Table of contents

0. Review of Algebra4h 18m
1. Equations & Inequalities3h 18m
2. Graphs of Equations43m
3. Functions2h 17m
4. Polynomial Functions1h 44m
5. Rational Functions1h 23m
6. Exponential & Logarithmic Functions2h 28m
7. Systems of Equations & Matrices4h 6m
8. Conic Sections2h 23m
9. Sequences, Series, & Induction1h 22m
10. Combinatorics & Probability1h 45m

1. Equations & Inequalities

Linear Equations

College Algebra

1. Equations & Inequalities

Linear Equations

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1:46 minutes

Problem 52

Textbook Question

In Exercises 35–54, solve each formula for the specified variable. Do you recognize the formula? If so, what does it describe?A = 2lw + 2lh + 2wh for h

Verified step by step guidance

Start with the given formula: $ A = 2lw + 2lh + 2wh $.

We need to solve for $ h $. Begin by isolating terms involving $ h $ on one side of the equation.

Subtract $ 2lw $ from both sides to get: $ A - 2lw = 2lh + 2wh $.

Factor out $ h $ from the right side: $ A - 2lw = h(2l + 2w) $.

Divide both sides by $ 2l + 2w $ to solve for $ h $: $ h = \frac{A - 2lw}{2l + 2w} $.

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Key Concepts

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

Algebraic Manipulation

Algebraic manipulation involves rearranging equations to isolate a specific variable. This process includes operations such as adding, subtracting, multiplying, or dividing both sides of the equation by the same value. Understanding how to manipulate equations is essential for solving for a variable, as it allows you to express one variable in terms of others.

Formulas and Their Applications

Formulas are mathematical expressions that describe relationships between different quantities. In this case, the formula A = 2lw + 2lh + 2wh represents the surface area of a rectangular prism. Recognizing the formula helps in understanding the context of the problem and the significance of the variable being solved for, which is height (h) in this instance.

Surface Area of a Rectangular Prism

The surface area of a rectangular prism is the total area of all its faces. The formula A = 2lw + 2lh + 2wh calculates this area by summing the areas of the length-width, length-height, and width-height pairs. Knowing this concept is crucial for interpreting the formula correctly and understanding how changes in dimensions affect the overall surface area.