Y varies directly as the square of x and y=96 when x=4. Find the value of y when x=5

Question

Y varies directly as the square of x and y=96 when x=4. Find the value of y when x=5

Answer 1

If Y varies directly as the square of X, then we can write the equation as:

Y = kX^2

where k is the constant of variation.

To find the value of k, we can use the given information that Y = 96 when X = 4:

96 = k(4^2)
96 = 16k
k = 6

Now we can use this value of k to find the value of Y when X = 5:

Y = 6(5^2)
Y = 150

Therefore, when X = 5, Y = 150.