A window is in the form of a 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.

A window is in the form of a rectangle surmounted by a semi-circular opening. The total perimeter of the window is 10 meters. Find the dimensions of the rectangle so as to admit maximum light through the whole opening.

A window is in the shape of a rectangle surmounted by a semi circle. If the perimeter of the window is of fixed length k then the maximum area of the window is

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

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

A window is in the form of a rectangle, together with a semi-circle on its top side as diameter. If the perimeter of the window is 80 inches, determine the dimensions of the rectangle, so that a maximum amount of light may be admitted.

A window of perimeter P (including the base of the arch) is in the form of a rectangle surrounded by a semi-circle. The semi-circular portion is fitted with the colored glass while the rectangular part is fitted with the clear glass that transmits three times as much light per square meter as the colored glass does. What is the ratio for the sides of the rectangle so that the window transmits the maximum light?

A ladder 10m long reaches a window 8 m above the ground. Find the distance of the foot of the ladder from base of the wall.

Length of a horizontal arm of ends of both the vertical arms pressure P_(0) = 10^(5) N//m^(2) . A liquid of density rho = 10^(3) kg //m^(3) is poured in the tube such that liquid just fills the horizontal part of the tube as a shown in Fig. Now one end of the open ends is sealed and the tube is then rotated about a vertical axis passing through the other vertical arm with angular speed omega_(0)=sqrt(40//3)rad//sec . If length of each vertical arm is a = 1 m and in the sealed end liquid rises to a height y = 1//2 m , find pressure in the sealed tube during rotation. (in xx 10^(5) N//m^(2))

A sheet of area 40m^2 is used to make an open tank with square base. Find the dimensions of the base such that the volume of this tank is maximum.

In a double slit interference experiment, the separation between the slits is 1.0 mm, the wavelength of light used is 5.0 x 10^ -7 m and the distance of the screen from the slits is 1.0 m. (a) Find the distance of the centre of the first minimum from the centre of the central maximum. (b) How many bright fringes are formed in one centimeter width on the screen ?