ElectricPavlov

dx/ dt is the speed of the particle in the x direction = 2

dy/dt is the y direction speed = 3

Use pythagorean theorem to calculate the  resultant  speed     =    sqrt (2^2 + 3^2 ) = sqrt 13

5xy              -10yz                     - 6xz                   since   x = -4  y = 1   z = -1.5   then

5 (-4)(1)       -10 ( 1)(-1.5)         -6 (-4)(-1.5)

SInce we know what x y and z supposedly are, we just sub them into the equations to see if true:

Here is the second equation

5 (-4)(1)     -10 ( 1)(-1.5)   -6 (-4)(-1.5)       does this equal -41 ????      do the same for the other two equations to check your answer....

IF this is true

i figured out that (a,b,c) is (-12,5,9)     then   x = -4   y =1    z = -1.5      sub those into the equations to see if it makes all three of them true...

Expand and simplify to get

2x^2 + 20x+38 = f(x)

roots ....via quadratic formula are   -5 +-sqrt6         axis if symmetry is x =  -5

deleted

Note that if the circles had the same center (concentric) , the value would be R1- R2

    But R2 is moved a distance  equal to  the distance between  C2 and C1   this reduces R1-R2   by this amount

So the line will be      (R1-R2) -  distance betweenC2 and C1    (sorry...that black R1 should be labelled R2)

The black line represents x =2         f(2) is the y value of where the black line crosses the graph....

Yes, that is it !

Here is a Venn diagram of this situation: