(MAT200 -PreCalclus) Wk9 HmWrk (Sctns 5.5-5.7)

(MAT200 -PreCalclus) Wk9 HmWrk (Sctns 5.5-5.7) - Student:...

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Unformatted text preview: Student: Shanna Hawxhurst Instructor: Christine Curley Assignment: Week Nine: Sections 5.5 - 5.7 Date: 319/09 Course: 903 CURLEY C, MAT 200 004 016 Time: 5:03 PM Back: Strayer University Math 200: Precalculus 1_ Decide whether or not the given matrices are inverses of each other. (Check to see if their product is the identity matrix In.) — l — l — ] IS 4 — 5 4 5 0 and - 12 - 3 4 0 l — 3 — 4 l 1 Are these two matrices inverses? Yes 'V' No 2. Find the inverse of the tbllowing matrix A, if possible. Check that AA _ I =I and A ‘ 1A =1. A = 6 5 6 6 5 1 _ _ . _ 1 . 6 The 1nverse, A 15 ~ 1 1 (Type N for each matrix element if the answer does not exist.) Find the inverse of the following matrix A, if possible. Check that AA _ I =1 and Lu A‘1A=I. A: 2 2 4 1 I __ . —1. 2 The Inverse, A 15 i i 2 2 (Type N for each matrix element if the answer does not exist.) Page 1 Student: Shanna Havvxhurst Date: 319/09 Instructor: Christine Curley Course: 903 CURLEY C, MAT 200 004 016 Time: 5:03 PM Back: Strayer University Math 200: Precalculus 4_ Find the inverse of the matrix. LII 6. — 1 — | —4 5 6 0 0 l — 19 114 23 - 24 The inverse matrix is — 95 — 19 20 — 5 — l 1 (Type N for each matrix element if the answer does not exist.) Find the inverse ofthe matrix A, ifpossible. 2 O —1 A: 0 -l 0 3 —2 —2 2 2 —1 A‘l— 0 —1 0 3 4 —2 - 1 - l - 8 5 6 O 0 l — 39 234 47 — 48 The inverse matrix is - 195 - 39 40 — 5 — l 1 (Type N for each matrix element if the answer does not exist.) Page 2 Assignment: Week Nine: Sections 5.5 - 5.7 Student: Shanna Havvxhurst Date: 39/09 Time:5:03 PM 7". —3 —3 A= 0 —5 3 0 0 —5 —3 Instructor: Christine Curley Course: 903 CURLEY C, MAT 200 004 016 Book: Strayer University Math 200: Precalculus Find the inverse of the following matrix A, A _ I, if possible. CheckthatAA_1=land A"A=L NNN A“=NNN NNN (Type N for each matrix element if the answer does not exist.) Find the inverse for the matrix. The inverse is (Type N for eaoh matrix element if the answer does not exist.) 1102 1—30—1 332—2 1210 0 1——1 2 3:; 510 5 inn; 5105 I_ 3 i 5 5 5 Page 3 Assignment: Week Nine: Sections 5.5 - 5.7 Student: Shanna Havvxhurst Date: 319/09 Time: 5:03 PM 9. 10. 11. Find the inverse for the matrix. 3 O The inverse 15 L 1 i m 1 5 (Type N for each matrix element if the answer does not exist.) Instructor: Christine Curley Course: 903 CURLEY C, MAT 200 004 016 Book: Strayer University Math 200: Precalculus 1102 1—30—1 3 32-2 1210 l _ 0 ——1 2 313.. 510 5 ins 510 5 L 3 i 5 5 5 Assignment: Week Nine: Sections 5.5 - 5.7 A system of equations is given, together with the inverse of the coefficient matrix. Use the inverse of the coefficient matrix to solve the system ofequations. 2x+7y= —5 3x+11y= 2 A_]_ _? —3 2 The solution of the system ofequations is ( — 69,19) . (Type an ordered pair.) A system of equations is given, together with the inverse of the coefficient matrix. Use the inverse of the coefficient matrix to solve the system of equations. 