A conical reservoir of water with a diameter of 8 meters and a depth of 10 meters is being emptied at a rate of 5 cubic meters per hour. At what rate is the level of water decreasing when the depth of water is 6 meters?

- FibonacciChick666

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- FibonacciChick666

|dw:1444017509430:dw|

- FibonacciChick666

This is sad, but I just don't know where to start. Any hints would be appreciated

- zepdrix

|dw:1444018001822:dw|so ummm

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## More answers

- zepdrix

\[\large\rm v'=-5\]And they told us the rate of change of the volume.

- FibonacciChick666

right, but I'm missing the jump from derivative of volume. I get from your pic that the outside edge of the cone is sqrt(116), but I don't see how that helps. V=1/3pi r^2h

- FibonacciChick666

Dv_r= 2/3 pirh
DV_h=1/3pir^2

- zepdrix

Hmm I don't think we care about the slant height at all actually.
The triangles were to give us an \(\large\rm r\) value to plug into our derivative.

- zepdrix

err i should actually say...
the triangles give us a way to relate r to h,
If I'm remembering correctly,
this is one of those problems:\[\large\rm V=\frac{\pi}{3}r^2h\]Where we need to write our volume function in terms of one variable before we differentiate.
Otherwise it's just a big mess.

- zepdrix

|dw:1444018471390:dw|\[\large\rm \frac{r}{h}=\frac{4}{10}\]

- zepdrix

\[\large\rm r=\frac{2}{5}h\]

- FibonacciChick666

oh, that was simple. Lemme do the rest

- dan815

for these problems, i think a good way to think is, so how is my volume changing as a function of height and how is my height changing as a function of time

- zepdrix

\[\large\rm V=\frac{\pi}{3}r^2h\qquad\to\qquad V=\frac{\pi}{3}\left(\frac{2}{5}h\right)^2h\]

- FibonacciChick666

give me a sec

- zepdrix

And make sure you understand what it is we're trying to solve for.
We're looking for \(\large\rm h'\), ya? :)
That's why I replaced the r, not the h.

- FibonacciChick666

dangit... I solved for h in v'... let me try again

- dan815

thats fine just use implicit

- FibonacciChick666

Just fixed that to what you said dan

- dan815

|dw:1444018906631:dw|

- FibonacciChick666

Your right Zep! Thank you! and thanks Dan!

- zepdrix

You're* (that's right, I went there)
yayyy team \c:/

- FibonacciChick666

oh goodness, my grammar...(don't worry I slapped myself with a ruler for it ;P ) Shows how much of an idiot I am though.... Gosh how I hate tests that can dictate the rest of your life

- zepdrix

oo stressin? :o

- FibonacciChick666

*Just a little*
(I get really bad test anxiety; hence, I am studying when my text is in 8 hours)

- FibonacciChick666

test*

- zepdrix

lot of related rates problems?
do you know how to do the big triangle one?
where the boats are going opposite directions, blah blah?

- dan815

haha breathee!

- dan815

my prof tells us that stress is a good thing if u think its a good thing for u... but i dont really believe him yet

- dan815

I think its better to just not worry about marks and have fun writing the test lel

- zepdrix

if you have any type of artistic ability,
always include a little doodle somewhere on the test. lolol
i dunno, maybe not if you have a really serious professor.
but a little silly picture can take their mind off of all that monotonous grading and get them in a good mood while they're on your test lol

- dan815

u gotta have fun tho!! im telling u this secret really works!! when u try to have fun.. it feels like a game, and the answers to questions just pop out at you

- FibonacciChick666

...it's a multiple choice test brought to us by the "geniuses" who think common core is a good idea.
And the last one I took I blacked out for most of the test. I wish not worrying was possible

- FibonacciChick666

My ENTIRE life/career rides on me scoring above the "scaled score" of 190 on this test.

- dan815

bahahha good luck!!

- FibonacciChick666

It's the only way I can make up for a crappy gpa

- dan815

but hey if you're able to have fun with something like this!! think about the outlook youll have in your future problems in life

- FibonacciChick666

haha yea, I shall try. How do I make it fun btw?

