, Ph.D., CPA, CIA Cynthia J. Rooney, Ph.D., CPAMcGraw-Hill/IrwinCopyright 2011 by the McGraw-Hill Companies, Inc. All right
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16 Accounting for Income TaxesPowerPoint Authors: Susan Coomer Galbreath, Ph.D., CPA Charles W. Caldwell, D.B.A., CMA Jon A. Booker, Ph.D., CPA, CIA Cynthia J. Rooney, Ph.D., CPAMcGraw-Hill/IrwinCopyright 2011 by the McGraw-Hill Companies, Inc. All rig
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18 Shareholders EquityPowerPoint Authors: Susan Coomer Galbreath, Ph.D., CPA Charles W. Caldwell, D.B.A., CMA Jon A. Booker, Ph.D., CPA, CIA Cynthia J. Rooney, Ph.D., CPAMcGraw-Hill/IrwinCopyright 2011 by the McGraw-Hill Companies, Inc. All rights rese
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spi94029_PVtable.qxdThis table shows the future value of an ordinary annuity of $1 at various interest rates (i) and time periods (n). It is used to calculate the future value of any series of equal payments made at the end of each compounding period.TA
University of Phoenix - ACC - 211
spi94029_PVtable.qxd 9/28/05 3:09 PMThis table shows the present value of an ordinary annuity of $1 at various interest rates (i) and time periods (n). It is used to calculate the present value of any series of equal payments made at the end of each comp
University of Phoenix - ACC - 211
spi94029_PVtable.qxdThis table shows the future value of an annuity due of $1 at various interest rates (i) and time periods (n). It is used to calculate the future value of any series of equal payments made at the beginning of each compounding period.T
University of Phoenix - ACC - 211
spi94029_PVtable.qxd 9/28/05 3:09 PMThis table shows the present value of an annuity due of $1 at various interest rates (i) and time periods (n). It is used to calculate the present value of any series of equal payments made at the beginning of each com
University of Phoenix - ACC - tax
Income Tax Fundamentals 2010 edition Gerald E. Whittenburg Martha Altus-Buller2010CengageLearning1Since 1913 - adoption of 16th amendment - the constitutionality of income tax has never been questioned Income taxes serve a multitude of purposes2010Cen
University of Phoenix - ACC - tax
Income Tax Fundamentals 2010 edition Gerald E. Whittenburg Martha Altus-Buller2010 Cengage LearningGross income is All income from whatever source derived All sources of income are included unless specifically excluded (see Table 2) Non-cash items incl
University of Phoenix - ACC - tax
Income Tax Fundamentals 2010 edition Gerald E. Whittenburg Martha Altus-Buller2010 Cengage LearningNet Rental Income/Loss is part of gross income Report on Schedule E - Part IVacation Homes If both personal and rental use of residence, must allocate
University of Phoenix - ACC - 400
Essentials of Accounting for Governmental and Not-for-Profit OrganizationsChapter 1 Introduction to Accounting and Financial Reporting for Governmental and Not-for-Profit OrganizationsMcGraw-Hill/Irwin Copyright 2011 by The McGraw-Hill Companies, Inc. A
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Essentials of Accounting for Governmental and Not-for-Profit OrganizationsChapter 2 Overview of Financial Reporting for State and Local GovernmentsMcGraw-Hill/Irwin2-1 Copyright 2011 by The McGraw-Hill Companies, Inc. All rights reserved.Overview of C
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Essentials of Accounting for Governmental and Not-for-Profit OrganizationsChapter 4 Accounting for the General and Special Revenue FundsMcGraw-Hill/IrwinCopyright 2011 by The McGraw-Hill Companies, Inc. All rights reserved.Overview of Chapter 4Descri
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Essentials of Accounting for Governmental and Not-for-Profit OrganizationsChapter 5 Accounting for Other Governmental Fund Types:Capital Projects, Debt Service, and PermanentMcGraw-Hill/IrwinCopyright 2011 by The McGraw-Hill Companies, Inc. All rights
