## FibonacciChick666 one year ago 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?

1. FibonacciChick666

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2. FibonacciChick666

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

3. zepdrix

|dw:1444018001822:dw|so ummm

4. zepdrix

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

5. 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

6. FibonacciChick666

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

7. 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.

8. 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.

9. zepdrix

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

10. zepdrix

$\large\rm r=\frac{2}{5}h$

11. FibonacciChick666

oh, that was simple. Lemme do the rest

12. 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

13. zepdrix

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

14. FibonacciChick666

give me a sec

15. 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.

16. FibonacciChick666

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

17. dan815

thats fine just use implicit

18. FibonacciChick666

Just fixed that to what you said dan

19. dan815

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20. FibonacciChick666

Your right Zep! Thank you! and thanks Dan!

21. zepdrix

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

22. 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

23. zepdrix

oo stressin? :o

24. FibonacciChick666

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

25. FibonacciChick666

test*

26. 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?

27. dan815

haha breathee!

28. 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

29. dan815

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

30. 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

31. 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

32. 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

33. FibonacciChick666

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

34. dan815

bahahha good luck!!

35. FibonacciChick666

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

36. 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

37. FibonacciChick666

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

38. dan815

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

39. dan815

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

40. FibonacciChick666

O.o?

41. dan815

What kind of methods they use to make a test tricky

42. dan815

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

43. 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 :)

44. 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.

45. 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

46. dan815

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

47. zepdrix

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

48. FibonacciChick666

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

49. dan815

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

50. dan815

you should take a look at it

51. FibonacciChick666

^^lol

52. zepdrix

oh my :o

53. 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

54. 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.

55. FibonacciChick666

what are you majoring in?

56. dan815

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

57. zepdrix

maf +_+

58. dan815

im doing physics fib

59. dan815

engineering physics / trying to fit in a math minor

60. FibonacciChick666

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

61. dan815

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

62. dan815

pure math cooool!!!

63. FibonacciChick666

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

64. dan815

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

65. dan815

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

66. 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.

67. 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

68. dan815

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

69. FibonacciChick666

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

70. dan815

oh okay maybe im thinking assignments

71. 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.

72. FibonacciChick666

73. FibonacciChick666

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

74. dan815

bahaha do u hate ur prof or something xD

75. FibonacciChick666

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

76. FibonacciChick666

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

77. dan815

yeahh thats true

78. dan815

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

79. 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

80. dan815

and chalk dust in the air

81. dan815

and you clap and it echoes through all the halls

82. dan815

xD hehehe

83. 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.

84. FibonacciChick666

This site was my only assistance

85. FibonacciChick666

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

86. 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.