The function f(x) = xπ−−√ gives the diameter, in inches, of a proposed spherical sculpture with a surface area of x square inches. The artist making the sculpture wants to know how the diameter changes if the surface area is increased. What is the average rate of change for the function as the surface area changes from 12.6 in.2 to 28.3 in.2? Round your answer to the nearest hundredth of an inch.

The average rate of change of f(x) = 3.14 inches⁻¹

The change in f(x) = 49.32 in

Step-by-step explanation:

The surface area of the spherical sculpture = x and its diameter f(x) = πx.

The average rate of change of f(x) as x changes is df(x)/dx = π = 3.14

Now the change in diameter Δf(x) = df(x) = (df(x)/dx)dx = πdx  

dx = Δx = 28.3 in² - 12.6 in² = 15.7 in²

df(x) = π × 15.7 = 49.32 in

a) t'(-3, 6) and v'(0, 3)  

step-by-step explanation:

answer: city needs 2.4 inches of rainfall more to match the record of 40 inches.

step-by-step explanation:

since we have given that

total annual rainfall a city record = 40 inches

this year, total rainfall recorded = 37.6 inches

number of inches of rainfall   is needed to match the record of 40 inches is given by

hence, city needs 2.4 inches of rainfall more to match the record of 40 inches.