Mathematics: Two people swing a jump rope. The highest point in the middle of the jump rope is 76 inches above the ground, and the lowest point is 4 inches. The rope makes 4 revolutions per second. Write a model for the height of the rope in inches as a function of time in seconds given that the rope starts at its lowest point.

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Two people swing a jump rope. The highest point

Ibnushuaibabutalhah

27.01.2022

h(t) = 36sin(1440x)+ 40

Step-by-step explanation:

Given the information:

highest point: 76 inches=>lowest point: 4 inches => 4 revolutions per second => period: $\frac{1}{4}$ per second = $\frac{360}{\frac{1}{4} } =1440$

y = a sin (bx+c) + k for different values of a, b, and c

=> Amplitude (a) = (highest point - lowest point) / 2 = 36

=> asymptom (k) = (highest point - lowest point) / 2 = 40

=> model for the height of the rope in inches as a function of time in seconds given that the rope starts at its lowest point is:

h(t) = 36sin(1440x)+ 40

Hope it will find you well.

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