Consider the cross-section below. A compressive load P is applied at any point (ex, ey) with respect to the principal axes x and y. The moment of P about these axes are respectively
Problem
A rectangular waterfront lot has a perimeter of 1000 feet. To create a sense of privacy, the lot owner decides to fence along three sides excluding the sides that fronts the water. An expensive fencing along the lot’s front length costs Php25 per foot, and an inexpensive fencing along two side widths costs only Php5 per foot. The total cost of the fencing along all three sides comes to Php9500. What is the lot’s dimensions?
| A. 300 feet by 100 feet | C. 400 feet by 200 feet |
| B. 400 feet by 100 feet | D. 300 feet by 200 feet |
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).
Problem
The number of hours daylight, D(t) at a particular time of the year can be approximated by
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 |
Problem
The local weather forecaster says “no rain” and his record is 2/3 accuracy of prediction. But the Federal Meteorological Service predicts rain and their record is 3/4. With no other data available, what is the chance of rain?
| A. 3/5 | C. 1/6 |
| B. 1/4 | D. 5/12 |
Problem
Find the term that is independent of x in the expansion of $\left( 2 + \dfrac{3}{x^2} \right)\left( x - \dfrac{2}{x} \right)^6$.
| A. 180 | C. -140 |
| B. 160 | D. -160 |
Problem
A spider eats three flies a day. Until he fills his quota, he has an even chance of catching any fly that attempts to pass. A fly is about to make the attempt. What are the chances of survival, given that five flies have already made the attempt today?
| A. 1/2 | C. 3/4 |
| B. 1/4 | D. 2/3 |
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.
A solid is a general prismatoid if
Where a, b, c, and d are arbitrary constants which may be positive, negative, or zero.
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...
| A. 1/16 | C. 1/12 |
| B. 1/24 | D. 0 |
| A. 1/16 | C. 1/12 |
| B. 1/24 | D. 0 |
| A. 3/8 | C. 1/16 |
| B. 23/24 | D. 5/12 |
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