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(1.98855±0.00025)×10³⁰ kg

333 000 x Earth

For the above post, using the matrix (mesh theorem) I have to do it like a matrix? or can i just do a vector cross product of the top line, then the bootm line, and please give an example if yes. How do I solve this 3 unknowns by not using simultaneous and perhaps by using Thevenins theorem instead? 

Why is it a i2=-i2 in the image. is it just because clockwise is positve. I got it. Thanks

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only two real posts on the last 3 pages, 4 if you included my two (made after counting btw). This is not good for you guys and detracts from the forum appeal. it also takes a lot of energy and time which is wasted on many anonymous post. The sign up is so easy that anonymous posting is not required imo.

46 = 23 x 2

Both 23 and 2 are prime......so that's all we can do......neither of the prime factors are "raised" to any higher power than 1

cuz biology

We tried to track down Anonymous to "remove" him/her..........but, we couldn't find any phone book listing for such a person.......apparently, "Anonomous" is one slippery character !!!......I guess it's true what they say, "You can catch the Devil.......but you can never hold him."

3sin(θ/2) = 3/2      divide both sides by 3

sin(θ/2) = 1/2

Now the sine θ = 1/2 when θ =  pi/6 and 5pi/6

So, set θ/2 =pi/6

Multiply both sides by 2

θ = pi/3

And set θ/2 = 5pi/6

Multiply both sides by 2

θ = 10pi/6 = 5pi/3

So...our two answers are pi/3 and 5pi/3 in the given interval

Great work Chris and Geno.

I'm going to hit it a different way.

$$\\\tan(\alpha+\beta)=\frac{tan\alpha+tan\beta}{1-tan\alpha tan\beta}\\\\
\tan(2x)=\frac{2tanx}{1-tan^2x}\\\\\\$$

so draw a right angled triangle and make one of the acute angles = 2x

the opposite side is $$2tanx=2*2=4$$

the adjacent side is $$1-tan^2x=1-2^2=1-4=-3$$    (the negative sign just means it will not be in the first quad )

Using pythagoras the hypotenuse will be

$$\\h=\sqrt{4^2+(-3)^2}\\
h=\sqrt{16+9}\\
h=\sqrt{25}\\
h=5\\$$

so

$$\\cos(2x)
=\frac{adj}{hyp}
=\frac{-3}{5}
=\;-0.6$$

$$\\x^3=x*x*x\\
$or if$\\
x^3=64\\
then\\
x=\sqrt[3]{64}=64^{1/3}=4\\
because\\
4*4*4=64$$

So the answser is 2 

I think the web2 calculator does this too.

example:

14 mod 3 means divide 14 by 3 and give only the remainder.

I entered it as

mod(14,3)

$${\mathtt{14}} \,{mod}\, {\mathtt{3}} = {\mathtt{2}}$$

the web2.0calc on the home page is pretty good too.  

The answer would be -31.6

do you mean 1 and 1/100 ?

that is already simple, it can also be written as 1.01

The calc is on the home page.  

Yes CPhill is very smart.    

Here is another way. 

$$\frac{45}{25}=\frac{45*4}{25*4}=\frac{180}{100}=1.8$$

If you divide 4.5  cakes between 25 people they will each get a bit that is a lot smaller than a whole cake.

Won't they?   

Sorry isi, this bit is incorrect

337.5 = 2.5(5x)

it should  be 

337.5=5(x+2.5)

$${\mathtt{337.5}} = {\mathtt{5}}{\mathtt{\,\times\,}}\left({\mathtt{x}}{\mathtt{\,\small\textbf+\,}}{\mathtt{2.5}}\right) \Rightarrow {\mathtt{x}} = {\mathtt{65}}$$

the tickets are $65 each just like Geno3141 said.

I'll give you points for your good effort.   

Here is the graph

Isilber17  is correct I shall try to explain.

There are 6 letters and they are all different.

I will assume that the letters cannot be repeated - I think that is the intended meaning of the question.

You choose the fist letter  there are 6 possible outcomes.

now you choose the next letter, there are 5 possible ourcomes because one has already been chosen.

so the number of ways 2 letters can be chosen is 6*5

now you choose the third letter.  there are 4 possible letters available to choose from.  

So the number of ways you can choose 3 letters is 6*5*4

etc

the number of ways you can choose all 6 letters where the order is very important is 6*5*4*3*2*1 = 6!

Does that help?

The answer is 7.

Sorry....but we DON'T need "common denominators" when we multiply fractions.....besides multiplying (-3 or so)  times (-4 or so) couldn't possibly give us 210 !!!.......that answer lacks the "reasonableness test "

Here's the way to do this..........

Convert both fractions to improper ones

-4 + 1/5 = -21/5    and  -3 + 1/3  = -10/3

Now....just multiply them together

(-21/ 5) (-10/3)....however...wait.......here's a trick to make it easier.......a negative times a negative will produce a positive result - we can "drop" the negative signs - and we can also "swap" denominators and "cancel" before we multiply....so we have...

(21/3) (10/5) = (7)(2) = 14 !!!

And that's definitely NOT 210 !!!