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HSC 2015 MX2 Marathon (archive) (1 Viewer)

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Drsoccerball

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Re: HSC 2015 4U Marathon

It is because if they share the same center and are tangents then the semi major or semi minor is equal to the radius. The value of the semi minor/semi major axis gives the distance from the center to the point. Therefore if they share the same center and the circle has a radius equal to the semi major or semi minor axis it is a tangent at both sides of the axis. Can't explain it D:
 

Drsoccerball

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Re: HSC 2015 4U Marathon

Hopefully, this suffices (still no LATEX):
http://i.imgur.com/QJNbrGy.jpg?1

Couple of fixes:
*r is the length of the semi-major/semi-minor axis (in final answer)
*gradients are equal
Start up a forum where you just post random Latex thats how me and ekman learnt it and i think usinng logic is more simpler than calculations for this
 

Sy123

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Re: HSC 2015 4U Marathon

It is because if they share the same center and are tangents then the semi major or semi minor is equal to the radius. The value of the semi minor/semi major axis gives the distance from the center to the point. Therefore if they share the same center and the circle has a radius equal to the semi major or semi minor axis it is a tangent at both sides of the axis. Can't explain it D:
That is sufficient to prove that if the radius and the one of the axes of the ellipse were equal, then they are tangent to each other. However the question is asking, given that they are tangent, that therefore the radius and one of the axes are equal.

So while the question asked to prove (P implies Q) you have shown (Q implies P)
 

glittergal96

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Re: HSC 2015 4U Marathon

Note that both of these shapes have reflective symmetry in the coordinate axes so it suffices to consider points P of tangential intersection in the first quadrant.

The problem then reduces to showing that the only normals to an ellipse that pass through the origin are the axes (which clearly do so I won't prove this).

If P does not lie on the coordinate axes, chucking (0,0) into the parametric normal equation and simplifying gives which has no solutions.


(The dot-product would provide a cleaner way of doing this because it avoids dealing with gradients, and the semi-minor axis is vertical.)
 

Kaido

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Re: HSC 2015 4U Marathon

Anyone got an efficient method to solve 2001 Q8 b) i)
I feel that for 2 marks, should be under 1 page =.=
 

Kaido

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Re: HSC 2015 4U Marathon

Cheers pokemon hunter, If I wrote that in the HSC, will they accept it and give the 2 marks?
 

T-R-O-L-O-L

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Re: HSC 2015 4U Marathon

Far this stuff looks hard, I'm sticking to 2 Unit.
 

Drsoccerball

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Re: HSC 2015 4U Marathon

I dont understand volumes slicing method D: i can't do even the simplest questions... need help
EDIT: for example i dont know what to put as the arbitary value of the x or y slice
 
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InteGrand

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Re: HSC 2015 4U Marathon

I dont understand volumes slicing method D: i can't do even the simplest questions... need help
EDIT: for example i dont know what to put as the arbitary value of the x or y slice
The slicing method uses . So you need to find the area of a typical slice at a point x (this isA(x)), and integrate this area function over the given interval.
 

Drsoccerball

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Re: HSC 2015 4U Marathon

The slicing method uses . So you need to find the area of a typical slice at a point x (this isA(x)), and integrate this area function over the given interval.
a simple question:
 

Ekman

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Re: HSC 2015 4U Marathon

solid explanation
Since the radius of the cylinders are 4-x, and the height/thickness of the cylinders is dy, you use the formula pir^2h to find the volume. The integral is the summation of the cylinders between 0 to 4
 

InteGrand

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Re: HSC 2015 4U Marathon

a simple question:
(It helps to draw a diagram)

If you're using the slicing method for this, you'll be integrating with respect to y, from y = 0 to y = 4 (since these are the y-values of the endpoints in question).

At a given , the radius of a typical slice will be equal to the distance of the line x = 4 to the point on the given curve where y = h. Since the curve is , at the point where y = h, we have .

So the required radius at a height h is . The thickness of the slice is . So the slice has the volume (using the formula for the volume of a cylinder).

Then the total volume is found by integrating from h = 0 to h = 4.
 
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Drsoccerball

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Re: HSC 2015 4U Marathon

so y=x^2, y=1, x=3 about x axis would be
?
 
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