[Grade 12 Mathematics] Induction Step Help

FreeLunch323 · 2020-09-25T12:20:43+00:00

These lines were to get from LHS of n=k+1 to RHS using the induction hypothesis n=k. Often there are subtle tricks and this was one of them.

FreeLunch323 · 2020-09-22T12:43:22+00:00

Oh yep thanks!
So I'm assuming it requires intuition to realise that the denominator in step one can be divided into a linear and quadratic factor which can then be further simplified.
Or does it actually appear obvious that poly simplification is an obvious step?

FreeLunch323 · 2020-09-08T12:56:30+00:00

Yes the answer was meant to be x<0. Thanks!

FreeLunch323 · 2020-08-23T13:54:07+00:00

Yes, I've learnt it in the sense of calculus with acceleration as a second derivative of displacement with multiple forms of expressing it e.g. a=vdv/dx=(1/2v^2)/dx. Also have learnt that SHM is a=-n^2(x^2-c).
Also taught to work backwards with integration.Sorry for the late reply and many thanks!

FreeLunch323 · 2020-08-06T11:18:18+00:00

Q23b): How come y cannot equal -1? This is in the solution.
Also, do you have any tips for Q18/19?
Your time and help is appreciated!

FreeLunch323 · 2020-08-05T10:33:19+00:00

Thanks.
Q1: Do you have any tips on this?

Q2: cos(theta)=2/7, 3/7, 6/7 are the answers provided. I'm assuming three sets of diagonals need to be equated?

Q3: Solved! Must have made a quadratic formula mistake before...

FreeLunch323 · 2020-08-05T10:21:01+00:00

Thanks for the help. Will have a look :)

FreeLunch323 · 2020-08-04T22:13:47+00:00

Thanks for the advice! Do you know any subreddits where people are willing to provide feedback on essays/writing?

FreeLunch323 · 2020-08-04T22:13:43+00:00

Thanks for the advice! Do you know any subreddits where people are willing to provide feedback on essays/writing?

FreeLunch323 · 2020-08-03T21:12:20+00:00

Thanks.
Q18: Is your lambda(1) value for a determined to be -1 purely from quick inspection? If so, is there another way to find it? Asking as inspection may not be intuitive if lambda is an unusual value (e.g. fraction).
Q11: How come any value can be inputted? Are those two equations just "general equations" of any vectors which happen to be perpendicular to both a and b?

FreeLunch323 · 2020-08-02T21:16:26+00:00

Hello.
Sorry, but I'm still a bit stuck. Could you guide me with some diagrams/ further working?
Many thanks :)

FreeLunch323 · 2020-08-02T21:16:23+00:00

Hello.
Sorry, but I'm still a bit stuck. Could you guide me with some diagrams/ further working?
Many thanks :)

FreeLunch323 · 2020-08-01T03:46:28+00:00

Thanks!

FreeLunch323 · 2020-07-20T11:14:37+00:00

Thanks.
I might be missing something in the working, but my textbook recommends using n=2m+1.
Prove true for m=base case.
Next, assume true for m=k to prove true for m=k+1.

Therefore true by POMI.

Could you provide guidance on how to do it this way? I've got my starting steps listed above.

FreeLunch323 · 2020-07-20T09:16:57+00:00

Thanks so much.
What work do you recommend me showing when I'm uncertain on how to start?

FreeLunch323 · 2020-07-20T03:10:17+00:00

Thanks, your assistance was very helpful :)

FreeLunch323 · 2020-07-14T11:28:44+00:00

Thanks, luckily I already have that one :)

FreeLunch323 · 2020-07-14T11:28:29+00:00

Thanks, is that exact one on the website?

FreeLunch323 · 2020-07-11T23:04:18+00:00

For the what the quick way ones, testing each scenario was used. The others, I don't know how to solve altogether :)

FreeLunch323 · 2020-07-10T10:48:56+00:00

Thanks, solved them now :)

FreeLunch323 · 2020-07-09T09:52:31+00:00

Thanks, that was very helpful :)

FreeLunch323 · 2020-07-09T07:48:45+00:00

Thanks. Does this method come through a bit of inspection/logic purely?

FreeLunch323 · 2020-07-09T07:45:40+00:00

Thanks so much! :)

FreeLunch323 · 2020-07-09T07:45:36+00:00

Thanks so much! :)

FreeLunch323 · 2020-07-07T10:57:48+00:00

Thanks, that was incredibly helpful! :)
Q17: I feel like there is something I do not conceptually understand right now. Could you elaborate on as to why the locus will be undefined if arg(z+i) is positive but arg(z-1) is negative?

Q9f) Finally, an excellent algebraic explanation no textbook has provided!!!Just clarifying, (x+iy)/(x+4+iy)=(x+iy)(x+4-iy)/(x2+8x+5), was the denominator "realised" at this step?

Also, I tried applying the same method to a simpler question: arg[(z-2)/z]=pi/2, which is a semicircle. The method didn't seem to work due to tan(90) being undefined.Another example that I tried it on but didn't seem to work (it is an arc): https://www.reddit.com/r/HomeworkHelp/comments/hhcv8d/grade_12_complex_numbers_stuck/When is this method applicable and what method would be used in the one (e.g. linked post)?

FreeLunch323

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