Quantcast

A community for students. Sign up today!

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

angelarios

  • one year ago

all edges of a cube are expanding at a rate of 3 centimeters per second. how fast is the volume changing when each edge is (a) 1 cm. (b) 10 cm.

  • This Question is Closed
  1. satellite73
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    looks like a related rate problem fortunately the formula for the volume of a cube is easy, it is \(V(x)=x^3\)

  2. satellite73
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    take the derivative with respect to time and get \[V'=3x^2x'\]

  3. satellite73
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    you are told \(x'=3\) so this is really \[V'=9x^2\] replace \(x\) by the various values to get \(V'\)

  4. angelarios
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    dV/dt=9x^2dx/dt ?:)

  5. satellite73
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    no

  6. satellite73
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    i used \(V'\) and \(x'\) instead of \(\frac{dV}{dt}\) and \(\frac{dx}{dt}\) because it was easier for me to write also for you it is easier

  7. satellite73
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    but in your notation, you have \[V=x^3\] so \[\frac{dV}{dt}=3x^2\frac{dx}{dt}\]

  8. satellite73
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    this line all edges of a cube are expanding at a rate of 3 centimeters per second tells you that \(\frac{dx}{dt}=3\)

  9. satellite73
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    that means \(\frac{dV}{dt}=3x^2\times 3=9x^2\)

  10. satellite73
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    let me know if i lost you there

  11. angelarios
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Ok got it(:

  12. angelarios
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    So dats da answer?:)

  13. 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.