help-13

[cedar kiln]

@zealous patio Has your question been resolved?

[wanton sail]

what's the difference between "residue of zero" and "no residue"?

yes you are correct, whenever n is odd or negative, the residue will be zero

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[tame heart]

So by u = a + x, I so far get to integral from a to a+T f(x-a) dx

But I don’t know how to change the f(x-a) to f(x)

Can anyone help

I know it’s a periodic function and I can imagine this statement is true in my brain but just can’t calculate it

[upper ruin]

Try using u = x - T instead

[tame heart]

Ohhh thx let me try

[upper ruin]

No wait yours is correct, because there are a's on the right

Sorry

[tame heart]

No worry, because the a is just a real number but not the period so f(x) is definitely not equal to f(x-a)

But in integration I know it is true

[worldly chasm]

Let a = u + kT for some integer k and u real in the interval [0, T)

[tame heart]

Let me see

I don’t quite understand

[worldly chasm]

(then you can use $\int_a^b f(x) , \dd{x} = \int_a^c f(x) , \dd{x} + \int_c^b f(x) , \dd{x}$)

[wraith dagger]

OmnipotentEntity

[tame heart]

Oh wait yes

OH

Thank you I know how to do now🙏

Thank you so much

❤️

[worldly chasm]

You're very welcome

[tame heart]

Ok cya

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[crimson sedge]

how that result follows from inequality?

[cedar kiln]

@crimson sedge Has your question been resolved?

[humble karma]

It's increasing, and since the sequence ln(2^n) isn't bounded, ln(x) isn't bounded either

[crimson sedge]

ohhhh

i see now

because we can take any lnx

and it will be not bounded

from above

may have lower bound

alr alr thats making sense now

🙏🏻 thank you

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[raven hornet]

Can anyone help me with proving that function is continous at 2 if x>0

With epsilon delta

I have no idea how to continue with the proof

[atomic chasm]

Should just be able to choose any delta greater than 2 right?

[raven hornet]

Idk this is what ige dine

ive done

I might be wrong

I wrote deinition wrong

I switched delta and epsilon placements

[atomic chasm]

Yeh, just choose an epsilon big enough to encompass the whole Uni step function. She’ll be right

Sorry, choose a delta

Don’t choose epsilon lol

[raven hornet]

Yea thats what ive done

One sec

So if i chose dwlta 0.1

What do i do next

What is difference between x and a

[cedar kiln]

@raven hornet Has your question been resolved?

[raven hornet]

I chose delta 0.1 and fixed a=2

Is it correct to do so?

Ok friends i gave up

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[icy wasp]

Hi ,so i got this question on my math test and i couldnt solve it :
root(x)(x-5)=2x-6

[vernal kite]

is the x * (x-5) all in the square root

or just the x

[slender ginkgo]

$\sqrt{x(x-5)} = 2x - 6$?

[wraith dagger]

k

[icy wasp]

no

only x

[vernal kite]

okay

[slender ginkgo]

$\sqrt{x}(x-5) = 2x - 6$?

[wraith dagger]

k

[slender ginkgo]

divide and then square?

[icy wasp]

that one

[icy wasp]

wdym

[slender ginkgo]

Divide both sides by x-5

With condition that x = 5 is not a solution

And then square both sides?

[icy wasp]

were gonna have x^3 at the end and i want it to be a x^2

[slender ginkgo]

Can’t u use rational root theorem after that

[vernal kite]

yes

i would say move everything to one side

[icy wasp]

x^3 - 14x^2 + 49x - 36 = 0

[vernal kite]

make it a polynomial

and factorise

but my method requires substituion

so idk if it makes it easier

[icy wasp]

my teacher solve like : x^3 - 14x^2 + 49x - 36 = 0 as we can see x=1 is a solution lmao

[slender ginkgo]

Yes

-36 and -14 makes -50

And u have +49 and +1

[icy wasp]

i know but it dosent make sense like how did u get 1 sould i try every x ?!

[vernal kite]

rational root theorem

[slender ginkgo]

Small x and then big x

[vernal kite]

test the factors of the first and last term

[slender ginkgo]

Try the ones that they’d probably use first

Like 1,2,3,-1,-2,-3

There are a lot for +36 and -36

But u get the idea

[icy wasp]

im not used to solve math like that like just guess what the x is

[icy wasp]

thx !

.cloes

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[woeful fractal]

Hey

[crimson sedge]

HI

[stable hull]

sup

[woeful fractal]

How good are you with probability?

[stable hull]

oh i suck at that

[woeful fractal]

rip @crimson sedge are you good

[stable hull]

everytime i try to find a conditional probability of an event, i somehow get something over 1

[woeful fractal]

lmao

i just did that with this question

[crimson sedge]

Probably

just send your question

[woeful fractal]

you roll a dice until you get a 6. given that you only see even numbers, what is the expected number of rolls?

so I did this and have the solution

you fin dhte probability that you roll a 6 given you only see evens

which is 1/4

and the probability of rolliung a 6 given this is 1/6 divided by 1/4 = 2/3

and the mean of this distribution is 3/2, so 3/2 rolls

I was doing the follow up question though and i'm unsure why you can't apply the same logic

follow up: you roll a dice until you get a 6. given that you see a 5, what is the expected number of rolls?

nah it's 3/2 look at the messages I sent after

wait are you in college or nah

cause I can also just open a help ticket later

all good then thx

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[crimson sedge]

ok.

