math p3 question... please help

[weesha]

november 08 question no. 8
An underground storage tank is being filled with liquid
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 = 4/3 h^3
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.
Show that h satisfies the differential equation
dh/dt= 5/h^2 − 1/20

 

[PlanetMaster]

dV/dt = (20-k)h², based on the info given in the problem.
However, V = 4h³/3, thus, dV/dt = 4h²(dh/dt).
Now substitute that into the first equation to get 4h²(dh/dt) = (20-k)h².
Dividing by 4h² yields dh/d t= 5/h² + k/4.
When h = 1,
dh/dt = 4.95 ==> 4.95 = 5+(k/4).
Thus k/4 = -0.05 = -1/20.
Hence, dh/dt = 5/h² - 1/20.

 

[weesha]

thanks alot planet master
i am also weak at solving vector questions... any suggestions?? i went through our book but it didnt help..

 

[PlanetMaster]

This might help you http://www.s-cool.co.uk/alevel/maths/ve ... lanes.html.

 

[ammadb]

how to solve nov08 que7ii??

 

[weesha]

for the intersection of two planes, u always have a line.. for the line equation u need a point and a parallel vector..
this can be done by getting two points on that line..
for those two points..first put any 2 of x y and z = 0
for example i am putting z=0 first in both the plane equations
equations will become 2x-y =7 and x + 2y = 0
by elimination or substitution solve them for x and y
u will get a point (14/5, -7/5, 0)
to get another point put x or y = 0
and get another point..with thoose two points, get the parallel vector and form the equation of line

 

[weesha]

i am stuck at Q10 part(ii) of november 03
The lines l and m have vector equations
r = i − 2k + s(2i + j + 3k) and r = 6i − 5j + 4k + t(i − 2j + k)
respectively.
Find the equation of the plane containing l and m, giving your answer in the form ax + by + cz = d.
markscheme states to calculate a:b:c by taking parallel vectors of both lines.. how to calculate this ratio??

 

[ammadb]

its simple assume the normal vector to be (a,b,c)
as these lines lie in the plane their direction vectors will be perpendicular to the normals.. hence their scaler products will be zero.
so (2,1,3).(a,b,c)=0
ths will become 2a+b+3c=0
put a=1 that will make it 2+b+3c=0

now go fr 2nd line
(1,-2,1).(a,b,c)=0
solve it similarly and u ll get
a-2b+c=0
take a=1 here as well
1-2b+c=0

solve both of these equations simultaneously..
the values which u ll have will be
b=1/7 and c= -5/7 a=1
multiply with 7 to make them whole number
a=7 b=1 c= -5
this is the normal of the plane =)

 

[weesha]

thanks a bunch man ... due to this i cudnt solve many quetions...

 

[Desconcertado]

Anyone please help me with mj 2008 question 7 i).............. Our teacher taught us that partial fraction are to broken in A/(x+1) + B/(X+..)............ BUT THE APPROACH IS DIFFERENT IN THE MARK SCHEME WHEN TO USE WHICH TECHNIQUE I AM VERY CONFUSED.............
PLZ help.............................................. Thanks in advance...

 

[ammadb]

no prob =)

 

[ammadb]

well take substitution
u= /X
the equation will becme
1/ u^2(4-U)
take derivative of the substitution whchis 2u..
multiply with ur eqution n u ll get the ans =)

 

[weesha]

The complex number u is given by u =(7 + 4i)/(3 − 2i).
(i) Express u in the form x + iy, where x and y are real.
(ii) Sketch an Argand diagram showing the point representing the complex number u. Show on the
same diagram the locus of the complex number z such that !z-u! = 2

(iii) Find the greatest value of arg z for points on this locus.

i am done with part i and ii.. i also sketched the cicle of radius 2 and centre 1+i2
but dont know how to calculate this graetest arg

 

[weesha]

this is nov 03 q7