Find the area of the trapezoid
2 answers:
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Answer:
a. see attached
b. H(t) = 12 -10cos(πt/10)
c. H(16) ≈ 8.91 m
Step-by-step explanation:
<h3>a.</h3>The cosine function has its extreme (positive) value when its argument is 0, so we like to use that function for circular motion problems that have an extreme value at t=0. The midline of the function needs to be adjusted upward from 0 to a value that is 2 m more than the 10 m radius. The amplitude of the function will be the 10 m radius. The period of the function is 20 seconds, so the cosine function will be scaled so that one full period is completed at t=20. That is, the argument of the cosine will be 2π(t/20) = πt/10.
The function describing the height will be ...
H(t) = 12 -10cos(πt/10)
The graph of it is attached.
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<h3>b. </h3>See part a.
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<h3>c.</h3>The wheel will reach the top of its travel after 1/2 of its period, or t=10. Then 6 seconds later is t=16.
H(16) = 12 -10cos(π(16/10) = 12 -10cos(1.6π) ≈ 12 -10(0.309017) ≈ 8.90983
The height of the rider 6 seconds after passing the top will be about 8.91 m.
Answer:
(0, 3) lies on the line joining (2, -2) and (-4, 13).
Step-by-step explanation:
The equation of the line joining the points (2, -2) and (-4, 13) is:
-2(y + 2) = 5(x - 2)
-2y - 4 = 5x - 10
5x + 2y - 6 = 0
When we substitute x = 0 and y = 3,
5(0) + 2(3) = 0 + 6 = 6
So, (0, 3) lies on the line joining (2, -2) and (-4, 13).