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[Alkenes]

Could someone explain me the two dot-points under the heading 'Notes'

Thanks

 

[Alkenes]

Could someone do q.10 please

 

[Nooblet94]

Could someone explain me the two dot-points under the heading 'Notes'

Thanks

That's worded terribly. Basically it's saying that if you're rotating the area about a point that is inside/on the edge of the area, you'll get slices that are disks. Whereas if it's outside the area you'll get a slice that's an annulus because there's a gap between the area and the axis of rotation. Even that's not worded great - it's much easier to understand if you look at it graphically.

View attachment 25621
Could someone do q.10 please

I can't be bothered actually doing it, but I'll tell you how. Solve them simultaneously and you'll get a quadratic in x. Take half the sum of roots (i.e. -b/2a) and that's the x-coordinate of the midpoint. Substitute that into the equation for PQ and you'll get the y-coordinate.

 

[Alkenes]

how do we find acute angle between asymptotes of a hyperbola???? :S

 

[nightweaver066]

how do we find acute angle between asymptotes of a hyperbola???? :S

Find the gradient of each (+ or - b/a), then use