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fff What is the maximum possible area of a rectangle if the perimeter is 280 m?
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fff Find the minimum possible perimeter of a rectangle if the area is 8100 m2. fff View Solution
fff The sum of two positive numbers is 30. What is the smallest possible value for the sum of their squares? fff View Solution
fff If x and y are two positive numbers whose sum is 20, then find the largest possible value for x2 y.
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fff A rectangle of perimeter 36 cm is rotated about its length, thus forming a right circular cylinder. What is the maximum possible volume of the cylinder?
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fff The sum of two positive numbers is 40. Find the smallest possible value for the sum of their cubes. fff View Solution
fff Find the largest possible area for a rectangle if the diagonal measures a cm. [a = 64] fff View Solution
fff Assuming that the petrol burnt per hour in driving a motor boat varies as the cube of its velocity, what will be the most economical velocity of the boat while going against a current of 4 miles per hour? fff View Solution
fff A rectangular box with a square base has a volume of 27000 cm3. What is the minimum possible total surface area of the box?
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fff Find the largest area of a rectangle inscribed in a circle of radius r = 2 cm. fff View Solution
fff The difference between two numbers x and y is 40 where 0 < y < x. Find the values of x, y, for which (x2 - 2y2) is maximum.
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fff What is the maximum area of a triangle, if two of its sides measure 8 units and 13 units?
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fff What is the perimeter of a triangle of maximum area having two sides 9 and 12?
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fff The velocity of a wave of wavelength k is given by (k4+64k) m/s. Find the minimum velocity of the wave. fff View Solution
fff The displacement s (in meters) of a particle in time t (in seconds) is given by, s = 5t - 6t2. Find the maximum displacement of the particle.
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fff The profit P(x) of a company is given by P(x) = - x33 + 441x - 595 , 0 ≤ x ≤ 25, where x is the volume of production. Find the value of x for which the profit is maximum.
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fff The equation f(v) = 22v + (2200v), where 0 < v < 30, relates the rate f(v) at which the engine works with its speed v. Find the value of v for which the rate is the least.
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fff The percent concentration of a certain drug in the bloodstream, x hours after the drug is administered is given by f(x) = xx2 + 25 . For what value of x, the concentration is the maximum?
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fff x, y are two positive numbers such that x2 + y2 = 32. Find the value of x + y so that x2 y2 is maximum.
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fff What is the maximum area of a triangle, if two of its sides measure 8 units and 11 units?
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fff What is the perimeter of a triangle of maximum area having two sides 12 and 16?
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fff A rectangular box with a square base has a volume of 125000 cm3. What is the minimum possible total surface area of the box?
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fff Find the largest area of a rectangle inscribed in a circle of radius r = 5 cm. fff View Solution
fff What is the maximum possible area of a rectangle if the perimeter is 80 m?
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fff Find the minimum possible perimeter of a rectangle if the area is 3600 m2. fff View Solution
fff The sum of two positive numbers is 20. What is the smallest possible value for the sum of their squares? fff View Solution
fff The sum of two positive numbers is 180. Find the smallest possible value for the sum of their cubes. fff View Solution
fff Assuming that the petrol burnt per hour in driving a motor boat varies as the cube of its velocity, what will be the most economical velocity of the boat while going against a current of 6 miles per hour? fff View Solution
fff If x and y are two positive numbers whose sum is 70, then find the largest possible value for x2 y.
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fff A rectangle of perimeter 12 cm is rotated about its length, thus forming a right circular cylinder. What is the maximum possible volume of the cylinder?
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fff Nathan is driving to his office. The graph shows the path he takes. This path is modeled by y = 12x. Find the shortest distance between the origin and the car. fff View Solution
fff Find the largest possible area for a rectangle if the diagonal measures a cm. [a = 36] fff View Solution
fff The sum of the perimeters of a square and a circle is given by p. If the sum of their areas is least when the side of the square is equal to k times the radius of the circle, then find k.
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ee  The difference between two numbers x and y is 80 where 0 < y < x. Find the values of x, y, for which (x2 - 2y2) is maximum.
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ee  Bill owns two triangular plots ABC, ADE with areas a ft2, b ft2 respectively. He wants to buy the triangular plots ABD, ACE as shown in the figure and he approached a bank for a loan. Bank accepted to give a loan of $1000 per square ft. Find the minimum amount that he can get from the bank to buy the triangular regions ABD, ACE.
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ee  The velocity of a wave of wavelength k is given by (k3+27k) m/s. Find the minimum velocity of the wave.  ee View Solution
ee  The equation w = et3+3et + 4 represents the change in mass 'w' (in grams) of a bacteria culture as time 't' (in hours) changes. Find the least mass of the culture.  ee View Solution
ee  The greatest volume of a cone of slant height l units is ____ cubic units.
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ee  The displacement s (in meters) of a particle in time t (in seconds) is given by, s = 2t - 3t2. Find the maximum displacement of the particle.
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ee  Find the central angle of a sector that has a perimeter k and a maximum area.  ee View Solution
ee  x, y are two positive numbers such that x2 + y2 = 128. Find the value of x + y so that x2 y2 is maximum.
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ee  A ball was thrown up. Its height above the surface of earth at time t is given by h(t) = at² + bt + c, where a, b, c are non-zero constants and a < 0. What is the maximum height attained by the ball?  ee View Solution
ee  The rate y of a chemical reaction is given by, y = kx(a - x), where x is the quantity of the product, a is the quantity of the material used for the reaction and k > 0. For what value of x is the rate of reaction maximum?
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ee  The profit P(x) of a company is given by P(x) = - x33 + 484x - 590 , 0 ≤ x ≤ 25, where x is the volume of production. Find the value of x for which the profit is maximum.
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ee  The equation f(v) = 21v + (8400v), where 0 < v < 30, relates the rate f(v) at which the engine works with its speed v. Find the value of v for which the rate is the least.
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ee  The percent concentration of a certain drug in the bloodstream, x hours after the drug is administered is given by f(x) = xx2 + 64 . For what value of x, the concentration is the maximum?
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