Expert: Paul Klarreich - 10/3/2010

Question
The resistance R of a wire varies directly as its length L and inversely as the
square of its diameter d. (Use k for the constant of variation.)

(a) Write an equation that expresses this joint variation.
R =   
(b) Find the constant of proportionality if a wire 1.4 m long and 0.007 m in
diameter has a resistance of 105 ohms. (Round your answer to six decimal
places.)
k =  
(c) Find the resistance of a wire made of the same material that is 4 m long
and has a diameter of 0.004 m. (Round your answer to the nearest whole
number.)
R =         ohms


Answer
Questioner:   Kristin
Country:  United States
Category:  Advanced Math
Private:  No
 
Subject:  Precalculus
Question:  The resistance R of a wire varies directly as its length L and inversely as the square of its diameter d. (Use k for the constant of variation.)

(a) Write an equation that expresses this joint variation.
R =

(b) Find the constant of proportionality if a wire 1.4 m long and 0.007 m in diameter has a resistance of 105 ohms. (Round your answer to six decimal places.)

k =  
(c) Find the resistance of a wire made of the same material that is 4 m long and has a diameter of 0.004 m. (Round your answer to the nearest whole number.)
R =         ohms

------------------------------------
I: "varies directly as its length L" means

= k times L

II: "varies inversely as the square of d" means

= k over d^2.

Put them together to get:
    kL
R = ----     (Eq 1)
    d^2

(b) Do some substituting:  

"a wire 1.4 m long"  means L = 1.4

"and 0.007 m in diameter" means  d = 0.007

"has a resistance of 105 ohms" means  R = 105

Now put those into your  Eq 1 and do the arithmetic to solve for k.  

[k will be  Rd^2/L, won't it?]

(c) Put the numerical answer for k back into Eq 1.

Now do more substituting.  I think you can take it from here.