First Year Mathematics A (Differentiation & Linear Algebra) (2 Viewers)

leehuan · May 22, 2016

Re: MATH1131 help thread

What's wrong with that?

According to the operation R5 = R5 - R4

Right hand column:

$(r_5-r_1) - (r_4+r_2-2r_1) = r_5 - r_4 - r_2 - r_1 + 2r_1 = r_5 - r_4 - r_2 + r_1$

Oh, didn't see IG in this thread

Flop21 · May 22, 2016

Re: MATH1131 help thread

Oh that's how you do it. I was literally sticking an on the end -R4. Which I knew was wrong but yeah bit silly.

Ha makes a lot of sense.

Drsoccerball · May 22, 2016

Re: MATH1131 help thread

leehuan said:
Oh, didn't see IG in this thread

Me when I see integrands name at the bottom of the page : *Rapidly types to finish solution so it doesn't all go to waste*

DatAtarLyfe · May 23, 2016

MATH1131 help thread

Drsoccerball said:
Me when I see integrands name at the bottom of the page : *Rapidly types to finish solution so it doesn't all go to waste*

Feels. Everytime

leehuan · May 23, 2016

Re: MATH1131 help thread

Drsoccerball said:
Me when I see integrands name at the bottom of the page : *Rapidly types to finish solution so it doesn't all go to waste*

Lmao I didn't even see his name this time when I scrolled down.

Normally if I see IG (unless of course I'm pleading SOS) I'm like
...walks away quietly

Flop21 · May 24, 2016

Re: MATH1131 help thread

How do you do this with no calculator?? What's going on in the second to third line?

leehuan · May 24, 2016

Re: MATH1131 help thread

Flop21 said:
How do you do this with no calculator?? What's going on in the second to third line?

Simplifying surds

$\frac{-24 \pm \sqrt{24^2-4(-35^2)}}{2}=\frac{-24 \pm \sqrt{5476}}{2}=\frac{-24 \pm 2 \sqrt{1369}}{2}\\=-12\pm \sqrt{1369} = -12\pm 37$

Flop21 · May 24, 2016

Re: MATH1131 help thread

leehuan said:
Simplifying surds

$\frac{-24 \pm \sqrt{24^2-4(-35^2)}}{2}=\frac{-24 \pm \sqrt{5476}}{2}=\frac{-24 \pm 2 \sqrt{1369}}{2}\\=-12\pm \sqrt{1369} = -12\pm 37$

How the hell do I get 24^2-4*35^2 = 5476 in my head is the issue???

leehuan · May 24, 2016

Re: MATH1131 help thread

Flop21 said:
How the hell do I get 24^2-4*35^2 = 5476 in my head is the issue???

If I had to do the whole thing I would've bashed it differently.

24^2 - 4(-35)^2 = 2^2*12^2 + 2^2+35^2

Factorised out the 2 earlier, you're left with proving 12^2 + 35^2 = 37^2

I find it difficult to believe that this was a quiz question and not a final exam question. But this is my method of tackling square roots:
______________

12^2 = 144 from primary education
35^2 can be done as an algorithm.
35^2 = 35*30 + 35*5 = 1050 + 175 = 1225

1225 + 144 = 1369

I conjecture that 1369 is a perfect square.

Note: A number squared ends in 9 IFF the original number ended in 3 or 7

1369 is closer to 1600 (= 40^2) than it is to 900 (= 30^2)

I therefore conjecture 1369 = 37^2

Test: 37*37 = 1369 by actually computing it

Therefore found my required number

Flop21 · May 24, 2016

Re: MATH1131 help thread

leehuan said:
If I had to do the whole thing I would've bashed it differently.

24^2 - 4(-35)^2 = 2^2*12^2 + 2^2+35^2

Factorised out the 2 earlier, you're left with proving 12^2 + 35^2 = 37^2

I find it difficult to believe that this was a quiz question and not a final exam question. But this is my method of tackling square roots:
______________

12^2 = 144 from primary education
35^2 can be done as an algorithm.
35^2 = 35*30 + 35*5 = 1050 + 175 = 1225

1225 + 144 = 1369

I conjecture that 1369 is a perfect square.

