An oil slick is expanding as a circle. The radius of the circle is currently 2.5 inches and is increasing at a rate of 6.5 inches per hour. Express the area of the circle, A as a function of h, the number of hours elapsed.

So we can express the radius in terms of the hours elapsed like this:

And the reason of this is because each hour the radius increase 6.5 inches, and if we replace in the formula of area we got:

And this function would represent the area of the circle as function of the hours elapsed,

Step-by-step explanation:

For this case we know the radius of a circle given and we also know the incresing rate for the radius:

And we want to express the are of the circle A as a function of h = the number of hours elapsed.

We know that the area of a circle is given by:

So we can express the radius in terms of the hours elapsed like this:

And the reason of this is because each hour the radius increase 6.5 inches, and if we replace in the formula of area we got:

And this function would represent the area of the circle as function of the hours elapsed,

Correct  2/3 < 3/4

Step-by-step explanation:

We will compare the following two fractions:

2/3  and 3/4

First we will find common denominator:

The common denominator for 3 and 4 is 12, then we will multiply

first fraction with 4  and second with 3 and get:

8/12 and 9/12   and we conclude that 9/12 is greater than 8/12

respectively that 3/4 is greater than 2/3

Second we will find common numerator:

The common numerator for 2 and 3 is 6, then we will multiply

first fraction with 3  and second with 2 and get:

6/9 and 6/8 and we conclude that 6/8 is greater than 6/9, the reason is, the greater the fraction, the smaller the denominator

respectively that 3/4 is greater than 2/3

God is with you!!!