Quantcast

A community for students. Sign up today!

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

ashleynguyenx3

  • 2 years ago

The sides of a square are increasing at a rate of 10 cm/sec. How fast is the area enclosed by the square increasing when the area is 150 cm^2.

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

    start by assigning a variable to represent the side length of the square. lets call it x. now, what would be the area of the square in terms of x?

  2. ashleynguyenx3
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    100?

  3. asnaseer
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    no - what is the area of a square if its side length is equal to x?

  4. ashleynguyenx3
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    I don't get it

  5. asnaseer
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    |dw:1350248149705:dw|

  6. ashleynguyenx3
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Oh, A=x^2

  7. asnaseer
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    :)

  8. asnaseer
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    good, so now you just need to differentiate both sides with respect to time (t). Do you know how to do that?

  9. ashleynguyenx3
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Derivative, right?

  10. asnaseer
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    yes

  11. ashleynguyenx3
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    dA/dt=2x(dx/dt)

  12. asnaseer
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    perfect! almost there now...

  13. asnaseer
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    now, when the area is 150 cm^2, then what would the side length of the square equal?

  14. asnaseer
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    i.e. what is the length of the side of a square if its area is 150 cm^2?

  15. ashleynguyenx3
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    sq rt of 150?

  16. asnaseer
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    yes

  17. ashleynguyenx3
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    So you would plug in x and dx/dt to get dA/dt?

  18. asnaseer
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    now, in the equation you derived, you got:\[\frac{dA}{dt}=2x\frac{dx}{dt}\]Your questions tells you how fast the side length is increasing, so this gives you the value for:\[\frac{dx}{dt}=10\]

  19. asnaseer
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    yes - you have it now - well done! :)

  20. ashleynguyenx3
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Yay, thank you! :)

  21. asnaseer
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    yw :)

  22. ashleynguyenx3
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    I would ask for more help, but it's okay.

  23. asnaseer
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    ?

  24. ashleynguyenx3
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    I don't really understand related rates.

  25. asnaseer
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    What you should do is find a specific example and then post that as a question. Otherwise it becomes difficult to explain in general terms.

  26. asnaseer
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    For example, in this question, the rate of increase of side length is RELATED to the rate of increase of area by the formula you just derived.

  27. ashleynguyenx3
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Well, I'm just doing this packet. I understand some, but not all. http://tutorial.math.lamar.edu/ProblemsNS/CalcI/RelatedRates.aspx

  28. asnaseer
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    In that case I would advise you to pick one that you don't understand and post it as a question. If you also include what parts of it you DO understand then it becomes easier for others to focus on the parts that you are having difficulties with.

  29. ashleynguyenx3
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Okay, thanks again :D

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

    • Attachments:

Ask your own question

Ask a Question
Find more explanations on OpenStudy

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.