Melody

This is not hard.  It is combinatory maths.  Use C on your calculator.

How many ways can you choose 4 from 5?

How many ways can you choose  8 from 10?

Multiply the answers.

Others: Please let guest answer for his/her self.

The easiest way to tackle this is to square both sides.

\(|4y+1|<|2y-3|\\ so\\ |4y+1|^2<|2y-3|^2\\ (4y+1)^2<(2y-3)^2\\ ...\\ 3y^2+5y-2<0 \)

Solve this for  =0

Then it is a concave up parabola so your solution will be the middle bit.

Added:  When I say it is a concave up parabola I mean   y=3x^2+5x-2  is a concave up parabola.

This is the most confusing bit.

> means greater than    so 6>6 is not true because 6 is not bigger than 6

\(\ge\)    means greater than or equal too.      so  \(6\ge6\)    is true because 6 is equal to 6

This is not that hard Riemann,   what have you tried for yourself?

I was going to give you a hint but it is too simple for that.

The centre is half way between the focal points, if that is what you mean.  

Are you just copying answers and plugging them in a box to see if they work?

I just made a careless mistake.

58/3 = 19.3333...    NOT   17.33333

So I also got 20 values of n

My attempt

All pronumerals are integers

LaTex not displaying so here is a pic that I took of it.

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

\(0

which means there are 18 possible vaues of g and hence 18 possible values of n

LaTex:

0 4n=2\mod6\\
2n=1\mod3\\
2n=3k+1\\
2n-3k=1\\
\text{One solution is n=2, k=1 }\\
2(2\qquad)-3(1\qquad)=1\\
2(2+3g)-3(1+2g)=1\\
so\\
n=2+3g\\
0<2+3g<60\\
-2<3g<58\\
-0.6 0\le g\le17

It is definitely not a dumb question.

It is very important to understand the relevance of a focal point.

A circle is the set of all points equidistant from the central point.  

An ellipse is the set of all points where the sum of the distance to each of the focal points stays constant.

So 

A circle is an ellipse where the 2 foci are in the same spot. 

Think of the way this guy draws the ellipse in the video below and you will see what I mean.

Here is how to draw one with two pins and a piece of string

Also,

If you want to add a useful answer to a locked question just send a message to a moderator, me or CPhill, and request it.

Don't lodge it as a formal 'complaint'