CPhill

The side of the square =    10 / √2   cm   =  5√2 cm

And the perimeter is  4 times this  =  20√2 cm

At  t = 0.5 seconds.....the pendulum is at its resting position

At  1 sec ...it is at its max displacement to the right

At  1.5 sec...it returns to its resting position

So ...  1.5 - 0. 5 =      1 second is required

(1)    Reflect  the function  about the y axis

(2)    Rotate the graph of (1)     90°  clock-wise

This will be the inverse 

First one  :  https://www.desmos.com/calculator/f34fdy3pga

Second one :  https://www.desmos.com/calculator/i1l4bgsjmp

Third one :   https://www.desmos.com/calculator/exbmqsekow

Last one : https://www.desmos.com/calculator/pqzzmgj0gg

First column                   Second column                 Third column

9.2 X 10^(-4)                  2.1 X 10^(-4)                       3.4 X 10^(-5)                   

2.1 X 10^(-3)                  8.3 X 10^(-5)                       2.8 X 10^(-7)

                                                                                   7.2 X 10^(-5)

The inverse just reverses the coordinates...so we have

(-3, 1), ( 3 , -2), (1, 5) , (4, 6)

We don't have any single "x"  associated with two different "y's".....so.....the inverse is a function

(7, -5), ( -8, -6) , ( -2, 1), ( 3, 10 )

Again...no single x is  associated with two different "y's"....so....the inverse relation is a function

Here's the way we can test for an inverse.....put first function into the second....then, put the second function into the first.....if we get an "x" as a result in both cases....they are inverses

First one

(x - 6) + 6   =   x

(x + 6) - 6  =   x         these are inverses

Second one

2  [ ( x + 7) / 2 ] - 7   =    x + 7 - 7   =  x

 ( [ 2x - 7 ] + 7 )  / 2  =      [2x] / 2   =  x             these are inverses

We  can use the Pythagorean Theorem here :

UM =  sqrt (JM^2 - JU^2 )   =   sqrt ( 12^2 - 8^2)  =  sqrt ( 144 - 64)  = sqrt ( 80)  =  4sqrt(5) units

Let the price of the small size = P   and let the quantity contained = Q

So....the unit price is     P /Q

Let the price of the meduim size =  1.5P

And let the quantity contained be   (2 - ..20)Q  =  1.8Q

So.....the unit price is    (1.5)P /  (1.8)Q   =  (5/6)P/Q

The large size price is (1.5)(1.3)P = 1.95 P

And the quantity is 2Q

So.....the unit price is  (1/95  P) / (  2Q)   =  (19/20)P/Q

So.....the best value from best to worst is

 ( 5/6)P/Q     (19/20)P/Q          P /Q  =

   M                  L                      S

Here you are :

OK......here you go :