/*! 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 75 Solve each formula for the speci... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 75

Solve each formula for the specified variable. \(I=p r t\) for \(r\)

Short Answer

Expert verified
\( r = \frac{I}{p t} \)

Step by step solution

01

Identify the Given Formula

The given formula is \(I = p r t\), where the goal is to solve for \(r\).
02

Isolate the Variable

To isolate the variable \(r\), we need to divide both sides of the equation by \( p t \) to get \(r\) alone. This gives us: \[ r = \frac{I}{p t} \]
03

Rewrite the Equation

The final equation with \(r\) isolated is: \[ r = \frac{I}{p t} \]

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 Equations
Algebraic equations are fundamental in mathematics, as they allow us to establish relationships between different quantities. In an algebraic equation, you typically have variables (like our example with I, p, r, and t) and constants. Variables represent unknown values that we aim to find.

An equation like I = prt shows how the product of p, r, and t equals I. Here, each term could be any value, and the relationship holds true as long as the equation balances.
When working with algebraic equations, it's helpful to:
  • Understand the meaning and role of each variable.
  • Recognize constants and coefficients.
  • Follow a logical sequence in solving for the unknowns.

Understanding these basic concepts will enable you to tackle any algebraic challenge with ease.
Variable Isolation
Variable isolation is a key technique in solving algebraic equations. The goal is to rearrange the equation so that the variable you are solving for stands alone on one side of the equation.

Let's take our equation, I = prt, and focus on solving for the variable r. The steps are straightforward:
  • Identify the target variable. Here, it鈥檚 r.
  • Perform arithmetic operations to isolate this variable.

In practice, you rearrange the equation by dividing both sides by pt, resulting in r = I/(pt).

The principle behind variable isolation is maintaining the balance of the equation. Whatever you do to one side must also be done to the other. This keeps the equation true and allows you to solve for the unknown variable accurately.
Formula Manipulation
Formula manipulation is about rearranging equations to make them easier to work with, often so you can isolate a variable or put the formula into a simpler form.

In the given exercise, we started with I = prt and needed to manipulate it to solve for r. The key steps were:
  • Recognize how p and t are currently interacting with r (they're being multiplied).
  • Divide both sides by pt to remove these multipliers from r.

This gives us the formula r = I/(pt).

Formula manipulation helps in a multitude of contexts, not just in math problems but also in physics, engineering, and economics. It allows you to reconfigure an equation to see different relationships between the variables, making the problem more understandable and solving it more straightforward.

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 inequality. Write the solution set in interval notation, and graph it. \(-1 \leq 1-5 q \leq 16\)

Solve each equation. $$ -3 x=\frac{1}{4} $$

On a 75 -point algebra test, Grady scored 63 points. What percent of the total points did he score?

Write the answer to each problem in terms of the variable. Claire has \(y\) dimes. Express the value of the dimes in cents.

Write each phrase as a mathematical expression using \(x\) as the variable. A number decreased by 9
See all solutions

Recommended explanations on Math Textbooks

Logic and Functions

Read Explanation

Statistics

Read Explanation

Pure Maths

Read Explanation

Discrete Mathematics

Read Explanation

Applied Mathematics

Read Explanation

Decision Maths

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.