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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 sector of a circle with radius 10 cm has a central angle of 120°. Find the arc length of the sector.
A semi-elliptical arch in a stone bridge has a span of 6 meters and a central height of 2 meters. Find the height of the arch at a distance of 1.5 m from the center of the arch.
A sequence of numbers is defined by the relation $\dfrac{a_{n + 1}}{a_n} = 3^n$ and it is known that $a_1 = 1$. Find the value of $\log_3 a_{100}$.
A series of siphon pipes of uniform diameter are to draw water to irrigate the farm instead of using the traditional method of flooding the area.
A ship lies 6 miles from a straight shore, and opposite a point 10 miles farther along the shore, another ship lies 18 miles offshore.
A slope of 20 degrees in percent is most nearly equal to:
A solid shaft made from copper is 90mm diameter and 8m long
A solid spherical ball remolded into a hollow spherical ball
A sphere is circumscribing a cubical box having a volume of 8000 cm3. Compute the volume of the space between the cubical box and the sphere.
A sphere of radius 18 inches is cut by two parallel planes that are 16 inches apart. Find the volume on the sphere included between these cutting planes if the radius of one of the circles cut is 15 inches.
A spherical zone of one base of height $h$ is cut from a sphere of radius $r$. What is the volume of the zone?
A spider eats three flies a day. Until he fills his quota, he has an even chance of catching any fly that attempts to pass.
A spider eats three flies a day. Until he fills his quota, he has an even chance of catching any fly that attempts to pass. A fly is about to make the attempt. What are the chances of survival, given that five flies have already made the attempt today?
A steel pipe is being carried down a hallway 9 ft wide.
A stone is dropped into a well and the report of the stone striking the bottom is heard 7.7 seconds after it is dropped.
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 store has three kinds of toys given in every purchase. What is the probability of getting all three toys in five purchases?
A strip of 640 m2 is sold from a triangular field whose sides are 96 m, 72 m, and 80 m. The strip is of uniform width h and has one of its sides parallel to the longest side of the field. Find the width of the strip.
A student goes to the library. The probability that she checks out (a) a work of fiction is 0.40, (b) a work of non-fiction is 0.30, and (c) both fiction and non-fiction is 0.20. What is the probability that the student checks out a work of fiction, non-f
A student in a chemistry laboratory wants to form a 32 milliliter mixture of two solutions to contain 30% acid.
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 student received grades of 72, 75, and 78 on three tests. What must her score in the next test be for her to have an average grade of 80 for all four tests?
A substance goes into a solution at the rate of 25% of the undissolved portion each minute. If the initial amount was 64/27 grams, what amount (in grams) is undissolved after 6 minutes?
A sum of money amounting to P5.15 consists of 10 cents and 25 cents. If there are 32 coins in all, how many 25 cents are there?
A system of streamline and orthogonal lines which show the idealized flow pattern for a given system of boundaries.
A tank is supplied by two pipes A and B and emptied by a third pipe C
A three-man jury has two members each of whom independently has a probability p of making the correct decision and a third member who flips a coin for each decision (majority rules).
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 Toyota Tamaraw FX leaves a certain station at noon, traveling due north at 40 kph.
A trapezoid has an area of 360 m2 and altitude of 20 m. Its two bases have ratio of 4:5. One of the bases i
A triangle has a variable sides x, y, and z subject to the constraint that the perimeter P is fixed to 18 cm. What is the maximum possible area of the triangle?
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 truck with axle loads of 40 kN and 60 kN on a wheel base of 5 m rolls across a 10-m span. Compute the maximum bending moment in kN m.
A truth serum given to a suspect is known to be 90% reliable when the person is guilty and 99% reliable when the person is innocent.
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?