Use the general slicing method to find the volume of the following solid.
the solid with a semicircular base of radius 11 whose cross sections perpendicular to the base and parallel to the diameter are squares. place the semicircle on the xy-plane so that its diameter is on the x-axis and it is centered on the y-axis. set up the integral that gives the volume of the solid. use increasing limits of integration.

Suppose a pendulum is l meters long. the time,t,in seconds that it tales to swing back and forth once is given by t=2.01

Does the function satisfy the hypotheses of the mean value theorem on the given interval? f(x) = 4x^2 + 3x + 4, [−1, 1] no, f is continuous on [−1, 1] but not differentiable on (−1, 1). no, f is not continuous on [−1, 1]. yes, f is continuous on [−1, 1] and differentiable on (−1, 1) since polynomials are continuous and differentiable on . there is not enough information to verify if this function satisfies the mean value theorem. yes, it does not matter if f is continuous or differentiable; every function satisfies the mean value theorem.

Adesigner charges a one time fee of $200 plus $40 an hour for each project. write an expression to represent how much money the designer will make for a project