Precalculus: Graphical, Numerical, Algebraic 8th Edition solutions

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1 and 2, find the component form of the vectors \(\text { (a) } \overrightarrow{O A} \text {, (b) } \overrightarrow{O B} \text {, and (c) } \overrightarrow{A B}\) where O is the origin. \(A=(-3,-2), B=(4,6)\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1 and 2, find the component form of the vectors \(\text { (a) } \overrightarrow{O A} \text {, (b) } \overrightarrow{O B} \text {, and (c) } \overrightarrow{A B}\) where O is the origin. \(A=(-1,3), B=(4,-3)\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 3 and 4, write an equation in point-slope form for the line through the two points. \((-3,-2),(4,6)\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 3 and 4, write an equation in point-slope form for the line through the two points. \((-1,3),(4,-3)\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 5 and 6, find and graph the two functions defined implicitly by each given relation. \(y^{2}=8 x\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 5 and 6, find and graph the two functions defined implicitly by each given relation. \(y^{2}=-5 x\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 7 and 8, write an equation for the circle with given center and radius. \((0,0), 2\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 7 and 8, write an equation for the circle with given center and radius. (-2,5), 3

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 9 and 10, a wheel with radius r spins at the given rate. Find the angular velocity in radians per second. r = 13 in., 600 rpm

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 9 and 10, a wheel with radius r spins at the given rate. Find the angular velocity in radians per second. r = 12 in., 700 rpm

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1-4, match the parametric equations with their graph. Identify the viewing window that seems to have been used. \(x=4 \cos ^{3} t, y=2 \sin ^{3} t\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1-4, match the parametric equations with their graph. Identify the viewing window that seems to have been used. \(x=3 \cos t, y=\sin 2 t\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1-4, match the parametric equations with their graph. Identify the viewing window that seems to have been used. \(x=2 \cos t+2 \cos ^{2} t, y=2 \sin t+\sin 2 t\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1-4, match the parametric equations with their graph. Identify the viewing window that seems to have been used. \(x=\sin t-t \cos t, y=\cos t+t \sin t\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 5 and 6, (a) complete the table for the parametric equations and (b) plot the corresponding points. \(x=t+2, y=1+3 / t\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 5 and 6, (a) complete the table for the parametric equations and (b) plot the corresponding points. \(x=\cos t, y=\sin t\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 7-10, graph the parametric equations \(x=3-t^{2}, y=2 t\), in the specified parameter interval. Use the standard viewing window \(0 \leq t \leq 10\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 7-10, graph the parametric equations \(x=3-t^{2}, y=2 t\), in the specified parameter interval. Use the standard viewing window \(-10 \leq t \leq 0\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 7-10, graph the parametric equations \(x=3-t^{2}, y=2 t\), in the specified parameter interval. Use the standard viewing window \(-3 \leq t \leq 3\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 7-10, graph the parametric equations \(x=3-t^{2}, y=2 t\), in the specified parameter interval. Use the standard viewing window \(-2 \leq t \leq 4\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 11-26, use an algebraic method to eliminate the parameter and identify the graph of the parametric curve. Use a grapher to support your answer. \(x=1+t, y=t\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 11-26, use an algebraic method to eliminate the parameter and identify the graph of the parametric curve. Use a grapher to support your answer. \(x=2-3 t, y=5+t\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 11-26, use an algebraic method to eliminate the parameter and identify the graph of the parametric curve. Use a grapher to support your answer. \(x=2 t-3, y=9-4 t, \quad 3 \leq t \leq 5\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 11-26, use an algebraic method to eliminate the parameter and identify the graph of the parametric curve. Use a grapher to support your answer. \(x=5-3 t, y=2+t, \quad-1 \leq t \leq 3\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 11-26, use an algebraic method to eliminate the parameter and identify the graph of the parametric curve. Use a grapher to support your answer. \(x=t^{2}, y=t+1\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 11-26, use an algebraic method to eliminate the parameter and identify the graph of the parametric curve. Use a grapher to support your answer. \(x=t, y=t^{2}-3\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 11-26, use an algebraic method to eliminate the parameter and identify the graph of the parametric curve. Use a grapher to support your answer. \(x=t, y=t^{3}-2 t+3\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 11-26, use an algebraic method to eliminate the parameter and identify the graph of the parametric curve. Use a grapher to support your answer. \(x=2 t^{2}-1, y=t\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 11-26, use an algebraic method to eliminate the parameter and identify the graph of the parametric curve. Use a grapher to support your answer. \(x=4-t^{2}, y=t\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 11-26, use an algebraic method to eliminate the parameter and identify the graph of the parametric curve. Use a grapher to support your answer. \(x=0.5 t, y=2 t^{3}-3,-2 \leq t \leq 2\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 11-26, use an algebraic method to eliminate the parameter and identify the graph of the parametric curve. Use a grapher to support your answer. \(x=t-3, y=2 / t,-5 \leq t \leq 5\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 11-26, use an algebraic method to eliminate the parameter and identify the graph of the parametric curve. Use a grapher to support your answer. \(x=t+2, y=4 / t, t \geq 2\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 11-26, use an algebraic method to eliminate the parameter and identify the graph of the parametric curve. Use a grapher to support your answer. \(x=5 \cos t, y=5 \sin t\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 11-26, use an algebraic method to eliminate the parameter and identify the graph of the parametric curve. Use a grapher to support your answer. \(x=4 \cos t, y=4 \sin t\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 11-26, use an algebraic method to eliminate the parameter and identify the graph of the parametric curve. Use a grapher to support your answer. \(x=2 \sin t \cdot y=2 \cos t \cdot 0 \leq t \leq 3 \pi / 2\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 11-26, use an algebraic method to eliminate the parameter and identify the graph of the parametric curve. Use a grapher to support your answer. \(x=3 \cos t, y=3 \sin t, 0 \leq t \leq \pi\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2732 find a parametrization for the curve. \(\text { The line through the points }(-2,5) \text { and }(4,2)\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2732 find a parametrization for the curve. \(\text { The line through the points }(-3,-3) \text { and }(5,1)\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2732 find a parametrization for the curve. \(\text { The line segment with endpoints }(3,4) \text { and }(6,-3)\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2732 find a parametrization for the curve. \(\text { The line segment with endpoints }(5,2) \text { and }(-2,-4)\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2732 find a parametrization for the curve. \(\text { The circle with center }(5,2) \text { and radius } 3\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2732 find a parametrization for the curve. \(\text { The circle with center }(-2,-4) \text { and radius } 2\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Exercises 33-36 refer to the graph of the parametric equations \(x=2-|t|, \quad y=t-0.5, \quad-3 \leq t \leq 3\) given below. Find the values of the parameter t that produces the graph in the indicated quadrant. Quadrant I

