Precalculus
Precalculus
17th Edition
ISBN: 9780077538286
Author: Julie Miller
Publisher: MCGRAW-HILL HIGHER EDUCATION
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Chapter 10.6, Problem 52PE

A golfer tees off on level ground, and hits the ball with an initial speed of 52 m/sec at an angle of 34 ° above the horizontal. Choose a coordinate system with the origin at the point where the ball is struck.

a. Write parametric equations that model the path of the ball as a function of time t (in sec).

b. For how long will the ball be in the air before it hits the ground? Round to the nearest hundredth of a second.

c. Approximate the horizontal distance that the ball travels before it hits the ground. Round to the nearest foot.

d. When is the ball at its maximum height? Find the exact value and an approximation to the nearest hundredth of a second.

e. What is the maximum height? Round to the nearest foot.

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Chapter 10 Solutions

Precalculus

Ch. 10.1 - Graph the ellipse, and identify the center,...Ch. 10.1 - Graph the ellipse and identify the center,...Ch. 10.1 - Graph the ellipse and identify the center,...Ch. 10.1 - Repeat Example 4 with 2x2+11y212x+44y+40=0 .Ch. 10.1 - Determine the standard form of an equation of an...Ch. 10.1 - A tunnel has vertical sides of 7 ft with a...Ch. 10.1 - Pluto is 7.376109 km at aphelion (farthest point...Ch. 10.1 - The circle, the ellipse, the hyperbola, and the...Ch. 10.1 - An is a set of points x,y in a plane such that...Ch. 10.1 - The line through the foci intersects an ellipse at...
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Let p...Ch. 10.3 - For Exercises 53-58, fill in the blanks. Let p...Ch. 10.3 - For Exercises 53-58, fill in the blanks. Let p...Ch. 10.3 - Prob. 58PECh. 10.3 - If the focal length of a parabola is 6 units and...Ch. 10.3 - Prob. 60PECh. 10.3 - Prob. 61PECh. 10.3 - Prob. 62PECh. 10.3 - For Exercises 61-68, determine the standard form...Ch. 10.3 - Prob. 64PECh. 10.3 - For Exercises 61-68, determine the standard form...Ch. 10.3 - For Exercises 61-68, determine the standard form...Ch. 10.3 - Prob. 67PECh. 10.3 - For Exercises 61-68, determine the standard form...Ch. 10.3 - Suppose that a solar cooker has a parabolic mirror...Ch. 10.3 - A solar water heater is made from a long sheet of...Ch. 10.3 - The Hubble Space Telescope was launched into space...Ch. 10.3 - The James Webb Space Telescope (JWST) is a new...Ch. 10.3 - The Subaru telescope is a large optical-infrared...Ch. 10.3 - A parabolic mirror on a telescope has a focal...Ch. 10.3 - Prob. 75PECh. 10.3 - A cable hanging freely between two vertical...Ch. 10.3 - Prob. 77PECh. 10.3 - For Exercises 77-78, solve the system of nonlinear...Ch. 10.3 - Given an equation of a parabola...Ch. 10.3 - Prob. 80PECh. 10.3 - The surface defined by the equation z=4x2+y2 is...Ch. 10.3 - A jet flies in a parabolic arc to simulate partial...Ch. 10.3 - For Exercises 83-86, graph the parabola from the...Ch. 10.3 - For Exercises 83-86, graph the parabola from the...Ch. 10.3 - For Exercises 83-86, graph the parabola from the...Ch. 10.3 - For Exercises 83-86, graph the parabola from the...Ch. 10.3 - For Exercises 1-8, identify each equation as...Ch. 10.3 - Prob. 2PRECh. 10.3 - Prob. 3PRECh. 10.3 - For Exercises 1-8, identify each equation as...Ch. 10.3 - For Exercises 1-8, identify each equation as...Ch. 10.3 - For Exercises 1-8, identify each equation as...Ch. 10.3 - Prob. 7PRECh. 10.3 - Prob. 8PRECh. 