Question

If m varies directly as the square root of y , inversely as p 2, and directly as n , what happens to m when y is quadrupled, p is tripled, and n is multiplied by 5?

Answer 1

This is the concept of proportionality, given that m is directly proportion to y  and n and inversely proportional to p^2. We are required to find what happens to m when y is quadrupled, p is tripled and n is multiplied by 5;

From the equation;
m=(yn)/p^2

when:
y is quadrupled we get 4y
p is tripled we get 3p
n is multiplied by 5 we get 5n

thus the new value of m will be:

m=(4y*5n)/(3p)^2
m=(20yn)/9p^2
m=(20/9)(yn/p^2)
that means that m will be increased bby 20/9