Melody

In how many ways can you do what?

Surface area is the area of the outside surface of a 3 dimensional shape.

Thanks Alan. :)

Thanks Chris, I should have recognised that. :)

@@ End of Day Wrap    Sun 22/3/15   Sydney, Australia    Time 7:25 pm   ♪ ♫

Hi all,

CPhill answered most of our questions today although Nauseated and Alan answer one each as well.  Thanks guys.

Interest posts:

mon 23/3/15

Sorry 315, my knowledge is not adequate for your questions :)

(-1,-1,3) x (-1,0,2)

$$\\\begin{pmatrix}
-1&-1&3 \\
\end{pmatrix}
&\times \begin{pmatrix}
-1& \\
0&\\
2&
\end{pmatrix} \\\\
=(-1*-1)+(-1*0)+(3*2))\\=1+0+6\\=7$$

$$\\\displaystyle\int \frac{x^2}{(x^2+3)(x+1)}\;dx\\\\
Let \\
\frac{x^2}{(x^2+3)(x+1)}=\frac{Ax+B}{x^2+3}+\frac{C}{x+1}\\\\
\frac{x^2}{(x^2+3)(x+1)}=\frac{(Ax+B)(x+1)}{(x^2+3)(x+1)}+\frac{C(x^2+3)}{(x^2+3)(x+1)}\\\\
so\\
(Ax+B)(x+1)+C(x^2+3)=x^2\\\\
Ax^2+Ax+Bx+B+Cx^2+3C=x^2\\\\
(A+C)x^2+(A+B)x+(B+3C)=x^2\\\\$$

$$\\so\\
A+C=1 \;(1)\;\rightarrow \\
A+B=0\;(2)\; \rightarrow \\
B+3C=0\;\; \rightarrow\;\;B=-3C\;\; (3) \;\;$sub into (2)$\\
A-3C=0 (4)\\
(1)-(4)\\
4C=1\\
C=\frac{1}{4}=0.25 \\
A=1-0.25=0.75\\
B=-3*0.25=-0.75\\\\$$

$$\\so\\
\frac{x^2}{(x^2+3)(x+1)}=\frac{(0.75x-0.75)(x+1)}{(x^2+3)(x+1)}+\frac{0.25(x^2+3)}{(x^2+3)(x+1)}\\\\
\frac{x^2}{(x^2+3)(x+1)}=\frac{(0.75x-0.75)}{(x^2+3)}+\frac{0.25}{(x+1)}\\\\
\frac{x^2}{(x^2+3)(x+1)}=\frac{0.75x}{(x^2+3)}-\frac{0.75}{(x^2+3)}+\frac{0.25}{(x+1)}\\\\
\frac{x^2}{(x^2+3)(x+1)}=\frac{0.375*2x}{(x^2+3)}-\frac{0.75}{(x^2+3)}+\frac{0.25}{(x+1)}\\\\\\
\displaystyle\int\;\frac{x^2}{(x^2+3)(x+1)}\;dx\\\\\\
=\displaystyle\int\;\frac{0.375*2x}{(x^2+3)}\;dx-\displaystyle\int\;\frac{0.75}{(x^2+3)}\;dx+\displaystyle\int\;\frac{0.25}{(x+1)}\;dx\\\\\\
=0.375\;ln(x^2+3)+0.35\;ln(x+1)-\displaystyle\int\;\frac{0.75}{(x^2+3)}\;dx\\\\\\
$ Now I don't know what to do. BUMMER!$$$

I guess I wasn't meant to do it that way afterall.      LOL

$$\\y=-2x^2+4x+6\\
y=-2(x^2-2x-3)\\
$concave down because of the neg coeff of $ x^2\\
y=-2(x+1)(x-3)\\
$roots are x=-1 and x=3$\\
$axis of symmetry $x=\frac{-1+3}{2}=1\\
$Vertex y value$\\
y=-2*1^2+4*1+6)=-2+4+6=8\\
vertex \;\;(1,8)$$