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:

answer:

given the linear inequality :

add 2y to both sides we get;

simplify:

add 12 to both sides of an equation;

simplify:

divide both sides by 2 we get;

or

the related equation for the inequality equation [1] is;

y-intercepts defined as the graph crosses the y-axis.

substitute x =0 in [2] to solve for y;

y = 6

x-intercepts defined as the graph crosses the x-axis.

substitute value y = 0 to solve for x;

subtract 6 from both sides we get

multiply both sides by 2 we get;

or

x = -12

now, plot these point (0, 6) and (-12, 0) on graph as shown below and shade the graph below the solid line.

step-by-step explanation:

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