Domanda del libro di testo
Determine whether each equation defines y as a function of x. 2x + y^2 = 6
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Ch. 2 - Functions and Graphs
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 3, Problema 6
Find the distance between each pair of points. If necessary, express answers in simplified radical form and then round to two decimal places. (0, 0) and (3,-4)
Guida verificata passo dopo passo1
Identify the coordinates of the two points: Point 1 is (0, 0) and Point 2 is (3, -4).
Recall the distance formula between two points \((x_1, y_1)\) and \((x_2, y_2)\):
\[d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\]
Substitute the given coordinates into the formula:
\[d = \sqrt{(3 - 0)^2 + (-4 - 0)^2}\]
Simplify inside the square root by calculating the differences and squaring them:
\[d = \sqrt{3^2 + (-4)^2}\]
Express the distance in simplified radical form by evaluating the squares and then the square root, and finally round the result to two decimal places if needed.
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Distance Formula
The distance formula calculates the length between two points in the coordinate plane. It is derived from the Pythagorean theorem and given by d = √((x2 - x1)² + (y2 - y1)²), where (x1, y1) and (x2, y2) are the coordinates of the points.
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Solving Quadratic Equations Using The Quadratic Formula
Simplified Radical Form
Simplified radical form means expressing a square root in its simplest form by factoring out perfect squares. For example, √50 can be simplified to 5√2. This helps in presenting exact answers before rounding.
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Rounding Decimal Numbers
Rounding involves approximating a number to a specified number of decimal places for simplicity. In this problem, after finding the exact distance, the result should be rounded to two decimal places to provide a practical numerical answer.
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