Jeremy has a handful of resistors. All of them, except one, have four bands. The exception has three. Why? A. He should use anot
1 answer:
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To solve this problem it is necessary to apply the concepts related to the geometry of a cylindrical tank and its respective definition.
The volume of a tank is given by
Where
d = Diameter
h = Height
Considering that there are two stages, let's define the initial and final volume as,
We know as well by definition that
Then we have for the statement that
Replacing the previous data
Solving to get h,
Therefore the change is
Therefore te change in the height of the water in the tank is 0.37mm
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:
