How do I do this HSC question? (1 Viewer)

[BlueGas]

I need help on question c i) and ii)

 

[InteGrand]

i) To find the coordinates of A, equate the equation of the line and the parabola. So at A (where ),

, i.e. .

Since at A, we can divide through by , to get .

To find the y-value of A, sub. in x = 1 into the equation of the line. So . So A = (1, -3).

ii) Shaded area is given by this integral: .

 

[BlueGas]

i) To find the coordinates of A, equate the equation of the line and the parabola. So at A (where ),

, i.e. .

Since at A, we can divide through by , to get .

To find the y-value of A, sub. in x = 1 into the equation of the line. So . So A = (1, -3).

ii) Shaded area is given by this integral: .

Does it matter what equation you sub x into? Obviously for this question you get the same answer for both equations how about for other questions, does it matter? If it does, how would I know what equation do I sub x into?

 

[nightweaver066]

Does it matter what equation you sub x into? Obviously for this question you get the same answer for both equations how about for other questions, does it matter? If it does, how would I know what equation do I sub x into?

Nope. Doesn't matter.
Solving 2 equations simultaneously means you're finding a solution that satisfies both of the equations (the point of intersection).
This means it doesn't matter whichever equation you sub it in to because you should yield the same y-value (to get the same point).