Problem
A job posted at jobstreet.com offered a starting salary of \$40,000 per year and guaranteeing a raise of \$1600 per year for the rest of 5 years. Write the general term for the arithmetic sequence that models potential annual salaries.
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.
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?
Problem 910
A timber beam AD, 6 in. thick by 10 in. high and loaded as shown in Figure P-910, is pinned at its lower end and supported by a horizontal cable CE. Compute the maximum compressive stress developed in the beam.
Problem 909
The bent steel bar shown in Figure P-909 is 200 mm square. Determine the normal stresses at A and B.
Problem
Samuel Pepys wrote Isaac Newton to ask which of three events is more likely: that a person get (a) at least 1 six when 6 dice are rolled (b) at least two sixes when 12 dice are rolled, or (c) at least 3 sixes when 18 dice are rolled. What is the answer?
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.
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 |
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.
| A. 49.8° | C. 39.2° |
| B. 50.8° | D. 40.2° |
Problem
Three marksman simultaneously shoot and hit a rapidly spinning spherical target. What is the probability that the three points of impact lie on the same hemisphere?
| A. 0 | C. 1 |
| B. 1/2 | D. 2/3 |
Problem
A 150 mm by 300 mm wooden beam having a simple span of 6 meters carries a concentrated load P at its midspan. It is notched at the supports as shown in the figure. For this problem, all calculations are based on shear alone using the 2010 NSCP specification given below. Allowable shear stress of wood, Fv = 1.0 MPa.
NSCP 2010 Section 616.4: Horizontal Shear in Notched Beams
When rectangular-shaped girder, beams or joists are notched at points of support on the tension side, they shall meet the design requirements of that section in bending and in shear. The horizontal shear stress at such point shall be calculated by:
Where:
