Question

If y is directly proportional to the square root of x and y = -37 when x = 289, find y if x= 83521

Answer 1

2.1765

Explanation:

We have the following relationship

`y \propto (1)/(√(x) )`

We can represent this inverse proportional relationship as

`y = k(1)/(√(x) ) = (k)/(√(x) )`

k is known as the constant of proportionality

Therefore

`k = y√(x)`

Given y = -37 when x = 289

k = -37 x √289

= -37 x 17

= - 629

We are asked t find y when x = 83521

With k = - 629 and x = 83521

`y = - 629 * (1)/(√(83521)) = -629 * (1)/(289) = 2.1765`

We can check if this is correct by noting that according to the rule of proportions:

`$(y)/(-37)=((1)/(√(83521)))/((1)/(√(289)))=((1)/(289))/((1)/(17))=(17)/(289)$`

So

`y = -37 * (1)/(17) = -(37)/(17) = - 2.1765`