help-39

[maiden cove]

do you still need the assistance or no

[inland laurel]

Need

Assistance

[maiden cove]

alright

so

you've done it good so far

what you need to do now though is remember that the denominator cannot equal zero

you've correctly determined the conditions for the expression under the radical to be non-negative

because [x] must yield a pure interger

[inland laurel]

Yes

[maiden cove]

we can break these absolute value inequalities down into precise interger sets

so

$|[x]| \leq 2 \implies [x] \in {-2, -1, 0, 1, 2}$

[jolly parrot]

Dr. Tropaiophoros, PhD

[maiden cove]

that would be case 1

[inland laurel]

Agree

[maiden cove]

then case 2 would be

$|[x]| > 3 \implies [x] \leq -4 \quad \text{or} \quad [x] \geq 4$

[jolly parrot]

Dr. Tropaiophoros, PhD

[maiden cove]

now comes the translating

[inland laurel]

Explain this

[maiden cove]

translating [x] to real intervals for c

x*

[maiden cove]

i got you

here let me get on pc

[inland laurel]

yeah

[inland laurel]

This is the step where I am getting stuck

[maiden cove]

so when we remember hte core rule here

keep in mind the definition of the greatest integer function

[x] rounds any number down to the nearest integer

so if [x] = n it means x lives in the half-open interval [n,n + 1]

so

how this applies to case 2

is

we can look at the first branch of case 2

[x] >_ -4

this condition means that the output of our greatest integer function must be an integer like -4,-5,-6,-7 and so on

and to get an output of -4 our real number x can be anything from -4 up to but not including -3

and written as an interval that would be [-4,-3)

to get an output of -5, x must be in the interval [-5,-4)

[inland laurel]

Agree

[maiden cove]

to get an output of -6, x must be in [-6,-5)

if you string al of these individual intervrals together traveling down the number line to negative infinity

they perfectly merge into one continous beam

x e (-infinity, -3)

and why is -3the open boundary

[inland laurel]

Got it

[maiden cove]

if x were to exactly equal -3 then [-3] would output -3 but our condition strictly demands that [x] must be less than or equal to -4

because [-3] = -3 breaks this rule

x is allowed to get infinitely close to -3 from the left side

but it can never actually touch it

we can also look at branch b

[x] >_ 4

this condition means the output of our greatest integer function must an integer like 4,5,6,7 and so on

the absolute smallest integer allowed in this set is 4

and the lowest possible real numbe that rounds down to 4 is 4 itself (since [4] = 4)

[inland laurel]

Yes

[maiden cove]

any number smaller than 4, even something like 3.999, will round down to 3

which violates our condition

[inland laurel]

Yes

[maiden cove]

therefore x must start exactly at 4 and can head out infinitely to the right to cover all higher integers (5,6,7)

[inland laurel]

So [4,infinity)

[maiden cove]

x e [4, infinity)

yes

just with the x and e

i cant sejnd the actual symbol but e is just representing it

[inland laurel]

It's not a big deal i understand it

[maiden cove]

so the summary of case 2 owuld be that when you combine both branches on the real number line you are left with two open ended intervals that completely skip over the region between -3 and 4

x e (-infinity, -3) U [4, infinity)

[inland laurel]

Yup

[maiden cove]

does that all make sense to you

and help you understand case 2 more

[inland laurel]

Yes

It makes sense

[maiden cove]

is there anything else you need help with?

[inland laurel]

No

[maiden cove]

okay how do we close this help channel

[inland laurel]

let me rethink about this whole solution and let you know if any help needed

Give 2 min

[maiden cove]

oka

[inland laurel]

If |[x]| > 3 then how to get those two inequalities [x]

[maiden cove]

so we wanna look at this purely from the perspective of distance on a number line

which is what absolute value measues

so |-4| = 4

|2| = 2

and when mapping it on the number line

if you start at 0 on a number line

and walk 3 units in either direction

you land exactly on 3 and -3

if you want a distance equal to 3

you are standing exactly on -3 or 3

if you want a distance less than 3 (|[x]| < 3)

you have to stay trapped inside the safe zone between -3 and 3

[inland laurel]

Yes

[maiden cove]

and if you want a distance greater than 3 ({[x]| > 3 you must break out of that middle zone and move further away from zero

[inland laurel]

Yes

[maiden cove]

so this naturally spits your path into two completely oppsite directions

heading to the right which is the positive side

this gives us [x] > 3

because to stay further than 3 units away from zero on the positive side

you have to move on to the right of 3

and since [x] can only ever be an integer the first integer strictly greater than 3 is 4

so this is functionally identical to saying

[x] >_ 4

but you can also head to the left which is the negative side

[inland laurel]

Yes

[maiden cove]

so to stay further than 3 units away from zero on the negative side you move to the left of -3

this guves us [x] < -3

[inland laurel]

Got it

[maiden cove]

so again since [x] must be an integer the first integer strictly less than -3 is -4\

so this is the exact same as saying [x] <_ -4

and sticking to the algebraic rule

any time you see an absolute value inequaltiy with a "greate than" sign

(|y| > k where k > 0)

it always splits into an "or" statement pointing away from the center

Y < -k or Y > k

[inland laurel]

Alright I'll remember this to save time from now

[maiden cove]

plugging in [x] for Y and 3 for k would equal

[x] < -3 or [x] > 3

[maiden cove]

yes good

let me know if you need anymore help

if not we can close

[inland laurel]

what would be our final answer as per question

[maiden cove]

the final answer to your original question?

[inland laurel]

Yws

[maiden cove]

that you're working on?

