Mathematics: Post your doubts here!

[reina81]

May 2006 p3 Q5. i don't get how they got the 250 part
http://www.xtremepapers.com/papers/...AS Level/Mathematics (9709)/9709_s06_qp_3.pdf

 

[sea_princess]

May 2006 p3 Q5. i don't get how they got the 250 part
http://www.xtremepapers.com/papers/CIE/Cambridge International A and AS Level/Mathematics (9709)/9709_s06_qp_3.pdf

the equation starts like this
dx/dt= kx -25
put dx/dt=75 and x= 1000
so u have
75= 1000k - 25
100= 1000k ( divide by 1000)
k= 0.1
so u have : dx/dt= 0.1x-25
by takin 0.1 as a common factor u get dx/dt= 0.1(x -250 ) >>>> the 250 came as you divided the 25 by 0.1

 

[reina81]

Q 10
http://www.xtremepapers.com/papers/...AS Level/Mathematics (9709)/9709_w04_qp_3.pdf

 

[sea_princess]

Q 10
http://www.xtremepapers.com/papers/CIE/Cambridge International A and AS Level/Mathematics (9709)/9709_w04_qp_3.pdf

i - okay first notice that the question gave you the base area( m^2) and the rate of flow in m^3 so when making the formula you divide 30 by 1000 to get the rate of increase in height
so now you have dh/dt =0.03 -k square root h
put h =1 and dh/dt = 0.02
0.02 = o.o3 - k ( square root of 1 is 1)
k = 0.03 -0.02 = 0.01
so now the equation is
dh/dt =0.03 - 0.01 square root h
by taking 0.01 as a common factor
dh/dt= 0.01 (3- square root h)
ii- this part is integration , u have the equation
( x-3 ) dx/dt =0.005 x ( divide both sides by o.oo5 x and put the integration sign)
(x- 3)/ 0.005x dx= dt ( you multiply both sides by dt)
separate the left side
x/ 0.005 x - 3/0.005x dx = dt
200 -600/x dx = dt ( now u can integrate)
200x - 600 ln (x) = t +c
put x=3 , t= 0
600 - 600 ln(3) = c
thus t = 200x - 600 ln (x) - 600+ 600 ln (3)
t= 200x + 600 ln (3/x) - 600 ( u can take 200 as common factor )
t = 200 (x + 3 ln (3/x) -3)

 

[sea_princess]

i - okay first notice that the question gave you the base area( m^2) and the rate of flow in m^3 so when making the formula you divide 30 by 1000 to get the rate of increase in height
so now you have dh/dt =0.03 -k square root h
put h =1 and dh/dt = 0.02
0.02 = o.o3 - k ( square root of 1 is 1)
k = 0.03 -0.02 = 0.01
so now the equation is
dh/dt =0.03 - 0.01 square root h
by taking 0.01 as a common factor
dh/dt= 0.01 (3- square root h)
ii- this part is integration , u have the equation
( x-3 ) dx/dt =0.005 x ( divide both sides by o.oo5 x and put the integration sign)
(x- 3)/ 0.005x dx= dt ( you multiply both sides by dt)
separate the left side
x/ 0.005 x - 3/0.005x dx = dt
200 -600/x dx = dt ( now u can integrate)
200x - 600 ln (x) = t +c
put x=3 , t= 0
600 - 600 ln(3) = c
thus t = 200x - 600 ln (x) - 600+ 600 ln (3)
t= 200x + 600 ln (3/x) - 600 ( u can take 200 as common factor )
t = 200 (x + 3 ln (3/x) -3)

iii- here there's a trick , notice the question said the height of water is 4 m
so u go back to the equation x= 3- square root h and put h =4
then u get x = 3- 2 = 1
put this x in the equation obtained in part (ii)
t= 200 (1 + 3 ln(3/1) - 3)
t= 259.2 seconds

 

[reina81]

iii- here there's a trick , notice the question said the height of water is 4 m
so u go back to the equation x= 3- square root h and put h =4
then u get x = 3- 2 = 1
put this x in the equation obtained in part (ii)
t= 200 (1 + 3 ln(3/1) - 3)
t= 259.2 seconds

thank you so much!!! really helped

 

[sea_princess]

thank you so much!!! really helped

you're welcome

 

[Uneeq]

How to solve this, 2-3x < |x-3|? The answer should be x > -1/2 only..

 

[farhan143]

This is so hard i cant understnd a thing...... can any 1 explain me this im in need of serious help!!!!!



Please help me solve this question .....
THIS IS 2011 OCT/NOVEMBER
STATISTICS PAPER 62

 

[leadingguy]

How to solve this, 2-3x < |x-3|? The answer should be x > -1/2 only..

please post the links of question papers too so the one solving can see the question that what is asked

 

[Uneeq]

How to solve this, 2-3x < |x-3|? The answer should be x > -1/2 only. This is from CIE Past Year Mathematics. Oct/Nov 09. Question 1. Variant 31

 

[smartangel]

http://www.xtremepapers.com/papers/CIE/Cambridge International A and AS Level/Mathematics (9709)/9709_w09_qp_61.pdf
Q5..permutations and combinations.. Please explain it.

also http://www.xtremepapers.com/papers/...S Level/Mathematics (9709)/9709_w09_qp_62.pdf
Q1 second part..how do we calculate sigma?

 

[Rabib_69]

Okay.. this is a tough one! Please, can ANYONE come up with the solution? - 6 (iv)

 

[1357913579]

How to solve this, 2-3x < |x-3|? The answer should be x > -1/2 only..

 

[smartangel]

http://www.xtremepapers.com/papers/...S Level/Mathematics (9709)/9709_s11_qp_61.pdf
on Q3 second part..how do we calculate the expected value?? PLEASE HELP!!

 

[Esme]

you have to find the probabilities of the other 7 integers which will be 1-(1/10) / 7. this is because the proabilities of all the other integers are equal. now the formula for expectance is sum of (X x P) . so multiply the variable X (eg -2) with its probability (9/70) and then add them all.

 

[Usmanraufjh]

Nvm I got it. Thanks

how did u get it.... plz xplain

 

[2pac]

The square root is not that terrible. It is just used to compensate certain squares.
Also to solve this question I think you need to master the trigonometric identities.
View attachment 7343

Thank you so much.Really helped a lot.
Could you also please explain the second question of the same paper?
I did the first step,that is,simplifying it with logarithm but then substituting the values using the graph and then solving it led to many errors.Have seen a similar question in p2 and so I will bother you with some p2 questions as well.

 

[DragonCub]

Thank you so much.Really helped a lot.
Could you also please explain the second question of the same paper?
I did the first step,that is,simplifying it with logarithm but then substituting the values using the graph and then solving it led to many errors.Have seen a similar question in p2 and so I will bother you with some p2 questions as well.

y = A (x^n), natural log each side to get
ln y = ln A + n (ln x)
The gradient is n and y-intercept is ln A.
Just draw the line of best fit to find the two values. It should not be hard.

 

[sea_princess]

can anyone please explain S1: October/ novemeber 2009 (variant 1) question 5 part a (ii)