• Math Archive: Questions from 2024-06-21

    A) The submersible that is missing near the wreck of the Titanic has one viewing port (window) that is circular with a diameter of 21 inches. Determine the force on this window at the depth of the Titanic wreck which is at 12, 500 feet. B) Determine the force on the window shown in the following illustration: Where I (the chord length) is given by 2(R2 − d2)1/2
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    A spherical balloon is being deflated at 7 in3/sec. At what rate is the radius changing when the radius is 5 in? A conical tank (point down) with height 15 ft and base radius 30 ft is filled with water so the depth of the water is increasing at a constant rate of 5 ft/hr. At what rate is volume of the water changing when the water is 10 ft deep?
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    A particle moves along a vertical line (up is the positive direction) so that its position at time t is given by s(t) = 16t − t3, t ≥ 0 (a) At what time(s) does the particle stop? (b) Is the particle speeding up or slowing down at t = 1? t = 3?
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