- dan815

hahahh this is how i think about it to make it fun

- dan815

I think about the profs who wrote this, what kidn of people they are

- FibonacciChick666

O.o?

- dan815

What kind of methods they use to make a test tricky

- dan815

i want to break it down, and understand their inner natures lol

- zepdrix

That's a tough question.
For me, it's fun because it's easy.
I really enjoy it if I understand it.
It's hard to force yourself to have fun. Hmm :)

- zepdrix

I shouldn't say that though.
I've really really enjoyed some of my super difficult classes,
even when I had no idea what they were talking about.

- FibonacciChick666

hmm... maybe I shall. I am so focused on just getting everything right though. And it's not that these are hard questions. It only goes up to like calc 1, but it has been soon long since calc. I had it in 11th grade

- dan815

yeah haha its kind of fun to take really hard classes, then u feel like ur learning a lot

- zepdrix

You're taking graph theory danny boy?
that class looks pretty cool

- FibonacciChick666

true, I loved graph theory. The material was so interesting

- dan815

that one is pretty nice so far, i have an interseting course actually about quantum computing

- dan815

you should take a look at it

- FibonacciChick666

^^lol

- zepdrix

oh my :o

- dan815

haha its not too bad, but its focring me to learn tensor products and stuff really fast pace to catch up to the math department folk

- zepdrix

Abstract Algebra is blowing my mind right now.
I'm doing very poorly in it,
but it's the most amazing class +_+
had completely changed my view of math.

- FibonacciChick666

what are you majoring in?

- dan815

oo cool, i always wanted to take one of those courses, i watched some youtube videos on it thats about it haha

- zepdrix

maf +_+

- dan815

im doing physics fib

- dan815

engineering physics / trying to fit in a math minor

- FibonacciChick666

You'll have no problem. Both of you are way smarter than me and I have a BA in Pure Math

- dan815

http://prntscr.com/8nvbam xD my last assignment in that course lol

- dan815

pure math cooool!!!

- FibonacciChick666

oh gawd.... that is Linear Alg on crack.

- dan815

hah its actually easier than it looks, their notation makes it look complicated

- dan815

but when i first saw this assignment it seemed like gibberish with all those new words

- FibonacciChick666

I bet... You see the one thing I will never understand is why in math classes, the homework is a new concept instead of review.

- dan815

ohh its actually good that way though, you get to like explore and learn new things that way, tests are the ones for review

- dan815

usually hw is there to like make you think about stuff, and really understand concepts

- FibonacciChick666

no... that is not the psychological definition of homework

- dan815

oh okay maybe im thinking assignments

- FibonacciChick666

If you made it a pre-assignment that wasn't graded, fine, but grading people on material that hasn't been covered is just crazy to me.

- FibonacciChick666

or grading for effort instead of correctness

- FibonacciChick666

but noooooo.... let's make students teach themselves the material so we can be crappy instructors.

- dan815

bahaha do u hate ur prof or something xD

- FibonacciChick666

(Why do you think my grades sucked?) and Sorry, pet peeve. It goes against everything I've learned about educational psychology.

- FibonacciChick666

Every student has a different learning style, some can learn via exploration, some can't. Their brains just are not wired that way.

- dan815

yeahh thats true

- dan815

i like nighttimes on a black board with like 1 or 2 friends

- dan815

sitting in one of the basement classes... at like 12 am when no one is around... and u see chalk and big black boards everywhere

- dan815

and chalk dust in the air

- dan815

and you clap and it echoes through all the halls

- dan815

xD hehehe

- FibonacciChick666

lol, I had a white board and myself. I didn't really fit in with most of the math people at my school. I was too social, working, and athletic. I swear all they did was eat sleep and do math.

- FibonacciChick666

This site was my only assistance

- FibonacciChick666

oh and female. That was another strike. They stuttered like an 80s movie talking to me

- FibonacciChick666

But anyways, thanks dan. You really managed to make me feel less anxious somehow. I appreciate it. As for you, if you need any supplementary books for graph theory or any other classes, I've heard of a library called genesis based out of russia where you may be able to find some books for free.

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