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anonymous

  • 5 years ago

At noon, ship a is 150km west of ship b. ship a is sailing east at 35 km/h and ship b is sailing north at 25 km/h. how fast is the distance between the ships changing at 4 pm

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  1. anonymous
    • 5 years ago
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    would i just take \[\Delta y / \Delta x \]

  2. amistre64
    • 5 years ago
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    you want dr/dt; so implicit this thing with respect to time.. your formula is the pythag thrm

  3. amistre64
    • 5 years ago
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    your dy/dt, or rather the d'north'/dt = 25; and d'e'/dt = 35

  4. amistre64
    • 5 years ago
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    e^2 + n^2 = r^2

  5. amistre64
    • 5 years ago
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    e' 2e + n' 2n = r' 2r ; divide it all by 2 e' e + n' n = r' r r' = [e' e + n' n]/ r

  6. anonymous
    • 5 years ago
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    ok so if i take that and introduce log i have f(x)+f'(x) which is

  7. amistre64
    • 5 years ago
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    log?

  8. anonymous
    • 5 years ago
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    \[e^2+n^2-r^2+ 1/2x +1/2n +1/2r\]

  9. anonymous
    • 5 years ago
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    well ln

  10. amistre64
    • 5 years ago
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    draw a triangle a right triangle with sides: n = 4(25); e = 4(35)+150; solve the pythag thrm for r r = sqrt(100^2 + e^2) :)

  11. amistre64
    • 5 years ago
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    there is no call for any log or ln in this problem... your thinking to much at it :)

  12. anonymous
    • 5 years ago
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    ok i am agreeing with using the pythag but i question your 4(35)+15 because of the direction of sail for the boat

  13. anonymous
    • 5 years ago
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    well 4(35)+150

  14. amistre64
    • 5 years ago
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    \[r' = \frac{35(e) + 25(n)}{\sqrt{100^2 + e^2}}\]

  15. anonymous
    • 5 years ago
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    because the boat is to the west and sailing east wouldn't it be 4(35)-150?

  16. anonymous
    • 5 years ago
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    ok let me work that out really fast

  17. amistre64
    • 5 years ago
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    150 + 4hours worth of 35 is.....150 + 4(35) :)

  18. amistre64
    • 5 years ago
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    ....maybe, i coulda read it wrong lol

  19. anonymous
    • 5 years ago
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    ok for your r' i am showing 140.9996308

  20. amistre64
    • 5 years ago
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    your right; 4(35) - 150 :)

  21. amistre64
    • 5 years ago
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    2850 ------ sqrt(100^2 + 10^2) = sqrt(10100) r' = 28.358 is what I get

  22. anonymous
    • 5 years ago
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    ok if i use the reg pythag a^2+b^2=c^2 will i end up with the right answer after i solve the correct values

  23. amistre64
    • 5 years ago
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    i just renamed the variables to keep track of them better; I know east is 35 and n is 25, so to keep the variables in shape I just rename them n and e

  24. anonymous
    • 5 years ago
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    ok i did the same thing as you and ended up with a different number i am trying to work back to your answer

  25. amistre64
    • 5 years ago
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    n = 100; n' = 25; n n' = 2500 e = 10; e' = 25; e e' = 250

  26. amistre64
    • 5 years ago
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    r = sqrt(100^2 + 10^2) r = sqrt(10000 + 100) r = sqrt(10100)

  27. anonymous
    • 5 years ago
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    when i do sqrt(10100) i end up with 100.4987562

  28. amistre64
    • 5 years ago
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    crap lol.....n' = 35 ;) e e' = 350

  29. anonymous
    • 5 years ago
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    ok little off track here why are we breaking down the east and north into double derives?

  30. amistre64
    • 5 years ago
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    its hard to keep up with my typos with my computer lagging so much...... you need to read thru them :)

  31. amistre64
    • 5 years ago
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    we derive implicitly with respect to time; so all our derived bits stay intact

  32. amistre64
    • 5 years ago
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    e^2 + n^2 = r^2 ; implicit with respect to "t"

  33. amistre64
    • 5 years ago
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    e' 2e + n' 2n ----------- = r' = dr/dt = how fast the boats r are moving away from each other

  34. amistre64
    • 5 years ago
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    thats 2r under there :) but all the twos factor out to 1 so they can dissapear

  35. amistre64
    • 5 years ago
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    e' e + n' n ----------- = r' = dr/dt r

  36. anonymous
    • 5 years ago
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    fantastic answer as always amistre, thanks a ton for the help

  37. amistre64
    • 5 years ago
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    35(10) + 25(100) ---------------- = r' = dr/dt sqrt(10100)

  38. amistre64
    • 5 years ago
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    youre welcome :)

  39. amistre64
    • 5 years ago
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    2850 ---------- = 28.3585 sqrt(10100)

  40. anonymous
    • 5 years ago
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    yup i agree our math was jiving on that last answer

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