CPhill

Note the repeating pattern  of  length  4

i^1   = i

i^2  = -1

i^3  = -i

i^4  =  1

So....the sum of this series  from i^1  to  i*96   = 0

So...the sum of the last  three terms   = i^97  + i^98  + i^99  = i + -1 +  -i   = -1

So...this series sums  to  0 + (-1)  = -1

(1/2) f (x - 2)  =  (1/2)  ( l  (x - 2) - 2 l - 5 )   =  (1/2) l x - 4 l   - 5/2   =  g(x)

To find the y intercept, let x  = 0  and we have

y  = (1/2)  l 0 - 4 l - 5/2  = (1/2) (4) - 5/2  =  2 - 5/2  =  -1/2

To find the x intercepts, let y  =  0

0  = (1/2) l x - 4 l  - 5/2   multiply through by 2

0  = l x  - 4  l - 5    add 5 to both sides

5  =  l x - 4  l

So either   

x  - 4  = 5    or             x  - 4   =  -5

x  = 9          or             x  = -1

(c)  Your answer is correct !!

(d) a  = 150    r  = 3m

Arc Length  =  2pi * 3 * (150 / 360)  ≈  7.85 m

(b) a = 74   r  = 2 ft

Arc Length  =  2 pi * 2 * (74 / 360) ≈ 2.58 ft

(a)  a  = 60     C  = 48 cm

Arc Length  =   48 * (60 / 360)  =  48 * (1/6)  =  8 cm

Let P  be the original price

The new  price  is   P(1.5)(.25)  = .375 P

So....to return to the original price.....we must increase this new price by

  1 / .375  ≈  2.66 ≈  266%

Last one

x + 3y - z  = 6    

4x - 2y + 2z = -10    

6x + z  = -12

Sorry..Johnny...but I gotta' go in just a minute

The answer to  this is   (x ,y , z)   = ( -3, 5, 6)

When I get back on...I'll give you a complete run through...if you need it  !!!

2x - 3y  = -27     multiply through by 3   ⇒   6x - 9y = -81    (1)

-3x + 2y  = 23   multiply through  by  2 ⇒   -6x + 4y  =  46    (2)

Add (1)  and (2)  and we get

-5y  = -35     divide both sides by  -5

y  = 7

And  using   2x  -  3y = -27  to  find x we get

2x - 3(7)  = -27

2x - 21  = -27     add 21 to  both sides

2x = -6    divide both sids by  2

x  = -3

So  (x ,y )  =  ( -3, 7)

x + y  = 6

x  =  y + 4        sub the second into the first for  x

(y + 4) + y  = 6

2y + 4  = 6

2y  = 2

y = 1

And   x   =  y + 4  =  1 + 4   = 5

So   (x, y)  = ( 5 , 1)

x + 5y  = -15

y  = (1/5) x + 1        sub the second into the first for y  and we have

x + 5 ( 1/5 x + 1)  = -15

x + x + 5  = -15

2x + 5  = -15     subtract 5 from  both sides

2x  = -20     divide both sides by 2

x  = -10

And using    y  = (1/5)x + 1  to find  x, we have   y  =(1/5) (-10) + 1  = -2 + 1   =  -1

So   (x , y)   = ( -10 , -1)