ElectricPavlov

I see the 9th one now....1 3 3 4

When denominator = 0    undefined 

roots =  4 +- sqrt 14          sum = 8    

Equate the two polynomials and solve for the x points of intersection

3-x = 1+x+x^2

x^2 +2x -2 = 0

Well it said 'graphing' in the Q ....so here is the graph of the two polynomials

  I think you can take it from here !

sqrt (3² + 4² +5⁵ ) = ..............

Here are some ways.....can you think of any more?

1 1 1 36

1 1 2 18

1 1 3 12

1 1 4 9

1 1 6 6

1 2 2 9

1 2 3  6

2 2 3 3

Range of values will be BIGGEST when x = 0        1/2

and will tend toward  0 as x gets larger and larger    (but never actually becomes zero)                  (0, 1/2]

Whatever Jenny multiplies by  sqrt2 needs to be a perfect square (or 2)

    sqrt 2   * sqrt 2    =  2

     sqrt2   * sqrt 8    =  sqrt 16 =  4

     sqrt 2 * sqrt 32 = sqrt 64 = 8  

    Red numbers are her possible fav's        

b.    let 's   see       sqrt 2 / sqrt 2 = 1

              sqrt8 / sqrt 2 = 2

              sqrt 32/sqrt 2 = 4                    Yes she gets an integer

Volume of cylinder = pi r^2 h         make sure units are in the same dimension  ....covert yards to feet

2500 yd³ *  27 ft³/yd³  = 3.14 * 36 * r^2

r = 24.44 ft     = 8.15 yd

There is no Question...........

e = k v^2       k = proportionality 'k'onstant

72 = k (24^2)

k =  72 / (24^2) = 0.125

e = .125 v^2

e = .125 * 27² = 91.125 j