Mathematics, Surveying and Transportation Engineering

Algebra, Trigonometry, Statistics, Geometry, Calculus, Differential Equations, Engineering Mechanics, Engineering Economy, Surveying, Transportation Engineering
 

Angle Correction for Repeated Measurement

Problem
The following interior angles (in degree) of a triangular traverse were measured with the same precision.
 

Expected Profit for the Acceptance of Estimate of an Engineering Company

Problem
An engineering company prepares an estimate for a job. The cost of preparing the estimate is Php10,000. The amount of profit over and above the Php10,000 is Php25,000 if their estimate is accepted. The probability that their estimate will be accepted 0.7 and the probability that their estimate will not be accepted is 0.3. What is the expected profit?

A.   Php12,500 C.   Php14,500
B.   Php13,500 D.   Php10,500

 

Rate of Change of Volume of Sand in Conical Shape

Problem
A conveyor is dispersing sands which forms into a conical pile whose height is approximately 4/3 of its base radius. Determine how fast the volume of the conical sand is changing when the radius of the base is 3 feet, if the rate of change of the radius is 3 inches per minute.

A.   2π ft/min C.   3π ft/min
B.   4π ft/min D.   5π ft/min

 

Duel of Two 50% Marksmen: Odds in favor of the man who shoots first

Problem
Smith and Jones, both 50% marksmen, decide to fight a duel in which they exchange alternate shots until one is hit. What are the odds in favor of the man who shoots first?

A.   1/3 C.   2/3
B.   1/2 D.   1/4

 

Velocity of Separation: How fast is the distance between two cars changing?

Problem
A Toyota Land Cruiser drives east from point A at 30 kph. Another car, Ford Expedition, starting from B at the same time, drives S30°W toward A at 60 kph. B is 30 km from A. How fast in kph is the distance between two cars changing after 30 minutes? Hint: Use the Cosine Law.

A.   70 kph C.   55 kph
B.   80 kph D.   60 kph

 

Centripetal Force of a Ball Revolving Uniformly in a Horizontal Circle

Problem
A 150 g ball at the end of a string is revolving uniformly in a horizontal circle of radius 0.600 m. The ball makes 2 revolutions in a second. What is the centripetal acceleration?

A.   74.95 m/sec2 C.   49.57 m/sec2
B.   94.75 m/sec2 D.   59.47 m/sec2

 

Radius of Circle of New Atom Smasher

Problem
A new kind of atom smasher is to be composed of two tangents and a circular arc which is concave toward the point of intersection of the two tangents. Each tangent and the arc of the circle is 1 mile long, what is the radius of the circle? Use 1 mile = 5280 ft.

A.   1437 ft. C.   1347 ft.
B.   1734 ft. D.   1374 ft.

 

Ratio of Volume of Water to Volume of Conical Tank

Problem
A conical tank in upright position (vertex uppermost) stored water of depth 2/3 that of the depth of the tank. Calculate the ratio of the volume of water to that of the tank.

A.   4/5 C.   26/27
B.   18/19 D.   2/3

 

Finding The Length Of Parabolic Curve Given Change In Grade Per Station

Problem
A +0.8% grade meets a -0.4% grade at km 12 + 850 with elevation 35 m. The maximum allowable change in grade per station is 0.2%. Determine the length of the curve.

A.   300 m C.   80 m
B.   240 m D.   120 m

 

Find y’ if x = 2 arccos 2t and y = 4 arcsin 2t

Problem
Find y’ if x = 2 arccos 2t and y = 4 arcsin 2t.

A.   2 C.   4
B.   -2 D.   -4

 

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