help-33

[unreal marsh]

?

[vestal forge]

it's like "why do wear a red pants?" "I like to"

[unreal marsh]

Btw thanks for clearing up that concept

[vestal forge]

the channel

and it's bri, autocorrect there

[unreal marsh]

Okay clears it up

Thank you

.close

[marsh citrus]

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[marble shoal]

yep

i wouldn't like dividing something by 0

[cloud iron]

Correct, because then you will be able to solve when the change in the values is zero, which we can't do if zero would appear in the denominator

[still temple]

more generally, when $f(h)$ is continuous at 0, $\lim_{h\to 0}f(h)=f(0)$ (treating $x$ as independent)

[elfin berry]

Toby

[still temple]

(and recall that polynomials are continuous)

[marsh citrus]

@open kayak Has your question been resolved?

[marsh citrus]

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[swift folio]

Need help with number one, I started with equation 3(1/x)+2(1/x+4)=1 and got different answer

[swift folio]

Need help quickly..

<@&286206848099549185>

[marsh citrus]

Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.

[hidden plaza]

You should get the same answer.

[swift folio]

I tried with myself and photo math and both got -3,4 since they should be positive numbers the answer should be only 4

But there's 8

[hidden plaza]

It says 4, 8

[swift folio]

Yea I meant to say 8

[hidden plaza]

Well the smaller number is 4

The bigger is 8

[swift folio]

Oh wait I'm dumb

Thanks for help

[hidden plaza]

[swift folio]

.close

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[marsh citrus]

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[sweet kiln]

Hello! I cant figure out what formula to use for the following question:
Disassemble the v Vektor (1,2,3) into 2 components, a vector perpendicular to a=(2,1,2) and into a vector parallel to b=(1,1,2)
I do know that for v to be perpendicular to a, v(point)a=0

[clever wharf]

maybe draw it first

[sweet kiln]

its a 3d space though, will drawing it in 2d help?

[clever wharf]

you can draw a 3d vector on a paper 🙂

[sweet kiln]

okay! let me try out

[clever wharf]

,rccw

[sweet kiln]

Sorry! Discord posts my pictures sideways, no matter how I take it

[clever wharf]

so you know the property of perpendicular vector. do you know the property of a parallel vector?

[sweet kiln]

axb= 0

where x is "cross product" and not a normal multiplication

[clever wharf]

ok, so we have three equations right?

with three coordinates (unknown variables)

[sweet kiln]

3 equations? a.v=0 and b x v=0

v · b = |v| |b| is this the 3rd one?

[clever wharf]

no, it's from the first sentence

decompose

[sweet kiln]

so v will be vk where k is an unknown scalar number? Though thats not really a full equation

I guess the 3rd one is V= Va+Vb (the 2 new components?)

[marsh citrus]

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[golden gulch]

hi! help, im confused on the wording— what exactly should i be looking for and hpw do i do it

[marsh citrus]

@golden gulch Has your question been resolved?

[marsh citrus]

@golden gulch Has your question been resolved?

[marsh citrus]

@golden gulch Has your question been resolved?

[golden gulch]

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[calm token]

Hello

[calm token]

Is this a valid proof that all cauchy sequences are bounded?

[marsh citrus]

@calm token Has your question been resolved?

[marsh citrus]

@calm token Has your question been resolved?

[bitter dawn]

No because n and m vary

You may want to fix $\epsilon$ and $N$

[elfin berry]

black_couscous

[marsh citrus]

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[marsh citrus]

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[fair flume]

Can someone tell me how to find common ratio in this formula

[main idol]

4-3x is the common ratio

[fair flume]

Is that always true

Like

Whatever is to the power of k

Is the common ratio

[main idol]

Usually yea

[fair flume]

Thanks

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[sand pewter]

I'm trying to figure out the convergence of the sequence q^n for each of its different cases
but I'm unsure about the case q=1 because that becomes 1^infinity after taking the limit
if infinity is real, it's indeterminate, but it seems that 1^infinity is 1 if infinity is rational

so what's the right answer for 1^n if I'm dealing with a sequence?

[crystal lintel]

that's just a sequence of 1s

it converges to 1

[sand pewter]

But 1^infinity is an indeterminate form

[crystal lintel]

so what?

[sand pewter]

That would mean it doesn’t evaluate to one- it doesn’t exist

[crystal lintel]

how??

I'm not saying it's 1 because when you plug in infinity for n you get 1^infinity which is 1 or anything

it's 1 because the sequence is 1,1,1,1,1,1,1,...

which converges to 1

seeing an indeterminate form just says something like plugging the limit point in doesn't help you find the limit

[marsh citrus]

@sand pewter Has your question been resolved?

[sand pewter]

oh ok

[marsh citrus]

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[sand pewter]

ty

[marsh citrus]

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[timber kiln]

Hello i have a question why its 3i? the understanding of i is for the negative hpwever i cant understand why its 3i and 3/2

[keen steppe]

It can be arranged in any product form you like

[timber kiln]

i is just to get the negative out right

so i is like -1 *

how do u get 3i 3/2 at the end though

<@&286206848099549185>

[marsh citrus]

@timber kiln Has your question been resolved?

