Civil Engineering Online Review

1    What is the minor of 5.

2    What is the co-factor of 2.

3    What is A times B.

Solution:

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The area of a rhombus is 132 sq.cm. It has one diagonal equal to 12cm.

1  Determine the length of the other diagonal.

2  Determine the length of the sides of the rhombus.

3   Determine the acute angle between the sides of the rhombus.

Solution:

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The vertical angle of the top of the flagpole as observed from point A is equal to 60°, and that of the bottom of the flagpole is 52°. The flagpole is placed on top of a pedestal. If the distance from A to the base of the pedestal is 14.20m.

1    Find the height of the pedestal

2    Find the height of the flagpole on top of the pedestal.

3    Find the distance from A to the top of the flagpole.

Solution:

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It is estimated that between the hours of noon and 7:00 P.M. the speed of a highway traffic flowing past the intersection of EDSA and Ortigas Avenue in approximately

S = t³ – 9t² +15t + 45 kph

Where “t” is the number of hours past noon.

1   At what time between noon and 7:00 P.M. is the traffic moving the fastest.

2   At what time between noon and 7:00 P.M. is the traffic moving the slowest.

3   What is the slowest speed it is moving at this time.

Solution:

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A triangular corner lot has perpendicular sides of lengths 120m. and 160m. respectively.

1   Find the area of the largest rectangular bldg. that can be constructed on the lot ***with sides parallel to the street.

2   Find the perimeter that encloses the bldg.

3   If it cost P6000 per square meter of floor area of a bldg., how much would be the ***approximate cost if a three story bldg. is to be constructed.

Solution:

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The equilateral hyperbola xy = 8 has the x-axis and y-axis as asymptote.

1   Determine the distance between the vertices.

2   Compute the length of the conjugate axis.

3   Compute the eccentricity of the hyperbola.

Solution:

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For a nominal rate of 6% compounded semi-quarterly for 8years in an ordinary annuity, compute the following

1   Sinking fund factor.

2   Present worth factor.

3   Capital recovery factor.

Solution:

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An ellipse has an equation of 9x² + 16y² = 144.

1  If the area enclosed by the ellipse on the first and 2^nd quadrant is revolved about ***the x-axis, what is the volume generated.

2  What is the length of arc in the first quadrant of an  ellipse.

3   What is the equation of the diameter of the ellipse which bisect all chords having a ***slope of 2.

Solution:

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Compute the interest for an amount of P200,000 for a period of 8 yrs.

1   If it was made at a simple interest rate of 16%.

2   If it was made at 16% compounded bi-monthly.

3   If it was made at 16% compounded continuously.

Solution:

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Given the technical description of a triangular lot.

LINES      BEARING           DISTANCE

AB         N. 40° W.                      ?

BC         N. 60° E.                  810 m.

CA         Due South                     ?

An area of 190,000 m² is to be segregated along the side BC starting from B.

1   Compute the location of the other end of the dividing line BD along the side CA ***measured from C.

2 Compute the length of the diving line.

3   Compute the bearing of the dividing line from B.

Solution:

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An easement curve has a length of spiral equal to 60m. having a central curve of a radius of 400m. The design velocity of the car allowed to pass thru this portion is 100kph.

1   Compute the rate of increase of centripetal acceleration.

2   If the friction factor is equal to 0.14, compute the super elevation rate in m/m ***width of roadway.

3  Compute the width of one lane of roadway if the difference in grade between the ***centerline and the edge of the roadway is 1/220.

Solution:

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The peak hour factor for traffic during rush hour is equal to 0.60 with a highest 5min. volume of 250 vehicles. The space mean speed of the traffic is 90 kph.

1   Compute the flow of traffic in vehicles/hour.

2   Compute the density of traffic in vehicles/km.

3   Compute the max. spacing of the cars in meters.

Solution:

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A line was determined to be 2395.25m. when measured with a 30m. steel tape supported throughout its length under a pull of 4kg at a mean temperature of 35°C. Tape used is of standard length of 20°C under a pull of 5kg. Cross-sectional area of tape is 0.03sq.cm. Coefficient of thermal expansion is 0.0000116°C. Modulus of elasticity of tape is 2 x 10⁶ kg/cm³.