10.3 - For Exercises 9-16, determine whether the equation...Ch. 10.3 - For Exercises 9-16, determine whether the equation...Ch. 10.3 - Prob. 11PRECh. 10.3 - For Exercises 9-16, determine whether the equation...Ch. 10.3 - Prob. 13PRECh. 10.3 - Prob. 14PRECh. 10.3 - Prob. 15PRECh. 10.3 - For Exercises 9-16, determine whether the equation...Ch. 10.3 - For Exercises 17-22, an equation of a degenerate...Ch. 10.3 - Prob. 18PRECh. 10.3 - Prob. 19PRECh. 10.3 - Prob. 20PRECh. 10.3 - Prob. 21PRECh. 10.3 - Prob. 22PRECh. 10.3 - Prob. 23PRECh. 10.3 - Prob. 24PRECh. 10.3 - Given Ax2+Cy2+Dx+Ey+F=0, show that the equation...Ch. 10.4 - Prob. 1SPCh. 10.4 - Suppose that the x- and y-axes are rotated 45...Ch. 10.4 - Write the equation xy=8 in terms of x and y given...Ch. 10.4 - Prob. 4SPCh. 10.4 - Prob. 5SPCh. 10.4 - Prob. 6SPCh. 10.4 - Prob. 1PECh. 10.4 - Prob. 2PECh. 10.4 - Suppose that the equation Ax2+Bxy+Cy2+Dx+Ey+F=0...Ch. 10.4 - The conic section defined by Ax2+Bxy+Cy2+Dx+Ey+F=0...Ch. 10.4 - For Exercises 5-8, the given equation represents a...Ch. 10.4 - For Exercises 5-8, the given equation represents a...Ch. 10.4 - Prob. 7PECh. 10.4 - For Exercises 5-8, the given equation represents a...Ch. 10.4 - Prob. 9PECh. 10.4 - For Exercises 9-14, assume that the x- and y-axes...Ch. 10.4 - Prob. 11PECh. 10.4 - For Exercises 9-14, assume that the x- and y-axes...Ch. 10.4 - Prob. 13PECh. 10.4 - For Exercises 9-14, assume that the x- and y-axes...Ch. 10.4 - Prob. 15PECh. 10.4 - For Exercises 15-18, assume that the x- and y-axes...Ch. 10.4 - Prob. 17PECh. 10.4 - Prob. 18PECh. 10.4 - Prob. 19PECh. 10.4 - Prob. 20PECh. 10.4 - For Exercises 19-22, assume that 02 . 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What angle does the line y=22x make...Ch. 10.4 - Prob. 51PECh. 10.4 - Prob. 52PECh. 10.4 - Discuss the graph of x22xy+y21=0.Ch. 10.4 - Discuss the graph of x28xy+y2=0.Ch. 10.4 - Prob. 55PECh. 10.4 - Prob. 56PECh. 10.4 - Prob. 57PECh. 10.4 - Given an equation in x and y, many graphing...Ch. 10.4 - Use the relationships between A,B,andC and...Ch. 10.4 - Prob. 60PECh. 10.4 - For a positive real number r, explain why the...Ch. 10.4 - Show that.x2+y2=r2 is invariant under rotation.Ch. 10.4 - Recall from Section 9.3 that a point Px,y can be...Ch. 10.4 - The set of pointsx1,y1,x2,y2,xn,yn can be...Ch. 10.5 - Graph the equation. r=822cosCh. 10.5 - Prob. 2SPCh. 10.5 - Graph the equation. r=1653cosCh. 10.5 - Rotate the ellipse r=1653cos and graph the result...Ch. 10.5 - Prob. 1PECh. 10.5 - Prob. 2PECh. 10.5 - Prob. 3PECh. 10.5 - Prob. 4PECh. 10.5 - For Exercises 5-10, a. Determine the value of e...Ch. 10.5 - For Exercises 5-10, a. Determine the value of e...Ch. 10.5 - For Exercises 5-10, a. Determine the value of e...Ch. 10.5 - Prob. 8PECh. 10.5 - Prob. 9PECh. 10.5 - Prob. 10PECh. 10.5 - Prob. 11PECh. 10.5 - Prob. 12PECh. 10.5 - For Exercises 11-22, graph the conic. (See...Ch. 10.5 - Prob. 14PECh. 10.5 - Prob. 15PECh. 10.5 - Prob. 16PECh. 10.5 - Prob. 17PECh. 10.5 - Prob. 18PECh. 10.5 - Prob. 19PECh. 10.5 - Prob. 20PECh. 10.5 - Prob. 21PECh. 10.5 - Prob. 22PECh. 10.5 - Prob. 23PECh. 10.5 - For Exercises 23-24, refer to the polar equation...Ch. 10.5 - Prob. 25PECh. 10.5 - For Exercises 25-26, refer to the polar equation...Ch. 10.5 - For Exercises 27-30, write an equation of the...Ch. 10.5 - For Exercises 27-30, write an equation of the...Ch. 10.5 - For Exercises 27-30, write an equation of the...Ch. 10.5 - For Exercises 27-30, write an equation of the...Ch. 10.5 - a. Write a polar equation to represent the...Ch. 10.5 - a. Write a polar equation to represent the...Ch. 