Question:
Consider a sample of helium gas in a container fitted with a piston as pictured below. The piston is frictionless, but has a mass of 10.0 kg. How many of the following processes will cause the piston to move away from the base and decrease the pressure of the gas? Assume ideal behavior.
I. Heating the helium. II.
II. toRemoving some of the helium from the container.
III. Turning the container on its side.
IV. Decreasing the pressure outside the container.
a) 0
b) 1
c) 2
d) 3
e) 4
Answer:
Only one process will cause the piston to move which is
i) Heating the helium
Explanation:
When helium is heated it becomes less dense or lighter. Heating the helium will cause an increase in volume which will make the piston to move away from the base. When the volume finishes increasing, the piston will stop moving which in turn will make the forces on both sides of the piston balanced, so the pressure inside will balance the weight of the piston and that of the atmosphere. From that we can see that there has been a pressure change as a result of heating.
Answer:
1. Lateral inversion is a phenomenon in which left appears to be right and vice versa. It is due to direction that light follows when it strikes a reflecting surface, generally a mirror.
These are the letters which don't show lateral inversion A,H,O,T,U
2. USES OF CONCAVE MIRROR
They are used as shaving mirrors to see a larger image of the face.
Dentists use concave mirrors to view large images of the teeth of the patients.
USES OF CONVEX MIRROR
It is is used as a rear view mirror in vehicles.
It is used as a vigilance mirror.
Answer: 272.82 drop/tile
Explanation:
Given that the Rain drops fall on a tile surface at a density of 4638 drops/ft2. There are 17 tiles/ft2. How many drops fall on each tile?
Tiles/ft^2 × drop/tiles = drop/ft^2
Tiles will cancel out. Leaving the answer to be drop/ ft^2
Substitutes all the magnitude of the above units.
17 × drop/tiles = 4638
Make drop/tiles the subject of formula
Drop/tiles = 4638/17
Drop/tiles = 272.82
Therefore, 272.82 drop/tile drops fall on each tile?
Answer:
Explanation:
We can solve the problem by using the following suvat equation:
where
v is the final velocity
u is the initial velocity
a is the acceleration
s is the displacement
For the car in this problem:
u = 0 (it starts from rest)
is the final velocity
s = 10 km = 10 000 m is the displacement
Solving for a, we find:
Answer:
, 
, 
Explanation:
The cube root of the complex number can determined by the following De Moivre's Formula:
![z^{\frac{1}{n} } = r^{\frac{1}{n} }\cdot \left[\cos\left(\frac{x + 2\pi\cdot k}{n} \right) + i\cdot \sin\left(\frac{x+2\pi\cdot k}{n} \right)\right]](https://tex.z-dn.net/?f=z%5E%7B%5Cfrac%7B1%7D%7Bn%7D%20%7D%20%3D%20r%5E%7B%5Cfrac%7B1%7D%7Bn%7D%20%7D%5Ccdot%20%5Cleft%5B%5Ccos%5Cleft%28%5Cfrac%7Bx%20%2B%202%5Cpi%5Ccdot%20k%7D%7Bn%7D%20%5Cright%29%20%2B%20i%5Ccdot%20%5Csin%5Cleft%28%5Cfrac%7Bx%2B2%5Cpi%5Ccdot%20k%7D%7Bn%7D%20%5Cright%29%5Cright%5D)
Where angles are measured in radians and k represents an integer between 
and 
.
The magnitude of the complex number is 
and the equivalent angular value is 
. The set of cubic roots are, respectively:
k = 0
![z^{\frac{1}{3} } = 3\cdot \left[\cos \left(\frac{1.817\pi}{3} \right)+i\cdot \sin\left(\frac{1.817\pi}{3} \right)]](https://tex.z-dn.net/?f=z%5E%7B%5Cfrac%7B1%7D%7B3%7D%20%7D%20%3D%203%5Ccdot%20%5Cleft%5B%5Ccos%20%5Cleft%28%5Cfrac%7B1.817%5Cpi%7D%7B3%7D%20%5Cright%29%2Bi%5Ccdot%20%5Csin%5Cleft%28%5Cfrac%7B1.817%5Cpi%7D%7B3%7D%20%5Cright%29%5D)
k = 1
![z^{\frac{1}{3} } = 3\cdot \left[\cos \left(\frac{3.817\pi}{3} \right)+i\cdot \sin\left(\frac{3.817\pi}{3} \right)]](https://tex.z-dn.net/?f=z%5E%7B%5Cfrac%7B1%7D%7B3%7D%20%7D%20%3D%203%5Ccdot%20%5Cleft%5B%5Ccos%20%5Cleft%28%5Cfrac%7B3.817%5Cpi%7D%7B3%7D%20%5Cright%29%2Bi%5Ccdot%20%5Csin%5Cleft%28%5Cfrac%7B3.817%5Cpi%7D%7B3%7D%20%5Cright%29%5D)
k = 2
![z^{\frac{1}{3} } = 3\cdot \left[\cos \left(\frac{5.817\pi}{3} \right)+i\cdot \sin\left(\frac{5.817\pi}{3} \right)]](https://tex.z-dn.net/?f=z%5E%7B%5Cfrac%7B1%7D%7B3%7D%20%7D%20%3D%203%5Ccdot%20%5Cleft%5B%5Ccos%20%5Cleft%28%5Cfrac%7B5.817%5Cpi%7D%7B3%7D%20%5Cright%29%2Bi%5Ccdot%20%5Csin%5Cleft%28%5Cfrac%7B5.817%5Cpi%7D%7B3%7D%20%5Cright%29%5D)
