ElectricPavlov

1   10    11   21   31   41     12   13   14   15   16   17  18  19       15 times

7¹ x 7¹ x  7¹ x 7¹ = 7^(1+1+1+1) = 7⁴      so  z = 7    y = 4

8 x 8 = 8²       so x = 2

Solve for y

2y-3 = x

2y = x + 3

y = 1/2 x + 3/2

A slightly different approach....see diagram below:

the angle between the inscribed angle legs of 18 and 25 is  45 degrees

   find c using cosine law

       c^2 = 18^2 + 25^2 - 2 (18)(25)(cos 45) = 312.604

Now  c  is also the hypotenuse of the isosceles triangle formed by the two radii

  use pythagorean theorem

     r^2 + r^2 = c^2

       2 r^2 = 312.604

          r = 12.50 inches         Hmmmmmm.....not the same as CPhill's answer....but close !       ~ EP

                    OK...I see what I did differently....I went to the points of contact at the wall.....not directly to the walls !!!

                                 SEE CPhill's answer ......it is best !!!!!!!!!

Add the 'like ' terms         x^3   +   5 x^3    = 6 x^3

c = 2/9 s

c = 2 ( s-32)         these are given......sub in the first equation to the second

2/9 s = 2 (s-32)

2/9 s = 2s - 64

16/9 s = 64

s = 64 * 9 / 16 = 36   originally 

151 - s   = (2)( 109-s)   given

151 - s = 218 - 2s

s = 218-151 = 67    amount given away  

4/7 * x   = 16      where x is total

x = 16 * 7/4 = 28 total

I don't think so....since part of the numerator cancels with the denominator it is just a line with a hole...

   if the numerator was something like   x^2-8    it would have a slant (oblique) asymtope   

Pythagorean theorem   for RIGHT triangles     a^2 + b^2  = c^2     where a and b are the legs (they are the two shorter lengths) and c is the hypotenuse ( the longest measurement)

     11^2 + 60^2   = 61 ^2   ????     If so, it is a right triangle    .....what do you think? 

do the same with the others.....