If Y varies inversely with the square of x. When x is 5, y is 4/5, how do you find value of y, when x equals 8?

Question

Jameson Allen · Accepted Answer

undefined To find the value of y when x equals 8, we can use the inverse variation equation.

First, we need to determine the constant of variation, which is denoted by k. In this case, since y varies inversely with the square of x, we have the equation y = k/x^2.

To find the value of k, we can use the given information when x is 5 and y is 4/5. Plugging these values into the equation, we get 4/5 = k/5^2.

Simplifying this equation, we have 4/5 = k/25. To solve for k, we can cross-multiply: 4 * 25 = 5 * k, which gives us k = 100/5 = 20.

Now that we have the value of k, we can substitute it back into the equation y = k/x^2. Plugging in x = 8, we get y = 20/8^2.

Simplifying further, we have y = 20/64, which can be reduced to y = 5/16.

Therefore, when x equals 8, the value of y is 5/16.

Eva Adamson · Answer

Set up the described equation, solve it for the proportionality constant, and then use your completed equation to calculate the new value.

First, set up the described equation. #y = a * 1/(x)^2# Then, given x = 5 and y = 4/5 we can solve for the proportionality constant of the equation. # 4/5 = a * 1/(5)^2 ; a = 4/5 * (5)^2 ; a = 4/5 *25 = 20# SO, our equation is #y = 20/(x)^2# #when x = 8, y = 20/(8)^2# ; y = 20/64 = 0.3125