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Numbers and Their Application to Math and Science

Homework for Numbers Lesson 14

  1. Evaluate the following rational number and compare it relative to e:    58,291/21,444.

     

  2. Evaluate the following rational number and compare it relative to e2:    158,452/21,444.

     

  3. Find a numeric decimal approximation for the real number halfway between e and [pi].

     

  4. Find a numeric decimal approximation for the real number halfway between [pi]e and e[pi].

     

  5. Find the circumference of a circle with diameter of 7", using the approximation [pi] [approximately equal to] 22/7.

     

  6. Find the exact and approximate area for a circle with radius 5 m. (Be sure to include proper units!)

     

  7. Give, to the nearest hundredth square foot, the area that can be irrigated by a circular sprinkler that spouts water 60' as it rotates around a fixed point. Give the circumference of the region to the nearest tenth foot.

     

  8. A circle has area 100[pi] sq. in. Find the exact radius, diameter, and circumference.

     

  9. On a 12" pizza, what does the 12" refer to? How many times as much of each ingredient is needed for a 16" pizza with the same thickness? What is the area of each slice when a 16" pizza is divided evenly among 6 people? (see textbook 8.8:10).

     

  10. Eight metal disks equally, but maximally sized, are cut out of a metal sheet 18" by 36". The rest is not used. What is the area of the metal that is not used? What percent of the metal is used? (see textbook 8.8:12).

     

  11. Find a can or bottle with a circular base. Measure the diameter (d) as accurately as possible. Measure the circumference (C) with a tape measure or by rolling the can on the ruler. Calculate the C/d ratio to the nearest hundredth. What number should it approximate? Explain any difference?

  12. Find which ordinal number corresponds to Andrew Jackson's presidency (as in which president was he?) and what year he was first elected. Relate this information to the number e.

     

  13. A sheik dies with 3 sons and 17 camels. Earlier he had told his steward to give the youngest son 1/2 his camels; his middle son 1/3 his camels; and his oldest son 1/9 his camels. Without any fractional camels, how did the steward do it? How many camels did each son get? (This is a puzzle question.)

     

  14. Add the first, then second, then third, ... terms in the following sequence: 0!-1 + 1!-1 + 2!-1 + 3!-1 + 4!-1 + 5!-1 + 6!-1 + 7!-1 + ... What transcendental number does the resulting series appear to approach?

     

  15. Add the first, then second, then third terms, ... in the following sequence: 4/1 - 4/3 + 4/5 - 4/7 + 4/9 - 4/11 + 4/13 - 4/15 + ... What transcendental number does the resulting series appear to approach (from above and below! and allbeit very slowly)?

     

  16. Convert 57° and 196° into radians and 5/9 into degrees.

     

  17. Evaluate: log381, log10100, and log93 without using a calculator.

     

  18. Convert log4x = 3 into exponential form and solve for x.

     

  19. Bonus: Look up Napier's Bones or Napier's Rods in an encyclopedia or dictionary. What were they? How many were there? What did they look like? How did they work? What specie bone were they?

     

  20. Read sections 8.8 in your geometry textbook. See problems 8.8: 2, 3, 6, 8 and 11.

     

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