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# The width of a rectangle is 8 inches and remains constant, while the length of the rectangle increases at a constant rate of 3 inches per minute. When the length of the rectangle is 6 inches, what is the rate of change, in inches per minute, of the length of a diagonal in the rectangle?

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jeanette54

check the picture below thus  $\bf r^2=x^2+y^2\impliedby \textit{now, "y" is a constant, thus }\implies r^2=x^2+64 \\\\\\ 2r\cfrac{dr}{dt}=2x\cfrac{dx}{dt}+0\implies \cfrac{dr}{dt}=\cfrac{x\frac{dx}{dt}}{r}\quad \begin{cases} x=6\\ \frac{dx}{dt}=3\\ r=\sqrt{x^2+y^2}\\ \qquad \sqrt{6^2+64}\\ \qquad 10 \end{cases} \\\\\\ \cfrac{dr}{dt}=\cfrac{6\cdot 3}{10}$

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