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[midnight bramble]

Hi, got around to this question and im stuck on the last part of calculating IRR

[midnight bramble]

I believe all of the formulas are correct

Step 6)
I inputted that into my calculator but got a weird answer of 1.27?

[runic garnet]

why is that weird

@midnight bramble

200k = 100k(1+i)^-1 + 103k(1+i)^-2 + 106090(1+i)^-3 + 109272.7(1+i)^-4 + 112550.88(1+i)^-5

[midnight bramble]

Because i think it should be greater than NPV

[runic garnet]

huh? do u understand what IRR means

[midnight bramble]

i think so

[runic garnet]

its a rate

not a cash value

it doesnt even take the same units as NPV

[midnight bramble]

huh, i mustve misunderstood my teacher

did i use the correct FV and PV?

[runic garnet]

that formula doesnt make much sense to me

how is it possible to find PV if u dont have the rate

after all, we're solving for the rate

[midnight bramble]

present value would be the value £233,634.02 from the total row

i think at least...

[runic garnet]

right but thats using the discount factor which is on a certain interest rate

[runic garnet]

this is the equation we want to solve for IRR

do u understand how i got it

k means 1000 btw so 10k is just 10 thousand

[midnight bramble]

sorry for pestering even more, what does i mean?

[runic garnet]

no worries

i is the IRR

so im taking our reference point to be period 0

discounting every cash flow back to period 0

using our IRR 'i'

[midnight bramble]

for this line of working. would i be safe to use this ?

[runic garnet]

yes thats exactly what i did, except i brought that C_0 to the other side of the equation

I set inflows equal to outflows

they just did inflows + outflows = 0

[midnight bramble]

ahh ok, i understand now

[runic garnet]

u should get an IRR of around 43.5%

[midnight bramble]

thank you thank you!

I shall very quickly attempt a few similar styled ones with a calculator and write it down as i go just so i remember it

:)

[runic garnet]

no problem, have a good one 👍

[midnight bramble]

Sorry for being a bit dense... i would blame the lack of sleep but thats not a good enough excuse

im just not very good at understanding

well undertsanding a 1hr pure content slot

[runic garnet]

no need to apologize, the understanding comes with time

[midnight bramble]

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[midnight bramble]

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✅

[midnight bramble]

I quickly did some more of the same styled question and about 80% of the time got the right IRR

thanks again Stephen

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[astral mulch]

,rccw

[astral mulch]

1. is prove that f is continuous on that interval
   2)a) is prove that …
   b) is prove that…. f’(alpha) = 0 and f’(1/alpha) = 0

im struggling w b

[solid juniper]

[astral mulch]

i did it w the mean value theorem

but only the first part

i couldnt prove that f’(1/alpha) = 0

[astral mulch]

[cedar kiln]

@astral mulch Has your question been resolved?

[astral mulch]

can someone help please?

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[vestal stirrup]

if arranging terms, do you need to put the constant terms (?) in chronological order?
ex. arrange.
a) 2a - 7 + 8d + 13c - 9 + 12b
= 2a + 12b + 13c + 8d - 7 - 9?

[formal copper]

yeah

[vestal stirrup]

right then, ty.

[formal copper]

nw

[vestal stirrup]

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[jovial glacier]

I am confused, it looks like the last step here is to take the integral of nothing

[jovial glacier]

Is it correct to interpret these as the same?

[dire geode]

they are the same yes

dx = 1dx

[jovial glacier]

gotcha, thanks

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[autumn gate]

Hi. I dont really understand this. I have started with linear algebra and it is difficult to really understand everything. Can someone perhaps help me?

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@autumn gate Has your question been resolved?

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@autumn gate Has your question been resolved?

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[upbeat pewter]

hey yall i got a question. How can I solve for the central angle of this arc if I know angle A which is the angle between the tangent and a perfectly horizontal line and i also know that angle B is the angle between the tangent and a perfectly horizontal line

[cedar kiln]

@upbeat pewter Has your question been resolved?

[upbeat pewter]

?

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[spiral prairie]

what does the * mean?

just 0?

im guessing its like an integer overflow or smth

[dawn junco]

https://www.mathworks.com/matlabcentral/answers/551554-what-does-the-stars-in-the-result-of-a-matrix-multiplication-mean it's prolly that

@spiral prairie

[spiral prairie]

its for this

is it fine to just write 0 in place of the star

for the eigen vectors

ig ill just use format longg

[dawn junco]

yeah might be a good idea to see how small these * actually are

[spiral prairie]

yea its e-17

insanity

aight ty

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[topaz sundial]

I'm not sure how to do this problem, I know the formulas for the left endpoint riemann sum and right endpoint riemann sum. But how do I compute them on the interval [1,b] for a uniform partition?

[topaz sundial]

A friend showed me the second step, but I don’t know how she got there at all

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[cedar rapids]

Let S=span${1+x+x^2,2+x}$ \
find all values of $\alpha \in \mathbb{R}$ knowing that $(\alpha + 5)+x+(\alpha^2 - 5)x^2 \in S$

[wraith dagger]

ransik (gmdn)

[cedar rapids]

these results could be correct

but they don't really look like they are

we don't have the answers sadly

did i make a mistake somewhere?

i think up until the simoultaneous equation part everything is correct

[cedar kiln]

@cedar rapids Has your question been resolved?