[inland laurel]

just a bit confused what to put in place of b and c

a= -3

[maiden cove]

so the final answer would be a + b + c = (-3) + (-2) +3 = -2

are you good now

can we close this help channel or do you still need help'

[inland laurel]

How b and c = -2 and 3

[maiden cove]

so

you need to find the left boundary (b)

and the right boundary (c)

so for b

if you plug x = -2 into the function

[-2] = -2

this is allowed

if you plug in a number slightly larger like x = -1.9 it rounds down to [-1.9] = -2

this is alsoa llowed

but if you pick a number even a tiny bit smaller than -2 like x = -2.1

it rounds down to [-2.1] = -3

but our condition strictly says [x] cannot be less than -2

so therefore the absolute lowest real number x can possibly be is exactly -2

which gives us our solid left boundary

[inland laurel]

Agree

[maiden cove]

and for our right boundary c

our condition says the absolute largest integer value that [x] is allowed to output is 2

if x = 2 then [2] = 2

this is allowed

if x = 2.99 it still rounds down to [2.99] = 2

this is also allowed

but when we see what happens when x reaches 3

[3] = 3

because [3] outputs 3 it breaks our rule that the maximum allowed integer is 2

this means that x can go all the way up to 2.999

getting infintely close to 3

but it cant touch 3

so that gives us our right boundary

make sense?

[inland laurel]

Yes

Thanks for all help

.close

[pearl pond]

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[pearl pond]

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[swift spindle]

apparently i went wrong here, but i dont understand why.

[versed mica]

where is your chain rule mate

[wicked edge]

You forgot -x^2.

You wrote 1 instead in the second line there.

[inland kindle]

true

[wicked edge]

Other than that then I do not any other errors so far.

[swift spindle]

h

[swift spindle]

i thought im chain rulling like everything

[swift spindle]

wait hwat

[versed mica]

please stop writing x for multiplication

you’re in calculus

i don’t see the chain rule being applied on your very first step

for arcsin(sqrt(3)/3 x)

[swift spindle]

ohh

i see

[swift spindle]

ohh i cancelled it instead. i see. thanks

ty guys

.close

[pearl pond]

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[hoary relic]

<@&268886789983436800> textwall/ads?

[pearl pond]

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[north talon]

can i have any hints for this? my friend said that ||the minimum is 9|| and he used something about ||base n||

[inland kindle]

think of the choices of x_1, ..., x_k

Each x_i can be chosen from l possible numbers, so there are at most l^k different printed values

[north talon]

yea

[inland kindle]

So first check whether k+l=9 is even possible

[north talon]

why 9?

[inland kindle]

Because that's the minimum

According to your friend

So you need to test if that works or not

[north talon]

i mean, yeah but how do i get to 9 without knowing that first

[north talon]

oh wait its 10 mb

but still

[inland kindle]

For each possible value of k+l, ask:

"What is the largest possible number of outputs l^k?"

Since it's fixed, you can calculate it

By testing small totals

[north talon]

ohh ok

yeah its not too bad if i look at it that way then

.close

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[vernal hinge]

can someone help me question 5

[vernal hinge]

is that uniform converges means that the function only convegent in (-1,0] right ?

and absolute convergent is sum |Un| is convergent

they are different right ?

i think im gonna delete D because cos and sin are not have exact asnwer so this answer cant be convergent

[ebon skiff]

yes

uniform convergence says:

After some N, the error is small for every x∈(−1,0] simultaneously.

normal convergence says:

For each fixed x, the series converges.

so converges on (-1,0] would mean that the sum converges in such a way that the convergence is controlled for all x in (−1,0] at the same time.

i think C is the easiest to throw away

C is basically x+x^2+x^3+...

and if you check for x=-1

it looks like

-1+1-1+1....

[dry trench]

1/2 is not in -1 to 0

[vernal hinge]

u cant take -1 , since the domain is (-1,0]

sum of x^n if |x| < 1 is convergent right

i think the answer can be C

[ebon skiff]

we are not taking -1

we are taking values that are very close to -1

which the function has to behave well for

so like −0.9999

because |-0.99999999999| is very close to 1 the function will stay large for a long time

[vernal hinge]

no no

[ebon skiff]

so its not uniform

[dry trench]

if we solve A with integration

[vernal hinge]

if u take a page of paper this is so small but if u sum all they will be a book not 0

[dry trench]

it would still be positive

probs not in (-1,0]

I think it's B or D

one of them

[ebon skiff]

it cant be C cuz near -1 the uniformity does not hold

[vernal hinge]

cuz they are switching betwen 0 and 1 right

yeah cant be C

[ebon skiff]

i mean sure i'd put my money on B intuitively

but i would have to check D first

to make sure

[vernal hinge]

i dont follow

[dry trench]

D is same as C near -1

except for n-5

[ebon skiff]

true

[vernal hinge]

its increasing right so delete A

[dry trench]

yep

[vernal hinge]

D is switching like C right

So B is the correct asnwer ?

[dry trench]

I think it's B

yeah

[vernal hinge]

i have to check again

[dry trench]

its decreasing

[vernal hinge]

thank u guys

[dry trench]

as n increases

[vernal hinge]

.close

[pearl pond]

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[ebon skiff]

you re welccome

[pearl pond]

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[languid gazelle]

i tried with a couple of entries but the axiom always holds for part (i), is it wrong maybe?

[autumn fossil]

can u show what you tried?

[languid gazelle]

wait let me rewrite it cleanly, its scattered

Like this

And used some other entries as c and d like (2,3)

[autumn fossil]

,rccw

[languid gazelle]

Or is this trial and error method not the way to solve?

