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 75   25   50   100   5   2   to find 431

75*5 + 50  + (100/25) + 2

375 + 50  +  4  + 2   =

425  + 4 +  2  =

431

1.) -x^2 + 4x = 13

-1x^2 + 4x - 13   = 0

a =  -1      b = 4       c =  -13

The Quadratic Formula is

-b ±√  [ b^2 - 4ac ]

______________

          2a

So....the solutions are

-4 ±√ [ 4^2 - 4(-1)(-13) ]                 - 4 ±√  [ 16  - 52]               -4  ±√[ -36]

___________________   =          _________________  =   __________  =  

           2(-1)                                             -2                                    -  2 

-4  ±  6i

_______    =        2 ±3i

      -2

a_{1 =} 2/5 (5)^0    2/5       r = 5

an = 5 (a_n-1)    (for n >=2)

Correct   !!!!

The distance  is given by

80  +  80[ 1 - (1/2)^4] / [ 1 - 1/2]  + 80(1/2)^5   =  232.5

I am confused.

Thank you!

        Bounce 1       2             3            4           5

80   +   40X2  +  20 x 2   + 10 x 2   + 5 x 2  + 2.5   = 232.5 ft   

.333333.....

33.33333....  %

it was actually -625 but thank you for your help

a₁  =  the first term     = 6

a_n   =  the nth term  =   a₁ (-3)^{n - 1}

For example.....the second term is

a₂  =  6 (-3)^2-1   =  6(-3)¹  =  6 * -3   =  - 18

No.  0 is just an extraneous root of the quadratic you synthesized.

The common ratio is   -100/-500 =   1/5  = r

The sum, S,  of the first n terms is given by

S =    first term [ 1 - common ratio ^(n - 1) ] / [ 1 - r ]

So...the sum of the first 8 terms is

S  = (-500) [ 1 - (1/5)^(8 - 1) ]  / [ 1 - 1/5]    =

(- 500 ) [ 1 - (1/5)^7 ] / [ (4/5) ]  =  -624.992

Rounding to 2 decimal places.....note that the third decimal place is < 5

So....we round to     -624.99

Just use the quadratic formula.

Use a bit of algebra to get all the terms on one side with 0 on the other.

\(g=2b\\ g+b = 30\\ b = ?\\ \dfrac{b}{30}=?\)

Im a little confused.. so how would i fill in this blank then:  a1=__?__ ; an= __?__

36000036

Explicit rule

a_n  =  (2/5)(5)^n-1

The common ratio is       -18 / 6  = -3

a₁  =  6

a_n  =  6(-3)^n-1    =   explicit rule

The recursive rule is

a_n =  a_n-1 (-3)

Relative max  =  3

Relative min =   - 1

If this forms a right triangle....then

45^2 + 56^2  = 72^2    ?????

2025 + 3136  = 5184

5161 =  5184  ????

No...not true....so.....not a right triangle

Appreciate it!!

I have just one other question on this if it's ok. how can i find the relative maximum and relative minimum of this function?

Sorry.....forgot to include that...!!!

Positve where the function is above the x axis

This occurs at   (-3.5, 2.5)  and ( ≈3.4, inf )

Negative where it is below the x axis

This occurs at  ( -inf, -3.5)   and (2.5, ≈ 3.4)