Results 1 to 12 of 12

Math Help - 4 Hard Questions!! Help Please!!

  1. #1
    Newbie
    Joined
    Aug 2009
    Posts
    5

    4 Hard Questions!! Help Please!!

    Can you please show work? You do not need to answer all the problems even if you know just one your help is appreciated

    1) A storage tank in the shape of a right circular cone has a height of 6 meters and a base of radius 2 meters. The cone is inverted and fluid is pumped in at a rate of .002m^3-minute (2 liters/min). At what rate is the level of the fluid rising when the tank is filled to a height of 3meters? Use V= (pie X r squared X h)/3 and R = (H)/3

    2) Verify the mean-value theorem for
    a) f(x) = x^3 - 3x^2 - 13x + 15 on (-3,1)
    (b) f(x) = cos 2x - 2 cos^2 x on ((-pie/2),(pie/4))

    3) Locate and classify all critical points, points of inflection, intervals where the Function increases/decreases and where the Function is concave up/down for
    a) f(x) = x^4 - 4x^2 + 4x^3 + 1
    b) f(x) = (1+ squareroot(x) + cuberoot(x))^9
    c) f(x) = x/(ln x)^2
    d) f(x) = e^x + e^-2x
    e) f(x) = e^(x^3 - x)

    4) Using differentials, approximate the numerical value of
    a) cuberoot(130)
    b) ln (3), you know ln (e) = 1
    c) log (8), you know log (10) = 1
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    11,695
    Thanks
    450
    Quote Originally Posted by alulla View Post
    Can you please show work?
    I would ask you the same question ...
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,657
    Thanks
    1607
    Awards
    1
    Quote Originally Posted by alulla View Post
    Can you please show work? You do not need to answer all the problems even if you know just one your help is appreciated

    1) A storage tank in the shape of a right circular cone has a height of 6 meters and a base of radius 2 meters. The cone is inverted and fluid is pumped in at a rate of .002m^3-minute (2 liters/min). At what rate is the level of the fluid rising when the tank is filled to a height of 3meters? Use V= (pie X r squared X h)/3 and R = (H)/3

    2) Verify the mean-value theorem for
    a) f(x) = x^3 - 3x^2 - 13x + 15 on (-3,1)
    (b) f(x) = cos 2x - 2 cos^2 x on ((-pie/2),(pie/4))

    3) Locate and classify all critical points, points of inflection, intervals where the Function increases/decreases and where the Function is concave up/down for
    a) f(x) = x^4 - 4x^2 + 4x^3 + 1
    b) f(x) = (1+ squareroot(x) + cuberoot(x))^9
    c) f(x) = x/(ln x)^2
    d) f(x) = e^x + e^-2x
    e) f(x) = e^(x^3 - x)

    4) Using differentials, approximate the numerical value of
    a) cuberoot(130)
    b) ln (3), you know ln (e) = 1
    c) log (8), you know log (10) = 1
    Correct me please if I am wrong.
    You are asking us to do these problems in detail for you.
    You then are absolved of any necessary to do any work on your part.
    You plan to use the reply as if it were your own.
    If this is wrong, what is right?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    Aug 2009
    Posts
    5
    Quote Originally Posted by Plato View Post
    Correct me please if I am wrong.
    You are asking us to do these problems in detail for you.
    You then are absolved of any necessary to do any work on your part.
    You plan to use the reply as if it were your own.
    If this is wrong, what is right?
    You are wrong. I know you won't believe me but I have an important test tomorrow and my professor gave us review sheets. This isn't being collected or even looked at. I just need to see how other people are solving it so I can see what I am doing wrong. If you want I can post my work:

    Here:

    For number 1) I have almost no work. I only drew the Cone out

    /\
    / \
    / \
    / \
    / \ the height is 6 and the radius is 2 as you know..but what do I do from there? The only thing I thought of doing was r = h/3 = .002...h = .006...which makes no sense whatsoever.

    number 2a) I know I have to use the formula f(b) - f(a)/b-a so
    0-0/-4 which is 0/-4....but what do I do with that??? I'm so confused

    number 3) I know to find the critical points i have to do f'(x) = 0 and for points of inflection i have to f"(x) = 0 and for increases and decreases and concave up and concave down I just have to plug them in to see + or -...but when I do 3a I get stuck at 4x^3 + 12x^2 - 8x = 0 (the derivative) and then I get that down to 4x(x^2 + 3x - 2)..but how does that factor??

    I've tried with great effort to try to do these problems, but the fact remains I just don't understand how to do it. If anyone could help it would be greatly appreciated. I know you probably won't believe me but this is for my own help...I myself don't cheat if someone cheats they are only cheating themselves..whats the point?
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,657
    Thanks
    1607
    Awards
    1
    If you are having a test on these questions, then you have seen similar questions before.
    Therefore, you have done similar questions before.
    So show us some effort on your part.
    If you cannot do any of these, then why should you not fail?
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Newbie
    Joined
    Aug 2009
    Posts
    5
    Quote Originally Posted by Plato View Post
    If you are having a test on these questions, then you have seen similar questions before.
    Therefore, you have done similar questions before.
    So show us some effort on your part.
    If you cannot do any of these, then why should you not fail?
    To be honest I deserve to fail ...I have known about this test since Thursday and have made almost 0 effort to study. This weekend I hung out with my cousins in another state..and was looking forward to having a 2 hour study session with a tutor my college provides on Monday. Unfortunately the tutor cancelled, and now I am stuck . So I am looking towards the great Internet for help hoping for someone to help me. I am a High School student taking a College Class for Extra Credit..I was shocked to see the pace at which the professors taught. I'm very sorry if you don't believe me though =(.
    Follow Math Help Forum on Facebook and Google+

