Question

Suppose c is inversely proportional to the square of d. If c=6 when d=3⁢, find the constant of proportionality and write the formula for c as a function of d?

c= ?
How would I write the formula?
Use your formula to find c when d is 7.

Enter the exact answer.
c=?
What would c equal?

Answer 1

The constant of proportionality is 54.

k = 54

c as a function of d:

`c(d) = (54)/(d^2)`

`c(7) = (54)/(49)`

Explanation:

We are given the following in the question:

c is inversely proportional to the square of d.

`\Rightarrow c\propto (1)/(d^2)\\\\\Rightarrow c = (k)/(d^2)\\\\\text{where k is constant of proportionality}`

When c = 6, d = 3.

Plugging the values, we get,

`6 = (k)/(3^2)\\\\\Rightarrow k = 6* 3^2 = 54`

Thus, the constant of proportionality is 54.

c as a function of d can be written as:

`c(d) = (54)/(d^2)`

We have to find value of c when d = 7.

Putting values, we get,

`c(7) = (54)/((7)^2)=(54)/(49)`

is the required value of c.