The assignment is to draw a contour diagram of an ordinary object of your choosing. the object should be somewhat a) the diagram should show the origin and at least 10 b) pick a point and calculate/estimate a directional irregularly shaped. contours. derivative in a direction of your choosing. while you are doing this, contemplate the thought that calculus is largely about how to measure quantitative change, and be sure to use units in your calculations. c) attach a photograph of the object. d) calculate/estimate the gradient at the same point. how does the gradient compare numerically to your directional derivative? how are the gradient and the level curve positioned with respect to each other? strive for accuracy, clarity, and focus. hopefully, this exercise will reveal a deep and technical understanding of the directional derivative. also, the word "slant" may come to have an enhanced meaning: that our understanding of it depends in large part on the direction in which we are looking. finally, try to enjoy the process of measuring, drawing, and thinking in this mathematical way!

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 need with 1.3.2 investigate cycling o2 and co2 apex

we need to see it

one "light year" is the distance that light travels, through vacuum, in one julian year.   that's 365.25 days, of 24 hours each.