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I'll give this one a try  !!!!

The volumes in the glasses don't really matter since they're the same......and the amount we put into each glass doesn't matter, either.......as long as it's the same...

Suppose there are 9 teaspoons of each liquid in each glass.

Taking a  tsp of water and putiing it into the glass of milk results a mixture of milk and water that is 9 parts milk and 1 part water.  {We assume this is well-mixed !!! }  Also, there are now 8 tsp of water left in the pure water glass.

Now taking a tsp of the water/milk mixture and putting it into the pure water glass results in a mixture of 8.1 tsp water and .9 tsp milk....a 9 : 1 ratio

But....the original pure milk glass now contains 9 tsp of the water/milk mixture....and 9 parts of this is milk (8.1 tsp) and 1 part is water (.9 tsp)

So......each glass is equally contaminated......the original pure milk glass contains .9 tsp of water and 8.1 tsp of milk.....a 1 : 9 ratio

And the original pure water glass contains .9 tsp of milk and 8.1 tsp of water....again, a 1 : 9 ratio.

Since the charge is negative for electrons and positive for protons just take the difference in the numb ers and multiply by the size of the charge:

net charge = (2.8 - 7.6)*10¹³*1.6*10^-19 C  (You can crunch the numbers) Because there are more electrons than protons the net charge is negative.

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all right.

so he is giving his favourite son 25% of the land, leaving a remaining 75%

four sons are left.

so we divide 75 by 4.

(18.75.)

so each one of the other sons gets 18.75 percen of the remaining land.

from the picture above, imagine removing the top left quarter.

now, take the top half of the top right corner and place it on the bottom left corner.

so now, split the remaining shape at 25%, 50% and 75% of the way across.

and there we have it :)

There are an infinite number of such numbers!

For example, a=3, b=4 and c=5 satisfy a² + b² = c² 

But if you multiply a, b and c by the same number, say, n then you will find that the numbers a=3n, b=4n and c=5n also satisfy a² + b² = c²

.

You are right up until the very last step shaniab29544.  On the next to last step you have x3 = 9.  Because the 3 comes after the x we assume this means x to the power 3 (at least that is what heureka and I have assumed), so x-cubed = 9.  This means that x is the cube root of 9 or ³√9.  

If you prefer to interpret this as just x times 3 then we would have x times 3 = 9 so that x would be 9 divided by 3, or x = 3.

.

I think that the middle school guys are right, 'cause you are really beatiful!!!!! ( And also hot... )

I think it right, I dont want to lie you...

How do you feel?

Good, right? This people are amazing...

It is a Link...

3*(4*3) = 3*4*3 = 36

Write the product as a sum: 6sin(47y)cos(21y) = ?

$$\boxed{
\small{\text{
Formula:
$
\begin{array}{rcl}
\sin u+\sin v=2\sin \frac{u+v}{2}\cos \frac{u-v}{2}
\end{array}
$}}
}$$

$$\small{\text{$
\begin{array}{rcl}
47y = \dfrac{u+v}{2} \qquad 21y=\dfrac{u-v}{2}\\\\
u=\dfrac{u+v}{2}+\dfrac{u-v}{2}=47y+21y=68y\\\\
v=\dfrac{u+v}{2}-\dfrac{u-v}{2}=47y-21y=26y\\\\
\end{array}
$}}$$

$$\small{\text{$
\begin{array}{rcl}
\sin u+\sin v&=&2\sin \frac{u+v}{2}\cos \frac{u-v}{2}\\\\
\sin {(68y)}+\sin {(26y)} &=&2\sin{( 47y )}\cos{( 21y )} \quad | \quad \cdot 3 \\\\
3\sin {(68y)}+3\sin {(26y)} &=&6\sin{( 47y )}\cos{( 21y )}
\end{array}
$}}$$

[x^2 + x - 2 ]  /  [x^3 + 2x^2 - 3x ]  =

[(x - 1)(x + 2)] / [ x ( x + 3) ( x - 1) ] =

[ x + 2 ] / [ x (x + 3) ]

This graph will have vertical asymptotes at x = 0 and x = -3 and a discontinuity  -   a ("hole")   -   at x = 1

If the item undergoes an 80% price reduction, the new sales price is just 20% of its original price.......so

20% x $95  =

.20 x $95 =

$19

√-1 - 5√-4  =

i  - 5√[-1 * 4] =

i - 5i√4  =

i - 5i(2)  =

i - 10i

-9i

i'm back

went to fuddruckers and to the coyote howl with the rest of the Royality gang for eating delicious burgers at Fuddruckers, and bidding for prizes at the Coyote Howl back in our old elementary school

sin(12v)   = sin(6v + 6v)  = sin6vcos6v + cos6vsin6v = 2sin6vcos6v

I think that that that that that student wrote on the blackboard was wrong.

I know. You know. I know that you know. I know that you know that I know.

The quick brown fox jumps over a lazy dog.

(This sentence have 26 English alphabets.)

cosu = √[1 - (-.085)^2]  = about .99638

cos(u/2)  = ±√[(1 + cosu) / 2 ] = ±√[(1 + .99638) / 2] = about   ± 0. 999

But, if u lies in Q4, then u/2 lies in Q2.....and the cos is negative in that quadrant.....so

cos(u/2)  ≈ -0.999

 Never trouble trouble till trouble troubles you.

sin(x+y)=sinx*cosy+cosx*siny

sin(x-y)=sinx*cosy-cosx*siny

so, sin(x+y)+sin(x-y)=sinx*cosy+cosx*siny+sinx*cosy-cosx*siny=2sinx*cosy

    sinx*cosy=1/2[sin(x+y)+sin(x-y)]

orginal qustion=6*sin(47y)*cos(21y)=（1/2）*6*[sin(47y+21y)+sin(47y-21y)=3*[sin68y+sin26y]

                     =3sin68y+3sin26y

sin2A  = 2sinAcosA.......     and sinA  = 8/17  .....so we have

2(8/17)(15/17)  =   240/289