The radius of a circle is increasing at a nonzero rate, and at a certain instant, the rate of increase in the area of the circle is numerically equal to the rate of increase in its circumference. at this instant, the radius of the circle is

r=1

So,radius of the circle,when the rate of increase in the area of the circle is numerically equal to the rate of increase in its circumference, is 1.

Step-by-step explanation:

Area of the circle=

Circumference of circle=

Both area and circumference of circle is increasing at the same rate.

Increase in Area of the circle=Increase in Circumference of the circle

By cancelling the common terms we will get:

r=1

So,radius of the circle,when the rate of increase in the area of the circle is numerically equal to the rate of increase in its circumference, is 1.

6 on both sides and twelve on the top and the bottom

step-by-step explanation:

b. 6

step-by-step explanation:

we are given the table representing an exponential function.

we can see from the table that, as x is increasing, the value of y is increasing in the power of 6.

i.e. the following relation is obtained,

x = 1, y = 6

x = 2, y = 36 =

x = 3, y = 216 =

x = 4, y = 1296 =

x = 5, y = 7776 =

so, the geometric series obtained is .

thus, the common ratio is given by = = 6.

hence, the common ratio is 6.