Y = 5xe−x, y = 0, x = 3; about the y-axis

(a) Set up an integral for the volume V of the solid obtained by rotating the region bounded by the given curve about the specified axis.
(b) Use your calculator to evaluate the integral correct to five decimal places.

The base of a triangle exceeds the height by 9 inches. if the area is 180 square inches, find the length of the base and the height of the triangle.

Which translation maps the vertex of the graph of the function f(x) = x2 onto the vertex of the function g(x) = x2 – 10x +2?

Adecorative window is made up of a rectangle with semicircles at either end. the ratio of ad to ab is 3: 2 and ab is 30 inches. what is the ratio of the area of the rectangle to the combined area of the semicircles? possible answers: a. 2: 3 b. 3: 2 c. 6: π d. 9: π e. 30: π