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Math Help - Trig Help Please

  1. #1
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    Trig Help Please

    Does someone mind checking my work for trig... I've completed an assignment but it's worth 34 marks... I've done as much as I could but I'm not sure if it's correct... The assignment is FULLY COMPLETED... I just need someone to check over it can someone help me out via email at shawn_24242@hotmail.com


    Thanks
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  2. #2
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    Hello agent2421
    Quote Originally Posted by agent2421 View Post
    Does someone mind checking my work for trig... I've completed an assignment but it's worth 34 marks... I've done as much as I could but I'm not sure if it's correct... The assignment is FULLY COMPLETED... I just need someone to check over it can someone help me out via email at shawn_24242@hotmail.com


    Thanks
    The idea of this web-site is that all the help given should be open to anyone to benefit from. Please scan or photograph your work (if you can't type it in using LaTeX), attach it to a posting, and someone will perhaps look at it for you on the open Forum.

    Grandad
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  3. #3
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    Okay thanks... this isn't trig but is for rate of change.. (I solved the trig question)... But can you help me out with this one question.

    Year Public Sector Employment (Number of People in Millions)

    1981 2.69009
    1982 2.72483
    1983 2.74130
    1984 2.76072
    1985 2.79665
    1986 2.84086
    1987 2.87816
    1988 2.94450
    1989 2.96726
    1990 3.02734
    1991 3.05678
    1992 3.06323
    1993 3.03748
    1994 3.00269
    1995 2.95784
    1996 2.85133
    1997 2.78940
    1998 2.77897
    1999 2.76987
    2000 2.78673
    2001 2.81360
    2002 2.84346
    2003 2.90811
    2004 2.94086
    2005 2.97973
    2006 3.04614






    1. When was the rate of change zero?


    2. Explain why, in terms of real-world happenings, the rate of change is zero at the year(s) specified.


    3. Does the employment situation of Canada look promising when you graduate from post secondary? Explain.


    ----

    My work:

    #1 i have no idea how to do


    #2 I said the # of lost jobs is equal to the # of people hired which is the reason the rate of change is 0


    #3 I said it does look promising because the rate is increasing....


    --------------

    Mainly I need help with #1... and tell me if my answers are right for #2 & 3... maybe help me out a bit more on #3 since I didn't explain it too much.


    Thanks so much... I know this is in the wrong catageory but I solved the last question that was trig.
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  4. #4
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    I recommend you graph the data in a calculator or speadsheet and visually determine when the rate of change is zero.
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  5. #5
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    Quote Originally Posted by skeeter View Post
    I recommend you graph the data in a calculator or speadsheet and visually determine when the rate of change is zero.

    How do we do it visually? Is there no specific formula to use in order to figure it out?
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  6. #6
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    Quote Originally Posted by agent2421 View Post
    How do we do it visually? Is there no specific formula to use in order to figure it out?
    Plot the points using excel or a graphical calculator. If your trig equation satisfies these points then differentiate that if you're familiar with calculus
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  7. #7
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    Quote Originally Posted by e^(i*pi) View Post
    Plot the points using excel or a graphical calculator. If your trig equation satisfies these points then differentiate that if you're familiar with calculus
    I actually haven't done calculus yet because it's next semester... I already plotted the points on curve expert... I'm just unsure how to figure it out now....
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  8. #8
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    Quote Originally Posted by agent2421 View Post


    1. When was the rate of change zero?

    This data is at a discrete time step so calculus won't help you unless you fit a curve to the data, even then it won't be accuarate.

    Rate of change = 0 when the difference in employment from one year to the next is zero. Look for change in employment changing from negative to postitive and vice versa.


