Answer:
t = 0.1111 s
Explanation:
Let's reduce the magnitudes to the SI system
d = 120 mm (1m / 1000 mm)
d= 0.120 m
w = 540 rpm (2pi rad / 1 rev) (1 min / 60s)
w= 56.55 rad / s
When at maximum speed we can use angular kinematic relationships to find the time for a sperm revolution with zero angular acceleration
W = θ / t
t = θ / w
t = 2π / 56.55
t = 0.1111 s
Answer: Heat will transfer from the water to the air. When a mass of air moves on a warmer surface it is heated by its base. Then thermal instability develops in the lower layers and then extends upwards. If the air initially contained inversions, these are destroyed and a strong gradient is established uniformly in the lower troposphere temperature.
The net force applied to the object equals the mass of the object multiplied by the amount of its acceleration." The net force acting on the soccer ball is equal to the mass of the soccer ball multiplied by its change in velocity each second (its acceleration).
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:
twelve facesFrom left to right the solids are tetrahedron (four sides), cube (six sides), octahedron (eight faces), dodecahedron (twelve faces), and icosahedron (twenty faces).
Explanation:
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