Mathematics: If y = 7.2 when x = 10, what is the value of x when y = 20? (y varies inversely as the square of x.) a. 6 b. 10 c. 14.4 d. 20

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If y = 7.2 when x = 10, what is the value of x when

teresaswinger

05.01.2022

The correct option is (A) 6..

Step-by-step explanation: Given that y varies inversely as the square of x and y = 7.2 when x = 10.

we are to find the value of x when y = 20.

Since y varies inversely as the square of x, so we have

$y\propto \dfrac{1}{x^2}\\\\\\\Rightarrow y=k\times \dfrac{1}{x^2}~~~~~~~~~~~~~~~~\textup{[where k is the proportionality constant]}$

When y = 7.2 and x = 10, then we get

$y=\dfrac{k}{x^2}\\\\\\\Rightarrow 7.2=\dfrac{k}{10^2}\\\\\Rightarrow k=7.2\times 100\\\\\Rightarrow k=720.$

So, we get the relation as follows :

$y=\dfrac{720}{x^2}~~~~~~~~~~~~~~~~~~~~~~~(i)$

When y = 20, then from equation (i), we get

$20=\dfrac{720}{x^2}\\\\\\\Rightarrow x^2=\dfrac{720}{20}\\\\\Rightarrow x^2=36\\\\\Rightarrow x=\pm 6.$

Thus, the required value of x is 6 or -6. Since x = -6 is not in the options, so option (A) is CORRECT.

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