FibonacciChick666
  • FibonacciChick666
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?
Mathematics
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FibonacciChick666
  • FibonacciChick666
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?
Mathematics
schrodinger
  • schrodinger
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
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FibonacciChick666
  • FibonacciChick666
|dw:1444017509430:dw|
FibonacciChick666
  • FibonacciChick666
This is sad, but I just don't know where to start. Any hints would be appreciated
zepdrix
  • zepdrix
|dw:1444018001822:dw|so ummm

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zepdrix
  • zepdrix
\[\large\rm v'=-5\]And they told us the rate of change of the volume.
FibonacciChick666
  • 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
  • FibonacciChick666
Dv_r= 2/3 pirh DV_h=1/3pir^2
zepdrix
  • 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
  • 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
  • zepdrix
|dw:1444018471390:dw|\[\large\rm \frac{r}{h}=\frac{4}{10}\]
zepdrix
  • zepdrix
\[\large\rm r=\frac{2}{5}h\]
FibonacciChick666
  • FibonacciChick666
oh, that was simple. Lemme do the rest
dan815
  • 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
  • zepdrix
\[\large\rm V=\frac{\pi}{3}r^2h\qquad\to\qquad V=\frac{\pi}{3}\left(\frac{2}{5}h\right)^2h\]
FibonacciChick666
  • FibonacciChick666
give me a sec
zepdrix
  • 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
  • FibonacciChick666
dangit... I solved for h in v'... let me try again
dan815
  • dan815
thats fine just use implicit
FibonacciChick666
  • FibonacciChick666
Just fixed that to what you said dan
dan815
  • dan815
|dw:1444018906631:dw|
FibonacciChick666
  • FibonacciChick666
Your right Zep! Thank you! and thanks Dan!
zepdrix
  • zepdrix
You're* (that's right, I went there) yayyy team \c:/
FibonacciChick666
  • 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
  • zepdrix
oo stressin? :o
FibonacciChick666
  • FibonacciChick666
*Just a little* (I get really bad test anxiety; hence, I am studying when my text is in 8 hours)
FibonacciChick666
  • FibonacciChick666
test*
zepdrix
  • 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
  • dan815
haha breathee!
dan815
  • 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
  • dan815
I think its better to just not worry about marks and have fun writing the test lel
zepdrix
  • 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
  • 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
  • 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
  • FibonacciChick666
My ENTIRE life/career rides on me scoring above the "scaled score" of 190 on this test.
dan815
  • dan815
bahahha good luck!!
FibonacciChick666
  • FibonacciChick666
It's the only way I can make up for a crappy gpa
dan815
  • 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
  • FibonacciChick666
haha yea, I shall try. How do I make it fun btw?
dan815
  • dan815
hahahh this is how i think about it to make it fun
dan815
  • dan815
I think about the profs who wrote this, what kidn of people they are
FibonacciChick666
  • FibonacciChick666
O.o?
dan815
  • dan815
What kind of methods they use to make a test tricky
dan815
  • dan815
i want to break it down, and understand their inner natures lol
zepdrix
  • 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
  • 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
  • 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
  • dan815
yeah haha its kind of fun to take really hard classes, then u feel like ur learning a lot
zepdrix
  • zepdrix
You're taking graph theory danny boy? that class looks pretty cool
FibonacciChick666
  • FibonacciChick666
true, I loved graph theory. The material was so interesting
dan815
  • dan815
that one is pretty nice so far, i have an interseting course actually about quantum computing
dan815
  • dan815
you should take a look at it
FibonacciChick666
  • FibonacciChick666
^^lol
zepdrix
  • zepdrix
oh my :o
dan815
  • 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
  • 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
  • FibonacciChick666
what are you majoring in?
dan815
  • dan815
oo cool, i always wanted to take one of those courses, i watched some youtube videos on it thats about it haha
zepdrix
  • zepdrix
maf +_+
dan815
  • dan815
im doing physics fib
dan815
  • dan815
engineering physics / trying to fit in a math minor
FibonacciChick666
  • FibonacciChick666
You'll have no problem. Both of you are way smarter than me and I have a BA in Pure Math
dan815
  • dan815
http://prntscr.com/8nvbam xD my last assignment in that course lol
dan815
  • dan815
pure math cooool!!!
FibonacciChick666
  • FibonacciChick666
oh gawd.... that is Linear Alg on crack.
dan815
  • dan815
hah its actually easier than it looks, their notation makes it look complicated
dan815
  • dan815
but when i first saw this assignment it seemed like gibberish with all those new words
FibonacciChick666
  • 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
  • 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
  • dan815
usually hw is there to like make you think about stuff, and really understand concepts
FibonacciChick666
  • FibonacciChick666
no... that is not the psychological definition of homework
dan815
  • dan815
oh okay maybe im thinking assignments
FibonacciChick666
  • 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
  • FibonacciChick666
or grading for effort instead of correctness
FibonacciChick666
  • FibonacciChick666
but noooooo.... let's make students teach themselves the material so we can be crappy instructors.
dan815
  • dan815
bahaha do u hate ur prof or something xD
FibonacciChick666
  • FibonacciChick666
(Why do you think my grades sucked?) and Sorry, pet peeve. It goes against everything I've learned about educational psychology.
FibonacciChick666
  • 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
  • dan815
yeahh thats true
dan815
  • dan815
i like nighttimes on a black board with like 1 or 2 friends
dan815
  • 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
  • dan815
and chalk dust in the air
dan815
  • dan815
and you clap and it echoes through all the halls
dan815
  • dan815
xD hehehe
FibonacciChick666
  • 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
  • FibonacciChick666
This site was my only assistance
FibonacciChick666
  • FibonacciChick666
oh and female. That was another strike. They stuttered like an 80s movie talking to me
FibonacciChick666
  • 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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