In this problem we will show that the volume of a right cone of radius r and height h is given by rh (a) Give an expression for the volume of the cone in terms of the integral of a two-variable function over a region of the plane (there are several ways to do this). (b) Compute the integral to establish the formula.

Q: Find the equation of the vertical line that divides the area of the region R bounded by 1 y = 20x2…

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Q: True or False The surface area of a sphere of radius r is 4/3 πr

A: Surface area of a sphere of radius of radius r is 43πr.

Q: Show that if a solid figure is revolved about the x-axis, its volume of revolution is given by V= a…

A: To show that if a solid figure is revolved around the x-axis, its volume of revolution is given by…

Q: (p+ q) ® (p →¬q) p+q p + nq (p+ q) © (p· T F |(Click to select) :) T F F (Click to select) : F T F F…

A: The given logic is                                     (p↔q)⊕(p↔¬q) And the truth table   p   q…

Q: How would I set up an integral that funds the volume of the cylinder?

A: This is question of calculusHere we have to find step for calculate the area of cylinderFurther…

Q: Find the area of the “triangular” region bounded on the left by x + y = 2, on the right by y = x2,…

A: Graph the given equations first.We have to find the area of the shaded region

Q: Consider the region T bounded by the graphs of y = x2, y = -3x, and x = 4. (a) Find the area of T. X…

A: Given that the region T is bounded by the graphs of y=x2, y=−3x and x=4. a We have to find the area…

Q: Which integral corresponds to the area of the shaded region? The parabola is y = x? –1 while the…

A: Given query is to find the the integral for the area of shaded region.

Q: A hole of radius 3 is bored through the center of a sphere of radius 5. Let the cross- section of…

A: we will draw region which can be rotated to create solid region whise volume needed to find . Then…

Q: A water tank is in the shape of an inverted cone (the vertex of the cone is the bottom of the tank).…

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Q: Use a change of variables to find the area of the curved rectangle above the x-axis bounded by…

A: Given,Area bounded by:y24-1≤x≤4-y216 , y264-16≤x≤9-y236 , x≥0

Q: A gasoline tank is in the shape of a right circular cylinder (lying on its side) of length 13 ft and…

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