Waste less time on Facebook — follow Brilliant.
Related Rates
How does pressure change in a combustion engine? How fast does the water level rise when filling a pool? Calculus quantifies the impact of change on areas, angles, distances, temperatures, and more.
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 \(a?\)
