Domanda del libro di testo
In Exercises 45–47, solve each formula for the specified variable. T = (A-P)/Pr for P
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Ch. 1 - Equations and Inequalities
Blitzer8th EditionCollege AlgebraISBN: 9780136970514
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TOC.tableOfContents
- Ch. P - Fundamental Concepts of Algebra311
- Ch. 1 - Equations and Inequalities398
- Ch. 2 - Functions and Graphs407
- Ch. 3 - Polynomial and Rational Functions306
- Ch. 4 - Exponential and Logarithmic Functions247
- Ch. 5 - Systems of Equations and Inequalities173
- Ch. 6 - Matrices and Determinants143
- Ch. 7 - Conic Sections124
- Ch. 8 - Sequences, Induction, and Probability251
Capitolo 2, Problema 47
In Exercises 35–54, solve each formula for the specified variable. Do you recognize the formula? If so, what does it describe? S = P + Prt for r
Guida verificata passo dopo passo1
Identify the formula given: $S = P + Prt$. This formula is known as the simple interest formula, where \(S\) is the total amount, \(P\) is the principal, \(r\) is the interest rate, and \(t\) is the time.
Our goal is to solve the formula for the variable \(r\). Start by isolating terms involving \(r\) on one side. Notice that \(P\) is common in the terms \(P\) and \(Prt\).
Rewrite the equation by factoring out \(P\) on the right side: \(S = P(1 + rt)\).
Next, divide both sides of the equation by \(P\) to isolate the expression with \(r\): \(\frac{S}{P} = 1 + rt\).
Finally, subtract 1 from both sides and then divide by \(t\) to solve for \(r\): \(r = \frac{\frac{S}{P} - 1}{t}\).
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Solving Formulas for a Specific Variable
This involves isolating the desired variable on one side of the equation. Techniques include using inverse operations such as addition, subtraction, multiplication, division, and factoring to rewrite the formula explicitly in terms of that variable.
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Solving Quadratic Equations Using The Quadratic Formula
Simple Interest Formula
The formula S = P + Prt represents the simple interest calculation, where S is the total amount, P is the principal, r is the interest rate, and t is time. It calculates the total amount after interest is added linearly over time.
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06:36Solving Quadratic Equations Using The Quadratic Formula
Algebraic Manipulation of Equations
This concept covers rearranging equations by applying algebraic rules to maintain equality. It is essential for solving for variables embedded in expressions, such as factoring out common terms or dividing both sides by a coefficient.
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05:09Introduction to Algebraic Expressions
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