Got Homework?
Connect with other students for help. It's a free community.
Here's the question you clicked on:
 0 viewing
angelarios
Group Title
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.
 10 months ago
 10 months ago
angelarios Group Title
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.
 10 months ago
 10 months ago

This Question is Closed

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
looks like a related rate problem fortunately the formula for the volume of a cube is easy, it is \(V(x)=x^3\)
 10 months ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
take the derivative with respect to time and get \[V'=3x^2x'\]
 10 months ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
you are told \(x'=3\) so this is really \[V'=9x^2\] replace \(x\) by the various values to get \(V'\)
 10 months ago

angelarios Group TitleBest ResponseYou've already chosen the best response.0
dV/dt=9x^2dx/dt ?:)
 10 months ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.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
 10 months ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
but in your notation, you have \[V=x^3\] so \[\frac{dV}{dt}=3x^2\frac{dx}{dt}\]
 10 months ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
this line all edges of a cube are expanding at a rate of 3 centimeters per second tells you that \(\frac{dx}{dt}=3\)
 10 months ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
that means \(\frac{dV}{dt}=3x^2\times 3=9x^2\)
 10 months ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
let me know if i lost you there
 10 months ago

angelarios Group TitleBest ResponseYou've already chosen the best response.0
Ok got it(:
 10 months ago

angelarios Group TitleBest ResponseYou've already chosen the best response.0
So dats da answer?:)
 10 months ago
See more questions >>>
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
 Engagement 19 Mad Hatter
 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.