# Exam II - of the initial-value problem 1 =-= ′ y xy x y 8...

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Mathematics 3B Honors – Castroconde Name: Exam II (Chapters 9 and 10) I.D.#: Page 1 2 3 4 Total Points To get full credit, you must show all your work. 1. Find the arc length of the curve 2 1 , 10 1 6 3 5 + = x x x y . 2. Find the area of the surface obtained by rotating 6 0 ), 2 cos( π = x x y , about the x -axis.

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3. The curve 2 1 , 3 = y x y , is rotated about the y -axis. Find the area of the resulting surface. 4. An aquarium 5 ft long, 2 ft wide, and 3 ft deep is full of water. Find the hydrostatic force on one end of the aquarium. The density of water is 62.5 lb/ft³. 5. Find the coordinates of the center of mass of the region bounded by . 0 , 4 2 = - = y x y
6. Verify that x x e e y - + = 3 2 is a solution of the differential equation 0 = - y y . 7. Use Euler’s method with step size 0.2 to estimate y(1.4) , where y(x) is the solution

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Unformatted text preview: of the initial-value problem ) 1 ( , =-= ′ y xy x y . 8. Solve each differential equation. a. y xy dx dy ln 2 = b. 2 ) 1 ( , , 1 2 = = + ′ y x xy y x 9. You invested \$800 at 6% interest for 3 years. Assuming that no deposits or withdrawals are made during that time, find: a. How much is in the account if interest is compounded quarterly. b. How much is in the account if interest is continuously compounded. 10. A tank contains 100 L of pure water. Brine that contains 0.1 kg of salt per liter enters the tank at a rate of 10 L/min. The solution is kept thoroughly mixed and drains from the tank at the same rate. How much salt is in the tank after 6 minutes?...
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Exam II - of the initial-value problem 1 =-= ′ y xy x y 8...

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