Apiece of wire 25 m long is cut into two pieces. one piece is bent into a square and the other is bent into an equilateral triangle.(a) how much wire should be used for the square in order to maximize the total area

10.87 m

Explanation:

Total length of the wire = 25 m

Let the length of one piece is y and other piece is 25 - y

Let the side of square is a.

So, 4 a = y

a = y / 4

And the side of triangle is b

3 b = (25 - y)

b = (25 - y) / 3

Area of square, A1 = side x side =

A1 = y² / 16

Area of equilateral triangle, A2 =

Total area, A = A1 + A2

For maxima and minima, fins dA /dy

It is equal to zero.

9y = 173.2 -6.928 y

15.928 y = 173.2

y = 10.87 m

So, the length of wire to make square is 10.87 m.

scattering of light by tiny particles in air to produce the colors we see on sky, is dependent on the following factors:

(i) wavelength of light

(ii) size of the scattering particle  

(iii) distance traveled by light through the atmosphere.

according to rayleigh's law of scattering, the amount of scattering is inversely proportional to the fourth power of its wavelength. shorter the wavelength, greater is its scattering. hence violet/blue light is scattered more than red.

sun's light is a composite light ( visible light) with wavelengths in the range 400 nm (violet) to 700 nm (red). as sunlight passes through our atmosphere, the molecules of air scatter light according to their wavelengths. during sunrise and sunset, the sun's position is below the horizon. hence light from the sun travels a greater distance in the atmosphere when compared to its position a noon.

as sunlight enters the earth's atmosphere, blue light is scattered away and at the end of its journey in the sky, only red and orange wavelengths remain in the beam.

hence at sunrise and sunset, the sky appears reddish orange.

i believe the answer is a hope it and is correct