Question

Urgent!
If t varies inversely as the cube of z and directly as the square of r, and t=4 when z=3 and r=6, find t when z=6 and r=9.
T= k (square) r/(cubed) z
4=k (square) 6/ (cubed) 3

The electrical conductance of a wire varies directly as the square of its a diameter and inversely as its length. The conductance of a wire 20 m long and 3 mm in diameter is 0.54 mho. If a wire of the same material has length 50 mm and diameter 5 mm, what is its conductance?

Let conductance = c, diameter = d, length = l
c= (square) d/l


Am I going in the right direction?? Please help and give solutions!! :)

Answer 1

t = k (1/z^3)(r^2)
for the given:
4 = k(1/27)(36)
k = 4(27)/36 = 3

so your equation is
t = 3r^2/z^3
for the data ...
t = 3(81)/216 = 9/8 or 1.125

#2

c = k d^2/l
sub in the given:
.54 = k (9)/20
k = .54(20)/9 = 1.2

so you have c = 1.2 d^2/l

in your first data, the length was given in metres, but in the second set of data the length is in mm
Is that a typo or do you want that?

I am going to assume that the original 20 m was really 20 mm,

c = 1.2(25)/50 = .6

Answer 2

No