Chapter 2: Q3. (page 110)

Translate each sentence into an equation.
The product of five and w is the same as w to the third power.

Short Answer

Expert verified

The required equation is $5 w = w^{3}$ .

Step by step solution

Step 1. Apply the concept of multiplication of a constant and a variable.

A constant is a number like $1, 2, 10.5,$ etc. A variable is a letter or a literal used to signify an unknown quantity.

When a constant is multiplied by a variable we just append the constant in front of the variable.

We are given a constant $5$ and a variable $w$ , so their product will be $5 w$

Step 2. Apply the concept of raising variable to an index.

When a variable is multiplied by itself we raise the index/exponent of the variable by two, when it is multiplied once more to this product we raise the index to three. In this fashion, variables are written for example,

$\begin{array}{l} x \times x = x^{2} \\ x \times x \times x = x^{3} \end{array}$

Thus $w$ raised to the third power is written as

$w^{3}$

Step 3. Evaluate the two results.

To get the final expression we equate the results of steps 1 and 2 to get:

$5 w = w^{3}$

Thus, the required equation is $5 w = w^{3}$ .

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Translate each sentence into an equation.
The product of five and w is the same as w to the third power.

Short Answer

Step by step solution

Step 1. Apply the concept of multiplication of a constant and a variable.

Step 2. Apply the concept of raising variable to an index.

Step 3. Evaluate the two results.

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Translate each sentence into an equation.The product of five and w is the same as w to the third power.

Short Answer

Step by step solution

Step 1. Apply the concept of multiplication of a constant and a variable.

Step 2. Apply the concept of raising variable to an index.

Step 3. Evaluate the two results.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Geometry

Mechanics Maths

Decision Maths

Applied Mathematics

Statistics

Study anywhere. Anytime. Across all devices.

Translate each sentence into an equation.
The product of five and w is the same as w to the third power.