[autumn fossil]

oh hmm, it indeed doesnt look like it should fail

c * (d * p(x)) = c * p(dx) = p(c(dx)) = p((cd)x) = (cd) * p(x)

weird, the question might be wrong

yeah, the question is just wrong

[pastel umbra]

yh this feels wrong to me too

[languid gazelle]

Fairs 👍

.close

[pearl pond]

Channel closed

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[pastel umbra]

That said - check that that is what "Axiom 9" is

Because it might be that they've misstated it in the question

[languid gazelle]

It's correct
c(du) = (cd)u

They wrote it at the top

The axiom list

.close

[pearl pond]

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[wicked edge]

How did you solve it?

What method did you apply?

I believe mod can be used here.

[sharp smelt]

or binomial tbh

6=7-1; 8=7+1

[sharp smelt]

looks like the answer is wrong

[sharp delta]

.w 6^83+8^83 mod 49

[sharp smelt]

,w (6^83 + 8^83) mod 49

[jolly parrot]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by math_rocks

[sharp smelt]

35 is right @languid bloom

[wicked edge]

Really?

35 must be correct.

[sharp smelt]

unless wolfram is tripping yea

[wicked edge]

It must be correct then.

[pearl pond]

@languid bloom Has your question been resolved?

[pearl pond]

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[delicate temple]

11th Problem. My approach: take |m -n| = x and by the equation I got, Minimise m+n and increase the numerator.

[delicate temple]

After having |m-n| = x
=> (m-n)²= x² to remove the mod.

But I'm stuck after this

[tropic plaza]

yo

[sweet junco]

I imagine long division of 3n^2-5n+16 by n+m could help

[delicate temple]

Not sure tho

If u can see it going then

👍

If some has good idea for the problem, then ping me.

[inland kindle]

Your idea of using |m-n| is natural, but minimizing m+n is risky because m and n are linked by the equation. A cleaner way is to force a factorization

[delicate temple]

Factorize what?

The numerator?

[inland kindle]

Factorize this expression:

(8n - 5)^2 - (4m)^2

Because it is a difference of squares

[delicate temple]

Ok leme

[delicate temple]

Done then?

[delicate temple]

Btw how u got this random expression?

[inland kindle]

It's not random. It comes from trying to make n side into a square

[delicate temple]

Alr

[inland kindle]

You start with:

m^2 = 4n^2 - 5n + 16

The annoying part:

4n^2 - 5n

[delicate temple]

Hmmm

[inland kindle]

Then continue

[delicate temple]

Fr

[delicate temple]

Okay

[inland kindle]

You can complete the square without fractions

[delicate temple]

Wait leme do myself

[delicate temple]

Mine is different

[inland kindle]

Yours is not wrong if you get:

m^2 = (2n - 4)^2 + 11n

Because.

(2n - 4)^2 = 4n^2 - 16n + 16

So:

(2n -4)^2 + 11n = 4n^2 - 5n + 16

Algebraically, yes, it matches. The problem is that it's not very useful

Because you still have a variable term 11n outside the square

What we want is a square plus a constant, because then we can factor

[delicate temple]

Ohhhh

[delicate temple]

I got it.

So wait

pls

[delicate temple]

But fraction

[delicate temple]

What next?

<@&268886789983436800>

[inland kindle]

Why did you ping the mods lmao

[wicked edge]

My friend?

[verbal whale]

There was a crypto spammer

[inland kindle]

Next, remove the fractions

[delicate temple]

Hey I got way ahead

[inland kindle]

(8n - 5 - 4m)(8n - 5 + 4m) = -231

[inland kindle]

Let

A = 8n - 5-4m

and

B = 8n - 5 + 4m

[delicate temple]

Let me go ahead, and if I'll stuck then I'll ping

[inland kindle]

So

AB = -231

Now check the factor pairs of -231

[delicate temple]

Its 231 ig

[inland kindle]

Since m is positive and B - A = 8m > 0, we need B > A

Solve the factor pairs using:

A + B = 16n - 10

and

B - A = 8m

[delicate temple]

Listen me

@inland kindle

[inland kindle]

That's the right number

[delicate temple]

Whats this

[inland kindle]

You need to chill a bit before I type the answer

That's the product -231

The factor pairs should have opposite signs

Because:

A B = -231

[delicate temple]

Alright got it carry on

pls

[inland kindle]

Then use:

A + B = 16n - 10

B - A = 8m

[delicate temple]

B = 8n+4m-5

By using urs

[inland kindle]

Yes, that's right

[delicate temple]

Ik

Now A

?

[inland kindle]

B = 8n + 4m - 5

Same as:

B = 8n - 5 + 4m

And

A = 8n - 5 - 4m

So:

A + B = 16n - 10
B - A = 8m

Now use the factor pairs of -231

AB = -231

Then check:

A = -77, B = 3

Then:

A + B = -74

So:

16n - 10 = -74
16n = -64
n = -4

And:

B - A = 3 - (-77) = 80

So:

8m = 80
m = 10

Then:

|m - n| = |10 - (-4)| = 14

Another valid one is:

A = -1, B = 231

That gives:

n = 15, m = 29

[delicate temple]

That's clever

[inland kindle]

So:

|m - n| = |29 - 15| = 14

Therefore the maximum is:

14

Got it now?

[delicate temple]

Wait leme do myself

[delicate temple]

Ur answer is verified.

[inland kindle]

Im glad lol

[delicate temple]

Ur pro

🫡

Tysm

[inland kindle]

Np

I'd hope my answer is correct

[delicate temple]

Its correct

[delicate temple]

Yup man the problem was easy

I js had the wrong start.

.close

[pearl pond]

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[untold latch]

hey someone hlep me with trigonometry

[delicate temple]

Practise problem from sources

[verbal whale]

!occupied

[pearl pond]

Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).