[marsh citrus]

@timber kiln Has your question been resolved?

[spark berry]

I mean 27 is just 3^3 right?

So you're only just getting 3^2 out of the square root

So a 3 is left behind

like 27 is 333

[timber kiln]

yea

i see that part

how about the denominator?

because 3/1?

[spark berry]

Just the same

I mean if you want to you can remove the radical symbol at 2, but all in all it's already correct if your teacher doesn't specify to remove the radicals at the denominator

[timber kiln]

seems rather complicating to remember is this required to do?

[spark berry]

Nah it's not

I mean, why memorize it?

[timber kiln]

Okay thanks for the info

yes thats true

[spark berry]

Just remember the fundamentals

[timber kiln]

my answer is correct also

[spark berry]

Yes it is

[timber kiln]

thanks

[spark berry]

I think you're not used to dealing with radicals

[timber kiln]

im studying math on my own thats why

never had this in school

[spark berry]

I see, if you're having any troubles you can just message me again

Hope that I helped you

[timber kiln]

Awesome thanks for the info it makes sense now

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[gleaming lance]

henlo

[gleaming lance]

can someone help me with integral test for series and sequences

how do I know that this is decreasing when it has no critical point

[hidden plaza]

f(n) is continuous, positive and decreasing for n>=1

[gleaming lance]

i did this

as a reasoning why it is decreasing

im not sure if it is valid

[hidden plaza]

Just differentiate

[hidden plaza]

This probably works but I’d differentiate

[gleaming lance]

okok thanks, i think i got it now

thanks again!

.close

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[hidden plaza]

[marsh citrus]

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[bright viper]

How do i prove this?

[marsh citrus]

@bright viper Has your question been resolved?

[marsh citrus]

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[flat junco]

what happens when automata is in state q_a and reads a ?

[stoic saddle]

it seems not to be specified.

is this automaton given to you in isolation or is it supposed to solve a specific problem?

[flat junco]

should generate this language

[stoic saddle]

right, so it's the language of all strings that contain the sequence ab somewhere in them.

in that case, it seems to me that reading a while in q_a should make you stay in q_a.

ie this

actually no

this

because otherwise there is ambiguity as to whether we should proceed to q_a or stay in q_ε when reading a in q_ε

[flat junco]

this one is deterministic, am i correct?

[stoic saddle]

yes

@flat junco i thought you were only dealing with deterministic automata, though i guess you didn't specify

[flat junco]

i'm dealing with both, that one i posted was NFA

[stoic saddle]

right

it still left the possibility for UB though

which i think is not allowed even for NFAs

[flat junco]

what is UB ?

[stoic saddle]

undefined behaior

behavior*

the specification of a NFA still needs to tell you to go SOMEWHERE for every state-symbol combo

[flat junco]

hmm, i think that is allowed (at least in my course), but im going to read more about that

still dont know when is appropriate to construct a NFA or DFA

[marsh citrus]

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[high pine]

that sigma is sum or what

[quick agate]

sigma is sum

Please, can anyone help me to solve this derivative? I have tried in several ways, but I couldn't get the correct answer. I know how to solve using the chain rule. But, I don't want a solution using the chain rule.

[marsh citrus]

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[sage igloo]

Hello, I have to calculate a limit and since this topic is new to me, I have no idea on how to get the result of the book

[sage igloo]

This is what I did so far:

Now I mean, if you substitute 0 to x,,,like isn’t the tangent of 0 = 0?

[high pine]

it's not equivalent

to tan(tan(x))

[sage igloo]

So why is the answer plus infinite?

[sage igloo]

Ah

Hhhh then I have no idea on what to do

[crimson frost]

Try substituting your original equation with closer and closer values to 0

and see what happens

[sage igloo]

Alright

Oh

It should be 0/1 approximately

So
No wait

[crimson frost]

[sage igloo]

I meant 1/0 sorry 😭

I exchanged the sin with the cos for a moment

[high pine]

in fact it's enough to examine sin(sin(x)) value for x closer to 0, since the numerator is cos(1) > 0

aka

$$\Big[\frac{\cos (1)}{0^{?}}\Big]$$

[elfin berry]

Modus

[sage igloo]

That’s infinite

Alright I got it

[high pine]

yes but + or -

it depends on the denominator

[sage igloo]

It should be 0+

I think

However I don’t understand how I should “write” this

Because this exercise was in a section where the exercises were all like these (with exponentials)

And they were like this

But I had to solve it by substituting the ^x with t

And since it’s in the same section

[high pine]

I'd do:
$$\lim_{x \to 0^+} \frac{\cos (\cos x)}{\sin (\sin x)} = \Big[\frac{\cos (1)}{0^{+}}\Big]=+\infty$$

[elfin berry]

Modus

[sage igloo]

Do I also have to use a t to show how to solve it?

[sage igloo]

Oh alright !

