Question

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

Answer 1

Answer: 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 (1)/(x^2)\\\\\\\Rightarrow y=k* (1)/(x^2)~~~~~~~~~~~~~~~~\textup{[where k is the proportionality constant]}`

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

`y=(k)/(x^2)\\\\\\\Rightarrow 7.2=(k)/(10^2)\\\\\Rightarrow k=7.2* 100\\\\\Rightarrow k=720.`

So, we get the relation as follows :

`y=(720)/(x^2)~~~~~~~~~~~~~~~~~~~~~~~(i)`

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

`20=(720)/(x^2)\\\\\\\Rightarrow x^2=(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.