[untold latch]

mainly angle of elevation and depression'

[delicate temple]

.close

[untold latch]

ok

[verbal whale]

.close

[jagged meteor]

Open ur own help channel if u have a doubt in a specific time Question

[verbal whale]

Oh it was already close

[delicate temple]

Yep

[verbal whale]

I guess we need to wait some minutes until it gets closed definitely

So let's not write here anymore

[pearl pond]

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[low sage]

I have a question about statistics: I have a known function with an unknown seed. The function produces a set of r outcomes (order does not matter). the seed is uniformily chosen but unknown (from 0 to n). I have to predict those r outcomes (hit or miss, order does not matter) over all possible seeds. the function produces NEARLY (but not completely) uniform outputs (there are duplicates). each member of the output can only be an integer from 0 to n. So overall there are r * n possible values. By calculating and sorting them by occurence, I see again that some have more duplicates than the expected r by a small margin (~20% more). Why should I not place my bet on the r most common values over the whole space?

[rough stream]

What is r? A real number?
Nvm I think r is an integer from 0 to n

[cinder flower]

i have a known function with an unknown seed
what does this mean?

[sterile gazelle]

[low sage]

f(x) is a function I know but I don't know x.

I think it does not matter that much for my question though. I have a space of r * n values and I am to predict, given a certain (small) budget as often as possible.

[low sage]

oh sry r is an integer, although not to n, but quite a bit smaller, let's say 100.

I'm sorry my presention is so messy, I have no formal eduction in mathematics so I'm trying as best to present the problem :(. For this purpose let's assume r=100 and n=10000, my given budget is r at most.

So my problem is that intuitively I find it obvious that one should just find the values with most occurrences and use that set as a prediction (since order does not matter - my prediction is better the more values I predicted correctly).

[pearl pond]

@low sage Has your question been resolved?

[pearl pond]

@low sage Has your question been resolved?

[pearl pond]

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[pearl pond]

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[still dirge]

Hello, is this solved correct? Second question, what do we get when we calculate this? I thought we were suppose to get size of area S?

[viscid shale]

Yea, as far as i can tell is correct.

And to be more clear, if you want the size of $S$, you do $\iint_S dxdy$

[viscid shale]

So you have a (1) as your function.

[still dirge]

Ah, okay. I didn't know. But what does this calculation give then?

0 is what?

[viscid shale]

If you recall what the integral of f(x) is, its just the area under the curve.

Well, here we have an f(x,y), so its the volume under the surface.

[still dirge]

.solved

[pearl pond]

Channel closed

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[pearl pond]

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[pearl pond]

@stoic imp Has your question been resolved?

[verbal whale]

Again?

I remember something really along the lines of that few hours ago

[viscid shale]

same problem in fact

[stoic imp]

how is w^12 in G6

how is w^16 in G4

[verbal whale]

#help-44｜stanley-🌲-v2-dans message YOUR answers

[stoic imp]

I know is true, I am just asking how

[verbal whale]

And now you've already forgotten them? What the heck is happening all the time when you do math problems? Do you at least write down things somewhere besides here in the chats?

[verbal whale]

Wdym how

[stoic imp]

is it illegal to ask math in this server?

[verbal whale]

Huh? I didn't say that 🤔

Sure you can 😅

[stoic imp]

why make a big fuss then

[verbal whale]

Because it annoys everyone helping you

[stoic imp]

nobody has helped me yet

[verbal whale]

.....

I meant in general...

[stoic imp]

asking math bothers people 😑

[verbal whale]

Again, I DIDN'T SAY THAT

[stoic imp]

anyways, anyone knows? why this holds if w is in G6

lets not derail from the math please

[verbal whale]

<@&268886789983436800>

[pearl pond]

@stoic imp Has your question been resolved?

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[woven river]

can anyone help check my work to the question above? I will send my work in a moment

um why this help channel not occupied

anyways, is my proof correct? Thanks in advance

[fleet ridge]

!occupied

No that doesn't work either

-# nice spelling

-# no. I know that mniip originally made it (he has the most commits) and ratgirl has the most recent commit. For some reason I can't see the 2nd most contributor on github

[woven river]

how to write like that

-#ok than

...

-#test#-

BROOO

[fleet ridge]

Add a space

-# True I dm'ed both of them already for other questions but no one responded

[woven river]

-# ok now it works, thanks lord

[woven river]

-# dont bury my question

[wraith jacinth]

-# was about to say come #chill

[fleet ridge]

-# oki

[fleet ridge]

.pin

[autumn fossil]

looks almost okay

but 2/n is only <= 2/k, not < 2/k

since you only assumed n >= k

and also, 2/k isnt = epsilon, but rather <= epsilon

[woven river]

oh yea shoot

ok ok thanks

[autumn fossil]

np

[woven river]

I will fix the sign

[autumn fossil]

.

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[fading hamlet]

can i get some help with these

[mossy lance]

Bro

[left steppe]

.pin

oh man i’m not high enough role

[left steppe]

ok do you know how to complete the square?

[mossy lance]

You need to have the helper role

[fading hamlet]

yes

[fading hamlet]

i think so

[left steppe]

let’s try the first one

[left steppe]

i think the bot is down

[alpine kettle]

Yo!

[mossy lance]

I don't know, seems like a reasonablr explanation.

[astral ocean]

it is

[left steppe]

ima test rq

!15m

yep

[alpine kettle]

There s someone who talk frenche here ?

[left steppe]

how would you start the first one

[fading hamlet]

uhh

first would i just but it into factorized?

[left steppe]

no it’s asking you to complete the square

so you won’t factor just yet

[fading hamlet]

ohh yea

i remember

[left steppe]

so…

what do you do first?

