TrueTears question thread

[TrueTears]

on second thought. The cartesian equation of OP is not a straight line:



But the above must be constnat for a striaght line going through origin. Hence the thing is not a straight line so method1 doesn't work. THe more general variation of it should though.

I think you did x/y there but anyways I think I get it now...

So how about finding the cartesian equation and making sure it's not a line?

[TrueTears]

For any , the complex roots of the equation are vertices of a polygon what perimeter?

[/0]

For all you get regular n-gons with circumradius 1.

If we put a point at (0,0) and draw lines connecting this point to each of the edges of the polygon, we can form isosceles triangles.

The inside angle of any of these isosceles triangles is radians, and the isosceles legs of the triangle both have length 1, so we can use the cosine rule to find the outside edge of these triangles:



But we need to multiply this by n to get the perimeter, so

Check: If we get a circle



Letting ,              ()

[TrueTears]

How do we form the isosceles triangle?

And how do you know they lie on a unit circle?

[NE2000]

How do we form the isosceles triangle?

And how do you know they lie on a unit circle?

A drawing would help in this case, but basically a regular polygon can be split into n isosceles triangles (where n is the number of sides) with one vertex of the triangle in the centre and two sides leading out to the corners of the polygon. The distance between the centre and any two corners would be the same. So looking at the centre of the polygon, you'll have lines converging into the middle. There are 360 degrees in the middle and you split that into n to find the angle for each of the isosceles triangles.

We know they lie on a unit circle because z^n = 1 because if you consider the general solutions of that you get and therefore r = 1 for all of them. The solutions form a polygon because all of the different solutions plotted on the complex plane can be joined with lines that make a polygon, but each of these solutions (which are vertices in the polygon) have a modulus of 1. Is that what you were asking about?

You can plot the polygon on the complex plane and it will make more sense:
centre is the origin
each vertex will be a point a distance of 1 away from the origin
each vertex will be separated from another vertex by an angle that is

[TrueTears]

Thanks.

[TrueTears]

Thanks!

[TonyHem]

is it a?

[TrueTears]

is it a?

Nope answer is C.

[Flaming_Arrow]

is it a?

thats what i got

[TrueTears]

I got C but I left out the information about a = 1.

I just did u = 0, a = -9.8 and t = 8 =S

[TonyHem]

Eh i see why mine is wrong =/

[kamil9876]

 and there is nothing that the acceleration of the balloon can tell you about the initial velocity of the balloon, which is also the initial velocity of the stone. I don't think this has a solution.

[TrueTears]

Yeah, because if the hot air balloon is accelerating... then the initial velocity of the stone can't be 0... but you can't find out the initial velocity of stone...

[/0]

I get something way off:
Assuming the balloon starts at rest, for the upwards journey,


And for the fall,