Y varies inversely with twice the value of x. When y = 8, x = 2. How do you find y when x = 8?

Question

Hazel Anglin · 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. In this case, y varies inversely with twice the value of x, so the constant of variation is 2.

Next, we can set up the inverse variation equation: y = k/(2x), where k is the constant of variation.

To find the value of k, we can substitute the given values of y and x into the equation: 8 = k/(2*2).

Simplifying the equation, we have: 8 = k/4.

To solve for k, we can multiply both sides of the equation by 4: 32 = k.

Now that we have the value of k, we can substitute it back into the inverse variation equation: y = 32/(2x).

To find y when x = 8, we substitute x = 8 into the equation: y = 32/(2*8).

Simplifying the equation, we have: y = 32/16.

Therefore, when x = 8, y = 2.

Kennedy Adams · Answer

#y=2" at "x=8#

#y= kxx1/(2x)#

#"so "2xy=k#

Given that when #y=8", "x=2# so we have:

#2(2)(8)=k#

#=> k=32#

So our equation becomes:

#y=32/(2x)#

This is the same as:

#y= 32/2 xx1/ x#

so #y= 16/x# '~~~~~~~~~~~~~~~~~~~~~~~~~~~ So when #x=8#

#color(brown)(y=16/x)color(blue)(" " ->" " y=16/8 = 2)#