10.5 - For Exercises 33-36, convert the equation to...Ch. 10.5 - For Exercises 33-36, convert the equation to...Ch. 10.5 - Prob. 35PECh. 10.5 - Prob. 36PECh. 10.5 - Prob. 37PECh. 10.5 - Prob. 38PECh. 10.5 - Prob. 39PECh. 10.5 - Prob. 40PECh. 10.5 - Prob. 41PECh. 10.5 - Discuss the difference between the graphs of...Ch. 10.5 - Prob. 43PECh. 10.5 - Prob. 44PECh. 10.5 - For Exercises 45-46, use the results of Exercises...Ch. 10.5 - For Exercises 45-46, use the results of Exercises...Ch. 10.5 - Graph the equations r1=210.6cos and r2=210.6cos on...Ch. 10.5 - Prob. 48PECh. 10.5 - Graph the equations r=11esin for e=0.8,1,and1.2 on...Ch. 10.6 - Prob. 1SPCh. 10.6 - Repeat Example 2 with the equations x=t1 and y=t1...Ch. 10.6 - Repeat Example 3 with the equations x=4cos and...Ch. 10.6 - Write parametric equations for the curve defined...Ch. 10.6 - Repeat Example 5 with an ant that begins at A72,10...Ch. 10.6 - Repeat Example 6 with a cannon ball launched from...Ch. 10.6 - If f and g are continuous functions of t over an...Ch. 10.6 - Prob. 2PECh. 10.6 - Identify the endpoints of the curve defined by...Ch. 10.6 - Suppose that an object travels along a straight...Ch. 10.6 - Prob. 5PECh. 10.6 - Prob. 6PECh. 10.6 - For Exercises 7-10, sketch the plane curve by...Ch. 10.6 - For Exercises 7-10, sketch the plane curve by...Ch. 10.6 - Prob. 9PECh. 10.6 - For Exercises 7-10, sketch the plane curve by...Ch. 10.6 - For Exercises 11-26, a. Eliminate the parameter...Ch. 10.6 - For Exercises 11-26, a. Eliminate the parameter...Ch. 10.6 - For Exercises 11-26, a. Eliminate the parameter...Ch. 10.6 - For Exercises 11-26, a. Eliminate the parameter...Ch. 10.6 - Prob. 15PECh. 10.6 - For Exercises 11-26, a. Eliminate the parameter...Ch. 10.6 - Prob. 17PECh. 10.6 - For Exercises 11-26, a. Eliminate the parameter...Ch. 10.6 - Prob. 19PECh. 10.6 - For Exercises 11-26, a. Eliminate the parameter...Ch. 10.6 - Prob. 21PECh. 10.6 - Prob. 22PECh. 10.6 - Prob. 23PECh. 10.6 - Prob. 24PECh. 10.6 - Prob. 25PECh. 10.6 - Prob. 26PECh. 10.6 - Prob. 27PECh. 10.6 - Prob. 28PECh. 10.6 - Prob. 29PECh. 10.6 - For Exercises 27-30, eliminate the parameter and...Ch. 10.6 - Prob. 31PECh. 10.6 - For Exercises 31-34, write parametric equations...Ch. 10.6 - Prob. 33PECh. 10.6 - For Exercises 31-34, write parametric equations...Ch. 10.6 - Prob. 35PECh. 10.6 - Prob. 36PECh. 10.6 - For Exercises 35-42, use the results of Exercises...Ch. 10.6 - Prob. 38PECh. 10.6 - For Exercises 35-42, use the results of Exercises...Ch. 10.6 - For Exercises 35-42, use the results of Exercises...Ch. 10.6 - For Exercises 35-42, use the results of Exercises...Ch. 10.6 - For Exercises 35-42, use the results of Exercises...Ch. 10.6 - For Exercises 43-46, write parametric equations on...Ch. 10.6 - For Exercises 43-46, write parametric equations on...Ch. 10.6 - For Exercises 43-46, write parametric equations on...Ch. 10.6 - For Exercises 43-46, write parametric equations on...Ch. 10.6 - For Exercises 47-48, an object undergoes uniform...Ch. 10.6 - Prob. 48PECh. 10.6 - Prob. 49PECh. 10.6 - A hospital is located 3mi west and 4mi north of...Ch. 10.6 - Prob. 51PECh. 10.6 - A golfer tees off on level ground, and hits the...Ch. 10.6 - Anna hits a softball at a height of 3ft from the...Ch. 10.6 - Tony hits a baseball at a height of 3ft from the...Ch. 10.6 - Prob. 55PECh. 10.6 - Two planes flying at the same altitude are on a...Ch. 10.6 - Suppose that a mortar is fired from ground level...Ch. 10.6 - Prob. 58PECh. 10.6 - Prob. 59PECh. 10.6 - Prob. 60PECh. 10.6 - Prob. 61PECh. 10.6 - For