A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

anonymous

  • 5 years ago

ALKJFSALJF. Two small planes approach an airport, one flying due west at 120mi/hr and the other flying due north at 150mi/hr. Assuming they fly at the same constant elevation, how fast is the distance between the planes changing when the westbound plane is 180mi from the airport and the northbound plane is 225mi from the air port?

  • This Question is Closed
  1. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    hey, you keep posting problems i can't catch up, which do you want to work on?

  2. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    haha sorry! i'm flustered. whatever you're heart desires to work on is good enough for me

  3. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    your*

  4. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    with these types of problems i always start by drawing the picture, did you do that?

  5. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    let me know if youre still here

  6. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    yeah i drew one

  7. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    sorry, you still there?

  8. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    still here!

  9. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ok so what does your picture look like? the question is asking for the rate of change of the distance. so we need an equation for the distance and take the derivative. how can we get an equation for the distance?

  10. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    i kind of made a triangle between the two planes. i'm use to doing rate of change of distance with a point and equation of a line given

  11. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    triangle sounds good, what kind of triangle

  12. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    right

  13. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    yes, so we are given rate of change of the sides of the triangle, so we want an equation for the distance as a function of the sides of the triangle

  14. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    basically we want d = (something with x's and y's), because we know x,y, dx/dt, dy/dt, so if we take the derivative we can find dd/dt

  15. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    say a is 180x and b is 225y then d(b-a)/dt=(180)x+(225)y just a guess

  16. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    hmm, now a and b is what you are using for the sides of the triangle?

  17. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    i was using x and y for that

  18. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    oh whoops!

  19. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    so if you want you can take everything i said and substitute a for x and b for y, it's the same thing

  20. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    now don't confuse 180,225 and the variables. it's 180 at a certain time, and x (or a), when you don't know what it is

  21. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    what's a formula for d in terms of a and b

  22. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    do you know the pythagorean theorem?

  23. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    a^2 + b^2 = c^2

  24. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    so what is c here in our problem

  25. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    we don't know c?

  26. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    wait 225^2 + 180^2 =83025 then take the square of that?

  27. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    what does c stand for though

  28. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    yes that is what c is when a and b are those numbers

  29. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    the distance between planes

  30. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    right

  31. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    so what's the equation for the distance between the planes in terms of a and b

  32. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ?

  33. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    the distance formula is a^2 + b^2 = c^2 and we want to derive with respect to time: (d/dt)(x^2) + (d/dt)(y^2) = (d/dt)(c^2) (dx/dt)(2x) + (dy/dt)(2y) = (dc/dt)(2c) To clean this up: (dx/dt) = x'; (dt/dt) = y'; and (dc/dt) = c'. x'2x + y'2y = c'2c solve for c': x'2x + y'2y ----------- = c' 2c the twos cancel to give us: x'(x) + y'(y) --------- = c' c y' = 150; x'=120; and c = whatever you got with the pythag. theorum. x and y values are their current values of x=180; y=225 So lets plug those in: 120(180) + 150(225) ------------------- = c' 288.14

  34. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    dt/dt = y' ?

  35. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    192mi/hr. i never would have gotten that

  36. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    lol....(dy/dt) = y' :)

  37. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    was I right is what I want to know :)

  38. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    haha i have to find that out....

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

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.