Thank you so much @high pine and @crimson frost

[crimson frost]

I didn't really help that much ty modus

[sage igloo]

.close

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[high pine]

you can make a system of equations

then solve for x - coord and square of radius

[viscid oak]

.close

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[unreal marsh]

Hi one question. Should I learn geometry (after algebra 1) before going into kinda calc 2 stage? If so, what do you learn in geometry snyways

[wet zenith]

I barely know any geometry and it hasnt been a problem in calculus yet

[unreal marsh]

Okay

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[opaque arch]

The angle of depression of a precinct from the top of a building that is 72 m high is 40°. How far is the precinct from the building?

[clever wharf]

draw it and it'll be clearer

[opaque arch]

thanks, ah wait i have to go to bed it's like 1 am here

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[prisma hawk]

..

[prisma hawk]

im in no. 5

[pale brook]

I am lost on what I am supposed to do here, I am also using a TI-84 for this if it is necessary.

[marsh peak]

For 5 find dy/dx using implicit differentiation

[pale brook]

college level stuff 💀

[charred edge]

z score I think

nvm

[pale brook]

ohhh so za/2??

ohhh

okay sorry

[charred edge]

I'm in stats but

[pale brook]

its like i dont know how to find the minimum number

[charred edge]

I'm bad at stats

[pale brook]

not much context at all

ik

[prisma hawk]

yeah, after what should i do

[pale brook]

stats isnt fun mate

[charred edge]

I like stats I'm just a moron lol.

[pale brook]

i know how to turn the c level into decimal

thats all i know to do

[prisma hawk]

@marsh peak like do i set them equal to eachother?

[pale brook]

like 2.54? i think

[charred edge]

So this is the bell curve right

[pale brook]

lemme check

[charred edge]

@pale brook It says 99% so it needs to be within 3 deviations

[pale brook]

-2,58

WAIT

[charred edge]

2 stdevs

[marsh peak]

And set it equal to 0*

[pale brook]

wait wouldnt 95% BE 2 SDEVS?

sorry for caps

[prisma hawk]

okay i got y = -2x @marsh peak

[charred edge]

Yeah 2.58 is 2 stdevs. 99% is 3 stdevs

[marsh peak]

Plug that into the first equation that you have in the problem

[charred edge]

I was talking abt your answer

[pale brook]

but when .99 is turned into a z score its 2.58

im los

[marsh peak]

You'll be able to solve for x and y, which are the coordinates of the points

[pale brook]

lost*

[prisma hawk]

yup, answer was sqrt (24/13) for x @marsh peak

but like i dont think thats right

[charred edge]

So 2 stdevs is 95

[pale brook]

right

[marsh peak]

Show your work then

[pale brook]

3stdevs is .99

so .99-1/2 is -.005

[charred edge]

Hmm it might not be z score I'm horrible at stats I'm more working with you than helping you lol

[pale brook]

no youre helping me break it down thankks

i have sm more harder shit later down the road

im just taking it one step ata time

[charred edge]

Wait so the crit value is 2.58 right

[pale brook]

its similar to a z score

[prisma hawk]

@marsh peak i put it in the chat

[high pine]

it's correct, remember about +/- doing 24/13 = x^2

[pale brook]

a critical value

[prisma hawk]

okay makes sense thank you

[pale brook]

but im looking for a minimum and maximum range with a max error of two??

brain hurts

[charred edge]

(2.58 * 5.2)/.4 = the square root of the answer

1124? I think

[prisma hawk]

being obsessed smells like desperation

.close

[marsh citrus]

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[marsh citrus]

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[languid harness]

What's the fastest way to do this ques ?

[languid harness]

I first calculated A³ then found out its determinant

[ripe rock]

determinant of |A^3| = |A|^3

[languid harness]

It comes in a form of a polynomial with a power of 6 which is not ez(takes a lot of time) to solve

[ripe rock]

I mean, you only need to compute |A| now

take cube root

[languid harness]

Ah ok so |A| = 5 ??

[ripe rock]

yes

[languid harness]

Or +- 5 ?

[ripe rock]

cube roots always have same sign as the original number

-125 would have cube root as -5

[languid harness]

I c so only +ve 5 is a possibility here ?

[ripe rock]

In general, taking an odd power keeps the same sign, and similarly taking a odd root
only even powers make everything positive

[ripe rock]

yes

[languid harness]

Thank you very much

.close

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[alpine scaffold]

$I have that x^5 = 1 x!=1 even though the numbers are complex would this still be equal to 1 for any real n (x^5)^n$

[main idol]

if you take principal branch, yes

[alpine scaffold]

👍

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[slate creek]

i need help with this statist s problem

[coral rivet]

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[slate creek]

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[keen steppe]

tell me what's wrong here

[trim quest]

Your case 1

Is true for all y

y^2-y^2=0

This is always true

@keen steppe

[keen steppe]

I get it

but the answers from the wolframalpha says otherwise

[trim quest]

It says there are particular solutions?

This appears to be true for all x where cos(x) =/= 0

[keen steppe]

Seriously it says:

x= 2pi*n +pi

this is the solution for that equation

[keen steppe]

I even plugged the pi/2 value in a calculator in the 2nd step and difference of LHS and RHS turns nonzero

@trim quest

[trim quest]

second step, the one that starts with cos^16?

