Skip to main content
Ch. 1 - Equations and Inequalities
Blitzer - College Algebra 8th Edition
Blitzer8th EditionCollege AlgebraISBN: 9780136970514Not the one you use?Change textbook
All textbooksBlitzer 8th EditionCh. 1 - Equations and InequalitiesProblem 41
Chapter 2, Problem 41

In Exercises 35–54, solve each formula for the specified variable. Do you recognize the formula? If so, what does it describe? E = mc2 for m

Verified step by step guidance
1
Identify the formula given: \(E = mc^2\). This is Einstein's mass-energy equivalence formula, which relates energy (\(E\)) to mass (\(m\)) and the speed of light (\(c\)).
The goal is to solve the formula for the variable \(m\), which means isolating \(m\) on one side of the equation.
Start by dividing both sides of the equation by \(c^2\) to isolate \(m\): \(\frac{E}{c^2} = \frac{mc^2}{c^2}\).
Simplify the right side since \(c^2\) divided by \(c^2\) is 1, leaving \(\frac{E}{c^2} = m\).
Rewrite the equation to express \(m\) explicitly: \(m = \frac{E}{c^2}\). This shows mass as energy divided by the square of the speed of light.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.
Video duration:
1m
Was this helpful?

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Solving Formulas for a Specified Variable

This involves rearranging an equation to isolate the desired variable on one side. It requires using algebraic operations such as addition, subtraction, multiplication, division, and sometimes roots or exponents to rewrite the formula in terms of the specified variable.
Recommended video:
06:36
Solving Quadratic Equations Using The Quadratic Formula

Understanding the Formula E = mc²

This famous formula, derived by Albert Einstein, expresses the relationship between energy (E), mass (m), and the speed of light (c). It shows that energy equals mass times the speed of light squared, highlighting the equivalence of mass and energy.
Recommended video:
4:47
The Number e

Physical Constants and Their Roles in Formulas

The speed of light (c) is a constant approximately equal to 3 × 10^8 meters per second. Recognizing constants helps in solving formulas and understanding their physical meaning, as constants remain fixed while variables can change.
Recommended video:
06:36
Solving Quadratic Equations Using The Quadratic Formula
Related Practice
Textbook Question

Exercises 27–40 contain linear equations with constants in denominators. Solve each equation. 3x/5 - (x - 3)/2 = (x + 2)/3

778
views
Textbook Question

In Exercises 35–46, determine the constant that should be added to the binomial so that it becomes a perfect square trinomial. Then write and factor the trinomial. x2−7xx^2 - 7x

977
views
Textbook Question

Exercises 41–60 contain rational equations with variables in denominators. For each equation, a. write the value or values of the variable that make a denominator zero. These are the restrictions on the variable. b. Keeping the restrictions in mind, solve the equation. 4/x = 5/2x + 3

972
views
Textbook Question

In all exercises, other than exercises with no solution, use interval notation to express solution sets and graph each solution set on a number line. In Exercises 27–50, solve each linear inequality. x/4 - 3/2 ≤ x/2 + 1

822
views
Textbook Question

In Exercises 37–52, perform the indicated operations and write the result in standard form. (- 2 + √-4)2

837
views
Textbook Question

Use the graph to a. determine the x-intercepts, if any; b. determine the y-intercepts, if any. For each graph, tick marks along the axes represent one unit each.

130
views