10th Edition

ISBN: 9781285057095

Author: Ron Larson, Bruce H. Edwards

Publisher: Cengage Learning

Concept explainers

‘Matrices’ is the plural form of the word matrix, and it is basically a spreadsheet in the form of a box. In mathematics, various functions can be carried out with matrices. Generally, a matrix comes in the shape of a square or rectangle. The elements ar…

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Textbook Question

Chapter 10.2, Problem 80E

Projectile Motion In Exercises 81 and 82, consider a projectile launched at a height h feet above the ground and at an angle _ with the horizontal. When the initial velocity is v0 feet per second, the path of the projectile is modeled by the parametric equations

x = ( v 0 cos θ ) t and y = h + ( v 0 sin θ ) t − 16 t 2 .

A rectangular equation for the path of a projectile is y = 5 + x − 0.005 x 2 .

(a) Eliminate the parameter I from the position function for the motion of a projectile to show that the rectangular equation is

y = − 16 sec 2 θ v 0 2 x 2 + ( tan θ ) x + h

(b) Use the result of part (a) to find h, v 0 . and θ . Find the parametric equations of the path.

(c) Use a graphing utility to graph the rectangular equation for the path of the projectile. Confirm your answer in part (b) by sketching the curve represented by the parametric equations.

(d) Use a graphing utility to approximate the maximum height of the projectile and its range.

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Chapter 10.2, Problem 79E

Chapter 10.3, Problem 1E

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Chapter 10 Solutions

Calculus

Ch. 10.1 - Matching In Exercises 5-10, match the equation...Ch. 10.1 - Matching In Exercises 5-10, match the equation...Ch. 10.1 - Matching In Exercises 5-10, match the equation...Ch. 10.1 - Matching In Exercises 5-10, match the equation...Ch. 10.1 - Matching In Exercises 5-10, match the equation...Ch. 10.1 - Prob. 6E Ch. 10.1 - Prob. 7E Ch. 10.1 - Prob. 8E Ch. 10.1 - Prob. 9E Ch. 10.1 - Sketching a Parabola In Exercises 1116, find the...

Ch. 10.1 - Sketching a Parabola In Exercises 1116, find the...Ch. 10.1 - Prob. 12E Ch. 10.1 - Prob. 13E Ch. 10.1 - Prob. 14E Ch. 10.1 - Prob. 15E Ch. 10.1 - Prob. 16E Ch. 10.1 - Prob. 17E Ch. 10.1 - Prob. 18E Ch. 10.1 - Prob. 19E Ch. 10.1 - Prob. 20E Ch. 10.1 - Prob. 21E Ch. 10.1 - Prob. 22E Ch. 10.1 - Prob. 23E Ch. 10.1 - Prob. 24E Ch. 10.1 - Prob. 25E Ch. 10.1 - Prob. 26E Ch. 10.1 - Prob. 27E Ch. 10.1 - Prob. 28E Ch. 10.1 - Prob. 29E Ch. 10.1 - Prob. 30E Ch. 10.1 - Prob. 31E Ch. 10.1 - Prob. 32E Ch. 10.1 - Prob. 33E Ch. 10.1 - Finding the Standard Equation of an Ellipse In...Ch. 10.1 - Prob. 35E Ch. 10.1 - Prob. 36E Ch. 10.1 - Prob. 37E Ch. 10.1 - Prob. 38E Ch. 10.1 - Prob. 39E Ch. 10.1 - Prob. 40E Ch. 10.1 - Prob. 41E Ch. 10.1 - Prob. 42E Ch. 10.1 - Prob. 43E Ch. 10.1 - Prob. 44E Ch. 10.1 - Prob. 45E Ch. 10.1 - Prob. 46E Ch. 10.1 - Prob. 47E Ch. 10.1 - Prob. 48E Ch. 10.1 - Prob. 49E Ch. 10.1 - Prob. 50E Ch. 10.1 - Prob. 53E Ch. 10.1 - Prob. 51E Ch. 10.1 - Prob. 52E Ch. 10.1 - Prob. 57E Ch. 10.1 - Classifying the Graph of an Equation In Exercises...Ch. 10.1 - Prob. 55E Ch. 10.1 - Prob. 54E Ch. 10.1 - Prob. 63E Ch. 10.1 - Prob. 69E Ch. 10.1 - Prob. 56E Ch. 10.1 - Prob. 59E Ch. 10.1 - Prob. 60E Ch. 10.1 - Prob. 61E Ch. 10.1 - Eccentricity Define the eccentricity of an...Ch. 10.1 - Prob. 64E Ch. 10.1 - Solar Collector A solar collector for heating...Ch. 10.1 - Beam Deflection A simply supported beam that is 16...Ch. 10.1 - Prob. 67E Ch. 10.1 - Proof (a) Prove that if any two tangent lines to a...Ch. 10.1 - Bridge Design A cable of a suspension bridge is...Ch. 10.1 - Prob. 71E Ch. 10.1 - Surface Area A satellite signal receiving dish is...Ch. 10.1 - Prob. 73E Ch. 10.1 - Prob. 74E Ch. 10.1 - Prob. 75E Ch. 10.1 - Prob. 76E Ch. 10.1 - Prob. 77E Ch. 10.1 - Prob. 78E Ch. 10.1 - Prob. 79E Ch. 10.1 - Prob. 80E Ch. 10.1 - Prob. 81E Ch. 10.1 - Conjecture Show that the equation of an ellipse...Ch. 10.1 - Prob. 83E Ch. 10.1 - Prob. 84E Ch. 10.1 - Prob. 85E Ch. 10.1 - Prob. 86E Ch. 10.1 - Prob. 87E Ch. 10.1 - Hyperbolic Mirror A hyperbolic mirror (used in...Ch. 10.1 - Prob. 89E Ch. 10.1 - Prob. 90E Ch. 10.1 - True or False? 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In Exercises 8792, determine...Ch. 10.1 - Prob. 96E Ch. 10.1 - For a point P on an ellipse, let d be the distance...Ch. 10.1 - Prob. 98E Ch. 10.2 - Prob. 1E Ch. 10.2 - Prob. 2E Ch. 10.2 - Prob. 3E Ch. 10.2 - Prob. 4E Ch. 10.2 - Prob. 5E Ch. 10.2 - Prob. 6E Ch. 10.2 - Prob. 7E Ch. 10.2 - Prob. 8E Ch. 10.2 - Prob. 9E Ch. 10.2 - Prob. 10E Ch. 10.2 - Prob. 11E Ch. 10.2 - Prob. 12E Ch. 10.2 - Prob. 13E Ch. 10.2 - Prob. 14E Ch. 10.2 - Prob. 15E Ch. 10.2 - Using Parametric Equations In Exercises 5-22,...Ch. 10.2 - Using Parametric Equations In Exercises 5-22,...Ch. 10.2 - Using Parametric Equations In Exercises 5-22,...Ch. 10.2 - Using Parametric Equations In Exercises 23-34, use...Ch. 10.2 - Using Parametric Equations In Exercises 23-34, use...Ch. 10.2 - Prob. 21E Ch. 10.2 - Prob. 22E Ch. 10.2 - Prob. 23E Ch. 10.2 - Prob. 24E Ch. 10.2 - Using Parametric Equations In Exercises 23-34, use...Ch. 10.2 - Prob. 26E Ch. 10.2 - Using Parametric Equations In Exercises 23-34, use...Ch. 10.2 - Using Parametric Equations In Exercises 23-34, use...Ch. 10.2 - 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Solution Summary: The author explains that the rectangular equation for the path of a projectile is y=5+x-0.005x2.

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