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e What is the maximum possible area of a rectangle if the perimeter is 280 m? e

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e Find the minimum possible perimeter of a rectangle if the area is 8100 m^{2}. e

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e The sum of two positive numbers is 30. What is the smallest possible value for the sum of their squares? e

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e If x and y are two positive numbers whose sum is 20, then find the largest possible value for x^{2} y. e

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e 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? e

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e The sum of two positive numbers is 40. Find the smallest possible value for the sum of their cubes. e

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e Find the largest possible area for a rectangle if the diagonal measures a cm. [a = 64] e

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e 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? e

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e A rectangular box with a square base has a volume of 27000 cm^{3}. What is the minimum possible total surface area of the box? e

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BB Find the largest area of a rectangle inscribed in a circle of radius r = 2 cm. BB

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BB The difference between two numbers x and y is 40 where 0 < y < x. Find the values of x, y, for which (x^{2}  2y^{2}) is maximum. BB

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BB What is the maximum area of a triangle, if two of its sides measure 8 units and 13 units? BB

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BB What is the perimeter of a triangle of maximum area having two sides 9 and 12? BB

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BB The velocity of a wave of wavelength k is given by (k4+64k) m/s. Find the minimum velocity of the wave. BB

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BB The displacement s (in meters) of a particle in time t (in seconds) is given by, s = 5t  6t^{2}. Find the maximum displacement of the particle. BB

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BB 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. BB

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BB 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. BB

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BB 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? BB

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BB x, y are two positive numbers such that x^{2} + y^{2} = 32. Find the value of x + y so that x^{2} y^{2} is maximum. BB

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BB What is the maximum area of a triangle, if two of its sides measure 8 units and 11 units? BB

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BB What is the perimeter of a triangle of maximum area having two sides 12 and 16? BB

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BB A rectangular box with a square base has a volume of 125000 cm^{3}. What is the minimum possible total surface area of the box? BB

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BB Find the largest area of a rectangle inscribed in a circle of radius r = 5 cm. BB

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BB What is the maximum possible area of a rectangle if the perimeter is 80 m? BB

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BB Find the minimum possible perimeter of a rectangle if the area is 3600 m^{2}. BB

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BB The sum of two positive numbers is 20. What is the smallest possible value for the sum of their squares? BB

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BB The sum of two positive numbers is 180. Find the smallest possible value for the sum of their cubes. BB

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BB 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? BB

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BB If x and y are two positive numbers whose sum is 70, then find the largest possible value for x^{2} y. BB

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BB 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? BB

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BB Find the largest possible area for a rectangle if the diagonal measures a cm. [a = 36] BB

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BB 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. BB

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BB The difference between two numbers x and y is 80 where 0 < y < x. Find the values of x, y, for which (x^{2}  2y^{2}) is maximum. BB

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BB The velocity of a wave of wavelength k is given by (k3+27k) m/s. Find the minimum velocity of the wave. BB

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BB 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. BB

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BB The greatest volume of a cone of slant height l units is ____ cubic units. BB

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BB The displacement s (in meters) of a particle in time t (in seconds) is given by, s = 2t  3t^{2}. Find the maximum displacement of the particle. BB

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BB Find the central angle of a sector that has a perimeter k and a maximum area. BB

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BB x, y are two positive numbers such that x^{2} + y^{2} = 128. Find the value of x + y so that x^{2} y^{2} is maximum. BB

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BB 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 nonzero constants and a < 0. What is the maximum height attained by the ball? BB

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BB 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? BB

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BB 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. BB

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BB 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. BB

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BB 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? BB

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BB 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. BB

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BB Bill owns two triangular plots ABC, ADE with areas a ft^{2}, b ft^{2} 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. BB

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