If E = {1 1 .} Show That C = C_0 Fe.

If 1

You want to prove that if 1
Since 1 < c, c must be positive. So, multiply each side of the inequality by c to get

c < c²

But, 1 < c, so

1 < c < c²

Done!

If 0 >c>1, show that 0>c2>c>1?

Assuming that you mean c^2 in the second equation,

c = x/y, such that x < y and x,y > 0

First

c^2 = x^2/y^2
0 = 0/y^2

x^2 / y^2 > 0 / y^2, so c^2 > 0

c^2 = x^2 / y^2
1 = y^2 / y^2
x^2 / y^2 < y^2 /y^2, so c^2 < 1

c^2 = x^2 / y^2
c = xy / y^2
x^2 / y^2 < xy / y^2, so c^2 < c

So 0 < c^2 < c < 1

Heat flow question with two metals?

Two aircraft rivets, one of iron and the other of copper, are placed in a calorimeter that has an initial temperature of 20C. Assume that the heat capacity of the calorimeter is negligible compared to those of the metals. The data for the metals are as follows:

Mass(g) Iron = 30.0 Copper= 20.0
Initial Temp(C) Iron= 0 Copper = 100
c (J/g*K) Iron= .45 Copper= .387

a) Will heat flow from Cu to Fe or Fe to Cu?
b) What is the final temperature of the system?