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Exercises 33-36 refer to the graph of the parametric equations \(x=2-|t|, \quad y=t-0.5, \quad-3 \leq t \leq 3\) given below. Find the values of the parameter t that produces the graph in the indicated quadrant. Quadrant II

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Exercises 33-36 refer to the graph of the parametric equations \(x=2-|t|, \quad y=t-0.5, \quad-3 \leq t \leq 3\) given below. Find the values of the parameter t that produces the graph in the indicated quadrant. Quadrant III

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Exercises 33-36 refer to the graph of the parametric equations \(x=2-|t|, \quad y=t-0.5, \quad-3 \leq t \leq 3\) given below. Find the values of the parameter t that produces the graph in the indicated quadrant. Quadrant IV

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Simulating a Foot Race Ben can sprint at the rate of 24 ft/sec. Jerry sprints at 20 ft/sec. Ben gives Jerry a 10-ft head start. The parametric equations can be used to model a race. \(\begin{array}{ll}x_{1}=20 t, & y_{1}=3 \\x_{2}=24 t-10, & y_{2}=5\end{array}\) (a) Find a viewing window to

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Capture the Flag Two opposing players in Capture the Flag are 100 ft apart. On a signal, they run to capture a flag that is on the ground midway between them. The faster runner, however, hesitates for 0.1 sec. The following parametric equations model the race to the flag: \(\begin{array}{ll}x_{1

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Famine Relief Air Drop A relief agency drops food containers from an airplane on a war-torn famine area. The drop was made from an altitude of 1000 ft above ground level. (a) Use an equation to model the height of the containers (during free fall) as a function of time t. (b) Use parametric

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Height of a Pop-up A baseball is hit straight up from a height of 5 ft with an initial velocity of 80 ft/sec. (a) Write an equation that models the height of the ball as a function of time t. (b) Use parametric mode to simulate the pop-up. (c) Use parametric mode to graph height agains

Precalculus: Graphical, Numerical, Algebraic 8th Edition
The complete graph of the parametric equations x=2cos t, y=2sin t is the circle of radius 2 centered at the origin. Find an interval of values for t so that the graph is the given portion of the circle. (a) The portion in the first quadrant (b) The portion above the x-axis (c) The port

