Answer:
a. A' = πr² + 14.5
b. 5.98 in
Step-by-step explanation:
a. Write an expression that represents the total area, in square inches, of the logo in terms of the radius, r, of the inner part of the logo.
Since the inner circle has a radius of r, its area is A = πr².
Now, the border has and area of 14.5 in². Thus, the total area, A' = area of inner circle + area of border
A' = πr² + 14.5
b. If the total area of the logo is 127 square inches, what is the approximate value of r?
Given that A' = total area of logo = 127 in²
So, A' = πr² + 14.5
πr² = A' - 14.5
dividing through by π, we have
r² = (A' - 14.5)/π
taking square-root of both sides, we have
r = √[(A' - 14.5)/π]
Substituting the value of A' into the equation, we have
r = √[(127 in² - 14.5 in²)/π]
r = √[(112.5 in²/π]
r = √[35.81 in²]
r = 5.98 in
