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Application of Quadratic Functions that involve finding equation

  1. May 21, 2016 #1
    1. The problem statement, all variables and given/known data
    upload_2016-5-21_13-36-25.png

    2. Relevant equations
    none

    3. The attempt at a solution
    upload_2016-5-21_13-37-47.png

    Is this correct?

    Thanks.
     
  2. jcsd
  3. May 21, 2016 #2

    SammyS

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    The answer is correct.

    There are errors in your work starting with the table.

    If x is the speed from Tokyo to Bangkok then reducing that by 200 gives a speed of x - 200 from Bangkok to Tokyo. Etc.
     
  4. May 21, 2016 #3

    Ray Vickson

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    Plug it in and see if it works.
     
  5. May 22, 2016 #4
    I understand where I made the error, the return trip speed decreased by 200 km/h, so it should have been (x-200) not (x+200), so I have corrected my answer:


    upload_2016-5-22_14-8-50.png

    Thanks for the help! :)
     
  6. May 22, 2016 #5

    SammyS

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    There's still a problem, x is the Tokyo to Bangkok speed. That can't be 600mph. 600 - 200 is 400, and that doesn't work out.

    So, where is the problem?

    You made a couple of errors.

    Sign errors in going from
    ##-960000=2x^2-400x ##​
    to
    ##2x^2+400x-960000= 0 ##​
    It should be
    ##2x^2-400x+960000= 0 ##​
    But there is no real solution to that.

    The problem is that it's the Tokyo to Bangkok time that's smaller, because the speed is greater. When you subtract to get 2 hours, you need to subtract in the opposite order.
     
  7. May 22, 2016 #6

    I tried doing it this way, but as you said there is no real solution.


    I don't understand what you mean, can you please explain?
     
  8. May 22, 2016 #7

    SammyS

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    If x > 200, then
    ##\displaystyle \frac{4800}{x-200}>\frac{4800}{x}##​
    .
    So you had these reversed.
     
  9. May 23, 2016 #8
    So even if I switch these two, can I not get the same answer I had originally? How does switching the two help with the answer to the problem? or is it just the proper way to write it?
     
  10. May 23, 2016 #9

    SammyS

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    It's what is needed of you want to make everything consistent.

    As I stated in my first reply, the answer you gave for the time from Bangkok to Tokyo was correct. (600 km/hr)

    But you had a number of inconsistencies.

    Added in Edit:
    You should get x = 800. Then x- 200 = 600, the answer.
     
    Last edited: May 23, 2016
  11. May 23, 2016 #10
    So like this:

    upload_2016-5-23_20-55-12.png
     
  12. May 23, 2016 #11

    SammyS

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    No.Not like that.
    The first three lines are correct.

    After that, there are at least two Algebra mistakes.

    As I stated in my previous post:
     
  13. May 24, 2016 #12
    This is an example from my lesson that I have been using as a reference to solve my problem:
    upload_2016-5-24_0-49-22.png

    upload_2016-5-24_0-49-45.png
     
  14. May 24, 2016 #13

    SammyS

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    Right. And they did not make algebra mistakes. You did.

    So (carefully) redo your algebra, starting at the third line of the following (from post #10), which is the last line that's correct.

    upload_2016-5-23_20-55-12-png.101169.png
     
  15. May 24, 2016 #14

    upload_2016-5-24_1-23-4.png


    4800x - 4800x + 960 000 = 2x2 - 400x (960 000 is positive because I multiplied -4800 and -200)

    960 000 = 2x2 - 400x (Now I move 960 000 to the right side and it becomes -960 000)

    2x2 - 400x - 960 000 = 0

    x2 - 200x - 480 000 = 0

    (x+600) (x-800)

    x= -600 or x = 800

    Does this make more sense? did I fix the algebra errors? if not please show me where I made errors.
     

    Attached Files:

  16. May 24, 2016 #15

    SammyS

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    Yes. That looks to be correct.
     
  17. May 24, 2016 #16
    Okay, so does that make the speed from Bangkok to Tokyo 800 km/h instead of 600 km/h since it is positive?
     
  18. May 24, 2016 #17
    So since x = 800, we need to solve for the jets's speed from Bangkok to Tokyo, so (like you said) sub x = 800 into x- 200, which gives:
    800 - 200 = 600 km/h

    So the jet's speed from Bangkok to Tokyo is 600 km/h.
     
  19. May 24, 2016 #18
    Thanks for the help, I really appreciate it :)
     
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