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Dive into the exciting world of mathematics with our engaging Jeopardy-style quiz review! This session covers a range of topics, including calculating volumes of solids formed by rotation, determining work needed for various tasks, and solving integrals. From finding the volume formed by rotating the area under curves to determining work required to lift objects, this review is designed to reinforce key math concepts in a fun, interactive format. Get ready for an intellectually stimulating competition!
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September 27, 2007 Welcome to the cavernous pit of math!
Revolution of the Working Classes (100) Find an integral equal to the volume formed by rotating the area in the first quadrant under x + y = 1around the line x = -2.
Revolution of the Working Classes (200) Find the amount of work needed to pull a 5 lb bucket up a 50 ft well.
Revolution of the Working Classes (300) Write an integral equal to the volume of the solid formed by rotating the area under y = sin x for 0 ≤ x ≤ around the y-axis.
Revolution of the Working Classes (400) Express the volume formed by rotating the area between y = x2 and y = x3around the y-axis as an integral.
Revolution of the Working Classes (500) Set up an integral equal to the amount of work needed to pump all the water out of a tank that is a circular cylinder with base radius 3 ft and height 8 ft, if the tank is half full of water. (Water weighs 62.5 lb/ft2.)
Potpourri (400) If then find an expression for tan in terms of x.