Question

Which of this quantities are inversely related?
a. side of a cube and it's surface area
b. diameter of a circle and it's circumference
c. the number of tickets sold and the gross sales​

Answer 1

Answer:

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diameter of a circle and it's circumference

Step-by-step explanation:

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Answer 2

Answer:

Direct Variation

Consider a freight train moving at a constant speed of 30 miles per hour. The equation that expresses the distance traveled at that speed in terms of time is given by

After 1 hour the train has traveled 30 miles, after 2 hours the train has traveled 60 miles, and so on. We can construct a chart and graph this relation.

In this example, we can see that the distance varies over time as the product of the constant rate, 30 miles per hour, and the variable, t. This relationship is described as direct variation and 30 is called the variation constant. In addition, if we divide both sides of

D

=

30

t

by t we have

In this form, it is reasonable to say that D is proportional to t, where 30 is the constant of proportionality. In general, we have

Key words Translation

“y varies directly as x”

y

=

k

x

“y is directly proportional to x”

“y is proportional to x”

Here k is nonzero and is called the constant of variation or the constant of proportionality.

Example 1: The circumference of a circle is directly proportional to its diameter, and the constant of proportionality is

π

. If the circumference is measured to be 20 inches, then what is the radius of the circle?

Solution:

Use the fact that “the circumference is directly proportional to the diameter” to write an equation that relates the two variables.

We are given that “the constant of proportionality is

π

,” or

k

=

π

. Therefore, we write

Now use this formula to find d when the circumference is 20 inches.

The radius of the circle, r, is one-half of its diameter.

Answer: The radius is

10

π

inches, or approximately 3.18 inches.

Typically, we will not be given the constant of variation. Instead, we will be given information from which it can be determined.