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

- anonymous

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- anonymous

would i just take \[\Delta y / \Delta x \]

- amistre64

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

- amistre64

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

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## More answers

- amistre64

e^2 + n^2 = r^2

- amistre64

e' 2e + n' 2n = r' 2r ; divide it all by 2
e' e + n' n = r' r
r' = [e' e + n' n]/ r

- anonymous

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

- amistre64

log?

- anonymous

\[e^2+n^2-r^2+ 1/2x +1/2n +1/2r\]

- anonymous

well ln

- 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) :)

- amistre64

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

- 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

- anonymous

well 4(35)+150

- amistre64

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

- anonymous

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

- anonymous

ok let me work that out really fast

- amistre64

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

- amistre64

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

- anonymous

ok for your r' i am showing 140.9996308

- amistre64

your right; 4(35) - 150 :)

- amistre64

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

- 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

- 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

- 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

- amistre64

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

- amistre64

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

- anonymous

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

- amistre64

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

- anonymous

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

- amistre64

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

- amistre64

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

- amistre64

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

- amistre64

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

- amistre64

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

- amistre64

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

- anonymous

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

- amistre64

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

- amistre64

youre welcome :)

- amistre64

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

- anonymous

yup i agree our math was jiving on that last answer

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