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Emily778

Write the resultant of the two vectors as an ordered pair. (-1,6) and (-3,-3) (-4, 3) (5, -6) (3, -4) (-6, 5)

  • one year ago
  • one year ago

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  1. johnweldon1993
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    i believe...the resultant would just be the sum of these 2 so add your x's...and then your y's -1 + -3 and -3 + 6 -4 and 3..that IS an option so i'm gonna go with that...anyone correct me if im wrong

    • one year ago
  2. Emily778
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    Thanks. Do you know this one? . Miguel is driving his motorboat across a river. The speed of the boat in still water is 11 mi/h. The river flows directly south at 2 mi/h. If Miguel heads directly west, what are the boat’s resultant speed and direction?

    • one year ago
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  3. johnweldon1993
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    haha good think i know some basic physics.... well lets think....what does that shape look like? a right triangle doesn't it? and we have 2 sides...and want the hypotenuse.....hmm...sounds like the pythagorean theorem right? A² + B² = C² where C² is the hypotenuse... we want that length right? so C = √A² + B² we have A and B...so plug those in...square them...add them...and then take the square root of that..what do you get?

    • one year ago
  4. Emily778
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    What is C and A and B?

    • one year ago
  5. johnweldon1993
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    C is the length of the hypotenuse of the right triangle.... A is any other one of the sides B is the remaining side

    • one year ago
  6. Emily778
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    can you just give me numbers

    • one year ago
  7. johnweldon1993
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    okay...well the hypotenuse is the long side...we dont know that...that's why I've rearranged that equation for C A can be 11 B can be 2 so plug those in

    • one year ago
  8. Emily778
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    So, it would be 'C= sqrt 11^2 + 2^2' ?

    • one year ago
  9. johnweldon1993
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    correct ...so evaluate farther

    • one year ago
  10. Emily778
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    I got C=15

    • one year ago
  11. johnweldon1993
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    11² = 121 right? 2² = 4 right? 121 + 4 = 125 sqrt of 125?

    • one year ago
  12. Emily778
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    11.1

    • one year ago
  13. Emily778
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    did I do the other thing wrong? ._.

    • one year ago
  14. Emily778
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    @johnweldon1993

    • one year ago
  15. johnweldon1993
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    sorry for the delay........and yes it is 11.18.....so round it to 11.2 now....we want what direction the boat is traveling in....meaning what angle is this line going at? we have all 3 sides....so...we can use any of the trig functions....but remember...since we DONT know the angle...we want to use the inverse of whatever trig function you use

    • one year ago
  16. Emily778
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    okay, what do I do next?

    • one year ago
  17. Emily778
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    @johnweldon1993

    • one year ago
  18. johnweldon1993
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    so you want the direction...remember what we did in that last problem with the inverse trig function? lets do it again...we have all the sides so we can choose ANY trig function...lets use tan here tan is opposite/adjacent right? so our opposite side of the angle will be 2 ...and the adjacent would be 11...so we do 2/11.....then the inverse tan of that answer

    • one year ago
  19. Emily778
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    wait..what? You mean 11.2?

    • one year ago
  20. Emily778
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    hello? Please help

    • one year ago
  21. Emily778
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    @johnweldon1993

    • one year ago
  22. johnweldon1993
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    no remember....tan is opposite over adjacent.... our opposite is 2 and adjacent is 11 so no it is 2/11

    • one year ago
  23. johnweldon1993
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    so it would look like this tan(x) 2/11 tan^-1 2/11 = x

    • one year ago
  24. johnweldon1993
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    and since your calculator hasn't been working correctly with the inverse trig functions....the result would be 10.3 degrees

    • one year ago
  25. Emily778
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    tan (x) 2/11? Where's the x? I can at least try to find it

    • one year ago
  26. johnweldon1993
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    no that was for context......if you ever see tan...it will ALWAYS be followed with an x...as well as sin and cos will be the same it would be tan^1 2/11 the "x" is what the answer will come out to be

    • one year ago
  27. Emily778
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    yeah, I keep getting 0. :/ I put in "tan 2/11" and I tried what you did.

