help-39

[real spindle]

Suppose in image a) I wanted to do the opposite. Meaning doing it for a instead of u. That’s confusing the heck out of me even trying to draw it.

[tender gate]

what

do you not understand the description of a?

[real spindle]

In the textbook here they’re projecting one onto the other etc

I just wonder what if I was asked to do the opposite

Instead of going from Q to the tip of U and drawing a perpendicular down there

[tender gate]

as in if you had a and you want to find u?

[real spindle]

Imagine that the first dot said drop a perpendicular from the tip of a to the line through through u

Starting from there I eventually get confused even trying to make sense of drawing it

[real spindle]

Replace it with this

[tender gate]

oh

well in that case then you would need to scale u by a large amount

[real spindle]

Yea that’s my first step

[tender gate]

since a is far and you need a perpendicular that means you basically create a triangle

[real spindle]

Yes so I draw a dotted line from the tip of a to where it intersects u

After that I’m confused

[tender gate]

yeah you can draw 2 straight lines but in that case you be projecting a onto u

[real spindle]

I’d just like to go through the second and third dot together

With the situation we’re currently in

[tender gate]

what they are asking for is to project u onto a

[real spindle]

By dot I mean the three key points or the steps in the textbook

[tender gate]

and you want to project a onto u

[real spindle]

Yes

Just for théories sake

[tender gate]

well yeah you could do that

[real spindle]

Idk why I get stuck after drawing my perpendicular

I scale u a bunch

I draw a line from tip of a to u

Then I’m stuck

Basically I don’t know how to construct w2 here

I get that my scaled up u becomes w1

[tender gate]

so this

[real spindle]

That’s what’s in the textbook for the w ones

But for my situation

What’s in red would be part of w1

[tender gate]

wait what

you want to have a on u correct?

oh wait you want to do this?

[real spindle]

Wait what

[tender gate]

you want w1 to be the tilted line

i don't think i understood what you want to do

you want what i have as u to be w1?

[real spindle]

I’m just following the exact three steps that are in the textbook but replacing the first line with the line I gave you earlier.

[tender gate]

well then it would be this no?

since you want to drop a perpendicular of a onto u

and in order to do that you would need to scale up your vector u which is a sum of w1 and w2

since vector addition goes like this

i don't think you can do what you want to do

since it wouldn't make too much sense

following vector addition you can't have w1 going the same direction as u

take w1 as the x coordinate of the vector and w2 as the y coordinate of the vector

and think of the tip of it as a point

and every vector is a line that goes from the origin to that point

[tender gate]

yeah no that wouldn't work

[real spindle]

That’s following the steps 1 and 2

Then step 3 would have to be

a-w1

Which would give me something like

Cause a - w1 would be

From tip of a

In opposite direction of w1

So parallel to my w1

[tender gate]

this is something of how you should see vectors

[real spindle]

I’d have my w2

[tender gate]

in this case w2 would be the dotted line

since your vectors are in R^2 you can't have that type of orthogonal vector

w2 in your case would be the perpendicular line from a to u

[real spindle]

Ok thanks

.close

[pearl pond]

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[silent flower]

I need help with number 6

[silent flower]

Hello?

<@&286206848099549185>

[pearl pond]

@silent flower Has your question been resolved?

[silent flower]

.close

[pearl pond]

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[chrome plank]

I've got it down to the following... working on the "prove u isn't prime" bit now

u^2 = 2v^2 + w^2

[silent flower]

.reopen

[pearl pond]

✅

[silent flower]

how did u get that?

[half bramble]

Hi, does anyone has a solution for this question?

[silent flower]

this channel thingy is being used mart 🥲

[chrome river]

#❓how-to-get-help

[chrome plank]

No, I've screwed up.

[silent flower]

Yea it looks like pythagreom

But there aren’t any right angles

[latent quail]

!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).

[silent flower]

But it’s alright

[chrome plank]

PRS and PQS are both right triangles

[silent flower]

Ohh

I see it now

[half bramble]

Sorry, first time here lol

[silent flower]

No problem!

Go to math help available

[pearl pond]

@silent flower Has your question been resolved?

[chrome plank]

getting there...

[pearl pond]

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[upper latch]

I need help with my math homework

[upper latch]

I need help with this one

How y'all do this

Im dumb ah hell

[rugged jolt]

okay. i'll get you started with the definition of an arithmetic sequence. An arithmetic sequence is a sequence in which each term differs by the previous one by a set number (ex: 1,3,5,7,...)

and a geometric sequence is a sequence in which each term is the previous term multiplied by a set value (ex: 2,4,8,16,32...)

and a series is where you add each term in a sequence together

the fibonacci sequence is a sequence in which the subsequent term is the previous two terms added (starts as 0 then 1, so 0, 1, 1, 2, 3, 5, 8,...)

the harmonic sequence is the sequence consisting of all fractions with 1 in the numerator, or the sequence of inverses (1,1/2,1/3,1/4,1/5 ...)

[upper latch]

I have a question for the geometric sequence

Could I ask my question???