5X+y=—2 4 1 —3 2x—y+3z=1 _] I A =— _ _ x+y+z =5 19 l 5 15 —3 4 7 Complete the solution. (EDD) (Type an exact answer.) Page 4 Student: Shanna Hawxhurst Instructor: Christine Curley Assignment: Week Nine: Sections 5.5 - 5.7 Date: 3/9109 Course: 903 CURLEY C, MAT 200 004 016 Time: 5 :03 PM Book: Strayer University Math 200: Preealculus 12_ Solve the following system of equations by using the inverse of the coefficient matrix A. (AX=B) x+8y= —37 Tx+6y= —59 .. _T The inverse of matrix A, A _ , IS ‘ The solution of the system is (Type an ordered pair.) 13. Solve the following system of‘equations by using the inverse of the coefficient matrix A. (AX=B) x +8y=3T — Tx +Sy=46 l _ L The inverse of matrix A, A _ I, is The solution of the system is (Type an ordered pair.) 14_ Solve the following system of equations by using the inverse of the coefficient matrix A. (AX = B) —2x—y+52= — 12 —6y+52= —20 -8x+6y+22 =24 __|—| The inverse of the coefficient matrix A, A _ 1, is I I ::D (Type an exact answer. Type N For each matrix element is the answer does not exist.) The solution of the system is (Type an ordered triple.) Page 5 Student: Shanna Hawxhurst Instructor: Christine Curley Assignment: Week Nine: Sections 5.5 - 5.7 Date: 319109 Course: 903 CURLEY C, MAT 200 004 016 Time: 5 :03 PM Book: Strayer University Math 200: Precalculus 15_ Evergreen Landscaping bought 3 tons of topsoil, 5 tons of mulch, and 7’ tons of pea gravel for $3184. The next week the firm bought 6 tons of topsoil, 4 tons of mulch, and 4 tons of pea gravel for $3070. Pea gravel costs $18 less per ton than topsoil. Find the cost of each product. The price per ton oftopsoil is $D. (Round your answer to the nearest dollar.) The price per ton of mulch is SD. (Round your answer to the nearest dollar.) The price per ton of pea grave] is $ (Round your answer to the nearest dollar.) 16_ Evaluate the determinant of the matrix. The determinant is 4V3— fi—z 17_ Evaluate the determinant. What is the value of the determinant? x4 9 x2 x9 (Slmpllty your answer.) 18_ Find the determinant. 6 7 2 A = 8 — l 9 10 3 3 det A = 350 l M12. 2 3 2 A = 5 3 — 2 0 l 5 M12: Page 6 Student: Shanna Hawxhurst Instructor: Christine Curley Assignment: Week Nine: Sections 5.5 - 5.7 Date: 319/09 Course: 903 CURLEY C, MAT 200 004 016 Time: 5:03 PM Book: Strayer University Math 200: Precalculus Find A12. 10 'i' 1 A = 7 3 — 2 0 l 5 A12 = — 21_ Find the determinant of this 3x3 matrix using expansion by minors about the second row. 4 4 — 3 A = — 3 0 0 3 l — 4 It will be easier to expand about the second row because it contains two zeros. This simplifies the multiplication considerably. What is the value of IAI‘? 4 4 —3 |A|= —3 0 0 = —39 3 1 —4 IX.) 1*.) Find the determinant of this 3x3 matrix using expansion by minors about the first column. 5 —4 —1 A= 6 —3 4 6 —4 6 5 —4 —1 |A|= 6 —3 4 =44 6 —4 6 Page 7' Student: Shanna Hawxhurst Instructor: Christine Curley Assignment: Week Nine: Sections 5.5 - 5.7 Date: 319/09 Course: 903 CURLEY C, MAT 200 004 016 Time: 5 :03 PM Back: Strayer University Math 200: Precalculus 2} Find M 14 and M33 for matrix A. 6 0 0 — 7 A = S 2 O 0 3 8 8 2 — 5 — 8 — 2 0 M I4 = D M33 = D 24_ Find the determinant of this 4 x 4 matrix using expansion by minors about the third row. 3 — 1 9 6 - 2 1 - 4 8 A = 8 0 0 IO 5 1 — 2 — 4 It will be easiest to expand about the third row because it contains two zeros. This simplifies the multiplication considerably. 3 - l 9 6 — 2 l — 4 8 IAI = =D 8 0 0 10 5 l - 2 - 4 25 Solve using Cramer's rule. What is the solution of the system? —2x+8y=12 X: #6 y=0 4x + 6y = — 24 26_ Solve using Cramer's rule. What is the solution of the system? 8x+8y=0 x=2 y: _2 "ix + 6y = 2 271 Solve using Cramer's rule. What is the solution of the system? Reduce any fractions. — 3x + 'i'y = 5 ?x+8y= 5 x= —.06849315| y= .6849315 Page 8 Student: Shanna Hawxhurst Instructor: Christine Curley Assignment: Week Nine: Sections 5.5 - 5.7 Date: 319109 Course: 903 CURLEY C, MAT 200 004 016 Time: 5 :03 PM Book: Strayer University Math 200: Preealeulus 23 Solve using Cramer's rule. What is the solution of the system? Reduce any fractions. 