Question

The quantity q varies inversely with the square of m and directly with the product of r and x. When q is 2.5, m is 4 and the product of r and x is 8. What is the constant of variation?

5/8
5/4
5
10

Answer 1

q = k * (r*x)/m^2 ⇒ k = q*m^2 /(r*x)

k = 2.5 (4)^2 / 8 = 5

Answer: 5

Answer 2

Answer: Third option is correct.

Explanation:

Since we have given that

The quantity q varies inversely with the square of m and directly with the product fo r and x.

According to question,

`q=k(rx)/(m^2)\\\\\text{ where k denotes constant of variation}`

Since q=2.5, m=4, rx=8,

So, we put the value of all of theses in our above relation:

`q=k(rx)/(m^2)\\\\2.5=k(8)/(4^2)\\\\2.5=k(8)/(16)\\\\2.5=k(1)/(2)\\\\2.5* 2=k\\\\5=k`

Hence, Third option is correct.