Domanda del libro di testo
Concept Check Match each equation in Column I with its graph in Column II. I II 47. A. 48. B. 49. C. 50. (x + 3)² + (y + 2)² = 25 D.
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Ch. R - Algebra Review
Lial12th EditionTrigonometryISBN: 9780136552161, 9780135440780, 9780136881117, 9780135440827, 9780135924891
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TOC.tableOfContents
- Ch. R - Algebra Review381
- Ch. 1 - Trigonometric Functions188
- Ch. 2 - Acute Angles and Right Triangles168
- Ch. 3 - Radian Measure and The Unit Circle155
- Ch. 4 - Graphs of the Circular Functions100
- Ch. 5 - Trigonometric Identities238
- Ch. 6 - Inverse Circular Functions and Trigonometric Equations158
- Ch. 7 - Applications of Trigonometry and Vectors148
- Ch. 8 - Complex Numbers, Polar Equations, and Parametric Equations15
Lial12th EditionTrigonometryISBN: 9780136552161, 9780135440780, 9780136881117, 9780135440827, 9780135924891Non è quello che usi tu?Cambia libro di testo
Capitolo 1, Problema 50
Find each root. See Example 3. ∛0.125
Guida verificata passo dopo passo1
Recognize that the problem asks for the cube root of 0.125, which means finding a number \( x \) such that \( x^3 = 0.125 \).
Express 0.125 as a fraction to make it easier to work with: \( 0.125 = \frac{1}{8} \).
Rewrite the cube root expression using fractional exponents: \( \sqrt[3]{0.125} = \left( \frac{1}{8} \right)^{\frac{1}{3}} \).
Apply the property of exponents to the fraction: \( \left( \frac{1}{8} \right)^{\frac{1}{3}} = \frac{1^{\frac{1}{3}}}{8^{\frac{1}{3}}} \).
Calculate the cube root of numerator and denominator separately: \( 1^{\frac{1}{3}} = 1 \) and \( 8^{\frac{1}{3}} = 2 \), so the cube root is \( \frac{1}{2} \).
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Cube Roots
The cube root of a number is a value that, when multiplied by itself three times, gives the original number. For example, the cube root of 8 is 2 because 2 × 2 × 2 = 8. It is denoted as ∛x.
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Percorso guidato
07:37
Complex Roots
Fractional Exponents
Fractional exponents represent roots; specifically, an exponent of 1/n corresponds to the nth root of a number. For example, x^(1/3) is the cube root of x. This notation helps in simplifying and calculating roots using exponent rules.
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Percorso guidato
4:02Solving Linear Equations with Fractions
Decimal to Fraction Conversion
Converting decimals to fractions can simplify root calculations. For instance, 0.125 equals 1/8, making it easier to find roots since roots of fractions can be found by taking roots of numerator and denominator separately.
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Percorso guidato
4:02Solving Linear Equations with Fractions
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