1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Rate of change: find rate length is changing at moment

  1. Apr 25, 2013 #1
    1. The problem statement, all variables and given/known data

    An equilateral triangle with side length x sits atop a rectangle with a base length of x, with the base of the triangle coinciding with the top base of the rectangle. the height of the rectangle is 7 times the length of its base. If the combined area of the figures is increasing at a rat of 8 mm^2/sec, find the rate at which a side of the triangle is lengthening at the moment the base of the rectangle is 20 mm.

    3. The attempt at a solution

    so i started by making a sketch. (I attached a sketch of the figures). then, i found the Area and then dA/dt:

    A=lw+1/2 bh
    =(7x)(x)+ 1/2 (x)((x*sqrt3)/2)
    =7x^2 + (x^2*sqrt3)/4

    dA/dt= 14x dx/dt + (x*sqrt3)/2 dx/dt

    then, plug in x=20 mm, and dA/dt=8 mm^2/min:

    8= 40 dx/dt + 2.474 dx/dt
    8= dx/dt (40+2.474)
    8= dx/dt (42.474)
    dx/dt = 0.188 mm^2/sec
     

    Attached Files:

  2. jcsd
  3. Apr 26, 2013 #2

    Simon Bridge

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    That's great - did you have a question?

    Note - for isomorphic change, $$A\propto x^2 \Rightarrow \frac{dA}{dt} \propto 2x\frac{dx}{dt}$$ ... which could save you a lot of trouble.
     
    Last edited: Apr 26, 2013
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Rate of change: find rate length is changing at moment
  1. Finding Rate of Change (Replies: 2)

Loading...