v(t)= 65t + 280 , were t is time , in minutes, the pump has been on . The pumps will turn off when the volume in the tank hits 10,000 gallons .To the nearest minute , after how long doesthis happen ?

Determine whether the following statements are true and give an explanation or counterexample. bold a. when using the shell method, the axis of the cylindrical shells is parallel to the axis of revolution. bold b. if a region is revolved about the y-axis, then the shell method must be used. bold c. if a region is revolved about the x-axis, then in principle it is possible to use the disk/washer method and integrate with respect to x or the shell method and integrate with respect to y.

Consider a cube that has sides of length l. now consider putting the largest sphere you can inside this cube without any point on the sphere lying outside of the cube. the volume ratio -volume of the sphere/ volume of the cube is 1. 5.2 × 10−1 2. 3.8 × 10−1 3. 1.9 4. 2.5 × 10−1 5. 3.8

If you double the input of a function and it results in half the output, and if you triple the input and it results in a third of the output, what can be guessed about the function? check all that apply.