A 3m. steel pipe is leaning against a vertical wall and the other end is on the horizontal floor. If the lower end slides away from the wall at 2 cm/sec., how fast is the other end sliding down the wall when the lower end is 2m. from the wall?
Solution:
A cylindrical cone having a diameter of its base equal to 1 meter has a height of 60cm. if it is filled with salt to a height of 36cm. compute the volume of the salt.
Solution:
What is the length of one arc of the curve having the following parametric equations.
********x = 2θ – 2 Sin θ
********y = 2 – 2 Cos θ
Solution:
Which of the following will minimize the cracking of pavement due to thermal expansion
a) compaction of subgrade
b) provide expansion joints and sectional porting of concrete
c) consistency of concrete mixed
d) insurance of strength of materials
Answer:
At what rate of interest compounded quarterly will an investment double in 5 years.
Solution:
The areas bounded by the water line of a lake contours 1, 2, 3, 4 and 5 are as follows, A1 = 8200 m2, A2 = 6680 m2, A3 = 6200 m2, A4 = 5520 m2, A5 = 4200 m2. If the contour interval is 2m., find the volume of water in the lake using prismoidal formula.
Solution:
Compute the modulus of elasticity of the sub-grade if the modulus of elasticity of the pavement is 120 MPa with stiffness factor of 0.50.
Solution:
The cross section notes of an earthwork is
Width of roadway = 8m.
Find area of cross section.
Solution:
P 36000 is to be divided among Arthur, Bernard and Carlos, such that their shares in same order form an arithmetic progression. Bernard’s share is 3 times of Arthur. How much is Bernard’s share?
Solution:
B – A = C – B
1B = A + C
B = 3A
A + B + C = 36000
2(3A) = A + C
6A = A + C
5A = C
A + 3A + 5A = 36000
9A = 36000
A = 4000
B = 3(4000)
B = 12000
The vertices of a triangle are at (2, 6), (-3, -2) and (4, 2). What is the abscissa of the centroid of the triangle.
Solution:
The distance between points A(2, 10, 4) and B(8, 3, z) is 9,434. What is the value of z.
Solution:
Suppose that “x” years after its founding in 1975, a certain national consumers association had a membership of
f(x) = 100 (2x3 – 45x2 + 264x)
At what time between 1975 and 1989 was the membership of the association the smallest?
Solution:
A is 12% older than B, while B is 11% older than C. By how much in % is A older than C.
Solution:
A contractor can buy dump trucks for P 800,000 each or rent them for P1200 per truck per day. The truck has a salvage value of P 100,000 at the end of its useful life of 5yrs. The annual cost of maintenance is P 20,000. Using annual cost method and 14% interest rate, determine the number of days per year that a truck must be used to warrant it purchased. Use Sinking fund method of depreciation.
Solution:
Two parallel tangents 12m. apart are connected by a reversed curve of equal radii. The chord length from P.C. to P.T. is 140m. What is the total length of the reversed curve.
Solution:
The tangent of a simple curve from P.I. to P.C. has a bearing of N. 65° E. and the other tangent from P.I. to P.T. has a bearing of N. 55° W. 150m. from P.C. along the tangent thru P.C. The right angle offset to point E on the curve is 6.2m. Determine the radius of the curve.
Solution:
Using an engineers level, the reading on a rod 80m. away was observed to be 2.81m. The bubble was leveled thru 5 spaces on the level tube and the rod reading increased to 2.874m. Determine the radius of curvature of the level tube if one space on the tube is 0.60mm. long.
Solution:
Find the difference between the sums of an annuity due and an ordinary annuity for the following data:
Periodic payment = P14,000
Payment interval = 3 months
Term: 16 years
Interest rate = 10% compounded quarterly.
Solution:
Find the volume generated by revolving the area enclosed by the curve x2 + y2 = 25 about the line x – 10 = 0.
Solution:
A man recorded 70, 71.5, 69.5 and 72 paces in walking along a 50m. course to determine his pace factor. He then took 460, 468, 471, 457, paces in walking an unknown distance AB. Compute the distance AB based on his pace factor.
Solution:
A spherical steel ball having a radius of 10cm. is placed into a vertical circular cylinder containing water, causing the water level to rise 10cm. What is the radius of the cylinder.
Solution:
In the spherical triangle ABC, A = 166°19’, B = 55°30’, C = 80°37’, Find the value of side a.
Solution:
A circle is circumscribed about a hexagon. The area outside the hexagon but inside the circle is 15m2. What is the area of the hexagon?
Solution:
A lateral edge of the rustum of a regular pyramid is 1.8m. long. The lower base is 2.4m x 2.4m. square while the upper base is 1m x 1m square. What is the volume of the frustum in cu.m.
Solution:
A body starting from point E is given a uniformly acceleration from zero at E to 1.8 m/s2 at F in 4 sec. The initial velocity at E is 3 m/s. Find the distance traveled at the end of 4 seconds.
Solution:
The center height for fill at station A (40 + 160) is 1.4m. and the center height for cut at station B (40 + 220) is 2.8m. The ground line makes a uniform slope of 5% from A to B. If the slope of the final roadway is 2%, compute the distance from A where cut will extend.
Solution:
To prepare for retirement at the end of 20yrs. a self employed engineer deposited 6000 pesos every end of 3 months in a fund that earns an interest rate of 10% annually compounded quarterly. Find the lump sum he could get at the end of the 20th year in pesos.
Solution:
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