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Area-Moment Method | Beam Deflections
A horn is generated by a circle which moves in the following manner:
Arithmetic, geometric, and harmonic progressions
A tugboat traveling at 40 kph leaves port at 4 PM carrying off some contraband goods. A patrol boat assigned to stop the goods leaves the same post an hour later and drove at 90 kph. What time will the patrol boat overtake the tugboat?
Area bounded by arcs of quarter circles
Age-related Problems
Arithmetic Progression
A student in a chemistry laboratory wants to form a 32-milliliter mixture of two solutions to contain 30% acid. Solution A contains 42% acid and solution B contains 18% acid. How many milliliters of each solution must be used?
A and B run a 1.5-kilometer race. In the first heat, A gives B a start of 11 meters and beats him by 57 seconds. In the second heat, A gives B a start of 81 seconds and is beaten by 88 meters. Find the rate of A in km/hr.
A and B compete in a race. A runs at a constant rate of 126 m/min while B runs 145 m the first minute, 143 m the second minute, 141 m the third minute and so on.
A man and a boy can do in 15 days a piece of work which could be done by 7 men and 9 boys in 2 days.
A wire with length of 52 cm is cut into two unequal lengths. Each par is bent to form a square. If the sum of the area of the two squares is 97 sq. cm., what is the area of the smaller square?
A circle is described by the equation x^2 + y^2 - 16x = 0. What is the length of the chord that is 4 units from the center of the circle?
A vending machine dispenses gumballs in a regular repeating cycle of ten different colors. If a quarter buys 3 gumballs, what is the minimum amount of money that must be spent before three gumballs of the same color are dispense?
An automobile tire is 30 inches in diameter. How fast in rpm does the wheel turn on the axle when the automobile maintains a speed of 50 mph?
A hot air balloon rising straight up from a level field is track by a range finder 500 ft from the point of lift off.
A pump discharges 50 ton of water per hour at the height of 8 m. The overall efficiency of the pumping system being 69%. Calculate the energy consumed by the pump in 2 hours, expressed in MJ.
A rectangle with sides parallel to the axes has vertices at (-3, 2), (2, 5), and (-3, 5). Find the coordinate of the fourth vertex.
A businessman wishes to earn 7% on his capital after payment of taxes. If the income from an available investment will be taxed at an average rate of 42%, what minimum rate of return, before payment of taxes, must the investment offer to be justified?
An equilateral triangle has an altitude of $5\sqrt{3}$ cm long. Find its area.
A factory is running at 80% efficiency with a fixed cost of P78,000.00, variable cost per unit of P130.00, selling price per unit of P416.00, and production capacity of 5000 units.
A flywheel is brought from rest up to a speed of 1500 rpm in 1 minute. What is the average angular acceleration, alpha?
A circle with radius r has a circumference equal to the perimeter of a square whose side is S. Which of the following is true?
A decagon has how many diagonals?
An arch 18 m high has a form of a parabola with a vertical axis. The length of a horizontal beam placed across the arch 8 m from the top is 64 m. Find the width at the bottom.
A large sewer system will cost P8,750,000 annually. There will be favorable consequences to the general public of P25,000,000 annually and adverse consequences to a small segment of the public of P2,500,000 annually. What is the benefit to cost ratio?
A highway has a gradient of 0.087. How many meters would an automobile rise vertically if it traveled 2 miles along the way?
A product has a current selling price of P325. If its selling price is expected to decline at the rate of 10% per annum because of obsolescence, what will be its selling price four years hence?
A car that accelerates uniformly passes at point A with a speed of 30 kph. It reaches point B, 21 km from A, after 18 minutes. Find the acceleration of the car.
A hollow glass bowl in the shape of a sphere of radius 4” is filled with water to a depth of 3”. If the water flows out through a small hole in the bottom so that the level drops 2”, how much water has escaped in in^3?
A cone was formed by rolling a thin sheet of metal in a form of a sector of a circle 72 cm in diameter with a central angle of 150 deg. Find the volume of the cone.
A right spherical triangle ABC of a sphere of radius 50 cm has angle C = 90 deg, A = 56 deg and side b = 47 deg. Find the area of the triangle in square centimeter.
A time deposits of P110,000 for 31 days earns P890.39 on maturity date after deducting the 20% withholding tax on interest income. Find the rate of interest per annum.
A trough has an open top 0.30 m by 6 m and closed vertical ends which are equilateral triangles 30 cm on each side. It is filled with water to half its depth. Find the volume of water in cubic meters.
A stone is projected from the ground with a velocity of 15 m/s at an angle of 30 deg; with the horizontal ground. How high will it rise?
A pipe can alone fill a tank in 5 hours, while a drain could do the contrary in 12 hours.