Set 12

Volcano

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A new volcano has suddenly appeared where a small strip mall used to be. You are the head of the intrepid surveying crew whose job it is to determine the height of the peak. Traveling bravely toward the volcano, you stop at a safe distance and measure an angle of elevation of 21� to the top. You continue resolutely for another half mile and measure an angle of elevation of 35�. You and your crew had better not get any closer just now — there’s a new spew of ash coming out from the peak. So retreat, do some calculating, and tell the waiting reporters just how tall the volcano is. (They’ll want the answer in feet, of course.)

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Crumbs on a Table

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A maid was about to wipe the crumbs off a rectangular table measuring 4 ft. by 8 ft. when the butler, a methodical type, took over. “You need a system!” he said. They both had very short arms and could only reach 2 feet with the dust cloth, so the butler decided to get all the crumbs together at center point C along one side. He walked along the opposite side, AB, pushing all the crumbs as far as he could directly toward C, and then did the same thing walking down each end; finally he went to the other long side to pull everything toward the dustpan. When he finished, the maid complained. Why?

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Width of Alley

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In a narrow, sinister alley of width w a ladder of length a is placed with its foot at point P between the walls. Resting against one wall at Q, a distance k above the ground, the ladder makes a 45° angle with the ground. Resting against the other wall at R, a distance h above the ground, the ladder makes a 75° angle with the ground. The width of the alley is equal to

  1. a
  2. RQ
  3. k
  4. (h + k)/2
  5. h

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Defined Operation 2; 5 Parts

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The operation x,y is defined by x,y = (x + 1)(y + 1) – 1 = xy + x + y. Which of these statements is false?

  1. x,y = y,x for all real x and y.
  2. x,(y + z) = (x,y) + (x,z) for all real x, y, and z.
  3. (x – 1),(x + 1) = (x,x) – 1 for all real x and y.
  4. x,0 = x for all real x.
  5. x,(y,z) = (x,y),z for all real x, y, and z.

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