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
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
Find the area of the largest right triangle whose hypotenuse is fixed at c.
Problem
A tour bus has 80 seats. Experience shows that when a tour costs P28,000, all seats on the bus will be sold. For each additional P1,000 charged, however, 2 fewer seats will be sold. Find the largest possible revenue.
A. P29,000
B. P28,500
C. P28,900
D. P28,700
A gutter whose cross-section is trapezoidal is to be made of galvanized iron sheet of 24 m wide. If its carrying capacity is maximum, find the dimension of the base.
A. 4 m
B. 6 m
C. 8 m
D. 10 m
Problem
The line y = 2x + 8 intersects the parabola y = x2 at points A and B. Point C is on the parabolic arc AOB where O is the origin. Locate C to maximize the area of the triangle ABC.
Problem 01
A 5-m line AD intersect at 90° to line BC at D so that BD is 2 m and DC = 3 m. Point P is located somewhere on AD. The total length of the cables linking P to points A, B, and C is minimized. How far is P from A?
Problem 1
Show that the largest triangle of given perimeter is equilateral.
