HI I NEED HELP WITH THIS QUESTION ASAP ITS URGENT PLEASE HELP A group of rowdy teenagers near a wind turbine decide to place a pair of
pink shorts on the tip of one blade. They notice that the shorts are at its
maximum height of 16 metres at t = 10 s and its minimum height of 2 metres at
t = 25 s.

a) Determine the equation of the sinusoidal function that describes
the height of the shorts in terms of time.

b) Determine the height of the shorts at exactly t = 10 minutes, to
the nearest tenth of a metre.

a) The sinusoidal function is y = 7·sin(π/15(t - 2.5)) + 9

b) The height of the shorts at t =  10 minute is approximately 6 meters

The above answers were arrived at as follows

a) The general form of a sinusoidal equation is presented as follows;

y = A·sin(B(t - h)) + k

Where;

A = The amplitude of the graph of the function

The period, T = 2·π/B

h = The horizontal shift

k = The vertical shift

The maximum height of the blade = 16 meters

The minimum height of the blade  = 2 meters

The time the blade moves from maximum height to minimum height = 25 s - 10 s = 15 s

Therefore, the time it takes the blade to move from maximum height to minimum height, the period, T= 2 × 15 s = 30 s

Therefore;

B = 2·π/30 = π/15

B = π/15

When B·(t - h) = π/2, t = 10

Therefore;

(π/15)·(10 - h) = π/2

10 - h = 15/2

h = 10 - 15/2 = 2.5

The horizontal shift, h = 2.5

The amplitude, A = (Max - Min)/2

∴ A = (16 - 2)/2 = 7

A = 7

The vertical shift, k = Min - (-Amplitude)

∴ k = 2 - (-7) = 9

The vertical shift, k = 9 Up

Therefore, the equation of the sinusoidal equation that describes the height of shorts in terms of time is given by plugging in the values of the variables, A, B, h, and k to  get the following equation;

y = 7·sin(π/15·(t - 2.5)) + 9

b) The height of the shorts at exactly, t = 10 minutes = 600 seconds, is given as follows;

y = 7·sin(π/15·(t - 2.5)) + 9

10 minutes =  600 seconds

When t = 10 minutes = 600 seconds

∴ y = 7·sin(π/15(600 - 2.5)) + 9 = 5.5 ≈ 6

The height of the shorts at exactly t = 10 minutes ≈ 6 meters.

Get more information on  sinusoidal functions here;

step-by-step explanation:

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