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Mathematics: Post your doubts here!

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I do not know how to get the invariant line for shear and stretch, i mean if you look for the prependiculat height, then its parallel to both at timess, or I don't know how to find an invariant line. I seriousllyy need hellpp URGENTLYY!
 
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PLEASE HELP!
the very last question in the paper attached

Question 9c
It's so hard and I have to understand it because my exam is tomorrow and I'm definitely sure that sequences are coming!!
They showed up on all the recent papers...

I've also attached the mark scheme. It might make it easier to explain.
 

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Guys can anyone show me how to draw stretch and shear transformation with a negative scale factor?
 
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It's easy:
h inverse (x) = x
h inverse (x) = 2
x = 2

Put x=2
h(x) = 3^x
h(x) = 3^2
h(x) = 9

Could you please help me with O/N 11 variant 42 question 7) f) i) as well please??
Thanks in advance! :)
http://www.xtremepapers.com/papers/CIE/Cambridge IGCSE/Mathematics (0580)/0580_w11_qp_42.pdf
x^3 - x^2 -2x + 1 = 0
Take 1 to the other side
x^3 - x^2 - 2x = -1
take 'x' common
x(x^2 - x - 2) = -1
x^2 - x - 2 = -1/x
bring -1/x back here and take -x - 2 back there
x^2 + 1/x = x + 2
a = 1
b = 2
 
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hey guys..can u confirm if mark scheme for sum number 2) d) iii paper october/november 2005 is wrong?
 
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Thank you so much! :)
how can h inverse of x=x?? since its h^x so how can you find the inverse of something if its something to the power of x?? :/
Actually, it's what you call a FACT or so my sir told me.
You can always write h inverse (x) = x
or
h inverse (323) = x
or
h inverse ('anything') = x

For example:

h(x) = x + 2
Find:
h inverse (23)

We can write
h inverse (23) = x
Move h inverse to the other side... the inverse is removed! (I know this is something new but it's always effective)

h(x) = 23
x + 2 = 23
x = 21

Now let's see that question

h inverse(x) = 2
Move h inverse to the other side
h(2) = x
h(2) = 3^2
h(2) = 9

Hard to understand but once you do, it's awesome :D
 
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Thank you so much! :)
how can h inverse of x=x?? since its h^x so how can you find the inverse of something if its something to the power of x?? :/

you write it as log y= x log 3
then x= log y / log3
hence (log x/ log 3)=2
which means 2*log 3
and then log inverse
 
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Actually, it's what you call a FACT or so my sir told me.
You can always write h inverse (x) = x
or
h inverse (323) = x
or
h inverse ('anything') = x

For example:

h(x) = x + 2
Find:
h inverse (23)

We can write
h inverse (23) = x
Move h inverse to the other side... the inverse is removed! (I know this is something new but it's always effective)

h(x) = 23
x + 2 = 23
x = 21

Now let's see that question

h inverse(x) = 2
Move h inverse to the other side
h(2) = x
h(2) = 3^2
h(2) = 9

Hard to understand but once you do, it's awesome :D

i dont think it would work for all equations...log is a lot easier
 
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