Problem
A +0.8% grade meets a -0.4% grade at km 12 + 850 with elevation 35 m. The maximum allowable change in grade per station is 0.2%. Determine the length of the curve.

Problem
Find y’ if x = 2 arccos 2t and y = 4 arcsin 2t.

Situation
If a chord is selected at random on a fixed circle what is the probability that its length exceeds the radius of the circle?

1. Assume that the distance of the chord from the center of the circle is uniformly distributed.

   A.   0.5	C.   0.866
   B.   0.667	D.   0.75

2. Assume that the midpoint of the chord is evenly distributed over the circle.

   A.   0.5	C.   0.866
   B.   0.667	D.   0.75

3. Assume that the end points of the chord are uniformly distributed over the circumference of the circle.

   A.   0.5	C.   0.866
   B.   0.667	D.   0.75

Problem
A regular octagon is made by cutting equal isosceles right triangles out from the corners of a square of sides 16 cm. What is the length of the sides of the octagon?

Problem
How many minutes after 3:00 o’clock will the hands of the clock be perpendicular to each other for the 1st time?

Problem
Divide the circle of radius 13 cm into four parts by two perpendicular chords, both 5 cm from the center. What is the area of the smallest part.
 

Situation
A beam 100 mm × 150 mm carrying a uniformly distributed load of 300 N/m rests on three supports spaced 3 m apart as shown below. The length x is so calculated in order that the reactions at all supports shall be the same.
 

1.   Find x in meters.

2.   Find the moment at B in N·m.

3.   Calculate the reactions in Newton.

Situation
A beam of uniform cross section whose flexural rigidity EI = 2.8 × 10¹¹ N·mm², is placed on three supports as shown. Support B is at small gap Δ so that the moment at B is zero.
 

1.   Calculate the reaction at A.

2.   What is the reaction at B?

3.   Find the value of Δ.