Math P2 MJ 2010 doubts

[HUSH1994]

i have a few doubts,paper 21 math MJ 2010:
Questions:
8.b
10
15.a+b
17.c

[elemis]

This was the paper I did for my IGCSEs PAWNED it Give me a minute to write the explanations

[HUSH1994]

good,im waitin and Thanks for it dude

[elemis]

Oh, actually speaking, this is a different variant from the one I did

For 8 b) look at the first link its an excellent powerpoint

For 10

3.5 *5 + 1.5*2 +

I basically used Pythagoras's Theorem to find the length of the diagonal wooden thingy.

For 15
a) 

Hence,

b) We've already found the gradient from (a) hence : y=-2x + c.

Inputing one of the coordinates into this equation : 5 = -2*2 +c

We solve for c. Hence c = 9   

I'm doing the rest.

[elemis]

Angle COD is subtended at the centre of the circle by the arc CD.

The angle CED is subtended by the same arc at the CIRCUMFERENCE of the circle.

Hence, you should know that angles subtended by the same arc at the centre are twice those subtended at the circumference.

Hence, CED = 19. And then EDO = 71

[Arthur Bon Zavi]

For The 15th one:

(a). See the pattern (sequence):

Y co-ordinates are 5, 3 and 1. Means -2 every time, i.e 5-2=3, then 3-2=1.
X co-ordinates are 2, 3 and k. This also has the sequence, i.e 2+1=3, then 3+1=4, so k(x co-ordinate)=4.

(b).
For the Gradient remember the formula:

y₂-y₁
-------
x₂-x₁

The Points are, (2,5), (3,3) and (4,1).

take any two points, e.g (2,5) and (3,3).

then:

3 - 5      -2
------ = ----- = -2
3 - 2       1

Gradient (Slope)= -2.

m = gradient = slope = -2.

so:

y=mx+c.
put any of the values.

3=-2*3+c

so,
c=9.

so equation goes:

y=-2*x+9

Or a simpler method if u have gradient, then:

y-y₁=m(x-x₁), where m is gradient (slope).

Example from this:

y-3=-2(x-3)
y-3=-2x+6
therefore: y=-2x+9. [It's Easy].

Another Method is when u don't have a gradient and have atleast two co-ordinates, so here u have 3 (more than necessary).  

take any two:

like (2,5), and (3,3).

Equation is :

y-y₁      x-x₁
-----  = ------
y₂-y₁    x₂-x₁

so, by substituting:

y -5     x - 2
----- = ------
3 -5     3 - 2

It gives:

y -5 = -2 (x - 2)
y - 5 = -2x+4
y = -2x + 9

[Arthur Bon Zavi]

This answer I just explained briefly with the help of alternative known methods, and other answers are explained by Ari.