Variation expressions

Question

If y is directly proportional to the square root of x and y=59 when x=576, find y if x=331776 . (Round off your answer to the nearest hundredth.)

Answer 1

When y is directly proportional to x it means y = kx (where k is the constant of proportionality). If you can determine k, you can predict any y value for a given x input. In this case, y is directly proportional to the square root of x so y = k√x

They gave you a data point so you can calculate the value of k by plugging in the x and y and solving for k.

59 = k√576

59 = 24k

k = 59/24

so the equation can be re-written as y = 59/24√x

Plugging in 331776 for x, we get: y = 59/24√331776 = 1416