You can google keywords: joint variation
There are many examples and explanations available.
Are you familiar with "direct variation"?
Joint variation is simply direct variation with extra variables.
For example, if y varies directly with x, then their relation is:
y = k * x
where k is some arbitrary constant.
The following equations are examples of direct variation between x and y.
y = 5x
y = (1/2)x
y = Pi * x
With joint variation, there are two (or more) variables that vary directly with y.
y = k * x * z
Here, we say that y varies jointly with x and z.
Again, k represents an arbitrary constant.
The following equations are examples of joint variation.
y = 5 x z
y = (1/2) x z
y = 444 x z
Of course, neither x nor z are required to be to the first power.
If y varies jointly as x and the square root of z, then we have the following.
y = k * x * sqrt(z)
If we're told that y = 616 when x = 7 and z = 16, then we find the value of k by subsituting all of the given values into the joint-variation equation, followed by solving the resulting equation for k.
616 = k * 7 * sqrt(16)
k = 22
Does this help?
If you need more assistance with this exercise, please show us what you've been able to do so far, or explain why you think you're stuck.
Cheers,
~ Mark