That gives 0 on both sides for x=pi/2

Wolframalpha gives the result as "true" which I believe means true in general, I'm not sure why it lists specific solutions after that

Graphing them both in desmos, they certainly look identical

[keen steppe]

Can I see the graphs?

[trim quest]

https://www.desmos.com/calculator/4prbydgeks

[keen steppe]

so x=0, y=1

[keen steppe]

then this directly contradicts with the answer I found @trim quest

[trim quest]

x=0, y=1 ?

I don't understand

[trim quest]

You basically proved that it's true for all x, except for when cos(x) = 0, which makes the RHS undefined

[keen steppe]

the graph above shows that the expression returns value '1' for the x value '0'

[trim quest]

Yeah, what's wrong with that?

Plug in x=0, both expressions give 1

[marsh citrus]

@keen steppe Has your question been resolved?

[trim quest]

@keen steppe Where is the contradiction you're seeing?

[keen steppe]

I just wanna know why wolframalpha outputted that answer

[trim quest]

Do you see wolframalpha also evaluated the equation to "true"?

It also runs out of computation time when you give it that input. So I suspect it's listing some solutions and then giving up

[keen steppe]

yeah, it ran out of standard computation time

[trim quest]

Right, but more importantly it says the equation is "true", as in, true in general

It is weird that it lists some particular solutions, I'm not sure why. But programs like wolfram aren't infallible. Your math is correct

[keen steppe]

Ok, I am then assuming my work is right anyway.

thanks

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[still temple]

Can someone help me solve these?

[marsh citrus]

@still temple Has your question been resolved?

[still temple]

<@&286206848099549185>

[limber star]

for the first one, do you think those triangles are congruent, is it possible that all their sides don’t have the same lengths?

[still temple]

Yes so both sides are equal

Wouldn't we need an angle to prove that

Or since they are vertical from eachother they are congruent by the vertical theorem or whatever shit

[limber star]

https://www.math.net/congruent-triangles

heres how u can determine whether two triangles are congruent ^

[limber star]

nah that doesn’t exist

[limber star]

yea u would

there’s no way to know for sure that the other sides are all equal

[still temple]

yeah

and for number 4 we would need another side

to show its congruent

right

like this

[marsh citrus]

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[still temple]

.reopen

[marsh citrus]

✅

[limber star]

yes

[still temple]

alright ty

[limber star]

or an angle

another angle i mean

[still temple]

yeah

[limber star]

np

[marsh citrus]

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[main idol]

<@&268886789983436800> i'm pretty tired of this attention seeker

[still temple]

it was 1400 before, is this a troll?

[quaint hill]

yes, dealt with

[main idol]

thank you

[quaint hill]

,purge 3

wheres texit

[hidden plaza]

Lol dead bot

[still temple]

dead

$1$

[quaint hill]

well sorry for the interruption in any case

try induction

[dry prawn]

In most cases, standard deviation is one of those things that you just kinda have to take a second and go through manually

(Without access to software anyway)

Must be nice

Maybe my profs were too ancient for that

[main idol]

oh you just simulate this?

[dry prawn]

But yeah the manual calculation is just long and boring unfortunately

[main idol]

there's a python server that i'm sure someone will look at

[dry prawn]

This is the way

[marsh citrus]

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[quaint chasm]

I have to prove injective, surjective and bijective.

Domain = Z (ingers from minus to pos), Range = N (0 to pos). I'd say that it's injective, because if we input any N it would map to a unique element. But not surjective because Z numbers go to minus but with this function for no N we can go to minus. Thus also not bijective. Would this be correct?

[quaint chasm]

Or is it asked there that does this function map from any Z to any N? Then it would be surjective.

[crystal lintel]

are you sure it's injective?

[quaint chasm]

I just did some random numbers in my head, 0,1,2. Looks like it

But not sure - no

[crystal lintel]

try a few more lol

[quaint chasm]

oh I c.

No wait. I don't see 😄

the pow(2) kind of makes sure of it.

[crystal lintel]

makes sure of what?

[quaint chasm]

That for any x from N will be unique element

[crystal lintel]

how?

[quaint chasm]

$$h(x)=0^{2}-(20)+2=2$$
$$h(x)=1^{2}-(21)+2=2$$
ooh...

[elfin berry]

Nurech

[quaint chasm]

okay. so not injective.

[crystal lintel]

your reasoning for it not being surjective makes no sense? 😕

[quaint chasm]

now that I'm thinking about it, that's garbage yeah.

What does the Z -> N mean here, what do I have to look?

For any Z we map to every N? or?

[crystal lintel]

yea I guess you can say it like that

doesn't quite make sense how you wrote it though

[quaint chasm]

But that's gonna be true, the pow(2) takes anything from Z (even negs to pos) and thus we will be able to map to some element

so it's surjective

[crystal lintel]

no lol

[quaint chasm]

dang it!

[crystal lintel]

can you try to say again what it means for h to be surjective?