Exercises 61-62, describe the differences in...Ch. 10.6 - Do the parametric equations x=t and y=t+5 define a...Ch. 10.6 - Is the point 16,12 on the curve defined by x=2t...Ch. 10.6 - For a short interval of time, a military supply...Ch. 10.6 - Prob. 66PECh. 10.6 - Suppose that an imaginary string of unlimited...Ch. 10.6 - For Exercises 68-70, use a graphing utility to...Ch. 10.6 - Prob. 69PECh. 10.6 - Prob. 70PECh. 10.6 - A cycloid is a curve created by rolling a circle...Ch. 10.6 - A cycloid is a curve created by rolling a circle...Ch. 10.6 - If a circle of radius r rolls around the exterior...Ch. 10.6 - If a circle of radius r rolls around the exterior...Ch. 10 - How are the graphs of these ellipses similar and...Ch. 10 - For Exercises 2-5, an equation of an ellipse is...Ch. 10 - For Exercises 2-5, an equation of an ellipse is...Ch. 10 - For Exercises 2-5, an equation of an ellipse is...Ch. 10 - For Exercises 2-5, an equation of an ellipse is...Ch. 10 - For Exercises 6-7, a. Write the equation of the...Ch. 10 - For Exercises 6-7, a. Write the equation of the...Ch. 10 - For Exercises 8-10, write the standard form of an...Ch. 10 - Prob. 9RECh. 10 - For Exercises 8-10, write the standard form of an...Ch. 10 - Jupiter orbits the Sun in an elliptical path with...Ch. 10 - A bridge over a gorge is supported by an arch in...Ch. 10 - Prob. 14RECh. 10 - For Exercises 15-16, an equation of a hyperbola is...Ch. 10 - For Exercises 15-16, an equation of a hyperbola is...Ch. 10 - For Exercises 17-20, an equation of a hyperbola is...Ch. 10 - For Exercises 17-20, an equation of a hyperbola is...Ch. 10 - For Exercises 17-20, an equation of a hyperbola is...Ch. 10 - For Exercises 17-20, an equation of a hyperbola is...Ch. 10 - For Exercises 21-22, a. Write the equation of the...Ch. 10 - For Exercises 21-22, a. Write the equation of the...Ch. 10 - For Exercises 23-25, write the standard form of an...Ch. 10 - For Exercises 23-25, write the standard form of an...Ch. 10 - For Exercises 23-25, write the standard form of an...Ch. 10 - Suppose that one hyperbola has an eccentricity of...Ch. 10 - Solve the system of equations. 6x22y2=122x2+y2=11Ch. 10 - Suppose that two people standing 2mi10,560ft apart...Ch. 10 - A 120-ft flight control tower in the shape of a...Ch. 10 - For Exercises 30-33, an equation of a parabola is...Ch. 10 - For Exercises 30-33, an equation of a parabola is...Ch. 10 - For Exercises 30-33, an equation of a parabola is...Ch. 10 - Prob. 33RECh. 10 - Prob. 34RECh. 10 - For Exercises 34-35, an equation of a parabola is...Ch. 10 - For Exercises 36-37, fill in the blank. Let p...Ch. 10 - For Exercises 36-37, fill in the blank. Let p...Ch. 10 - For Exercises 38-40, determine the standard form...Ch. 10 - For Exercises 38-40, determine the standard form...Ch. 10 - Prob. 40RECh. 10 - Solve the system of equations. y+22=3x5xy=7Ch. 10 - Prob. 42RECh. 10 - Two large airship hangars were built in Orly,...Ch. 10 - Prob. 44RECh. 10 - For Exercises 44-45, the given equation represents...Ch. 10 - Prob. 46RECh. 10 - Prob. 47RECh. 10 - For Exercises 46-48, assume that the x- and y-axes...Ch. 10 - For Exercises 49-51, an equation of a conic...Ch. 10 - Prob. 50RECh. 10 - Prob. 51RECh. 10 - For Exercises 52-53, the equation represents a...Ch. 10 - Prob. 53RECh. 10 - Prob. 54RECh. 10 - Prob. 55RECh. 10 - For Exercises 54-59, a. Identify the type of conic...Ch. 10 - For Exercises 54-59, a. Identify the type of conic...Ch. 10 - Prob. 58RECh. 10 - Prob. 59RECh. 10 - Prob. 60RECh. 10 - Prob. 61RECh. 10 - Prob. 62RECh. 10 - Prob. 63RECh. 10 - Prob. 64RECh. 10 - x=4t2 and y=2t for 2t2 Sketch the plane curve by...Ch. 10 - Prob. 66RECh. 10 - Prob. 67RECh. 10 - Prob. 68RECh. 10 - Prob. 69RECh. 10 - Prob. 70RECh. 10 - For each given curve, the parameter t represents...Ch. 10 - Prob. 72RECh. 10 - Suppose that the origin on a computer screen is at...Ch. 10 - A stunt man drives a car at a speed of 25m/sec off...Ch. 10 - Suppose that a baseball is thrown at an angle of...Ch. 10 - How are the graphs of these ellipses similar, and...Ch. 10 - Prob. 2TCh. 10 - Write the standard form of an equation of an...Ch. 10 - Prob. 4TCh. 10 - Prob. 5TCh. 10 - Prob. 6TCh. 10 - Write the standard form of an equation of a...Ch. 10 - Write the standard form of an equation of a...Ch. 10 - For Exercises 9-16, a. Identify the equation as...Ch. 10 - For Exercises 9-16, a. Identify the equation as...Ch. 10 - For Exercises 9-16, a. Identify the equation as...Ch. 10 - For Exercises 9-16, a. Identify the equation as...Ch. 10 - For Exercises 9-16, a. Identify the equation as...Ch. 10 - For Exercises 9-16, a. Identify the equation as...Ch. 10 - Prob. 15TCh. 10 - For Exercises 9-16, a. Identify the equation as...Ch. 10 - The entrance to a tunnel is in the shape of a...Ch. 10 - Prob. 18TCh. 10 - Suppose that two people standing 1.5mi7920ft apart...Ch. 10 - Prob. 20TCh. 10 - Prob. 21TCh. 10 - Prob. 22TCh. 10 - Write the standard form of an equation of an...Ch. 10 - Write the standard form of an equation of a...Ch. 10 - Prob. 25TCh. 10 - If the major axis of an ellipse is 26 units in...Ch. 10 - Prob. 27TCh. 10 - Prob. 28TCh. 10 - If the asymptotes of a hyperbola are y=35x+1 and...Ch. 10 - Solve the system of equations. 3x24y2=135x2+2y2=13Ch. 10 - Describe the graph of the equation. x=41y29Ch. 10 - Prob. 32TCh. 10 - Prob. 33TCh. 10 - Prob. 34TCh. 10 - Prob. 35TCh. 10 - For Exercises 36-37, an equation of a conic...Ch. 10 - Prob. 37TCh. 10 - Prob. 38TCh. 10 - Prob. 39TCh. 10 - Prob. 40TCh. 10 - For Exercises 41-42, a. Eliminate the parameter....Ch. 10 - For Exercises 41-42, a. Eliminate the parameter....Ch. 10 - Prob. 43TCh. 10 - A pyrotechnic rocket is fired from a platform 2ft...Ch. 10 - Prob. 45TCh. 10 - Prob. 46TCh. 10 - Use the parametric mode to graph the curve on a...Ch. 10 - Prob. 1CRECh. 10 - Is 4 a zero of the polynomial fx=3x46x3+5x12?Ch. 10 - Prob. 3CRECh. 10 - Prob. 4CRECh. 10 - For Exercises 4-5, simplify completely....Ch. 10 - Find the midpoint of the line segment with...Ch. 10 - Given fx=x73, write an equation defining f1x.Ch. 10 - Prob. 8CRECh. 10 - Determine the asymptotes of the graph of y=csc2x2Ch. 10 - For Exercises 10-15, solve the equation or...Ch. 10 - For Exercises 10-15, solve the equation or...Ch. 10 - For Exercises 10-15, solve the equation or...Ch. 10 - Prob. 13CRECh. 10 - For Exercises 10-15, solve the equation or...Ch. 10 - For Exercises 10-15, solve the equation or...Ch. 10 - Prob. 16CRECh. 10 - Graph y=2sinx4 over one completed period.Ch. 10 - Prob. 18CRECh. 10 - Prob. 19CRECh. 10 - Prob. 20CRECh. 10 - Prob. 21CRECh. 10 - Prob. 22CRECh. 10 - For Exercises 21-24, graph the equations and...Ch. 10 - For Exercises 21-24, graph the equations and...Ch. 10 - For Exercises 25-26, solve the system....Ch. 10 - For Exercises 25-26, solve the system....Ch. 10 - For Exercises 27-29, refer to the matrices A and B...Ch. 10 - For Exercises 27-29, refer to the matrices A and B...Ch. 10 - For Exercises 27-29, refer to the matrices A and B...Ch. 10 - Use Cramer's rule to solve for z ....

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