The volume v = (4/3)π r^3 of a spherical balloon changes with the radius. a. at what rate (ft^3/ft) does the volume change with respect to the radius when r = 2 ft? b. by approximately how much does the volume increase when the radius changes from 2 to 2.2 ft?

a)

b)

Step-by-step explanation:

We are given the following information in the question:

Volume of sphere =

a) We have to find the rate at which the volume change with respect to the radius when r = 2 ft.

Differentiating, we get,

Putting r = 2

b) Approximate change in volume when radius changes from 2 to 2.2 feet

Putting the values, we get:

pentagon

step-by-step explanation:

the coordinates   a(5, -2), b(3,-1),c(-4,-4) d(-3,8) and e(-1,4) forms the vertices of the polygon when they are connected in order.

in order to classify that which polygon is it with the given coordinates, first count the number of vertices and then count the number of sides it can make with these vertices.

since, the given coordinates have five vertices, therefore, it will make five sides. moreover, pentagon is regular in nature therefore it will be convex.

now, a polygon with five sides is known as pentagon, therefore, the given polygon is the pentagon.