[cedar rapids]

nope but for anyone looking into this im currently re-solving the system

all done

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[dusky furnace]

What is the name of the symbol pointed to by the arrow, and what does it mean?

[hollow trail]

it means "if and only if" (or iff for short)

[dusky furnace]

ah, got it.

Thank you

Somehow, I never saw a symbol for iff; only ever saw it written as the words or "iff".

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[rose cliff]

how is this 71

it should be 27

[vivid wadi]

context?

[vivid wadi]

you can't use isdigit to check if it's an integer

"-2".isdigit() is False

[rose cliff]

Oh k

do i jus do int(i) then

[vivid wadi]

that would throw an exception if the string is not convertable to int

you would need to do a try-except

[rose cliff]

Ok

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[harsh cypress]

heres a multiple choice question can someone tell me the answer and show me the step by step working out the did to get to the option they got to. thanks

[kindred storm]

We can't give you the answer outright, but we can help you to get it.

They have rules in that square box.

You have (P => P) <=> Q.

So, let's look at that.

You have P => P as part of it.

So, look at the two => rules.

One is contraposition. The other is implication elimination.

Contraposition doesn't get us any closer to CNF.

So, use the implication elimination one.

What does that say to do with P => P?

[cedar kiln]

@harsh cypress Has your question been resolved?

[harsh cypress]

-p v p?

[kindred storm]

Right.

[harsh cypress]

I thought I was meant to eliminate the bicondition first tho?

[kindred storm]

So, now you have:

(P => P) <=> Q
(!P v P) <=> Q

You can do it either way.

[harsh cypress]

Ah ok

[kindred storm]

If you want to do the biconditional, there's one rule for that.

[harsh cypress]

Yh it turns it into implications?

[kindred storm]

Right.

[harsh cypress]

Would I have to eliminate implications again after that

[kindred storm]

((P => P) => Q) v (Q => (P => P))

[harsh cypress]

Yh I got up to there

[kindred storm]

Yes, CNF is a product of sums.

So, you need (!x v y) ^ (y v z v a).

You have nots for variables.

You have ors inside of parentheses to connect the variables inside the parentheses.

[harsh cypress]

I get confused on what’s a and what’s b here

[kindred storm]

Oh, you start out with a <=> b.

So, a is what's on the left to start with.

Which is (P => P).

Then b is what's on the right, which is Q.

[harsh cypress]

So at this stage ( (p -> p)-> q) is a?

[kindred storm]

So, then we fill that in:

(a => b) ^ (b => a)
((P => P) => Q) ^ (Q => (P => P))

No, a is alpha in the rule.

You start out with a <=> b.

Then, you figure out what a is.

It's (P => P).

[harsh cypress]

Ok

[kindred storm]

Then, you figure out what b is.

It's Q.

Then, you write out the rule's right side: ((a => b) ^ (b => a)).

Then, you fill in what you figured out a is wherever you see a.

And the same with b.

[harsh cypress]

Now we do implication elimination again?

[kindred storm]

Yes.

((P => P) => Q) ^ (Q => (P => P))
(!(P => P) v Q) ^ (Q => (P => P))

We had (P => P) => Q, so a = (P => P) and b = Q.

Then, it says to change that to !a v b.

[harsh cypress]

Yh I’m with u so far

[kindred storm]

So, we fill in a and b to get !(P => P) v Q.

Then, you do that with the (P => P) in that.

[harsh cypress]

And what about (Q ->(p -> p)

[kindred storm]

The outer operation there is the => between Q and P => P.

So, use one of the => rules.

[harsh cypress]

So !p v p

[kindred storm]

No, you have Q => (P => P).

That's like a => b.

a = Q
b = (P => P)

Then, you apply one of the => rules.

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[kindred storm]

.reopen

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✅

[harsh cypress]

!Q v (p -> p)?

[kindred storm]

Right.

So, you have (!(P => P) v Q) ^ (!Q v (P => P))

[harsh cypress]

So a just means the thing b4 the operator/symbol and b is what’s after it?

[kindred storm]

Right.

[harsh cypress]

Ah ok

[kindred storm]

It's like a pattern.

If a pattern was a + b - c and you had (3 + 4) + 6 - 7, then a = (3 + 4), b = 6, c = 7.

Then, the right side is a pattern too.

You just fill in the a on the left side into the a on the right side.

And so forth.

[harsh cypress]

(!(!p v p) v Q) ^ (!Q v(!p v p))

Is that correct?

[kindred storm]

Yes, that's right.

[harsh cypress]

Now what do I do

[kindred storm]

OK, so what does CNF look like?

[harsh cypress]

Not sure😭

[harsh cypress]

Like one of these options ig😅

U still there @kindred storm ?

[kindred storm]

Yes, one moment.

[kindred storm]

OK, so CNF works with variables.

Like P and Q.

Those variables can have ! directly in front.

! can only appear right in front of a variable, not in front of parentheses.

So, we have either variables or negated variables.

[harsh cypress]

Oh ok so that HAS to be the case

[kindred storm]

Right, with CNF, that has to be the case.

[harsh cypress]

Ok got it

[kindred storm]

Then, we can v those variables together.

[harsh cypress]

So everything that’s out I just put in?

[kindred storm]

And put them in parentheses.

Like (A v B v !C).

