synthesisFR
School Spirit Skit 1
this might be a dumb question but wouldn't u take the abosolute value of b as 1/sqrt3 so then it would be +- the answer?
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- Thread starter synthesisFR
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this might be a dumb question but wouldn't u take the abosolute value of b as 1/sqrt3 so then it would be +- the answer?
WeiWeiMan
Well-Known Member
Test on calculator, if it works sure, if not no
synthesisFR
School Spirit Skit 1
did we have to assume the volume of the two tanks r equal cus they didnt say
I guess not, they’d be more specific about something like that in the hsc
synthesisFR
School Spirit Skit 1
what r the most worthwhile topics to study which will likely be tested this year in q14??
synthesisFR
School Spirit Skit 1
where r the values coming from im a bit confused for the dashes?
synthesisFR
School Spirit Skit 1
like i got it but now i dont got it anymore??
synthesisFR
School Spirit Skit 1
could someone explain what they did for part ii lol
I got the same answer but i just did they collide so equated y = y then got V = 20sin(alpha) at collision, and just subbed in a=72 from i. But idk where they got the triangle and stuff from?
Masaken
Unknown Member
so it's a parametric q basically, i remember doing it (syd grammar 2023?)
for x = f(t), t = 2 is the point where the curve meets the tangent. the gradient of the tangent *at this point* is basically rise/run. so for the x curve that's f'(2) = -1/2 (see that little 'triangle' made with the dotted line rising up to the point and the t axis from 2 to 4?). similarly for y = g(t) when t = 2 y = 1 the curve touches the tangent at that point, so finding the gradient of the tangent at that point is just rise/run so g'(2) = 1.
it asks gradient of tangent for curve C, but since that's defined parametrically in terms of three variables you need to technically 'join' them together to get only y and x with the gradient of the tangent being dy/dx. since you have dx/dt [f'(2)] and dy/dt [g'(2)] to cancel out the dr variable and then you should get -2
synthesisFR
School Spirit Skit 1
ohhh makes sensei wasnt using the tangent line function for sum reason when finding the gradient for g'(t) that makes sm sense tyty
STILL MANAGED TO GET FULL MARK IN MCQ BY GUESS THIS THO
synthesisFR
School Spirit Skit 1
this question i had no idea how to use part i
because like how do u know that fx - gx = -px ??? and how do u know if it would have a double root
because if you treat g(x) as the x axis for f(x), the two times which it touches immediately turn back, making them double roots. hence, this has two roots of multiplicity two, which is P(x)
synthesisFR
School Spirit Skit 1
i get what ur saying but i dont get it?
Pretend that g(x) is an x axis. The points where f(x)=g(x) would therefore be the zeros of f(x) relative to this g(x). Therefore, as you can see on the graph, there are two double roots, so, you can equate your equation from earlier g(x)-f(x) to P(x) (they flip both sides but it achieves the same thing) because P(x) can represent any polynomial with 2 double roots
synthesisFR
School Spirit Skit 1
but how do u know fx - gx = px or -px im confused
the coefficient of x^4 must be the same, and p(x) is monic so it’s coefficient is 1. as you can see in its equation, the coefficient in f(x) is -1, so to match that if you want to equate a positive f(x) you need a negative p(x)
synthesisFR
School Spirit Skit 1
can i please borrow just 5 of your brain cells for fridays exam?
SB257426
Very Important User
the volume of the 2 tanks arent equal ... its the change of volume. As water in P is leaving a certain rate.... water in P is rising at the same rate