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Thanks for your support.w**3/11 - 108*w**2/11 + 33*w. Find j, given that k(j) = 0.
-2, 0, 2
Let n(x) be the first derivative of -2*x**3/3 + x**2/2 + 3. Suppose n(i) = 0. Calculate i.
0, 1/2
Factor 3/2*n**3 + 12 - 3/4*n**4 - 33/4*n**2 + 12*n.
-3*(n - 4)**2*(n + 1)**2/4
Let j(p) be the third derivative of -p**8/1176 + p**7/735 + p**6/210 - p**5/105 - p**4/84 + p**3/21 - 8*p**2. Factor j(z).
-2*(z - 1)**3*(z + 1)**2/7
Let y(a) be the first derivative of -a**6/540 - a**5/45 - a**4/9 - a**3 + 4. Let x(j) be the third derivative of y(j). Find o such that x(o) = 0.
-2
Let z = -4 - -6. Let p(a) be the first derivative of a + z*a**2 - 1/3*a**3 - 1. Factor p(m).
-(m - 1)**2
Let m(b) = -b**3 - 2*b**2 + 2*b + 5. Let q(o) = -o**
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- There are thousands of nebulae and it is beyond the power of human imagination to list them all. The glorious universe is filled with clouds of gas and dust, most of them are cold but some are warmer and glow with life.
- The fundamental characteristic of nebulae is the turbulent atmosphere in which these phenomena can easily take place. Nebulae are visible in all parts of the universe, and in our own galaxy we see nebulae that are far from the brightest stars.
- The most spectacular nebulae are the larger ones, the ones with a diameter from a few tens to a few hundreds parsecs.
- As long as there are stars in the universe, the nebulae are present and provide us with interesting pictures.
- Nebulae differ among themselves by their shape, by the brightness and by the density of their gases. A nebula gives birth to stars and is one of the local manifestations of the interstellar medium.
- The word nebula means vortex, and it can be defined as an interstellar cloud of gas and dust suspended in the interstellar medium. The visible part of the nebula is its gaseous outer layer.
- The larger and more massive nebulae are called molecular clouds and the smaller and weaker ones are called photoionized clouds.
- The gas in a nebula is not stable, it is always undergoing changes. This happens thanks to shocks between two neighbouring clouds, between a cloud and a neighbouring star or between a cloud and itself.
- Nebulae are of different shapes, many of them are found only in the vicinity of a star. Others, however, do not change their form, but they are much smaller than the ones that originate from a star.
- The gases in a nebula are in some cases ionized. With the emission of UV radiation from the star, it becomes visible to the naked eye as a nebula.
- Nebulae form within the molecular clouds. They are formed by supernova explosions, stellar winds and by a slowly expanding shock wave with the interstellar medium.
- Nebulae are composed of gaseous clouds and dust particles. The dust has a size of a few microns. When the size of a dust particle is less than the size of a wavelength in the visible region, a particle can be invisible in the visible region, but it is so light that it will be seen in the infrared region.
- If there is enough light, the dust can emit its own
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