Answer:
a)
, b)
solar masses
Explanation:
Let suppose that galaxy can be treated as a puntual mass.
a) The acceleration experimented by the star is:
![a_{r} = G\cdot \frac{M}{r^{2}}](https://tex.z-dn.net/?f=a_%7Br%7D%20%3D%20G%5Ccdot%20%5Cfrac%7BM%7D%7Br%5E%7B2%7D%7D)
![a_{r} = \left(6.674\times 10^{-11}\,\frac{m^{3}}{kg\cdot s^{2}} \right)\cdot (8.0\times 10^{11})\cdot\frac{\left(1.989\times 10^{30}\,kg\right)}{\left[(6.0\times 10^{4}\,ly)\cdot \left(9.461\times 10^{15}\,\frac{m}{ly} \right)\right]^{2}}](https://tex.z-dn.net/?f=a_%7Br%7D%20%3D%20%5Cleft%286.674%5Ctimes%2010%5E%7B-11%7D%5C%2C%5Cfrac%7Bm%5E%7B3%7D%7D%7Bkg%5Ccdot%20s%5E%7B2%7D%7D%20%5Cright%29%5Ccdot%20%288.0%5Ctimes%2010%5E%7B11%7D%29%5Ccdot%5Cfrac%7B%5Cleft%281.989%5Ctimes%2010%5E%7B30%7D%5C%2Ckg%5Cright%29%7D%7B%5Cleft%5B%286.0%5Ctimes%2010%5E%7B4%7D%5C%2Cly%29%5Ccdot%20%5Cleft%289.461%5Ctimes%2010%5E%7B15%7D%5C%2C%5Cfrac%7Bm%7D%7Bly%7D%20%5Cright%29%5Cright%5D%5E%7B2%7D%7D)
![a_{r} = 3.296\times 10^{-10}\,\frac{m}{s^{2}}](https://tex.z-dn.net/?f=a_%7Br%7D%20%3D%203.296%5Ctimes%2010%5E%7B-10%7D%5C%2C%5Cfrac%7Bm%7D%7Bs%5E%7B2%7D%7D)
The angular speed of the star is:
![\omega = \sqrt{\frac{a_{r}}{r} }](https://tex.z-dn.net/?f=%5Comega%20%3D%20%5Csqrt%7B%5Cfrac%7Ba_%7Br%7D%7D%7Br%7D%20%7D)
![\omega = \sqrt{\frac{3.296\times 10^{-10}\,\frac{m}{s^{2}} }{(6.0\times 10^{4})\cdot (9.461\times 10^{15}\,\frac{m}{ly} )} }](https://tex.z-dn.net/?f=%5Comega%20%3D%20%5Csqrt%7B%5Cfrac%7B3.296%5Ctimes%2010%5E%7B-10%7D%5C%2C%5Cfrac%7Bm%7D%7Bs%5E%7B2%7D%7D%20%7D%7B%286.0%5Ctimes%2010%5E%7B4%7D%29%5Ccdot%20%289.461%5Ctimes%2010%5E%7B15%7D%5C%2C%5Cfrac%7Bm%7D%7Bly%7D%20%29%7D%20%7D)
![\omega = 7.62\times 10^{-16}\,\frac{rad}{s}](https://tex.z-dn.net/?f=%5Comega%20%3D%207.62%5Ctimes%2010%5E%7B-16%7D%5C%2C%5Cfrac%7Brad%7D%7Bs%7D)
The period is:
![T = \frac{2\pi}{\omega}](https://tex.z-dn.net/?f=T%20%3D%20%5Cfrac%7B2%5Cpi%7D%7B%5Comega%7D)
![T = \frac{2\pi}{7.62\times 10^{-16}\,\frac{rad}{s} }](https://tex.z-dn.net/?f=T%20%3D%20%5Cfrac%7B2%5Cpi%7D%7B7.62%5Ctimes%2010%5E%7B-16%7D%5C%2C%5Cfrac%7Brad%7D%7Bs%7D%20%7D)
![T = 8.246\times 10^{15}\,s](https://tex.z-dn.net/?f=T%20%3D%208.246%5Ctimes%2010%5E%7B15%7D%5C%2Cs)
![T = 26.147\times 10^{7}\,y](https://tex.z-dn.net/?f=T%20%3D%2026.147%5Ctimes%2010%5E%7B7%7D%5C%2Cy)
b) The period is:
![T = 6\times 10^{7}\,y](https://tex.z-dn.net/?f=T%20%3D%206%5Ctimes%2010%5E%7B7%7D%5C%2Cy)
![T = 1.892\times 10^{15}\,s](https://tex.z-dn.net/?f=T%20%3D%201.892%5Ctimes%2010%5E%7B15%7D%5C%2Cs)
The angular speed is:
![\omega = \frac{2\pi}{1.892\times 10^{15}\,s}](https://tex.z-dn.net/?f=%5Comega%20%3D%20%5Cfrac%7B2%5Cpi%7D%7B1.892%5Ctimes%2010%5E%7B15%7D%5C%2Cs%7D)
![\omega = 3.321\times 10^{-15}\,\frac{rad}{s}](https://tex.z-dn.net/?f=%5Comega%20%3D%203.321%5Ctimes%2010%5E%7B-15%7D%5C%2C%5Cfrac%7Brad%7D%7Bs%7D)
The acceleration experimented by the star is:
![a_{r} = \left(3.321\times 10^{-15}\,\frac{rad}{s} \right)^{2}\cdot (6\times 10^{4}\,ly)\cdot \left(9.461\times 10^{15}\,\frac{m}{ly} \right)](https://tex.z-dn.net/?f=a_%7Br%7D%20%3D%20%5Cleft%283.321%5Ctimes%2010%5E%7B-15%7D%5C%2C%5Cfrac%7Brad%7D%7Bs%7D%20%5Cright%29%5E%7B2%7D%5Ccdot%20%286%5Ctimes%2010%5E%7B4%7D%5C%2Cly%29%5Ccdot%20%5Cleft%289.461%5Ctimes%2010%5E%7B15%7D%5C%2C%5Cfrac%7Bm%7D%7Bly%7D%20%5Cright%29)
