The brightness of some stars can fluctuate over time Suppose

The brightness of some stars can fluctuate over time. Suppose that the brightness of a certain star can be modeled by the following. B(t) = 7.7+ 10.7sin(2 pi/69 t) In this equation, B(t) represents the magnitude of brightness, and r is the time (in days). Suppose we start at t = 0 days. During the first 69 days, when will the star\'s magnitude of brightness be 12? Do not round any intermediate computations, and round your answer(s) to the nearest day. (If there is more than one answer, enter additional answers with the \"or\" button.)

Solution

We have given the equation

B(t) = 7.7 +10.7 sin(2pi*t/69)

now given that B= 12 and we need to find time t. In order to find the value of t plugging the value of B in the above equation

12= 7.7 +10.7 sin(2pi*t/69)

=> 12-7.7 = 10.7 sin(2pi*t/69)

=> 4.3 = 10.7 sin (2pi*t/69)

=> 4.3/10.7 = sin (2pi*t/69)

=> 0.4018691588785047 = sin (2pi*t/69)

=> 2pi*t/69 = arcsin( 0.4018691588785047)

=> 2pi*t/69 = 0.413557175447

=> t= 4.5438606856437898

Rounded to nearest day

t= 5 days