[quaint chasm]

If the range of f(x) is basically a subset of Z it's surjective

[crystal lintel]

umm no not at all lol

[quaint chasm]

what the frick 😄

[crystal lintel]

try again

[quaint chasm]

because 0 is never an output?

idk, do I have to prove this? Z -> N f(x) = z^2 - 2*z - 2 ; z € Z

[crystal lintel]

prove what?

[quaint chasm]

If I replace z from any Z I should get some N? is this pretty much what I have to keep in mind.

[crystal lintel]

if that wasn't already the case, h wouldn't even be a function

[quaint chasm]

idk. Seems to me that if we take any element from domain Z (e.g. -4) we are going to map to some elements of N.

f(x)=(-4)^2 - 2*(-4) + 2=16-8+2=10

[crystal lintel]

yea, h(x) will be a natural number for any integer x

but that doesn't tell you anything about whether it's surjective

[quaint chasm]

should I solve for quadratic equation?

[crystal lintel]

probably not

[quaint chasm]

could it be that the quadratic equation is using sqrt that's gonna mess things up?

[crystal lintel]

you seem to maybe not quite get it yet but this shows h is not surjective

[quaint chasm]

because with 0 were just gonna get a line? nothing's gonna be mapped?

oh, we can never reach N (0)

for any Z we take, nothing leads to 0?

[crystal lintel]

it's because for any x in Z, h(x) is not 0

[quaint chasm]

awesome! I haz so many smarts.

Lol, anyway ty for taking your time

[crystal lintel]

np ^-^

[quaint chasm]

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[placid oak]

This is the area of interest in this question ^

I'm getting the conditional probability to be 2.

Why is that?

I need help.

[marsh citrus]

@placid oak Has your question been resolved?

[placid oak]

<@&286206848099549185>

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@placid oak Has your question been resolved?

[placid oak]

<@&286206848099549185>

[placid oak]

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[placid oak]

🚶🏻‍♂️

[marsh citrus]

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[woven harness]

why does this have to be in radian mode

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[still temple]

these, just tell me what criteria or terms to use, thats all i need

[solar moss]

Looking at the format im asuming that is Summation?

[glacial hedge]

Does it go to 0 ? If so use the ratio test. It doesn't look like anything else is needed here

[solar moss]

idk i might be wrong

[glacial hedge]

It's obviously series

[solar moss]

oh then im just stupid

[still temple]

yeah, i need to check which divergence and which convergence to +infinity

[glacial hedge]

When your toolkit is so small, it's quite obvious what to use

[still temple]

probably, my brain just cannot understand series to save my life

[glacial hedge]

You mean have an intuition for it ?

[still temple]

pretty much, yea

[glacial hedge]

Honestly I'd say it comes from experience, you gain an understanding of what is going to do what

[glacial hedge]

I can say thay because by experience, I know that all exponential vs polynomial go the same way

Pretty much

But in general, when you see quotients like this, ratio test isn't a bad idea usually

Except at a higher level, since then the ratio test is useless because it only gives an answer for series whose nature was already obvious

Or close to obvious

[still temple]

so all of them can be pretty much solved with ratio test

[glacial hedge]

When all you have is ratio and root, it isn't hard to find what method works given one of them does

[still temple]

i see, imma try that and see what it gives me

thanks!

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[flat junco]

can anyone help me with this proof

[flat junco]

i dont know how to continue

[stoic saddle]

well the beginning of your proof is already bad. what is q? you did not introduce it yet you use it still.

you need to determine q in terms of x

[flat junco]

that's the problem, i dont know how to deal with the q

[stoic saddle]

maybe before going into the proof, observe that fut(q_0) = L(A) and ε\L = L, for some immediate consequences of the definitions of \ and fut given here.

[stoic saddle]

in the statement to be proved, it is under an existence quantifier

so you do not "deal" with it really

[flat junco]

$x \backslash L(A) \subseteq fut(q)\newline$
$y \in x \backslash L(A) \implies \exists w \in \Sigma^* : xw \in L(A) \implies \exists q_x$ such that $(q_0,xw) \vdash^* (q_x, \epsilon)$

[stoic saddle]

no, bad!

line 1 again!

you don't have any q yet!

[elfin berry]

Michal

[stoic saddle]

x\L(A) is the language of all words which, if you attach x before them, become words in L(A)

fut(q) is the language of all words which, if fed into the automaton when it's in state q, put it in an accepting state.

idk how to say this without giving it away
but you want q to be the state which the automaton ends in when it scans x.

[flat junco]

let me think about it again, few minutes

[stoic saddle]

it is basically the only reasonable way to go from a word to a state.

[flat junco]

$\exists q \in K \ such \ that \ x \backslash L(A) \subseteq fut(q)\newline$
$y \in x \backslash L(A) \implies \exists w \in \Sigma^* : xw \in L(A) \implies \exists q_f \in F \ and \ \exists q_f \in K $ such that $(q_0,xw) \vdash^* (q_x, w) \vdash^* (q_x, \epsilon)$

dont know what to do next tbh

[elfin berry]

Michal

[marsh citrus]

@flat junco Has your question been resolved?

