Mathworldcom Classification Geometry Plane Geometry Rectangles Moe uses a mower

Mathworldcom classification geometry plane geometry

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Mathworld.com Classification: Geometry > Plane Geometry > Rectangles
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Moe uses a mower to cut his rectangular 90-foot by150-foot lawn. The swath he cuts is 28 inches wide,but he overlaps each cut by 4 inches to make surethat no grass is missed. He walks at the rate of 5000feet per hour while pushing the mower. Which of thefollowing is closest to the number of hours it will takeMoe to mow his lawn? (A)0.75(B)0.8(C)1.35(D)1.5(E)3 2003 AMC 10 B, Problem #52003 AMC 12 B, Problem #4“Moe cuts about two square feet for each foot hepushes the mower forward.” Difficulty: Medium-hard NCTM Standard: Geometry Standard for Grades 9–12: Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships. Mathworld.com Classification: Geometry > Plane Geometry > Miscellaneous Plane Geometry > Area
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Many television screens are rectangles that are measured by the length of their diagonals. The ratio of the horizontal length to the height in a standard television screen is 4 : 3 . The horizontal length of a “27-inch” television screen is closest, in inches, to which of the following? Diagonal Height (A) 20 (B) 20 . 5 (C) 21 (D) 21 . 5 (E) 22 2003 AMC 10 B, Problem #6 2003 AMC 12 B, Problem #5 “The height, length, and diagonal are in the ratio 3 : 4 : 5 .” Solution Answer (D): The height, length, and diagonal are in the ratio 3 : 4 : 5 . The length of the diagonal is 27, so the horizontal length is 4 5 (27) = 21 . 6 inches . Difficulty: Medium-hard NCTM Standard: Geometry Standard for Grades 9–12: Use trigonometric relationships to determine lengths and angle measures. Mathworld.com Classification: Geometry > Trigonometry > General Trigonometry
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The symbolism b x c denotes the largest integer not exceeding x . For example, b 3 c = 3 , and b 9 / 2 c = 4 . Compute b 1 c + b 2 c + b 3 c + · · · + b 16 c . (A) 35 (B) 38 (C) 40 (D) 42 (E) 136 2003 AMC 10 B, Problem #7 “Let ( a +1) 2 x < a 2 , for some integer x and a . b x c = a - 1 .” Solution Answer (B): The first three values in the sum are 1, the next five are 2, the next seven are 3, and the final one is 4 for a total of 3 · 1 + 5 · 2 + 7 · 3 + 1 · 4 = 38 . Difficulty: Medium NCTM Standard: Number and Operations Standard for Grades 9–12: Understand meanings of operations and how they relate to one another. Mathworld.com Classification: Number Theory > Rounding > Floor Function
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  • Winter '13
  • Kramer
  • Natural number, Prime number, Geometric progression

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