Bazza's 3/4 Question Thread

[WhoTookMyUsername]

So is that link definitely correct lol?
http://math.uchicago.edu/~vipul/teaching-1011/152/concaveinflectioncusptangentasymptote.pdf

Cntrl f points of vertical ( different link)
Same university.. Seems to imply points of vertical tangent are NOT looool

[WhoTookMyUsername]

Any quick way to find angle between two vectors on CAS?

thanks!

[Conic]

Any quick way to find angle between two vectors on CAS?

thanks!

solve( a.b = |a|*|b|*cos(x),x) or arccos((a.b)/(|a|*|b|))

a.b = dot product of a and b

[WhoTookMyUsername]

Need some help with this question!

A body moves in a straight line so that at time t its accel is a where a =f(v)
Given that v=v0 when t=t0 the time taken for the velocity to change from v0 to v1 is given by?

I think it is S(v1,v0)( terminals) 1/f(v) dv

But the solution has a + t0 at the end of the equation,
I thought that t0 would give you the time at t1 not the change in time?
Am i missing something?
Thanks!

[kamil9876]

Is this a multiple choice question? Because there isn't only one possible answer.

[pi]

Yes, from memory, this would be from an older SAC as an MCQ question (a question of this type occurs every year at mhs)

[WhoTookMyUsername]

Sorry, didn't realise there was more than one possible answer D:

Attached that question
(1) attachment

i feel there shouldn't be a t0 at the end of option A because it's a change in time question, not a "time" question

and for the other attached q
(2) attachment

i have absolutely no idea, conceptually what is required for part c (4c) and i'm quite worried about it lol, does anyone know how to (baby steps preferably ) explain it (referring to paths, NOT particles themselves)
thanks a lot!

x=11/sqrt(174) y= 2/sqrt(174) z = 7/sqrt(174) for part 4a)

for b) r(0) = i - 2j
s(0) = j


also

3) how can we determine what info we're allowed to use in vector proofs? For e.g. can we assume that isoceles has 2 same angles in 2 corners?
Can we use any reasonable assumption that is not the thing we have to prove?

4) Let's say you sketch a hyperbola over the domain [0,4] (like should you indicate the asymptote?
5) if sketching a parametric equation should we indicate the normal things like asymptotes? (i thought we should, but i saw a hyperbola graph over domain [0,oo] with none D: (and range [0,oo])


thanks very much

[Jenny_2108]

^ Q1) Imo, ans is A
   
    Q2) Solve equations (by hand or put in CAS)
 






You get







b) Substitute t=0 into the postition vectors

c) you calculate s(t)-r(t) then find their distance = magnitude of the resulted vector
    Then find derivative and let derivative = 0, you get minimum value of t
    Sub back, you get the distance

    Is the answer

[WhoTookMyUsername]

thanks for your help, though with 1 the answer according to solutions is A, but i think there shouldn't be a + t0 at the end because it's a change in time question

and with c) no, it's asking for the minimum distance between the paths of the particles, not the particles themselves

[WhoTookMyUsername]

Please see post 3 posts up and provide some insightful insight if able to

Thankyou !

[BubbleWrapMan]

[WhoTookMyUsername]

thanks for your help
though because it says the "time taken for the velocity to change from" it's t1-t0 isn't it? which is just the integral without the t0 at the end?

I stil have no idea about 4c) second attachment (5 posts up)

[Lasercookie]

though because it says the "time taken for the velocity to change from" it's t1-t0 isn't it? which is just the integral without the t0 at the end?

t0 is not necessarily equal to zero. We're calculating an area under a curve. If t0 has a value, then that curve will be translated up and down, correct? That will mean the area would be altered. By the fact that we're using a definite integral, we've already accounted that there's an initial time and a final time (the interval we're integrating over).

[BubbleWrapMan]

It must be asking for the time taken from t = 0, regardless of what t_0 is. So it's ambiguous I guess. But given those choices, the correct answer should be obvious.

[Jenny_2108]

^ Actually this is the formula in Spesh course you can apply directly without doing antiderivative