  7. #7
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,657
    Thanks
    1607
    Awards
    1
    Quote Originally Posted by alulla View Post
    To be honest I deserve to fail ...I have known about this test since Thursday and have made almost 0 effort to study. This weekend I hung out with my cousins in another state..and was looking forward to having a 2 hour study session with a tutor my college provides on Monday. Unfortunately the tutor cancelled, and now I am stuck . So I am looking towards the great Internet for help hoping for someone to help me. I am a High School student taking a College Class for Extra Credit..I was shocked to see the pace at which the professors taught. I'm very sorry if you don't believe me though =(.
    Thank you for being honest with yourself. That is a rare happening.
    Good luck. Learn from this.
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Newbie
    Joined
    Aug 2009
    Posts
    5
    Quote Originally Posted by Plato View Post
    Thank you for being honest with yourself. That is a rare happening.
    Good luck. Learn from this.
    Okay thank you. Is there anyone else who would care to help me a little?
    Follow Math Help Forum on Facebook and Google+

  9. #9
    Member
    Joined
    Jul 2009
    Posts
    111
    Thanks
    1

    Hints.

    Quote Originally Posted by alulla View Post
    Can you please show work? You do not need to answer all the problems even if you know just one your help is appreciated

    1) A storage tank in the shape of a right circular cone has a height of 6 meters and a base of radius 2 meters. The cone is inverted and fluid is pumped in at a rate of .002m^3-minute (2 liters/min). At what rate is the level of the fluid rising when the tank is filled to a height of 3meters? Use V= (pie X r squared X h)/3 and R = (H)/3

    2) Verify the mean-value theorem for
    a) f(x) = x^3 - 3x^2 - 13x + 15 on (-3,1)
    (b) f(x) = cos 2x - 2 cos^2 x on ((-pie/2),(pie/4))

    3) Locate and classify all critical points, points of inflection, intervals where the Function increases/decreases and where the Function is concave up/down for
    a) f(x) = x^4 - 4x^2 + 4x^3 + 1
    b) f(x) = (1+ squareroot(x) + cuberoot(x))^9
    c) f(x) = x/(ln x)^2
    d) f(x) = e^x + e^-2x
    e) f(x) = e^(x^3 - x)

    4) Using differentials, approximate the numerical value of
    a) cuberoot(130)
    b) ln (3), you know ln (e) = 1
    c) log (8), you know log (10) = 1
    //

    I just thought I could give hints for the problem you posted. you are supposed to find the rate at which the level of the fluid is increasing inside the container. Level corresponds to 'h' which means, you gotta find a value of dh/dt. This gives you the rate at which the height of the liquid changes in the container.

    V = [pi * r^2* h] /3

    You have already got the important substitution to be made. r = h/3
    So, V = [pi * (h^2/9) *h ]/3
    = [pi * h^3]/ 27

    Now, we've expressed the volume entirely as a function of the height. You can follow this up and do the steps given below.

    i) By elementary differentiation, find an expression for dv/dt.
    ii) This value dv/dt is given in the question as 0.002 m^3/min.
    iii) Plug-in other values such as pi and h as given in the question.
    iv) Simplify the equation to find the value for dh/dt.

    This is quite easy. Hope it helped your preps.

    2) a) You were right in your step where you found that [f(b)-f(a)]/b-a = 0. Now, you gotta find a c belonging to [-3,1] such that it f '(c)= 0. f'(x) = 3x^2-6x-13 .

    Just solve this equation for the value '0'. i.e 3c^2 - 6c -13 = 0. Basic theory on quadratic equations would help you with the rest of the problem.

    b) the 'b' part would be simple as it involves similar steps as to that of 2.a.

    MAX
    Last edited by MAX09; August 3rd 2009 at 05:52 PM. Reason: Added hints for another problem
    Follow Math Help Forum on Facebook and Google+

  10. #10
    Newbie
    Joined
    Aug 2009
    Posts
    5
    Thank you max!!

    With your help I think I got the solution

    dH/dT= (dV/dT) * (9/pie) * (1/3) * (1/h^2)

    dH/dT=~2.12

    right? Thanks a lot max!! Your reply helped a lot!!!
    Follow Math Help Forum on Facebook and Google+

  11. #11
    Junior Member enjam's Avatar
    Joined
    Jul 2009
    Posts
    26
    Hmm.. I got something a little different. v = pi r^2 h / 3 = pi h^3 / 27
    dV / dH = pi (h^2) / 9
    so when h = 3
    dV / dH = 9 pi / 9 = pi
    So we have dV / dT = dV / dh x dh / dt
    0.002m^3/min = pi m^3 / m x dh / dt
    giving dh / dt = (0.002 / pi) m / min
    Follow Math Help Forum on Facebook and Google+

  12. #12
    Member
    Joined
    Jul 2009
    Posts
    111
    Thanks
    1

    Thumbs up @alulla

    Can you verify your calculation?
    there seems to be a minor error somewhere.
    Also, check the hints I gave for the problem on mean value theorem

    I get the same answer given by 'enjam'.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Few hard questions
    Posted in the Calculus Forum
    Replies: 5
    Last Post: September 25th 2010, 08:39 AM
  2. Hard Questions
    Posted in the Geometry Forum
    Replies: 3
    Last Post: October 7th 2009, 10:48 PM
  3. Hard questions are here...
    Posted in the Geometry Forum
    Replies: 0
    Last Post: January 23rd 2009, 08:17 AM
  4. Really hard questions...
    Posted in the Geometry Forum
    Replies: 2
    Last Post: June 2nd 2008, 10:13 PM
  5. [SOLVED] Help!! hard math questions
    Posted in the Algebra Forum
    Replies: 2
    Last Post: February 4th 2008, 08:52 PM

Search Tags


/mathhelpforum @mathhelpforum