If y varies inversely as X^2 and X = 9 when y = 64, how do you find the value of y when x = 4?

Question

Avery Alexander · Accepted Answer

undefined To find the value of y when x = 4, we can use the inverse variation equation.

First, we need to determine the constant of variation, denoted as k.

Given that y varies inversely as x^2, we can write the equation as y = k/x^2.

To find k, we can substitute the given values of x and y into the equation.

When x = 9 and y = 64, we have 64 = k/9^2.

Simplifying, we get 64 = k/81.

To solve for k, we can multiply both sides of the equation by 81, resulting in 5184 = k.

Now that we have the value of k, we can substitute it back into the inverse variation equation.

Thus, when x = 4, y = k/4^2 = 5184/16 = 324.

Therefore, when x = 4, y = 324.

Eva Adamson · Answer

#y=324# #"varies inversely means " 1/"variable"# #rArr"the initial statement is " yprop1/(x^2)# #"to convert to an equation, multiply by k, "# #"the constant of variation"# #rArry=kxx1/x^2=k/x^2# #"to find k, use the condition given"# #y=k/x^2rArrk=x^2y# #"given " x=9" when " y=64# #rArrk=9^2xx64=5184# #rArr" equation is " color(red)(bar(ul(|color(white)(2/2)color(black)(y=5184/x^2)color(white)(2/2)|)))# #"when x = 4 then"# #y=5184/16=324#