Problem
Mar wants to make a box with no lid from a rectangular sheet of cardboard that is 18 inches by 24 inches. The box is to be made by cutting a square of side x from each corner of the sheet and folding up the sides. Find the value of x that maximizes the volume of the box.

A.   4.3 inches C.   10.6 inches
B.   5.2 inches D.   3.4 inches

 

Problem
A farmer owned a square field measuring exactly 2261 m on each side. 1898 m from one corner and 1009 m from an adjacent corner stands Narra tree. A neighbor offered to purchase a triangular portion of the field stipulating that a fence should be erected in a straight line from one side of the field to an adjacent side so that the Narra tree was part of the fence. The farmer accepted the offer but made sure that the triangular portion was a minimum area. What was the area of the field the neighbor received and how long was the fence? Hint: Use the Cosine Law.

A.   A = 972,325 m2 and L = 2,236 m
B.   A = 950,160 m2 and L = 2,122 m
C.   A = 946,350 m2 and L = 2,495 m
D.   A = 939,120 m2 and L = 2,018 m

 

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 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