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## 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.

# Word Problems - Basic

A $$13\text{ feet}$$ long ladder is leaning against a wall and sliding toward the floor. If the foot of the ladder is sliding away from the base of the wall at a rate of $$17\text{ feet/sec},$$ how fast is the top of the ladder sliding down the wall (in feet/sec) when the top of the ladder is $$5\text{ feet}$$ from the ground?

At time $$t=0 \mbox{ s}$$, the radius of a circle is equal to $$19 \mbox{ cm}$$. The radius of the circle increases at a rate of $$\frac{1}{2} \ \mbox{cm/s}$$. The rate of change of area at $$t=18 \mbox{ s}$$ is equal to $$m\pi \ \mbox{cm}^2\mbox{/s}$$, where $$m$$ is a positive integer. What is the value of $$m$$?

Throwing a stone in a calm lake forms concentric ripples, as shown in the above picture. If the radius of one ripple increases at the rate of $$10 \text{cm}$$ per second, what is the rate of increase of the area of the ripple $$2$$ seconds after a stone is thrown (in $$\text{cm}^2/\text{s}$$)?

During a rainstorm, the area of a circular pool of water increases at the rate of $$4000\pi\text{ in}^2\text{/sec}.$$ At what rate is the radius expanding (in inches/sec) when the radius is $$200\text{ inches}?$$

A point is moving along the parabola $$x+5y^2=0$$ toward the origin with $$x$$-coordinate increasing at the rate of $$5\text{ units/s}$$ and $$y$$-coordinate positive. How fast is the point moving in terms of the remaining distance to the origin as it passes through the point $$(-5,1)$$ on the parabola?

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