A pendulum is swinging next to a wall. The distance from the bob of the swinging pendulum to the wall varies in a periodic way t
hat can be modeled by a trigonometric function.
The function has period 0.80.80, point, 8 seconds, amplitude 6 \text{ cm}6 cm6, start text, space, c, m, end text, and midline H = 15 \text{ cm}H=15 cmH, equals, 15, start text, space, c, m, end text. At time t = 0.5t=0.5t, equals, 0, point, 5 seconds, the bob is at its midline, moving towards the wall.
Find the formula of the trigonometric function that models the distance HHH from the pendulum's bob to the wall after t seconds. Define the function using radians.
The function has period 0.80.80, point, 8 seconds, amplitude 6 \text{ cm}6 cm6, start text, space, c, m, end text, and midline H = 15 \text{ cm}H=15 cmH, equals, 15, start text, space, c, m, end text. At time t = 0.5t=0.5t, equals, 0, point, 5 seconds, the bob is at its midline, moving towards the wall.
Find the formula of the trigonometric function that models the distance HHH from the pendulum's bob to the wall after t seconds. Define the function using radians.
1 answer:
Answer:
H(t) = 15 -6sin(2.5π(t -0.5))
Step-by-step explanation:
For midline M, amplitude A, period T and time t0 at which the function is decreasing from the midline, the function can be written as ...
H(t) = M -Asin(2π/T(t -t0))
Using the given values of M=15, A=6, T=0.8 and t0 = 0.5, the equation is ...
H(t) = 15 -6sin(2.5π(t -0.5))
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The measures of central tendency for this data set are as follows:
- Mean = 3.55.
- Median = 3.5.
- Mode = 3.
In Mathematics, there are three (3) main measures of central tendency and these include the following:
- Mean
- Median
- Mode
For the mean, we have:
Mathematically, the mean for this data set would be calculated by using this formula:
Mean = [F(x)]/n
For the total number of data, we have:
F(x) = 0 + 1 + 1 + 1 + 2 + 2 + 3 + 3 + 3 + 3 + 4 + 4 + 4 + 5 + 5 + 5 + 6 + 6 + 6 + 7
F(x) = 71
Substituting the parameters into the formula, we have:
Mean = [F(x)]/n
Mean = 71/20
Mean = 3.55.
For the median, we have:
First of all, we would order the data from lowest to highest and then determine the median as follows:
Data = {0, 1, 1, 1, 2, 2, 3, 3, 3,} 3, 4, {4, 4, 5, 5, 5, 6, 6, 6, 7}
Median = {3 + 4}/2
Median = 7/2
Median = 3.5.
<h3>How to calculate the mode?</h3>A mode refers to the most frequently occurring number in a data set. Thus, the mode for this data set is equal to 3.
In conclusion, a box plot of the measures of central tendency for this data set is shown in the image attached below.
Read more on mean here: brainly.com/question/9550536
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