ElectricPavlov

I'll try , Ant!

Say your fist pick is

white       then there are 3 choices w    4 choices br     2 choices bl

First pick is

brown    then there are 4 choices w    3 choices br    2 choices bl

First pick is

blue      then there are  4 choices w   4 choices br     1 choice bl

Add the red choices up....looks like 7 ways to get a pair of mathcing socks !

(I do not promise this is correct , Ant.....just my best try)

Yes,  'A'

...and you got the correct answer!   Good job, Julius.  Thanx for finding my error...I corrected it anyway.

You are correct Julius   ...I got the derivative of  5x^2 + 3x.....

    sorry the solution methodology is the same though ...I will correct it.

IF the little red arrows mean the lines are 'slanted' the same, then you would have similar triangles because all three angles in each are the same

First one

take the ratio of the long sides of each triangle   66/55  = 1.2

   take the ratio of the NEXT longest legs             60/50 = 1.2     Good so far

IF the ratio of the third legs is the same (1.2), the triangles are similar

   55/45 = 1.2222    Uh-Oh......    the triangle are NOT similar (Close though)

Second one

    can you tell me for what the little red arrows stand ?

sqrt 1/4   /   (1/8)^1/4

= 1/2   /   (1/2^3)^1/4

= 1/2   /  1/2^3/4

=2^-1  * 2^3/4

= 2^-(1/4)

1/2^(1/4)

=.841

Perfect!  Way to go !!!! 

Circumference = pi x d     or 

d = circumference/pi = 100 in/pi = 31.83 in

At x = -2    f(x) = 5 (-2^2) + 3 = 23        y = 23

The slope of f(x) is the derivative      10x    and at -2   this equals  -20

So we have a point  -2,23   and slope = -20

y=mx+b form of this line    23 = -20(-2) + b      or b = -17

so the tangent line is    y = -20x-17   Now just set this equal to g(x)

g(x) = x      x = -20x-17       21x=-17     x =  -17/21 = -.81

So the point of intersection is    -.81 , -..81   

Here is a graph: