Derive Eqs. 4-9 from Eqs. 1-3. The following two hints should help you get started in the...

Derive Eqs. 4-9 from Eqs. 1-3. The following two hints should help you get started in the right direction:

1) To find R1 as a function of Ra, Rb, and Rc, first subtract Eq. 2 from Eq. 3 and then add this result to Eq. 1. Use similar manipulations to find R2 and R3 as functions of Ra, Rb, and Rc.

2) To find Rb as a function of R1, R2, and R3, take advantage of the derivations obtained by hint (1),namely, Eqs. 4-6. Note that these equations can be divided to obtain

,

and

.

Now use these ratios in Eq. 3 to eliminate Ra and Rc. Use similar manipulations to find Ra and Rc as functions of R1, R2, and R3.

Equation. 1

Equation. 2

Equation. 3

Equation. 4

Equation. 5

Equation. 6

Equation. 7

Equation. 8

Equation. 9