[fading hamlet]

1 min checking my notes

x^2+4x+4 =3+4

?

ok sorry i gotta go have dinner, i think i remember how to do it now, thanks for your help and i will prob come back if i need anything else

[fiery haven]

This is my first proof in Real Analysis, could anyone check if this is correct.

.open

.close

bot seems asleep

[wraith jacinth]

yup

[autumn fossil]

looks good to me though

[fiery haven]

thanks. I will use #1021175428326633542 when I have another proof that I want to get checked. @wraith jacinth

[wraith jacinth]

-# i was just putting here for anyone who comes new to teh channel sorry if i interrupted you 😭

bots currently not working please head to #1021175428326633542 and make a post there instead!!

[fiery haven]

no, you're good

[misty haven]

how to do enlargement??

this question specifically

[autumn fossil]

,rcw

[autumn fossil]

We can start by dilating ("enlarging") the corners

you can draw a line connecting the center and the corner like this

[quartz atlas]

hello ! I have to find all maximal solution of the differential equation yy′′ = 1, then, yy′′ = f where f is a map from R to R. Have you any idea about where can I begin ?

[autumn fossil]

Hi, please go to #1021175428326633542 , the bot is currently broken so there aren't enough help channels

[quartz atlas]

thx !

[autumn fossil]

then since we're enlarging it by a factor of 3, you need to make the distance from center 3 times larger

you can see that its indeed 3 times larger

do this for all 4 corners and then simply connect those corners to get the enlarged rectangle

@misty haven you still here?

[misty haven]

hi! thank u for ur help, i got it now

[empty rover]

hi, is this channel taken?

[autumn fossil]

It's free now

[empty rover]

how do I connect the voltmeter to find the voltage in point A?

[autumn fossil]

um, afaik, there is no such thing as "voltage at a point"

can you send the og question exactly as it was stated?

[empty rover]

so that means its just point A to B?

[autumn fossil]

voltage is measured between 2 points, for example in your picture, it measures voltage between a and e

[empty rover]

actually I'm trying to understand on how to construct a series circuit and finding voltage and current through an ammeter

[misty haven]

btw is this correct

[wraith jacinth]

-# becuase u connected it in parrler and not series the voltage here will be equal to that of the voltage in the circut which is usually what we use to measure voltage

-# connecting it to series to find only point a or b would give u an innacurate answer

[empty rover]

true, so I have to connect to 2 points right?

[wraith jacinth]

-# recally the voltage rule in series vrs paralleri series its vt = v1 = v2 = v3 , in series its vt = v1 + v2 +v3 etc. also this is occupied so come to #1021175428326633542 and make achannel there!

[autumn fossil]

Ill use one analogy I like:
Electricity is like water flow, current is analogical to the current of the water (how much water flows through the point per some unit of time)
voltage is analogical to the difference in heights. So for example battery can be thought of as a water pump which pumps the water up (thus provides voltage), etc..

This explains why voltage cant really be measured at one point, by connecting it in series like the ampermeter - because difference of water levels at a single point is 0. So the voltmeter would just show 0.

[empty rover]

hmmm that makes sense

I've another doubt

to connect an ammeter, I got to break open the circuit that I've constructed earlier right

then I connect the red wire to positive terminal and then the black wire to the next electrical component

[autumn fossil]

yeah

[empty rover]

I see, also how do I use the voltage and current divider rule?

[autumn fossil]

oh btw the top one is 2x^2 + 9x - 6

[bitter herald]

there does exist the concept of nodal voltages, but this is contingent on there being a defined system ground

in which case the other point you are measuring from is ground anyway

[empty rover]

what

[wraith jacinth]

you mean how to use the rule It = i1 + i2?

[autumn fossil]

i think that the these rules are for resistors in series / parallel? In series, the voltage splits and in parallel the current splits.

[empty rover]

what if the resistors are just in series?

do I still need to use it?

[autumn fossil]

Then you can use it to calculate the voltage accross eaxh resistor

So between the 2 ends of each resistor

[wraith jacinth]

-# for in series u just do R = R1 +R2 + R3 i belive

this may be useful.

[empty rover]

For this why are there two V?

I know one is total voltage

[wraith jacinth]

-# that is wierd... it should be one voltage?

i mean if ur measuring the voltage in the end it will just be 0 surely thats not it..

[bitter herald]

your instructor is meant to give you the voltages to measure

[bitter herald]

all the resistors in the circuit should have a voltage drop across them

[empty rover]

so those 2 voltages are like voltages from point A to B, point C to D etc?

[bitter herald]

yes

[wraith jacinth]

oh that makes alot more sense now!

[bitter herald]

it also took me a minute due to the lack of context from OP

[empty rover]

sorry sorry

its just that this paper is a sample for my lab test tomorrow

[bitter herald]

it is fine

You have to do no calculations in fact

since the question is asking you to use a digital multimeter

[empty rover]

yeah that's I was asking earlier on how to connect the voltmeter

[bitter herald]

what you do is put the red probe of your multimeter in the V connection, and the black pin in the COM connection. Afterwards, you probe the resistor(s) in parallel

When measuring the current you should be VERY CAREFUL

[wraith jacinth]

-# also btw lex where did ur roles go?

[bitter herald]

when measuring the current, you need to ensure that the red pin is in the mA or the A pin of the multimeter and select the A or mA option and make sure to place ur multimeter in series and NOT in parallel

[empty rover]

wait I thought the resistors are in series

[bitter herald]

because the multimeter in current-measuring mode presents a very small input impedance, which when placed in parallel to a component causes a short circuit and may potentially fry your device

[wraith jacinth]

-# i didnt know this either this is very usefull info ty ty

https://cdn.discordapp.com/emojis/1211361728516857988.gif?name=GoldenNod&size=48

[bitter herald]

i left and rejoined the server

[bitter herald]

the resistors are in series to each other, yes, but your multimeter may be in series or in parellel depending on how you place it

[empty rover]

voltmeter is mV right?

