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:
Given that:
mass of stone (M) = 0.100 kg
mass of bullet (m) = 2.50 g = 2.5 ×10 ⁻³ kg
initial velocity of stone (
) = 0 m/s
Initial velocity of bullet (
) = (500 m/s)i
Speed of the bullet after collision (
) = (300 m/s) j
Suppose we represent
to be the velocity of the stone after the truck, then:
From linear momentum, the law of conservation can be applied which is expressed as:





∴
The magnitude now is:


Using the tangent of an angle to determine the direction of the velocity after the struck;
Let θ represent the direction:


Answer:
D By looking all the way to the cosmological horizon, we can see the actual conditions that prevailed all the way back to the first instant of the Big Bang.
Explanation:
Astrophysicists are able to determine the conditions that existed in the early universe, by using instruments such as telescopes to observe and study cosmic horizons. More ideas about the early universe can be found from the thermal light present in cosmic backgrounds.
Scientists study these details that provide an insight into the conditions that existed so many years ago. They have been able to determine that the Big Bang involved so many collisions from these observations.
It’s because conductors have nearly zero resistance to the flow of electrons that go through them. This leaves the electrons free to move and current can travel with full strength.
Answer:
true
Explanation:
<h3><em>A healthy body will keep you in shape and less risk of getting sick</em></h3>