State the meaning of inverse proportion.
If r varies inversely with a, write an equation that uses k as the constant of variation.
In the equation y = \dfrac{18}{x}, y varies inversely with x. When x = 6, y = 3.
Solve for y when x = 2.
For these two ordered pairs, what is the result when the y -value is multiplied by the x -value?
Suppose that y varies inversely as the square of x, and that y = 0.0023 when x = 0.4.
Find the constant of variation, k. Round your answer correct to six decimal places.
Write the variation equation for y in terms of x.
State whether the following equations are examples of inverse variation:
y = \dfrac{7}{x}
y = 6 x + 8
y = - \dfrac{9}{x}
y = \dfrac{8}{x^{2}}
y = 2 x^{2} - 7 x - 4
y = 3 - x
x = 1 + y^{3}
x = \dfrac{8}{y^{2}}
y = 6 x + 8
x y = - 7
x = \dfrac{2}{y}
x y = 5 x
Consider the inverse variation equation y = \dfrac{6}{x}.
Complete the following tables:
| x | \dfrac{1}{4} | \dfrac{1}{2} | 1 | 2 | 4 |
|---|---|---|---|---|---|
| y |
Plot the data from the table of values on a number plane.
If y is inversely proportional to x, and y = 20 when x = 10:
Find the constant of variation, k.
Express y in terms of x.
Find the value of y when x = 5.
Which of the following tables could represent an inversely proportional relationship between x and y?
| x | 1 | 2 | 3 | 4 |
|---|---|---|---|---|
| y | 3 | 1.5 | 1 | 0.75 |
| x | 1 | 2 | 3 | 4 |
|---|---|---|---|---|
| y | 36 | 18 | 12 | 9 |
| x | 1 | 5 | 6 | 10 |
|---|---|---|---|---|
| y | 3 | 75 | 108 | 300 |
| x | 1 | 2 | 3 | 4 |
|---|---|---|---|---|
| y | 4 | 5 | 6 | 7 |
Find the equation relating n and r given the table of values:
| n | 1 | 2 | 3 | 4 |
|---|---|---|---|---|
| r | 5 | \dfrac{5}{2} | \dfrac{5}{3} | \dfrac{5}{4} |
Consider the equation s = \dfrac{375}{t}.
State the constant of proportionality.
Find the value of s when t = 6.
Find the value of s when t = 12.
The time, t, taken by a typist to type up a document is inversely proportional to his typing speed, s. That is, the quicker the typing speed, the less time it will take. If it takes a typist 20 minutes to type a particular document, typing at a speed of 61 words per minute:
Find the constant of variation k.
How long (in minutes) will it take a typist with a typing speed of 30.5 words per minute to type up the document?