All Answers 358417 Answers

A great tip,

If you can't find the answer, try writing everything into the same thing (such as cos)

It might take a while, but it usually does deliver an answer.

(oh, and I used x for the answer because it was a lot easier to use)

$$\frac{tan^2(x)+2}{1+tan^2(x)} = 1+cos^2(x)$$

rewrite this to

$$tan^2(x)+2 = (1+cos^2(x))(1+tan^2(x))$$

Now given that

$$tan^2(x) = (tan(x))^2 = (\frac{sin(x)}{cos(x)})^2 = \frac{sin^2(x)}{cos^2(x)}$$

We write

$$\frac{sin^2(x)}{cos^2(x)}+2 = (1+cos^2(x))(1+\frac{sin^2(x)}{cos^2(x)})$$

Make common denominators

$$\frac{cos^2(x)}{cos^2(x)}$$

$$\frac{sin(x)^2}{cos(x)^2}+\frac{2cos^2(x)}{cos^2(x)} = (1+cos^2(x))(\frac{cos^2(x)}{cos^2(x)}+\frac{sin(x)^2}{cos(x)^2})$$

$$\frac{sin^2(x)+2cos^2(x)}{cos^2(x)} = (1+cos^2(x))(\frac{cos^2(x)+sin^2(x)}{cos^2(x)}$$

Multiply both sides by

$$cos^2(x)$$

$$sin^2(x) + 2cos^2(x) = (1+cos^2(x))(cos^2(x) + sin^2(x))$$

Make use of the identity

$$sin^2(x)+cos^2(x) = 1 \Leftrightarrow sin^2(x) = 1 - cos^2(x)$$

$$1-cos^2(x)+2cos^2(x) = (1+cos^2(x))(cos^2(x)+1-cos^2(x))$$

$$1+cos^2(x) = 1+cos^2(x)$$

Reinout 

As a general rule I don't think this is correct.

Yes, I am embarrased.     

I think this is an odd question.

Usually completing the square is done as a quadratic equation solving technique.  

But if you just want to know what constant needs to be added to make it a perfect square then this is what I'd do.

(it is very similar to what heureka has done)

$$4x^2-4x-27\\\\
=4(x^2-x-\frac{27}{4})\\\\
=4(x^2-1x+\frac{1}{4}-\frac{28}{4})\\\\
=4(x^2-1x+\frac{1}{4}-\frac{28}{4})\\\\
=4(x^2-1x+\frac{1}{4})-28\\\\
=2^2(x^2-\frac{1}{2}x+\frac{1}{4})-28\\\\
=2^2(x-\frac{1}{2})^2-28\\\\
=\left(2(x-\frac{1}{2})\right)^2-28\\\\
=\left(2x-1\right)^2-28\\\\$$

So the expression would be a perfect square if 28 were added.

Could stand for energy too as in

E=mc²

Simple interest or compound interest? 

Is the rate per annum?

If it is compound interest then how often is it compounded?

Hi GoldenLeaf,

You mean on the web2 calculator?

I'm not sure what was meant.  Anonymous can come back and clarify the question if he/she wants to.

I= Prt is the forumla for simple interest.

So $48.60 is correct for simple interest!

Thanks anonymous.

Then you want to know how do add fractions to fractions or decimals to decimals?

Start here.

You could so it straight on the calc

$${\left({\frac{\left({\mathtt{7.634\: \!1}}{\mathtt{\,\times\,}}{{\mathtt{10}}}^{-{\mathtt{23}}}\right)}{{\mathtt{0.968}}}}\right)}^{{\mathtt{\,-\,}}\left({\frac{{\mathtt{1}}}{{\mathtt{3}}}}\right)} = {\mathtt{23\,318\,780.670\: \!183\: \!264}}$$

OR YOU CAN SIMPLIFY BY HAND FIRST

$$\left(\frac{7.6341\times 10^{-23}}{0.968}\right)^{-1/3}\\\\
\left(\frac{7.6341}{0.968\times 10^{+23}}\right)^{-1/3}\\\\
=\left(\frac{0.968\times 10^{+23}}{7.6341}\right)^{+1/3}\\\\$$

$${\left({\frac{{\mathtt{0.968}}{\mathtt{\,\times\,}}\left({{\mathtt{10}}}^{{\mathtt{23}}}\right)}{{\mathtt{7.634\: \!1}}}}\right)}^{\left({\frac{{\mathtt{1}}}{{\mathtt{3}}}}\right)} = {\mathtt{23\,318\,780.670\: \!183\: \!264}}$$

If you want to know how to deal with negative indices, look here.

I just googled "lateral surface area of a cone"  you could have done this too.  

You need to find the perpendicular height first.  You can do this using pythagoras' Theorum.

That should be enough help.  If not then post again.

how about

$$\frac{X+4}{10}=2$$

Look here.

6÷3=2 : 6/3=2

$${\frac{{\mathtt{47\,629}}}{{\mathtt{252\,274}}}}{\mathtt{\,\times\,}}{\mathtt{100}} = {\mathtt{18.879\: \!868\: \!714\: \!175\: \!856\: \!4}}$$

18.9% to one decimal place

$$8\frac{1}{3}-16\sqrt3\\\\
=\frac{25}{3}-\frac{16\times 3\sqrt3}{3}\\\\
=\frac{25-48\sqrt3}{3}$$

This is the nicest presentation for this question.

This will help you remember it

Draw the triangle first.

$$\begin{array}{rll}
sin 35^0&=&\frac{40.5}{L}\\\\
L\times sin 35^0&=&40.5\\\\
L&=&\frac{40.5}{sin 35^0}\\\\
\end{array}$$

etc

they are both 36.6m to one decimal place.  

Yes there are 2 equal signs in here.

Make sure your questions make sense BEFORE you publish!

If you were a member si would not matter quite as much because you would be able to edit you post afterwards!

The answer is: 23318780.7117252

1. 10^-23= 0.00000000000000000000001

2. 7.6341 * 0.00000000000000000000001 = 0.000000000000000000000076341

3. 0.000000000000000000000076341 / 0.968 = 0.000000000000000000000078864669

4. 0.000000000000000000000078864669 ^-1/3 (or -0.3333333333333333) = 23318780.7117252

3-i-5-2i= -2-3i

The formula for interest is: I = P * R * T

Therefore, we do: I = 135$ * 0.072 (percentage) * 5 

It gives us: 48.6$

this question makes no sense.

If 1.5 = .40 then what is X = .60?

Your question doesn't make sense.  

1.5 does not = 0.40

I think you forgot to put an X in there somewhere.