CPhill

4. (Again).......!!!

The central angle formed  by two radial lines draw to each point of intersection of the two circles = 120°.......so.....the arc length, S, of the rest of one of the circles =   2pi(9)(240/360)  = 12pi

So......twice this = the length of the solid line in the figure = 24pi  = about 75.398 cm

OK, Alan, thanks......I see that makes sense.....!!!

I assume this is :

(6x^2-x+10) - (-4+2x^2+8x)     if so........distribute the negative over the terms in the parentheses

6x^2 - x + 10  + 4 - 2x^2 - 8x       combine like terms

4x^2 - 9x + 14

5. 

Area of sector OBC = pi (20)^2/ 6  = 200pi/3 cm^2

Area of equilateral triangle   (1/2) 20^2 sin60  = (1/2) 400* [√3/ 2] =  100√3 cm^2

Area between area of sector OBC and equilateral triangle = [ 200pi/3 -100√3] cm^2  →   (1)

And AC is the radius of the smaller circle  = (1/2)20cm  = 10cm

So....the shaded area = (1/2) area of the smaller circle  - (1)   =

[pi (10)^2/2  - (200pi/3 - 100√3) ] cm^2  = about 120.85 cm^2

3. Total area of sector  AOC =  pi(36)/ 3 =  12pi units^2

If the orange area = the blue area.....then, by symmetry......area BCEF   = the orange area 

And the area of the sector formed by OED = the blue area.....so......all these areas are equal and they divide the total area of sector AOC into 4 equal parts.......so area ODEF  (1/2) the area of sector AOC  = 6pi units^2

So....we have that OD is the radius of the the smaller circle

And we have:

1/3 area of the smaller circle  =  Area ODEF  = [ pi * OD^2] / 3

6pi = [ pi * OD^2] / 3      multiply both sides by 3

18  = OD^2

OD  = √18 units   =  3√2 units  = about 4.24 units

1.

a. Area of the rectangle  - area of smaller sector  =  the "large" white area in the rectangle  =

         [24 - 4pi] cm^2

b. Area of the large sector  - area of "large" white part of the rectangle = the total area of the shaded region =

  [ 9pi - ( 24 - 4pi)] cm^2  = [ 13pi - 24] cm^2   = about 16.841 cm^2  = about 16.8 cm^2

I assume you want either :

0.3444..... [4s repeating] 

Or 

0.343434.......[ 34 repeating ]

1st case

[  34  - 3] /  90   = 31/90   = 0.344444.........

2nd Case

[34 - 0] / 99  = 34/99  =  0.343434.......

d)  40 → 84

( [84 - 40] / 40 * 100) %      = ( 44/40 * 100)%  = (11/10 * 100)% =

(1100/10)% =  110 %

e)  4 → 13

( [ 13 - 4] / 4  *100) %   = (9/4 * 100)%  = (2.25 * 100) %  =  225%

Here's another approach....using Alan's interpretation

log₂x = log₄(4x)

log₂x  = log₄4  + log₄x

log₂x - log₄x  = log₄4

log₂x - log₄x  = 1

logx/log2  - logx/log 4   = 1

logx [ log4 - log 2] / [log2 * log 4]  = 1

logx  = [log2 * log4] / [ log4 - log2]

logx = [log2 * log4] / [log (4/2)]

logx = [log2 * log4] / [log2]

log x  = log 4

x = 4