PSAT Math : How to use the inverse variation formula
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Example Question #8 : Direct And Inverse Variation
The square of 
When two quantities vary inversely, their products are always equal to a constant, which we can call k. If the square of x and the cube of y vary inversely, this means that the product of the square of x and the cube of y will equal k. We can represent the square of x as x2 and the cube of y as y3. Now, we can write the equation for inverse variation.
x2y3 = k
We are told that when x = 8, y = 8. We can substitute these values into our equation for inverse variation and then solve for k.
82(83) = k
k = 82(83)
Because this will probably be a large number, it might help just to keep it in exponent form. Let's apply the property of exponents which says that abac = ab+c.
k = 82(83) = 82+3 = 85.
Next, we must find the value of y when x = 1. Let's use our equation for inverse variation equation, substituting 85 in for k.
x2y3 = 85
(1)2y3 = 85
y3 = 85
In order to solve this, we will have to take a cube root. Thus, it will help to rewrite 8 as the cube of 2, or 23.
y3 = (23)5
We can now apply the property of exponents that states that (ab)c = abc.
y3 = 23•5 = 215
In order to get y by itself, we will have the raise each side of the equation to the 1/3 power.
(y3)(1/3) = (215)(1/3)
Once again, let's apply the property (ab)c = abc.
y(3 • 1/3) = 2(15 • 1/3)
y = 25 = 32
The answer is 32.
Example Question #71 : Algebra
Square both sides, and the expression becomes
meaning that 
Example Question #71 : Algebra
Setting 
Setting 
meaning that 
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