CPhill

k+8+7k =

1k + 8 + 7k =    [combine like terms]

8k + 8

x - 7 - 8  =

x - 15

- [ 4 + 1/5 ]  - -[13 + 1/10]=

-[ 4 + 1/5 ] + [ 13 + 1/10 ] =

13 - 4 - 1/5 + 1/10  =       .......  [1/5 = 2/10 ]......

9 - 2/10 + 1/10  =

9 - 1/10  =

8 + 9/10

Use the x^y key on the calculator  or the " ^ " symbol on your keyboard......

Here's a good explanation of this.......http://tutorial.math.lamar.edu/Classes/CalcI/NewtonsMethod.aspx

Basically, we're picking [ guessing] some point on a curve, drawing a tangent line to the curve at that point, and then using the coordinate  of the x intercept of this tangent line as our next "guess."  Then, we repeat the process to get the next x-intercept point, etc. As long as the derivative exists in each case [ and is non-zero ], we should arrive at a pretty good approximation of the solution to our function  after several iterations.

Very nice, Omi.....!!!!!!

x^2 - 7x + 6    the y intercept  occurs at (0, 6)

To find the x intercepts, set the function to 0 and factor, so we have....

x^2 - 7x + 6 = 0

(x - 6) (x - 1)  = 0     and setting each factor to 0, the x intercepts occur at  x = 6 and x = 1, i.e., at (6, 0) and (1, 0)

The turning point occurs at the vertex  whose x coordinate is given by -[-7 ] / [ 2(1)]  = 7/2 = 3.5

And the y coordinate of the vertex is : (7/2)^2 - 7(7/2) + 6   =  - 49/4 + 24/4  = -25/4  = -6.25

Here's the graph........https://www.desmos.com/calculator/a0qnjcwsnh

We have this

y = a (x - h)² + k     where h, k = 2,5....and we know that (x,y) = (3, 7).is a point on the parabola.....so we have

7 = a(3  - 2)²  + 5  simplify

7 = a(1)² + 5

2  = a

So...the equation is

y = 2(x - 2)² + 5

(A)  6500(1 + . 15) =  7475 tonnes

(B)  7800 ( 1 - .125) =  $6825

If you want to factor this, it's just :

3 (a + 6)