Serpentine Curve Consider the parametric equations x = 2 cot θ and y = 4 sin θ cos θ , 0 < θ < π (a) Use a graphing utility to graph the curve. (b) Eliminate the parameter to show that the rectangular equation of the serpentine curve is ( 4 + x 2 ) y = 8 x
Serpentine Curve Consider the parametric equations x = 2 cot θ and y = 4 sin θ cos θ , 0 < θ < π (a) Use a graphing utility to graph the curve. (b) Eliminate the parameter to show that the rectangular equation of the serpentine curve is ( 4 + x 2 ) y = 8 x
Solution Summary: The author explains how to graph the parametric equation cx=2mathrmcotthetaandy=4
The path of a projectile that is launched h feet above the ground with an initial velocity of vo feet per second and at an angle 0 with the horizontal is given by the parametric equations shown below,
where t is the time, in seconds, after the projectile was launched.
x= (vo cos 0) t, y=h+ (Vo sin 0) t-16t2
Use a graphing utility to obtain the path of a projectile launched from the ground (h=0) at an angle of 0 = 65° and initial velocity of v = 130 feet per second. Use the graph to determine the maximum
height of the projectile and the time at which it reaches this height, as well as the range of the projectile and the time it hits the ground.
Choose the correct graph of the path of the projectile.
OA.
Q
G
OB.
○ C.
O D.
Q
Q
E
G
[0,1000]x[0,300]
[0,1000] x [0,300]
[0,1000]x[0,300]
What is the maximum height of the projectile?
feet (Type an integer or decimal rounded to the nearest tenth as needed.)
At what time does the projectile reach this maximum height?
seconds (Type an integer or…
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