1272 Exam 2 KEY - MATH 1272, LEC 30 (Knoche): CALCULUS 11...

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Unformatted text preview: MATH 1272, LEC 30 (Knoche): CALCULUS 11 SPRING 2011 MIDTERM EXAM 2 / Name Signature Student ID Number Section ##_* TA Score: Problem 1 (12) Problem 2 (10) Problem 3 (20) Problem 4 (10) Problem 5 (14) Problem 6 (14) Problem 7 (10) Problem 8 (10) TOTAL (100) Instructions Show all of the details/steps of your set ups/solutions for full credit. You may use a scientific calculator with no graphing or symbolic manipulation capabilities. No books or notes allowed. Please turn off your cell phone during the exam. Good writing and GOOD LUCK! Math 1272—030 Spring 2011 Midterm Exam 2 20f6 1.) Find the area encchSed by the x—axis and the curve. Parametric (12 points) SET UP ONLY and factor out any constants in the integrand. x=2+92t, y=2t2—4t g: ’ZHJ-vD-zo 6|- .— I r v 0‘ A @ ‘virr—fln""éfi"”léo flirt—0 AV E 61+ Math 1272—030 Spring 2011 Midterm Exam 2 3 of 6 3.) A tank contains 180 kg of salt dissolved in 5000 L of water. Brine that contains 0.02 kg salt per liter of water enters the tank at a rate of 70 L/min. The solution is kept thoroughly mixed and drains from the tank at the same rate. How much salt remains in the tank after 3 hours ? (20 points) SET UP, SOLVE FOR Y6), AND EVALUATE Y(t) AT t = 3 HOURS (3: 1 z: ELF : [If-II-Out'Jng'S'UOO 2:) '2? I00 @ f a (a) 3%. 2-: 0,01 bi "49.1.21: REL “Fol:- --€3- \ '— ' (ix 1:5 W” 57000 1— W " Math 1272—030 Spring 2011 Midterm Exam 2 4 of 6 4.) Find the length of the curve. Polar SET UP ONLY and factor out any constants in the integrand. (10 points) 492 1: 31: H‘ = —- < -——-- r Ssecfl ' 3 fl 6 S 4 {aw—"j: m: IL: I fifekmz-S) 'L'Livdéalyma) r’ '2. r: i a C03 ‘9' '9 1r _ _ T 3/ “EH—unw—fl If; r" ‘715__V_Mw~n=- “fr I «LU- :-ig‘;¢»ri9 .. LR“ Ycoszfi “1”’d&) ‘16} !L 5.) Find the area of the surface obtained by rotating the curve about the y—axis. Cartesian SET UP AND SOLVE THE DEFINITE INTEGRAL (14 points) 1—952. 05x51 _ r=>f=€3rf1fi Math 1272—030 Spring 2011 Midterm Exam 2 5 0f 6 6.) A dam that is shaped like an isosceles trapezoid is 38 m wide at the top and 16 m wide at the bottom with a total height of 18 m. If the water is present from the base of the dam up to a height of 14 m, find the total hydrostatic force against the side of the dam. SET UP ONLY and factor out any constants in the integrand. (14 points) Math 1272—030 Spring 2011 Midterm Exam 2 6 of 6 7.) Find the centroid (center of mass) of the region bounded by the given curves. SET UP ONLY and factor out any constants in the integrand. (1n points) _ ..._ 2 y—x+2,y—x X22X+l '2. "-‘-X at / If 1 _r __ '1'; O “t '; 'L X X "xxx “E q} x 1- . __ .. (x H [w M t O '2 K ‘ 9' Ix WE VOW—H096 :3?“ J ~r i [ I) 4 f — w :(w—flZ-wfxfl I710” a 8.) Identify the curve by finding a Cartesian equation for the curve and describe the curve. 1‘ <1" = 25in6 + 2c056> (10points) 1 + 1v Lug—a (9 +- 2rqu ...
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This note was uploaded on 02/02/2012 for the course MAP 2303 taught by Professor Bramson during the Fall '11 term at University of Florida.

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1272 Exam 2 KEY - MATH 1272, LEC 30 (Knoche): CALCULUS 11...

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