2x +7y = 4 — 3x +2y = 5 2? 22 X = — —' y = —‘ 25 25 29_ Solve this system of equations using Cramer's Rule. What is the solution of the system? —8x— 8y+?z= — 17 x = 491.6666666666667 y = 1?.666666666666668 — 5x + Ty +42 = — 16 z = 579.6666666666666 (Simplify your answers. Type integers or fractions.) —6X+4y+52=19 30_ Solve using Cramer's rule. What is the solution of the system? Tx+2y+4z=—64 x= w6 y= H] 2= —5 6x+5y+Sz=—66 3x+4y+4z=—42 Solve using Cramer's Rule. Lu _. x+y+z=12 x—y+z=6 2x+y+z=15 What is the solution of the system? x=D~y=Daz=D Use Cramer's Rule to solve the linear system in three variables. La 1*.) x-3y=l5 3y+z=5 —x+z= -2 The solution set is {(D,D,l:l)}. (Simplify your answers. Type integers or fractions.) Page 9 Student: Shanna Hawxhurst Instructor: Christine Curley Assignment: Week Nine: Sections 5.5 - 5.7 Date: 3/9/09 Course: 903 CURLEY C, MAT 200 004 016 Time: 5:03 PM Book: Strayer University Math 200: Preealculus 33. Graph the inequality on a plane. ny-3 Choose the correct graph. 34_ Graph the inequality. 2x-3yfi6 Choose the correct graph. 35. Graph the inequality. y +3): 2 1 Which graph is the solution of the inequality? Page 10 Student: Shanna Hawxhurst Instructor: Christine Curley Assignment: Week Nine: Sections 5.5 - 5.7 Date: 3/9/09 Course: 903 CURLEY C, MAT 200 004 016 Time: 5:03 PM Book: Strayer University Math 200: Precalculus 36_ Graph the inequality on a plane. x +y < 6 Choose the correct graph on the right. 3?_ Graph the inequality. 5x +4y 2 20 Choose the correct graph. 3g_ Graph the inequality on a plane. - 95:; A A x< 4 10—: : 10—: l I I: I I I I : | I I Choose the correct graph on the right. 40 -- g- -: 1o -10. g :- 10 #05 'i -105 l ' A 10—: mm 1 if: 40 . .E. 405' Page 11 Student: Shanna Hawxhurst Instructor: Christine Curley Assignment: Week Nine: Sections 5.5 - 5.7 Date: 3/9/09 Course: 903 CURLEY C, MAT 200 004 016 Time: 5:03 PM Book: Strayer University Math 200: Precalculus 39_ Graph on a plane. — 3 < y 1 4 Choose the correct graph. 40_ Graph the system of inequalities. x+3y$9 3x+ys9 yZO x20 Which graph is the solution of the system? 41_ Find a system of inequalities with the graph below. Choose the appropriate system of equations. nofy. yZ —X+? viiyé —X+? ' ' yz x+l yS x+1 x20 x20 yZO yZO ys x + "f ii y? x + 7 ys —x +1 yZ ‘X +1 x20 x20 yZO yZO Page 12 Student: Shanna Hawxhurst Instructor: Christine Curley Assignment: Week Nine: Sections 5.5 - 5.7 Date: 3/9/09 Course: 903 CURLEY C, MAT 200 004 016 Time: 5:03 PM Book: Strayer University Math 200: Preealculus 42_ Graph the system of inequalities. Then find the _ _ _ Mi _ _ _ _ _ _ coordinatesofthevertex. :::::::::--:::::ZZZZE y23—x IIIIIIIII._IIIIIIIIII Use the graphing tool on the right to graph the I I I _ I I I I system of inequalities. "1.0I isI ’5 I 4.1 I 2.2: I 2. I 4' I 5 I3 I1:0 3g flfig Ziiiiifieéiifiiiii n .mumfiflmmfl What are the coordinates ofthe vertex? D I I I I I I I I'_1o_ I I I I I I I I I (Type an ordered pair. Type an integer or a fraction.) 43. Graph the system ofinequalities. _ _ _ _ _ _ _ _ _ A3 _ _ _ _ _ _ _ _ m 333333333-333333333; yS—X+5 :13:::fi":fi:::fi:' Usethegraphingtoolontherighttographthe 3:313:1312—133331131- ystem of inequalities. I ' || _ —I _ .