Find the dimensions of a closed rectangular box with a volume of 540 cm³, where the length is twice the width, to minimize the surface area.
A rectangular box with a square base has a volume of 4000 cm³. Find the dimensions of the box that would minimize the amount of material needed for its construction.
Two forces, (F1 = 5i + 4j) and (F2 = 2i + 3j), act on an object. Calculate the angle between the two forces.
An investment of ₹10,000 grows to ₹12,000 in 2 years at a compound interest rate compounded annually. Find the rate of interest.
A standard deck has 52 cards. Two cards are drawn one after another without replacement. What is the probability that both cards drawn are kings?
A closed cylindrical can with a volume of 500 cm³ is to be constructed. Find the dimensions that minimize the surface area of the can.
A product sells for p = 100 -0.5x dollars, where “x” is the number of units sold. Find the number of units to be sold to maximize revenue.
A ladder 10 meters long is leaning against a wall. If the bottom of the ladder slides away from the wall at a rate of 2 meters per second, find the rate at which the top of the ladder slides down the wall when the bottom is 6 meters away.
A person is standing 10 meters away from a 20-meter high building. At what angle of elevation should they look up to maximize the view of the building?
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