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Assignment calculus,simultaneous equation and logarithm

  1. Jan 24, 2012 #1
    1. The problem statement, all variables and given/known data

    Hi, teachers

    I have been doing some work but I am confused.

    Have you ever heard of this great math website www.wolframalpha.com (Google for maths).

    This is one questions I done differantiate 3e^-4tsin(5t) and here is the link for the answers from

    http://www.wolframalpha.com/input/?i=differantiate++3e^-4tsin(5t)


    Although what I did is confusing to what the answers there?


    This my solution

    y=3e^-4t sin(5t)

    u=3e^-4t v =sin(5t)

    dy/dt=-12e^-4t dv/dt=-5cos(5t)


    chain rule/product rule (1 of them)

    ds/dt= 3e^-4t x 5cos(5t) + sin(5t) x -12e^-4t

    factor

    =3e^-4t (5cos(5t) - 4sin (5t))

    Am I or the computer correct ?



    Also while you are there? May you look at these two questions below


    1) The table gives a firm’s monthly profits for their first few months of business. The numbers are rounded to the nearest £100.


    Number of months after start up (x) 1 2 3 4 5 6
    Profit for this month (£y) 500 800 1200 1900 3000 4800


    The firm’s profits, £y, for the xth month after start up are modelled by

    y = k x 10ax

    where a and k are constants.

    Plot this data on semi log paper to verify if this relationship is true.

    Its about plotting semi-log paper but am confused. Can you give me guide on where to start answering the question.

    Thanx agin



    2)
    Simultaneos question
    y = x2 – 5x + 5 a



    5x + 3y = 30. b



    Find location of points collide?


    Add a+b

    x2 + 2y -25=0


    quadratic formula use

    x= -2+ square root(2^2-(4x1x(-25))/2 x = 4.09901

    or

    x= -2 - square root(2^2-(4x1x(-25))/2 x=-6.09


    subsitue y etc
     
  2. jcsd
  3. Jan 24, 2012 #2

    Mark44

    Staff: Mentor

    The first derivative is du/dt, not dy/dt.
    In the other derivative, you have a sign error.
    Why ds/dt? Your original function is y, so the derivative would be dy/dt.

    Also, don't use x for multiplication. If there happens to be a variable named x, you will confuse yourself.
    This looks fine to me.
    Please start a new thread with each of these problems.

    Be sure to include the three parts of the homework template.
    Again, don't use x for multiplication
     
  4. Jan 24, 2012 #3

    SammyS

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member


    Hello maali5. Welcome to PF !

    I used the link. What you asked WolframAlpha to differentiate, 3e^-4tsin(5t) , is equivalent to differentiating
    [itex]\displaystyle\frac{3 t\sin(5 t)}{e^4}\,.[/itex]​
    You need to put parentheses around the -4t if you want WolframAlpha to differentiate
    [itex]\displaystyle\frac{3 \sin(5 t)}{e^{4t}}\,.[/itex]​
    Write your function as 3e^(-4t)sin(5t) .
     
  5. Jan 25, 2012 #4

    Thanx for your help. I got it.
     
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