CPhill

We have the following system of equations

 a    +  b   +   c   =    13    (1)

-a     - b    + c     =    -1     (2)

-8a  -2b    + c     =   -32   (3)

Adding  (1)  and (2) we have that  2c  = 12  ⇒   c  = 6

So (2) and (3) become

-a     -  b   =   -7   ⇒    -2a   -   2b    =    - 14     ⇒  2a  +   2b     =  14      (4)

-8a  -2b   =  -38      (5)

Add (4)  and (5)   and we have that

-6a   =   -24    ⇒   a  = 4

So

a  +  b  + c  =  13

4  +  b   + 6   = 13

b =  3

So    a  =  4, b = 3   and   =  6

2002 revenue   =  d (1 + x% )   where x is expressed as a decimal

Good to see you, PM....welcome back.......!!!

Very nice application of Decartes Rule of Signs, X²  ......this is often very useful in these types of problems ....however....I rarely think to use it    !!!!   

Avg Rate of Change  =

[ f(5) - f(0)] /  [ 5 - 0 ]  =

[(1/2) ( 3^5 - 3^0) ] /  5  =

(243  - 1) / 10   =

242 /  10  =

24.2

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[ f(2)  - f(0)]  / [ 2 - 0]  =

[ 250  [ (1/2)^2  - (1/2)^0 ]  / 2  =

125  [ 1/4  - 1 ]  =

125 (-3 / 4)   =  -93.75

1. Avg Rate of Change  is

[ f(4)  - f(2)] / [ 4 - 2 ]   =

[ (4^4 - 1) - (4^2 - 1) ]  / [ 2 ]

[  256   -  16  ]   /  2 =

240  /  2   =

120 per hour

2.  Avg Rate of Decrease

[ f(2)  - f(1) ] /  [ 2 - 1]

[ 10000(.73)^2  - 10000(.73)^1]  / 2  =

[ 5329 - 7300]  / 2 =

[ -1971 ] / 2  =

- 985.5 per year

3.  Linear   .... y changes by 1.5  when x changes by 1

     Exponential  ....the function is   2^x

     Linear     ......y changes by  20   when x changes by 2

     Neither..... there appears  to be no linear or exponential relationship between x and y

4.   a. Linear      b. Exponential      c. Exponential

Nice detective work, hectictar.....!!!!

(8v + s)^5   =

(s + 8v)^5

All  terms are positive  and we will have 6 of them

The first is  s^5      and the last is   (8v)^5  = 32768v^5

And the second term  is    C(5,1) * s^4 * 8v   = 5* s^4 * 8v  =  40s^4v

So....the last answer is correct.....NSS!!!!!

3.

2x^4 - 5x^3 + 53x^2 -125x  + 75  =  0

Write as

2x^4  -  5x^3  +  3x^2  + 50x^2 - 125x + 75  = 0

x^2 (2x^2 - 5x + 3))  +  25 (2x^2 - 5x + 3)  =  0

x^2  [  (2x - 3) (x - 1) ]  + 25 [ (2x^2 - 3) (x - 1) ]  = 0

[ (2x- 3) ( x - 1)]   [ (x ^2 + 25 ]   = 0

The   roots are     3/2, 1  and  ±5i

2. 

If   7 + √3   and 2 -  √6   are roots....so are their conjugates....

7  - √3    and     2  + √ 6