[empty rover]

but shouldnt current meter be in series only?

[bitter herald]

yes, that's what i am saying

[empty rover]

ah I see

[bitter herald]

make sure when you are toggling your multimeter to be an ammeter to have it be in series, not in parallel

[empty rover]

alrighty, think I'm kinda ready now, can you test me on some stuff related to constructing the series circuit tho

[bitter herald]

uhh

you want theoritical questions or practical ones?

[empty rover]

both

[bitter herald]

how do you connect two resistors in series on a breadboard

[empty rover]

wait

I'm not using breadboard

hold on

I'm using something like this

[bitter herald]

same idea i guess

[empty rover]

the resistors are kinda arranged tho

I just gotta plug the wires

[still dirge]

hello

[desert cliff]

how do we answer this?

[twilit crane]

👀

[empty rover]

brother

you learnt multiplication scalar?

[twilit crane]

you already have all the answers

[desert cliff]

yes i have the answers , i am looking

[empty rover]

so brother

[desert cliff]

if these options

[empty rover]

why are you here then

[twilit crane]

I mean the last picture already give you all the answer

[desert cliff]

which?

[twilit crane]

it already tell you Aa= b and Av = 0

use linearity

[desert cliff]

yeah but is these options a possible x vector

[desert cliff]

the variable?

[rough forge]

u fixed the help channels

[twilit crane]

you know properties of matrix multiplication?

you need $A (\vec{u} + \vec{v}) = A\vec{u} + A\vec{v}$

[jolly parrot]

夜靈

[desert cliff]

ok I get it now

sorry haha thanks

.close

[pearl pond]

Channel closed

Closed by @desert cliff

Use .reopen if this was a mistake.

[desert cliff]

.reopen

[pearl pond]

✅ Original question: #help-39 message

[desert cliff]

ok now im stuck with b

part b

[wraith jacinth]

.pin

[desert cliff]

how is this true?

[toxic fractal]

how is what true?

[desert cliff]

i dont get this basically

[toxic fractal]

again, what is "this"

is that your answer and are looking why you got it wrong?

[desert cliff]

its not the first case, where is no solution

but how do we tell if there is a unique solution or

many solutions

I also know its not the case where its a unique solution but my question is how can it be inffiiniatemy many solutions if there is only 2 solutions found?

[humble root]

If Ax = b is a solution and Ay = b is also a solution, is it possible to find another solution different to x and y?

(Also, are you asking how there are an infinite amount of solutions if you know that there are two distinct solutions to a linear equation? What's your question?)

[humble root]

I imagine whatever video you are looking at will explain this concept to you soon, but you basically need to show that A is not invertible

You may recall that a function is invertible if: f(a) = f(b) implies a = b. This is pretty much saying that every equation with an invertible function has a unique solution.

In fact however, it is not too surprising to learn that not all functions are invertible - there are functions that have multiple solutions within one equation. In particular, not all linear operators are invertible either (a linear operator is a type of function).

So in any equation Ax = b, you have three choices as outlined; you either have no solutions, you have one solution, or you have infinitely many.

[humble root]

Answering this will help explain why there are infinitely many (i.e you can't just have only two solutions).

[pearl pond]

@desert cliff Has your question been resolved?

[pearl pond]

Channel closed

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[worldly pier]

part h

[woven matrix]

Y can only take 2 values, so it's an easy conditional split

P(X > Y) = P(X > Y and Y = 2.5) + P(X > Y and Y = 4.5)

= P(X >= 3 and Y = 2.5) + P(X >= 5 and Y = 4.5)

[worldly pier]

ya no idea

[woven matrix]

= P(die was rolled once) * P(X >= 3 | die was rolled once) + P(die was rolled twice) * P(X = 5 | die was rolled twice)

[worldly pier]

i just know y can be 2.5 or 4.5

[woven matrix]

I mean I've written all the logical steps you only have to understand and use this last formula

you can even simplify P(X >= 5 and Y = 4.5) before when I did

X >= 5 already means X = 5 since 5 is the max, and it already happens only when die was rolled twice so Y = 4.5

P(X >= 5 and Y = 4.5) is just P(X = 5)
P(X >= 3 and Y = 2.5) can be interpreted as rolling 3 or 4 on the first and only roll, so it's simply 1/2

[shut monolith]

y got these 2 values for 2 diff values of R

now u can check the values of D corresponding to R for those values

and hence X

[worldly pier]

my confusion is just for the 4.5 part

cz cant you get 5 from 2 and 3 as well not just 1 and 4

[woven matrix]

if you get 2 or 3 you don't roll the dice a 2nd time

[worldly pier]

ohhh right

ya nvm i just clocked it

thanks

[worldly pier]

now this makes sense

[pearl pond]

@worldly pier Has your question been resolved?

[pearl pond]

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[sharp smelt]

Let $A$ be a ring $\neq 0$. Then Show the set of primie idelas has minimal elements wrt inclusion.

[jolly parrot]

what a wonderful world(wai)

[sharp smelt]

What even is the lattice here

the power set of ideals?

[pearl pond]

@sharp smelt Has your question been resolved?

[sharp smelt]

.close

[pearl pond]

Channel closed

Closed by @sharp smelt

Use .reopen if this was a mistake.