    • one year ago
  28. johnweldon1993
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    okay....do 2/11 first....after you get that answer...do the "shift" "tan" of that answer.....or whatever it was you had to do before to get the answer

    • one year ago
  29. Emily778
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    I got 11.3

    • one year ago
  30. Emily778
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    When I round up the number I got

    • one year ago
  31. Emily778
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    when I don't round up, I get 10.203

    • one year ago
  32. johnweldon1993
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    woh....how are you rounding? 10.203 rounds up to 11.3??? but anyways....2/11 = .1818181818 right? \[\tan^{-1} .1818181818\] = 10.30484647

    • one year ago
  33. Emily778
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    And when i add the 3rd number from the answer I got, I get 10.259

    • one year ago
  34. Emily778
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    yep.

    • one year ago
  35. Emily778
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    how do you do the second part?

    • one year ago
  36. Emily778
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    how do I do the second part on my calculator?

    • one year ago
  37. johnweldon1993
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    that's what I'm not sure of...i would call back @Hope_nicole for that....she knew how to work with your calculator. but with mine that's all I do...wish i could give you a good perspective

    • one year ago
  38. Emily778
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    well,I need the rest. :( I'm almost done. Can you at least try to help? maybe @jim_thompson5910 can help :D Maybe..

    • one year ago
  39. johnweldon1993
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    lol yeah @jim_thompson5910 is very intelligent :)...hopefully he can give a fresh perspective

    • one year ago
  40. Emily778
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    so are you:D @johnweldon1993 I just need the rest. :(

    • one year ago
  41. johnweldon1993
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    thank you :) ...so wait...what exactly are you still looking for right now? the direction right? in this case ..the angle?

    • one year ago
  42. Emily778
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    after "atan.181"

    • one year ago
  43. johnweldon1993
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    ahh.....see like i said for my calulator...i just type in \[\tan^{-1} 2/11\] and pop comes the 10.30484647 just wish i could explain your calculator

    • one year ago
  44. Emily778
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    it's on my computer. it's a graphing calculator.

    • one year ago
  45. johnweldon1993
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    and hang on ......try atan(2/11) put the parenthesis around 2/11

    • one year ago
  46. johnweldon1993
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    and i'm sure as you know...atan means arc tan...also known as \[\tan^{-1}\]

    • one year ago
  47. Emily778
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    I got .18.1

    • one year ago
  48. johnweldon1993
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    and your in degree mode?

    • one year ago
  49. Emily778
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    how do I put it in degree mode?

    • one year ago
  50. johnweldon1993
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    hmm you said at the top of your calculator...you had a "mode" button right? click that....and see if it says anything about radians and degrees

    • one year ago
  51. Emily778
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    angle mode. It says 1. deg 2. rad 3 grad 4. cyc

    • one year ago
  52. johnweldon1993
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    right......so type...or click 1.....you want deg mode

    • one year ago
  53. johnweldon1993
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    and try the atan(2/11) again

    • one year ago
  54. Emily778
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    I got it now! :) Thanks so much!

    • one year ago
  55. johnweldon1993
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    AWESOME! lol finally haha! yes always have it in degree mode for problems like these :) ha! i feel accomplished! :D

    • one year ago
  56. Emily778
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    So, is that x? x=10.30

    • one year ago
  57. johnweldon1993
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    correct....that is the direction the boat is heading...heading at 10.30 degrees in that direction and 11.18 would be the speed :)

    • one year ago
  58. Emily778
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    so, I'd put x=10.30?

    • one year ago
  59. johnweldon1993
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    well technically...its 10.30 degrees at THAT direction...but if the answer wanted to be technical...it would be 180 + 10.30...so 190.30 degrees.... if you would like me to explain...i will...but it may be hard to digest

    • one year ago
  60. Emily778
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    I already turned it in...-_-

    • one year ago
  61. johnweldon1993
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    well technically it's not wrong....just have to explain it....

    • one year ago
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