The only thing that can happen inside of parentheses is variables being ved together.

Then, those parenthesized parts can be ^ed together.

[harsh cypress]

So( !!p v p) v q

[kindred storm]

Like (A v B v !C) ^ (D v F).

That's CNF.

You have (!(!P v P) v Q) ^ (!Q v (!P v P)).

[harsh cypress]

So ((!!p v p) v q) ^ (!q v (!p v p))

Is that correct

[kindred storm]

You're missing a parenthesis.

[harsh cypress]

Is it correct now

[kindred storm]

No.

[kindred storm]

This is correct ^

You changed a ! that applies to (!P v P) into a ! that applies to !P.

[harsh cypress]

Oh but u said we can’t have it outside the brackets? Is has to be in front of the letter?

[kindred storm]

Yes, but you have to follow the rules to change things.

Right now you have !(!P v P).

There's no rule that changes that to (!!P v P).

https://media.discordapp.net/attachments/903430334681608232/1309790144097816586/Image_22-11-2024_at_21.25.jpeg?ex=6742dca1&is=67418b21&hm=030d00e82922f35dbffb69ef387cc15b8eae098b01fad7aefe110d418ebe0bf4&=&format=webp&width=1972&height=904

[harsh cypress]

De Morgan rule?

[kindred storm]

Right.

[harsh cypress]

Isnt that what I did

[kindred storm]

No, notice the pattern.

You start with !(a v b) and you get (!a ^ !b).

The v changes to ^.

All terms inside get ! in front.

It basically flips everything.

v changes to ^ or vice versa.

And ! in front of all the things inside.

[harsh cypress]

So a already has ! So I don’t add another

[kindred storm]

No, it says to put a ! in front of a.

So, what's a?

[harsh cypress]

!p

[kindred storm]

So, you put a ! in front of a.

What does that give you?

[harsh cypress]

So !!p

[kindred storm]

Right.

It's very literal.

!a means put ! in front of whatever a is.

Even if it already has ! in front.

You just put another one in front of that.

[harsh cypress]

Ahh ok got it

[kindred storm]

Right, so we have ((!!P ^ !P) v Q) ^ (!Q v (!P v P)).

No, there's no ! on the outside of parentheses there, so you can't use DeMorgan's.

[harsh cypress]

Oh Yhh mb

[kindred storm]

OK, so we want it like (A v B v !C) ^ (D v F).

Do we have a bunch of variables ved together in parentheses and then the parenthesized parts ^ed together?

[harsh cypress]

Is this like a rule. CNF always looks like this

[kindred storm]

Yes.

[harsh cypress]

Ok I will it’s it down

Note it down*

[harsh cypress]

Ok so we r done with de Morgan now?

[kindred storm]

Yes.

[crimson sedge]

Is there tutoring here or it's a non tutoring discord

[kindred storm]

You can ask questions to get explanations and things like that. See #❓how-to-get-help for how.

[kindred storm]

Now what I notice is that the left side has an ^ inside parentheses where CNF only allows them outside of parentheses.

The right side only has v inside parentheses, which is fine.

Which one do you want to work on first?

Sorry, the right side has v inside.

[harsh cypress]

Let’s work on the left one

[kindred storm]

OK, so what rule fits (!!P ^ !P) v Q?

There are a few.

[harsh cypress]

Second to last

^ over v

[kindred storm]

You have v outside the parentheses and ^ inside. Which rule fits that?

[harsh cypress]

Ohh the last one v over ^

[kindred storm]

Right, but remember that everything is very literal.

The pattern there is a v (b ^ c), but you have (b ^ c) v a.

How can you fix that so that the pattern is exact?

[harsh cypress]

P ^ !p would turn into only !p?

[kindred storm]

Which rule does that?

[harsh cypress]

Lemme see

No clue sorry😭

[kindred storm]

OK, so we're at ((!!P ^ !P) v Q) ^ (!Q v (!P v P)).

You want to use the a v (b ^ c) rule, right?

[harsh cypress]

Yh

[kindred storm]

OK, so like I said, it's very literal.

You have (!!P ^ !P) v Q.

The rule says a v (b ^ c).

Do you see how (!!P ^ !P) v Q is like (b ^ c) v a?

[harsh cypress]

So we don’t use that rule?

Cos it don’t fit?

[kindred storm]

We use that rule.

[harsh cypress]

Why? The Rule says a v (b ^ c) and we have (b ^ c) v a

[kindred storm]

Right.

Do you see how (!!P ^ !P) v Q is like (b ^ c) v a?

[harsh cypress]

Yes

[kindred storm]

OK, do you see what rule you can use to change that to a v (b ^ c)?

[harsh cypress]

Honestly no I don’t see the rule sorry😭

[kindred storm]

Look at the second rule.

What does it allow you to do?

[harsh cypress]

(A v b) = (b v a)?

[kindred storm]

Right. It allows you to swap the sides of an v.

And if you use it on (b ^ c) v a, what do you get?

[harsh cypress]

(A v c) v b? Or is it (a v c) ^ b. One do them?

[kindred storm]

No, look at the rule.

It allows you to swap the sides of an v, right?

[harsh cypress]

Yh b a switches

[kindred storm]

Right, so with (b ^ c) v a, look at the v.

What's on the left side of v?

[harsh cypress]

Ohh it’d be a v (b ^ c)

[kindred storm]

Right.