[flat junco]

$\exists q \in K \ such \ that \ x \backslash L(A) \subseteq fut(q)\newline$
$y \in x \backslash L(A) \implies \exists w \in \Sigma^* : xw \in L(A) \implies \exists q_f \in F \ and \ \exists q_x \in K $ such that $(q_0,xw) \vdash^* (q_x, w) \vdash^* (q_x, \epsilon)$

[elfin berry]

Michal

[flat junco]

@stoic saddle what do you think?

[stoic saddle]

not good

you are trying to do it formally but failing. and you are still making it sound like you are flatly asserting your goal (or part of it somehow) at the start...

[flat junco]

hmm

now really dont know what to do

[stoic saddle]

let q_x be the state in which the automaton ends up after scanning x

show that x\L(A) = fut(q_x), or die trying.

remind yourself later how to prove exists-statements! you have mixed it up in your head with proofs of set equality and put the pieces back together in a nonsensical way.

[marsh citrus]

@flat junco Has your question been resolved?

[flat junco]

I have never learned how to prove exists statements

[stoic saddle]

really now? not even proofs by example?

[flat junco]

I don't think so

We didn't learn it explicitly as far as I know

I'm CS major

but i will take another attempt to prove it

[marsh citrus]

@flat junco Has your question been resolved?

[flat junco]

@stoic saddle slightly improved i think, but still without result, i got the first inclusion but i cant justify it properly

[stoic saddle]

what do you mean by "justify it properly"? your justification sounds fine to me.

some minor issues with your English, but let's ignore those for now

[flat junco]

\subseteq i need to somehow end this inclusion proof, i need to say that y is also in fut(q_x)

[flat junco]

i will sumbit it in my native...

[stoic saddle]

well you know that (q_x, y) |- (q_f, "")

and that verifies that y in fut(q_x)

[flat junco]

ohh yes, true

that was easy

[stoic saddle]

yes it is

[flat junco]

i dont get i why i couldnt conclude this on my own

but sturuggling with the opposite direction

[stoic saddle]

it's similarly easy

now you know that (q_x, y) |- (q_f, "") for some accepting state q_f

and you know that scanning x first takes us from q_0 to q_x (that's the definition of q_x)

so we know exactly how scanning xy will go

[flat junco]

but basically this definition of q_x wasn't given, is it okay to conclude it from that?

[stoic saddle]

what do you mean?

q_x is ours

we defined q_x to be the final state of the automaton after reading x

or rather, we know that it will end up in some state after reading x (and there is only one such state, bc deterministic), and we give this state the name q_x

[flat junco]

hmm

[flat junco]

I did it like this

[still temple]

Easy

[flat junco]

?

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[still temple]

(5+59)[5x3+7:10(5x89)]=

[still temple]

can you please just send a picture of it

that's just a confusing mess of text

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[hybrid canopy]

Im not sure if you mean [] as some sketchy matrix or an alternative to ()

[marsh citrus]

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[lavish cape]

I dont know how to do this

[ivory sundial]

so if a quadratic has roots A and B how can I write this polynomial?

[lavish cape]

idrk tbh

can you give a hint

[still temple]

(-b-sqrt b^2-4ac)/2a is first root

(-b+sqrt b^2-4ac)/2a is second

[ivory sundial]

So if A is a root then f(A)=0

By factor theorem if f(A)=0 then the polynomial can be expressed as (x-A)q(x) where q(x) is a polynomial

[still temple]

that mean it should be like (-2-2√2)/6

[ivory sundial]

But in this case f(B)=0 so you can actually find q(x) (as we know it's a quadratic

[still temple]

cause 2 gone

Im sorry to interrupt max

[ivory sundial]

no worries, im a bit confused what you are doing?

there is a lot simpler method to this

[lavish cape]

still confused

[ivory sundial]

Basically if A and B are roots of a quadratic you can write it as a(x-A)(x-B) where a is some number

so you can do that in this case

replacing A with the number in the question on the left and replacing B with the number in the question on the left

and then a will be a number so that the number in front of x^2 is 1

[still temple]

i dont think it can be solved this way

since the point where the parabola intersects the y axis is not given, we cannot find the coefficient "a

oh sorry it says it equals to 1

I didnt see this so I thought to find it by reversing the root

[lean flame]

a(x-root1)(x-root2)

[marsh citrus]

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[marsh citrus]

@lavish cape Has your question been resolved?

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[teal isle]

i found the first perp bisector

[teal isle]

how do i use it to find a cooridnate

[indigo prism]

is L1 perpendicular bisector of PQ ?

[teal isle]

yes

its y=x-5

do i do y=y or

[indigo prism]

then just L1 = L2

then find x

then y

[teal isle]

okay

[indigo prism]

got it right ?

[teal isle]

yeah ill try get it

[indigo prism]

how did you get L1 ?

[teal isle]

first i found the m2=-1/m1 gradient

then found the coordinates

then plugged it into y=mx+b

and solved for b

then put b back into it

and got

y= x-5

[indigo prism]

great you solved it then, problem was only to find L1, then you can just equate and find the coordinate

[teal isle]

i made it y=y, and so far im at, 3y=20

so i gotta do 20/3 = y? then sub it in for x

?

