Complete Question
The complete question is shown on the first uploaded image
Answer:
Harry's hunger is [tex]H(t) = 7.5 cos (\frac{\pi}{2} t ) + 22.5[/tex]
Step-by-step explanation:
From the question we are told
The hunger of harry is [tex]H(t) = a \cdot cos (b \cdot t ) + d[/tex]
The hunger of harry is maximum at t = 0
The hunger of harry is minimum at t = 2 hours
The mass of pig desires at maximum hunger is [tex]H(0) = 30 \ kg[/tex]
The mass of pig desires at minimum hunger is [tex]H(2) = 15 \ kg[/tex]
Generally at maximum hunger we have
[tex]H(0) = a * cos (b* 0 ) +d = 30[/tex]
=> [tex]a * cos (0 ) +d = 30[/tex]
=> [tex]a + d = 30 --- [1][/tex]
Now at minimum hunger
[tex]H(2) = a* cos (2 b ) + d = 15[/tex]
[tex]a* cos (2 b ) + d = 15[/tex]
Generally the minimum value of [tex]cos (\theta ) = -1[/tex]
So
At minimum
[tex]cos (2b) = -1[/tex]
=> [tex]2b = cos^{-1} [-1][/tex]
Generally from trigonometric rules
[tex]cos^{-1} [-1] = (2n + 1 )\pi[/tex] here n = 0 , 1 , 2 , 3
Now since we are considering the minimum = 0
So
[tex]cos^{-1} [-1] = (2(0)+ 1 )\pi[/tex]
=> [tex]cos^{-1} [-1] = \pi[/tex]
So
[tex]2b = \pi[/tex]
=> [tex]b = \frac{\pi }{2 }[/tex]
So
[tex]a* cos (\pi ) + d = 15[/tex]
=> [tex]-a + d = 15 --- [2][/tex]
Adding [tex]equation\ (1 ) \ and \ (2)[/tex]
[tex]=> \ 2d = 45[/tex]
=> [tex]d = 22.5[/tex]
From equation 1
[tex]a + 22.5 = 30[/tex]
=> [tex]a = 7.5[/tex]
So we can represent the harry hunger as
[tex]H(t) = 7.5 cos (\frac{\pi}{2} t ) + 22.5[/tex]
