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In Exercises 5-8, assume that the radius $r$ of a sphere is expanding at a rate of 30 $\mathrm{cm} / \mathrm{min.}$ The volume of a sphere is $V=\frac{4}{3} \pi r^{3}$ and its surface area is 4$\pi r^{2} .$ Determine the given rate. Volume with respect to time when $r=15 \mathrm{cm}$
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Textbook problem
Jacob F.
A laser pointer is placed on a platform that rotates at a rate of 20 revolutions per minute. The beam hits a wall 8 $\mathrm{m}$ away, producing a dot of light that moves horizontally along the wall. Let $\theta$ be the angle between the beam and the line through the searchlight perpendicular to the wall (Figure 10). How fast is this dot moving when $\theta=\frac{\pi}{6} ?$
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