1   Determine the error of the tape due to change in temperature.

2   Determine the error due to tension.

3   Determine the corrected length of the line.

Solution:

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The centerline of a proposed road cross section crosses a small valley between station 10 + 022 (elevation 123.00m.) and station 10 + 060 (elevation 122.50m.). The stationing at the bottom of the valley is 10 + 037 (elevation 111.2m.). The grade line of the proposed road passes the ground points at the edges of the valley (sta. 10 + 022) and (10 + 060) and the section at any of these stations are three level sections. Width of road base = 10m. with sideslope of 2:1. Assume that the sides of the valley slope directly to the lowest point from the edges.

1  Find the cross sectional area of fill at station 10 + 037.

2  Compute the volume of fill from station (10 + 022) to (10 + 037)

3  Compute the volume of fill from station (10 + 037) to (10 + 060).

Solution:

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The tangents of a simple curve have bearings of N.20°E and N.80°E. respectively. The radius of the curve is 200m.

1   Compute the external distance of the curve.

2   Compute the middle ordinate of the curve.

3   Compute the stationing of point A on the curve having a deflection angle of 6° from ***the P.C. which is at 1 + 200.00.

Solution:

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A simple curve of the proposed extension of Mantabahadra Highway have a direction of tangent AB which is due north and tangent BC bearing N.50°E. Point A is at the P.C. whose stationing is 20 + 130.46. The degree of curve is 4°.

1  Compute the long chord of the curve.

2  Compute the stationing of point D on the curve along a line joining the center of **the curve which makes an angle of 54° with the tangent line passing thru the P.C.

3  What is the length of the line from D to the intersection of the tangent AB.

Solution:

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A simple curve has a central angle of 36° and a degree of curve of 6°.

1  Find the nearest distance from the mid point of the curve to the point of **intersection of the tangents.

2  Compute the distance from the mid point of the curve to the mid point of the long **chord joining the point of curvature and point of tangency.

3  If the stationing of the point of curvature is at 10 + 020, compute the stationing of **a point on the curve which intersects with the line making a deflection angle of 8° **with the tangent through the P.C.

Solution:

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Given the equation of ellipse as 25x² + 4y² = 100

1  Find the equation of the diameter of ellipse which bisects chords having a slope of **½.

2  Find the slope of the curve at point(1.2, 4).

3  Find the perimeter of the curve.

Solution:

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The max. area of the parabola inscribed in a right circular cone having a diameter of 24cm. is equal to 207.8 cm³.

1  Compute the base of the parabola inscribed in a right circular cone.

2  Compute the height of the parabola of max. area.

3  Compute the volume of the right circular cone.

Solution:

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Two sets of students are collecting traffic data at the two sections A and B of a highway 200m. apart. Observation at A shows that 5 vehicles passes that section at intervals of 8.18sec., 9.09sec., 10.23sec., 11.68sec., and 13.64sec., respectively. If the speeds of the vehicles were 80, 72, 64, 56 and 48 kph respectively.

1  Compute the density of traffic in vehicles per km.

2  Compute the time mean speed in kph.

3  Compute the space mean speed in kph.

Solution:

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An area of 50,977.84 sq.m. is to be segregated from a triangular  lot ABC with one of its sides BC equal to 400m. and the boundary of this segregated area DEBC has side DE parallel to BC. The length of the side DE is equal to 150m. and the angle ABC is 50°.

1  At what angle is the side AC making with side BC?

2  What is the area of the whole lot?

3  What is the area of section ADE?

Solution:

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Given the equation of he curve y = 0.10 (1600 – x²)

1  Compute the area bounded by the curve and the x-axis.

2  Compute the moment of inertia with respect to y-axis

3  Compute the radius of gyration with respect to the y-axis.

Solution:

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A right circular cylinder is inscribed in a right circular cone of radius 6cm.

