Z varies directly as x^2. If z = 48 when x=4, find z when x=5

Question

Z varies directly as x^2. If z = 48 when x=4, find z when x=5

Answer 1

If there is a direct relationship between z and x^2, then z=a*x^{2,where a is a constant,} 

z=48 when x=4, this will help us find a

48 = a*4²

a = 3 so the relationship can be written as

z = 3x²

 

Then, when x=5

z = 3*5²

z = 75