A parabolic curve has a descending grade of -1.2% which meets an ascending grade of +0.60%. the allowable change of grade per 20m. station is 0.18. Find the length of the curve.
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The rate of flow at a point in the highway is 1200 vehicles per hour. Find the space mean speed if the density is 25 vehicles per mile.
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Determine the integral of 3e2 sin θ (3 cosθ dθ) if the lower and the upper limits are 0 and π/2, respectively.
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A car driver approached a hazard and traveled a distance of 61 m. during the perception-reaction time of 2.8sec. What was the car’s speed of approach in mph?
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The volume of the frustum of a regular triangular pyramid is 135 cu.m. The lower base is an equilateral triangle with an edge of 9m. The upper base is 8m. above the lower base. What is the upper base edge in meters?
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The lateral area of a right circular cone is 40 π sq.m. The base radius is 4 m. What is the slant height?
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With only 381.7 sq.m. of materials, closed cylindrical tank of maximum volume is to be made. What should be the height of the tank, in m?
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What is the volume of an circular cylindrical tank whose lateral area = 1.58 m2 and base area = 4.524 m2 ?
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Determine the moment of inertia with respect to x-axis of the region in the first quadrant which is bounded by the curve y2 = 4x, the line y = 2 and the y-axis.
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There are 4 geometric means between 3 and 729. Find the fourth term of the geometric progression.
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Find the volume, in the first octant, common to equal cylinders of revolution whose axes intersect at right angles, if the radius of each cylinders is 2m. Answer in cu.m.
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The perimeter of an ellipse is 28.448cm. the major axis is 10cm. long and lies on the x-axis with its center at the origin. Determine the equation of the ellipse.
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(6, -1) and (-3, 7) are the coordinates of two corners of a triangle. What should be the ordinate of the third corner so that the centroid would be at the origin?
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With a wind velocity of 40kph, it takes an airplane as long to travel 1,200 km with the wind as 900 km against it. How fast can the airplane travel in still air?
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Find the area of the spherical triangle ABC, if A = 125°, B = 73°, C = 84° and r = 30 m.
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An equipment costs P480,000 and has a salvage value of 10% of its cost at the end of its economic life of 35,000 operating hours. In the first year, it was used for P4,000 hours. Determine its book value at the end of the first year.
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An investment earns 20 percent, compounded semi-annually. After how many years will quadruple?
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Ryan invest P5,000 at the end of each year in an account which gives a nominal annual interest of 7.5% compounded continuously. Determine the total worth of his investment at the end of 15 years.
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