Answer:

Explanation:
For this case we know the following info :
represent the initial volume
represent the final volume
We know that the pressure and volume are related with the following expression:

Where a is a constant given 
And we need to calculate the work associated to this process.
We have a compression, and by definition the work is defined with the following general expression:

If we replace the expression for P we got:

If we integrate we got:

Using the fundamental theorem of calculus we have:

And replacing the values we got:

Wait what is the question?
Answer:
8100 lbin²
Explanation:
Moment or inertia is expressed using the formula
I = mr²
M is the mass of the body
r is the radius of gyration
Given
W = 100lb
r = 9in
Required
Moment of inertia
I = Wr²
I = 100(9)²
I = 100×81
I = 8100lbin²
Hence the moment of inertia about the center of gravity for the rotator is
8100 lbin²
Answer:
Best case = 2 gloves
Given Information:
Red gloves = 5 pairs
Yellow gloves = 4 pairs
Green gloves = 2 pairs
smallest number of gloves you need to select to have at least one matching pair in the best case = ?
Explanation:
How many gloves do you need to make one matching pair?
2
Yes, you are right. 2 gloves makes a matching pair and it is the smallest number of gloves you need to select to have at least one matching pair.
But what about worst case?
lets say
you tried all 5 red gloves either all of them were left or right
then you tried 4 yellow gloves either all of them were left or right
then you tried 2 green gloves either all of them were left or right
Now all the left or right gloves are tried (5 + 4 + 2 = 11) and the 12th one will definitely be either matching red, yellow or green.
Therefore, in the worst case scenario, the smallest number of gloves you need to select to have at least one matching pair is 12.
Answer:


Explanation:
For this case we have given the following data:
represent the temperature for the air
represent the velocity of the air
represent the specific heat ratio at the room
represent the gas constant for the air
And we want to find the velocity of the air under these conditions.
We can calculate the spped of the sound with the Newton-Laplace Equation given by this equation:

Where K = is the Bulk Modulus of air, k is the adiabatic index of air= 1.4, R = the gas constant for the air,
the density of the air and T the temperature in K
So on this case we can replace and we got:

The Mach number by definition is "a dimensionless quantity representing the ratio of flow velocity past a boundary to the local speed of sound" and is defined as:

Where v is the flow velocity and
the volocity of the sound in the medium and if we replace we got:

And since the Ma<0.8 we can classify the regime as subsonic.