Mathematics: Post your doubts here!

[Esme]

View attachment 26119
Why do we equate the denominator of the derivative to zero for value of y

That's because gradient of any line parallel to the y-axis is 1/0
So when you say dy/dx = 1/0
y/(x (3y^3-1) ) = 1/0
Cross multiply and automatically y becomes 0.

 

[Alice123]

(20+12<x<20-12)
now you have to imagine the graph in your head, and you have to come into a conclusion that it is symmetrical.

Now imagine the z of 20+12 that is 32 is x
So the z of 20-12 that is 8 will be a negative number -x

Both of them are x but one is negative, because they are the same distance from the mean

Let the probability of x is p
so the probability of -x is 1-p

we know that difference of the two probability is 0.94

so p - (1-p) = 0.94
p - 1 + p = 0.94
2p = 0.95 + 1 = 1.94
p = 0.97

Now is p is 0.97 z is from the table, 1.882 (or 1.881)

now continue normally

1.882 = 32-20 / sd
sd = 12/1.882
=6.38
This was done by Phyzac before
littlecloud11

 

[littlecloud11]

Thank you both so much!! Much appreciated
PhyZac Alice123

 

[Esme]

http://papers.xtremepapers.com/CIE/...S Level/Mathematics (9709)/9709_s10_qp_31.pdf
http://papers.xtremepapers.com/CIE/...S Level/Mathematics (9709)/9709_s10_ms_31.pdf

Q7iii) I still don't know how to do these type of questions How to pin point the exact point ? I know we have to make a tangent from the origin to the lowest point on the circle, but which point to take ?
Anika Raisa or PhyZac... Please

 

[PhyZac]

7iii) View attachment 21999
As the question states that the argument of z is least, z must represent the lowest possible point in the shaded region. Draw a tangent from the center to the lowest point on the circle (this doesn't have to be accurate) as shown by the blue line. This line represents |z|. The angle between the radius and the tangent is always 90 so a right-angled triangle is formed. The opposite side, with is equal to the radius is 1 unit. The magnitude of complex u is the hypotenuse and the adjacent represents |z|. you can easily find |u|, √(2^2+2^) = √8.
So, |z| =√(√8)^2 -1^2 = √8-1 =√7

Esme
There you go, littlecloud11 have answered this before.

 

[Esme]

Esme
There you go, littlecloud11 have answered this before.

Thank you so much.. finally I know now.

littlecloud11 Masha'Allah genius.. I would have never thought of working it out like that, and even my teacher couldn't explain these questions

 

[leosco1995]

Please help with this.

 

[Alice123]

Please help with this.

please excuse my handwriting

 

[leosco1995]

please excuse my handwriting

Great! Thanks for the fast reply.

 

[Esme]

please excuse my handwriting

Anika Raisa You also asked this question... there you go. Alice123 has solved it

 

[19islandprincess96]

Please help! This paper http://papers.xtremepapers.com/CIE/Cambridge International A and AS Level/Mathematics (9709)/9709_s07_qp_3.pdf
Question 5 part 2!
And question 8?
How do we do them?

 

[HubbaBubba]

Statistics Paper 6 Question

1. The volume of milk in millilitres in cartons is normally distributed with mean (u) and standard deviation 8. Measurements were taken of the volume in 900 of these cartons and it was found that 225 of them contained more than 1002 millilitres.
(i) Calculate the value of (u)

Can anybody tell me how they found the value of z ?

 

[iKhaled]

how can i solve question 10 omggg! someone pls help

http://papers.xtremepapers.com/CIE/...S Level/Mathematics (9709)/9709_s12_qp_33.pdf

 

[Silent Hunter]

http://papers.xtremepapers.com/CIE/...AS Level/Mathematics (9709)/9709_s08_qp_3.pdf

Q8 (i) ?

applepie1996
Rutzaba

or anyone?

Thanks

 

[Esme]

http://papers.xtremepapers.com/CIE/Cambridge International A and AS Level/Mathematics (9709)/9709_s08_qp_3.pdf

Q8 (i) ?

applepie1996
Rutzaba

or anyone?

Thanks

Area of triangle PTN = tanx
1/2 x TN x PN = tanx
1/2 x TN x y = tanx

dy/dx = PN/TN
TN = PN x dx/dy
TN = y x dx/dy

Now substitute TN in area of triangle
1/2 ( y x dx/dy) y = tanx
1/2 y^2 (dx/dy) =tanx
dy/dx = (1/2 y^2)/tanx
dy/dx = 1/2 y^2 cotx

Hope you got it

 

[Rutzaba]

Statistics Paper 6 Question

1. The volume of milk in millilitres in cartons is normally distributed with mean (u) and standard deviation 8. Measurements were taken of the volume in 900 of these cartons and it was found that 225 of them contained more than 1002 millilitres.
(i) Calculate the value of (u)

Can anybody tell me how they found the value of z ?

link

 

[Rutzaba]

Please help! This paper http://papers.xtremepapers.com/CIE/Cambridge International A and AS Level/Mathematics (9709)/9709_s07_qp_3.pdf
Question 5 part 2!
And question 8?
How do we do them?

gimme 5 mins

 

[HubbaBubba]

link

Question 1
http://papers.xtremepapers.com/CIE/Cambridge International A and AS Level/Mathematics (9709)/9709_s09_qp_6.pdf

 

[syed1995]

HubbaBubba
1. The volume of milk in millilitres in cartons is normally distributed with mean (u) and standard deviation 8. Measurements were taken of the volume in 900 of these cartons and it was found that 225 of them contained more than 1002 millilitres.
(i) Calculate the value of (u)

Can anybody tell me how they found the value of z ?

P(x>1002)=225/900
P(x>1002)=0.25
P(z>1002-u/8)=inversePhi(0.25)
P(z>1002-u/8)=-inversePhi(0.75)
P(z<-(1002-u/8))=-inversePhi(0.75)
-(1002-u)/8=-0.674
1002-u/8=0.674
1002-u=5.392
u=996.6 Answer

 

[syed1995]

Question 1
http://papers.xtremepapers.com/CIE/Cambridge International A and AS Level/Mathematics (9709)/9709_s09_qp_6.pdf

Done above ^^