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Chapter 1: Problem 71

Solve for the indicated variable. $$ a=\frac{k F}{m} \text { for } m $$

Short Answer

Expert verified
m = \frac{kF}{a}

Step by step solution

01

Isolate the variable

The equation given is: \[ a = \frac{kF}{m} \] Our goal is to solve for the variable \(m\). To isolate \(m\), we can start by multiplying both sides of the equation by \(m\) to remove the denominator from the right side.
02

Remove the denominator

Multiply both sides by \(m\): \[ a \times m = kF \] Now the equation is: \[ am = kF \]
03

Solve for \(m\)

We need \(m\) by itself on one side. To isolate \(m\), divide both sides of the equation by \(a\): \[ m = \frac{kF}{a} \]

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Isolation of Variables
Isolation of variables is the process of rearranging an equation to get a specific variable alone on one side of the equation. It is a fundamental technique in algebra used to solve for unknowns. For example, given the equation \( a = \frac{kF}{m} \), our goal is to isolate the variable \( m \).
Algebraic Manipulation
Algebraic manipulation involves using rules and properties of algebra to rearrange and simplify equations. In this exercise, we start with the equation \( a = \frac{kF}{m} \). By recognizing that we want \( m \) by itself, we use algebraic steps to simplify the expression. Initially, we multiply both sides by \( m \) to clear the denominator, resulting in \[ a \times m = kF \]. These actions simplify the equation and set the stage for the next steps.
Division in Algebra
Division in algebra allows us to isolate variables by breaking down equations into simpler forms. With \( am = kF \), we need \( m \) alone on one side to solve for it. Thus, we divide both sides by \( a \): \( m = \frac{kF}{a} \). This final step provides the solution. Division is crucial as it balances the equation and helps separate the variable we are solving for.

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Most popular questions from this chapter

Solve the equations. \(|3 y+5|=|y+1|\)

A box of cereal is labeled to contain 16 oz. A consumer group takes a sample of 50 boxes and measures the contents of each box. The individual content of each box differs slightly from 16 oz, but by no more than 0.5 oz. a. If \(x\) represents the exact weight of the contents of a box of cereal, write an absolute value inequality that represents an interval in which to estimate \(x\). b. Solve the inequality and interpret the answer.

Solve the equations. a. \(|m+1|=5\) b. \(|m+1|=0\) c. \(|m+1|=-1\)

a. Write an absolute value equation or inequality to represent each statement. b. Solve the equation or inequality. Write the solution set to the inequalities in interval notation. The distance between a number \(x\) and 4 on the number line is 6 .

Answer true or false given that \(a>0, b<0, c>0,\) and \(d<0\). $$\text { If } a
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