The function 퐻 gives the height, above the ground, of a point on a spinning wheel. The function 퐴 gives the height of a point on a different spinning wheel and is defined by 퐴(푡)= 1.2퐻(3푡). Here, 푡 is time in seconds since the wheels started moving. How does the spinning wheel modeled by function 퐴 compare to the wheel for 퐻 ? Explain how you know. (2pts)
Question
The function 퐻 gives the height, above the ground, of a point on a spinning wheel. The function 퐴 gives the height of a point on a different spinning wheel and is defined by 퐴(푡)= 1.2퐻(3푡). Here, 푡 is time in seconds since the wheels started moving. How does the spinning wheel modeled by function 퐴 compare to the wheel for 퐻 ? Explain how you know. (2pts)
Solution
The function A(t) = 1.2H(3t) tells us two things about the spinning wheel it models compared to the wheel modeled by H.
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Amplitude: The multiplier 1.2 in front of H(3t) indicates that the height of the points on the wheel modeled by A is 1.2 times the height of the points on the wheel modeled by H. This means that the wheel modeled by A is larger, or has a greater amplitude, than the wheel modeled by H.
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Speed: The argument of the function H is 3t instead of t, which means that the wheel modeled by A completes 3 rotations in the time it takes the wheel modeled by H to complete 1 rotation. This means that the wheel modeled by A is spinning 3 times faster than the wheel modeled by H.
So, in summary, the wheel modeled by function A is larger and spins faster than the wheel modeled by function H.
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