Civil Engineering Online Review

If P500,000 is deposited at a rate of 11.25% compounded 2 monthly, determine the compounded interest after 7 years and 9 months.

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A 40kg block is resting on an inclined plane making an angle of 20° from the horizontal. If the coefficient of friction is 0.60, determine the force parallel to the incline that must be applied to cause impending motion down the plane. Use g = 9.81

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A car starting at 12:00 noon travels west at s speed of 30 kph. Another car starting from the same point at 2:00 P.M. travel north at 45 kph. Find how fast the two are separating at 4:00 P.M.

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At 6% find the capitalized cost of a bridge whose cost is P250M and life is 20 years, if the bridge must be partially rebuilt at a cost of P100M at the end of each 20years.

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The top of a tower signal at B 2000 m. from A away was sighted through a transit with recorded vertical angle of 2°30’. The height of above the point where it is set is 1.10 m. the elevation of the point under the transit A is 133.3 m. Compute the elevation of the base of the signal B.

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A man inherited a regular endowment of P100,000 every and of 3 months for 10 years. However he may choose to get a single lump sum payment at the end of 4 years. How much is this lump sum if the cost of money is 14% compounded quarterly?

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A Norman window is in the shape of a rectangle surmounted by a semi-circle. What is the ratio of the width of the rectangle to the total height so that it will yield a window admitting the most light for a given perimeter.

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A train upon passing point A at a speed of 72 kph accelerates at 0.75 m/s², for one minute along a straight path then decelerate at 1.0 m/s². How far in km. from point A will it be 2 min. after passing point A.

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A ball is thrown from a tower 30 m. high above the ground with a velocity of 300 m/s directed at 20° from the horizontal. How long will the ball hit the ground?

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Find the area of the given cross-section if the width of roadway is 10 m.

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Determine the distance from (5, 10) to the line x – y = 0

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Find the radius of a simple curve having a degree of curve f 5° using chord basis.

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A parabolic curve AB, 400 m. long is connected by tangents having an upgrade of +6.5% and a downgrade of   -3% intersecting at sta. 20 + 800 at elevation 102.5 m. Find the distance from B to the highest point of the curve.

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In a triangle BCD, BC = 25 m. and CD = 10m. The perimeter of the triangle maybe.

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Find the equation of a line normal to the curve x² = 16y at (4, 1).

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The volume of water in a spherical tank having a diameter of 4 m. is 5.236 m³. Determine the depth of the water on the tank.

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The volume of the water is a spherical tank is 1470.265 cm³. Determine the depth of water if the tank has a diameter of 30 cm.

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If the edge of a cube is increased by 30% by how much is the surface area increased?

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

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Find the area of a triangle whose vertices are A(-3, -1),  B(5, 3) and (2, -8)

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How many 4 digit numbers can be formed without repeating any digit, form the following digits 1,2,3 and 6.

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Find the derivative of

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Evaluate the integral of if it has an upper limit of 1 and a lower limit of 0.

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From the given data of a closed traverse, compute the bearing of line 3-4.

LINE                  BEARING              DISTANCES

1-2                      N. 58° E.                       80 m.

2-3                      Due N.                           50 m.

3-4                     ———–                   ———–

4-1                      S. 36.74° E.                   89.8

Solution:

LINE        BEARING        DISTANCES     LAT.       DEP.

4-1            S. 36.74° E.             89.8             -71.96     +53.72

1-2              N. 58° E.                80 m.          +42.39     +67.84

2-3              Due N.                    50 m.          +50.00

3-4                                                                   ______ _______

**********************************-20.43     -121.56

Bearing = S. 80.46° W.

Find the 6^th term of the expansion of

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Evaluate the integral of (3x² + 9y²)dx dy if the interior limit has an upper limit of y and a lower limit of 0, and whose outer limit has an upper limit of 2 and lower limit of 0.

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Find the area of a quadrilateral having sides AB = 10 cm., BC = 5 cm., CD = 14.14 cm. and DA = 15 cm. if the sum of the opposite angles is equal to 225°.

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Find the value of Sin (90 + A)

Solution:

Sin(90 + A) = Sin 90 Cos A + Sin A Cos 90

Sin(90 + A) = Cos A

Compute the value of x by determinants:

Solution:

x = -28

What is the differential equation of the family of parabolas having their vertices at the origin and their foci on the x-axis.

Solution:

x(y’)² = a

What is the radius of the circle circumscribing an isosceles right triangle having an area of 162 sq.cm.?

Solution:

r = 12.73

A service car whose cash price was 540,000 was bought with a down payment of P162,000 and monthly installments of P10,874,29 for 5 years. What was the rate of interest if compounded monthly?

Solution:

Rate = 0.24 = 24%   compounded monthly

The area in the second quadrant of the circle x² = y² =36 is revolved about the line y + 10 = 0. What is the volume generated?

Solution:

V = 2228.83

Find the integral of 12 sin⁵ x cos⁵ x dx if lower limit =0 and upper limit = π/2.

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