An agricultural sprinkler distributes water in a circular pattern of radius 100 ft. It supplies water to a depth of e^-r feet per hour at a distance of r feet from the sprinkler. If 0 < R ≤ 100, what is the total amount of water supplied per hour to the region inside the circle of radius R centered at the sprinkler?

A circle of radius ft has area sq ft. For any fixed , water will reach a depth of ft. You can think of the total volume of water supplied within a radius of the sprinkler as the volume of the "cylinder" with "height" given by for some .

This volume is

cu ft.

the length of o'p' is .

step-by-step explanation:

it is given that the quadrilateral m'n'o'p' is the image of quadrilateral mnop after dilation.

the center of dilation is origin and the scale factor is 1.5.

in dilation the image and preimge are similar figures. it means the sides of image and preimage are proportional.

the scale factor is defined as

the scale factor is 1.5.

multiply both sides by op.

note: if the value of op is given, then multiply the value of op with 1.5 to get the length of side o'p'.

therefore length of o'p' is .