Domanda del libro di testo
Solve each polynomial inequality in Exercises 1–42 and graph the solution set on a real number line. Express each solution set in interval notation. 6x2+x>1
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Ch. 3 - Polynomial and Rational Functions
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 4, Problema 15
Write an equation that expresses each relationship. Then solve the equation for y. x varies jointly as y and z and inversely as the square root of w.
Guida verificata passo dopo passo1
Identify the type of variation described: "x varies jointly as y and z" means x is proportional to the product of y and z, so we write \(x = k \cdot y \cdot z\) where \(k\) is a constant of proportionality.
Since x also varies inversely as the square root of w, include this inverse relationship by dividing by \(\sqrt{w}\). The equation becomes \(x = \frac{k \cdot y \cdot z}{\sqrt{w}}\).
Write the full equation expressing the relationship: \(x = \frac{k \cdot y \cdot z}{\sqrt{w}}\).
To solve for y, multiply both sides of the equation by \(\sqrt{w}\) to get rid of the denominator: \(x \cdot \sqrt{w} = k \cdot y \cdot z\).
Finally, isolate y by dividing both sides by \(k \cdot z\): \(y = \frac{x \cdot \sqrt{w}}{k \cdot z}\).
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Joint Variation
Joint variation describes a relationship where one variable varies directly as the product of two or more other variables. In this case, x varies jointly as y and z means x is proportional to the product y * z, expressed as x = k * y * z, where k is a constant.
Inverse Variation
Inverse variation means one variable varies inversely as another, so as one increases, the other decreases proportionally. Here, x varies inversely as the square root of w, meaning x is proportional to 1 divided by √w, or x = k / √w.
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Percorso guidato
4:30
Graphing Logarithmic Functions
Solving for a Variable in an Equation
Solving for y involves isolating y on one side of the equation. After writing the joint and inverse variation equation, algebraic manipulation such as multiplication, division, and taking square roots is used to express y explicitly in terms of x, z, w, and the constant k.
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Percorso guidato
05:28Equations with Two Variables
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