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Remember what this says...it says that the cosine of some angle = 1 ..  and where does that happen???  When the angle = 0 ..... and, of course, every multiple of 360° after this......

That's it !!

So we have, using a property of logs.....

log(3/x) + log(x^2) + log(3x)^3 =

log(3/x) + log(x^2) + log (27x^3)     .....and by another property pf logs, we have

log((3/x)*(x^2)*(27x^3)) =

log (81x^4)

We could also write this as log(3x)^4 = 4 log(3x)

Let's call the number that went to the hall "x".....then the number that went to the stadium is just "20-x"

And the number that went to the hall times the price of a hall ticket plus the number who went to the stadium times the price of a stagium tickest = $750. Mathematically, we have...

(x)(30) + (20-x)(60) = 750     simplify this.......

30x + 1200 - 60x  = 750

-30x = -450    divide both sides by -30

x = 15    and this is the number who went to the hall

And (20-x)  = (20-15) = 5......and that's the number who went to the stadium

okay i'd give u a hint of how to get the answer!

to find the average of something we add that thing and then divide it by its number!so just add these numbers and divide it by how many they are!

if any other help required u can call out!

Let's multiply through by -1 to get rid of all those nasty negatives !!.....so we have

7/(x+1) = 8 + 5/(x - 2)   ....and getting a common denominator on the right , we have....

7/(x+1) = [8(x-2) + 5]/(x-2)  ..... simplify on the right

7 /( x+1) = (8x - 16 + 5) / (x-2)

7 / (x+1) = (8x - 11) /(x -2)   .....one way to solve this is just to cross-multiply

7(x-2) = (x+1)(8x-11)

7x - 14 = 8x^2 - 3x - 11  ......subtract 7x and add 14 to both sides

0 = 8x^2 - 10x + 3      ......see if this factors

(2x - 1)(4x - 3) = 0

And setting each factor to 0, we have that x = 1/2 or x = 3/4

i think so!But dont worry it may take years to pass you both becoz both of u are still climbing though slowly!

Loved the humorous pics, rosala....and I agree......what's the point of making posters if no one can SEE THEM???......what a waste of time...!!!!

If Melody and I don't start answering more questions, we might get "passsed" one day !!!.....I think you young guys are just too fast for us !!!!

There are multiple ways to do this. I will show you the simplest.

First, we must make each equation equal y.

-3x +8y = 5

8y = 5 +3x

y = 5/8 +3x/8

6x -2y = 10

-2y = 10 -6x

y = -5 +3x

Now because both equations equal y, we can say they equal each other.

5/8 +3x/8 = -5 +3x

45/8 = 21x/8

45 = 21x

x ≈ 2.14

To get an idea of how large a "googol" is, let's suppose that we could write out one billion zeroes per second.

Now, one billion seconds is about 31.7 years......and let's suppose that we lived for three billion seconds, or about 95 years. And let's suppose that we started writing our zeroes at birth and never took a break for our entire lifetime !!!

Then the number of zeroes that we could write is  (3 x 10⁹ x 10⁹ ) = (3 x 10¹⁸)

So the number of "lifetimes"  that would be required for us to complete the job is, approximately............ (10¹⁰⁰ ) / [3 x 10¹⁸ ] = about  [3.33 x 10⁸²] "lifetimes"

DragonSlayer why did u give yourself -5 points!you didnt do such a big mistake!that was a warning Melody gave u not a punishment!

The formula for simple interest is:

Original Money x Interest / 100 x (time / time for interest to do one "cycle")

Cycle isn't the right word, put it's the per annum or per day bit.

7,800 x 4.8 / 100 x (8 / 12)

= 37,440 / 100 x 0.75

= 374 x 0.75

= 280.50$

This means you end up with 8080.50$ if you include the original money.

Tes every thing in the first bracket by everything in the second bracket 2x(x-4)+4 (x-4)

2xsquared -8x +4x -16

2x squared - 12x -16

Assuming that the base angles are the equal ones meauring 75° each, we can use the Law of Sines to find the height. We have....

