Asquare-based shipping crate is being designed that must contain a volume of 16 ft3 . the material that is used for the base and the lid costs 3 dollars/ft2 , while the material used for the sides costs 2 dollars/ft2 . what are the most cost-effective dimensions of such a crate?

Explanation:

Given

volume

Suppose base is square with side L

height of crate is h

Volume

Cost of top and bottom area

Cost of Side area

Total Cost

Total Cost

Differentiate C w.r.t Length

Dimensions are    

harry byrd declared organized resistance by southern states would prevent racial integration.

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.