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Try to ask Einstein, this is impossible!

I had try to solve, but...

Yeah, I hate long exams. Just are a c**p! Well, if you have to wait to July for the mark, we try to make your wait shorter!!!!!

Here you' ve got me if you need a shoulder for cry ( Just kidding )...

1+2+3+4+5+6+7+8+9+10 = ?

$$\begin{array}{rcl}
1+2+3+4+5+6+7+8+9+10\\
&=&(1+10)+(2+9)+(3+8)+(4+7) +(5+6)\\
&=&(11)+(11)+(11)+(11) +(11)\\
&=& 5\cdot (11) \\
&=& 55
\end{array}$$

y=16x+44 and y= -x^2+8x+28 finding it in elimination

$$\boxed{ \\ y=16x+44 \qquad y= -x^2+8x+28 }\\\\
\begin{array}{rcl}
y = 16x+44 &=& -x^2+8x+28 \\\\
16x+44 &=& -x^2+8x+28 \\\\
x^2+16x-8x+44-28&=&0\\\\
x^2+8x+16&=&0\\\\
(x+4)\cdot(x+4) &=& 0 \\\\
x &=& - 4 \\
\\
\hline
\\
y &=& 16\cdot (-4) + 44 \\\\
y &=& -64+44 \\\\
y &=& -20
\end{array}$$

x = -4   and y = -20

This might help

5√16x + 7√25x

$$\small{\text{
$
\begin{array}{rcl}
5\cdot\sqrt{16x} + 7\cdot\sqrt{25x}\\
&=&5 \cdot\sqrt{16}\cdot\sqrt{x} + 7\cdot\sqrt{25}\cdot\sqrt{x}\\
&=&5 \cdot\sqrt{16}\cdot\sqrt{x} + 7\cdot\sqrt{25}\cdot\sqrt{x} \quad | \quad \sqrt{16} = 4 \qquad \sqrt{25} = 5\\
&=& 5\cdot4\cdot\sqrt{x} + 7\cdot5\cdot\sqrt{x}\\
&=& 20\cdot\sqrt{x} + 35\cdot\sqrt{x}\\
&=& \sqrt{x}\cdot \left( 20 + 35\right)\\
&=& \sqrt{x}\cdot 55\\
&=& 55 \cdot \sqrt{x}\\
\end{array}
$}}$$

How many minutes are in one day ?

$$\dfrac {24~\rm{h} } { 1~\rm{day} } \cdot \dfrac { 60~\rm{min.} } { 1~\rm{h} }\\\\
= 24\cdot 60~\dfrac { \rm{min.} } { \rm{day} } \\\\
= 1440 ~\dfrac { \rm{min.} } { \rm{day} }$$

1440 minutes are in one day.

4 x  (8/9 )  =   ????

Divide the final price by  (1 + the sales tax percentage converted to decimal form. )

For instance.......

Final price = $110   ...  Sales tax = 10%   = .10 in decimal form......so we have...

110 / (1 + .10)  = 110 / 1.10  = $100   =  cost

[ 9.3 x 10^7 ] / [ 1.86 x 10^5] =

5 x 10^2  = 

5 x 100  = 500 seconds   { 8 min 20 seconds }

9log x-3log y      we can write

log x^9 - log y^3     and by a log property we have

log [ x^9  / y^3 ]

Area = (h/2)(b₁ + b₂)   where h is the height and b₁, b₂ are the bases....so we have....

Area  = (4/2) (9 + 5)  = (2)(14)  = 28 sq cm

Thanks, Melody.........these conics have many facets......I barely touched the surface.....LOL!!!!

1 / 365 = 0.0027397260273973 = about .274%  {rounded to thousandths}

in order to understand History, you must go to Titanium Rome, and he will lead you to the World Temple, where the throne of Father David rises. David is Mother Nature's brother and is also the History God, according to the teachings of Royaltinism

i could                            

Thanks Chris, these are really interesting questions.  There is much I could learn from your answer  :)

Thanks Jgricus01,

If you want to answer questions like these use the [Calculation eg 1+2=3] button

then you can do the calc straight onto the forum and we can see if it is correct at a glance :)

like this

$${\mathtt{5\,416.68}}{\mathtt{\,\times\,}}{\mathtt{12.5}}{\mathtt{\,-\,}}{\mathtt{5\,416.68}} = {\mathtt{62\,291.82}}$$

I'd just do it like this (this is easier)   :)

$$\\ |4x-3|<8\\\\
-8<4x-3<8\\\\
$add 3 to all 3 'sides'$\\\\
-8+3<4x-3+3<8+3\\\\
-5<4x<11\\\\
\frac{-5}{4}

We can solve this with a "tip-to-tail" method.

Let the "flowing water " vector be represented by < 1 , 0 >

Let the angle we wish to head be = [90 - 64] = 26 degrees

And let the magnitude of this direction be = 4

So.....using the Law of Cosines.....the length of the side connecting these two vectors is :

l^2  = 4^2 + 1 - 2(4)cos 26 = 9.809647629608

So.....l = 3.1320357005640916

And using the Law of Sines, the angle between the "flowing water" vector and this vector is given by :

sinΘ/4 = sin26/  3.1320357005640916

sin-1 ( 4 *sin 26 / 3.1320357005640916)  = Θ  =145.954257197431°

But, because vectors will follow the law of parallelograms,, we need to proceed on an angular line that is supplementary to this  = 34.045742802569° at a rate of  3.1320357005640916 mph

Let us prove that this is correct.....

The x component of the resultant is given by  1 +  3.1320357005640916*cos( 34.045742802569 )  = 3.5951761851965269745587204588

And the y component of the resultant is given by 3.1320357005640916*sin( 34.045742802569) = 1.7534845871557995584901543276

the magnitude of the resultant is given by √[ 3.5951761851965269745587204588^2 + 1.7534845871557995584901543276^2 ] = 4 which is correct

And the angle of the resultant is given by  

tan^-1 ( 1.7534845871557995584901543276/3.5951761851965269745587204588) =  26°   ..which is also correct.....

And converting  34.045742802569° to a heading, we get N 55.954257197431 E  at a speed of 3.1320357005640916 mph

Rounded, we have  N 56° E  at 3 mph........

Here's a pic of the actual situtation.........

CA is the resultant, CB is the " flowing water" vector, and CD is the line of travel we need to take to reach "A"

The "flowing water' vector serves to pull our "maintained" speed and direction towards the resultant vector...

ok Civonamzuk  :))

I have added this to the Sticky topic "Great answers to Learn From"

If anyone would like to take an interest in organising some of our reference material that would be great.