So, with (!!P ^ !P) v Q, you can use the second rule to give you Q v (!!P ^ !P).

[harsh cypress]

Yh

[kindred storm]

Then you can use the last rule.

[harsh cypress]

So (a v b)^(a v y) is what I’m tryna get

[kindred storm]

Right.

[harsh cypress]

What’s ‘y’?

A rn is Q and b rn is (!!p ^ !p)

But what’s y

[kindred storm]

OK, look at the pattern.

It's a v (b ^ c).

You have Q v (!!P ^ !P).

What's a there?

[harsh cypress]

Q would be a there

[kindred storm]

What's b?

[harsh cypress]

(!!p ^ !p)

[kindred storm]

OK, look at the pattern.

[harsh cypress]

Ohh no

It’d be !!p

[kindred storm]

Right.

[harsh cypress]

Cos a we have a c

[kindred storm]

So, what's c?

[harsh cypress]

!p

[kindred storm]

Right.

Now, fill those into the pattern on the right side.

[harsh cypress]

(Q v !!p) ^ (Q v !p)

[kindred storm]

Right.

[harsh cypress]

I got this now

[kindred storm]

So now we have ((Q v !!P) ^ (Q v !P)) ^ (!Q v (!P v P)).

[harsh cypress]

Yh

So now what I do

[kindred storm]

OK, so we can simplify the parentheses a bit.

(Q v !!P) ^ (Q v !P) ^ (!Q v !P v P)

[harsh cypress]

Ok got it

[kindred storm]

Now remember how ! could only appear in front of variables?

You have one ! that appears in front of something that's not a variable.

[harsh cypress]

Ahh the ! Is in front of another !. ! Isn’t a variable so we gotta get rid of it

[kindred storm]

Right, so which rule can you use?

[harsh cypress]

I was thinking Double negation elimination? But what we have rn it’s all inside parenthesis

[kindred storm]

Yes, you should use that.

[harsh cypress]

Ok so I use it when I have ‘!!’ Does it matter when this step is done

[kindred storm]

Yes, you can use it whenever you have !!.

[harsh cypress]

Ok so (q v p)

[kindred storm]

Right.

Now there were some steps I skipped over.

They involve the associative and commutative rules.

But you should be able to see which answer is correct.

[harsh cypress]

Oh ok so from what I have now I can choose one of the multiple choice options

[kindred storm]

Right.

[harsh cypress]

(Q v P) ^ (Q v !P) ^ (!Q v !P v P)

Sorry just writing it down

Gna check the options now

It’s not any of them😭

[kindred storm]

This is a bit like basic algebra.

You can rearrange things, for example.

Like a + b + c can become c + a + b.

See if there's an answer that's suitably rearranged from yours.

[harsh cypress]

Ok

[harsh cypress]

Is it a?

[kindred storm]

Yes.

[harsh cypress]

Ok so in the end I gotta see if it has all the variables I have with their operators

Just different order

[kindred storm]

Right, v is like addition and ^ is like multiplication.

So, (q + p)(q - p)(-q - p + p) = (p - p - q)(-p + q)(p + q)

It's like that.

[harsh cypress]

Ok thank you this was extremely helpful I will go over what we went thru a few times again in my own time

[kindred storm]

You're welcome.

Just be aware that to do the rearrangements, you need to do some busywork with the associative and commutative rules.

We didn't really cover that here.

[harsh cypress]

Yh this is quite a long question😭

But if I skip those I can still get the option tho

Like we did

If so than I’d prolly skip them to save time in the exam

[kindred storm]

Yeah, if it's multiple choice, you just need to do enough work to figure out the answer, you don't have to do all the work.

One early clue was that CNF has v inside parentheses and ^ outside, and only two answers have that.

So, you can throw away the other two.

[harsh cypress]

Yh thanks again was just screen recording. That’s ok right

[kindred storm]

Yes, that's fine.

You can also get a message link and go to it later.

Like <#help-13 message>

[harsh cypress]

Yh I’m just gna write it down the working out cos I did all this on my phone n In bed😭

[kindred storm]

Oh, OK.

[harsh cypress]

Thanks

[kindred storm]

No problem.

[harsh cypress]

.close

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[cedar kiln]

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[violet owl]

weird 3d triangle

[solid juniper]

T-T

[violet owl]

hey!

[solid juniper]

[violet owl]

thoughts?

[solid juniper]

my thoughts are T-T

[violet owl]

oh lol

[cedar kiln]

@violet owl Has your question been resolved?

[nimble veldt]

express PQ and PR as vectors and then the area of the triangle through this vectors. should give you a function in t.

[violet owl]

how do i do area like that?

I just found the length of the lines (which are equal right?) and am going to find maximum for the equation

then i can do normal triangle formula

[nimble veldt]

https://www.maths.usyd.edu.au/u/MOW/vectors/vectors-11/v-11-7.html

[violet owl]

i know it isnt a proper method but it that ok?

ohhhh thank you!

how do i do this with unknowns?

[nimble veldt]

what is "this"?

[violet owl]

like cross product

ive only done it on a calculator

one sec ill look it up first

is it cross product of just timesing the length?

[cedar kiln]

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[earnest fog]

im stuck on q18 bi

I alr hv the domain but I’m stuck on finding the range

this is what I hv so far

I’m not sure how to find the vertex as it’s still algebraic

[dreamy void]

What's the range of f(x)?

