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A hot-air balloon is released at 1:00 P.M. and rises vertically at a rate of 6 m/sec. An observation point is situated 100 meters from a point on the ground directly below the balloon (see the figure). If t denotes the time (in seconds) after 1:00 P.M., express the distance d between the balloon and the observation point as a function of t, and simplify completely.
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