anonymous
  • anonymous
At noon, ship A is 130 km west of ship B. Ship A is sailing east at 30 km/h and ship B is sailing north at 20 km/h. How fast is the distance between the ships changing at 4:00 PM? This is kinda confusing...need help please!!!
Mathematics
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
jamiebookeater
  • jamiebookeater
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
Babynini
  • Babynini
What..college do you go to by chance? xD I legit just did this question!
anonymous
  • anonymous
Really? University actually!
Babynini
  • Babynini
Calc 1?

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

Babynini
  • Babynini
Bah unoriginal problem-writers! xP
anonymous
  • anonymous
yope
Babynini
  • Babynini
oh how fuun o.o
anonymous
  • anonymous
yh yh...not so fun!
anonymous
  • anonymous
what's confusing is the 4pm..not sure how to go about that
Babynini
  • Babynini
Righto. let me look through all my scratch paper to try and find it lol. You multiply the x and the y by 4 eventually. since the time form noon to four is four hours.
Babynini
  • Babynini
Have you tried drawing it out? :)
anonymous
  • anonymous
lol...okay...yeah, I did...just wasn't sure of the time like would it be from 12am or 12noon?
Babynini
  • Babynini
12 noon, for sure.
Babynini
  • Babynini
K, so still need help?
Babynini
  • Babynini
|dw:1446619451979:dw| so this is sort of how I drew it xD
Babynini
  • Babynini
all make sense thus far?
anonymous
  • anonymous
yeah, similar to my drawing...lol...please do go on!
anonymous
  • anonymous
oh my goodness, the question said at noon...lol...didn't see that
Babynini
  • Babynini
gorgeous, gorgeous. Ok so from that we can get the simple triangle|dw:1446619724508:dw|
Babynini
  • Babynini
it's ok, we've all been there haha does that all make sense?! I got confused at that part in class so don't hesitate to ask questions!
Babynini
  • Babynini
|dw:1446619924579:dw|
Babynini
  • Babynini
for now we don't really care about z, so no worries about finding it
anonymous
  • anonymous
yeah, it makes sense...is making sense
Babynini
  • Babynini
is it..is it reaaally?
anonymous
  • anonymous
wait, the 30km/h dosn't necessarily have to be negative does it?
Babynini
  • Babynini
It does because the space is getting smaller and getting smaller means negative. I mean, the space between the ships is getting smaller and A is approaching B which is why the A if negative and not the B.
Babynini
  • Babynini
haha sorry if that was more confusing xD make sense, sort of?
anonymous
  • anonymous
ummm, yeah...sort of
Babynini
  • Babynini
|dw:1446620270925:dw|
anonymous
  • anonymous
okay...I get
Babynini
  • Babynini
...ok haha. Sorry, idk how to explain it better :/ Anyway. Thats all at noon and we care about what happens between then and 4 So we need another triangle! Since from noon to 4 = 4 hours, we're going to take the numbers from the last triangle and multiply each side by 4
Babynini
  • Babynini
so x = -30 y = 20 multiply those each by 4
anonymous
  • anonymous
okay..so what I did was sum both and multiply sum by 4...totally wrong I'm guessing?
Babynini
  • Babynini
You're looking for 2 different sides, so you won't want to add them :) just x = -30*4 = ? y = 20*4 = ?
anonymous
  • anonymous
yeah...right!...-120 and 80
Babynini
  • Babynini
make sense? Ok so y is pretty straight forward, for x though we want to subtract 120 from 130 (the distance from A to B so 130-120= ?
Babynini
  • Babynini
|dw:1446620783497:dw|
Babynini
  • Babynini
|dw:1446620869735:dw|
Babynini
  • Babynini
Does that work for you? :)
Babynini
  • Babynini
And all that was from the ORIGINAL Because the speed of B = 20km/h and the speed of A = 30km/h
anonymous
  • anonymous
okay...the question says how fast is the distance between the ships changing...that suggests one answer...so if A is changing at 10km/h and B is changing at 80km/h then...
anonymous
  • anonymous
wait!...when we subtracted 120 from 130 we ignored the minus sign?
Babynini
  • Babynini
it's 130+(-120) so we're fine :)
Babynini
  • Babynini
sorry, I just skipped over that. Thanks for correcting me!
Babynini
  • Babynini
ok, the end is near xD from that last triangle with x = 10 and y =80 can you find z for me, please?
anonymous
  • anonymous
SQRT 6500
Babynini
  • Babynini
Perfect. And using that Pythagorean theorem again we can find our dy/dt!!
Babynini
  • Babynini
x^2 +y^2 = z^2 can you find the derivative of that?
anonymous
  • anonymous
2x+2ydy/dt=2z?
anonymous
  • anonymous
or nah!
Babynini
  • Babynini
super close. These always mess me up too. 2x(dx/dt)+2y(dy/dt)=2z(dy/dt)
Babynini
  • Babynini
notice anything we can factor out?
anonymous
  • anonymous
oh okay...divide through by 2?
Babynini
  • Babynini
absolutely!! and we end up with?
Babynini
  • Babynini
[I would go over getting that derivative later on your own, I would explain more but I gotta go to bed soon lol, just to make sure you understand it because it is confusing :/]
anonymous
  • anonymous
yeah sure...thanks for your time really
Babynini
  • Babynini
np. After you factor out 2 you end up with...
anonymous
  • anonymous
xdx/dt+ydy/dt=zdy/dt...and then we isolate dy/dt..or at least take like terms to one side?
Babynini
  • Babynini
Perfect! yeah we want to isolate dy/dt so we would end up with [x(dx/dt)+y(dy/dt)]/z = dy/dt yeah?
Babynini
  • Babynini
gah! the one by y should e z should be (dz/dt) and we're looking for dz/dt not dy/dt
Babynini
  • Babynini
so [x(dx/dt)+y(dy/dt)]/z = dz/dt sorry about that :)
anonymous
  • anonymous
right
Babynini
  • Babynini
so our values we know are x= y= z= dx/dt= dy/dt= Can you fill those in? :)
Babynini
  • Babynini
for z, y, x look at the last triangle we drew. Where z was a square root..
anonymous
  • anonymous
x=10,y=80,z=SQRT6500
anonymous
  • anonymous
dx/dt=30?
Babynini
  • Babynini
don't forget the negative. But yes!
anonymous
  • anonymous
dy/dt=20?
Babynini
  • Babynini
exactly. So now you take those numbers and plug them all in and solve for dy/dt!
anonymous
  • anonymous
dz/dt
Babynini
  • Babynini
\[\frac{ (10(-30))+80(20) }{ \sqrt{6500}} = \frac{ dy }{ dt }\]
Babynini
  • Babynini
agaihg idk why I keep saying dy. Yeah you're right.
Babynini
  • Babynini
Then simplify the square root and all that fun stuff. You got it from here? :)
anonymous
  • anonymous
yeah...absolutely!...thank you so much for your time!!!
Babynini
  • Babynini
Of course! Good luck man :) Hopefully this will help me remember how to do it too xD
Babynini
  • Babynini
http://www.mathwarehouse.com/arithmetic/square-root-calculator.php ...just in case you're not good at simplifying sq roots. I suck at it xD
anonymous
  • anonymous
lol...Okay!...thanks man!...do have a good night!
anonymous
  • anonymous
thanks a bunch :-D
Babynini
  • Babynini
no problem :)

Looking for something else?

Not the answer you are looking for? Search for more explanations.