Question

Given that y varies directly as the square of x, if y = 20 when x = 2, what is y when x = 3?

Answer 1

For the given variation, we can find the constant of variation and use it to solve for y when x=3.

Step-by-step explanation:

Given that y varies directly as the square of x, we can write the equation y = kx^2, where k is the constant of variation. To find the value of k, we can plug in the given values of y and x.

When y = 20 and x = 2, we have 20 = k(2^2). Solving for k, we get k = 5.

Now we can use the value of k to find y when x = 3. Substitute x = 3 into the equation y = kx^2: y = 5(3^2) = 45. Therefore, when x = 3, y = 45.