Alan

If we exclude complex numbers then the domain is -9 ≤ x ≤ 9 and the range is 0 to 9.  If x lies outside this range then we are looking at the square root of a negative number.

Probably comes from a geometrical interpretation.  A square of side length L has an area of L².  A cube of side length L has a volume of L³.

cartesian to polar:

$$r=\sqrt{x^2+y^2}$$

$$\theta=\tan^{-1}(\frac{y}{x})$$

polar to cartesian:

$$x=r\cos{\theta}$$

$$y=r\sin{\theta}$$

What about it?  You need to ask a specific question!

From what?  What information do you have from which you want to work out the angles?

Do you mean you want to expand sin(x+2)?

Use sin(a+b) = sin(a)*cos(b) + sin(b)*cos(a)

Area = pi*diameter²/4

i is √(-1)

-8i*-3i = (-8)*(-3)*(i*i) = 8*3*(-1) = -24

You need the density of the particles.  If we say this is ρ kg/m³, and we assume the 0.3 μm is the diameter of a particle, then the mass of a particle is

m = ρ*(4/3)*pi*(3*10^-7/2)³kg = ρ*pi*(9/2)*10-²¹kg = ρ*pi*(9/2)*10^-15mg

The number density is 6000 particles per cm3, so the volumetric mass density is

  ρ*pi*(9/2)*10^-15*6000mg/cm³ =  ρ*pi*27*10^-12mg/cm³

Can't go any further without knowing the value of  ρ (in kg/m³)