Question
Asked Dec 17, 2019
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Variable stars are ones whose brightness varies periodically. The brightness of a certain star is modeled by the function
b(t) = 8.5 – 2.6 cos( t)
158
where t is measured in days.
(a) Find the period.
days
(b) Find the maximum and minimum brightness.
(minimum)
(maximum)
(c) Graph the function b.
8,5
316
79
8.5-
8.5
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Variable stars are ones whose brightness varies periodically. The brightness of a certain star is modeled by the function b(t) = 8.5 – 2.6 cos( t) 158 where t is measured in days. (a) Find the period. days (b) Find the maximum and minimum brightness. (minimum) (maximum) (c) Graph the function b. 8,5 316 79 8.5- 8.5

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Expert Answer

Step 1

To find the period we divide 2pi by coefficient of t. 

Answer(a): Period = 316 days

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b(t)=8.5-2.6cos 158 2n =2(158)=316 Period= 158

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Step 2

cos theta lies between -1 to 1. 

We use that to find max and min.

Answer(b) : Mi...

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-1<cos -t|<1 -1(-2.6)2-2.6cos 158 -t>1(-2.6) [multiply by -2.6] 2.62-2.6cos( 158 2-2.6 -t)28.5-2.6 [add 8.5] 8.5+2.6>8.5-2.6cos( 158 11.128.5-2.6cos()25.9 158 5.9<8.5-2.6cos( - (11.1 158

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Math

Calculus