Problem of the Week 11

The following examples show how the total resistance of electrical circuits, measured in ohms, can be found.

SERIES:

week11a

 

 

PARALLEL:

week11b

 

 

 

 

 

Find the total resistance for the circuit shown in the following diagram.  Express the answer as a fraction in lowest terms.

week11c

 

 

 

 

Alternate Problem 11

Complete the following multiplication table for modulo 7.

x

0

1

2

3

4

5

6

0            

 

 

1            

 

 

2            

 

 

3            

 

 

4            

 

 

5            

 

 

6            

 

 

 
List the reciprocals (if they exist) for 0, 1, 2, 3, 4, 5, 6 in modulo 7. How many reciprocals does each number have?

 

Extension Problem 11

Find the remainders upon division for (12! + 1)/13 and (16! +1)/17. Then, make a conjecture about the remainder for (n! + 1)/(n +1) where n +1 is a positive integer.