3. A small toy in the shape of a right pyramid with a square base is floating 4 points in a pool of water. The height of the pyramid is 5 inches. One-third of this
height is above the surface of the water and two-thirds of it is below the
surface of the water. The square cross section of the pyramid at the
surface of the water has an area of 3.6 square inches. This cross section is
parallel to the base. What is the volume, in cubic inches, of the portion of
the pyramid that is above the water ? Enter your answer below*

Inverse Variation

Inverse Variation

The statement "y varies inversely as x means that when x increases, ydecreases by the same factor. In other words, the expression xy is constant:

xy = k    

where k is the constant of variation.

We can also express the relationship between x and y as:

y =      

where k is the constant of variation.

Since k is constant, we can find k given any point by multiplying the x-coordinate by the y-coordinate. For example, if y varies inversely as x, and x = 5 when y = 2, then the constant of variation is k = xy = 5(2) = 10. Thus, the equation describing this inverse variation is xy = 10 or y = .

Example 1: If y varies inversely as x, and y = 6 when x = , write an equation describing this inverse variation.

k = (6) = 8  

xy = 8 or y =  

Example 2: If y varies inversely as x, and the constant of variation is k = , what is y when x = 10?

xy =  

10y =  

y = × = × =  

k is constant. Thus, given any two points (x1, y1) and (x2, y2) which satisfy the inverse variation, x1y1 = k and x2y2 = k. Consequently, x1y1 = x2y2 for any two points that satisfy the inverse variation.

Example 3: If y varies inversely as x, and y = 10 when x = 6, then what is y when x = 15?

x1y1 = x2y2  

6(10) = 15y  

60 = 15y  

y = 4  

Thus, when x = 6, y = 4.