Note: A number squared ends in 9 IFF the original number ended in 3 or 7

1369 is closer to 1600 (= 40^2) than it is to 900 (= 30^2)

I therefore conjecture 1369 = 37^2

Test: 37*37 = 1369 by actually computing it

Therefore found my required number

Thank you I appreciate it.

But damn what were they thinking, this is from test 2 algebra version 2b in 2014. Why would they even choose such large numbers.

leehuan · May 24, 2016

Re: MATH1131 help thread

Flop21 said:
Thank you I appreciate it.

But damn what were they thinking, this is from test 2 algebra version 2b in 2014. Why would they even choose such large numbers.

Very foolish move on their part.

iforgotmyname · May 24, 2016

Re: MATH1131 help thread

Flop21 said:
How do you do this with no calculator?? What's going on in the second to third line?

Which question was this?

Flop21 · May 24, 2016

Re: MATH1131 help thread

iforgotmyname said:
Which question was this?

Question 1 of test2 version2b 2014 algebra.

Flop21 · May 25, 2016

Re: MATH1131 help thread

Why does cos simplify to this? Or how do you work it out?

Flop21 · May 25, 2016

Re: MATH1131 help thread

How do I know which ones are the conjugate pairs to write them next to each other like they have here?

leehuan · May 25, 2016

Re: MATH1131 help thread

Write them as their principal arguments instead, not that horrendous form.

$2e^{\frac{11\pi}{6}i}=2e^{-\frac{\pi}{6}i}$

By definition of the conjugate you should know that
$\arg(\bar{z})=-\arg(z)$

InteGrand · May 25, 2016

Re: MATH1131 help thread

Flop21 said:
How do I know which ones are the conjugate pairs to write them next to each other like they have here?

Conjugate pairs are ones where the angles add up to 0 (or any integer multiple of 2pi). If you convert all the arguments to principal arguments, the conjugate pairs are the ones where the angles are negatives of each other (i.e. add up to 0).

Flop21 · May 25, 2016

Re: MATH1131 help thread

leehuan said:
If I had to do the whole thing I would've bashed it differently.

24^2 - 4(-35)^2 = 2^2*12^2 + 2^2+35^2

Factorised out the 2 earlier, you're left with proving 12^2 + 35^2 = 37^2

Where is the 37 coming from?

https://youtu.be/t7nVFnFougM?t=21m34s

He does it at that point of the video.

But firstly I don't understand why -4*(-35)^2 becomes entirely positive? (-35)^2 would be +, then +*-4, would result in -. Or what am I doing wrong here?

Then of course I don't get where 37 comes from. We take out 2, giving us 2(12^2-2*35^2). But obviously I'm going wrong here too somewhere. What is it I'm doing wrong?

leehuan · May 25, 2016

Re: MATH1131 help thread

Flop21 said:
Where is the 37 coming from?

https://youtu.be/t7nVFnFougM?t=21m34s

He does it at that point of the video.

But firstly I don't understand why -4*(-35)^2 becomes entirely positive? (-35)^2 would be +, then +*-4, would result in -. Or what am I doing wrong here?

Then of course I don't get where 37 comes from. We take out 2, giving us 2(12^2-2*35^2). But obviously I'm going wrong here too somewhere. What is it I'm doing wrong?

The negative doesn't belong in the square
It's -35² not (-35)²

leehuan · May 25, 2016

Re: MATH1131 help thread

Ohh ok that video is interesting

Here's that method broken down:
__________________
12^2 is MUCH smaller than 35^2

I conjecture that 12^2 + 35^2 is also a perfect square, like last time.
__________________
That value, say, x, is going to be much closer to 35^2

(We know already, of course that its 37^2)

So they basically recognised in advance that the answer (37) would be close to 35

So they end up solving this randomly generated equation: 12^2 + 35^2 = (35+u)^2

The purpose of using this equation is that 35^2 cancels out

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