The variable y varies directly with the square of X. If y is 50 when x is 5, find y when x is 4.

Question

The variable y varies directly with the square of X. If y is 50 when x is 5, find y when x is 4.

Answer 1

Hello, Amber,

We can translate "y varies directly with the square of x" to:

y =Ax²

I added the "A" since we don't know if there is another factor involved. To find A we can use the data provided (5,50).

50 = A*5²

A = 2

The equation is y = 2*x²

Use x = 4, and we find that y = 2*4²

y= 2*16

y = 32

Answer 2

If variable y varies directly with the square of x, in equation form we can write y = ax², where a is a constant. They tell us y = 50 when x = 5, so let's plug that into the equation we just wrote: 50 = a(5)² --> 50 = a(25) --> a = 2.

So now that we figured out the value of our constant, we get the equation y = 2x²

Let's plug in x = 4, to find y.

y = 2(4)² --> y = 2(16) --> y = 32

Therefore, y = 32 when x = 4