If y varies directly to the square root of k, and k = 36 when y = 41. Find k when y = 205.

Question

If y varies directly to the square root of k, and k = 36 when y = 41. Find k when y = 205.

Answer 1

Alexis,

 

First, you can write  y = a(k)^0.5  , with unknown constant a and the square root of k, because the problem states that y varies directly with the right side.

 

Now you solve for the constant a using the given info that y =41 when k = 36

41 = a(36)^0.5  = a(6)  since the square root of 36 is 6

So a = 41/6

 

Knowing a, you can now solve for k when y = 205

205 = (41/6)(k)^0.5

and 205(6/41) = 30 = (k)^0.5  , you now square both sides of the equation to remove the square root.

(30)² = k  = 900   that's your answer.