2b - MA 241 Test 2 Form B Fall 2007*No Calculators No Cell...

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Unformatted text preview: MA 241 Test 2 Form B Fall 2007 *No Calculators, No Cell Phones, No PDAs. *Show all work neatly. Begin each problem on a new page in the blue book, please! *Circle your final answer. * Please do not leave if you have to pass over someone on your row. Wait for me to offer “leave times” at various times. Thanks! 1. Solve the differential equations. Begin each problem on a new page. a. (14 pts) V1 — x2 16—3} = xy y(0) = 1 (explicit solution) dy b. (12 pts) 2; = xy(y + 6) (implicit solution) (10 pts) Find the orthogonal trajectories of the family of curves for xy2 = C . Is the orthogonal family hyperbolas, straight lines, ellipses, parabolas or concentric circles? 1 (10 pts) Use Euler’s Method with step size Ax = E to approximate y(1) given dy —— = x — and O = 4. l y y( ) For problems a, b, c and (1, set up the definite integral with all appropriate numbers that solves the problem. Do not integrate. Put each problem on a separate page in your blue book. a. (14 pts) A cable that weighs 2 lbs/ft is used to lift 1000 lbs of coal up a mineshaft 800 ft deep. Find the work done to lift the coal to the top. Continue on next page Form B continued Recall: Set up definite integral with appropriate numbers. Do not integrate. b. (14 pts) Water weighs 62.5 An inverted conical tank with radius 8 it and height 12 ft is filled within 3 feet of the top with water. Find the work required to pump all the water to the top of the tank. c. (14 pts) A 20-ft long trough is filled with water and its vertical ends have the shape of a parabola 5 ft high and 10 ft across the top. Find the it hydrostatic force on one end of the trough. Water weighs 62.5 f1 f _ K 5 l d. (12 pts) For the lamina with density p and its region bounded by y = cos(x),0 s x 5—725 Find My, the moment with respect to y. I l i r. A I ' - - - - i I 1.. 2 r I :2. I 90,6 ’ I I i a I I * =»<— - ’A . % —o——___. A V , .4 ; |_Q¥_ , , i I-V_- ’ ’ r .—'—'——"—' i: i 3 (A ...
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