Question

3.9 1. Balloons A spherical balloon is inflated and its volume increases at a rate of 15 in/min. What is the rate of change of its radius when the radius is 10 in? 2. Ladder against the wall A 13-foot ladder is leaning against a vertical wall (see figure) when Jack begins pulling the foot of the ladder away from the wall at a rate of 0.5 ft/s. How fast is the top of the ladder sliding down the wall when the foot of the ladder is 5 ft from the wall? 13 3. A lighthouse problem A lighthouse stands 500 m off a straigh shore, and the focused beam of its light revolves (at a constant rate) four times each minute. As shown in the figure, P is the point on shore closest to the lighthouse and Q is a point on the shore 200 m from P. What is the speed of the beam along the shore when it strikes the point Q? 500 m 200 m

Answer 1

volume of Sphere Ev) = 4 TV3 at Paking derivative with respect to time olu = H па (3) 놋 닐 (31220) = 41522 do 15 in3/min, r= to in. dv at ho (312.2014) JE Әу It so 15 in/min HIT (30 in)2 ar at Ir 0.0375 din 2/min. gt T So rate of 0.0375 in/min or change of radious 0.0119-39 in2/min is