Domanda del libro di testo
CONCEPT PREVIEW Perform the operations mentally, and write the answers without doing intermediate steps. √25 + √64
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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 8
CONCEPT PREVIEW Fill in the blank(s) to correctly complete each sentence. The circle with equation x² + y² = 49 has center with coordinates ________ and radius equal to _______.
Guida verificata passo dopo passo1
Recognize that the given equation is in the form of a circle equation: \(x^{2} + y^{2} = r^{2}\), where the center is at the origin \((0,0)\) and \(r\) is the radius.
Identify the center coordinates by comparing the equation to the standard form \((x - h)^{2} + (y - k)^{2} = r^{2}\). Here, \(h = 0\) and \(k = 0\), so the center is \((0,0)\).
Determine the radius by taking the square root of the constant on the right side of the equation. Since the equation is \(x^{2} + y^{2} = 49\), the radius \(r = \sqrt{49}\).
Express the radius as \(r = 7\) (without calculating the final value, just the expression to find it).
Summarize: The center is at \((0,0)\) and the radius is \(7\).
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Standard Equation of a Circle
The standard form of a circle's equation is (x - h)² + (y - k)² = r², where (h, k) represents the center coordinates and r is the radius. Recognizing this form helps identify the circle's center and radius directly from the equation.
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Percorso guidato
06:03
Equations of Circles & Ellipses
Center of a Circle
The center of a circle is the fixed point equidistant from all points on the circle. In the equation (x - h)² + (y - k)² = r², the center is at (h, k). If the equation is x² + y² = r², the center is at the origin (0, 0).
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Percorso guidato
06:11Introduction to the Unit Circle
Radius of a Circle
The radius is the distance from the center to any point on the circle. It is the square root of the constant term on the right side of the equation (r²). For example, if the equation is x² + y² = 49, the radius is √49 = 7.
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Percorso guidato
06:11Introduction to the Unit Circle
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