From the following differential leveling notes, compute the difference in elevation between station 5 and 6.
STA B.S. F.S. ELEV.
1 2.565 33.971
2 10.875 5.821
3 7.035 1.946
4 3.560 5.741
5 7.186 9.736
6 4.123 7.977
1 4.123
Solution:
Using the prismoidal correction formula, find the corrected volume of cut between stations 80 m. apart if the areas of irregular sections in cut at stations are 26 sq.m. and 68 sq.m. respectively. Base width = 8 m. and side slope is 1:1.
The elements of a compound curve are as follows:
I1 = 18° D1 = 2°
I2 = 23.5° D2 = 4°
Determine the stationing of the P.C. if the stationing of P.I. = 42 + 89.6. Use arc basis.
Given the following data of a closed traverse. Compute the bearing of line DE.
LINE BEARING DIST(m.)
AB N. 72°10’ E. 64.86
BC S. 48°28’ E. 107.72
CD S. 35°30’ W. 44.37
DE ————– 137.84
EA ————– 12.83
Find the determinants of x:
Solution:
The correct distance between point E and f IS 213.5 m. If a 100m. tape that is 0.025 m. too long is used to measure EF, what will be the measured distance in meters?
Solution:
Find the remainder if 3x3 – 4x2y + 5xy2 + 6y3 is divided by x2 – 2xy + 3y2
Solution:
The bases of a right prism is a hexagon with one of each side equal to 6 cm. The bases are 12 cm. apart. What is the volume of the right prism?
Solution:
A train starting at initial velocity of 30 kph travels a distance of 21 km. in 18 min. Determine the acceleration of the train at this instant.
Solution:
Determine the length of the latus rectum of the ellipse having an equation 4x2 + 9y2 – 64x + 54y + 301 = 0.
Solution:
The base of a right prism is pentagon with one of each side is 6 cm. long. If the bases are 12 cm. apart, what is the volume of the right prism in cu.m.
Evaluate the log6 845 = x
Solution:
The volume of a pyramid is 140 cu.m. If it has a rectangular upper base of 3 m. x 4 m. and an altitude of 5 m., determine the dimensions of the lower base.
Find the remainder if we divide 4y3 + 18y2 + 8y – 4 by 2y + 3
Solution:
Another Solution:
A turbine started from rest to 180 rpm in 6 min. at a constant acceleration. Find the number of revolutions that it makes within the elapse time.
Solution:
wo = 0
wf = 180 rpm
t = 6 min
wf = wo + αt
180 = 0 + α (6)
α = 30 rev/s2
wf2 = wo2 + 2 α θ
1802 = 0 + 2 (30) θ
θ = 540 revolutions
The cost of equipment is P500,000 and the cost of installation is P30,000. If the salvage value is 10% of the cost of equipment at the end of 5 years, determine the book value at the end of the fourth year. Use straight line method.
Solution:
Cost of equipment = P500,000
Installation cost = P30,000
First Cost = 500,000 + 30,000
First Cost = 530,000
Salvage value = 50,000 @ +
da = 96000
D4= 96000 (4)
D4 = 384000
B4 = F.C. – D4
B4 = 530,000 – 384,000
B4 = P 146,000
The sides of the triangle are 12, 16 and 21. Find the area of the triangle.
Solution:
Find the derivative of Arc Sin 3x with respect to x:
Solution:
Find the area of the region bounded by the curve r2 = 16 Cos θ.
Solution:
Area bounded by the curve r2 = 16 Cos θ
|
θ |
0 |
30° |
45° |
60° |
90° |
-30 |
-45 |
-60 |
|
r |
4 |
3.7 |
3.4 |
2.8 |
0 |
3.7 |
3.4 |
2.8 |
The angle of elevation of the top of tower B from the top of tower A is 28° and the angle of elevation of the top of tower A from the base of tower B is 46°. The two towers lie in the same horizontal plane. If the height of tower B is 120 m., find the height of tower A.
Solution:
Find the number of terms for a progression 5,8,11,14……whose sum is 1025.
Solution:
Points A and B are 100 m. apart and are of the same elevation as the foot of the bldg. The angles of elevation of the top of the bldg. from points A and B are 21 degrees and 32 degrees respectively. How far is A from the bldg. in meters?
Solution:
Find the slope of the line having the parametric equations x = t – 1 and y = 2t.
Solution:
Find the volume of a cone to be constructed from a sector having a diameter of 72 cm. and a central angle of 210°.
Solution:
Car A moves due East at 30 kph at the same instant car B is moving S. 30° E. with a speed of 30 kph. The distance from A to B is 30 km. Find how fast is the speed between them are separating after one hour.
Solution:
A corporation uses a type of motor truck which costs P5000 with life 2 yrs. and final salvage value of P800. How much could the corporation afford to pay for another type of truck of the same purpose whose life is 3 yrs. with a final salvage value of P1000. Money is worth 4%.
Solution:
A parabolic curve having a forward tangent of -3% intersects a back tangent of 6.5% at station 10 + 800 whose elevation is 5260 m. If the length of the curve is 400 m., find the stationing of the highest point of curve.
Solution:
A quadrilateral has sides equal to 12 m., 20 m., 8 m. and 16.97 m. respectively. If the sum of the two opposite angles is equal to 225°, find the area of the quadrilateral.
A 5cm. x 5cm. is cut from a corner of 20cm x 30cm, cardboard, find the centroid from the longest side.
Solution:
A1 = 20 (30)
A1 = 600
A2 = 5 (5)
A2 = 25
A = A1 +A2
A = 600-25
A = 575
Ay = A1y1 – A2y2
575y = 600 (10) – 25 (2.5)
y = 10.33 m.
Find the differential equations of the family of lines passing through the origin.
Solution:
A frustum of a regular pyramid has an upper base of 8 m. x 80 m. and a lower base of 10 m. x 100 m. and an altitude of 5 m. Find the volume of the pyramid.
Solution:
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