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I would suggest that you also use brackets like this

(1 + 3/4) + (5 + 4/9)

It won't make any difference for this question but if you were subtractin or multiplying or dividing it would be necessary so you might as well do it all the time.

There are many ways.

On the insert drop down menu you can find special characters.  It towards the end of the second line.

OR

you can just use superscript zero.  the superscripts are under the format drop down menu.  Press once for on and press again for off.

Alan's method is definitely correct Rosala.  I am glad that you are paying close attention and learning. 

Also, your scientific notation questions are correct but you do not need the extra 0s after the decimal point.   They serve no purpose.

7162.000 is better written as 7162

This is an old thread that was mainly on dealing with negative indices.

It is definitely worth a look.

Where do I start?

Thank you Alan.  I assume that the image was too big before.  Andre has now introduced coding so that oversized images are shrunk to an appropriate size.

Thank you reinout.

Thank you Rosala.  Your explaination was really great.  There is one thing I would like to point out though.  Consider this question.

$$x\times x^3$$      I know that you know the answer is  $$x^4$$

But you said that $$x$$ has no index.  This is not right.  $$x$$ ha an 'invisable' index of 1.

I often talk about invisable things.  It often makes understanding easier.  So

$$x \times x^3=x^1\times x^3=x^{1+3}=x^4$$

simplify z-8/z -5z-38/11z

I'm going to assume that you either mean this:  z-8/z -5z-(38/11)z 

or this:   z- 8/z -5z-38/(11z)

If it's the first, we have  [z - 5z - (38/11)z)] - 8/z  = (-82/11)z - 8/z =

-[(82z^2 + 88] / (11z)]

If it's the second, we have (z - 5z) - [(38/(11z) + 8/z)]    = (-4z)  -[(38/(11z) + (88/(11z)] = -[44z^2 + (126)] / (11z)]

To find the volume of the tank, you must mulitiply all of the sides. 50*40*30

V= 60,000    However, the water only occupies a space of 30,000 since it's only half filled.

To find the volume of the cubes, you cube the side length given, and multiply by 4 because there are 4 cubes.

4(15^3) = 13,500

That means the water level will rise 13,500. So add that to the water level of 30,000.

43,500 cm is the height of the water level.

Think of it this way, Anon.

Pretend you had four quarters of one pizza, or 1/4 for each quarter. You could divide the pizza so that it mysteriously 'vanishes', or so that when the pizza is served, well, there is no pizza to give out. Simply put, this means that there are zero quarters of pizza to give to three other people and yourself. This is why 0/4 is perfectly normal, and equals zero. Sadly, taking all four quarters for yourself will probably leave you with three angry friends and one satisfied (and probably stuffed) self.

However, if you have four slices of pizza and three friends plus yourself, you can't just not give the pizza away, even to yourself. This option is not feasible, and thus is invalid. I like to think of it as the pizza goes nasty, and thus nobody wants it, and it isn't good. This is why 4/0 is undefined, and this is simply because you can't just have something that is givable without giving it to something.

It's my weird way of thinking about it.

$${\mathtt{z}}{\mathtt{\,-\,}}{\frac{{\mathtt{8}}}{{\mathtt{z}}}}{\mathtt{\,-\,}}{\mathtt{5}}{\mathtt{\,\times\,}}{\mathtt{z}}{\mathtt{\,-\,}}{\frac{{\mathtt{38}}}{{\mathtt{11}}}}{\mathtt{\,\times\,}}{\mathtt{z}}$$

PEMDAS

No P

No E

M and D are present

1z - 8/z - 5z - 38/11 * 1z

z(1z - 8/z - 5z - 38/11 * 1z)

1z^2 - 8z/z - 5z^2 - 38z/11 * 1z^2

1z^2 - 8 - 5z^2 - (38z*1z^2)/11

1z^2 - 8 - 5z^2 - (1z^2*38z)/11

$${\mathtt{1}}{\mathtt{\,\times\,}}{{\mathtt{z}}}^{{\mathtt{2}}}{\mathtt{\,-\,}}{\mathtt{8}}{\mathtt{\,-\,}}{\mathtt{5}}{\mathtt{\,\times\,}}{{\mathtt{z}}}^{{\mathtt{2}}}{\mathtt{\,-\,}}{\frac{\left({\mathtt{1}}{\mathtt{\,\times\,}}{{\mathtt{z}}}^{{\mathtt{2}}}{\mathtt{\,\times\,}}{\mathtt{38}}{\mathtt{\,\times\,}}{\mathtt{z}}\right)}{{\mathtt{11}}}}$$

