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Mathematical Modelling, Vectors and Parametric Equations

  1. Jun 7, 2015 #1
    1. The problem statement, all variables and given/known data
    Sorry to disappoint the math fanatics but no this is not a question that integrates all three topics at once but individual ones. I still need assistance though with the following more so in the reasoning behind them as I feel my logic is flawed.

    2. Relevant equations
    There are not really any relevant equations but look at my solutions below.

    3. The attempt at a solution
    I am pretty sure these are wrong
  2. jcsd
  3. Jun 7, 2015 #2


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    Please also state your reasoning behind your answers. Simply selecting on random does not really qualify as an attempt and it will be easier for everyone to see when/if you have the wrong idea.
  4. Jun 7, 2015 #3
    Sorry my good sir,
    22) To be completely honest , the approach to this one is fuzzy for me as I have only done two variables at a time before this but i thought that i could square the x and y to get that x2 + y2 = r2cos2θ and then adding z squared would produce x2 + y2 +z2 = r2cos2θ + r2sin2θ= r2, is this correct , is there no simpler approach if so
    28) This one was even trickier I imagined that is they were perpendicular then their dot product = 0 , but things got hairy when r.s came up , as I only had so far (r-s)(2r+3s)=0, I said r=s for one solution so r.s must me rs which makes no sense when I repeat it now .
    42) I found the first derivative and assumed where it was greater than zero , the graph was increasing
    43) I said it was 10 years between 1990 and 2000 and so it was zero to ten.
  5. Jun 7, 2015 #4
    Is this not satisfactory ?
  6. Jun 8, 2015 #5


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    Your reasoning and answer for 22 and 42 are fine.
    For 43, you are right, but your explanation is a bit vague. Note the exact statement of the start and end times.
    For 28:
    Expand that and isolate r.s.
  7. Jun 8, 2015 #6
    Darn should have went with first instinct
    2r.r +3 s.r - 2s.r - 3s.s=0
    2r2 + s.r -3s2=0
    s.r= 3s2-2r2
    Making A the answer, Thanks Mr. Haruspex Sir
    About the integral one though, it was just basically an intuitive guess , I still don't understand why I would start at 0 and why end at 10 , why that would not work out to 11 years versus the 10 from 1990 to 1999 ( Because it is not the end of 2000), I am pretty clueless about that one, no intuition whatsoever
  8. Jun 8, 2015 #7


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    Exactly how many years are between Jan 1, 1990, and Jan 1, 2000? You are allowed to use decimals.
  9. Jun 8, 2015 #8
    10 years , yes ok but why do we start at zero , is that a general rule ?
  10. Jun 8, 2015 #9


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    No, this must be chosen according to how the time t=0 was selected, but this is not explicitly stated in the problem.
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