ElectricPavlov

50p coins     are    n+7  

n         +    n-3      +     n+7      =    61

3n+4 = 61

n = 19                         20p coins are   n - 3          19-3 = 16 coins

                                                                                  the VALUE of 16  20p coins = 320p

                                                                                                                                =  £ ..... 

slope  =  (y1-y2) / (x1-x2)      use this to find the slope between the first two points

                                                     then use this same slope you find to equate it to the slope equation

                                                        with one of the given points and  6,c        then solve for 'c'

square both sides

x^2 + 2x+1   =   \(\sqrt[2]{x^4+4x^3-x}\)      square both sides again

x^4 + 4x^3 + 6x^2 + 4x +1    =    x^4 + 4x^3 - x

6x^2 + 5x + 1 = 0    

                   quadratic formula shows   x = -1/3   and  -1/2

16 miles   in m minutes

                    + m minutes   for coffee

  k miles   in    2m minutes

average = 13 miles/  m minute

(16 + k )/ (m + m + 2m)   = 13 miles/m            NOTE:  16 + k      not    16k

(16+k) / 4m = 13/m

(16+k) / 4 = 13

16 + k = 52

k = 36

Can you clarify......   from the coffee shop for 2m minutes          to point Z?

and this :    13 miles m minute

~EP

...and yes , you can cancel out the m's     if you multiply both sides by m you will get

16km / 4m  = 13m/m

   and you are left with       16k/4 = 13        (hope you math is correct up until this point)

Put it into standard circle form   (x-h)^2 + (y-k)^2 = r^2    

x^2 - 6x         + y^2 -8y        = 0    complet ehte square for 'x' and 'y'

(x-3)^2           + (y-4)^2       =  9+16 = 25        soooooo      r^2 = 25      r = 5

The ladder is the hypotenuse of a right triangle  8.5 m

  one leg is   7.5

    you are looking for the other leg

Pythagorean theorem

   8.5² = 7.5²   +   x²           solve for positive value of 'x' which is the base-wall distance

No idea here either......

  using a calculator   a = sqrt 2    

    a⁴  = 4

  second term = 2

So you are left with      (4 +2 -7)²⁰¹⁶  =   (-1)²⁰¹⁶  = 1          I guess !

2 + sqrt5       the other root would be    2 - sqrt5

SO the quadratic factored loks like this:

(x - (2+sqrt5) )(x-(2-sqrt5) )       if you multiply this out

x^2 -4x-1         now you can add   p  and  q