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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

would i just take $\Delta y / \Delta x$

2. amistre64

you want dr/dt; so implicit this thing with respect to time.. your formula is the pythag thrm

3. amistre64

your dy/dt, or rather the d'north'/dt = 25; and d'e'/dt = 35

4. amistre64

e^2 + n^2 = r^2

5. amistre64

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

ok so if i take that and introduce log i have f(x)+f'(x) which is

7. amistre64

log?

8. anonymous

$e^2+n^2-r^2+ 1/2x +1/2n +1/2r$

9. anonymous

well ln

10. amistre64

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

there is no call for any log or ln in this problem... your thinking to much at it :)

12. anonymous

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

well 4(35)+150

14. amistre64

$r' = \frac{35(e) + 25(n)}{\sqrt{100^2 + e^2}}$

15. anonymous

because the boat is to the west and sailing east wouldn't it be 4(35)-150?

16. anonymous

ok let me work that out really fast

17. amistre64

150 + 4hours worth of 35 is.....150 + 4(35) :)

18. amistre64

....maybe, i coulda read it wrong lol

19. anonymous

ok for your r' i am showing 140.9996308

20. amistre64

your right; 4(35) - 150 :)

21. amistre64

2850 ------ sqrt(100^2 + 10^2) = sqrt(10100) r' = 28.358 is what I get

22. anonymous

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

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

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

n = 100; n' = 25; n n' = 2500 e = 10; e' = 25; e e' = 250

26. amistre64

r = sqrt(100^2 + 10^2) r = sqrt(10000 + 100) r = sqrt(10100)

27. anonymous

when i do sqrt(10100) i end up with 100.4987562

28. amistre64

crap lol.....n' = 35 ;) e e' = 350

29. anonymous

ok little off track here why are we breaking down the east and north into double derives?

30. amistre64

its hard to keep up with my typos with my computer lagging so much...... you need to read thru them :)

31. amistre64

we derive implicitly with respect to time; so all our derived bits stay intact

32. amistre64

e^2 + n^2 = r^2 ; implicit with respect to "t"

33. amistre64

e' 2e + n' 2n ----------- = r' = dr/dt = how fast the boats r are moving away from each other

34. amistre64

thats 2r under there :) but all the twos factor out to 1 so they can dissapear

35. amistre64

e' e + n' n ----------- = r' = dr/dt r

36. anonymous

fantastic answer as always amistre, thanks a ton for the help

37. amistre64

35(10) + 25(100) ---------------- = r' = dr/dt sqrt(10100)

38. amistre64

youre welcome :)

39. amistre64

2850 ---------- = 28.3585 sqrt(10100)

40. anonymous

yup i agree our math was jiving on that last answer

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