  .75 m / sin (15 ) = h / sin (75)    multiply each side by sin(75)

(.75 m)(sin(75)/sin(15) = height = about 2.8 m

Here's a picture if the situation....

you can't solve it because there is nothing on the other side of the equal sign.

However you can simplify it   

$$\\log (x^{2}*y) + log \frac{1}{xy}\\
=log (yx^{2}*\frac{1}{xy}) \\
=log (x) \\$$

So we would do this like

8 divided by -2 3/4

8 ÷ (-2 3/4)     ( so out here we would  change the mixed fraction into improper fraction by multiplying 2 by 4 and and adding 3 to it)

=8 ÷ ( -11/4)   ( and now we will  change the division sign to multiplivcation one as well as reciprocate the fraction)

=8 x ( - 4/11)    ( and now out here as none of these can be cut or reduced we will simply multiply 8 with 4 and add the subtraction sign as well )

=-32/11   ( and now we can change this into a mixed fraction as well as a decimal)

= -2.9090909090909091        A decimal answer!

=2 10/11    A mixed fraction answer!

And I will give you both some points 

$$I belive you mean:\\
$216(\frac{1}{4})$\\
To solve this, we multiply $216 \times \frac{1}{4}$\\
$216 \times \frac{1}{4} = \frac{216\times 1}{4} = \frac{216}{4} = 54$$$

So...we know an angle and an adjacent side....and we're looking for the opposite side...so we have....

tan (32°) = opp (height) / 25

height = 25tan(32°) = about 15.6 ft.

Thurs 28/8/14

An interesting function query.

@@ End of Day Wrap :     Wed 27/8/14        Sydney, Australia          Time 11:55pm          ♬

Hi everyone,

Lots of great answers today from Cphill, TakahiroMaeda, Alan, AzizHusain, DragonSlayer554, Rosala, Therealquestioner, zoomasd, HalleyWoodall17, Kitty   

Therealquestioner, zoomasd and halleywoodall are all faily new.  A big welcome to each of you, I hope that you enjoy our web2 forum and that you learn a lot as well.  

We are starting to get swamped in questions but even so I want to remind people that we are trying to help people to learn.  Just giving answers is sometimes the opposite of this because the asker does not have to think at all.  Please do not give full answers if there is a reasonable alternative.  For instance, if a calc answer is requested, tell them that the web 2 calc can be found on the home page.  You can tell them what keys to press but don't actually do it for them.  This is defeating the whole purpose.

Another worthwhile response might be to suggest someone googles an answer. 

Another might be to send them off to a learning site like a "mathsisfun" page or a video clip where they can learn more from other resources.  

Now for some interest posts:

* 1) I thought this quadratic equation was just a little different from usual

This might refer to

(1) a 45°/45° right-triangle, with sides in the ratio 1:1:√2 so 

     sin(45°) = 1/√2,  cos(45°) = 1/√2,  tan(45°) = 1

(2) a 30°/60° right-triangle with sides in the ratio 1:√3:2 so

     sin(30°) = 1/2,  cos(30°) = √3/2, tan(30°) = 1/√3

     sin(60°) = √3/2, cos(60°) = 1/2,  tan(60°) = √3

That's OK, Alan......I still gave you some points !!!

The square floor must have sides of 6 inches.  The depth of the folded sides of the box must be (10 - 6)/2 = 2 inches.

Beaten to it by Chris this time!!

Let the sides of the cut squares  = x....and when we fold these up, the dimensions of the floor area of the box are just (10 - 2x) (10-2x)...and this area = 36 sq in

So we have

(10 - 2x)^2 = 36    take the square root of both sides

10 - 2x = ±√36.......so we have

2x = 10 ±√36

x = (10 ±√36) / 2

So x = (10 + 6) / 2    or   x = (10 - 6) / 2

So, x = 8 or x  = 2

But, we must reject 8 because that would mean the sides of the floor area would be (10 - 2(8)) = (10 -16) = -6 inches  ...and this is impossible.....

So the sides of the floor area are (10 - 2(2)) = (10 - 4) = 6 in.   And the height is just x = 2 in. .....I'm assuming that, since I can't see a picture, that "depth" equates to "height."