Natalie Helmer's Potw
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The problem asks to determine without a calculator whether the square root of two or the cube root of three is greater. The square root of two is the length of the side of a unit square, and is approximately 1.414. The cube root of three is the length of the side of a unit cube with a volume of three, and is approximately 1.442. Therefore, the cube root of three is greater than the square root of two.
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Jordan's solution
The document defines the function f(f(x)) and shows that it equals x+1. It then defines f(f(f(x))) and shows that it equals 3+2x. It concludes that for these functions to be defined, x cannot equal -1 or 2.
Rp solution
The document summarizes how to simplify the expression of fractions with denominators following an i, -i pattern. It groups the fractions into pairs where the denominators differ by 2i. There are 13 such pairs, with one term left over. The summary combines all the terms to arrive at the final simplified expression of 27i.
Ryan Proctor's POTW solution
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Sarah’s potw
A right triangle with sides of 3, 4, and 5 units has an area of 6 square units and a perimeter of 12 units, so the area and perimeter have the same numerical value of 12.
Sarah’s potw
A right triangle with sides of 3, 4, and 5 units has an area of 6 square units and a perimeter of 12 units, so the area and perimeter have the same numerical value of 12.
Keegan’s potw solution
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Jordan's solution
The document defines the function f(f(x)) and shows that it equals x+1. It then defines f(f(f(x))) and shows that it equals 3+2x. It concludes that for these functions to be defined, x cannot equal -1 or 2.
Rp solution
The document summarizes how to simplify the expression of fractions with denominators following an i, -i pattern. It groups the fractions into pairs where the denominators differ by 2i. There are 13 such pairs, with one term left over. The summary combines all the terms to arrive at the final simplified expression of 27i.
Ryan Proctor's POTW solution
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Sarah’s potw
A right triangle with sides of 3, 4, and 5 units has an area of 6 square units and a perimeter of 12 units, so the area and perimeter have the same numerical value of 12.
Sarah’s potw
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Keegan’s potw solution
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Natalie Helmer's Potw
- 1. Natalie Helmer’s Problem of the Week 11/16/09
- 2. Without the use of a calculator determine which is greater in value, the square root of two or the cube root of three.