[indigo prism]

yeah substitute in any of the one line

[teal isle]

wait i think i was meant to set it y= first

ill do that part again

[indigo prism]

ok, ping if have doubt

[teal isle]

it says x is meant to be 10

but i got 20

im not sure where i messed up

ohh wait

nvm makes sense

@indigo prism thanks !

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[next cobalt]

Solution pls

[upper briar]

rref

[next cobalt]

??

you mean reference

[upper briar]

no

rref

google it

[next cobalt]

ah ok

sorru

y

so first step i need to make rref for both

and after that?

@upper briar

[upper briar]

er

if u get identity matrix it means they only soln is trivial soln

if u get like a row of zeros then it means infinite solns

if u get a row of all zeros in matrx and the augmented part aka the = stuff is non zero then no soln

[next cobalt]

Thank you :>

[upper briar]

np

[next cobalt]

.close

[marsh citrus]

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[soft trellis]

How do i deal with this fraction for this matrix multiplication?

[marsh citrus]

@soft trellis Has your question been resolved?

[marsh citrus]

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[still temple]

how would this be wrong?

[cobalt sentinel]

Show ur work

Do u know the derivative of arctan

@still temple

[still temple]

1 / 1+x^2

[cobalt sentinel]

Could u show ur work

[still temple]

one second

got it

[cobalt sentinel]

Nice

[marsh citrus]

@still temple Has your question been resolved?

[marsh citrus]

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[sonic mortar]

,rccw

[sonic mortar]

I dont know how to finish this problem

[late geode]

(volume in trunk) / (total volume)

[sonic mortar]

I got 8

But it says fraction

[late geode]

how are you getting 8

[marsh citrus]

@sonic mortar Has your question been resolved?

[sonic mortar]

.close

[marsh citrus]

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[marsh citrus]

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[ionic owl]

[\sqrt{13^2 - (-5)^2} = x]
[12 = x]

[elfin berry]

dopediscorduser

[ionic owl]

What am I missing here?

Wait

Q3

[\sqrt{13^2 - (-5)^2} = x]
[-12 = x]

[elfin berry]

dopediscorduser

[ionic owl]

.close

[marsh citrus]

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[inland plover]

From what my teacher have told us, all the data from P(X=x) should equal to 1

[hollow sparrow]

correct

[inland plover]

but the negative is throwing me off

[inland plover]

so would i just pretend the negative is not there in this case?

[hollow sparrow]

probabilities for basic prob and stats class can't be negative

I think what that was -?- to represent your missing probability

[inland plover]

ahhhhh lolll

[hollow sparrow]

and it just looks like negative

[inland plover]

yeaa threw me off

thanks!

[hollow sparrow]

yeah no worries!

[inland plover]

.close

[marsh citrus]

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[austere raft]

Uh

[marsh citrus]

Please don't occupy multiple help channels.

[austere raft]

Can somebody send link to my old channel I opened ?

[marsh citrus]

@austere raft Has your question been resolved?

[nova totem]

.close

[marsh citrus]

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[austere raft]

Send link to my old channel pls

[nova totem]

It's legit below you

#help-10

[marsh citrus]

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[near fox]

help

[near fox]

i haven't learnt dis at school yet

but i need to know rn

i am making a list of stuff i want to buy in cvs pharmacy

and it all costs up to $29.06

so i'll save up till that

but i need to add tax

and i have no idea how

[proper cove]

well whats sales tax

[near fox]

no idea honestly

[proper cove]

do they tell you in the question ?

[near fox]

no its a real life situation

it's not a word probelm

problem

[proper cove]

well google sales tax in your state

[near fox]

the only time im using math ;-;

[mystic minnow]

Say your sales tax is 8%
Convert that to a decimal by dividing by 100. Which gives .08
Then multiply your number by 1.08

[near fox]

i live in california

[proper cove]

• 1.0725

there are district taxes too

so you might wanna google that

[near fox]

10.25% is the sales tax acc to googl

e

[proper cove]

then * 1.1025

[near fox]

oh as decimal?

okay then we multiply 29.06 x 1.1025?

[proper cove]

yes

again depends on the actual tax rate in your district

[near fox]

32.03865

[near fox]

sale tax?

[proper cove]

yes

[near fox]

wait 1 question

where i live

my sales tax is

$10.25

so isn't it already a decimal?

[proper cove]

to add on 10.25% you multiply by 1 + (10.25 / 100)

which is 1.1025

[proper cove]

this

[near fox]

ohh

[near fox]

oh

so if i multiply 1.1025 x 29.06

32.03865 is the answer

so is that the final cost?

[proper cove]

thats 29.06 + 10.25% tax yeah

[marsh citrus]

@near fox Has your question been resolved?

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[marsh citrus]

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[inland wolf]

help

[spark otter]

What can you say about the function f(x) = 1 - 5/sqrt(x) ? Is it increasing ? Decreasing ?

[inland wolf]

decreasing?

