- -
Solved Examples
Click on a 'View Solution' below for other questions:
e   What is the maximum possible area of a rectangle if the perimeter is 280 m?
   e
View Solution
e   Find the minimum possible perimeter of a rectangle if the area is 8100 m2.   e View Solution
e   The sum of two positive numbers is 30. What is the smallest possible value for the sum of their squares?   e View Solution
e   If x and y are two positive numbers whose sum is 20, then find the largest possible value for x2 y.
   e
View Solution
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
View Solution
e   The sum of two positive numbers is 40. Find the smallest possible value for the sum of their cubes.   e View Solution
e   Find the largest possible area for a rectangle if the diagonal measures a cm. [a = 64]   e View Solution
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 View Solution
e   A rectangular box with a square base has a volume of 27000 cm3. What is the minimum possible total surface area of the box?
   e
View Solution
e   Find the largest area of a rectangle inscribed in a circle of radius r = 2 cm.   e View Solution
e   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.
   e
View Solution
e   What is the maximum area of a triangle, if two of its sides measure 8 units and 13 units?
   e
View Solution
e   What is the perimeter of a triangle of maximum area having two sides 9 and 12?
   e
View Solution
e   The velocity of a wave of wavelength k is given by (k4+64k) m/s. Find the minimum velocity of the wave.   e View Solution
e   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.
   e
View Solution
e   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.
   e
View Solution
e   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.
   e
View Solution
e   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?
   e
View Solution
e   What is the maximum area of a triangle, if two of its sides measure 8 units and 11 units?
   e
View Solution
e   What is the perimeter of a triangle of maximum area having two sides 12 and 16?
   e
View Solution
e   A rectangular box with a square base has a volume of 125000 cm3. What is the minimum possible total surface area of the box?
   e
View Solution
e   x, y are two positive numbers such that x2 + y2 = 32. Find the value of x + y so that x2 y2 is maximum.
   e
View Solution
e   Find the largest area of a rectangle inscribed in a circle of radius r = 5 cm.   e View Solution
e   What is the maximum possible area of a rectangle if the perimeter is 80 m?
   e
View Solution
e   Find the minimum possible perimeter of a rectangle if the area is 3600 m2.   e View Solution
e   The sum of two positive numbers is 20. What is the smallest possible value for the sum of their squares?   e View Solution
e   The sum of two positive numbers is 180. Find the smallest possible value for the sum of their cubes.   e View Solution
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 6 miles per hour?   e View Solution
e   If x and y are two positive numbers whose sum is 70, then find the largest possible value for x2 y.
   e
View Solution
e   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?
   e
View Solution
e   Find the largest possible area for a rectangle if the diagonal measures a cm. [a = 36]   e View Solution
e   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.
   e
View Solution
e   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.
   e
View Solution
e   The velocity of a wave of wavelength k is given by (k3+27k) m/s. Find the minimum velocity of the wave.   e View Solution
e   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.   e View Solution
e   The greatest volume of a cone of slant height l units is ____ cubic units.
   e
View Solution
e   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.
   e
View Solution
e   Find the central angle of a sector that has a perimeter k and a maximum area.   e View Solution
e   x, y are two positive numbers such that x2 + y2 = 128. Find the value of x + y so that x2 y2 is maximum.
   e
View Solution
e   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?   e View Solution
e   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?
   e
View Solution
e   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.
   e
View Solution
e   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.
   e
View Solution
e   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?
   e
View Solution
e   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.   e View Solution
e   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.
   e
View Solution