/*! 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 10: Problem 73

Solve each formula for the specified variable. \(V=\sqrt{\frac{2 K}{m}}\) for \(K\)

Short Answer

Expert verified
K = \frac{mV^2}{2}

Step by step solution

01

- Square Both Sides

Start by squaring both sides of the equation to eliminate the square root. This gives us:\[V^2 = \frac{2K}{m}\]
02

- Multiply Both Sides by m

Next, to clear the fraction, multiply both sides of the equation by \(m\). This gives us:\[mV^2 = 2K\]
03

- Solve for K

Finally, divide both sides by 2 to isolate \(K\):\[K = \frac{mV^2}{2}\]

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 refers to the process of rearranging and simplifying equations to isolate a specific variable or to solve for it. This involves using basic algebraic operations, such as addition, subtraction, multiplication, and division, to change the form of equations without altering their solutions.
In our example, we started with the equation:\(V = \sqrt{\frac{2K}{m}}\)
To isolate \(K\), we need to make a series of manipulations: squaring both sides to eliminate the square root, multiplying both sides by \(m\) to remove the fraction, and then dividing both sides by 2 to solve for \(K\).
Isolating Variables
Isolating the variable means rearranging an equation to get the variable of interest on one side while moving all other terms to the opposite side. This often requires combining like terms and performing inverse operations.
In our example, the goal is to solve for \(K\). Starting with the equation\(V = \sqrt{\frac{2K}{m}}\), we first square both sides to get rid of the square root:\[V^2 = \frac{2K}{m}\]
Next, we multiply both sides by \(m\) to clear the fraction:\[mV^2 = 2K\]
Finally, we divide both sides by 2, isolating \(K\):\[K = \frac{mV^2}{2}\].
This sequence of steps strategically moves all terms except for \(K\) out of the way.
Squaring Both Sides
Squaring both sides of an equation is a method used to eliminate square roots. It is essential to remember that when you square both sides, you must apply the square to the entire side, not just the individual terms.
For the equation\(V = \sqrt{\frac{2K}{m}}\), squaring both sides removes the square root, yielding:\[V^2 = \frac{2K}{m}\]
This transformation simplifies the problem by changing it from a radical equation into a more straightforward algebraic equation involving multiplication. Always check for extraneous solutions, although in this straightforward equation, none arise.
Fractions in Equations
Equations containing fractions can be tricky, but we can manage them through strategic multiplication to eliminate the denominators. By doing so, equations become easier to solve.
For our equation\(V = \sqrt{\frac{2K}{m}}\), after squaring both sides, we get:\[V^2 = \frac{2K}{m}\].

To eliminate the fraction, multiply both sides by \(m\): \[mV^2 = 2K\].
Multiplying by \(m\) clears the fraction, resulting in an equation that is simpler to handle. This step is crucial for isolating the variable \(K\), and it showcases how fractions, while initially complicating an equation, can be managed through multiplication.

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

Simplify. Assume that all variables represent positive real numbers. \(\sqrt{300 z^{3}}\)

Write each radical as an exponential and simplify. Leave answers in exponential form. Assume that all variables represent positive numbers. $$ \sqrt[4]{\sqrt[3]{m}} $$

Find the distance between each pair of points. (-1,5) and (-7,7)

Simplify. Assume that all variables represent positive real numbers. \(\sqrt[3]{-16 z^{5} t^{7}}\)

Find the distance between each pair of points. \((x+y, y)\) and \((x-y, x)\)
See all solutions

Recommended explanations on Math Textbooks

Discrete Mathematics

Read Explanation

Applied Mathematics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Calculus

Read Explanation

Mechanics Maths

Read Explanation

Geometry

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.