Question

Question.

Answer 1

Please move to Question 9.
http://www.xtremepapers.com/CIE/International%20A%20And%20AS%20Level/9709%20-%20Mathematics/9709_s02_qp_1.pdf

Answer 2

I'm doing A levels too, lol,

Answer 3

I'm assuming normal is the perpendicular line?

Answer 4

substitute x into dy/dx then find dy/dx

Answer 5

then use m1m2=-1 find the m2

Answer 6

Yes @KingGeorge .

@.Sam. Awesome. Are you in A2?

Answer 7

yeah A2

Answer 8

im in AS.. im doing P1 and M1 this year.

Answer 9

Then, substitute in 1 for x, and solve for dy/dx. You should get \[{12\over{(2*1 + 1)^2}} = {12\over9}={4\over3}\]To find the slope of the normal, find the negative multiplicative inverse, or \[-{3\over4}\]

Answer 10

After you have found the normal equation, it says that Q is at x-axis, so Q(j,0)

Answer 11

Once you've found the slope of the normal, use the point-slope formula to find the equation of the actual line and use that to find the x-intercept.

Answer 12

For (ii) just integrate using substitution and use the given point to determine the integration constant.

Answer 13

Normal equation i found is y=-3x/4 + 23/4

Answer 14

substitute Q(j,0) to y=-3x/4 + 23/4

Answer 15

Things are going over my top.
Let me read the whole thing again.

Answer 16

Let me try it myself..

Answer 17

(ii) Find the equation of the curve.
Use integration

Answer 18

General question, why we substitued the "x" in dy/dx ?

Answer 19

After substituting, i got 4/3.
What is that?

Answer 20

Because you're looking for the normal to a curve at a point, you first need to find the slope of the original curve at that point. That's what the 4/3 is.

Answer 21

4/3 is correct, because its a "normal" to the point, then m1m2=-1

Answer 22

Oh, got till this point..

Answer 23

Then, to find what the slope of the normal at that point, you have to invert 4/3 and negate it. You do this because the normal is perpendicular.

Answer 24

After using m1m2 = -1, then?

Answer 25

m2 = -3/4

Answer 26

\[\frac{4}{3}m _{2}=-1\]
\[m _{2}=-\frac{3}{4}\]

Answer 27

Then build another equation\[y-y _{1}=m _{2}(x-x _{1)}\]

Answer 28

Now, you use that value in the point-slope intercept form of a line to find the equation of the normal. \[y-5=-{3\over4} (x-1)\]

Answer 29

Using point P

Answer 30

Ah, nice.. let me calculate.

Answer 31

Since you're solving for the intercept Q(J, 0), let y=0, and solve for x.

Answer 32

y = --.75x + 5.75

Answer 33

That's a single minus sign*

Answer 34

Perfect. :D

Answer 35

WAit.!