Civil Engineering Online Review

Compute the rectangular coordinates of a point having a polar coordinates of (7, 38°).

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Data on a traffic accident recorded on a certain intersection for the past 4 years has an accident rate of P9200 per million entering vehicles (ARMV). If the total number of accidents is 802, find the average daily traffic entering the intersection during the 4 year period.

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Lot ABCDFA is a closed traverse in the form of a regular hexagon with each side equal to 100m. The bearing of AB is N.25° E., what is the bearing of FA.

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The axis of the cone makes an angle of 60° with the horizontal. If the length of the axis is 30cm. and its base radius is 20cm., compute for the volume of the curve.

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Determine the area bounded by the curve x² + y² – 6y = 0

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Determine the magnitude of the resultant force F = 3i + 4j + 12k.

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Find the area of the region bounded by the curves x² = 3y and y² = 3x.

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A certain firm produces certain product at a labor cost of P402 per unit, variable and material cost per unit of P320. If the selling price is P1200 per unit, how many units must be produced each month to break even assuming that the fixed monthly cost is P502,000.

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An object is projected vertically upward. If the distance traveled by the object can be expressed as h = 100t – 16.1t² where “h” is in meters and “t” is the time in seconds, what is the velocity of the object after 2 seconds.

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The geometric mean of two numbers is 8 and the arithmetic mean is 17. Find one of the numbers.

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A businessman wishes to have P1,000,000 in a certain investment fund at the end of 20 years. How much should he invest in the fund that will pay 7% compounded continuously?

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A man deposited P100,000 annually for 10 years and waited for another 10 years. If money is worth 8% after tax find the amount after 20 years.

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10666.67 cu.units A solid has a circular base of diameter 40 cm. Find the volume of the solid if every section perpendicular to a fixed diameter is an isosceles right triangle.

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A vehicle moving at 60 kph along an incline surface was slopped by applying brakes and the braking distance was 30m. if the coefficient of friction is 0.50, compute the slope of the inclined surface.

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Point A is in between B and C and the distances of B and C from point A are 1000m. and 2000m. respectively. Measured from point A, the angle of elevation of point B is 18°30’ while that of C is 8°15’. Considering the effect of earth’s curvature and refraction, compute the difference in elevations of B and C.

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The angle of intersection of a circular curve is 53°40’ and its radius is 800 m. If the stationing of P.C. is at 35 + 180, compute the right angle offset from the tangent passing thru the P.C. to station 35 + 280 on the curve.

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On one side of a paved path walk is a pedestal with a flog staff on top of it. The pedestal is 2m. in height while the flag staff is 3m. high. At the opposite edge of the path walk the pedestal and flag staff subtends an equal angles. Compute the width of the path walk.

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From station A (35 + 220) with center height of 4.5 m. in cut, the grade of the ground surface is -6% from station A to B (35 + 300) whose center height is 2.6m. in fill. Compute the slope of the finished roadway.

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Solve for B from the given expansion of partial fractions.

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Twenty eight (28) men can finish the job in 60 days. At the start of the 16^th day 5 men were laid off and after the 45^th day 10 more men were hired. How many days were they delayed in finishing the job?

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A vertical summit parabolic curve AB has tangent grades of +4.25% and -3.25% intersecting at station 10+020, whose elevation is 998m. If the length of curve AB equals 316m. find the elevation of B.

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The scale of a map is 1/250,000. If the error in the map = 0.02mm., find the error in the ground.

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The base of a cylinder is a hexagon inscribed in a circle. If the difference in the circumference of the circle and the perimeter of the hexagon is 4cm., find the volume of the cylinder if it has an altitude of 20cm.

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The area of a triangle is 65sq.cm. and its perimeter is 48cm. Compute the radius of the inscribed circle.

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Find the distance between the foci of the curve 9x² + 25y² – 144x + 200y + 751 = 0.

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A closed cylindrical tank has a surface area of 381.7sq.cm. Compute the radius of the cylinder that will give the max. volume.

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Find the equation of the curve whose slope is 6x – 2 and passing through (5, 3)

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The area is bounded by the curve y = Sin x, the line x = 0 and x = π. Find the volume generated when the area is revolved about the x-axis.

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The technical description of a closed traverse is as follows:

LINE               DISTANCE (m)            BEARING

1 – 2                     64.86                            ?

2 – 3                   107.72                           ?

3 – 4                     44.37                  S. 35°30’ W

4 – 5                   137.84                 N. 57°15’ W

5 – 1                     12.83                  N. 1°45’ E

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The center height of the road at STA. 7 + 110 is 2m. fill, while at STA 7 + 160 it is 1.2m. cut from STA 7 + 110 to the other station, the ground makes a uniform slope of 4.8 percent. How far, in m. from STA 7 + 160 toward STA 7 + 110 will the excavation extend?

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The interior angles 1, 2 and 3 of a triangular traverse were measured with the same precision. Find the most probable value of angle 2.

ANGLE          VALUE (DEGREES) NO. OF MEASUREMENTS

1                                39                                    3

2                                65                                    4

3                                75                                    2

Determine the corrected angle at station B.

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A projectile is fired with a muzzle velocity of 300 m/s from a gun aimed upward at an angle of 20° with the horizontal, from the top of a building 30m. high above a level ground. When will it hit the ground?

Solution:

V₁ = 300 Sin 20°

V₁ = 102.61 m.

V₂² =V₁² – 2gh

0 = (102.61)² – 2(9.81) h

h = 536.64 m.

V₂ = V₁ – gt₁

0 = 102.61 – 9.81 t₁

t₁ = 10.46 sec.

H = ½ gt₂²

566.64 = (9.81 / 2) t₂²

t₂ = 10.75 sec.

Total time = 10.46 + 10.75

Total time = 21.2 sec.

From point A on a simple curve, the perpendicular distance to the tangent, at point Q, is 64m. The tangent passes through the P.C. the distance from Q to P.C. is 260m. Find the length of the curve from the P.C. point A, in m.

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