A spherical balloon is inflating with helium at a rate of 320x ft / min. How fast is the balloon's radius increasing at the instant the radius is 4 ft? How fast is the surface area increasing? The balloon's radius is increasing at a rate of ft / min at the instant the radius is 4 ft. (Simplify your answer.)A light shines from the top of a pole 50 ft high. A ball is dropped from the same height from a point 40 it away from the light. How fast is the shadow of the ball moving Ball at time t=0 along the ground sec later? (Assume the ball falls a distance s = 161- in t sec.) sec later 50-ft pole Shadow 40 X x(t) The shadow is moving at a velocity of |ft/sec. (Type an integer or a decimal.)A lighthouse stands 525 m off a straight shore and the focused beam of its light revolves four times each minute. As shown in the figure, P is the point on shore closest to the Lighthouse . lighthouse and Q is a point on the shore 325 m from P. What is the speed of the beam along the shore when it strikes the point Q? 525 m TOP 325 m . . . Let x be the distance along the shore from point P to the beam and let 0 be the angle through which the light revolves. Write an equation that relates x and 0