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A swimmer is in the sea at a distance k miles from the nearest point A on a
straight shore. The house of the swimmer is on the shore at a distance 1 miles
from the point A. He can swim at a speed of u miles per hour and walk at a
speed of v miles per hour (v > u). At what point of the shore should he land,
so that he reaches his house in the shrtest possible time. Find the shorted he land,
so that he reaches his house in the shrtest possible time . Find the shortest time
also.
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| Show that the semi vertical angle of the cone of maximum volume and of giv |
| slant height is |
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Show that a closed rright circular cylinder of given total surface area and
maximum volume is such that its height is equal to the diameter of its base.
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Prove that a cylindrical vessel of given volume requires the least surface area
when its height is twice its radius.
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A conical tent of given capacity has to be construcetd. Find the ratio of the
height to the radius of the base or the minimum amount of the canvas required for the tent
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Find the height of the right circular cylinder of maximum volume that can be
inscribed in a sphere of radius 3 inch
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