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Essentials of Accounting for Governmental and Not-for-Profit OrganizationsChapter 6 Proprietary FundsMcGraw-Hill/IrwinCopyright 2011 by The McGraw-Hill Companies, Inc. All rights reserved.Overview of Chapter 6 Review of common characteristics of pro
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Essentials of Accounting for Governmental and Not-for-Profit OrganizationsChapter 7 Fiduciary (Trust) FundsMcGraw-Hill/IrwinCopyright 2011 by The McGraw-Hill Companies, Inc. All rights reserved.Overview of Chapter 7Overview of fiduciary funds Agenc
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Essentials of Accounting for Governmental and Not-for-Profit OrganizationsChapter 8 Government-Wide Statements, Fixed Assets, Long-term DebtMcGraw-Hill/IrwinCopyright 2011 by The McGraw-Hill Companies, Inc. All rights reserved.Overview of Chapter 8Ov
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Essentials of Accounting for Governmental and Not-for-Profit OrganizationsChapter 9 Accounting for Special Purpose Entities, Including Public Colleges and UniversitiesMcGraw-Hill/IrwinCopyright 2011 by The McGraw-Hill Companies, Inc. All rights reserve
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Essentials of Accounting for Governmental and Not-for-Profit OrganizationsChapter 10 Accounting for Private and Not-For-Profit OrganizationsMcGraw-Hill/IrwinCopyright 2011 by The McGraw-Hill Companies, Inc. All rights reserved.Overview of Chapter 10T
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Essentials of Accounting for Governmental and Not-for-Profit OrganizationsChapter 12 Accounting for Hospitals and Other Health Care ProvidersMcGraw-Hill/IrwinCopyright 2011 by The McGraw-Hill Companies, Inc. All rights reserved.Overview of Chapter 12
E. Michigan - ECE - ece351
The first concept that will be applied to the case study is self-efficacy. Self-efficacy lies at the heart of Banduras social learning theory. Social learning theory focuses on the learning that occurs within a social context. Self-efficacy holds that peo
E. Michigan - ECE - ece351
Introduction: The Native American population is currently facing an educational crisis. There is a major disparity of educational attainment between Native Americans and those of other ethnic groups. Specifically in Ohio, there are 750,000 Native American
E. Michigan - ECE - ece351
John Unverzagt Classics 222 Essay #1 retype Hope in Hesiod In Hesiods Theogony, Pandora is sent to humanity as a punishment for Prometheus stealing fire from Zeus. She is the source of all women. Pandora also brought with her the gifts from the gods in a
E. Michigan - ECE - ece351
Teaching as a Way to Give Back to the Community My name is David Fields and I intend to enroll in the Master of Education (M.Ed.) Program in Integrated Social Studies starting Summer Quarter of 2011. I was born and raised in Columbus Ohio and the son of a
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INTRODUCTION I. Background For Civil Procedure: The United States Government and American Courts II. An Overview of Civil Procedure A. The Idea and the Practice of Procedure 1. Locating Procedure 2. Procedure, Lawyers, and Clients B. Where Can the Suit Be
Aachen University of Applied Sciences - TH - 141
CHAPTER 8FLEXIBLE BUDGETS, VARIANCES, AND MANAGEMENT CONTROL: IILEARNING OBJECTIVES1. Explain in what ways the planning of variable overhead costs and fixed overhead costs are similar and in what ways they differ 2. Identify the features of a standard-
Aachen University of Applied Sciences - WZ - 254
PODSTAWYMETODYCZNEWANALIZIE EKONOMICZNEJISTOTA ANALIZY I JEJ MIEJSCE W SYSTEMIE ANALIZ 2 MIEJSCE ANALIZY W SYSTEMIE 2 ZAKRES ANALIZY EKONOMICZNEJ W PRZEDSIBIORSTWIE 4 RODZAJE ANALIZ SPORZDZANYCH W PRZEDSIBIORSTWIE 5 KLASYFIKACJA ANALIZ EKONOMICZNYCH W P
Aachen University of Applied Sciences - WZ - 254