11(1z^2 - 8 - 5z^2 - (1z^2*38z)/11)

11z^2 - 88 - 55z^2 - 11z^2 * 418z

(11z^2 - 88 - 55z^2 - 11z^2)/418z

$${\frac{\left({\mathtt{11}}{\mathtt{\,\times\,}}{{\mathtt{z}}}^{{\mathtt{2}}}{\mathtt{\,-\,}}{\mathtt{88}}{\mathtt{\,-\,}}{\mathtt{55}}{\mathtt{\,\times\,}}{{\mathtt{z}}}^{{\mathtt{2}}}{\mathtt{\,-\,}}{\mathtt{11}}{\mathtt{\,\times\,}}{{\mathtt{z}}}^{{\mathtt{2}}}\right)}{\left({\mathtt{418}}{\mathtt{\,\times\,}}{\mathtt{z}}\right)}}$$

(1z/38) - (8/38) - (5z/38) - (1z/38)

(1z/38) - (5z/38) - (1z/38) - (8/38)

- (5z/38) - (8/38)

- (5z) - (8)

$${\mathtt{\,-\,}}{\mathtt{5}}{\mathtt{\,\times\,}}{\mathtt{z}}{\mathtt{\,-\,}}{\mathtt{8}}$$

I have no clue if this is correct. If it isn't, could somebody point me where I went wrong?

Let's write

y = 8x^3 - 6       Let's get x by itself   ....  add 6 to both sides

y + 6 = 8x^3      Divide by 8 on both sides

(y + 6) / 8   =   x ^3           Take the cube root of both sides.....

[(y + 6)/ 8]^(1/3)  = x        Now "swap" x and y

[(x + 6)/ 8]^(1/3)  = y        And, for y, write f ^-1(x) and there's the inverse

We can use an informal way to check that this is the inverse - it isn't foolproof, but it will work in most cases.....

Note that the inverse should "reverse" the x and y coordinates on a graph. So, in the original problem, let x = 1 and y will = 2. Then, in the inverse, let x =2, and we should get y =1...and we do!!   So, we're pretty sure it's correct.......

I think you are nit picking reinout but it was funny.  Thumbs up for humour.  

Here's the way  to do it...

To figure your share, it's just...

[(square footage you use)/ (total square footage)]  x  rent

And your roommate's share is just

[(square footage he/she uses)/ (total square footage)]  x  rent

I don't know much about this, but the way I understand it is that the infimum of a set of numbers is the largest number that is less than or equal to all the numbers in the set.
The supremum of a set of numbers is the smallest number that is greater than or equal to all the numbers in the set. 

Also, as I understand it, the infimum of a set doesn't actually have to belong to the set itself. Based on this, -2 should be your answer, because it's the largest number that is less than or equal to all the members of (-2, 3]. Notice that it doesn't belong to the set itself.

If someone on the forum knows more about this, I'll stand corrected......

Please, when you post questions like this you need to use brackets!

CPhill has 'guessed' what you want!  I am sure he has guessed correctly but it is NOT what you asked for.

This is what you asked for

3t^2-11t+6/3t^2+7t-(6 divided by 9t^2)-12t+4/3t^2/3t^2+7t-6

This is what CPhill answered

(3t^2-11t+6/3t^2+7t-6) divided by (9t^2-12t+4/3t^2/3t^2+7t-6)

 THEY ARE DIFFERENT!!!!!

*

mONDAY  6/5/14

Truncated Cube

that is really interesting.

Here is a truncated cube

It has 14 faces.  6 regular octogons and  8 equilateral triangles.  

I LIKE IT!!!

Okay Rosala

Now I have identified some of your problems.  You cannot do equations because there are earlier concepts that you need to understand first!

I would like you to work through this unit.

When we divide, the 3t^2 +7t - 6 terms "cancel" with each other, so we're left with

(3t^2 - 11t + 6) / (9t^2 - 12t + 4)      Factoring, we have

[(3t - 2)(t - 3)] / [(3t -2)(3t - 2)]     And we're left with

(t - 3) / (3t - 2)

We can write

(-2 - √x)  (-2 - √x)

We can factor a "-1" out of both expressions

(-1) (2 + √x) * (-1)(2 + √x)   =      (-1)(-1)(2 + √x)(2 + √x) = (2 + √x)(2 + √x)

So, multiply the 2's together to get 4

And multiplying 2 times √x  and 2 times √x and adding them together gives 4√x

And √x *√x  = x

So putting all this together gives us

4 + 4√x + x

0 divided by any number always give you 0 but

any number divided by 0 is imposible... 

fgt

4*8*9=288

fgt=288