3.9 Variation

Hello everyone! Today, after eating cake and brownies for Mr. W's birthday, we learned about variation.


Variation is used to describe relationships between variable quantities.

The graph of y=kx is linear,

And the graph of y=k/x looks like this:

The book gives guidelines to solving variation problems:

1. Write a general formula using the variables and k (the constant of variation).
2. Find the value of k using the given values.
3. Put the value of k that you found in guideline 2 into the equation, giving you the specific equation for that problem.
4. Use your new formula (involving the value of k) to solve the problem.

An example problem (Example 3 on page 248):

A variable w varies directly as the product of u and v and inversely as the square of s. 

       

        a. If w = 20, when u = 3, v = 5, and s = 2, find the constant of variation (k). 

        b. Find the value of w when u = 7, v = 4, and s = 3.

The general formula for w is:

Now, we can do part a, plugging in the numbers given for the variables:

For part b, all we need to do is plug the values given for the variables and the value of k into the general formula:

Extra tips: When the problem says that one thing (ex. weight) varies directly/proportionally with something else (ex. product of length and width), it means that you are multiplying by the constant. If it varies inversely, you divide the constant by it.

That's all, I guess. Have a good rest of you evening everyone and

HAPPY BIRTHDAY MR. WILHELM!!!

- Jessica Harrison