MATHalino

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.