May 2016

Dimensions of the Lot for a Given Cost of Fencing

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

 

Amount of Sales Needed to Receive the Desired Monthly Income

Problem
A salesperson earns \$600 per month plus a commission of 20% of sales. Find the minimum amount of sales needed to receive a total income of at least \$1500 per month.

A.   \$1500 C.   \$4500
B.   \$3500 D.   \$2500

 

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.

 

Number of days the project delayed

Problem
A contractor estimates that he could finish a project in 15 days if he has 20 men. At the start, he hired 10 men then after 6 days, 10 more men are added. How many days was the project delayed?

A.   5 C.   6
B.   3 D.   4

 

Answer Key

The Distance the Particle Travels with Given Position Function x(t) = t^4 - 8t^2

Problem
Given the position function x(t) = t4 - 8t2, find the distance that the particle travels at t = 0 to t = 4.

A.   160 C.   140
B.   150 D.   130

 

Answer Key

 

Weight of Copper and Tin to Produce an Alloy of 30% Copper and 10% of Tin

Problem
A given alloy contains 20% copper and 5% tin. How many pounds of copper and of tin must be melted with 100 lb of the given alloy to produce another alloy analyzing 30% copper and 10% tin? All percentages are by weight.

A.   20.5 lb copper and 4.5 lb tin
B.   17.5 lb copper and 7.5 lb tin
C.   19.5 lb copper and 5.5 lb tin
D.   18.5 lb copper and 6.5 lb tin

 

2016-may-math-mixture-problem-copper-tin-alloy.gif

 

Nutrition: Amount of food A, B and C to Meet the Nutrient Requirements

Problem
A nutritionist in a hospital is arranging special diets that consist of a combination of three basic foods. It is important that the patients on this diet consume exactly 310 units of calcium, 190 units of iron, and 250 units of vitamin A each day. The amounts of these nutrients in one ounce food are given in the following table.
 

  Units Per Ounce
Calcium Iron Vitamin A
Food A 30 10 10
Food B 10 10 30
Food C 20 20 20

 

How many ounces each food must be used to satisfy the nutrient requirements exactly?

A.   6 ounces of Food A, 5 ounces of Food B and 3 ounces of Food C
B.   3 ounces of Food A, 5 ounces of Food B and 6 ounces of Food C
C.   6 ounces of Food A, 3 ounces of Food B and 5 ounces of Food C
D.   5 ounces of Food A, 3 ounces of Food B and 6 ounces of Food C

 

Strength of Temporary Earth Retaining Wall Made from Wooden Planks

Situation
A temporary earth retaining wall consists of wooden plank driven vertically into the ground. The wall is designed to resist 2.4 m height of soil.

Given the following:
Cross-sectional dimensions of the plank = 300 mm wide × 75 mm thick
Allowable bending stress of the plank = 10.4 MPa
Allowable shear stress of the plank = 0.8 MPa
Unit weight of retained soil = 17.3 kN/m3
Active earth pressure coefficient = 1/3

1.   Calculate the maximum flexural stress.

A.   12.7 MPa C.   8.6 MPa
B.   14.2 MPa D.   10.1 MPa

2.   Calculate the maximum shear stress.

A.   1.11 MPa C.   0.99 MPa
B.   0.33 MPa D.   0.77 MPa

3.   Calculate the minimum thickness of the plank to prevent failure.

A.   90 mm C.   110 mm
B.   80 mm D.   100 mm

Burning Bale from Catapult to Travel 150 ft and Clear Over 35 ft Castle Wall

Problem
A catapult is placed 100 ft from the castle wall, which is 35 feet high. The soldier wants the burning bale of hay to clear the top of the wall and land 50 feet inside the castle wall. If the initial velocity of the bale is 70 feet per second, then at what angle should the bale of hay be launched so that it travel 150 feet and pass over the castle wall. Use g = 32 ft/sec2.
 

2016-may-math-catapult.jpg

 

A.   49.8° C.   39.2°
B.   50.8° D.   40.2°

 

Equation of the Diameter of Parabola Bisecting Parallel Chords of Given Slope

Problem
A parabola has an equation of y2 = 8x. Find the equation of the diameter of the parabola, which bisect chords parallel to the line xy = 4.

A.   y = 2 C.   y = 4
B.   y = 3 D.   y = 1

 

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