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Question 129424: what in the world is this stuff?
y varies directly as x and inversely as the square root of w; write the sentence as an equation.
Answer by Earlsdon(6294)   (Show Source):
You can put this solution on YOUR website! This "stuff" is algebra!
The topic is "variations"
When one quantity varies (changes) as a result of a change in another quantity, you can write the equation of variation that shows this relationship.
A simple example might be a person's salary depends on how many hours he/she works. The more hours worked, the more salary is earned, right?
This is called a "direct" variation because, as the hours worked go up, the salary goes up. This is usually stated as:
The salary "varies directly" as hours worked. Notice that the salary does not equal the hours worked.
So you cannot write: S = H, rather, you would write: S = kH, the k is called the constant of variation.
Another example would be the more you exercise, the less you weigh (hopefully).
This is called an "inverse" variation because as the number of hours of exercise go up, the weight goes down.
This can be stated as: The weight "varies inversely" as the hours of exercise.
Again, notice that the weight is not equal to the inverse of the number of hours exercised so you cannot write W = 1/H, rather, you would write W = k/H where, k is the constant of variation.
Now to your problem:
"y varies directly as x ( ) and inversely as the square root of w ( )
You can combine these two statements into one equation but you will use only one constant of variation, k.
 This is the equation you need!
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