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The answer to "(2 - 3)^2 - (4^2 - 3^2)" would be -6.

To solve "(2 - 3)^2 - (4^2 - 3^2)", we should start by simplifying everything in the parantheses. That way all of the numbers in the parantheses will be simplified into just one simple value.

Let's start with "(2 - 3)". We can subtract 2 and 3 easily, like so:

2 - 3 = -1

Remember that since 3 is being subtracted from 2, we would not have 1, but we would instead have -1 because 3 is greater than 2.

Now we have a number that we can plug into our equation in place of "(2 - 3)":

-1^2 - (4^2 - 3^2)

Now let's simplify "(4^2 - 3^2)". Here we need to find the squares of 4 and 3 and then subtract them. We can multiply the numbers by themselves to obtain:

4 * 4 = 16

and:

3 * 3 = 9

So now we can replace "4^2" with 16 and "3^2" with 9:

(16 - 9)

And from here we can easily subtract 9 from 16:

16 - 9 = 7

Now we can plug 7 into our original equation just as we did with -1:

-1^2 - 7

Next, we need to find "-1^2" so that we can subtract 7 from that to obtain our answer:

-1 * -1 = 1

Note that -1 * -1 would not be -1, because multiplying a negative number by a negative number will always give a positive number.

Now we can plug in 1 for "-1^2" to obtain "1 - 7". The final step is to subtract 7 from 1, giving:

1 - 7 = -6

So our answer is -6. I hope I helped.

-pokemonfan58

The answer to 65000 divided by 10% would be 650,000.

To find 65000 divided by 10%, we need to convert 10% into a decimal. To do this we can simply divide the percentage by 100, like so:

10 / 100 = 1 / 10 = 0.1

So now our equation is 65000 divided by 0.1. We can divide the two easily:

65000 / 0.1 = 650000

Thus, our answer would be 650,000.

-pokemonfan58

OK, subtract 2x from both sides....this gives

2/y = 2x + 2       divide everything by 2....we have

1/y = x +1          subtract 1 from both sides

1/y - 1  = x         which we could write as

(1 - y)/y  = x

And that's it....

Good job, snip3s and nice graphic ND......points and thumbs for both...!!!

BTW, ND......how DO you generate graphics like that??....very impressive....!!!

No, -1.4 is less than -0.8.

Although it may seem like -1.4 is bigger than -0.8, we have to remember that these are negative numbers.

Here are the two numbers on a number line:

Here you can see that -1.4 is to the left of -0.8, so it is smaller than it.

no because the lower the number in negatives the larger it really is so if you were to look at a number line -0.8 will be closer to 0 while the -1.4 is farther to the left which makes it a smaller number 

Your Welcome!

Hi Melody

Your missing combinations are in your 'two the same' section. You also have to include contributions from two the same and the other two the same as well, (and you have to be careful as to the calculation of that number).

here we are o find x by solving -2x=6 so well do it like this!

-2x=6

x=6/-2 

x=-3  ANSWER

Deleted Deleted

Just give it up melody just give it up.

I just had a thought!

The letters and numbers can be ordered when they are first collected or when they are fitted to the tumbler.  

I think Tud (and therefore the original Melody and CPhill) might be right afterall

If the 3 numbers are collected such that order matters then there will be 6^3 possibilities

If the 4 numbers are collected such that order matters then there will be 26^4 possibilites.

Since order is already taken into account then now we just need to know how many ways 3 can be chosen from 7 without order   7C3

So yes for the moment I am thinking that our original answers were correct and i can understand Tud's frustration at my inability to see that

So for now i am going with     

$$6^3*26^4*7C3 = 3,454,738,560$$

I reserve the right to change my mind again!

Now i have to think about whether the post above is correct or not.  It probably is not.  I will think about it again another time.    

I believe we are looking for 10% of 2.000

10% is really .1 as a decimal, because if we had 100% it would be 1.

of means to multiply

So now we have:

.1 x 2.000

which comes out to:

0.2

yes thats also true!but mine also wasnt that bad!lol!

According to Wikipedia, "Mathematics is the study of topics such as quantity, numbers, structure, space, and change. There is a range of views among mathematicians and philosophers as to the exact scope and definition of mathematics.^"

I want to simplify this question and play with it.

We have 26 letters and 6 digits .  Repetition is allowed.

I want to know how many combinations of 2 letters and 2 numbers that there are.

-------------------

there are 26^2=676 letter combinations

Now I know that in 26*1=26 of these the 2 letters are the same so the rest must be different.

That would be 26*25= 650 (Yes that works)

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there are 6^2=36 number combinations

6 have repetition and 30 do not

-------------------

Now when I put this together i can have

2 letters the same and 2 numbers the same    4!/(2!2!) = 3

26*6*3=468

2 letters the same and 2 numbers different      4!/2! = 12

26*30*12= 9360

2 letters diff and 2 numbers the same    4!/2!=12

26*25*6*12= 46800

2 letters diff and 2 numbers diff          4! = 24

26*25*6*5*24 = 78000

SO I think that the number of 4 tumbler codes would be  468+9360+46800+78000= 134,628

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NOW, I would like Sir CPhill and Chiurgeon Tud to comment on my solution to this simplified problem please.

Do you think that it is correct?

Math is the short form of Mathematics!

beasue of lyou

1acre = 43560 squarefeets  !

Good! Looks like a new stalk ! I have a supply of these !these are much helpful!

Density is mass per unit volume, so volume = mass/density.  Volume of a sphere is (4/3)pi*r³, where r is the radius.  Put these together to get 

r = (3*mass/[4pi*density])^1/3.

$${\mathtt{r}} = {\left({\frac{{\mathtt{3}}{\mathtt{\,\times\,}}{\mathtt{60\,000}}}{\left({\mathtt{4}}{\mathtt{\,\times\,}}{\mathtt{\pi}}{\mathtt{\,\times\,}}{\mathtt{19.5}}\right)}}\right)}^{\left({\frac{{\mathtt{1}}}{{\mathtt{3}}}}\right)} \Rightarrow {\mathtt{r}} = {\mathtt{9.022\: \!827\: \!957\: \!982\: \!585}}$$

r ≈ 9 cm

(Note that I've expressed the mass as 60000 grams because the density is given as grams/cm³)

Add 18 to both sides....this gives

x/5 = 2     multiply both sides by 5

x = 10

And that's it......!!!!

I assume you mean this:

log₃ 7         ......  We can use the "Change of Base" rule to evaluate this....it says that the "power" - let's call it "x" - needed to raise 3 to 7 is given by:

x = log(7)/log(3)  ≈  1.7712437491614222

Check for yourself that 3^{1.7712437491614222}  ≈ 7

To solve this, we just need to divide 7.717 by 95.

You could do this with long division, but I usually just use a calculator when dividing numbers with decimals.

$${\frac{{\mathtt{7.717}}}{{\mathtt{95}}}} = {\mathtt{0.081\: \!231\: \!578\: \!947\: \!368\: \!4}}$$

 Or we can round this up to about 0.08 miles a minute for practical purposes.