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Calculus
Related Rates
Suppose a \(20 \text{ cm} \times 20 \text{ cm}\) rectangle is modified such that the width of a rectangle increases at a rate of \(10\) cm per second, while the length of the rectangle decreases at a rate of \(3\) cm per second. What is the ratio \[ \text{Width} : \text{Length} \] when the rate of change of the area of the rectangle is \(0?\)
The radius of a circle starts at \(10\text{ cm}\) and increases at the rate of \(1\text{ mm}\) per second. If \(S(t)\) is the area of the circle (in \(\text{cm}^2\)) after \(t\) seconds and \(S'(14) = a\pi \text{ cm}^2\text{/s},\) what is \(a?\)
