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Mathematics: Post your doubts here!

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rearrange the equation such that it is in the form:
lny = lnA - kx^2
-->
lny = -kx^2 + lnA

from this u can see that ur gradient will be -k and ur y-intercept is lnA

find the gradient using the coordinates of the two given points and equate it to -k .... then put in the values of lny , k, and x^2 from one of the points in the equation and find c i.e. lnA

got it?
Brilliant! (y)
 
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rearrange the equation such that it is in the form:
lny = lnA - kx^2
-->
lny = -kx^2 + lnA

from this u can see that ur gradient will be -k and ur y-intercept is lnA

find the gradient using the coordinates of the two given points and equate it to -k .... then put in the values of lny , k, and x^2 from one of the points in the equation and find c i.e. lnA

got it?
but in the exam how am i supposed to know that i should rearrange and do such stuff? :(
 
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NOTE i am considering @ as thita

as u found out in part i ..
4Cos@ + 3Sin@ = 5Cos(@-0.6435)

5Cos(@-0.6435) = 2
Cos(@-0.6435) = 2/5
@ = Cos^-1(2/5) + 0.6435

@= 1.8028 radians
and
2(pie)-1.8028 = 4.48 radians

can't seem to grasp onto the last part tho :p
 
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Two particles P and Q move on a line of greatest slope of a smooth inclined plane. The particles start
at the same instant and from the same point, each with speed 1.3ms−1. Initially P moves down the
plane and Q moves up the plane. The distance between the particles t seconds after they start to move
is d m.
(i) Show that d = 2.6t.
 
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Plz help me with these questions.

May June 2012 paper 61 maths q6 part iii.maths

October November 2011 paper 33 q10 maths

May June 2011 paper 33 q7 part iii.
Thanks aloooot!
 

asd

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Gradient = dy/dx = PN/TN= tanx = 1/2(PN)(TN)

For part (i): Rearrange PN/TN = tanx to give TN= PN/tanx
Substitute this into Area of the triangle (1/2 PN*TN) which gives 1/2* (PN)*(PN/tanx)
Note that PN= y.
So it goes down to 1/2. y^2. cotx

Now for part (ii): Separate the variables and integrate.
int(2/y^2) dy = int(cotx)dx
= -2/y = int(cosx/sinx) dx
= -2/y = ln(sinx) + c

Plug in (Pi/6, 2) to evaluate c. c= -0.31 Idk why they have it as 0.3 in the ms.
then rearrange to express y interms of x.
 
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