All Answers 358087 Answers

Good try anon but you multiplied in the 3rd line instead of dividing.

$$\\498-3x^8=216\\
-3x^8=-282\\
x^8=94\\
x=\pm\; 94^{1/8}\\$$

$${{\mathtt{94}}}^{\left({\frac{{\mathtt{1}}}{{\mathtt{8}}}}\right)} = {\mathtt{1.764\: \!578\: \!493\: \!147\: \!236}}$$

$$x\approx \pm\; 1.76457849314$$

$${\frac{{\mathtt{9\,120}}}{\left({\mathtt{12}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{40}}}{{\mathtt{60}}}}\right)}} = {\mathtt{720}}$$    

720 km/hour

Let the 2 short sides be x and the long side be y

$$\\2x+y=812\\
y=812-2x\\\\
Area(A)=x*y\\
A=x(812-2x)\\
A=812x-2x^2\\\\
\frac{dA}{dx}=812-4x\\\\
\frac{d^2A}{dx^2}=-4 \quad \cap\\
$This means that any stationary point will be a maximum$\\\\
$find stat point $\frac{dA}{dx}=0\\\\
0=812-4x\\
4x=812\\
x=203\\
$The tray will be of maximum are if the sides are 20.3cm by 40.6cm$$$

A clock is circular and therefore has 360 degrees. At 2:30, the clock's long hand is pointing down at six, and its short hand is halfway between two and three. To calculate the angle, we need to find out how many degrees are between The short hand and the long hand.

The easiest way to do this is to find out how many degrees are between the little hand and three, and add that to 90° (This is because the long hand is 90° away from three, because six to three is 1/4 of the clock and 1/4 of 360°.)

Since the short hand is is halfway between two and three, and two and three are 1/3 of 90° (Again, another quarter on the clock: twelve to three.), then we multiply 90° * 1/2 * 1/3 = 15°. Adding that to 90°, we get 105° angle, which is an obtuse angle.

Assuming conservation of energy:

.

y=1/2x+5;(4,-3) Says to write a equation in slope-intercept form for the line that is parallel to the given line and that passes through the given point.

$$\small{\text{
given line:
}} y=\frac{1}{2}x+5 \qquad m = \frac{1}{2}\\\\
\small{\text{
line parallel:
}} y=\frac{1}{2}x+b \quad\small{\text{
m must be equal for the parallel line.}}\\
\small{\text{The Point }} (4,-3) \small{\text{ gives us b: }} \\
-3 = \frac{1}{2}*(4) + b\\
-3 -\frac{1}{2}*(4) = b\\
-3 -2 = b\\
b = -5 \\\\
\small{\text{
line parallel:
}} y = \frac{1}{2}x - 5$$

@@ End of Day Wrap       Wed 3/12/14       Sydney,   Australia        Time 9:50 pm        ♬

Hi everyone,

It has been really busy.  But as always there were many fabulous answers. 

Our wonderful answerers were geno3141, mathematician, j*z123, BrittanyJ, Happyturtles, Shaniab29544, Tiddle, Happy7, PotatoPrincess, Angie22 and Alan.  Thank you.:)

Now for the interest posts:

1) Great fun thread  and Brittany introduces herself properly :)  Thanks Happy7 and BrittanyJ

Thurs 4/12/14

There were many polynomial questions today (which is very unusual), I collected all the addresses and put them in this post.

498-3*x^8=216

-3X^8=216-498

-3X^8=-282  //*-3

X^8=846 // ROOT 8

X=2.322315898...=2.3                              

answer 2.3

It is 2 because 2*2=4

$$\sqrt4=2$$

-2*-2 =4 as well but if the square root is written into the question you only take the positive answer.  :)

YES there are.  Thanks   

answer is 125

100% of what?

100% of 81000=81000

so 

81000+81000=162000

There are two solutions, Mel.

+6i and -6i

There is no school level expansion of this.   

No, Yours is probably the BEST long division that i have seen presented on the forum (or other forums for that matter)

I have done algebraic division using LaTex.  It was alright but not supurb.  

This was one of my attempts at algebraic division using LaTex

>> whats nine plus ten

For you, I think it's bedtime!

-1000=5t(6.73-t)

$$\begin{array}{rll}
-1000&=&5t(6.73-t)\\
-200&=&t(6.73-t)\\
-200&=&6.73t-t^2\\
t^2-6.73t-200&=&0\\
t&=&\frac{6.73\pm\sqrt{6.73^2+4*1*200}}{2}

\end{array}$$

$${{\mathtt{t}}}^{{\mathtt{2}}}{\mathtt{\,-\,}}{\mathtt{6.73}}{\mathtt{\,\times\,}}{\mathtt{t}}{\mathtt{\,-\,}}{\mathtt{200}} = {\mathtt{0}} \Rightarrow \left\{ \begin{array}{l}{\mathtt{t}} = {\mathtt{\,-\,}}{\frac{\left({\sqrt{{\mathtt{8\,452\,929}}}}{\mathtt{\,-\,}}{\mathtt{673}}\right)}{{\mathtt{200}}}}\\
{\mathtt{t}} = {\frac{\left({\sqrt{{\mathtt{8\,452\,929}}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{673}}\right)}{{\mathtt{200}}}}\\
\end{array} \right\} \Rightarrow \left\{ \begin{array}{l}{\mathtt{t}} = -{\mathtt{11.171\: \!960\: \!652\: \!075\: \!797\: \!6}}\\
{\mathtt{t}} = {\mathtt{17.901\: \!960\: \!652\: \!075\: \!797\: \!6}}\\
\end{array} \right\}$$

You could re-write the second equation as  x-3 -2(y+3) = 0

Let a = x-3,   b = y+3

Now your two equations become

a² + b² = 5

a - 2b = 0  so a = 2b

so

(2b)² + b² = 5  or b² = 1  so  b = ±1  so  a = ±2

Therefore we must have x = a+3 = ±2 + 3  and  y = b-3 = ±1 - 3

or x = 5 and 1  with  y = -2 and -4

.

Just click the export button, and select the format you want. 

                                                                           limits of  $$0\times\infty$$                 is 1 or 0 or $$\infty$$

I watched the video Heureka but I don't get how it helps with 0 * infinty  ?

find two numbers whose sum is 138 and whose difference is 88

$$\\
\small{\text{ number }} 1 = \frac{sum+difference}{2} = \frac{138+88}{2} = 113\\\\
\small{\text{ number }} 2 = \frac{sum-difference}{2} = \frac{138-88}{2} = 25\\\\
\small{\text{ number }} 1 +\small{\text{ number }} 2 = 113 + 25 = 138 \small{\text{ okay }} \\
\small{\text{ number }} 1 -\small{\text{ number }} 2 = 113 - 25 = 88\small{\text{ okay }}$$

455 /24

there is a calc on the home page.

NO real number squared = a negative number.

a negative * a negative = a positive

and

a positive * a positive = a positive

So there is no real answer.

the imaginary answer is  6i