Some P3 question from oct / november 2009

[nipuna92]

Can someone do these they are a bit hard.

Question 1
Solve the equation 3^(x+2) = 3^x + 3^2, giving your answer correct to 3 significant figures.

Question 2
A curve has equation y = e^-3x tan x. Find the x-coordinates of the stationary points on the curve in the
interval ?0.5pi < x < 0.5pi
Give your answers correct to 3 decimal places.

Question 3
With respect to the origin O, the points A, B and C have position vectors given by
OA = i ? k,  OB = 3i + 2j ? 3k and  OC = 4i ? 3j + 2k.
The mid-point of AB is M. The point N lies on AC between A and C and is such that AN = 2NC.
(i) Find a vector equation of the line MN. [4]
(ii) It is given that MN intersects BC at the point P. Find the position vector of P. [4]

Thanx in advance for ur replies

[AndrewCedric]

First Question

 Substitute 3^x=y

3^x . 3^2=3^x +9
9y-y=9
y= 9/8

3^x=9/8
x= lg (9/8)/ lg 3=0.107


2nd question

dy/dx= tanx . -3e^-(3x) + e^(-3x) . (sec x)^2
insert dy/dx=0
 and u get the answer 

3rd question

too long to type. see mark scheme. lol

[nipuna92]

i dont get this part
since 3^x = y
how do you do for  3^x+2
can u explain that bit