Civil Engineering Online Review

Find the sum of the values of a, b and c from the given equations.

2a + 3b + 7c = – 39        Eq.1

-2a + 2b + c = – 13         Eq.2

3a – 2b – 5c = 55           Eq.3

Solution:

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Water is flowing into a frustum of a cone at a rate of 100 liters/min. The upper radius of the frustum of a cone is 1.5m. while the lower radius is 1m. and a height of 2m. If the water rises at the rate of 0.04916 cm/sec., find the depth of water.

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A man observes the angle of elevation of a tower from point A which is equal to 30°. He then moves towards the tower at a distance of 25m. at B and observes that the angle of elevation of the tower is 40°. He then moves 20m. towards the tower at point C and observe that the vertical angle at the point is 70°. Find the height of the tower.

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The corrected area of a square lot is 10000m² and the error in the computed area is 4.004m², compute the value of the error in the length of tape which is too short if a 100m. tape is used.

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Evaluate the following integral of x Cos 4x dx from 0 to π/4.

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A spherical ball having a diameter of 60cm. is placed on a cylindrical tank which contains a liquid inside the tank. If the water level inside the tank rises by 10cm., what is the diameter of the cylindrical tank?

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From station A with center heights of 1.4m. in fill, the ground line makes a uniform slope of 5% to station B whose center height is 2.8m. in cut. If the distance from A to B is 60m., find the grade of the finished roadway.

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A driver traveling at 50 mph sees a wall at a certain distance ahead. The driver applies the brakes immediately (perception time is 3 seconds) and begins slowing the vehicle at 6 m/sec² (decelerating). If the distance from the stopping point to the wall is 12m., how far was the car from the wall upon perception?

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A railway curve having a radius of 420m. has a distance between their rails of 1.5m. and the outer rail is 15cm. higher than the inner rail. Find the max. speed that a train could move along this curve so that there will be no lateral pressure on the wheels and the rails.

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A reversed curve having a radius of the first curve of 220m. and a central angle of 10° has a stationing of P.C. equal to 32 + 108.2. Compute the stationing of the P.R.C.

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The distance of mid point of a simple curve to the P.I. is equal to 14m. If the radius of the curve is 220m., find the central angle of the curve.

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The observed interior angles of a triangle and their corresponding number of times measured are as follows.

STATION      ANGLES       NO. OF MEASUREMENTS

A                            41°                          5

B                            77°                          6

C                            63°                          2

Find the probable value of angle C.

Solution:

A + B + C = 180°

41° + 77° + 63° = 181°

Error = 1° or 60° to be subtracted

STATION     ANGLES     NO. OF MEASUREMENTS

A                          41°                          5

B                          77°                          6

C                          63°                          2

STATION     WEIGHT           CORRECTION

A                     30/5 = 6              6/26 (60) = 13.84°

B                     30/6 = 5              5/26 (60) = 11.54°

C                     30/2 = 5 ******5/26 (60) = 34.62°

****************26                                        60°

Corrected angle C = 63° – 34.62°

Corrected angle C = 62° – 25.38°

Corrected angle C = 62° – 62.423°

A solid has a circular base of radius 20cm. Find the volume of the solid if every plane section perpendicular to a particular fixed diameter is an equilateral triangle.

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Compute the length of the latus rectum of an ellipse x² + 2y² + 4x + 4y + 4 = 0.

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Find the second eccentricity of an ellipse if the distance from the nearest focus to the vertex is 4 and the distance from the farthest focus to the vertex is 16.

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Find the area bounded by the curve y = 1/x and the lines 2x – y = 0, x = 6 and y = 0.

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Find the present worth of a perpetuity of a perpetuity of P10,000 payable every 3 months if money is worth 10% compounded monthly.

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A businessman buys a property which is worth P2M. He paid a down payment of P500,000 and at the end of the first year he paid another P1M and the remaining balanced to be paid at the end of the 3^rd year. How much is the balance to be paid on the 3^rd year if money is worth 24% compounded semi-annually.

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How many 4 digit combination could be made from 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9.

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The area of the inner triangle AEF is 3/5 that of triangle ABC. AE = 100m., AB = 160m., AC = 190m. Point E is along AB and point F is along line AC. Find the length of the segment AF.

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The production cost of a certain company is equal to P40 per unit and fixed charges amounts to P320,000 annually. If the selling price amounts to P60 per unit, how many units must be produced and sold annually to break even?

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The area of a triangle inscribe in a circle having a radius of 7.5cm. is equal to 54cm. If one of the sides of the triangle is 15cm., find one of the sides of the triangle.

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The sum of two numbers is equal to S. Find the minimum sum of the cube of the two numbers.

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A trough having an equilateral triangle end sections has sides equal to 0,4m. if the rough is full of water and is 8m. long, compute the volume of water in the trough.

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In a triangle ABC, AB = 36cm., BC = 24cm. and CA = 18cm. Find the length of the median from the vertex C to the line AB.

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Find the moment of inertia with respect to y-axis of the curve x² = 8y bounded by the line y = 2 and x = 0,

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A man leaves his house at 8:00 A.M. and traveling at an average speed of 2kph, arrives at his office 3 minutes ahead of the expected time. Had he left the house at 8:30 A.M. and traveled at an average speed of 3kph, he will arrive 6 minutes late of the expected time. Find the distance that he had traveled?

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Find the center of the curve x² + y² + 8x + 4y = 81

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Compute the normal acceleration of a rotating fly wheel having a diameter of 4m. if it has an angular speed of 8 rpm.

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Water is flowing into a conical vessel 18cm. deep and 10cm. across the top. If the rate at which the water surface is rising is 27.52 mm/sec. How fast is the water flowing into the conical vessel when the depth of water is 12cm.?

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A hydrographic survey was conducted for the purpose of locating channel depths. The survey party consists of the shore party and the boat party. On the shore, a staff gage was established in a securely place to such a depth that it will give a definite reading. The staff reading at the instant the sounding was taken was 14.2m. The depth of the sounding as recorded was found to be 17.6m. The elevation of the zero mark of the staff gage was 140.15m. Determine the elevation of the point where sounding was observed.

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A closed traversed has the foll, data:

Compute the bearing and distance of line E – A.

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A 45cm. x 45cm. plate horizontal plate ABCD of uniform thickness is supported by three vertical strings. The fist string is located at A, the second is at the point midway of side BC and the third is located 15cm. from D along side CD. What percentage of the total load is being supported by the 1^st and 2^nd strings?

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A messenger travels from points A to B. If he will leave A at 8:00 A.M. and travel at 2 kph, he will arrive at B 3 minutes earlier than his expected time of arrival. However, if he will leave at 8:30 A.M. and travel at 3 kph, he will arrive 6 minutes later than the expected time. What is the expected time of arrival?

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Find the 5^th term of the series whose sum of n terms is given by 3ⁿ⁺² – 6.

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