Answer:
h'=0.25m/s
Explanation:
In order to solve this problem, we need to start by drawing a diagram of the given situation. (See attached image).
So, the problem talks about an inverted circular cone with a given height and radius. The problem also tells us that water is being pumped into the tank at a rate of
. As you may see, the problem is talking about a rate of volume over time. So we need to relate the volume, with the height of the cone with its radius. This relation is found on the volume of a cone formula:

notie the volume formula has two unknowns or variables, so we need to relate the radius with the height with an equation we can use to rewrite our volume formula in terms of either the radius or the height. Since in this case the problem wants us to find the rate of change over time of the height of the gasoline tank, we will need to rewrite our formula in terms of the height h.
If we take a look at a cross section of the cone, we can see that we can use similar triangles to find the equation we are looking for. When using similar triangles we get:

When solving for r, we get:

so we can substitute this into our volume of a cone formula:

which simplifies to:


So now we can proceed and find the partial derivative over time of each of the sides of the equation, so we get:

Which simplifies to:

So now I can solve the equation for dh/dt (the rate of height over time, the velocity at which height is increasing)
So we get:

Now we can substitute the provided values into our equation. So we get:

so:

Answer:

Explanation:
<u>Uniform Acceleration
</u>
When an object changes its velocity at the same rate, the acceleration is constant.
The relation between the initial and final speeds is:

Where:
vf = Final speed
vo = Initial speed
a = Constant acceleration
t = Elapsed time
It's known a train moves from rest (vo=0) to a speed of vf=25 m/s in t=30 seconds. It's required to calculate the acceleration.
Solving for a:

Substituting:


We could use the formula for the Power supply in order to find the wattage capacity and it would be:
P = V²/R or P = V * I
Hope this helps!
Answer:
the weight of the object decreases when it is taken from the Earth to the Moon
Explanation:
The weight of an object is defined as the product of the mass of the object with the acceleration due to gravity of the Planet.

where,
W = weight of the object
m = mass of the object
g = acceleration due to gravity on the planet
The mass of an object remains constant everywhere in the universe. Therefore, the weight is directly proportional to the value of acceleration due to gravity.
The value of acceleration due to gravity on the Moon is lesser than its value on the Earth.
<u>Hence, the weight of the object decreases when it is taken from the Earth to the Moon </u>
As charges move in a closed loop, they gain as much energy as they lose.
<h3>What is principle of
conservation of energy?</h3>
- According to the principle of conservation of energy, in a closed or isolated system, the total energy of the system is always conserved.
- The energy gained by the particles or charges in a closed system is equal to the energy lost by the charges.
Thus, we can conclude the following based on principles of conservation of energy;
- As charges move in a closed loop, they gain as much energy as they lose.
Learn more about conservation of energy here: brainly.com/question/166559