Hungry Harry is a giant ogre with an appetite that fluctuates throughout the day. H(t)H(t)H, left parenthesis, t, right parenthesis models the weight of sheep (in \text{kg}kgstart text, k, g, end text) that Harry would like to swallow ttt hours after he wakes up. Here, ttt is entered in radians. H(t) = 12\sin\left(\dfrac{2\pi}{24}t\right) + 15H(t)=12sin( 24 2π t)+15H, left parenthesis, t, right parenthesis, equals, 12, sine, left parenthesis, start fraction, 2, pi, divided by, 24, end fraction, t, right parenthesis, plus, 15 What is the second time after Harry wakes up that he feels like consuming 17{\text{ kg}}17 kg17, start text, space, k, g, end text of sheep?

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sqdancefan sqdancefan · Answer 1 · 2020-06-02T22:02:38+02:00

Answer:

t = 11.36

Step-by-step explanation:

We want to find t such that ...

17 = 12sin(2πt/24) +15 . . . . H(t) = 17

2/12 = sin(2πt/24) . . . . . . . subtract 17, divide by 12

t = 24/(2π)·arcsin(1/6) . . . . solve for t

t = (12/π)arcsin(1/6) or (12/π)(π -arcsin(1/6))

We want the larger of these values of t, so ...

t = (12/π)(π -0.167448) ≈ 11.36

11.36 hours after Harry wakes up, he will feel like consuming 17 kg of sheep for the second time.

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