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Writing to Learn Consider the two pairs of parametric equations \(x=3 \cos t, y=3 \sin t \text { and } x=3 \sin t, y=3 \cos t\) for \(0 \leq t \leq 2 \pi\). (a) Give a convincing argument that the graphs of the pairs of parametric equations are the same. (b) Explain how the parametrizations

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Hitting a Baseball Consider Kevins hit discussed in Example 9. (a) Approximately how many seconds after the ball is hit does it hit the wall? (b) How high up the wall does the ball hit? (c) Writing to Learn Explain why Kevins hit might be caught by an outfielder. Then explain why his h

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Kirby hits a ball when it is 4 ft above the ground with an initial velocity of 120 ft/sec. The ball leaves the bat at a 30 angle with the horizontal and heads toward a 30-ft fence 350 ft from home plate. (a) Does the ball clear the fence? (b) If so, by how much does it clear the fence? If n

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Hitting a Baseball Suppose that the moment Kirby hits the ball in Exercise 44 there is a 5-ft/sec split-second wind gust. Assume the wind acts in the horizontal direction out with the ball. (a) Does the ball clear the fence? (b) If so, by how much does it clear the fence? If not, could the

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Two-Softball Toss Chris and Linda warm up in the outfield by tossing softballs to each other. Suppose both tossed a ball at the same time from the same height, as illustrated in the figure. Find the minimum distance between the two balls and when this minimum distance occurs.

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Yard Darts Tony and Sue are launching yard darts 20 ft from the front edge of a circular target of radius 18 in. on the ground. If Tony throws the dart directly at the target, and releases it 3 ft above the ground with an initial velocity of 30 ft/sec at a 70 angle, will the dart hit the target?

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Yard Darts In the game of darts described in Exercise 47, Sue releases the dart 4 ft above the ground with an initial velocity of 25 ft/sec at a 55 angle. Will the dart hit the target?

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Hitting a Baseball Orlando hits a ball when it is 4 ft above ground level with an initial velocity of 160 ft/sec. The ball leaves the bat at a 20 angle with the horizontal and heads toward a 30-ft fence 400 ft from home plate. How strong must a split-second wind gust be (in feet per second) that acts

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Hitting Golf Balls Nancy hits golf balls off the practice tee with an initial velocity of 180 ft/sec with four different clubs. How far down the fairway does the ball hit the ground if it comes off the club making the specified angle with the horizontal? \(\begin{array}{l}\text{(a) } 15^{\circ}\

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Analysis of a Ferris Wheel Ron is on a Ferris wheel of radius 35 ft that turns counterclockwise at the rate of one revolution every 12 sec. The lowest point of the Ferris wheel (6 o'clock) is 15 ft above ground level at the point (0, 15) on a rectangular coordinate system. Find parametric equations f

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Eliminate the parameter t from the parametric equations of Example 5 to find an equation in x and y for the line. Verify that the line passes through the points A and B of the example.

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Cycloid The graph of the parametric equations x = t - sin t, is y = 1 - cos t a cycloid. (a) What is the maximum value of y=1-cos t? How is that value related to the graph? (b) What is the distance between neighboring x-intercepts?

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Hypocycloid The graph of the parametric equations x = 2 cos t + cos 2t, y = 2 sin t - sin 2t y = 1 - cos t? is a hypocycloid. The graph is the path of a point P on a circle of radius 1 rolling along the inside of a circle of radius 3, as illustrated in the figure. (a) Graph simultaneous

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 55-58, a particle moves along a horizontal line so that its position at any time t is given by . Write a description of the motion. [Hint: See Example 7.] \(s(t)=-t^{2}+3 t, \quad-2 \leq t \leq 4\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 55-58, a particle moves along a horizontal line so that its position at any time t is given by . Write a description of the motion. [Hint: See Example 7.] \(s(t)=-t^{2}+4 t, \quad-1 \leq t \leq 5\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 55-58, a particle moves along a horizontal line so that its position at any time t is given by . Write a description of the motion. [Hint: See Example 7.] \(s(t)=0.5\left(t^{3}-7 t^{2}+2 t\right), \quad-1 \leq t \leq 7\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 55-58, a particle moves along a horizontal line so that its position at any time t is given by . Write a description of the motion. [Hint: See Example 7.] \(s(t)=t^{3}-5 t^{2}+4 t, \quad-1 \leq t \leq 5\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
True or False The two sets of parametric equations \(x_{1}=t-1, y_{1}=3 t+1 \text { and } x_{2}=(2 / 3) t-4 / 3, y_{2}=2 t\) correspond to the same rectangular equation. Justify your answer.

