The Tide in Bay of Fundy: The Depths of High and Low Tides

Problem
The tide in Bay of Fundy rises and falls every 13 hours. The depth of the water at a certain point in the bay is modeled by a function d = 5 sin (2π/13)t + 9, where t is time in hours and d is depth in meters. Find the depth at t = 13/4 (high tide) and t = 39/4 (low tide).

  1. The depth of the high tide is 15 meters and the depth of the low tide is 3 meters.
  2. The depth of the high tide is 16 meters and the depth of the low tide is 2 meters.
  3. The depth of the high tide is 14 meters and the depth of the low tide is 4 meters.
  4. The depth of the high tide is 17 meters and the depth of the low tide is 1 meter.

 

Longest Day of the Year: Summer Solstice

Problem
The number of hours daylight, D(t) at a particular time of the year can be approximated by
 

$D(t) = \dfrac{K}{2}\sin \left[ \dfrac{2\pi}{365}(t - 79) \right] + 12$

 

for t days and t = 0 corresponding to January 1. The constant K determines the total variation in day length and depends on the latitude of the locale. When is the day length the longest, assuming that it is NOT a leap year?

A.   December 20 C.   June 20
B.   June 19 D.   December 19

 

The Prismatoid and the Prismoidal Formula

The General Prismatoid

A general prismatoid is a solid such that the area of any section, say Ay, parallel to and distant y from a fixed plane can be expressed as a polynomial of y of degree not higher than the third.
 

general-prismatoid.jpg

 

A solid is a general prismatoid if

$A_y = a + b_y + cy^2 + dy^3$

Where a, b, c, and d are arbitrary constants which may be positive, negative, or zero.
 

Probability That 1, 2, 3, 4 of the Recruits Will Receive the Correct Size of Boots

Situation
Four army recruits went to the supply room to get their military boots. Their shoe sizes were 7, 8, 9 & 10. The supply officer, after being informed of their sizes, prepared the four pairs of boots they need. If the boots are handed to each of the four recruits at random, what is the probability that...

  1. exactly 3 of them will receive the correct shoe size?
    A.   1/16 C.   1/12
    B.   1/24 D.   0

     

  2. all of them will receive the correct shoe size?
    A.   1/16 C.   1/12
    B.   1/24 D.   0

     

  3. none of them will receive the correct shoe size
    A.   3/8 C.   1/16
    B.   23/24 D.   5/12

 

11 - Distance Traveled By A Messenger From Rear To Front Then Back To Rear Of A Marching Battalion

Problem
A battalion, 20 miles long, advances 20 miles. During this time, a messenger on a horse travels from the rear of the battalion to the front and immediately turns around, ending up precisely at the rear of the battalion upon the completion of the 20-mile journey. How far has the messenger traveled?