The length of a rectangle is 5t+6 and its height is t^6 , where t is time in seconds and the dimensions are in inches. Find the

rate of change of area, A, with respect to time

Mathematics

1 answer:

Nataly_w [17]2 years ago

7 0

$\bf \textit{area of a rectangle}\\\\
A=l\cdot w\qquad 
\begin{cases}
l=length\\
w=width\\
-----\\
l=5t+6\\
w=t^6
\end{cases}\implies A(t)=(5t+6)t^6
\\\\\\
A(t)=5t^7+6t^6\implies \cfrac{dA}{dt}=35t^6+36t^5$

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