[drowsy relic]

This is just a matter of rearranging the equation (or am I just stupid?).

And substitution.

[spark otter]

Let's go through the steps of why it is increasing, not decreasing

Sqrt(x) is an increasing function

So, by taking the inverse, 1/sqrt(x) is a decreasing function

[inland wolf]

ok

[spark otter]

sorry it's increasing just needed to correct myself

[spark otter]

Multiplying by a negative constant, -5/sqrt(x) is increasing

So 1 - 5/sqrt(x) is increasing

(Adding a constant doesnt change)

[inland wolf]

:0

[spark otter]

Ok, so if a function is increasing, where should we look to find the values at which it is smallest ?

[inland wolf]

hm

M>=..?

[spark otter]

Should we look at the start to find minimum values ? The middle ? The end ?

[inland wolf]

uh

umm

[spark otter]

If f is increasing, that means that values goes up when you go towards the end

(The end meaning $+\infty$)

[elfin berry]

rafilou2003

[spark otter]

So to get the values to go down, we don’t want to go closer to + infinity

So we look at ? (Choose between The start/the middle/the end)

[inland wolf]

start

[upper briar]

this font looks bad

looks unbounded

[marsh citrus]

@inland wolf Has your question been resolved?

[marsh citrus]

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[marsh citrus]

@bitter parrot Has your question been resolved?

[marsh citrus]

@bitter parrot Has your question been resolved?

[odd crest]

which one?

[marsh citrus]

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[deft ivy]

Hello, can anybody expalin goniometric functions to me. I mean sinus, cosinus, tangens…

[deft ivy]

I understand the basics, but i struggle with defining what function should i use

[quasi osprey]

Wait sinus?

U mean sine?

[worthy trellis]

Sine

I think

[quasi osprey]

Do u mean geometric functions, sine, cosine, and tangent? Or is that some other math word idk yet

[deft ivy]

Yes yes i thought its the same in every language

i need help exactly with that

[worthy trellis]

What do you need to understand?

[quasi osprey]

Ok here is a very useful acronym: SOH CAH TOA

[worthy trellis]

Mind elaborating?

[quasi osprey]

Pronounce sow Kah towah

[worthy trellis]

That doesn’t help with the understanding

[quasi osprey]

Getting there…drawing up something…

[deft ivy]

Ok so lets say we got a triangle

abc

And a is 5 Cm

And alpha is 20 degrees

And i need to fér the rest

[quasi osprey]

Is it a right triangle?

[deft ivy]

Of sides and degrees

yes

[quasi osprey]

I see

[deft ivy]

I need to use one of the functions

[deft ivy]

?

Nono

I will show you

[quasi osprey]

Ok

[deft ivy]

Is there drawing on iPhone ?

Or smthng like that ?

The alpha is at a

Oh no wait

I am just stupid

U got it right

[quasi osprey]

That’s alright!

I’ll draw it slightly different then

Wait

When u say a and alpha, u mean side and angle, right?

[deft ivy]

Angle

U need to calc the inner angles

I get that thats easy

U do 180- the alpha - 90

[quasi osprey]

So this is the triangle now, after what u said

[deft ivy]

Exactly

[quasi osprey]

And here is how sin and cos and tan work, as a refresher

NOTICE that knowing an angle and its opposite side, u can use the sin theta = opp/hyp to find hypotenuse and use tan theta = opp/adjacent to find the adjacent side!

[deft ivy]

Yes i know this

But here is the catch

How do i know which one of these do i use

[quasi osprey]

U know opposite o and sin theta and tan theta

[deft ivy]

Ok so

[quasi osprey]

U can plug in those value for the soh and the toa

To solve for the hypotenuse and the adjacent

Sin theta = opposite/hypotenuse

You know theta

U know opposite

[deft ivy]

Can i send some examples and we can try to solve them together

[quasi osprey]

Yes!

[deft ivy]

Right triangle with right angle at c, a = 7 Cm, c = 8 Cm

And we need to get the degrees and the side

It should look like this right

I am thinking that i will use pythagoras

For the side

8 x 8 - 7 x 7

[quasi osprey]

Yes Pythagorean theorem

[deft ivy]

Ok and now

For the angles

For the beta

I will use

Cos?

-1

[quasi osprey]

,w arccos(7/8)

[elfin berry]

Results provided by WolframAlpha

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Requested by ❤Pauli Excluder❤#3063

[deft ivy]

So is it right ?

[quasi osprey]

If u r using cos(beta) = adjacent/ hypotenuse = 7/8, then beta = arccos(7/8)

0.505 should be right

Can u tell me how you got -1?

[deft ivy]

Teacher told us that when u calc angles its always -1

[quasi osprey]

You mean cos^(-1)?

[deft ivy]

Yes it should be

[quasi osprey]

Yeah, that’s the same thing as arccos

So you are right

[deft ivy]

Lets goo

Can we try one more ?

[quasi osprey]

Sorry gtg

[deft ivy]

Okok

But thank a lot

[quasi osprey]

Np!

[marsh citrus]

@deft ivy Has your question been resolved?