If y varies inversely as x. When y = 12, x = 7. How do you find the constant of variation and use it to determine the value for y when x = 4?

Question

Eva Abramson · Accepted Answer

undefined To find the constant of variation, we can use the formula for inverse variation: y = k/x, where k is the constant of variation.

Given that when y = 12, x = 7, we can substitute these values into the formula to solve for k: 12 = k/7.

To find the value of k, we can cross-multiply and solve for k: k = 12 * 7 = 84.

Now that we have the constant of variation (k = 84), we can use it to determine the value of y when x = 4.

Using the formula y = k/x, we substitute the values of k and x: y = 84/4 = 21.

Therefore, when x = 4, y = 21.

Ethan Adkins · Answer

The constant of variation is #84#
When #x=4# then #y=21# If #y# varies inversely as #x# then #color(white)("XXX")xy=c# for some constant of variation #c# We are told #(x,y)=(7,12)# is a solution for this equation so #color(white)("XXX")7xx12=c# #rArr##color(white)("XXX")c=84# When #x=4# #color(white)("XXX")4y=84# #rArr##color(white)("XXX")y=21#