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 14
Write an equation that expresses each relationship. Then solve the equation for y. x varies directly as the cube root of z and inversely as y.
Guida verificata passo dopo passo1
Identify the given variation relationships: x varies directly as the cube root of z, and inversely as y. This means we can write the equation as \(x = k \frac{\sqrt[3]{z}}{y}\), where \(k\) is the constant of proportionality.
Write the equation explicitly: \(x = k \frac{z^{\frac{1}{3}}}{y}\).
To solve for \(y\), multiply both sides of the equation by \(y\) to get rid of the denominator: \(xy = k z^{\frac{1}{3}}\).
Next, isolate \(y\) by dividing both sides by \(x\): \(y = \frac{k z^{\frac{1}{3}}}{x}\).
The equation is now solved for \(y\): \(y = \frac{k z^{\frac{1}{3}}}{x}\). To find the specific value of \(k\), you would need additional information such as a set of values for \(x\), \(y\), and \(z\).
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Direct Variation
Direct variation describes a relationship where one variable is proportional to another. If x varies directly as the cube root of z, it means x = k * ∛z for some constant k. This shows that as ∛z increases, x increases proportionally.
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Maximum Turning Points of a Polynomial Function
Inverse Variation
Inverse variation means one variable changes in the opposite way to another, expressed as x = k / y. Here, x varies inversely as y, so as y increases, x decreases proportionally, and vice versa, with k being a constant.
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Solving for a Variable in an Equation
Solving for y involves manipulating the equation algebraically to isolate y on one side. This requires understanding operations like multiplication, division, and roots to rewrite the equation in terms of y, making it the subject of the formula.
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05:28Equations with Two Variables
Pratica correlata
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In Exercises 1–16, divide using long division. State the quotient, and the remainder, r(x). (6x3+13x2−11x−15)/(3x2−x−3)
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Domanda del libro di testo
In Exercises 9–16, a) List all possible rational zeros. b) Use synthetic division to test the possible rational zeros and find an actual zero. c) Use the quotient from part (b) to find the remaining zeros of the polynomial function. f(x)=2x3+x2−3x+1
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As __
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Divide using long division. State the quotient, and the remainder, r(x). (x4+2x3−4x2−5x−6)/(x2+x−2)
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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.
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