Suppose that y varies directly as the square root of x​, and that y=30 when x=25. Find x when y=36.

Question

Suppose that y varies directly as the square root of x, and that y=30 when x=25. Find x when y=36.

Answer 1

Hi Cort,

 

If y varies directly as the square root of x, that means there is a constant that determines the relationship. We can write the relationship as

 

y = a*sqrt(x)

 

if y = 30, when x = 25, then we can find a

 

30 = a*sqrt(25)

30 = 5a

a = 6

 

then the relationship is y=6*sqrt(x)

36 = 6*sqrt(x)

6 = sqrt(x)

x = 36