anonymous
  • anonymous
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
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
would i just take \[\Delta y / \Delta x \]
amistre64
  • amistre64
you want dr/dt; so implicit this thing with respect to time.. your formula is the pythag thrm
amistre64
  • amistre64
your dy/dt, or rather the d'north'/dt = 25; and d'e'/dt = 35

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amistre64
  • amistre64
e^2 + n^2 = r^2
amistre64
  • 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
  • anonymous
ok so if i take that and introduce log i have f(x)+f'(x) which is
amistre64
  • amistre64
log?
anonymous
  • anonymous
\[e^2+n^2-r^2+ 1/2x +1/2n +1/2r\]
anonymous
  • anonymous
well ln
amistre64
  • 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
  • amistre64
there is no call for any log or ln in this problem... your thinking to much at it :)
anonymous
  • 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
  • anonymous
well 4(35)+150
amistre64
  • amistre64
\[r' = \frac{35(e) + 25(n)}{\sqrt{100^2 + e^2}}\]
anonymous
  • anonymous
because the boat is to the west and sailing east wouldn't it be 4(35)-150?
anonymous
  • anonymous
ok let me work that out really fast
amistre64
  • amistre64
150 + 4hours worth of 35 is.....150 + 4(35) :)
amistre64
  • amistre64
....maybe, i coulda read it wrong lol
anonymous
  • anonymous
ok for your r' i am showing 140.9996308
amistre64
  • amistre64
your right; 4(35) - 150 :)
amistre64
  • amistre64
2850 ------ sqrt(100^2 + 10^2) = sqrt(10100) r' = 28.358 is what I get
anonymous
  • 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
  • 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
  • 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
  • amistre64
n = 100; n' = 25; n n' = 2500 e = 10; e' = 25; e e' = 250
amistre64
  • amistre64
r = sqrt(100^2 + 10^2) r = sqrt(10000 + 100) r = sqrt(10100)
anonymous
  • anonymous
when i do sqrt(10100) i end up with 100.4987562
amistre64
  • amistre64
crap lol.....n' = 35 ;) e e' = 350
anonymous
  • anonymous
ok little off track here why are we breaking down the east and north into double derives?
amistre64
  • amistre64
its hard to keep up with my typos with my computer lagging so much...... you need to read thru them :)
amistre64
  • amistre64
we derive implicitly with respect to time; so all our derived bits stay intact
amistre64
  • amistre64
e^2 + n^2 = r^2 ; implicit with respect to "t"
amistre64
  • amistre64
e' 2e + n' 2n ----------- = r' = dr/dt = how fast the boats r are moving away from each other
amistre64
  • amistre64
thats 2r under there :) but all the twos factor out to 1 so they can dissapear
amistre64
  • amistre64
e' e + n' n ----------- = r' = dr/dt r
anonymous
  • anonymous
fantastic answer as always amistre, thanks a ton for the help
amistre64
  • amistre64
35(10) + 25(100) ---------------- = r' = dr/dt sqrt(10100)
amistre64
  • amistre64
youre welcome :)
amistre64
  • amistre64
2850 ---------- = 28.3585 sqrt(10100)
anonymous
  • anonymous
yup i agree our math was jiving on that last answer

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