A rental car company charges $52.99 per day...?

Question

whats the answer to this question and how did you solve it....thanks for your help : )

A rental car company charges $52.99 per day, including 200 free kilometers. There is a charge of $0.12/km for additional kilometers. Write a linear equation that models this situation.

and one more question.....

the area of a circle varies directly as the square of the radius. if the radius is tripled, by what factor will the area increase?

answer either question or both if you can, thanx

Answer 1

D= distance driven

For D <= 200
Cost = 52.99

For D> 200
cost = 52.99 + 0.12*(D-200)

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Area of a circle= pi * r*r
where r is the radius
where pi=3.14159265


If we assume a radius of 1 then area is equal to pi
Area = pi * 1 *1

If we triple the radius to 3

Area= pi*(3)*(3)
= 9*pi

Factor
9*pi - 1*pi = 8*pi

Answer 2

If first circle has radius of 3 and we triple that radius to 9, then 9 squared is 81.
81 is 27 times the original 3 . So it goes up by a factor of 27 which is 3 x( 3 squared) or 3 x 9

If first circle has radius of 2 and we triple that radius to 6, then 6 squared is 36.
36 is 18 times the original 2 . So it goes up by a factor of 18 which is 2 x (3 squared) or 2 x 9

so the formula is:
new area = original radius x (factor of size increase) squared