If y varies inversely as twice x. When x = 4, y = 10. how do you find y when x = 8?

Question

Nathan Axel · Accepted Answer

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

First, we need to determine the constant of variation, which is denoted as k. In this case, y varies inversely as twice x, so we can write the equation as y = k/(2x).

To find k, we can substitute the given values of x and y into the equation. When x = 4 and y = 10, we have 10 = k/(2*4).

Simplifying this equation, we get 10 = k/8.

To solve for k, we can multiply both sides of the equation by 8, resulting in 80 = k.

Now that we have the value of k, we can substitute it back into the inverse variation equation: y = 80/(2x).

To find y when x = 8, we substitute x = 8 into the equation: y = 80/(2*8).

Simplifying this equation, we get y = 80/16.

Therefore, when x = 8, y = 5.

Avery Alexander · Answer

#color(red)(y=5# when #color(blue)(x=8)# If #y# varies inversely as twice #x#, then #color(white)("XXX")color(blue)y=color(magenta)c/(2color(green)x)color(white)("xxx")#for some constant #color(magenta)c# We are told that #color(green)x=color(green)4#, #color(blue)y=color(blue)(10)# is a solution to this relation. so #color(white)("XXX")color(blue)10=color(magenta)c/(2 * color(green)4)# #color(white)("XXX")rarr color(magenta)c=80# Therefore the relation is #color(white)("XXX")color(blue)y=color(magenta)(80)/(2color(green)x)# When #color(green)x=color(green)8#, we have #color(white)("XXX")color(blue)y=color(magenta)(80)/(2 * color(green)8) = 5#