Search results

\ Perpendicular distance is minimised distance between a line and a point, any other magnitude between the point (u) and the line (lambda(v)) willl be greater or equal to, just draw a diagram to prove the given is perpendicular distance with projection formulae, and construct the line...

do the regular projectile motion things to find time of flight (let y=0 etc), solve simultaneously for x and rearrange, you're left with: R_{max} (sin2\theta-sin\theta)=d Then, optimise the function on the LHS and you get the maximum value of y (sin2\theta-sin\theta) is equal to 0.369..., so...

Your comment on 13c, this was what I wrote as well. Something like g(x)=arcsinx is defined only for x [-1,1], but f(x)=sinx is defined for x across the reals. They even specified x across all real for f(x)=sinx, which to me made it seem clear they wanted you to conclude false due to domain/range...

thanks, that's very helpful!

yeah D is right, but if it did it would be A haha

although, i think if f(x) is strictly increasing then (A) is correct.

this example is not correct, see the one i posted before: the question specified both the functions were differentiable and real across all x and y, which hyperbolas are not.

consider the example y=-x^3 inverse function is y=(-x)^1/3 They intersect at three places, but only one of them is along y=x.

I think UAC uses only the HSC aligned mark and then scales that based on their own thing, which is skewed non-linearly from the very high marks (which is what adjusts it so that a student who gets 98-->100 is rewarded over the 67-->90), which is what counts to your aggregrate: I'm not sure nesa...

I think the way UAC calculates atar from the HSC marks makes it slightly more fair, not sure though

just draw the slopes at each P, Q, R ? (i.e. sub in the values (x,y) at each point and then draw a line segment of the gradient at the point)

doesn’t t-subbing create an asymptote? edit: never mind, integrated it a different way and I believe B is right

anyone else get 16d as 358

i got it dmax=0.369Rmax

wasn’t 14c just showing that sin2theta - sintheta maxes out at ≈0.37 after factorising out Rmax

it does matter, because there are different arrangements of the 3 depending on which spots are chosen, 7C3 chooses the spots but doesn't order the 3 within them

I also get the same answer, but I consider the complement as well; case 1, all three students together ways=7! * 3! case 2, two students together ways=(3C2*2!)(7C2*2!)(6!)=3P2*7P2*6! [i prefer the ‘choose’ operator as it makes more intuitive sense to me, they’re identical though] then the...

yeah, thinking around 63-65 based on previous years' scaling and difficulties

the converse was very straightforward if you take the contrapositive edit: didn't see that solutions were already posted... oops

although to be fair when you sent I just skimmed over it and thought yeah I think I can do this after a bit of thinking so it just made it quicker in the test rather than letting me know how to do it