Melody

thanks Chris.  

the slope is the gradient :)

Thanks Chris :)

Thanks anon,

That is an approximation of pi.  

If you roll a wheel one complete rotation then it will travel exactly  $${\mathtt{\pi}}$$  times the diameter of the circle in distance.

pi is an irrational number which means that it cannot be expessed exactly in digits.

It is approximately  3.14158 

[I give credit to flflvm97 for first using this Gif on the forum.  Thanks fl :) ]

Thanks Chris :)

This cannot be simplified unless you have values for a or b or c :)

I am just thinking here.

If we increase something by a factor of 1 this is meaningless.  To a mathematician it means multiply by 1 so it stays the same and is not increased at all.

If you told a lay person in the street to increase the size of something by a factor of 1 they could either mistakenly add one unit to it or erroneously double the size. They could easily think that if it was 4 units long before and increase it by a factor of 1 that it must now be 8 units (what it was before plus one more of what it was before 1+1more) .  Of course this is really increasing by a factor of 2 (1*2) but I can see how it could be very confusing.

If the dimensions of a solid double    That is they (the lengths) are 2 times  greater

then the surface area will increase by a factor of 2^2=4   That is it will be 4 times  greater

and

the volume will increase by a factor of 2^3 =8.    That is it will be  8 times greater.

This is a really handy thing to know 

Arc trig functions are the same as inverse trig functions.

Do you know what trigonometry is?

This looks pretty yucky