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Chapter72008 - Chapter 7 Test No Calculators x = 8 y Name x...

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Chapter 7 Test January 31, 2008 No Calculators Name 1. Find the area of the region bounded by the graphs of the equations x = 8 y, x = - 8, and x = - y 3 2. A solid has as its base the region in the xy - plane bounded by the graph of the equations 4 x 2 + y 2 = 16. Every cross section by a plane perpendicular to the x - axis is an equilateral triangle, with one side in the xy - plane. Find the volume of the solid. 3. Find the volume of the solid generated by revolving the region bounded by the graphs of the equations y = sin x ÄÄÄÄ 2 and y = cos x ÄÄÄÄ 2 , on the interval A 0, p ÄÄÄÄ 2 E , about the x - axis.
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4. Find the volume of the solid generated by revolving the region bounded by the graphs of the equations y = x - x 2 and y = 0, about the line x = 2. 5. Find the length of the arc for y = ln H secx L from H 0, 0 L to i k j j j p ÄÄÄÄ 4 , ln 2 ÄÄÄÄÄÄÄÄÄÄÄÄ 2 y { z z z . 6. A tank is in the shape of a hemisphere with radius 5 feet. The tank contains a brackish liquid that weighs 30 lbs ê ft 3 , and this liquid almost fills the tank, to a height 1 foot from the top of the tank. You need to evacuate the tank,
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