Problem
A grade of -5% is followed by a grade of 1%, the grades intersecting at the vertex (Sta. 10 + 060). The change of grade is restricted to 0.4% in 20 m. Compute the length of the vertical parabolic sag curve in meters.

Problem
A tensile load of 8000 kg elongates a 1-m long square rod by 1 mm. Steel modulus of elasticity is 2 × 10⁶ kg/cm². What is the dimension of a side of the rod?

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

Problems
A compound curve has the following characteristics:

Compute the stationing of P.C.C.

Problem
The sum of the first n terms of a series is 3^(2n - 1) + b. What is the quotient of the 9^th and the 7^th term?

Problem
Compute the value of b if A and B are orthogonal.
$${\bf A} = 2{\bf i} + b{\bf j} + {\bf k}$$

$${\bf B} = 4{\bf i} - 2{\bf j} - 2{\bf k}$$

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.
 

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