SOLUTION: The total solar radiation H on a particular surface during an average clear day is given by:
H=5000/T^2+10
where t (-6 < equal to or less than t < equal to or less than 6 ) i
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Question 328484: The total solar radiation H on a particular surface during an average clear day is given by:
H=5000/T^2+10
where t (-6 < equal to or less than t < equal to or less than 6 ) is the number of hours from noon. Note that 6 a.m. is equivalent to t = -6. Find the instantaneous rate of change of H with respect to t at 3 p.m.
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
\ =\ \frac{5000}{t^2\ +\ 10})
Use the Quotient Rule:
\ =\ \frac{\left(t^2\ +\ 10\right)\ -\ 10000t}{\left(t^2\ +\ 10\right)^2})
You want
\ =\ \frac{\left((3)^2\ +\ 10\right)\ -\ 10000(3)}{\left((3)^2\ +\ 10\right)^2})
You can do your own arithmetic.
You can also use the chain rule on this one:
Let 
Then
^2)
and
and
\left(\frac{du}{dt}\right)\ =\ -\frac{10,000t}{\left(t^2\ +\ 10\right)^2)
And again, you are seeking the value of
=\ -\frac{10,000(3)}{\left((3)^2\ +\ 10\right)^2)
John
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