Mathematics: Post your doubts here!

GriM ReapeR

GriM ReapeR

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20150831_214250.jpg Assalamualaykum everyone, I have a formula doubt. This was written in my statistics notebook without any context, someone please explain.
thank you
 
Rizwan Javed

Rizwan Javed

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manya said:
View attachment 57018
Click to expand...
(ii)
gradient of normal : (1+x) (√(1-x^2)) --- (1)

differentiating (1) wrt to x

dy/dx = (1)(√(1-x^2)) + (1+x)(1/2√(1-x^2))*(-2x)
for max values , dy/dx = 0, so

0 = (1)(√(1-x^2)) + (1+x)(1/2√(1-x^2))*(-2x)
0 = 1 - x - 2x^2

(x+1) (2x-1) = 0

either x = -1 or x = 1/2

since the x-coordinate of P is +ive, so x=-1 is rejected.

hence the x-coordinate of P is 1/2
 
manya

manya

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Rizwan Javed said:
(i)
y= (1-x)^0.5 / (1+x)^0.5
dy/dx = ( ( (1+x)^0.5) * (-1/2√(1-x) ) - ( (1-x)^0.5 * (1/2√(1+x) ) ) ) / (1+x)
after solving ....
dy/dx= -1 / ( 1+x ) ( √(1-x^2) ) = m

the gradient of normal = -1/m
so, gradient of normal = ( 1+x ) ( √(1-x^2) ) (shown) :)
Click to expand...
jazakallah khair. :) i see ur method is a bit different than asked in the question but in ms they are giving point for this method as well.:) however, i noticed a mistake ie the minus sign with the power of the differenciated one since its gonna be (1-1/2)=-0.5
 
C

cool Hassan

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Hi eureka!
As u can see that the mass is attached to the disc via a string
So it must have the same angular velocity as that of the disc
Where as it has different "linear velocity" from that of the disc
Now..
As Angular velocity=2π/T where T is "time period"
Now as we know that the angular velocity of disc and mass is same
So the value of T for both must be "same"
Hence
Distance travelled by point A on the disc in one revolution i-e in time T
Equals to 2πr=2π(0.5)
Now as the question says that linear velocity of mass is 1.6 times that of point A on disc
Hence
2π(0.5)/T=(1.6*(2π(0.5+0.8sin theta)))/T
"T" cancels out
Now you can solve the equation to find the value of theta
(b) this part is simple
T cos theta= weight of particle
Solve it and get the value of T
(c) for this part u need to form two equations and solve them simultaneously to get the ans
As v=r* angular velocity (omega)
Firstly consider the point A on disk let the veloctiy of that point to be "x" and the angular velocity of point A and particle to be "y"
For point A => x=0.5y
For particle =>1.6x=(0.5+0.8sin theta) y
Solve these equations to get the value of "y"
U will get the value of angular velocity..
Hope u understood..
 
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Ankitaagg

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do we get a formula sheet for stats and pure maths in as level???
if yes please upload the file.
thank you
 
Rizwan Javed

Rizwan Javed

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For P1 I use 'Advanced Level Mathematics : Pure Mathematics 1 by Hugh Neil and Douglas Quadling'.
For P3 I use 'Advanced Level Mathematics : Pure Mathematics 2 & 3 by Hugh Neil and Douglas Quadling'.
FOr Stats, S1 I use : 'Concise Course in Adcanved Level Statistics by J.Crawshaw and J.Chambers'

Btw I have a few books for edexcel Mathematics in pdf format. If you want I can upload them for you.
 
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