/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 73 Solve each formula for the speci... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 73

Solve each formula for the specified variable. \(V=L W H\) for \(H\)

Short Answer

Expert verified
H = \frac{V}{L W}

Step by step solution

01

- Write the equation

Start with the given formula: \[ V = L W H \]
02

- Isolate the variable

To solve for \(H\), we need to isolate \(H\) on one side of the equation. To do this, divide both sides of the equation by \(L W\): \[ \frac{V}{L W} = \frac{L W H}{L W} \]
03

- Simplify the equation

On the right-hand side, \(L W\) in the numerator and denominator cancel out, leaving: \[ H = \frac{V}{L W} \]

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

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

Algebraic Manipulation
Algebraic manipulation involves rearranging equations to isolate specific variables or to simplify expressions. This skill is necessary when you work with formulas like the one in our exercise. If you have an equation like \(V = L W H\), and you need to solve it for another variable such as \(H\), you will have to use algebraic manipulation techniques.
For example:
  • Use inverse operations (e.g., division to cancel multiplication).
  • Apply the same operation to both sides of the equation to keep it balanced.
In our exercise, we handled \(L W\) by dividing both sides to isolate \(H\). Algebraic manipulation becomes easier with practice and is a crucial skill in math and science.
Isolating Variables
Isolating a variable means getting it alone on one side of the equation, making it easier to understand and solve. This is especially important in formulas where you need to find the value of a particular variable.
In the example \(V = L W H\), to isolate \(H\):
  • Identify the variable you need to isolate, in this case, \(H\).
  • We see \(H\) is multiplied by \(L W\). To isolate \(H\), divide both sides by \(L W\).
  • Simplify both sides to get \(H = \frac{V}{L W}\).
Now, \(H\) stands alone, making it easy to calculate its value. This skill is valuable not just in algebra, but in solving real-world problems too.
Volume Formula
The volume formula, \(V = L W H\), is used to calculate the volume of a rectangular prism, which is essentially a box-shaped object. Here's a deeper look:
  • \(V\) represents the volume.
  • \(L\) stands for the length.
  • \(W\) is the width.
  • \(H\) is the height.
To use this formula, you multiply the length by the width by the height. If you're given the volume and need to find one of the dimensions, you rearrange the formula. For example, to find \(H\), you divide both sides by \(L W\) resulting in \(H = \frac{V}{L W}\). Understanding this formula helps solve many practical problems, like finding how much space is inside a box.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Write an equation using the information given in the problem. Use x as the variable. Then solve the equation. Three times a number is 17 more than twice the number. Find the number.

Solve each problem. \(18 \%\) of what number is \(108 ?\)

On June \(13,\) researchers at West Okoboji Lake tagged 840 fish. A few weeks later, a sample of 1000 fish contained 18 that were tagged. Approximate the fish population to the nearest hundred.

Solve each problem. (Assume that all items are equally priced.) (In Exercises 53鈥�56, round answers to the nearest tenth.) A wall map of the United States has a distance of 8.0 in. between New Orleans and Chicago, two cities that are actually \(912 \mathrm{mi}\) apart. The actual distance between Milwaukee and Seattle is \(1940 \mathrm{mi}\). How far apart are Milwaukee and Seattle on the map?

If 8 U.S. dollars can be exchanged for 103.0 Mexican pesos, how many pesos can be obtained for \(\$ 65 ?\) (Round to the nearest tenth.)
See all solutions

Recommended explanations on Math Textbooks

Probability and Statistics

Read Explanation

Logic and Functions

Read Explanation

Statistics

Read Explanation

Applied Mathematics

Read Explanation

Geometry

Read Explanation

Calculus

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.