Question

I have no clue what to do on these questions.

1.Two resistors a and b are connected in parallel. The total resistance R in such a circuit is found by formula R= 1/a + 1/b. If R=5/6 ohms and b is one more ohm than a, find the number of ohms in a and b.

2. The profit function for producing blank CD's was projected to be P(x)=x^2 + 5x-6 where x is the number of CD's produced in hundreds. The average profit for a cd is found by P(x)/x. At what level of production must the company produce the CD's for the average profit to be greater than zero?

Answer 1

1. aren't you told that
b is one more ohm than a ?
so -----> b = a+1

sub in the equation
5/6 = 1/a + 1/(a+1)
multiply by 6a(a+1) , the LCD

5a(a+1) = 6(a+1) + 6a
5a^2 + 5a = 6a + 6 + 6a
5a^2 - 7a - 6 = 0
(a-2)(5a + 3) = 0
a = 2 or a = -3/5, but I believe that a > 0

so a = 2 ohms and b = 3 ohms

check:
1/2 + 1/3 = 5/6 , all is good!

Answer 2

5/6 = 1/a + 1/(a+1)

5 a(a+1) = 6(a+1) + 6 a

5 a^2 + 5 a = 6 a + 6 + 6 a

5 a^2 - 7a - 6 = 0

(5a+3)(a-2) = 0
a = 2
b = 3

Answer 3

Where is P(x) zero?
(x+6)(x-1) = 0
You can not make a negative number of blank CDs
so where x>1 the profit is positive, so is P(x)/x