If y varies inversely with x, and y= 6 when x= 18, how do you find y when x= 8?

Question

Kennedy Adams · Accepted Answer

undefined To find y when x=8, we can use the inverse variation equation. The equation for inverse variation is y = k/x, where k is the constant of variation.

First, we need to find the value of k. We can do this by substituting the given values of y and x into the equation.

When y=6 and x=18, we have 6 = k/18.

To solve for k, we can multiply both sides of the equation by 18:

6 * 18 = k

k = 108

Now that we have the value of k, we can substitute it into the inverse variation equation to find y when x=8.

y = k/x

y = 108/8

y = 13.5

Therefore, when x=8, y is equal to 13.5.

Nathan Axel · Answer

#y=13.5# #y prop 1/x or y = k*1/x or x*y=k; y=6 ; x=18 :. 6*18=k or k=108# k= constant of variation. So the inverse variation equation is #x*y=108# Now #x=8 :. 8*y=108 or y=108/8=13.5#[Ans]

Eli Assouline · Answer

#y = 13/5# Inverse variations look like this: #y = k/x# We need to make our own inverse variation given #y=6# and #x=18#. We can plug this into the standard inverse variation with variables. #y = k/x# #6 = k/18# #108 = k# We've determined that #k=108#. Now we have what it takes to create an inverse variation. This is our final equation: #y = 108/x# We still need to find what #y# equals when #x# is #8#. Let's plug in #8# for #x#. #y = 108/x# #y = 108/8# #y = 13.5#