-._4._._. .4. . .1: a. cuckto 1.0.19.5. .2.2_. _ 3.8.0 .. enlarge fig. ._3_ BEUE®Q§ a Page 13 Student: Shanna Hawxhurst Instructor: Christine Curley Assignment: Week Nine: Sections 5.5 - 5.7 Date: 3/9/09 Course: 903 CURLEY C, MAT 200 004 016 Time: 5:03 PM Book: Strayer University Math 200: Precalculus 44_ Graph the system of inequalities. Then, find the coordinates of the vertex. x S 2 y 2 5 — 3X Choose the correct graph. Find the coordinates of the vertex. E] (Simplify your answer. Type an ordered pair.) 4 5_ Graph the system of inequalities. Then, find the coordinates of the vertex. x+ySl,x—y22 Choose the correct graph for the system. Find the coordinates of the vertex. D (Simplify your answer. Type an ordered pair. Type integers or fractions.) Page 14 Student: Shanna Hawxhurst Instructor: Christine Curley Assignment: Week Nine: Sections 5.5 - 5.7 Date: 3/9/09 Course: 903 CURLEY C, MAT 200 004 016 Time: 5:03 PM Book: Strayer University Math 200: Preealculus 46_ Graph the system of inequalities. 4X + 5y 5 20, 5x +4y S 20, x 2 0, y 2 0 Choose the correct graph. Page 15 Student: Shanna Hawxhurst Instructor: Christine Curley Assignment: Week Nine: Sections 5.5 - 5.7 Date: 3/9/09 Course: 903 CURLEY C, MAT 200 004 016 Time: 5 :03 PM Book: Strayer University Math 200: Precalculus 47h Find the maximum and minimum values of the objective function P. subject to the conditions listed below. P=19x—2y+19 7x+8y$56 OSyS6 OSXS3 What is the maximum value? GA. 76.00 GB. 0 Dc. 7.00 0.0. (300,000) Where does the maximum occur? [)A. 76.00 GB. (300,000) 0 c. (000.600) :30. 700 What is the minimum value? DA. (000,600) DB. (0,0) QC. 76.00 DD. 7.00 Where does the minimum occur? OA. 76.00 as. (300,000) QC. 7.00 On. (000.600) Page 16 Student: Shanna Havvxhurst Date: 319/09 Instructor: Christine Curley Course: 903 CURLEY C, MAT 200 004L 016 Assignment: Week Nine: Sections 5.5 - 5.7 Time: 5 :03 PM Book: Strayer University Math 200: Precalculus 4ft Yawaka manufactures motorcycles and bicycles. To stay in business, the number of bicycles made cannot 49. exceed five times the number of motorcycles. They lack the facilities to produce more than 90 motorcycles, or more than 200 bicycles, and the total production of motorcycles and bicycles cannot exceed 240. If Yawaka makes $1060 on each motorcycle and $360 on each bicycle, how many of each should be made to maximize profit? Yawaka should make l:| motorcycles and D bicycles. Jamaal is planning to invest up to $19000 in City Bank or State Bank. He wants to invest at least $2000 in City Bank, but not more than $15000; since State Bank does not insure more than $7000, he wants to invest no more than this amount in State Bank. The interest at City Bank is 6%, and the interest at State Bank is l 1%. How much should he invest in each bank to earn the most interest? He should invest $|:| in City Bank and $lj in State Bank. Carlo and Anita make mailboxes and toys in their craft shop near Lincoln. Each mailbox requires 1 hour work from Carlo and l hour from Anita. Each toy requires I hour work from Carlo and 2 hours from Anita. Carlo cannot work more than 8 hours per week and Anita cannot work more than 12 hours per week. If each mailbox sells for $9 and each toy sells for $15, then how many of each should they make to maximize their revenue? The maximum revenue of $96 is attained by making D mailboxes and D toys. Page 17 ...
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This note was uploaded on 01/19/2012 for the course MATH MAT200 taught by Professor Unknown during the Spring '11 term at Strayer.

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(MAT200 -PreCalclus) Wk9 HmWrk (Sctns 5.5-5.7) - Student:...

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