A large window has the shape of a rectangle surmounted by an equilateral triangle.if the perimeter of the window is 12m, find the dimensions of the rectangle that will produce the largest area of the window?

The points on the curve 9y^{2} = x^{3}, where the normal to the curve makes equal intercepts with the axes are

(A) (B)

(C) (D)

A rectangle is inscribed in a semi circle of radius 'r' with one of its sides on the diameter of the semi circle. Find the dimensions of the rectangle so that its area is maximum. Also find this area.

Prove that curve(x/a)^{n}+(y/b)^{n}=2 touches the straight line x/a+y/b=2 at (a,b) for all values of n belongs to N at the point (a,b)..

A helicopter is flying along the curve y= x2+2.A soldier is placed at the point (3,2). Find the nearest distance between the soldier and the helicopter.(2010Sp)

Prove that the radius of the base of right circular cylinder of greatest curved surface area which can be inscribed in a given cone is half that of the cone

An isosceles triangle of vertical angle 2a is inscribed in a circle of radius r.Show that the area of triangle is maximum when a=(pi)/6.

A given quanitity of metal is to be cast into a half cylinder with a rectangular base and semi circular ends. Finfd ratio of length of the cylinder to the diameter of its semi-circular ends.

Show that the altitude of the right circular cone of maximum volume that can be inscribed in a sphere of radius r is.

show that the line x/p+ y/q =1, touches the curve y=e^(-x/p) at the point where it crosses the y axis

the cost of fuel for running a train is proportional to square of speed generated in km/h.it cost rs 48/h when the train is moving at speed of 16km/h.what is its economical speed if the fixed charges are rs 300/hour over and above the running cost!

A point on the hypotenuse of a right angled triangle is at distances 'a' and 'b' from the sides .

A window is in the form of rectangle surmounted by a semicircular opening. The total perimeter of the window is 10 m. Find the dimensions of the window to admit maximum light through the whole opening.

Find the volume of the largest right circular cylinder that can inscribed in a sphere of radius r cm.

Prove that the area of a right angled triangle of given hypotenuse is maximum when the

A large window has the shape of a rectangle surmounted by an equilateral triangle.if the perimeter of the window is 12m, find the dimensions of the rectangle that will produce the largest area of the window?

The points on the curve 9

y^{2}=x^{3}, where the normal to the curve makes equal intercepts with the axes are(A) (B)

(C) (D)

A rectangle is inscribed in a semi circle of radius 'r' with one of its sides on the diameter of the semi circle. Find the dimensions of the rectangle so that its area is maximum. Also find this area.

Prove that curve(x/a)

^{n}+(y/b)^{n}=2 touches the straight line x/a+y/b=2 at (a,b) for all values of n belongs to N at the point (a,b)..A helicopter is flying along the curve y= x2+2.A soldier is placed at the point (3,2). Find the nearest distance between the soldier and the helicopter.(2010Sp)

Prove that the radius of the base of right circular cylinder of greatest curved surface area which can be inscribed in a given cone is half that of the cone

An isosceles triangle of vertical angle 2a is inscribed in a circle of radius r.Show that the area of triangle is maximum when a=(pi)/6.

A given quanitity of metal is to be cast into a half cylinder with a rectangular base and semi circular ends. Finfd ratio of length of the cylinder to the diameter of its semi-circular ends.

Show that the altitude of the right circular cone of maximum volume that can be inscribed in a sphere of radius

ris.show that the line x/p+ y/q =1, touches the curve y=e^(-x/p) at the point where it crosses the y axis

the cost of fuel for running a train is proportional to square of speed generated in km/h.it cost rs 48/h when the train is moving at speed of 16km/h.what is its economical speed if the fixed charges are rs 300/hour over and above the running cost!

A point on the hypotenuse of a right angled triangle is at distances 'a' and 'b' from the sides .

raised to 2/3 +araised to 2/3}the whole raised to 3/2bA window is in the form of rectangle surmounted by a semicircular opening. The total perimeter of the window is 10 m. Find the dimensions of the window to admit maximum light through the whole opening.

Find the volume of the largest right circular cylinder that can inscribed in a sphere of radius r cm.

Prove that the area of a right angled triangle of given hypotenuse is maximum when the