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.
$${\bf A} = 2{\bf i} + b{\bf j} + {\bf k}$$

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