Name ______Date______Pd ______
REVIEW #17 – PARAMETRICS
For each pair of parametric equations:
a) Draw the graph and show the orientation.
b) Write the rectangular equation.
1. x = -t2 + 2 and y = 2t2 – 6 , for t in (-, )
a)b)
2. x = and y = 2 – t, for t in [0,9]
a)b)
For the following graphs:
a) Write the parametric equations.
b) Find the rectangular equation.
3. 4.
x = ______x = ______
y = ______y = ______
For the following rectangular equation,
a) Write parametric equations.
b) Obtain a complete graph on your calculator.
c) Sketch the graph showing the scale on the axes. Label the
endpoints.
5. y = xsinx for t in [ -4π, 4π]
For the following parametric equations, sketch a complete graph showing the scale on the axes.
6. x = tsint and y = tcost for t in [0, 4]
Applications. TRACE the graph to approximate your answers.
7. Shawn starts out in his car traveling 55 mph from Houston to Dallas, 250 miles away. Mark starts out fromDallas one hour later to Houstonat a speed of 70 mph.
a) Write parametric equations to represent both trips.
Shawn: Mark:
x1 = ______x2 = ______
y1 = ______y2 = ______
Window: Tmin______x-min______
Tmax______x-max______
Tstep______y-min______
y-max ______
b) When and where will they pass each other? ______
______
c) Who will arrive at his destination first? ______
Shawn arrives: ______Mark arrives: ______
8. A stone is thrown upward with an initial speed of 42 ft/sec from a height of 100 ft.
a)Write parametric equations that describe the motion of the stone as a function of time.
x = ______y = ______
b)When is the stone at its maximum height? ______
c)What is the maximum height? ______
d)How long is the stone in the air? ______
9. From a point 35 yards (105 ft) directly in front of the goal post, a football is kicked at an elevation of 25 with an initial velocity of 70 ft/sec. At the moment the football is kicked, there is a 5 mph (8.8ft/sec) wind blowing from directly behind the kicker. Given that the goal post crossbar is 10 feet above the ground, answer the following:
a) Draw a complete graph of the situation.
b) Write parametric equations describing the path of the ball.
x1 = ______y1 = ______
c) Write parametric equations to describe the goalpost as a vertical line segment of height 10 feet.
x2 = ______y2 = ______
d) Record the window used.
Tmin: ______x-min: ______
Tmax: ______x-max: ______
Tstep: ______y-min: ______
y-max: ______
e) Does the ball pass over the goal post?______
f) What is the maximum height of the ball?______
g) What is the distance of the kick in yards?______
h) How long is the ball in the air? ______
i) If the angle of the kick is 30˚, will the football go over the goalposts? ______
Review.Non-Calculator.
Simplify.
10. (-2x3y2)5 11.
12. ab-2(ab2 - 3b3)13.
14. Solve.15.
Graph.
16. f(x) = 17. f(x) =
Answers to Review #17
1. a)
b) y = -2x – 2
2. a)
b) y = 2 – x2
3. x = 6 + 4cost
y = 4sint
(x – 6)2 + y2 = 16
4. x = -2 + 8cost
y = -6 + 2sint
5. x = t
y = tsint
6.
7. a) x1 = 55t, y1 = 2
x2 = 250 – 70(t-1), y2 = 4
b) 2.5-2.6 hours, 138 – 145 miles
c) Approximately the same time.
4.5 – 4.6 hours
8. a) x = 3, y = -16t2 + 42t + 100
b) 1.3 sec
c) 127.56 ft
d) 4.1 – 4.2 sec
9. b) x1 = 70tcos25° + 8.8t
y1 = -16t2 + 70tsin25°
c) x2 = 105, y2 = 10t(t ≤ 1)
e) No
f) 13.665 ft
g) 130 – 137 ft or 43.333 – 45.667 yds
h) 1.8 – 1.9 sec
i) Yes
10. -32x15y10
11.
12. a2 – 3ab
13. a
14.
15. 35
16.
17.