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

Answer:  Third option is correct.

Step-by-step 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,

$q=k\frac{rx}{m^2}\\\\\text{ where k denotes constant of variation}$

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

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

$q=k\frac{rx}{m^2}\\\\2.5=k\frac{8}{4^2}\\\\2.5=k\frac{8}{16}\\\\2.5=k\frac{1}{2}\\\\2.5\times 2=k\\\\5=k$

Hence, Third option is correct.

Answer 2

Q = k * (r*x)/m^2 ⇒ k = q*m^2 /(r*x)

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

Answer: 5