ElectricPavlov

y= mx + b   = equation for a line

m= slope = (y2-y1)/(x2-x1) =  (sqrt2-9)/(5-3) = (sqrt2-9)/2

y = (sqrt2-9)/2  x    +  b

9 = (sqrt2-9)/2  (3) + b

9 = (3 sqrt2-27)/2 + b

b =  9 - (3sqrt2-27)/2

   =  18/2  - (3sqrt2)/2 + 27/2

b= 45/2 - (3sqrt2)/2

so equation becomes    y = (sqrt2-9)/2  x  +   45/2  - (3sqrt2)/2       Multiply everything by '2'

2y = (sqrt2-9)x + 45 - (3sqrt2)      subtract 2y from both sides and you will see your answer !

3x^2 + 36 = 0      divide both sides by 3

x^2 +12 = 0

x^2 = -12

x = +- 2i sqrt3

The slope, m ,  is given by   tan(58) = 1.600334529041  ~ 1.6

y= 1.6x + b        and   -3,0 is a point     substituting

0 =1.6(-3) +b

b= 4.8

y= 1.6 x + 4.8   is your line

r=4    each subsequent term is 4x the previous one

Yet ANOTHER aproach

7 (sqrt(10)(sqrt(14)  / (6 sqrt (35)

=  7 sqrt(140) / 6 sqrt(35)

=7 sqrt(4) / 6 = 7*2 /6 = 14/6 = 7/3

The dental kind of calculus....or the mathematical type of calculus ????     LOL

You will need to know the density (mg/ml)  to calculate this....or you can do a displacement test where you put the sample into a graduated beaker full of water (if comatible) and see how much the water irs raised in ml.

x * x = 3x

x^2 = 3x

x^2 -3x=0

x(x-3) = 0      so x = 0  or 3

3x + xi - 2y = 12-iy-i    add iy  and i to both sides

3x + xi -2y +iy +i = 12    and 'reverse distributive property'

3x + i(x+y+1) -2y = 12    now you cannot do much more unless you have another equation relating x and y 

                                           to reach a discrete solution for x,y  (though you can solve for x in terms of y    or y in terms of x as guest 1  did above....but you cannot find an answer for x,y)

or you could say   x(3+i) - y(2-i)  + i = 12

Let's work on numerator first    expand

3sqrt5 - 6 +5 -2sqrt5 = sqrt5 -1

so you have  ( sqrt5-1)  / ( 5-sqrt5)   now multiply and expand by  (5+sqrt5)/(5+sqrt5)=

(5sqrt5 +5 -5 -sqrt5 ) /  (25 + 5 sqrt5-5sqrt5 -5)     Simplify by collecting like terms

4sqrt5 / 20        and now, simplify the fraction

sqrt5 / 5