ENM1500 Introductory engineering mathematics Assignment

Question 1.

Figure 1 shows the circular cross-section of an oil pipeline. Given are the maximal depth of the oil, h, and radius of the pipe, r. Find the area S occupied by the air above the oil. Your answer will be a formula S = ... containing h and r in the right-hand side.

Question 2.

Because of the Earth curvature, an observer can only see as far as the horizon. In order to view distant land objects an observer needs to rise above the surface. A communications satellite is positioned in a very high stationary orbit directly above the Earth’s equator. What is the hight of the orbit, h, if the most distant object the satellite can see on land is located at the distance l measured along a straight line from the satellite? The radius of the Earth is R. Make a sketch. Your answer will be a formula h = ... containing R and l in the right-hand side.

Question 3.

There exist three angles, namely ?/6, ?/4 and ?/3, for which sine and cosine have exact values presented by ordinary fractions. Determine exact values of

Question 4.

Find all angles ? in radians from the range 2? < ? < 4>

Question 5.

A patio has a non-rectangular shape as shown in Figure 2. Note two right [50 marks] angles in the Figure marked by little squares. Determine the area S of the patio in terms of the angles ? and ? and side length a. Your answer will be a formula S = ... containing symbols ?, ? and a in the right-hand side.

Question 6.

For the vectors a = (3, ?1, 0), b = (2, 3, 1) and c = (?4, 5, 1) find