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# rates of change watch

1. can someone help me with this question please?

because the water is entering and leaving the cylinder simultaneously, I figured that

????

because its leaving at a rate proportional to the square root of the height?

should I look for in terms of ??
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2. dh/dt= dh/dv times dv/dt. Find expressions for both and use the fact that V=4000h
3. (Original post by Maths&physics)
can someone help me with this question please?

because the water is entering and leaving the cylinder simultaneously, I figured that

????

because its leaving at a rate proportional to the square root of the height?
Not quite.

The total volume of the cylinder is . Using the fact that the cross section is , you can find the radius of the cylinder .

Differentiating w.r.t time yields .

We know that so we can use this with the first eq. and obtain the answer.
4. (Original post by RDKGames)
Not quite.

The total volume of the cylinder is . Using the fact that the cross section is , you can find the radius of the cylinder .

Differentiating w.r.t time yields .

We know that so we can use this with the first eq. and obtain the answer.
isn't the volume of a cylinder:

5. (Original post by Maths&physics)
isn't the volume of a cylinder:
That formula is for the volume of a cone.
6. (Original post by RDKGames)
That formula is for the volume of a cone.
thank you!

im not with it today
7. (Original post by RDKGames)
That formula is for the volume of a cone.
I would do

?
8. (Original post by Maths&physics)
I would do

?
Not sure why...

9. (Original post by RDKGames)
Not sure why...

thanks but I dont understand why youre differentiating volume with respect to time?
10. (Original post by Maths&physics)
thanks but I dont understand why youre differentiating volume with respect to time?
Because the information tells how much flows in and how much flows out every second therefore it is logical to try to obtain .
11. For these types of questions, I like to start by writing out what it is you want to find.

In this case, you are solving for
You also need to identify that ,
where is some constant of proportionality.
Now we see that we have 3 different variables, and
, so it would be make sense to apply the chain rule in order to solve for .
So,
Since , we can obtain and so is simply its reciprocal. We also know this to be
Now we just have to substitute our differentials into our chain rule equation, and acquire an expression for
Once you multiply this through, you'll find that your answer looks very similar to what the question is asking for. But remember that is just some constant, and so we can define a new constant in terms of the coefficients of

Hope this helps!
12. (Original post by RDKGames)
Because the information tells how much flows in and how much flows out every second therefore it is logical to try to obtain .
does give us area? I thought gave us area?
13. (Original post by Maths&physics)
does give us area? I thought gave us area?
TBH just use the solution that was posted above, I feel like my approach is only confusing you...
14. (Original post by RDKGames)
TBH just use the solution that was posted above, I feel like my approach is only confusing you...
yeah, im pretty confused
15. (Original post by RDKGames)
Not sure why...

That's not very helpful - you need to explain why.
16. (Original post by DisneylandChina)
For these types of questions, I like to start by writing out what it is you want to find.

In this case, you are solving for
You also need to identify that ,
where is some constant of proportionality.
Now we see that we have 3 different variables, and
, so it would be make sense to apply the chain rule in order to solve for .
So,
Since , we can obtain and so is simply its reciprocal. We also know this to be
Now we just have to substitute our differentials into our chain rule equation, and acquire an expression for
Once you multiply this through, you'll find that your answer looks very similar to what the question is asking for. But remember that is just some constant, and so we can define a new constant in terms of the coefficients of

Hope this helps!
,

I get that.

and you do:

where do you go from here?
17. (Original post by Maths&physics)
yeah, im pretty confused
18. (Original post by Muttley79)
That's not very helpful - you need to explain why.
Half the stuff he writes doesn't make sense, or is hard to follow where it comes from, or is unclear as to what he's trying to do with it so I give up after a while. I don't really need to explain anything.
19. (Original post by Muttley79)
all help is welcome.

I thought: or

but I'm unfamiliar with his approach although its probably the best. however, I still get stuck in the next part.

so,

or in the case of RDK:
20. (Original post by Maths&physics)
all help is welcome.

I thought: or

but I'm unfamiliar with his approach although its probably the best. however, I still get stuck in the next part.

so,

or in the case of RDK:
since hence , so that's fine.

But I don't understand where you pull the last line from. The RHS of it is basically . So the LHS needs to reflect that it is change in volume over time, and dV/dt is most certainly not 4000 as you have it.

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