Pure math(p3)

[preity]

Can someone help me with this questions

M/J 02 Q1
M/J 03 Q1
0/N 04 Q4

[astarmathsandphysics]

Can someone try this cos i wont be home for 3 hours.

[xcon89]

for j02

open the right hand side
and then

2/tan2@

then
2/(2tan@/1-tan^2@)

then >  2(1 - tan^@)/2Tan@

(1 - tan^2@)/tan@

1/tan@ - tan^2@/tan@

cot@ - tan@

[xcon89]

others are easy aswell but since they involve alot of latex and i am unfamiliar with latex, I can't write it here
sorry

[twilight]

hang on .. i'll solve them

[twilight]

Can someone help me with this questions

M/J 02 Q1
M/J 03 Q1
0/N 04 Q4

for m/j 2003 Q1(i)

sin(x-60) - cos(30-x) = 1
     use the formula sheet here
     sin x cos 60 - sin 60 cos x - ( cos 30 cos x + sin 30 sin x ) = 1
     sin x cos 60 - sin 60 cos x - cos 30 cos x - sin 30 sin x = 1
    (1/2)sin x - (3/2)cos x - (3/2)cos x - (1/2)sin x = 1

    (-3)cos x = 1

     cos x = -1/3

[twilight]

Can someone help me with this questions

M/J 02 Q1
M/J 03 Q1
0/N 04 Q4

m/j 2003 Q1(ii)

cos x = -1/3

reference angle = cos^-1 (1/3) = 54.7^o

therefore x = 180 + 54.7 = 125.3^o

[candy]

The polynomial x^4 - 2x^3 - 2x^2 +a is denoted by f(x). It is given that f(x) is divisible by x^2 - 4x +4.
(i) Find the value of a.
(ii) When a has this value, show that f(x) is never negative.


can someone please explain part (ii)
i don't understand the question

[astarmathsandphysics]

The polynomial x4 ?2x3 ?2x2 +a is denoted by f(x). It is given that f(x) is divisible by x2 ?4x +4.
(i) Find the value of a.
(ii) When a has this value, show that f(x) is never negative.


can someone please explain part (ii)
i don't understand the question

can you modify this post? the question is not clear

[ITS MEE...]

can someone solve the last part please
An underground storage tank is being filled with liquid as shown in the diagram. Initially the tank is
empty. At time t hours after filling begins, the volume of liquid is V m3 and the depth of liquid is h m.
It is given that V = 4
3h3.
The liquid is poured in at a rate of 20m3 per hour, but owing to leakage, liquid is lost at a rate
proportional to h2. When h = 1,
dh
dt = 4.95.
(i) Show that h satisfies the differential equation
dh
dt = 5
h2 ? 1
20
. [4]
(ii) Verify that
20h2
100 ?h2 ? ?20 + 2000
(10 ?h)(10 +h). [1]
(iii) Hence solve the differential equation in part (i), obtaining an expression for t in terms of h.

[ITS MEE...]

oops it looks so awkward but its nove 2008 p3 CIE

[astarmathsandphysics]

Can someone help me with this questions

M/J 02 Q1
M/J 03 Q1
0/N 04 Q4

M/J 02 Q1

cotx-tanx=cosx/sinx-sinx/cosx
=((cosx)^2-(sinx)^2)/sinxcosx=cos2x/(1/2sin2x)=2cot2x

M/J 03 Q1

sin(x ? 60 ) ? cos(30 ? x) = 1
sinxcos60-cosxsin60-cos30cosx-sin30sinx=1
sinx*1/2-cosx-cosx-1/2sinx=1
cosx=1 so cosx=1/

0/N 04 Q4
tan(45 + x) = 2 tan(45 ? x)

(tan45+tanx)/(1-tan45tanx)=2(tan45-tanx)/(1tan45tanx)


(1+tanx)/(1-tanx)=2(1-tanx)/(1+tanx)
cross multiply
(1+tanx)^2=2(1-tanx)(1-tanx)
1+2tanx+tan^2x=2-4tanx+2tan^2x
tan^2x-6tanx+1=0

[ITS MEE...]

OK can someone do
nov08 question 7)ii
                     10)iv
                     8)iii
thank u

[ITS MEE...]

please someone answer

[twilight]

Can someone help me with this questions

M/J 02 Q1
M/J 03 Q1
0/N 04 Q4

for 0/N 04 Q4
(i) tan(45+x) = 2tan(45-x)                use tan(a+b)= (tan a + tan b)/(1- tan a tan b )     in the formula sheet
   (tan 45  +  tan x)/(1 -  tan 45  tan x) = 2(tan 45  - tan x)/(1 +  tan 45 tan x )
(1+tan x )/(1-tan x) = (2-2tan x)/(1+tan x)
cross multiply to get  tan²x - 6tanx + 1 = 1

(ii) substitute tanx by y
then solve by y=   -b+(b²-4ac)
                       ________________
                                  2a
then y =   -b-(b²-4ac)
            _________________
                       2a

then substitute back with tanx and do the usual method to get the values for x for + and -