Civil Engineering Online Review

Find the slope of the curve y = (1 – 2x)³ at (1, -1).

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Find the integral of 5^4x dx using lower limit = 0 and upper limit = 1.

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The deflection angles of points D and E from the tangent through the P.C. of a simple curve are 4” and 12” respectively. If the chord distance between D and E is 50m., find the length of chord from P.C. to E.

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Find the distance from 8x – 5y – 121 = 0 from point (1, 1).

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A Ferris wheel has a radius of 10m. Its center is 12m. above the ground. When a passenger is 17m. above the ground he is moving vertically at the rate of 1.81 m/s. What is the speed of rotation of the wheel in rpm?

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A car starting from rest accelerates uniformly from zero at B to 3 m/s² for 5 sec. at C, then decelerates uniformly at 2 m/s² and stop at D. Compute  the time the car has traveled from B to D.

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The total cost of producing a gift item is C = 60x² – 0.01x³ where x = no. of units produced. Determine the value of x to make the average unit cost minimum.

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Determine angular speed of a wheel after 3 sec. if it decelerates at -12 rad/sec² starting from an angular speed of 100 rad/sec. Answer in rad/sec.

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A machine costs P500,000.00. Using the sum of the years digit method of depreciation, its first year depreciation cost is estimated to be P1,00,000.00. What is the salvage value when retired at the end of 5 years?

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The total cost of producing a gift item is C = 60x² – 0.01x³ where x = no. of units produced. Determine the value of x to make the average unit cost minimum.

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Determine angular speed of a wheel after 3 sec. if it decelerates at -12 rad/sec² starting from an angular speed of 100 rad/sec. Answer in rad/sec.

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A machine costs P500,000.00. Using the sum of the years digit method of depreciation, its first year depreciation cost is estimated to be P1,00,000.00. What is the salvage value when retired at the end of 5 years?

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The distance between the foci of an ellipse is 5. If its eccentricity is 0.50, what is the distance between the directrices?

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An engineer promised to pay 36000 pesos at the end of 90 days. He was offered a 10% discount if he pays in 30 days. Find the rate of interest.

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A self-employed engineer wants to get a lump sum of 5 million pesos when he retires at the end of 25yrs. How much in pesos should he deposit every end of 3 months in a fund that gives an interest of 10% compounded quarterly to satisfy his desire?

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What is the equation of the radical axis of the circles x² + y² – 18x – 14y + 121 = 0 and x² + y² – 6x + 6y + 14 = 0.

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A solid material in the form of a rectangular parallelepiped 4’x 6’x 8’ is painted blue. How many cubes will have 3 blue faces if the block is cut to form 1’x 1’x 1’?

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The sides of a parallelogram are 68cm.and 83cm. and one of the diagonal is 42cm. Solve for the biggest interior angle of the parallelogram.

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What is the surface area of a sphere whose volume is 2060 cu.cm.?

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The volume of a regular tetrahedron is 85.92m³. Determine the dimension of the edge in meters.

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Solve for n if n P₆ = 3n P₅ where P stands for permutation.

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Find the period of the graph of y = Cos x.

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Find the summation of (5K – 3) from K = 1 to K = 16.

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How many two digit combination can be formed using digits from 0 to 9.

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The geometric mean of two numbers is 8 while the arithmetic mean is 4. Determine the cube of the harmonic mean.

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Find the value of log_x 18 = 3.154.

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The sides of a triangle are 45m. and 55m. long. If its area is 785.48m², find the sum of all the sides.

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Determine the slope of the tangent to the curve y = 2 ln x at the point where x = 1.

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Determine the distance from the point (8, 10) to the farthest point on the circle x² + y² = 16y.

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Determine the max. speed in kph that a car could run around a 5° curve if the impact factor of the curve is 0.14. Neglect friction between tires and pavement.

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A downgrade of 3.2% meets a rising grade of 4.6% at station 73 + 180 where the elevation is 998m. A sag curve 440m. long connects the gradelines from A at the downgrade to B at the upgrade. Find the stationing of B.

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The super elevation of a highway curve is 6° At what maximum speed can a car ran on it such that there is no lateral pressure on the wheels. The radius of the curve is 150m.

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The distance from the mi-point of the curve to the mid-point of the chord connecting the P.C. to the P.T. is 8.12m. If the central angle is 40°, find the radius.

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1    What is the minor of 5.

2    What is the co-factor of 2.

3    What is A times B.

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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.

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