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Suppose that an airplane is asked to stay in a holding pattern near an airport. The distance of the plane to the airport is described by the following.\newlined(t)=132+66sin(2π11t)d(t)=132+66 \sin\left(\frac{2\pi}{11}t\right)\newlineIn this equation, d(t)d(t) is the distance of the plane to the airport (in miles), and tt is the time (in minutes) after the plane enters the holding pattern.\newlineDuring the first 1111 minutes after the plane enters the holding pattern, when will the plane be 170170 miles from the airport?\newlineDo not round any intermediate computations, and round your answer(s) to the nearest hundredth of a minute. (If there is more than one answer, enter additional answers with the "or" button.)\newlinet=t=◻" minutes "◻" or "

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Q. Suppose that an airplane is asked to stay in a holding pattern near an airport. The distance of the plane to the airport is described by the following.\newlined(t)=132+66sin(2π11t)d(t)=132+66 \sin\left(\frac{2\pi}{11}t\right)\newlineIn this equation, d(t)d(t) is the distance of the plane to the airport (in miles), and tt is the time (in minutes) after the plane enters the holding pattern.\newlineDuring the first 1111 minutes after the plane enters the holding pattern, when will the plane be 170170 miles from the airport?\newlineDo not round any intermediate computations, and round your answer(s) to the nearest hundredth of a minute. (If there is more than one answer, enter additional answers with the "or" button.)\newlinet=t=◻" minutes "◻" or "
  1. Set distance function equal: First, set the distance function d(t)d(t) equal to 170170 miles to solve for tt.170=132+66sin(2π11t)170 = 132 + 66 \sin\left(\frac{2\pi}{11}t\right)
  2. Subtract to isolate sine: Subtract 132132 from both sides to isolate the sine function.\newline170132=66sin(2π11t)170 - 132 = 66 \sin\left(\frac{2\pi}{11}t\right)\newline38=66sin(2π11t)38 = 66 \sin\left(\frac{2\pi}{11}t\right)
  3. Divide to solve sine: Divide both sides by 6666 to solve for the sine function.\newline3866=sin(2π11t) \frac{38}{66} = \sin\left(\frac{2\pi}{11}t\right) \newline0.57576=sin(2π11t)0.57576\ldots = \sin\left(\frac{2\pi}{11}t\right)
  4. Use inverse sine function: Use the inverse sine function to solve for (2π11t)\left(\frac{2\pi}{11}t\right).(2π11t)=sin1(0.57576...)\left(\frac{2\pi}{11}t\right) = \sin^{-1}(0.57576...)(2π11t)=0.619... radians\left(\frac{2\pi}{11}t\right) = 0.619... \text{ radians}
  5. Multiply to solve for tt: Multiply both sides by (112π)\left(\frac{11}{2\pi}\right) to solve for tt.\newlinet=(112π)×0.619t = \left(\frac{11}{2\pi}\right) \times 0.619\ldots\newlinet=1.08t = 1.08\ldots minutes

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