[sharp smelt]

.reopen

[pearl pond]

✅ Original question: #help-39 message

[sharp smelt]

yea, I don't get the question

[modern talon]

you could try using zorn's on the set of prime ideals ordered by reverse inclusion instead, and show that has a maximal element (hence a minimal element when ordered by inclusion)

[sharp smelt]

No, i don't get the question

What lattice am i examining here

[jolly parrot]

blanketism

[sharp smelt]

Ah, A&M talks about that 10 excises later

[modern talon]

actually let me be a bit clearer, spec(A) only refers to commutative rings lol

[jolly parrot]

blanketism

[sharp smelt]

Okay so i just need to show this set has a minimal element

Cool

Tysm

.close

[pearl pond]

Channel closed

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[rough forge]

your prime set looks interesting

[pearl pond]

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[trail falcon]

How do u divide without calculator with decimals

[trail falcon]

Pls someone explain to me in a quick way I don’t have a longtime

[worldly heart]

Yo

What u wanna calculate

[trail falcon]

1.25 /120

[worldly heart]

Speak that table of the that is dividing

It will be better if I show u

[trail falcon]

Huh

[trail falcon]

Oh wait no

120/1.25

[worldly heart]

Ok

U first try to create 10 100 or etc it will make it more see if u multiple 1.25 *8 u get 10

So multiply up and down with 8

[trail falcon]

How cooked will I be if idk how to divide decimals for my math final tmr

Not much or a lot ?

[worldly heart]

In which grade u are

[trail falcon]

9

[worldly heart]

Hell nah bro u should be doing stuff in grade 4 in india

First try to simplify denominator and numberaor

[trail falcon]

Idk how to simplify a decimal

The whole point of simplyifng is to not make it reach a point of decimals

[worldly heart]

1.25 can be written as 125/100 and 100 goes up i

[trail falcon]

I don’t get it

[worldly heart]

Therefore it will be 120*100/125

?

U got this

[trail falcon]

Ok nvm, I’ll ask my teacher tmr إن شاء الله

Thank u for ur time

.close

[pearl pond]

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[pearl pond]

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[urban thunder]

Could someone help walk me through this? Some of these steps I’m confused where they’re getting their numbers at. Thank you!

[urban thunder]

this is the first thing I’m confused about, how did we get from the circled area to where the arrow is pointing

[light helm]

multiply both sides by 8

[urban thunder]

I don’t see what’s being multipied by 8 because 8 x 2 is 16 and 8 x √3 is a longer decimal, but rounded is 14.

[light helm]

why are you multipyl the 2 with 8

don't round

don't use a calc

note that:
$$p \times \frac qr = \frac{pq}{r} \redneq \frac{pq}{pr}$$

[jolly parrot]

ραμOmeganato5

[light helm]

multiply both sides of the equation by 8, not everything you see by 8

$8 \times \frac{b}{8} = 8 \times \frac{\sqrt{3}}{2}$

[jolly parrot]

ραμOmeganato5

[urban thunder]

Ohhh okay I think I see what you mean ty

How is this process supposed to be helping us find the area of the triangle?

[light helm]

doesn't it get explained further down the article?

a can be found by similar reasoning

and once you have the legs (which are perpendicular to each other)
you have enough to info to get the numerical value of area

[urban thunder]

oh wait is the proportion we are following to give us the length of b so we can put that into the triangle area formula?

[light helm]

yes

but not because the letter is the same

[urban thunder]

if b is x√3 and we know the hypotenuse is 8 and 2x, couldn’t we automatically figure that 4 x 2 = 8 meaning that x is 4 and place it in as 4√3 for b? Is there a reason they make us follow that proportion or is it just an alternative way to solve for it? I hope this makes sense, lmk if it doesn’t

[light helm]

alt way

[urban thunder]

okay thank you

I tried it on my own for a problem and got a long decimal instead of a whole number so I think I did something wrong

[pearl pond]

@urban thunder Has your question been resolved?

[regal adder]

did you try putting that answer in

[light helm]

don't use a calculator

[regal adder]

oh yeah it says use simplified radical form

so just enter yr answer with the radical

[pearl pond]

Channel closed

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[urban thunder]

.reopen

[pearl pond]

✅ Original question: #help-39 message

[urban thunder]

Sorry the messages weren’t loading on my end

let me try that, thank you!

i got it!! Tysm!!

.close

[pearl pond]

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[pearl pond]

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[spring crystal]

which one am i supposed to apply the formula to

only B?

[quiet tendon]

to B

[spring crystal]

what is U for then

[quiet tendon]

U is the entire subspace that you care about, but gram-schmidt is used to produce an orthogonal basis. a basis being a set of linearly independent vectors that spans your subspace

so gram-schmidt is always applied to a basis

[hollow barn]

B is the basis, U is the subspace spanned by this basis (i.e any linear combination of these vectors in the basis)

[hollow barn]

and yes this

[spring crystal]

ok so the answer is (2,1,0) and (-0.6,1.2,0)

[spring crystal]

so i just ignore u completely all the time

whys it even here

[hollow barn]

remember that a set B is a basis if it spans a space and is made up of linearly independent vectors

so its just kinda reaffirming that B is a valid basis for U

since it has to span U in the first place

and its easy to check it is lin indep.

[pearl pond]

@spring crystal Has your question been resolved?

[pearl pond]

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[swift spindle]

Is this correct?

[dense jasper]

,w integrate 2x+8+\frac{24x-32}{x^2-4x+4} dx from 0 to 1

[jolly parrot]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by civil_service_pigeon

[dense jasper]

-48+12 is not -32

[swift spindle]

oh wait

[swift spindle]

is this better?

[swift spindle]

wait what

oh no way

I read that like five times too

thank u sm

[dense jasper]

[swift spindle]

.close

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[swift spindle]

how is this sign wrong?

