Mastery Check Solutions

Show What You Know

Use the equation to complete the problem.

$x = \frac{k w \sqrt[3]{z}}{y^{3}}$

Two students were given an equation and asked to describe the variation in words. Explain the errors and how to correct the misunderstanding.

Sample: Cruz did not include that the numerator represents joint variation rather than direct. If there is more than one variable multiplied together, this is joint, not direct variation. The constant of variation is not included in the verbal description.

Sample: Terri confused the cubed root of z with z-cubed. Terri also said “divided by” but needs to replace that with “inverse variation.”

Note

It may be helpful to complete part B and then come back to part A. Having the correct answers may help you better describe the errors. This is also a reason to complete the problem and then check your work.

Correctly describe the equation in words.

Sample: x varies jointly as w and the cube-root of z, and inversely with y to the third power.

Write the equation with the value of the constant of variation when $w = 7,$ $x = 10,$ $y = 2,$ and $z = 125 .$

$\begin{array}{rcl} (10) & = & \frac{k (7) \sqrt[3]{(125)}}{{(2)}^{3}} \\ 10 & = & \frac{k (7) (5)}{8} \\ (\frac{8}{35}) 10 & = & \frac{35 k}{8} (\frac{8}{35}) \\ k & = & \frac{16}{7} \\ x & = & \frac{16 w \sqrt[3]{z}}{7 y^{3}} \end{array}$

Say What You Know

In your own words, talk about what you have learned using the objectives for this lesson and your work on this page.

Note

Restate the objectives of the lesson in your own words. If you are unable to restate the lesson objectives, go back and reread the objectives and then explain them.

Calculate the constant of variation or missing values given the type of variation.
Determine the type of variation in words or symbols.
Write and/or solve the variation equation.