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Numbers and Their Application to Math and Science

Odd Solutions for HW Numbers Lesson 14

  1. Evaluate the following rational number and compare it to e:   58,291/21,444.
    A. e = 2.718281828..., Correct to
    58291/21444 = 2.718289498...; 5 decimal places

  3. Find a numeric decimal approximation for the real number halfway between e and [pi].
    A. (e + [pi])/2 [approximately equal to] 2.929937241024...

  5. Find the circumference of a circle with diameter of 7", using the approximation [pi] [approximately equal to] 22/7.
    A. C = [pi] d [approximately equal to] (22/7)7" = 22"

  7. Give, to the nearest hundredth square foot, the area that can be irrigated by a circular sprinkler 60' long rotating around a fixed point. Give the circumference of the region to the nearest tenth foot.
    A. A = [pi] r2 = [pi](60')2 = 11309.73 sq.ft.
    C = 2 [pi] r = 2[pi](60') = 377.0'

  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?
    A. 12" is the diameter. Area: 82/62 = 1.777...times
    The slice area is 64[pi]/6 [approximately equal to] 33.51 sq.in.

  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? Why is your number different?
    A. [pi], Slippage or other errors.

  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 sheik's steward do it? How many camels did each son get?
    A. The steward adds his camel to 17 and thus,
    1/9 = 2, 1/2 = 9, 1/3= 6 leaving his camel.

  15. Add the first, then the second, then the 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)?
    A. The sum of terms one by one: 4, 2.666...,
    It is approximating [pi].

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

    A. log381 is the same as saying 3x = 81, so x = 4.
    log10100 = 2, since 102 = 100.
    log93 = 1/2, since the square root of 9 is 3.

  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??? Bonus for bringing in a picture or demonstrating how used?

    A.

  20. Read sections 8.8 in your geometry textbook. Do problems 8.8: 2,3,6,8,11.
    2.
    3. Estimate the area to the nearest square inch of a circle with radius 70".
    Answer: 702 = 15,394 in2

    6.
    8.
    11. Use concentric circles of x and 4x radii. If a dart lands randomly in the large circle, find the probability it will land

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