Help with Holiday Homework

[darkphoenix]

How would you:

Factorise over C

[TrueTears]

Hint: Let

.

[darkphoenix]

Hm any more help? hahah

[TrueTears]

From where I left off:







Try DOPS on the first factor and factorise the second one normally.

[darkphoenix]

Alrite got it, thanks TT

EDIT: Got another question:

If is a zero of , find the other two zeroes.

[TrueTears]

is a factor.







Rest is trivial.

[darkphoenix]

Wait so how did you get the answer after you divided by

[TrueTears]

Long division is used. I would use paint to show long division but my paint skills really suck.

[darkphoenix]

Ah ok fair enough. How about a question on vectors:

A Hiker travels 3km north, then 4km west. How far is the hiker from the starting point? What is the bearing of the resultant displacement?

I've worked out the distance is 5km from starting point already.

[TrueTears]

Does the question say, the bearing from the starting point or the bearing from the final position of the hiker?

If it doesn't state you can work out either angle (I assume you have drew a graph)

[darkphoenix]

Yeah it doesnt say.

EDIT: How would i approach this question?

Use vectors to show that the diagonals of a square intersect at right angles.

Would i just use the scalar product and show that 2 of the lines equal 0 are are perpendicular or something?

[Mao]

In a square ABCD, let AB = a, BC = b, then CD = - a, DA = - b, also that a.b = 0, |a| = |b|

The diagonals are AC = AB + BC = a + b, and BD = BC + CD = b - a
Then, AC.BD = a.b - a.a + b.b - a.b = -|a|^2  + |a|^2 = 0

Therefore, diagonals intersect at right angles.

[darkphoenix]

Alrite cool thanks Mao

[ChristineNguyen]

Hi how would you
use the formula 
 tan = 2x 2tanx/ 1-tan^2x to find a surd expression for tan pie/8

[kyzoo]

Let






So we have






But because is a positive number

Therefore