Precalculus: Graphical, Numerical, Algebraic 8th Edition
True or False The graph of the parametric equations \(x=t-1, y=2 t-1,1 \leq t \leq 3\) is a line segment with endpoints (0,1) and (2,5). Justify your answer.

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Which of the following points corresponds to t=-1 in the parametrization \(x=t^{2}-4\), \(y=t+\frac{1}{t}\)? (A) (-3,-2) (B) (-3,0) (C) (-5,-2) (D) (-5,0) (E) (3,2)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Which of the following values of t produces the same point as \(t=2 \pi / 3\) in the parametrization \(x=2 \cos t, y=2 \sin t\)? (A) \(t & =-\frac{4 \pi}{3}\) (B) \(t=-\frac{2 \pi}{3}\) (C) \(t=\frac{-\pi}{3}\) (D) \(t & =\frac{4 \pi}{3}\) (E) \(t=\frac{7 \pi}{3}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
A rock is thrown straight up from level ground with its position above ground at any time \(t \geq 0\) given by \(x=5, y=-16 t^{2}+80 t+7\), At what time will the rock be 91 ft above ground? (A) 1.5 sec (B) 2.5 sec (C) 3.5 sec (D) 1.5 sec and 3.5 sec (E) The rock never goes that high.

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Multiple Choice Which of the following describes the graph of the parametric equations \(x=1-t, y=3 t+2\) \(t \geq 0\)? (A) A straight line (B) A line segment (C) A ray (D) A parabola (E) A circle

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Parametrizing Circles Consider the parametric equations \(x=a \cos t, \quad y=a \sin t, \quad 0 \leq t \leq 2 \pi\) (a) Graph the parametric equations for a= 1, 2, 3, 4 in the same square viewing window. (b) Eliminate the parameter t in the parametric equations to verify that they are a

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Group Activity Parametrization of Lines Consider the parametrization \(x=a t+b, \quad y=c t+d\) where a and c are not both zero. (a) Graph the curve for \(a=2, b=3, c=-1, \text { and } d=2\) (b) Graph the curve for \(a=3, b=4, c=1, \text { and } d=3\) (c) Writing to Learn Elimin

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Throwing a Ball at a Ferris Wheel A 20-ft Ferris wheel turns counterclockwise one revolution every 12 sec (see figure). Eric stands at point D, 75 ft from the base of the wheel. At the instant Jane is at point A, Eric throws a ball at the Ferris wheel, releasing it from the same height as the bottom

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Throwing a Ball at a Ferris Wheel A 71-ft-radius Ferris wheel turns counterclockwise one revolution every 20 sec. Tony stands at a point 90 ft to the right of the base of the wheel. At the instant Matthew is at point A (3 o'clock), Tony throws a ball toward the Ferris wheel with an initial velocity o

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Two Ferris Wheels is on a Ferris wheel of center (0,20) and radius 20 ft turning counterclockwise at the rate of one revolution every 12 sec. Kuan is on a Ferris wheel of center (15,15) and radius 15 turning counterclockwise at the rate of one revolution every 8 sec. Find the minimum distance between

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Two Ferris Wheels and Kuan are riding the Ferris wheels described in Exercise 69. Find the minimum distance between Chang and Kuan if Chang starts out (t=0) at 3 o'clock and Kuan at 6 o'clock.

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Exercises 7173 refer to the graph C of the parametric equations \(x=t c+(1-t) a, \quad y=t d+(1-t) b\) where \(P_{1}(a, b) \text { and } P_{2}(c, d)\) are two fixed points Using Parametric Equations in Geometry Show that the point P(x,y) on C is equal to (a) \(P_{1}(a, b) \text { whe

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Exercises 7173 refer to the graph C of the parametric equations \(x=t c+(1-t) a, \quad y=t d+(1-t) b\) where \(P_{1}(a, b) \text { and } P_{2}(c, d)\) are two fixed points Using Parametric Equations in Geometry Show that if t=0.5, the corresponding point (x,y) on C is the midpoint of the

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Exercises 7173 refer to the graph C of the parametric equations \(x=t c+(1-t) a, \quad y=t d+(1-t) b\) where \(P_{1}(a, b) \text { and } P_{2}(c, d)\) are two fixed points What values of t will find two points that divide the line segment \(P_{1} P_{2}\) into three equal pieces? Four equa