Analiza metoda postpowania naukowego polegajca na podziale badanego zjawiska na czci i rozpatrywaniu kadej z nich z osobna. Poznawana jest w ten sposb struktura i zalenoci badanego zjawiska,szczeglniepowizaniaprzyczynowoskutkoweorazmechanizmjegofunkcjonow
Aachen University of Applied Sciences - WZ - 254
PROBLEMY METODYCZNE WYKORZYSTANIA ANALIZ 3 POJCIE I RODZAJE ANALIZ 3 RDA INFORMACJI DO ANALIZ 6 OBSZARY ANALITYCZNE SCHEMAT ANALIZY 7 METODY BADAWCZE W ANALIZIE 8 Przekroje porwnywania zjawisk ekonomiczno-finansowych 8 PORWNAWCZE BADANIA PRZEDSIBIORSTWA 9
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Wskanikiefektywnocizaangaowaniakapitaw Analiza rentownoci jest przeprowadzana z rnych punktw widzenia i moe obejmowa zarwno okrelone rodzaje kapitaw, jak i rne wielkoci wyniku, np. w literaturze ekonomicznej wyrniasinajczciej: rentowno kapitau cakowitego
Aachen University of Applied Sciences - WZ - 254
ANALIZAFINANSOWASTRUKTURA MAJTKU I KAPITAUPodstawoweznaczeniemaj: Wsk.wyposaeniaprzedsibiorstwawrodkigospodarcze Udziatrwaychskadnikwmajtkuwaktywachogem=majtektrway/aktywaogem*100%. Udziarzeczowychskadnikwmajtkuwaktywachogem=rzeczoweskadnikimajtku/aktyw
Aachen University of Applied Sciences - WZ - 254
ISTOTA ANALIZY 1 RODZAJE ANALIZY EKONOMICZNEJ 2 METODY ANALIZY FINANSOWEJ 3 BILANS 7 Wskaniki oceny aktyww 8 Wskaniki oceny pasyww 9 Rodzaje kapitau: 11 ANALIZA WYNIKU FINANSOWEGO 12 ANALIZA KOSZTW 14 ANALIZA WYNIKU FINANSOWEGO 17 ANALIZA WSKANIKOWA 22IS
Aachen University of Applied Sciences - WZ - 254
Elementyskadowesprawozdaniafinansowego: - rachunekwynikw - bilans - przepywypienine - informacjadodatkowa - sprawozdaniezarzduzdziaalnoci Analizapionowa czylistruktury,gdzierazemaktywastanowi 100%(dotyczy bilansuirachunkuwynikw) Analizapoziomatomajteki rd
Aachen University of Applied Sciences - WZ - 254
ANALIZAPIONOWAIPOZIOMASPRAWOZDA FINANSOWYCH ANALIZAZMIANWIELKOCIBILANSOWYCHW CZASIESporzdzanie sprawozda finansowych okrela ustawa z dnia 29 wrzenia 1994 roku o rachunkowoci. Sprawozdaniefinansoweskadasiz: 1. bilansu 2. rachunkuzyskwistrat 3. sprawozdani
Aachen University of Applied Sciences - WZ - 254
ANALIZASTRATEGICZNAFIRMYStrategiajestjednymzpodstawowychinstrumentwzarzdzania.Towaniedobrejstrategii wielefirmwgospodarcerynkowejzawdziczaswjsukces,aconajmniejrwniewieleniepowodze monawyjanistrategicznymibdamiwzarzdzaniu. Analizastrategicznatopostpowanie
Aachen University of Applied Sciences - WZ - 254
AnalizawskanikowasprawozdafinansowychOcenakondycjifinansowejprzedsibiorstwa Analizawskanikowaprzeprowadzanajestnapodstawiesprawozdafinansowych: - bilans - sprawozdazdochodwikosztw - sprawozdaprzepywwpieninych Wskanikamizainteresowanis - osobyzarzdu - kred
Aachen University of Applied Sciences - WZ - 254
EtapyanalizystrategicznejAnalizastrategiczna jestzbioremdziaa wykorzystujcychzarwnometodyilociowejaki jakociowezrnychdziedzin,tj.ekonomii,finansw,psychologii,statystyki,marketingu,ktremaj naceluzebranie,zinterpretowanieikonfrontacjdanychdotyczcychzarwnos
Aachen University of Applied Sciences - WZ - 254
OcenakondycjifinansowejprzedsibiorstwaPrzedsibiorstwodokonujenabiecornychoperacjigospodarczych,ktrewpywaj odpowiednionazmianwielkociorazstrukturyjegoaktywwipasyww.Operacjetes rejestrowanenabiecoprzezksigowoinatejpodstawiesporzdzanessprawozdania finansowe
Aachen University of Applied Sciences - WZ - 254
SPISTRECI1. OCENA KONDYCJI EKONOMICZNO- FINANSOWEJ PRZEDSIBIORSTWA.2 1.1. METODY OCENY KONDYCJI EKONOMICZNO - FINANSOWEJ PRZEDSIBIORSTWA.2 1.2. PODSTAWOWE WIELKOCI KSZTATUJCE I CHARAKTERYZUJCE WYNIKI EKONOMICZNO - FINANSOWE PRZEDSIBIORSTWA .7 1.3. OCENA
Aachen University of Applied Sciences - WZ - 254
Projektsystemuzarzdzaniaagencji reklamowej1)Profilfirmy Naszafirmajestagencj reklamow.PocztkowymobszaremjejdziaaniajestwojewdztwomazowieckiezukierunkowaniemrozwojunaobszarcaejPolskiawprzyszocinaEurop.Centrala spkiznajdujesi wWarszawie,obecniepowstaj tr