Consider F and C below. F(x, y, z) = yz i + xz j + (xy + 18z) k C is the line segment from (2, 0, −2) to (6, 6, 2) (a) Find a function f such that F = ∇f. f(x, y, z) = (b) Use part (a) to evaluate C ∇f · dr along the given curve C.

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.

Order the measurements from the least to the greatest. 2,720 ml , 24.91 l , 0.0268 kl

Kayaks rent for $35 per day. which expression can you use to find the cost in dollars of renting 3 kayaks for a day?