Emily778 Group Title 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

1. johnweldon1993

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

2. Emily778

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?

3. johnweldon1993

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?

4. Emily778

What is C and A and B?

5. johnweldon1993

C is the length of the hypotenuse of the right triangle.... A is any other one of the sides B is the remaining side

6. Emily778

can you just give me numbers

7. johnweldon1993

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

8. Emily778

So, it would be 'C= sqrt 11^2 + 2^2' ?

9. johnweldon1993

correct ...so evaluate farther

10. Emily778

I got C=15

11. johnweldon1993

11² = 121 right? 2² = 4 right? 121 + 4 = 125 sqrt of 125?

12. Emily778

11.1

13. Emily778

did I do the other thing wrong? ._.

14. Emily778

@johnweldon1993

15. johnweldon1993

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

16. Emily778

okay, what do I do next?

17. Emily778

@johnweldon1993

18. johnweldon1993

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

19. Emily778

wait..what? You mean 11.2?

20. Emily778

21. Emily778

@johnweldon1993

22. johnweldon1993

no remember....tan is opposite over adjacent.... our opposite is 2 and adjacent is 11 so no it is 2/11

23. johnweldon1993

so it would look like this tan(x) 2/11 tan^-1 2/11 = x

24. johnweldon1993

and since your calculator hasn't been working correctly with the inverse trig functions....the result would be 10.3 degrees

25. Emily778

tan (x) 2/11? Where's the x? I can at least try to find it

26. johnweldon1993

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

27. Emily778

yeah, I keep getting 0. :/ I put in "tan 2/11" and I tried what you did.

28. johnweldon1993

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

29. Emily778

I got 11.3

30. Emily778

When I round up the number I got

31. Emily778

when I don't round up, I get 10.203

32. johnweldon1993

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

33. Emily778

And when i add the 3rd number from the answer I got, I get 10.259

34. Emily778

yep.

35. Emily778

how do you do the second part?

36. Emily778

how do I do the second part on my calculator?

37. johnweldon1993

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

38. Emily778

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

39. johnweldon1993

lol yeah @jim_thompson5910 is very intelligent :)...hopefully he can give a fresh perspective

40. Emily778

so are you:D @johnweldon1993 I just need the rest. :(

41. johnweldon1993

thank you :) ...so wait...what exactly are you still looking for right now? the direction right? in this case ..the angle?

42. Emily778

after "atan.181"

43. johnweldon1993

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

44. Emily778

it's on my computer. it's a graphing calculator.

45. johnweldon1993

and hang on ......try atan(2/11) put the parenthesis around 2/11

46. johnweldon1993

and i'm sure as you know...atan means arc tan...also known as \[\tan^{-1}\]

47. Emily778

I got .18.1

48. johnweldon1993

49. Emily778

how do I put it in degree mode?

50. johnweldon1993

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

51. Emily778

angle mode. It says 1. deg 2. rad 3 grad 4. cyc

52. johnweldon1993

right......so type...or click 1.....you want deg mode

53. johnweldon1993

and try the atan(2/11) again

54. Emily778

I got it now! :) Thanks so much!

55. johnweldon1993

AWESOME! lol finally haha! yes always have it in degree mode for problems like these :) ha! i feel accomplished! :D

56. Emily778

So, is that x? x=10.30

57. johnweldon1993

correct....that is the direction the boat is heading...heading at 10.30 degrees in that direction and 11.18 would be the speed :)

58. Emily778

so, I'd put x=10.30?

59. johnweldon1993

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

60. Emily778