PRECALCULUS HELP IM BEGGING YOU
1 answer:
Answer: Period = 2 seconds
Graph is shown below
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Explanation:
1 minute = 60 seconds
We have 30 revolutions every 60 seconds, so we can write the ratio
30 rev: 60 sec
Divide both parts by 30 to turn that "30 rev" into "1 rev"
30 rev: 60 sec
30/30 rev: 60/30 sec
1 rev : 2 sec
This tells us that each full revolution takes 2 seconds. This is the period of the ferris wheel. The period is the length of each cycle.
The cyclic or periodic nature of this motion heavily implies we'll be dealing with a sine or cosine function of some kind. Let's go with sine.
Side note: cosine is really a sine function in disguise (it's just a phase shifted version of it).
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The general sine curve equation is
y = A*sin(B(x-C)) + D
where
- |A| = amplitude
- B = 2pi/T with T being the period
- C handles phase shifts (left and right shifting)
- D handles vertical shifting, and y = D is the equation of the midline
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The wheel is 10 feet in diameter, so 10/2 = 5 is the radius. This is also the amplitude because it is the distance from the midline to either the highest point (10 ft) or lowest point (0 ft). So A = 5.
Since T = 2 is the period, this means,
B = 2pi/T
B = 2pi/2
B = pi
We don't have any phase shifts to worry about so C = 0.
The midline is D = 5 since this is halfway up
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Putting all the pieces together, we get this sine equation
y = A*sin(B(x-C)) + D
y = 5*sin(pi*(x-0)) + 5
y = 5*sin(pi*x) + 5
The graph is shown below.
x = time in seconds, y = height of the seat
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Answer:
(a) scalene, see attachment
(b) acute, see attachment
(c) correct; isosceles
Step-by-step explanation:
(a) The sides of the triangle all have different lengths, so the triangle is scalene. Differences in coordinates between the points of the triangle are (6, 2), (5, 2), and (4, 1), so no two distances between these points can be the same.
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(b) The angle opposite the longest side is clearly an acute angle, so the triangle is an acute triangle.
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(c) Miles and Brad live on the same north/south line. Jose lives at a distance that is halfway between those houses in the north-south direction. Hence the distance to Miles' and Brad's houses must be the same from Jose's house. That means the triangle connecting Miles', Brad's, and Jose's houses will be an isosceles triangle.
