4x^3 = 405x divide both sides by 5
x^3 = 81x subtract 81x from both sides
x^3 - 81x = 0 factor
x ( x^2 - 81) = 0
x (x - 9) (x + 9) = 0 and we can write this as
(x - 0 ) ( x - 9) ( x + 9 ) = 0
The solutions are
0, 9, -9
x^3 - 8x^2 - x + 8 = 0 factor by grouping
x^2 (x - 8) - 1(x - 8) = 0 ( x - 8 ) is the common factor
(x - 8) (x^2 - 1) = 0
(x - 8) ( x + 1) ( x - 1) = 0
Change the signs on the integers inside the parentheses to get the solutions of :
8 , -1, 1
x^2 + 18x + 45 = 0
(x + 15) ( x + 3) = 0
Once we have this form, change the signs on the integers inside the parentheses to get the roots
⇒ -15, -3
We are using the property that
axm * bxn = (a*b) (xm * xn) = (a*b) (xm+n )
So...for instance ..... 3x3 (7x2) = (3*7) (x3+2) = 21x5
So......the last three are correct
f(x) = 4sin(x) + 6
g(x) = 3x + 5
Maximize ( f ° g ) (x)
( f ° g) (x ) = 4 sin ( 3x + 5) + 6
Note that the maximum value of sine = 1
So......the max value of (f ° g) (x) =
4 (1) + 6 =
10
Note that g(x) doesn't really matter.....it's a "red herring"
(6x - 4) (3x - 1) =
6x (3x - 1) = 18x^2 - 6x
+ -4 (3x - 1) = -12x + 4
____________ ______________
18x^2 - 18x + 4
(x+2)(−3x^2+3x+1) { we can line this up just like regular addition as follows }
x (−3x^2+3x+1) = -3x^3 + 3x^2 + x
+ 2 (−3x^2+3x+1) = -6x^2 + 6x + 2
_______________ ____________________
3x^3 - 3x^2 + 7x + 2
Area =
L * W =
(x + 1) (3x - 5) =
3x^2 + 3x - 5x - 5 =
3x^2 - 2x - 5
If f(x ) = sec x , tan (x) = 1 and x is in Quadrant I what is the value of (f * f)(x) ??
If tan (x) = 1, then x = pi/4
And
(f * f) (x) = f(x) * f(x)
So
(f * f) (pi/ 4) = f(pi/4) * f(pi/4) = sec(pi/4) * sec(pi/4) = √2 * √ 2 = 2
Note that we are trying to minimze this sum for some value of r
S = 9 / (1 - r)
If r = -1/2 the sum is 6
If r = -4/5 the sum is 5
If r = -5/4 the sum is 4
But l r l must be < 1 ......so r = -5/4 isn't allowed
So.....it appears that the sum is minimized to an integer whenever r = -4/5 and the minimized sum is 5