9.5 Parametric Equations

​9.5 Parametric Equations

Multiple Choice

The variable "t" is called a... #6

• parameter

• parallel

• paralegal

• paradise

Multiple Choice

Converting parametric equations to a rectangular equation is called _________________ the parameter. #1

• eliminating

• finding

• converting

• jumping

Multiple Choice

Eliminate the parameter from x(t) = t² + 5 and y(t) = t² - 4. Which of the following sketches results? #2

• Linear

• Quadratic

• Quartic

• Square Root

Multiple Choice

Find the point based on the parametric equations. t = 3 #3

x = 1 - 2t

y =4t + 1

• (-5, 13)

• (13, -5)

• (5, 13)

• (13, 5)

Multiple Choice

Find the ordered pair based on the parametric equations. #4

t = -2

x = t² - 2

y = -t + 2

• (2, 4)

• (4, 2)

• (-6, 0)

• (0,-6)

Multiple Choice

Write the rectangular equation for the following parametric equations. #5

x = 4cosθ

y = 3sinθ^

• $$\frac{x^2}{9}+\frac{y^2}{16}=1$$

• $$\frac{y^2}{9}+\frac{x^2}{16}=1$$

• $$\cos^2\theta+\sin^2\theta=1$$

• $$\frac{x^2}{9}-\frac{y^2}{16}=1$$

Multiple Choice

What is the center and radius of the curve: #7

x=1+3cost

y=-2+3sint

• (-1,2) , r=3

• (-1,2) ,  r=9

• (1,-2) ,  r=3

• (1,-2) ,  r=9

Multiple Choice

Which set of parametric equations satisfies the given data table? #9

• x(t) = t³ - 1 y(t) = 2t

• x(t) = t³ - 1 y(t) = t + 2

• x(t) = t + 8 y(t) = t + 2

• x(t) = t + 8 y(t) = 2t

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Multiple Choice

Kait hits the golfball at an angle of 27° with the horizontal at an initial speed of 22 m/s.  How far has the ball traveled horizontally after 2 seconds? #20

• 50.068 meters

• 19.976 meters

• 39.204 meters

• 42.077 meters

Multiple Choice

A cannonball is fired at a 45.0° angle and an initial velocity of 625 f/s. Assume no air resistance. Find the horizontal coordinate of the cannonball after 2 seconds. #24

• 1250 f/s

• 883.9 f/s

• 441.9 f/s

• 328.3 f/s

Multiple Choice

An NFL punter at the 20-yard line kicks a football downfield with an initial velocity of 75 ft/sec at an angle of 66⁰. The ball leaves his foot at a height of 3 feet.

Model the scenario using parametric equations. #25

• x = (20cos(66⁰))t; y=-16t² + (20sin(66⁰)t + 75

• x = (20cos(66⁰))t; y=-16t² + (20sin(66⁰)t + 3

• x = (75cos(66⁰))t; y=-16t² + (75sin(66⁰)t + 20

• x = (75cos(66⁰))t; y=-16t² + (75sin(66⁰)t + 3

Multiple Choice

A ball is thrown horizontally at a height of 2.2 ft at a velocity of 65 ft/s. Assume no air resistance. How long until the ball reaches the ground? #26

• 0.45 s

• 0.37 s

• 0.22 s

• 0.47 s

Multiple Choice

Mr. Salaam hits a baseball to Mr. Shakin at 3 ft above the ground with an initial speed of 150 ft/sec and at an angle of 18 degrees with the horizontal.

Model the y component with a parametric equation. #32

• y = -16t²+(150 sin 18)t

• y = -16t²+(150 sin 3)t+18

• y = -16t²+(150 sin 18)t+3

• y = 16t²+(150 sin 3)+18

Multiple Choice

Mr. Salaam hits a baseball to Mr. Shakin at 3 ft above the ground with an initial speed of 150 ft/sec and at an angle of 18 degrees with the horizontal. #33

How far away is the ball from Mr. Salaam

after 1.5 seconds?

• 180.988 feet

• 36.529 feet

• 46.353 feet

• 213.988 feet

Multiple Choice

Suppose that a ball is thrown with an initial horizontal velocity of 25 ft/sec and an initial vertical velocity of 15 ft/sec. Assume that the only force acting on the object is due to gravity. Let t = time in seconds since the ball was thrown.

x(t) = 25t; y(t) = -16t² + 15t

Graph the parametric equations and find the coordinate point corresponding to t = 0.5. #44

• (12.5, 3.5)

• (12.5, 7.5)

• (12.5, 1)

• (12.5, 10.2)