/*! 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 19 Solve each formula for the speci... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 8: Problem 19

Solve each formula for the specified variable $$ D=\sqrt{k h} \text { for } h $$

Short Answer

Expert verified
h= frac{D^2}{k}

Step by step solution

01

- Understand the Formula

The given formula is $$D= sqrt{k h} $$ and we need to solve for h.
02

- Square Both Sides

To eliminate the square root, square both sides of the equation: $$ (D)^2=( sqrt{k h})^2 $$ which simplifies to: $$ D^2=k h $$.
03

- Isolate h

Divide both sides of the equation by k to isolate h: $$ frac{D^2}{k}=h $$.

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.

Formula Manipulation
Formula manipulation is a key skill in solving equations. When faced with an equation, the goal is often to rearrange or manipulate it to isolate a specific variable. This involves:
  • Understanding the structure of the formula.
  • Applying mathematical operations to both sides of the equation.
  • Keeping the equation balanced by performing the same operation on each side.

In our exercise, we started with the formula \(D = \sqrt{k h}\). To solve for \(h\), we needed to manipulate this equation. This means reorganizing it in a way that isolates \(h\) on one side. The first step was recognizing that squaring both sides would be necessary to remove the square root and further simplify the equation. This initial understanding is crucial before moving on to the actual manipulation.
Isolating Variables
Isolating variables is fundamental in solving algebraic equations. This process involves:
  • Identifying the variable you need to solve for.
  • Rearranging the equation so that the desired variable stands alone on one side of the equation.

In our example, the variable \(h\) is what we want to isolate from the original equation \(D = \sqrt{k h}\). After squaring both sides to get \(D^2 = k h\), we needed to isolate \(h\) by getting rid of the constant \(k\) that is multiplying \(h\). To do this, we divided both sides of the equation by \(k\). This step-by-step process simplifies the equation to \(h = \frac{D^2}{k}\), achieving our goal of isolating \(h\).
Squaring Both Sides
Squaring both sides of an equation is a method to eliminate square root terms. Here's what you need to remember:
  • When you square a square-root, you get the term inside the root.
  • The action must be performed on both sides of the equation to maintain equality.
  • Be cautious as squaring can introduce extraneous solutions in some cases.

In our exercise, to eliminate the square root in the formula \(D = \sqrt{k h}\), we squared both sides. This step converts the equation into a form without a square root, making it easier to isolate our variable. So, squaring both sides, we obtained \(D^2 = k h\). From here, further steps could be taken to solve for the desired variable \(h\). Recognizing opportunities to use this technique is an essential part of mastering algebraic equations.

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

Solve each problem. When appropriate, round answers to the nearest tenth. The diagonal of a rectangular rug measures \(26 \mathrm{ft}\), and the length is \(4 \mathrm{ft}\) more than twice the width. Find the length and width of the rug.

Solve each equation. Check the solutions. $$3(m+4)^{2}-8=2(m+4)$$

The following exercises are not grouped by type. Solve each equation. $$x^{6}-10 x^{3}=-9$$

The following exercises are not grouped by type. Solve each equation. $$\sqrt{m+1}=-1+\sqrt{2 m}$$

In the 1939 classic movie The Wizard of Oz, Ray Bolger's character, the Scarecrow, wants a brain. When the Wizard grants him his "Th.D." (Doctor of Thinkology), the Scarecrow replies with the following statement. Scarecrow: The sum of the square roots of any two sides of an isosceles triangle is equal to the square root of the remaining side. His statement sounds like the formula for the Pythagorean theorem. Use wording similar to that of the Scarecrow, but state the Pythagorean theorem correctly.
See all solutions

Recommended explanations on Math Textbooks

Mechanics Maths

Read Explanation

Discrete Mathematics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Geometry

Read Explanation

Statistics

Read Explanation

Applied Mathematics

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.