[earnest fog]

oh hi it’s u again!

f(x) is larger or equal to -1/8

for range

why does it also apply to the range of fg(x)

im confused

[dreamy void]

ok see

1/x can be any number except for 0

[earnest fog]

yes

[dreamy void]

so basically you can already say that f(1/x) will have the same image except for one value that you need to check

that is f(x) = 0

like f(0) = 0 but we ask now what about f(1/x) = 0 as well

right now we can only say so far image of f(1/x) is the same image of f(x) without 0 since x != 0 now

so I would check f(1/x) = 0 if there is a non 0 solution and if there is then they have the same image

[earnest fog]

ok

I see

I get like 80% of this

[dreamy void]

well 20 % is luck

[earnest fog]

haha

Lemme check the value first

hol up

how am I suppose to check f(1/x) = 0

[wraith dagger]

𝔸dωn𝓲²s

[dreamy void]

So there is a non-0 solution so 0 is also part of the image of f(1/x)

that is for x = 2 now

[cedar kiln]

@earnest fog Has your question been resolved?

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[solid sage]

I've considered the a^3 +b^3 factorisation

[opaque root]

What are the instructions?

[solid sage]

rationalise denominator

[opaque root]

Use subtitution

Notice $36 = 6^2$

[wraith dagger]

Samuel

[opaque root]

Do you know the difference of cubes formula?

[solid sage]

yes

[opaque root]

Write here

[solid sage]

a^3 - b^3 = (a-b)(a^2 +ab + b^2)

[opaque root]

In the denominator which part of the difference of cubes u have?

[solid sage]

is it (a^2 +ab + b^2)

[opaque root]

So u need to multiply and divide by…

[solid sage]

a-b

[opaque root]

And a and b are

[solid sage]

6^2/3 and 6^1/3

[opaque root]

No

Check better

a^2 is cube root of 6^2

Try again

Remember we look for a, not a^2

[solid sage]

b = 1 a = 6^1/3

[opaque root]

Good

So now you multiply and divide by a-b

And you are done

[solid sage]

ty

/close

$close

!close

close

.close

[cedar kiln]

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[solid sage]

?close

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[ornate rune]

,rccw

[ornate rune]

How do u get rid of the absolute values

[ancient lodge]

https://math.stackexchange.com/questions/1118400/trig-substitution-why-can-we-ignore-the-absolute-value

You’re looking for this

[cedar kiln]

@ornate rune Has your question been resolved?

[ornate rune]

alr ill check that out

[cedar kiln]

@ornate rune Has your question been resolved?

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[torpid cargo]

can someone help me with my PDF? honestly i have a test tomorrow and i don't have much time to solve it and it's useless

[torpid cargo]

it's 15 questions of Functions and Transformation of functions

[sonic thicket]

Which question do you need help with? What did you try?

[torpid cargo]

i honestly didn't try any because i don't have time (bio test tomorrow)

and the assignment is due today

[cedar kiln]

@torpid cargo Has your question been resolved?

[cedar kiln]

@torpid cargo Has your question been resolved?

[cedar kiln]

@torpid cargo Has your question been resolved?

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[midnight bramble]

Could someone recommend me a video about PDF's (Probability density function)

[midnight bramble]

I have been trying to find a way to calculate the height of a PDF at any given point but i cant seem to find any notes

[long swan]

the height of the pdf is just the y value?

lol?

[midnight bramble]

What if we arent given the y value

For example

[long swan]

the pdf is a function

[midnight bramble]

Find height (Y value) at x=0

[long swan]

just plug in the x value to obtain the y value

[midnight bramble]

I may have forgotten how to do that, could you give me an example please?

.close

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[west edge]

really confused with this question, dont know where to start

[astral leaf]

by any chance are u doing a levels further math

[dreamy void]

Is the a part missing on the right? Also for the other part you can use IVT.

[cedar kiln]

@west edge Has your question been resolved?

[west edge]

i dont think so

ill check rq

[west edge]

yep lol

[carmine bronze]

He's talking about this part. Is that all there is or is a part missing?

[astral leaf]

i js finished my a lvl papers lol

[west edge]

its just a comma after

[astral leaf]

try using gc to see how ur curve looks like

[west edge]

graphing calc?

[astral leaf]

yes

[west edge]

wait

ignore the scribbles

p would be like there

i think i got here before

just no idea what to do with the tan and stuff

[astral leaf]

what’s the gradient of the tangent to the curve at point P

@west edge

[west edge]

idk

like

[astral leaf]

as u can see

it’s parallel to the line theta = pi/2

[west edge]

yh

[astral leaf]

try finding gradient function of the curve

using dy/dx btw

[west edge]

so convert it to cartesian first

[astral leaf]

don’t need to

[west edge]

alr

anyway wouldnt it be undefined in cartesian

[astral leaf]

hint:
x=rcostheta
y=rsintheta

[astral leaf]

yes

exactly

use parametric

dy/dx = (dy/dθ) / (dx/dθ)

[west edge]

dont think ive done that yet, let me look it up

[astral leaf]

try

it’s pretty simple

[astral leaf]

here u go

r’ is basically dr/dθ

[west edge]

alr

[astral leaf]

u know how to make it undefined right

[west edge]

icl i have no idea whats going on

[astral leaf]

also for the second part, have u learnt numerical methods?

