Answer:
A. investigates the overall structure and history of the Universe.
Explanation:
Astronomy is the branch of natural science that studies the objects of a celestial nature.
Cosmology is a part of astronomy that examines the origin and the how the universe changes with the passage of time. The model which is widely accepted as how the universe came into being is the Lambda-CDM model.
According to the Lambda-CDM model the universe consists of cold dark matter, matter and dark energy.
Answer:
The resultant velocity is <u>169.71 km/h at angle of 45° measured clockwise with the x-axis</u> or the east-west line.
Explanation:
Considering west direction along negative x-axis and north direction along positive y-axis
Given:
The car travels at a speed of 120 km/h in the west direction.
The car then travels at the same speed in the north direction.
Now, considering the given directions, the velocities are given as:
Velocity in west direction is, ![\overrightarrow{v_1}=-120\ \vec{i}](https://tex.z-dn.net/?f=%5Coverrightarrow%7Bv_1%7D%3D-120%5C%20%5Cvec%7Bi%7D)
Velocity in north direction is, ![\overrightarrow{v_2}=120\ \vec{j}](https://tex.z-dn.net/?f=%5Coverrightarrow%7Bv_2%7D%3D120%5C%20%5Cvec%7Bj%7D)
Now, since
are perpendicular to each other, their resultant magnitude is given as:
![|\overrightarrow{v_{res}}|=\sqrt{|\overrightarrow{v_1}|^2+|\overrightarrow{v_2}|^2}](https://tex.z-dn.net/?f=%7C%5Coverrightarrow%7Bv_%7Bres%7D%7D%7C%3D%5Csqrt%7B%7C%5Coverrightarrow%7Bv_1%7D%7C%5E2%2B%7C%5Coverrightarrow%7Bv_2%7D%7C%5E2%7D)
Plug in the given values and solve for the magnitude of the resultant.This gives,
![|\overrightarrow{v_{res}}|=\sqrt{(120)^2+(120)^2}\\\\|\overrightarrow{v_{res}}|=120\sqrt{2} = 169.71\ km/h](https://tex.z-dn.net/?f=%7C%5Coverrightarrow%7Bv_%7Bres%7D%7D%7C%3D%5Csqrt%7B%28120%29%5E2%2B%28120%29%5E2%7D%5C%5C%5C%5C%7C%5Coverrightarrow%7Bv_%7Bres%7D%7D%7C%3D120%5Csqrt%7B2%7D%20%3D%20169.71%5C%20km%2Fh)
Let the angle made by the resultant be 'x' degree with the east-west line or the x-axis.
So, the direction is given as:
![x=\tan^{-1}(\frac{|v_2|}{|v_1|})\\\\x=\tan^{-1}(\frac{120}{-120})=\tan^{-1}(-1)=-45\ deg(clockwise\ angle\ with\ the\ x-axis)](https://tex.z-dn.net/?f=x%3D%5Ctan%5E%7B-1%7D%28%5Cfrac%7B%7Cv_2%7C%7D%7B%7Cv_1%7C%7D%29%5C%5C%5C%5Cx%3D%5Ctan%5E%7B-1%7D%28%5Cfrac%7B120%7D%7B-120%7D%29%3D%5Ctan%5E%7B-1%7D%28-1%29%3D-45%5C%20deg%28clockwise%5C%20angle%5C%20with%5C%20the%5C%20x-axis%29)
Therefore, the resultant velocity is 169.71 km/h at angle of 45° measured clockwise with the x-axis or the east-west line.
Answer:
a) 8 cents
b) 25.6 cents
c) 2.4 cents
Explanation:
Given:
Cost of electricity = 8 cents/kWh
Total cost = Wattage ×Time × Electricity cost
a) cost of running a lamp of 100 W for 10 h will be
Energy consumed = 100 W ×10 h = 1000 Wh or 1 kWh [1 kW = 1000 W]
Total cost = Energy consumed × electricity cost
⇒Total cost = 1 kWh × 8 cents/kWh = 8 cents
b) cost of running a TV of 400 W for 8 h will be
Energy consumed = 400 W × 8 h = 3200 Wh or 3.2 kWh
Total cost = Energy consumed × electricity cost
⇒Total cost = 3.2 kWh × 8 cents/kWh = 25.6 cents
c) cost of running a microwave of 1200 W for 15 min will be
Energy consumed = 1200 W ×
= 300 Wh or 0.3 kWh [1h = 60 min]
Total cost = Energy consumed × electricity cost
⇒Total cost = 0.3 kWh × 8 cents/kWh = 2.4 cents
The cosmic microwave background<span> (CMB) is electromagnetic </span>radiation<span> as a remnant from an early stage of the universe in Big Bang cosmology. In older literature, the CMB is also variously known as </span>cosmic microwave background radiation<span> (CMBR) or "relic </span>radiation<span>"</span>
Elementary charge used to determine charges of other objects is equal to a charge of electron or proton. It's value is roughly
![1.6* 10^{-19} C](https://tex.z-dn.net/?f=1.6%2A%2010%5E%7B-19%7D%20C)
. All other charges are whole-number multipliers of this elementary charge, meaning that we multiply elementary charge by {...,-2,-1,0,1,2,...}.
To find out if the measured charge can be accepted we need to divide it with elementary charge to see if we get whole number as result.
There are three possible values of measured charge:
![8.7* 10^{-19} C\\ 8.8* 10^{-19} C \\ 8.9* 10^{-19} C](https://tex.z-dn.net/?f=8.7%2A%2010%5E%7B-19%7D%20C%5C%5C%208.8%2A%2010%5E%7B-19%7D%20C%20%5C%5C%208.9%2A%2010%5E%7B-19%7D%20C)
![N_{1} = \frac{8.7* 10^{-19} C }{1.6* 10^{-19} C } =5.44 \\ N_{2} = \frac{8.8* 10^{-19} C }{1.6* 10^{-19} C } =5.5 \\ N_{3} = \frac{8.9* 10^{-19} C }{1.6* 10^{-19} C } =5.56](https://tex.z-dn.net/?f=%20N_%7B1%7D%20%3D%20%5Cfrac%7B8.7%2A%2010%5E%7B-19%7D%20C%20%7D%7B1.6%2A%2010%5E%7B-19%7D%20C%20%7D%20%3D5.44%20%5C%5C%20N_%7B2%7D%20%3D%20%5Cfrac%7B8.8%2A%2010%5E%7B-19%7D%20C%20%7D%7B1.6%2A%2010%5E%7B-19%7D%20C%20%7D%20%3D5.5%20%5C%5C%20N_%7B3%7D%20%3D%20%5Cfrac%7B8.9%2A%2010%5E%7B-19%7D%20C%20%7D%7B1.6%2A%2010%5E%7B-19%7D%20C%20%7D%20%3D5.56)
As we can see none of the possible values of a measured charge is whole-number multiplier of elementary charge so the researcher should not accept the value.
This charge can be achieved by using quarks which have value of 1/3 of elementary charge but they do not remain stable for long enough.