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erik [133]
3 years ago
13

I really need help with this calculus 1 question?

Mathematics
1 answer:
Dima020 [189]3 years ago
6 0

Answer:

a) The rate of change brightness after 't' years

  \frac{dB}{dt}  = 5.0+0.55cos(  \frac{2\pi(t) }{4.7})(\frac{2\pi }{4.7})

b) The rate of increase after five years

(\frac{dB}{dt})_{t=5}  = 0.67688

Step-by-step explanation:

a) Given B(t) = 5.0+0.55sin(\frac{2\pi(t) }{4.7}   .....(1)

The rate of change of the brightness after 't' days that is

\frac{dB}{dt}

now differentiating equation (1) with respective to 't'

\frac{dB}{dt}  = 5.0+0.55cos(  \frac{2\pi(t) }{4.7})\frac{d}{dt} (\frac{2\pi(t) }{4.7})       { using d/dx(sin x) =cos x}

\frac{dB}{dt}  = 5.0+0.55cos(  \frac{2\pi(t) }{4.7})(\frac{2\pi }{4.7})

b) The rate of increase after five days    

substitute t = 5 in equation dB/d t

\frac{dB}{dt}  = 5.0+0.55cos(  \frac{2\pi(5) }{4.7})(\frac{2\pi }{4.7})

after calculation (\frac{dB}{dt})_{t=5}  = 0.67688

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