[west edge]

dont think so

im in y12

doing maths and fm at same time

so i have a fair amount of gaps

[astral leaf]

ohh

what country u from

[west edge]

the uk

[astral leaf]

ohh

[west edge]

but doing cie for some reason

[astral leaf]

shi i’m in singapore js finished everything

u know how to get dr/dθ?

look at ur original equation

@west edge first differentiate ur original equation to get dr/dθ

[astral leaf]

then plugin this formula

[west edge]

ohh

[astral leaf]

this formula can be derived easily so i don’t think u need to officially learn it in lessons

[west edge]

product rule right

[astral leaf]

yessir

[west edge]

-(theta)sin(theta) + cos(theta)

[astral leaf]

yes

[astral leaf]

use this formula

plugin dr/dtheta and r

[west edge]

ohhh

[astral leaf]

u want the gradient to be undefined right

this is a fraction

what’s an easy way to make the fraction undefined

[west edge]

alr

[astral leaf]

got it yet?

[west edge]

still plugging stuff in

[astral leaf]

alright

[astral leaf]

when u plug them in u realise there’s a big fraction correct

[west edge]

yh

[astral leaf]

how do u make a fraction undefined

easy way

since ur desired outcome should be undefined gradient

[west edge]

get its denominator to 0?

[astral leaf]

yessir

now it’s just manipulation

and u should be able to get the question requirement

[west edge]

alr

thank u so much

[astral leaf]

yep no problem

second part there’s a very easy way to do it

[west edge]

i think i get it now

[astral leaf]

u haven’t learned numerical methods right

[astral leaf]

alr nice

[west edge]

nah, ill see when i do

[astral leaf]

this method is essentially making use of change of sign

let’s say a graph is continuous

and let’s say there’s an interval which contains the root

if u plugin the interval bounds into the function, you’ll notice one will be negative and the other positive

which implies there exists a root in that interval

[west edge]

alr

[astral leaf]

the presentation is
let f(x) = …
f(a) = … > 0
f(b) = … < 0
since f(x) is continuous in the interval [a,b], there exists a root in the interval [a,b]

[cedar kiln]

@west edge Has your question been resolved?

[cedar kiln]

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[still crystal]

help, how get DC?

[lusty pawn]

first find BD

[still crystal]

i did its 4

[lusty pawn]

use trig

[still crystal]

how

[lusty pawn]

tan pi/6 = BD/CD

Put values of tan pi/6 and BD

then solve for CD

[still crystal]

yeah no clue

[lusty pawn]

you just got BD =4

[still crystal]

yes that was easy

[lusty pawn]

what's the value of tan(pi/6) ?

[still crystal]

u want me to put that in a calculator

[lusty pawn]

so you don't know it

nevermind calculator will give you a hell of decimal expansion

[still crystal]

yes

[lusty pawn]

i suggest you remember the trigonometric values of some important angles

tan(pi/6) = 1/sqrt(3)

nso we get BD/ CD =1/sqrt(3)

put the value of BD and find CD

and you're done

[still crystal]

what

[lusty pawn]

just solve the equation

to find CD

[still crystal]

so um uh

yeah no clue

[lusty pawn]

do you know how to solve an equation

?

[still crystal]

yes probably

[lusty pawn]

ok now just write 4 instead of BC here

[still crystal]

4 / cd = 1sqrt(3)

cd is an x?

[lusty pawn]

yeah

and also 1/sqrt(3)

[still crystal]

oh

how u solve that one

[lusty pawn]

isolate x

[still crystal]

yes

does that mean you push numbers to right and x to left

[lusty pawn]

yeah

[still crystal]

cd = -4/ 1/sqrt(3)

this good?

@lusty pawn

[lusty pawn]

why - sign?

[still crystal]

when it goes over the sign equal it becomes negative no?

or should i just do

1/sqrt(3) - 4

[lusty pawn]

no

sign changes only whe adding or subtracting

here it is multiplication and division

so sign does not change

[still crystal]

ok so

4 / 1/sqrt(3)

and that will get me cd

and then i can solve for bc

with pythagora

[lusty pawn]

yeah

[lusty pawn]

you can smiplify further

[still crystal]

how did u get this

[still crystal]

ye calculatorgivesme 4sqroot3

[lusty pawn]

yeah

[lusty pawn]

unit circle

[still crystal]

are u sure its 1/ sqroot3

i turn it into degrees and put tan(30)

and get 3/sqroot(3)

[lusty pawn]

i am ded sure tan(pi/6) is 1/sqrt(3)

[still crystal]

erm

calculator also gives that

which left me a little confused

pi / 6 in degrees is 30

[lusty pawn]

yeah √3/3 is the same as 1/√3

[still crystal]

oh

ye it is

thanks

i gotta go nwo

[lusty pawn]

ok

close the channel

[still crystal]

how

[lusty pawn]

.close

[still crystal]

.close

[cedar kiln]

Channel closed

Closed by @still crystal

Use .reopen if this was a mistake.

[broken garnet]

they banned me from tsb😭

[lusty pawn]

bro this ain't gen chat

go to general chat

[cedar kiln]

Available help channel!

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[spice pasture]

If a bullet goes at a speed to a target and every second its speed gets devided by 2 an infinite amout of time, can it reach the target? Is it right to say it will take infinite time to reach it? like the bullet goes at 1 meters / second speed and the target is at 10 meters away.

