A block having a weight of 200 N is placed at a distance 2.5m. from the center of a horizontal platform of 4m. radius. If the platform is rotated at 15rpm, what is the minimum coefficient of friction between the block and platform to prevent sliding?
Solution:
The acceleration of the particle is given by a = 2 + 12t in m/s2 where t is the time in minutes. If the velocity of this particle is 11 m/s after 1 min., find the velocity after 2 minutes.
Solution:
Find the area bounded by the curve y = 4 sin x and the lines x = π/3 and x = π and the x-axis.
Solution:
Determine the equation of the diameter of ellipse 4x2 + 9y2 = 144 that bisects the chords of slope ¾
Solution:
Which of the following number is not a prime number.
a) 109 ►c) 77
b) 107 d) 7
Note:
A prime no. is a no. which has two factors, one equal to 1 and the other equal to the number itself.
The no. which is not prime is 77.
Water is flowing into a conical vessel 24cm. deep and 12cm. across the top at the rate of 16cm3/sec. How fast is the water rising in the conical vessel when the depth of water is 12cm.?
Solution:
The longitudinal ground profile and gradeline shows that the length of cut is 540m. long while the length of fill is 760m. The width of roadway is 10m. for both cut and fill. The grade line are 4800 m2 for cut and 5292 m2 for fill. Find the difference in the volume of cut and fill in cu.m. if the side slope are 1.5:1 for cut and 2:1 for fill.
Solution:
The area bounded by the circle x2 + y2 = 9 on the second and third quadrant is revolved about the line x = 3. What is the volume generated?
Solution:
Two equal sides of a triangle have lengths of 14 cm. long. If the angles between these sides and the 3rd side are variable find the max. possible area of the triangle.
Solution:
The sides of a parallelogram are 84cm. and 63cm. respectively. If one of its diagonal is 48cm. long, compute the smallest interior angle of the parallelogram.
Solution:
A vehicle is moving at a speed of 80 kph along an incline surface having a slope of 4%. If the coefficient of friction is 0.30, compute the braking distance.
Solution:
The lengths of chords from P.C. to P.C.C. and that of the P.C.C. to P.T. of a compound curve is equal to 78.6m. and 48.2m. respectively. The common tangent of the compound curve makes an angle of 14° and 20° respectively with the tangents of the compound curve. Compute the length of the long chord connecting P.C. to P.T. if it is parallel to the common tangent.
Solution:
A circular curve has a central angle of 20°. Compute the radius of the simple curve if the tangent offset from the tangent thru the P.C. to the point of tangency (P.T.) is 8m.
Solution:
A transit has a stadia internal factor (f / i) = 99.96 and a stadia constant of 0.30. Compute the horizontal distance from the transit to a point where the stadia is placed if the stadia intercept is 0.60.
Solution:
Compute the compounded amount factor if it takes 10 yrs. For a uniform payment series if the nominal rate of interest is 9% ?
Solution:
If the effective rate of interest is 8%, what would be the normal rate of interest if it is compounded continuously?
Solution:
The first cost of an equipment is P150,000 with a salvage value of P20,000 at the end of its life of 10 years. Using Declining Balance Method, compute the book value at the end of 6 yrs.
Solution:
A truncated prism with a horizontal square base have vertical edges of 7cm., 7cm,. 10cm., and 10cm. respectively. If the volume of the prism is 4000 cu.cm., find the area of the base.
Solution:
The area of a triangle inscribed in a circle having a radius of 9cm. is equal to 43.23 cm2. If one of the sides of the triangle is 18cm., find one of the other sides.
Solution:
The surface area of an open cylindrical tank is 68m2. If the diameter 2(2/3) of its height, compute the height of the tank.
Solution:
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