Civil Engineering Online Review

The slope of the curve x=6y³ – 2y² at (6, 3) is equal to:

Solution:

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Find the sum of the geometric progression 2x, 4x+14, 20x-14 …. Up to the 10^th term.

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The volume of the frustum of a regular triangular pyramid is 135 cu.m. The lower and the upper bases, both equilateral triangles have edges equal to 9 m. and 3 m. respectively. Find its altitude.

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The log of the product MN is equal to 1.62324929 and the log of the quotient M/N is equal to -0.066946789. Find the value of N.

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Eleven (11) men can finish the job in 15 days. Five (5) men were working at the start and after 6 days four (4) men were added. How many days will it take to finish the job?

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Find the area of the region bounded by the polar curve r² = a² Cos 2θ

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Find the radius of curvature of the curve 4x – y² = 0 at point (1,2).

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A coin is tossed 3 times. What is the probability of getting 3 tails up?

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Find the equation of the diameter of the ellipse which bisects all chords having a slope of 1/5 the equation of ellipse is 64x² + 25y² = 1600.

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A truck travels from point M north ward for 30 min., then eastward for one hour, then shifted N. 30° W. If the constant speed is 40 kph, how far directly from M in km, will it be after 2 hours?

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A traverse has the following data:

LINE                   BEARING                    DISTANCE

AB                      N. 73°23’ E                         33.48

BC                      S. 39°30’ E                            8.11

CD                      S. 43°40’ W                        39.42

DE                      N. 39°50’ W                          7.08

EA                      N. 17°33’ W                        22.02

Determine the amount of correction for the latitude of the    line CD using transit rule.

Solution:

LAT = DIST Cos Bearing

DEP = DIST Sin Bearing

LINE                      LAT                     DEP

AB                      + 9.57                   +32.08

BC                      -  6.26                   +  5.16

CD                      -28.52                    -27.22

DE                       + 5.44                     -4.54

EA                      +20.99 ******* **-6.64

*************+36.00                +37.24

*************- 34.78 *******- 38.40

*************+  1.22                 -   1.16

************ 36.00                      37.24

********** **34.78 ******* ** 38.40

********** **70.78                     75.64

FOR LINE CD:

A line 100 m. log was placed by a surveyor for four times with the following data: 142, 145, 145.5 and 146. Then another line was paced for four times again with the following results, 893, 893.5, 891 and 895.5. Determine the length of the line.

Solution:

Distance of new line = 893.25 (0.691)

Distance of new line = 617.236 m.

A driver traveling at mph is 80 m. from a wall ahead. If the driver applies the brakes immediately (perception time is 2 seconds) and begins slowing the vehicle at 10 m/sec² (decelerating), find the distance from the stopping point to the wall.

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A stadia intercept reading of 3.0 m. was taken on a rod using a transit having a stadia interval factor of 100 and a stadia constant of 0.3 m. if the line of sight is inclined at an angle of 3°15’, determine the horizontal distance from the transit to the rod.

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Data on a traffic accident recorded on a certain intersection for the past 5 years has an accident rate of 4160 per million entering vehicles (ARMV). If the average daily traffic entering the intersection is 504, find the total number of accidents during the 5 year period.

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The areas of cut of two irregular sections 60 m. apart are 32 sq.m. and 68 sq.m. respectively. The base width is 8 m. with a side slope of 1:1. Find the corrected volume of cut in cu.m. using prismoidal correction formula.

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A vertical sag curve has a descending grade of -1.7% and an ascending grade of +2.3%. If the sag curve ahs a length of  135 m., compute the length of the sight distance?

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A driver traveling at mph is 80 m. from a wall ahead. If the driver applies the brakes immediately (perception time is 2 seconds) and begins slowing the vehicle at 10 m/sec² (decelerating), find the distance from the stopping point to the wall.

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A highway curve has a super elevation of 7°. Find the radius of the curve so that there will be no lateral pressure between the tires and the roadway at a speed of 40 mph?

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A machine costing P720,000 is estimated to have a life of 10 yrs. If the annual rate of depreciation is 25% determine the total depreciation using a constant percentage of declining balance method.

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Compute the surface area of the cone having a slant height of 5 cm. and a diameter of the base equal to 6 cm.

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Find the distance from a point (5, -3) to the line 7x – 4y = 28.

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If the volume of the sphere is equal to 36 cu.cm, find the surface area of the sphere.

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Water is the flowing into a conical vessel 15 cm. deep and having a radius of 3.75 cm. across the top. If the rate at which water is rising is 2 cm/sec. how fast is the water flowing into the conical vessel when the depth of water is 4 cm?

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How many years will P100,000 earned a compound interest of P50000 if the interest rate is 9% compounded quarterly?

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Find the length of the common chord of the curves x² + y² = 64 and x² + y² – 16x = 0.

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The area bounded by the curve x³ = y, the line y = 8 and the y-axis. Determine the centroid of the volume generated.

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The deflection angles of two intermediate points A and B of a simple curve are 3°15’ and 8°15’ respectively from the P.C. if the chord distance between A and B is 40 m, find the length of curve from P.C. to B.

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A circle having an area of 201 sq.m. is cut into segments by a chord which is 3 m. from the center of the circle. Compute the area of the smallest segment

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A closed traverse has the following data. Compute the bearing of line 1-2.

LINE                   BEARING                    DISTANCE

1-2                      ————-                          58.7

2-3                      ————-                          27.3

3-4                      N. 86.78° E.                        35.2

4-5                      S. 5 – 3° E.                            35.0

5-1                      S. 72.7° W.                          78.96

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A manufacturer produces certain items at a labor cost of P115 each, material cost of P76 each and variable cost of P2.32 each. If the item has a unit price of P600, how many number of units must be manufactured each month for the manufacturer to break even if the monthly overhead is P428,000.

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A man loans P187,400 from a bank with interest at 5% compounded annually. He agrees to pay his obligations by paying 8 equal annual payments, the first being due at the end of 10 yrs. Find the annual payments.

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The angular speed of a flywheel having a diameter of 6m. is 20 rpm. Compute its tangential velocity.

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The radius of the earth is 3960 miles. If the gravitational acceleration of the earth surface is 32.16 ft/sec²., what is the velocity of escape from the earth in miles/sec.?

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