Some P3 question from oct / november 2009

[XWTBSILT]

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

 

[muhammad.ali]

well bro.....deze questions are piece of cake ...apart frm the fact that i aint gt no clue abt hw to solve em....lawl.....
so ya....me also waiting fo sm1z help..))

 

[hina]

Q1) using simple indices first split up 3^x+2 into 3^x * 3^2 then 3^x * 3^2= 3^x + 3^2
getting common terms on one side we get.. 3^x(3^2-1)=3^2
which is 3^x(8)=9 therefore we get 3^x=9/8 which can then be solved by using ln
xln3=ln(9/8) so x=ln(9/8)/ln(3)