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Exam_exam_4_M - 62.5 pounds Do not evaluate the integral...

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MIDTERM 4 — MATH 141 — FALL 2002 — BOYLE Put your name, your TA’s name and the question number on EACH page. Use exactly ONE answer sheet per question (use the back of the sheet if needed). Put a BOX around the final answer to a question. No books, no notes, no calculators. Before handing in your test: on your first answer sheet, please copy the pledge, and sign. ———————————————————————————————————– 1. (25 points) A cylindrical water tank has a radius of 3 feet and a height of 10 feet. Express as an integral the work in foot-pounds which is required to pump all the water in the tank to a height of 12 feet. (Recall, a cubic pound of water weighs
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Unformatted text preview: 62.5 pounds.) Do not evaluate the integral. 2. (a)(20 points) ±ind the volume V of the solid whose base is a circle of radius 2, such that the cross sections of the solid perpendicular to a Fxed diameter of the base are squares. (b) (20 points) Let S be the region bounded between the curves y = x 2 and y = 1. The area of S is 4/3. Compute ( x, y ), the center of gravity of S . 3. (25 points) ±ind the length L of the curve described parametrically by ( x,y ) = ( e-t cos( t ) ,e-t sin( t )) , ≤ t < π . 4. Suppose z = 1 + i √ 3. (a) (3 points) What is | z | ? (b) (3 points) ±ind real numbers a,b such that a + ib = 1 /z . (c) (4 points) ±ind real numbers R,θ such that z = Re iθ ....
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