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Numbers and Their Application to Math and Science

Homework for Numbers Lesson 11

Note: all values should be given as exact, which means in simplified radical form. (Remember to rationalize the denominator, if necessary.) Decimal approximations are optional, also lend completeness, but must be clearly identified as approximations.

  1. Using the Pythagorean Theorem in its three dimensional form (a2 + b2 + c2 = d2), find and simplify the three face diagonals and the body diagonal of a parallelopiped (box/cuboid) with a = 240, b = 44, c = 117.

     

     

  2. Using the Pythagorean Theorem in its three dimensional form (a2 + b2 + c2 = d2), find and simplify the three face diagonals and the body diagonal of a parallelopiped (box/cuboid) with a = 104, b = 153, c = 672.

     

     

  3. Find the length of the hypotenuse of a right triangle if the other sides are the same length of 5.

     

     

  4. Given the hypotenuse of an isosceles right triangle as 12, what are the lengths of the other two sides.

     

     

  5. Given a 30°-60°-90° triangle with the hypotenuse 14, find the lengths of the other two sides.

     

     

  6. Given a 30°-60°-90° triangle with the side opposite the 60° angle being 12, find the length of the other two sides.

     

     

  7. Find the distance between the points (-12, 6) and (4, -6).

     

  8. Find the distance between the two points (3,5) and (1, -1).

     

  9. Driving to Dairy Queen from the MSC, you go 1/4 a mile to the left. The road bends (90°) to the right, and you proceed on for another mile to Main street. At Main Street, you take a left and continue for another 2 miles. Dairy Queen will be on the left side of the road. If you happened to walk directly from MSC to Dairy Queen, how many miles would you save by not driving?

     

     

  10. George lives 5 miles north and 2 miles east of the MSC, while Jenni lives 1 mile west and three miles south of the MSC. How far apart do they live? (Assume a flat earth!)

     

     

  11. A circle is the set of points equidistant from a given point. If (4,2) is the center with (6,3) on the circle, prove that (2,3) is also on the circle. Note: (x - h)2 + (y - k)2 = r2 gives the relationship for a circle centered at (h,k) with radius r.

     

     

  12. The distance from point A to (3,2) is 15. Find point A. How many answers could you have?

     

     

  13. Verify rows 3 through 5 of the Fermat-Catalin Conjecture table.

     

     

  14. Verify that Goldbach's Conjecture is true for 58 and 74. How many different sums satisfy Goldbach's Conjecture for 58? For 74? (An example is 78: 71 + 7 = 11 + 67 = 17 + 61)

     

     

  15. Read section 8.6 in your geometry textbook and look at problems 8.6: 12-14, 20-21, 24.

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