Civil and Environmental Engineering Answers

The following consecutive readings were taken with a level and a 4-metre leveling staff on a continuously sloping ground at common intervals of 30 m:

0.855 (on A), 1.55 m, 2,335, 3.825, 0.455, 1.380, 2.055, 2.855, 3.455, 0.585, 1.015, 1.850, 2.755, 3.845 (on B).

The RL of A was 380.500. Make entries in a level book and apply the usual checks. Determine the gradient of AB.

A 30 m steel tape was standardised at a temperature of 20^o C and under a pull 5 kg. The tape was used in catenary to fix a distance of 28 m between two points at 40^o C and under a pull of 5 kg. Given that the cross-sectional area of the tape = 0.02 cm², total weight 470 g. Young’s modulus of steel = 2.1 X 10⁶ kg/cm, and coefficient of linear expansion = 11 x10^-6per ^oC, (a) find the correct distance between the points, and (b) find the value of pull for which the measured distance would be equal to the correct distance.

A battery having a voltage source of cos t is connected to a series circuit on which the

inductance is 0.75 henry and the resistance is 15 ohms. Determine the current i at any time t if the

initial current is zero.

A large tank initially contains 220 gal of brine where there is dissolved 35lb of salt. Starting

at time t = 0, a brine containing 3lb of dissolved salt per gallon flows into the tank at the rate of

6gal/min is kept uniform by stirring and the well-stirred mixture simultaneously flows out of the

tank at a slower rate of 3gal/min. How much salt is in the tank at the end of 20 min?

According to the data listed at the Philippine Statistics Authority, the Philippine total

population reached 4 billion persons in year 2020 and was then increasing at the rate of 250

thousand persons each day. Assuming that natural population growth at this rate continues, what

will be the population at year 2060?

PART B. Non-Homogenous Linear Differential Equations

7. (D ^ 2 - 3D + 2) * y = (1 + e ^ (- x)) ^ 2

6. (D ^ 2 + 1) * y = x * cos x

PART B. Non-Homogenous Linear Differential Equations

5.(D^ 2 +25)y=sin x+cos 2x

5. (D ^ 2 + 4) * y = tan 2x

Non-Homogenous Linear Differential Equations

1. (2D ^ 2 + 3D + 1) * y = e ^ (- 3x)

2.(D^ 2 -2D+5)y=25x^ 2 +12

4. (D ^ 2 - 3D + 2) * y = 14sin 2x - 18cos 2x

Homogenous Linear Differential Equations

6. (D ^ 3 - 2D ^ 2 - 3D) * y = 0

5. (D ^ 3 - 3D ^ 2 + 4) * y = 0

7. (4D ^ 3 - 3D + 1) * y = 0

Homogenous Linear Differential Equations

1. (D ^ 2 + 3D) * y = 0

2.(D ^ 2 + D - 7) * y = 0