CPhill

√8 - √9  =

√(4*2) - 3 =

√4 * √2 - 3 =

2√2 - 3

If we're talking about ratios...the cross product refers to the equal products formed thusly:

a / b  = c / d   →   ad  = bd

If we're talking about vectors, the cross product of two linearly independent 3D vectors produces a vector that is perpendicular to both....you can read more here:

THe volume of a cylinder is given by

V_c = pi * r^2 * h       ...   where r is the radius and h is the height ...

Can you take it from here??

Here's a rather simplified "proof"

3!  = 4! / 4

2! =  3!/ 3

1!  = 2! / 2

So

0!  = 1! / 1  = 1

Another alternative is to note that, since the triangle is equilateral, all the angles measure 60 degrees

So, using  A  = (1/2)(s^2)[ sin60 ]   and letting s = 6, we have

A = (1/2)[(6)^2][√3/2]= (36/4)√3  = 9√3 sq units

Here's your breakfast, rosala....come and get it...!!!

rosala....1:30 PM  sounds more like something I usually call  ...."lunch"

4x^2-bx+(5-a)     ...I'm assuming that the "optimal value" occurs at the vertex

Taking the derivative of this, we have

8x - b ....  this gives the slope at any point...and since the slope at the vertex = 0 and the x value of the vertex = 10, we have

8(10) - b = 0  →   b = 80    and substituting this back into the original function, we can solve for "a"  thusly:

15 = 4(10)^2 - 80(10) + (5 - a)     simplify

15 = 400 - 800 + 5 - a     rearrange

a = 400 -  800 + 5 - 15  = - 410

So   a = -410 and b = 80 

And our function is

y = 4x^2 -80x + 415

This doesn't make sense to me......(anyone else ???)