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$${\sqrt{-{\mathtt{2}}}} = {\mathtt{1.414\: \!213\: \!562\: \!373\: \!095}}{i}$$

Awesomeee, this question is asked, and responded to, very rudely!

It is time for you to be polite and to start participating in your own learning.

Perhaps I have missed something but I have seen no evidence that you have learned anything from us.  

You just seem to be collecting the answers!

Next time you ask a question ask politely and tell us what ideas you have come up with on your own!

When we answer or give you a hint then respond to us, and make sure you are polite!

 We want to see if we are actually teaching you anything.

Answerers, a big thankyou to each of you :)

This is meaningless to me.

perhaps you mean    

8/3^0-1 

=8/1-1

=8-1

=7

The denominator of both is already 1

Perhaps you mean the biggest common factor which is x    

I am going to say the same as Alan and the video clip  LOL

1024 is the biggest power of 2 that goes into 2015, so I will start there 

2015

= 1024 with 991 remaining

=1024+512+479 remaining

=1024+512+256+223 remaining

=1024+512+256+128+95remaining

=1028+512+256+128+64+31remaining

=1028+512+256+128+64+16+15remaining

=1028+512+256+128+64+16+8+7remaining

=1028+512+256+128+64+16+8+4+3remaining

=1028+512+256+128+64+16+8+4+2+1

$$\\=2^{10}+2^9+2^8+2^7+2^6\qquad+2^4+2^3+2^2+2^1+2^0\\
=11111011111$$

Of course you could just use this converter

Please correct me if I am wrong Alan but

I think that you have always made a big point of telling me that I am not allowed to swap the x and y over and rearrange afterwards.

I have never understood why but i think it is because you have to be very careful that the inverse is still a function.  

That is, in the original function every x value must map to a unique y value (vertical line test)

and if you are going to get an inverse function then every original y value must map to a unique original x value.

So if you take an inverse of a function you may have to limit the domain of the new inverse function or else it may not be a function at all.

Most times I do not think that there is any problem with doing it this way but you have to be careful.

Did I get this it right Alan ?

$${\left(-{\mathtt{3}}\right)}^{{\mathtt{3}}} = -{\mathtt{27}}$$

I just did it on the calculator, as you can see, the answer that I got was -27 and this is correct  

Add 5.1 to both sides and you will have your answer.    

Speed is an example of a rate of change because it is distance travelled  divided by time taken :)

hi anon,

 I did this post ages ago and it is definitely the method I would use when the coefficient of  x^2 is greater than 1.

Just divide 17000 with 120000 and multiply the answer with hundred to get the answer in percent.

$${\mathtt{100}}{\mathtt{\,\times\,}}\left({\frac{{\mathtt{17\,000}}}{{\mathtt{120\,000}}}}\right) = {\frac{{\mathtt{85}}}{{\mathtt{6}}}} = {\mathtt{14.166\: \!666\: \!666\: \!666\: \!666\: \!7}}$$

the answer is 14,17%

I like this solution too Alan, it is really neat   

Try working through these

e is an irrational number with special qualities.  Much like the number pi  $$\pi$$

$${\mathtt{e}} = {\mathtt{2.718\: \!281\: \!828\: \!459\: \!045\: \!2}}$$

That is an approximation since e is an irrational number  

This is an IMAGINARY NUMBER answer.

YOU CANNOT MULTIPLY ANY REAL NUMBER BY ITSELF AND GET A NEGATIVE ANSWER.

THAT IS IMPOSSIBLE!

A negative times a negaive = a positive     !!

A positive times a positive = a positive      !!

Hi Fiora,

Your Desmos graph has spun me out!     

Your graph is brilliant but have you ever tried to use GeoGebra?   

It is heaps easier for this and it is a free download.  

Your GeoGebra diagram is really impressive too CPhill - You are becoming an expert  

You could fold it over many times to make it thicker, then if you have vernier calipers, you could measure the layered foil and then divide by how many layers that you have.

If you do not have vernier calipers I suppose you could still do the same thing but it would not be very accurate.

I am thinking that if you have a roll of foil and you know the total length, you could probably also use some form of calculus to work it out ??

The is a square root button on the calc or you could just input 

sqrt(6)

Thanks MathsGod but you need to get rid of that word 'doubled' (you used it twice I think)

Doubled means multiply by two and that in NOT what you are doing here.

The word you need is 'squared' or simply 'multiplied by itself'     

The rest is good :)

Much better Dbg  

I've given you the points now.

It would have been a tad better if you had explained where your 5 came from :)

I know I explained it in a later post but it could have been with yours as well :)

Here's a detailed breakdown of the steps needed to turn 2015 decimal into binary:

.

$$\left({\frac{{\mathtt{7}}}{{\mathtt{3}}}}\right){\mathtt{\,\times\,}}{\mathtt{X}} = {\mathtt{2}}$$

$${\mathtt{x}} = \left({\frac{{\mathtt{3}}}{{\mathtt{7}}}}\right){\mathtt{\,\times\,}}{\mathtt{2}} \Rightarrow {\mathtt{x}} = {\mathtt{0.857\: \!142\: \!857\: \!142\: \!857\: \!1}}$$

Here is the solution to 2 decimal places {rounded}

The curved part of the perimeter of a semicircle is (1/2)*pi*diameter. To this you need to add the length of the diameter, so perimeter of semicircle = (1/2)pi*diameter + diameter.  

You can fill in the numbers.

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