What we covered today in this chapter of wonder is only the first part of it: direct variations.
According to our trusty book, these types of equations are extremely common in everyday business and physical science life. If those are part of your life, this may mean the world to you.
When Y is said to 'VARY DIRECTLY AS X', it means that Y is dependent on a multiple of X.
This is known as direct variation. An easy way to remember this is to just remember the formula
Y = KX .
Good? What this means is basically what was just said; that Y is dependent to a multiple of X: aka, KX.
(y is proportional to x.)
So, in order to be able to say this, really powerful people who can make laws about math have decided to give the number that you multiply x with (k) a handy dandy name. They call it...
THE CONSTANT OF VARIATION!
Whew.
In a direct variation, (which is what were covering right now,) as long as K is greater than zero...
AS X INCREASES, Y ALSO INCREASES.
So, in a real world situation, K would be the constant in the problem. For instance, if you want to find the cost for buying yummy in my tummy candy bars, (Snickers, of course,) they will always cost the same. I mean, theoretically, and for the sake of the problem, the cost will never change. This means that the cost is CONSTANT, meaning it is THE CONSTANT OF VARIATION, or K! Easy enough. The equation to write this would be:
y = (COST OF SNICKERS) x
Y would equal your final cost, and x would be how many snickers you bought. And, again, since the cost of the snickers is positive (k), the more snickers you buy, the higher the cost will be.
There!
And that is about it for DIRECT VARIATION problems, in simplicity.
JARED is the next scribe.
This is a problem that Jojo showed us today:
ReplyDeleteThe area of a circle varies directly as the square of its radius. A circle with radius 3 in. has area 28.278 square inches.
A=kr^2
28.278=k(3)^2
28.278=9k
------ --
9 9
3.142=k
A=3.142 r^2
A=πr^2