CPhill

Ah, yes......I see now that it IS the binomial formula........!!!!!

A simple case of CDD for me......maybe Nauseated could prescribe a tonic......!!!!!!

It doesn't.....

4/3*(3.0*10^-3)^3  =

(4/3)(3^3 * 10^-9)  =

[ 4 * 3^3] / 3   *   10^-9  =

4*3^2 * 10^-9 =

4 * 9 * 10^-9  =

36 * 10^-9  =

3.6 * 10^-8

Dragonlance.....if you got a box of horse manure........you wouldn't be "SOL"........you would be "SIL,"   wouldn't you ??????

Thanks, Melody......I see this easier as a binomial probability problem, too.......however......the formula that the guest has provided might be worth exploration......!!!!

(1)/(cot(x)) - (sec(x))/(csc(x)) = cos(x)

As written, this simplifies to :

[1/cot(x) ] - sec(x)/csc(x)  =

tan(x) - sin(x) / cos(x)  =

sin(x)/cos(x) - sin(x)/cos(x) =

0  =   cos (x)         ??????

Since the sine is negative  and the tangent is positive, this must be a third quadrant angle.......so....x must be negative......

So

x = -sqrt [10^2 - 7^2]  = -sqrt[100 - 49]   = -sqrt[51]

And

sec =   r / x   =  - 10 / [ -sqrt[51]     or   [-10/51]*sqrt(51)  if you prefer

Thanks, Melody.......

No prob, Shades.......!!!!

9x^2 - 6x     first, factor out the 9

9 [x^2 - (2/3)x ]       Now, inside the brackets, take 1/2 of the coefficient on x = (1/2)(2/3) = 1/3   ....square it .... (1/3)^2  = 1/9.......add this and subtract it.....so we have

9 [ x^2 -(2/3)x + 1/9  - 1/9]        factor the 1st three terms

9 [ ( x - 1/3)^2  - 1/9 ]               distribute the 9 back across everything

9(x - 1/3)^2 -  1

The second one is similar

9y^2 + 12y

9 [ y ^2 + (4/3)y]       ........         (1/2)(4/3)  = 2/3      ......(2/3)^2  = 4/9

9[ y^2 + (4/3)y + 4/9   - 4/9]  =

9 [ (y + 2/3)^2 - 4/9]  =

9(y + 2/3)^2 - 4

Good answer, Solveit.......you are exactly correct....!!!!

A perpendicular line will have the negative reciprocal slope to 8/3   =  -3/8

So.....we have

y - 3 = -(3/8)(x - [-2] )

y = (-3/8)x -6/8 + 3

y = (-3/8)x + 18/8

y = (-3/8)x + 9/4

Here is the graph of both lines......https://www.desmos.com/calculator/btb92kqc5y