maxima and minima
55 - Greatest angle subtended by a picture
Problem 55
The lower edge of the picture is a ft, the upper edge is b ft, above the eye of an observer. At what horizontal distance should he stand, if the vertical angle subtended by the picture is to be greatest?
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26-27 Horizontal rod entering into a room from a perpendicular corridor
Problem 26
A corridor 4 ft wide opens into a room 100 ft long and 32 ft wide, at the middle of one side. Find the length of the longest thin rod that can be carried horizontally into the room.
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24-25 Largest rectangle inscribed in a circular quadrant
Problem 24
Find the area of the largest rectangle that can be cut from a circular quadrant as in Fig. 76.
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23 - Sphere cut into a pyramid
Problem 23
A sphere is cut in the form of a right pyramid with a square base. How much of the material can be saved?
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22 - Smallest cone that may circumscribe a sphere
Problem 22
A sphere of radius a is dropped into a conical vessel full of water. Find the altitude of the smallest cone that will permit the sphere to be entirely submerged.
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20-21 Width of the second corridor for a pole to pass horizontally
Problem 20
A pole 27 feet long is carried horizontally along a corridor 8 feet wide and into a second corridor at right angles to the first. How wide must the second corridor be?
19 Direction of the man to reach his destination as soon as possible

Problem 19
A man on an island a miles south of a straight beach wishes to reach a point on shore b miles east of his present position. If he can row r miles per hour and walk w miles per hour, in what direction should he row, to reach his destination as soon as possible? See Fig. 57.
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17-18 A man in a motorboat needs to catch a bus
Problem 17
A man in a motorboat at A receives a message at noon, calling him to B. A bus making 40 miles per hour leaves C, bound for B, at 1:00 PM. If AC = 30 miles, what must be the speed of the boat, to enable the man to catch the bus?
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16 - Light placed above the center of circular area
Problem 16
A light is to be placed above the center of a circular area of radius a. What height gives the best illumination on a circular walk surrounding the area? (When light from a point source strikes a surface obliquely, the intensity of illumination is
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14-15 Ladder reaching the house from the ground outside the wall
Problem 14
A wall 10 ft high is 8 ft from the house. Find the length of the shortest ladder that will reach the house, when one end rests on the ground outside the wall.
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- 800 reads










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