[spice pasture]

also there is no gravity no nothing that can stop the bullet

[cedar kiln]

@spice pasture Has your question been resolved?

[cedar kiln]

@spice pasture Has your question been resolved?

[spice pasture]

.close

[cedar kiln]

Channel closed

Closed by @spice pasture

Use .reopen if this was a mistake.

[cedar kiln]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[empty locust]

can someone please check on my working

[empty locust]

these are the parts 1 and 2

and this is my solution

[cedar kiln]

@empty locust Has your question been resolved?

[cedar kiln]

@empty locust Has your question been resolved?

[cedar kiln]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[worldly chasm]

I was just in your thread a moment ago. Thinking about this, when I noticed you closed it. Please don't clopen your threads.

!noclopen

[cedar kiln]

Please don't repeatedly close and claim a new channel with the exact same question. This erases all previous progress made towards your problem and is confusing for helpers, making it more difficult to help you. Please be patient, even if your channel has not received much attention.

[glad dust]

thats completely my bad sorry

[worldly chasm]

now because I've context switched I have to start over again.

[glad dust]

i apologize

[worldly chasm]

It's fine. Just a little bit frustrating.

i have to draw its state diagram as well so i've kinda boiled it down to these informal instructions to guide me:

Go all the way left. go right until finding a 2. mark it with x and go back left to the beginning.

Go right until you find two 1's. mark each with y. go back left until beginning. This process is
repeated for all 2's in the input string unless no unmatched 1's remain, in which case transition
to the accpet state and halt.

from the beginning go right. if no unmatched 1's remain, transition to the accept state and halt.
if any unmatched 1's remain, transition to the accept

from previous thread.

[glad dust]

sorry like 7 hours had passed so i kinda figured it fell too far

didnt think anyone would be working on it by then

[worldly chasm]

No such thing, I just got online and I always look through the old threads.

[glad dust]

youre very appreciated i will keep that in mind for the future

[worldly chasm]

I just generally figure that if the thread is old, then there's no urgency, so I typically try to think it all of the way through before answering.

[glad dust]

yeah that makes complete sense

ill stop bothering now feel free to take your time

[worldly chasm]

So let's be explicit. The Turing machine will have 5 symbols, we can name them 0, 1, 2, x, _. The string is initially filled with _ except for the string being tested, and we start with the head at the beginning of the string WLOG. (We can simply put the head to the beginning of the string by performing a search left and right until we read a non _ character, and then follow it to the front of the string once found.)

Your proposed algorithm will start in state A. Move right until a 2 is found, transition to state B and write an x. Go back to the beginning, transition to state C, move right until a 1 is read, overwrite with an x and transition to state D, which is the same as state C, continue on find another 1 and overwrite with an x, transition to state E. If we reach the end of the string and read a _ in states C or D then we have finished and proven that the number of 1s is less than twice the number of 2s. This is a halt success state.

Or I guess we can output success by transitioning to state S, move right once and write a 1. So we will have __00xx020x0x0_1_ on the tape or similar.

then half after writing a 1.

if we fall off of the end of the tape in state A then that's a failure.

(this is why I suppose exactly twice is treated as a failure. Otherwise handling the case where it's exactly twice would be a little bit tricky.)

@glad dust Does the above make sense?

[glad dust]

oh yeah marking 1's specifically with y is unnecessary considering we never use the markings. The first message regarding the algorithm makes sense but I'm confused on the 2nd one.

[glad dust]

What is state S? I don't think im too sure I understand what you're trying to say, is the 1 what my current algorithm is doing?

[worldly chasm]

state S for success

[glad dust]

ah

[worldly chasm]

to write the 1 after the end of the string to indicate it passed.

and then halt. Rather than just halting.

[glad dust]

is that necessary? i do not understand why

[worldly chasm]

It's nice to have some sort of output. Though if you have some other method of communicating success or failure then it's not necessary.

(such as a halt-true or halt-false state)

[glad dust]

additionally, im a little confused on whether youre saying my algorithm is properly functional or not

[worldly chasm]

It's properly functional

[glad dust]

i do not so i will keep that in mind

[worldly chasm]

it just needs you to make it explicit.

I did that kinda sorta here

But in order to make it properly explicit you need to implement the state transition matrix.

and the write matrix.

[glad dust]

thank you, is it not necessary to mention any of the interactions with 0 in my explanation? i understand because it doesnt fit the requirements it can be anywhere but should i add a sentence in each state's equivalent to say "continue left/right if 0"

[worldly chasm]

Essentially, the interaction with 0 will be continue moving left/right, write a 0, and do not change state.

It's a "noop"

you do need to explicitly write it.

[glad dust]

i see, so by being "explicit" youre saying to specifically identify the differing states and how the tm should traverse between them?

[worldly chasm]

yes.

[glad dust]

okay that makes sense

[worldly chasm]

You can do this via 3 matrices

a state transition matrix, a write matrix, and a move matrix.

[glad dust]

is it wholly necessary even in the context of just "giving a description of a turing machine"? my professor didnt provide that himself in the lecture examples

[worldly chasm]

well, if your professor isn't interested in the explicit turing machine state transition tables, etc. then a written explanation will suffice; however, making it explict does allow you to actually test your ideas.

https://turingmachinesimulator.com/