    Year # Employ Change
    1981 2.69009
    1982 2.72483 0.035
    1983 2.7413 0.016
    1984 2.76072 0.019
    1985 2.79665 0.036
    1986 2.84086 0.044
    1987 2.87816 0.037
    1988 2.9445 0.066
    1989 2.96726 0.023
    1990 3.02734 0.060
    1991 3.05678 0.029
    1992 3.06323 0.006
    1993 3.03748 -0.026
    1994 3.00269 -0.035
    1995 2.95784 -0.045
    1996 2.85133 -0.107
    1997 2.7894 -0.062
    1998 2.77897 -0.010
    1999 2.76987 -0.009
    2000 2.78673 0.017
    2001 2.8136 0.027
    2002 2.84346 0.030
    2003 2.90811 0.065
    2004 2.94086 0.033
    2005 2.97973 0.039
    2006 3.04614 0.066



    Sometimes this can be proportioned to population growth. In this case it seems not as you don't have that information.



    Quote Originally Posted by agent2421 View Post



    2. Explain why, in terms of real-world happenings, the rate of change is zero at the year(s) specified.


    Your answer defined the rate of change being zero, not why it could be.


    Quote Originally Posted by agent2421 View Post



    3. Does the employment situation of Canada look promising when you graduate from post secondary? Explain.
    Your answer is fine although it would be unwise to infer this long term.
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  9. #9
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    Quote Originally Posted by pickslides View Post
    This data is at a discrete time step so calculus won't help you unless you fit a curve to the data, even then it won't be accuarate.

    Rate of change = 0 when the difference in employment from one year to the next is zero. Look for change in employment changing from negative to postitive and vice versa.


    Year # Employ Change
    1981 2.69009
    1982 2.72483 0.035
    1983 2.7413 0.016
    1984 2.76072 0.019
    1985 2.79665 0.036
    1986 2.84086 0.044
    1987 2.87816 0.037
    1988 2.9445 0.066
    1989 2.96726 0.023
    1990 3.02734 0.060
    1991 3.05678 0.029
    1992 3.06323 0.006
    1993 3.03748 -0.026
    1994 3.00269 -0.035
    1995 2.95784 -0.045
    1996 2.85133 -0.107
    1997 2.7894 -0.062
    1998 2.77897 -0.010
    1999 2.76987 -0.009
    2000 2.78673 0.017
    2001 2.8136 0.027
    2002 2.84346 0.030
    2003 2.90811 0.065
    2004 2.94086 0.033
    2005 2.97973 0.039
    2006 3.04614 0.066



    Sometimes this can be proportioned to population growth. In this case it seems not as you don't have that information.





    Your answer defined the rate of change being zero, not why it could be.




    Your answer is fine although it would be unwise to infer this long term.
    but for #1 that's the problem...

    difference in employment from one year to the next is zero


    I don't think there is a year when the rate of change is 0.... Unless 1992 since that's the least one with 0.006
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  10. #10
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    Quote Originally Posted by agent2421 View Post
    but for #1 that's the problem...

    difference in employment from one year to the next is zero

    I don't think there is a year when the rate of change is 0.... Unless 1992 since that's the least one with 0.006
    You are on the right track. Let's say these figures represent the # number employed at the end of the year given.

    You have identified that at the end of 1992 the rate of change from the previous year was 0.006. The rate of change at the end of the following year 1993 is negative. To get from postive to negative (or vice versa) we must pass thropugh zero, so we can say at some point in 1993 the rate of change was zero.

    How does that sound?
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  11. #11
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    Sounds good I suppose...... but wouldn't 2000 also be an answer because it goes from negative to positive? So do i have 2 ansewrs... 1993 and 2000 ?
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  12. #12
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    Quote Originally Posted by agent2421 View Post
    So do i have 2 ansewrs... 1993 and 2000 ?
    Sounds fair, to me.
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  13. #13
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    Actually there's a problem.. I asked the teacher and he told me this:

    He said it's between 1992 and 1999... when the tangent to the curve = 0 or is a horizontal line. And this also occurs only at the turning points in the function...

    so this might change the answer a bit... thoughts anyone?
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