![a_{r} = 6.261\times 10^{-9}\,\frac{m}{s^{2}}](https://tex.z-dn.net/?f=a_%7Br%7D%20%3D%206.261%5Ctimes%2010%5E%7B-9%7D%5C%2C%5Cfrac%7Bm%7D%7Bs%5E%7B2%7D%7D)
The mass of the galaxy is:
![M = \frac{a_{r}\cdot r^{2}}{G}](https://tex.z-dn.net/?f=M%20%3D%20%5Cfrac%7Ba_%7Br%7D%5Ccdot%20r%5E%7B2%7D%7D%7BG%7D)
![M = \frac{\left(6.261\times 10^{-9}\,\frac{m}{s^{2}} \right)\cdot \left[(6.0\times 10^{4}\ly)\cdot (9.461\times 10^{15}\,\frac{m}{ly} )\right]^{2}}{6.674\times 10^{-11}\,\frac{m^{3}}{kg\cdot s^{2}} }](https://tex.z-dn.net/?f=M%20%3D%20%5Cfrac%7B%5Cleft%286.261%5Ctimes%2010%5E%7B-9%7D%5C%2C%5Cfrac%7Bm%7D%7Bs%5E%7B2%7D%7D%20%5Cright%29%5Ccdot%20%5Cleft%5B%286.0%5Ctimes%2010%5E%7B4%7D%5Cly%29%5Ccdot%20%289.461%5Ctimes%2010%5E%7B15%7D%5C%2C%5Cfrac%7Bm%7D%7Bly%7D%20%29%5Cright%5D%5E%7B2%7D%7D%7B6.674%5Ctimes%2010%5E%7B-11%7D%5C%2C%5Cfrac%7Bm%5E%7B3%7D%7D%7Bkg%5Ccdot%20s%5E%7B2%7D%7D%20%7D)
![M = 3.023\times 10^{43}\,kg](https://tex.z-dn.net/?f=M%20%3D%203.023%5Ctimes%2010%5E%7B43%7D%5C%2Ckg)
Which is equal to
solar masses.
Answer : Capacitors
Explanation : Capacitors are normally placed on transmission or distribution lines when to reduce inductive reactance.
This is because it enhances electromechanical and voltage stability , limit voltage dips at network nodes and reduces the power loss.
So, we can say that inductive reactance normally replace by the capacitors.
Answer:
The answer is below
Explanation:
Speed is the ratio of total distance traveled to the total time taken. It is given by the formula:
Speed = Distance / time taken
Given that the speed = The polynomial 45.000 mph.
In a day there are 24 hours, hence, the distance traveled is:
Speed = Distance / time taken
45 mph = Distance / 24 hours
Distance = 45 mph × 24 h = 1080 miles
But 1 mile = 1609.34 m
1080 miles = ![1080\ miles*\frac{1609.34 \ m}{1\ miles}=1738092\ m](https://tex.z-dn.net/?f=1080%5C%20miles%2A%5Cfrac%7B1609.34%20%5C%20m%7D%7B1%5C%20miles%7D%3D1738092%5C%20m)
Given that Altuve = 1.65 m
Hence, the number of Altuve traveled = 1738092 m / 1.65 m = 1053389
1053389 Altuves was traveled
the third once because if you multiply them you get 2800 and 14 days is the same as 2 weeks
Answer: A. burning fossil fuels
B. metamorphism of limestone
C. volcanism
G. animal respiration
Explanation:
The carbon cycle is a biogeochemical cycle. In this, the carbon is exchanged among different spheres of the earth atmosphere, biosphere, geosphere, hydrosphere and pedosphere on planet Earth.
Burning of fossil fuels: The fossil fuels when burn releases carbon chemicals in the form of gases such as carbon dioxide and carbon monoxide.
Metamorphism of limestone: The metamorphism of limestone released carbon dioxide gas to the atmosphere.
Volcanism: Volcanism is an act of emergence of hot magma under the surface of the earth. Along with magma, the hot gases like carbon dioxide and carbon monoxide are also released which contribute to the carbon cycle.
Animal respiration: The animals when respire release carbon dioxide to the atmosphere as a metabolic byproduct.