1  Find the radius of the cylinder if its volume is maximum.

2  Find the max. volume if the altitude is 12cm.

3  Find the radius of the radius of the cylinder if its lateral area is maximum.

Solution:

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From the given data of a closed traversed, compute the following.

1  Bearing of line DA.

2  Distance of line DA.

3  Area of lot ABCD in acres.

LINE              BEARING           DISTANCE

AB                 S.8°51’W.             126.90 m.

BC                 N.18°51’W.             90.20 m.

CD                 N.32°27’3.            110.80 m.

DA                 ————-         ————

Solution:

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To prepare for his retirement at a certain period “n” years from now, a self employed engineer deposits a uniform amount of P2500 at the  end of each year into a fund that earns an interest of 2.5% compounded annually.

1  Find the value of “n” when the compound amount factor due to the series of equal **deposits (annuity) is equal to 25.5447.

2  How much is the worth of the fund at the end of ”nth” year?

3  If he wants to retire in 8 yrs, how much will be the worth of his deposits at this **time?

Solution:

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Given:

STATION           ELEV.(m)           DISTANCE(km)

Alpha                  680 m.               Alpha to Bravo= 12 km

Bravo                  645 m.               Bravo to Charlie= 15 km

Charlie               620 m.

1  Compute the elevation of the line of sight at station Bravo with the instrument **placed at station Alpha such that station Charlie would be visible from station **Alpha considering the effect of curvature and refraction correction.

2  Assuming that station Bravo will obstruct the line of sight from station Alpha while **observing station Charlie and a 4m. tower is constructed on top of station Bravo. **Compute the height of equal towers at stations Alpha and Charlie in order that the **three stations as observed from station Alpha will still be intervisible.

3  Without constructing any tower at station Bravo, what height of tower must be **constructed at station Charlie so that both station Bravo and Charlie would be **visible from station Alpha.

Solution:

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The tenth term of a G.P. is 39366 and the 4^th term is 54.

1   Find the common ratio.

2   Find the first term.

3   Find the 7^th term.

Solution:

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The equation of ellipse is given as 16x² + 36y² = 576.

1   Compute the equation of polar of the point (4, -6) with respect to the ellipse.

2   Compute the equation of the diameter of ellipse which bisects all chords having a ***slope of 3.

3    Compute the second eccentricity of the ellipse.

Solution:

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Two identical closed conical tanks contains equal amount of liquid. The first tanks horizontal base is at the bottom while that of the second is at the top. The liquid in the first tank stands 3m. deep.

1   What is the volume of the liquid in the 2^nd tank?

2   How deep is the liquid in the second tank if its altitude is 6m. and the base radius ***is 2m?

3   If the unit weight of the liquid is 9100 N/m³, what is the weight of the liquid inside ***the tank in quintals?

Solution:

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A swimming pool is constructed in the shape of two overlapping identical circles having a radius of 9m. and each circle passes through center of each other.

1   Find the area common to the two circles.

2   Find the area of the swimming pool.

3   Find the perimeter of the swimming pool.

Solution:

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Find the area bounded by the curve x² – 10x + y² + 10y + 25 = 0

Solution:

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Find the equation of the line whose slope is 2/3 and passes through the intersection of the lines x – 2y + 4 = 0 and 4x – 2y + 1 = 0.

Solution:

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x years from now, one investment plan will be generating profit at the rate (50 + x²) thousand pesos per year, while a second plan will be generating at the rate of (200 + 5x) thousand pesos per year. Find the total net excess profit if you invest in the second plan instead of the first plan up to the time the two plans yield equal profits.

Solution:

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Find the volume in the first octant, bounded by the surface x = 1 and x² = y + 2z.

Solution:

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A 1.2 tons car moving with a velocity of 30 kph bumps the rear of a 1.8 ton car moving in the same direction with a velocity of 20kph. The bumpers get locked during the collision. Determine the velocity of the cars immediately after impact.

Solution:

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