Answer:
Directly proportional: as one amount increases another amount increases at the ... The "constant of proportionality" is the value that relates the two amounts ... Example: y is directly proportional to x, and when x=3 then y=15. ... Speed and travel time are Inversely Proportional because the faster we go the shorter the time.
Answer:
The surface gravity g of the planet is 1/4 of the surface gravity on earth.
Explanation:
Surface gravity is given by the following formula:

So the gravity of both the earth and the planet is written in terms of their own radius, so we get:


The problem tells us the radius of the planet is twice that of the radius on earth, so:

If we substituted that into the gravity of the planet equation we would end up with the following formula:

Which yields:

So we can now compare the two gravities:

When simplifying the ratio we end up with:

So the gravity acceleration on the surface of the planet is 1/4 of that on the surface of Earth.
Answer:
The number density of the gas in container A is twice the number density of the gas in container B.
Explanation:
Here we have
P·V =n·R·T
n = P·V/(RT)
Therefore since V₁ = V₂ and T₁ = T₂
n₁ = P₁V₁/(RT₁)
n₂ = P₂V₂/(RT₂)
P₁ = 4 atm
P₂ = 2 atm
n₁ = 4V₁/(RT₁)
n₂ =2·V₁/(RT₁)
∴ n₁ = 2 × n₂
Therefore, the number of moles in container A is two times that in container B and the number density of the gas in container A is two times the number density in container B.
This can be shown based on the fact that the pressure of the container is due to the collision of the gas molecules on the walls of the container, with a kinetic energy that is dependent on temperature and mass, and since the temperature is constant, then the mass of container B is twice that of A and therefore, the number density of container A is twice that of B.
The change in potential energy of an object is given by

where
m is the mass of the object
g is the gravitational acceleration

is the increase in altitude of the object
In our problem,

is the mass of the book,

and

is the increase in altitude of the book, so its variation of potential energy is