The Sea Dragon, a pendulum ride at an amusement park, moves from its central position at rest according to the trigonometric function P(t)=−10sin(pi/3t), where t represents time, in seconds. How many seconds does it take the pendulum to complete one full cycle?
A= 3
B= 5
C= 6
D= 10
Answers
Answer:T = 2*Pi / (Pi / 3) = 6 seconds
Step-by-step explanation:
The time (in seconds) that it take the pendulum to complete one full cycle is given by: Option C: 6 (seconds)
What is the period of sine function?Trigonometric functions are periodic. They repeat their values after some specific constant input interval (constant depends on the trigonometric function chosen).
For sine function, its period is 2π
Thus, we get:
[tex]y = \sin(x) = \sin(x+2\pi) = \sin(x + 2\pi n) ; n \in \mathbb Z[/tex] integer, and y is some constant at some constant value of x)
For this case, the pendulum's motion is modeled by:
[tex]P(t) = -10\sin\left(\dfrac{\pi}{3} t\right)[/tex]
Let it takes 'd' seconds to do one full cycle, then we get:
[tex]P(t) = P(t+d) = P(t+2d) = P(t + nd); n \in \mathbb Z - \mathbb Z^{-}[/tex] (n is non-negative integer).
Using the formula, we get:
[tex]-10\sin\left(\dfrac{\pi}{3} t\right) = -10\sin\left(\dfrac{\pi}{3} (t + nd)\right)\\\sin\left(\dfrac{\pi}{3} t\right) =\sin\left(\dfrac{\pi}{3}t + \dfrac{\pi}{3}nd\right)[/tex]
But we know that:
[tex]\sin\left(\dfrac{\pi}{3} t\right) =\sin\left(\dfrac{\pi}{3}t +2\pi n\right)[/tex]
Thus, we get:
[tex]2\pi n = \dfrac{\pi}{3}nd\\[/tex] (compared for non-negative values of n)
This gives:
[tex]d = \dfrac{2\pi n \times 3}{\pi n} = 6[/tex] (in seconds)
Thus, the time (in seconds) that it take the pendulum to complete one full cycle is given by: Option C: 6 (seconds)
Learn more about periodic functions here:
https://brainly.com/question/12529476
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Chris has scored the following points in his last five basketball games: 13,10,14,9,6
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Answers
Answer:
he must score 32 points in the next game in order to average 14 points per game.
Step-by-step explanation:
14 x 6 = 84
84-(13+10+14+9+6)=32
checking:
32 + 13 + 10 + 14 + 9 + 6 = 84
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Step-by-step explanation:
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Step-by-step explanation:
Given the expression 10x^3 + 16x^2 - 18x, we are to find the GCF
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Answer:
.2(x+1)(x+5)
Step-by-step explanation:
Well first lets start with the x intercepts which are -1 and negative 5 so the equation must be either -0.2(x+1)(x+5) or .2(x+1)(x+5)
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Answer:
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A. 11.5 cm
O B. 23 cm
O C. 30 cm
D. 38 cm
E.46 cm
Answers
Answer:
e
Step-by-step explanation:
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Answer:
E. 46cm
Step-by-step explanation:
Perimeter of a rectangle= 2(l+b)
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Answers
Answer:
D'wayne plans to wallpaper 43.5 square feet of the wall.
Step-by-step explanation:
72.5% = 72.5/100 = 0.725
mulitiply that by 60
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Answer:
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Step-by-step explanation:
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Answers
Answer:
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Step-by-step explanation:
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Answer:
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Step-by-step explanation:
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You ask 196 of your classmates how they feel about the school year being made longer. Complete the two-way frequency table to show the results of the survey. Use pencil and paper. Combine the very unhappy and unhappy categories into one category called dislike and combine the happy and very happy categories into one category called like. Complete a new two-way frequency table.
Answers
Answer:
13, 11, 2, 25, 66, 5, 12, 25, 45
Step-by-step explanation:
Right to Left
Number of 6th graders that are very unhappy is 14
Number of 6th graders that are happy is 13
Number of 7th graders that are neutral is 12
Number of 7th graders that are happy is 30
Total number of 7th graders is 80
Number of 8th graders that are very unhappy is 20
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Number of unhappy students is 59
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Step-by-step explanation:
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Step-by-step explanation:
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Answer:
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Step-by-step explanation:
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Answer:
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Step-by-step explanation:
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Answer:
Results are below.
Step-by-step explanation:
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Principal (P)= $2,500
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Answer:
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Step-by-step explanation:
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Step-by-step explanation:
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Step-by-step explanation:
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Answer:
c
Step-by-step explanation:
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Answer:
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Step-by-step explanation:
Use the midpoint formula and equate to the coordinates of the midpoint.
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Step-by-step explanation:
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Answer:
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Step-by-step explanation: