Mathematics: 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?

Suppose c is inversely proportional to the square

leahandmaryssa

23.01.2022

The constant of proportionality is 54.

k = 54

c as a function of d:

$c(d) = \dfrac{54}{d^2}$

$c(7) = \dfrac{54}{49}$

Step-by-step explanation:

We are given the following in the question:

c is inversely proportional to the square of d.

$\Rightarrow c\propto \dfrac{1}{d^2}\\\\\Rightarrow c = \dfrac{k}{d^2}\\\\\text{where k is constant of proportionality}$

When c = 6, d = 3.

Plugging the values, we get,

$6 = \dfrac{k}{3^2}\\\\\Rightarrow k = 6\times 3^2 = 54$

Thus, the constant of proportionality is 54.

c as a function of d can be written as:

$c(d) = \dfrac{54}{d^2}$

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

Putting values, we get,

$c(7) = \dfrac{54}{(7)^2}=\dfrac{54}{49}$

is the required value of c.

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