[floral river]

👋

[fierce sky]

What makes you think it is wrong?

It looks right to me. The double negative becomes a positive

[swift spindle]

oh wait yea i think teh answers weer wrong

thanks

.close

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[elder valley]

@fleet ridge yes I finished it

[fleet ridge]

Oh ok

[lament dawn]

I think you've inadvertently opened a new help channel, if you've a question, do ask away, otherwise, type .close

[pearl pond]

@elder valley Has your question been resolved?

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[royal galleon]

how to proceed I will have infinity minus infinity and I don't think that means anything

[sturdy bane]

you can factor out x

x(loga - blogx/x)

logx/x -> 0

[autumn fossil]

and that e^xloga - e^blogx looks wrong

[sturdy bane]

btw not sure whats up with your third expression that just seems wrong

yea

[royal galleon]

ye should be multiplication

ok so it then approaches +infinity

thanks

.solved

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[hoary relic]

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[inland walrus]

Let S = {1, 2, 3, ..., 10}. Consider the set
X = {R : R is an equivalence relation on the set S such that R has exactly 42 elements}.
Then the number of elements in X is ________.

[smoky musk]

Wait, I have an easier way to solve.

If R ∈ X, prove that there is at least 5 elements and at most 6 elements of S that is equal to each other according to R.

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@inland walrus Has your question been resolved?

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[hazy quail]

can anyone help me with expansion of limh->0
[(x+h)^n + (x)^2]/h so the result it into power rule

[plush bramble]

binomial theorem

[hazy quail]

alright

.close

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[hardy rose]

not sure if theres something im not getting how does tis make sense

[hardy rose]

so the x there at the blue point should be 12

but when i do 16/2 it gives 8

so is it 8 or 12

[runic shoal]

that 16m segment doesnt go from x = 0

[hardy rose]

oh

wait the 16 helps u find the gap between the summit and the (a,14)

so its (4,14) and(16,14)

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[junior anchor]

Wait why is pi not constructible

[junior anchor]

Can't we draw a circle of radius 0.5

[ivory basin]

How does that allow you to construct pi

You don't have any way to draw a line with the circumference of a circle as its length

[junior anchor]

Hmm

Right

Makes sense

Yed

Yes

I got fooled

[ivory basin]

Pi is not even algebraic

[junior anchor]

Hmm yed

[ivory basin]

Constructible is a far cry

[junior anchor]

Yes

Constructible is a subset of algebraic numbers I assume?

[ivory basin]

Yes

[junior anchor]

Nice

Thanks

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[vocal heron]

how do i find the geometric mean of 12 and 20?

[vocal heron]

i have the formula figured but i’m not so sure on what answer to input

[woven matrix]

the formula for the geometric mean of two numbers is the square root of their product

[vocal heron]

i’m a bit lost about the x^2 = ab / x = √ab

[woven matrix]

several ways to do it as always, because it's algebra
if you don't want to think, take the product, then the square root
12*20 = 240
so the geometric mean is the square root of 240

if you prefer smaller numbers, you can use the square root before

sqrt(12) = 2sqrt(3) and sqrt(20) = 2sqrt(5)

so their product is 4sqrt(15)

which is the same thing as sqrt(240)

[vocal heron]

i didn’t like how my math program presented the way that geometric mean is a/x = x/b

[woven matrix]

well, your math program probably does this to introduce the geometrical point of view at some point

[vocal heron]

sighh

teaching in geometry btw

so odd theyre asking with introducing the point of view that way

i think i’ll have to keep close tabs and see if x = √ab even helps

-# (they said 15.5) ???

[plush bramble]

,calc sqrt(12 * 20)

[jolly parrot]

Result:

15.49193338483

[plush bramble]

yes to 1 decimal place

[vocal heron]

oh to the tenth </33

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[vocal heron]

.reopen

[pearl pond]

✅ Original question: #help-39 message

[fathom pagoda]

yes?

[vocal heron]

okay now they did introduce smth slightly different which is "the geometric mean of a n and 4x the number is 22. what is the number" i wonder why that is

[fathom pagoda]

solving equation? like just more practice

[flint basalt]

what do you mean by why that is? why what is?

like why are they introducing variables into this?

[sterile gazelle]

[fathom pagoda]

i think he meant the geometric mean of a number n and 4n is 22, what is n

[vocal heron]

yea thats what i meant ^^

i got so confused

[flint basalt]

well its the same thing you did here, you're just solving for the variable now.

[vocal heron]

it kinda clicked that it had something to do with decimal numbers being multiplied

https://tenor.com/view/max-verstappen-shock-f1-meme-reaction-gif-11301909184524064481

oh maybe not

ykw it is

[vocal heron]

it did say 22 is the geometric mean is number and 4x the number

[plush bramble]

does 4x the number mean 4 times the number?

x is usually meant for a variable in math

if you want to use multiplication, the symbol is *

[fathom pagoda]

this ^^

[vocal heron]

i assume so

[flint basalt]

yes you have n and 4n, so put that into sqrt(ab) and set that equal to 22, then proceed to use algebra to solve.

[fathom pagoda]

$\sqrt{n \times 4n} = 22$

[jolly parrot]

IdelUser404

[pearl pond]

@vocal heron Has your question been resolved?

[cyan lotus]

I would like to ask for assistance.
If you are willing to help, please contact me.
thx.

[light helm]

#❓how-to-get-help

[cyan lotus]

can I conect directly?

[light helm]

wdym

[cyan lotus]

Let's tell on DM

[light helm]

most people dislike helping through dms

claming a dedicated channel is the most efficient way of getting help in this server