CPhill

The perimeter  is given by 2W + 2L     where W and L are the width and length

And we are told that  L = 2W - 6  .... so we have

84   = 2W + 2 ( 2W - 6)   simplify  

84 =  2w + 4W - 12

84 = 6W - 12    add 12 to both sides

96  = 6W    divide both sides by 4

96 / 6 = Width   =  16 cm

And the Length is   2(16) - 6  =   32 - 6   =   26 cm

5! ways  = 120 ways

Look at the graph, here :  https://www.desmos.com/calculator/wsr4thr9vo

Note that the function is defined for all values of x.

2 sqrt (5) / [ 2 sqrt (7) + 3 sqrt (3) ]

Note that 2 sqrt (7) = sqrt (28)  and 3 sqrt (3)  = sqrt (27)

So we have

2 sqrt(5) / [ sqrt (28) + sqrt (27) ]

Multiply top/bottom by the conjugate of the denominator → [sqrt (28) - sqrt (27) ]] 

And we have

[2 srqt (5)] [ sqrt (28) - sqrt (27)] / [  28 - 27 ]  =

[2 srqt (5)] [ sqrt (28) - sqrt (27)] / 1 =

[2 srqt (5)] [ sqrt (28) - sqrt (27)]   =

[2 sqrt (5)] [ 2 sqrt (7)  - 3 sqrt (3) ]=

4 sqrt (35)  - 6 sqrt (15)

3 / [ sqrt (7) - sqrt (2) ]          

Multiply top/bottom by the conjugate  of  [ sqrt (7) - sqrt (2) ] →  [ sqrt (7) + sqrt (2) ]

3  [ sqrt (7) + sqrt (2) ] / (  [ sqrt (7) - sqrt (2) ]  [ sqrt (7) + sqrt (2) ]   )   =

3  [ sqrt (7) + sqrt (2) ] / ( 7  -  2 )   =

3  [ sqrt (7) + sqrt (2) ]  / 5  =

(3/5)sqrt (7)   +  (3/5)sqrt (2)

Distance  / Rate   = Time   .....so...

17.5 /  7   =  2.5 hours

Wheels required  =  4 * 236  = 944      (1)

Wheels available =  748      (2)

Wheels needed  =  (1) - (2)  = 196

Cars that wll have no wheels  =  196 / 4  =  49

Here's the frist one :

The linear distance traced out by one revolution of the ball will be

 2* pi (1 inch)  = 2pi inches

And 5 ft  = 60 inches

So......,the number of revolutions  =  60 / [ 2 pi]   =  30 / pi ≈ 9.5 revolutions

Here's the third one......

Circumference of coaster = 2pi (radius)

12.56  = 2pi (radius)    divide by 2pi

12.56 / [ 2pi] = radius =    6.28/pi  inches

Then....the radius of the glass  =  [ 6.28/pi -  1/2] inches

So......the circumference of the glass =

2 * pi * radius  =

2 * pi * [ 6.28/pi - 1/2) ]  ≈ 9.42 in 

I don't quite see what you're asking, here.