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.d(t)=132+66sin(112πt)In this equation, d(t) is the distance of the plane to the airport (in miles), and t is the time (in minutes) after the plane enters the holding pattern.During the first 11 minutes after the plane enters the holding pattern, when will the plane be 170 miles from the airport?Do 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.)t=◻" minutes "◻" or "
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.d(t)=132+66sin(112πt)In this equation, d(t) is the distance of the plane to the airport (in miles), and t is the time (in minutes) after the plane enters the holding pattern.During the first 11 minutes after the plane enters the holding pattern, when will the plane be 170 miles from the airport?Do 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.)t=◻" minutes "◻" or "
Set distance function equal: First, set the distance function d(t) equal to 170 miles to solve for t.170=132+66sin(112πt)
Subtract to isolate sine: Subtract 132 from both sides to isolate the sine function.170−132=66sin(112πt)38=66sin(112πt)
Divide to solve sine: Divide both sides by 66 to solve for the sine function.6638=sin(112πt)0.57576…=sin(112πt)
Use inverse sine function: Use the inverse sine function to solve for (112πt).(112πt)=sin−1(0.57576...)(112πt)=0.619... radians
Multiply to solve for t: Multiply both sides by (2π11) to solve for t.t=(2π11)×0.619…t=1.08… minutes
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