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Further Mathematics: Post your doubts here!

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hi guys,
i've been working on momentum and impulse,but i'm getting some difficulty concerning coeff. of restitution on inclined planes.
here's an example:
A ball drops vertically onto a smooth plane inclined to the horizontal at an angle α. It hits the plane
with speed 8ms−1 and rebounds horizontally. The coefficient of restitution between the ball and the
plane is 1/3.
Find the value of α and the speed with which the ball rebounds.
(j06/1)
i would really appreciate it if anybody could help me out with this question.
thanks.
Here you go! :)
 

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Hi guys,i'm getting some difficulty in roots of polynomial equations as i've just started this new chapter.
i'm stuck on this question.i would really appreciate some help.thanks.:)
The roots of the equation x^3 + x + 1 = 0 are α, β, γ . Show that the equation whose roots are
4α + 1/α + 1,
4β + 1/β + 1,
4γ + 1/γ + 1

is of the form
y^3 + py + q = 0,
where the numbers p and q are to be determined.
Hence find the value of

(4α + 1/α + 1)^n + (4β + 1/β + 1)^n + (4γ + 1/γ + 1)^n
for n = 2 and for n = 3.
(nov06/6)
 
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Hi guys,i'm getting some difficulty in roots of polynomial equations as i've just started this new chapter.
i'm stuck on this question.i would really appreciate some help.thanks.:)
The roots of the equation x^3 + x + 1 = 0 are α, β, γ . Show that the equation whose roots are
4α + 1/α + 1,
4β + 1/β + 1,
4γ + 1/γ + 1

is of the form
y^3 + py + q = 0,
where the numbers p and q are to be determined.
Hence find the value of

(4α + 1/α + 1)^n + (4β + 1/β + 1)^n + (4γ + 1/γ + 1)^n
for n = 2 and for n = 3.
(nov06/6)
First step is to let y = the roots in terms of x for the new equation, then rearrange until you have x in terms of y. Sub the x into the old equation and voila! The second part just involves finding S.O.R., P.O.R. etc
 

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First step is to let y = the roots in terms of x for the new equation, then rearrange until you have x in terms of y. Sub the x into the old equation and voila! The second part just involves finding S.O.R., P.O.R. etc
thanks again.
Really!! you're awesome.
 
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Somebody plz help me with this:
1) Solve: 2^(2x-1) < 3^(3x-2)
2) Solve: (3* Mod(x)) / (x-1) < 2 , where Mod() means modulus or absolute value.
 
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can any one do Q10 oct/nov2012/13
taking derivative: 3x^2 + 3(y^2)y'=3y + 3xy' (1) (cut the 3s out)
>> x^2-y = (x-y^2)y' >> if y'=0 then x^2=y
using the original equation: x^3 + x^6=3x^3 >> x=2^(1/3) and y=2^(2/3)
taking derivative again of (1): 2x + 2y(y')^2 + (y^2)y'' = y' + y' + xy''
>> since y'=0 , 2x + (y^2)y''= xy'' >>y'' = 2x/(x-x^4) >> putting x=2^(1/3) gives us y''=-2 <0. Hence, the stationary point is maximum.
 
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Help plz solve this step by step, I can't integrate this, need help
 

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Hey everyone, how to get A star for Further Mathematics? I m just mostly getting a B or seometimes an A in my school exams. Pls help if u can
 
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Can someone please explain to me how you read of the amplitude from the given information. Thanks
 

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