Melody

For any triangle ABC, prove that a+b = cos A-B/2

                                                      2       sin c/2

Do you mean

For any triangle ABC,  prove that

\(\frac{a+b}{2}=\frac{cos(A-\frac{B}{2})}{sin(\frac{C}{2})}\)

Hi 8MP and Ginger,

Since Ginger has not expalined how she worked out this answer I have decided to give it a go. :)

Maybe this is what she did....   

1) The reflection.  Maybe this was the best place to start,  it seem right because it would orient the star so that when it was rotated anticlockwise it would have D on the top.

2) Now  just looked at the B point. I'd  want to move it so that (afterwards) when it was rotated 90 anticlockwise the B point would end up on the negative x axis. But there obviously had to be a dilation to get B into the correct position first.

Now when B was rotated about (5,0) it would need to be on the x axis.

So I draw the line x=5.  B would need to be moved to a point on that line.

3) I'd then my attention to the dilation that would be needed.

I drew a line from the centre of the dilation (-5,0) through B’ and subtended it till it intersected with x=5

That point of intersection would need to be the new B value.  i.e.   B’’

4) B’ was the point (0,9.5)

I could see from the diagram that B” was the point (5,19)

So it was clear that B’’ had to be twice as far as B’ from the centre of the dilation.

So I needed a dilation factor of 2

Now I did the dilation and the 3rd star was born.

3)  Now I just had to rotate it 90 degrees anticlockwise to get B onto the x axis.

Lastly Ginger had to counter the enlargement so she implemented a dilation of 0.5 centred at (-5,0)

Here is the pic

Is this how you thought about it too Ginger?

3=(1+i/52)^260

Hi asinus

If you look at this question it is reasonable to assume that i is not the imaginary i but rather that

i stands for interest rate.

It is the formula for compound interest

It is asking what nominal yearly rate compounded monthly will turn $1 into $3 in the space of 260 weeks

Just as our guest has already explained :)

49^(1/2)

means   

\(\sqrt{49}\)

Can you do it now?

It is just.  What times by itself = 49  :))

Here is Ginger's answer.

It is brilliant.

Thanks Ginger, I'd give you 100 points if I could!

1) Reflect over y=x from      Why did you add this bit?  (-1.5,-1.5) to (1.5, 1.5)

2) Dilate to scale factor of 2 about (-5, 0)

3) Rotate by 90° about (5, 0)           anticlockwise

4) Dilate to scale factor of 1/2 about (-5, 0)

How did you do it.   I mean can you give me any insite to your thinking process?

Very nicely answered DarkWyvren   :))

k^8/k^3

\(\frac{k^8}{k^3}\\ =\frac{kkkkkkkk}{kkk}\\ =\frac{\not{k}\not{k}\not{k}^1kkkkk}{\not{k}\not{k}\not{k}^1}\\ =\frac{1*k^5}{1}\\ =k^5\)

d^2*d^6

= d*d    *    d*d*d*d*d*d

there are 8 d's all multiplied together

\(=d^8\)

cos^-1   is the same as acos   :)

LOL guest.

I think you should join up.

We need people who can invent maths humour :))