[rugged jolt]

yes?

you don't have to ask to ask a question

go ahead

[upper latch]

So for geometric

It's 2 4 8 16 right???

So is 3 6 9 12 15

[rugged jolt]

no, that would be arithmetic

generally, a geometric series is $a_0a^n$ where $a_0$ is an initial value

[jolly parrot]

fish

[upper latch]

Ah I see

[pearl pond]

@upper latch Has your question been resolved?

[pearl pond]

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[tender gate]

yooo

circuit

[naive dirge]

it asks for the current on each resistor respectively.

I'm fked up.

help me please

[tender gate]

you need to find the total current in the circuit first

[naive dirge]

I got 3/2

[tender gate]

how did you get that

i did not get 3/2

unless i did it wrong

but i got 3

on the right you have the 4 and 2 ohm resistors

[naive dirge]

1

[tender gate]

no

[naive dirge]

am I wrong

why

[tender gate]

do you know about series and parallel connections

[naive dirge]

sure

[tender gate]

well some resistors are in parallel here

[naive dirge]

bro, I'm so stress

[tender gate]

no need

[naive dirge]

it feel like im detach a bomb

[tender gate]

lmao

nah dw about it

[naive dirge]

I think these things on the blue encircled group can be considered as one.

[tender gate]

perfect yes

[naive dirge]

and then the red and blue resistor are parallel

[tender gate]

yes

[naive dirge]

therefore we can consider the blue and red as one and simplify the situation.

[tender gate]

yes but you don't simply add them

you add them in the way you add parallel resistors

[naive dirge]

what would the ohm of the blue group be

I do not know how to get it.

[tender gate]

1/Rtot = 1/R1 + 1/R2

you should get 2

[naive dirge]

shouldn't it be 6, the ohm of the blue group.

[tender gate]

yes

[tender gate]

but when you add them with this formula you get 2

in this case you don't have R3

[naive dirge]

should I memorize it?

[tender gate]

probably

you will be using it a lot

[naive dirge]

what does the "sub eq" mean

[tender gate]

equivalent

[naive dirge]

I see

I need a clear circuit right?

I'm stress daaaaaamn

[naive dirge]

I do not know how to apply this on the situation

[tender gate]

is it your first time solving circuits?

[naive dirge]

yes.

[tender gate]

okay

its simple

instead of R1 and R2

put 3 and 6

and then calculate it

[naive dirge]

should I consider the 3 ohm and 6ohm resistors as one? like simplify the situation?

is it the usual way to solve a circuit?

[tender gate]

yeah and the value of the resistor can be obtained by calculating it with the formula

[naive dirge]

could you tell me a funny thing or two about solving a circuit. I feel it tedious and stressful.

How should I interpret it

[tender gate]

find the connections that are in series or in parallel simplify them till you get to a simpler form

where you have a resistor, and a power source

[naive dirge]

im actually try to prove the formula

deriving the result from R=V/I

but I stuck in the middle

[tender gate]

bro what 😭

you don't have the current

[naive dirge]

I'm fked up again

[naive dirge]

Should I just remember that formula for R_eq

memorize it

[tender gate]

yeah just remember it

don't complicate it too much

just keep it simple

[naive dirge]

But I'M SO CURIOUS ABOUT HOW TO DERIVE IT FROM R=V/I

[naive dirge]

does V_A = V_B = V

[naive dirge]

Is it true

[tender gate]

yes

the voltage across resistors in parallel is the same but the current isn't

you have different currents and different resistance valeus

you have the total current = I1 + I2

then you replace them with their values

[naive dirge]

But the resistor should lower the voltage.

voltage is kinda like energy of electric charges

when the charges passess through resistor, their energy should be reduced

[tender gate]

thats the proof

[naive dirge]

that is the voltage should be reduced, resulting in V_A, V_B, V be different.

[tender gate]

the voltage across resistors that are in parallel is the same

[naive dirge]

why passing a resistor would not reduce the voltage of a electric charge.

that's so strange.

[tender gate]

it has different current, but the voltage is the same

[naive dirge]

Oh...

[tender gate]

okay so back to the problem

[naive dirge]

is there any intuitive way to think of it.

[tender gate]

did you get the simplified version of the circuit?

[naive dirge]

I haven't yet.

[tender gate]

yes

[naive dirge]

what is it

[tender gate]

this. here both resistors are connected to the + and - terminals of the battery

so the voltage across them is the same since at the bottom its 0 and at the top is V

[naive dirge]

How do you know it is 0 at the bottom

[tender gate]

the black wire is ground

and usually ground is 0V

[naive dirge]

what if it is not, I do not see the ground symbol.

[tender gate]

okay

hol on

lets say our battery thats connected is 12V

at the top we know that its 12 volts

[naive dirge]

sure

[tender gate]

and we can calculate the potential by taking the + over the -

12- x = 12

what's x

potential difference in a circuit we go from higher potential to lower potential

from + to -

[iron basin]

why is there an arrow pointing to "12 V" on the righT?

[naive dirge]

The teacher of the video simplify the situation

and show on the right

I'm astounished by his magic trick

[naive dirge]

I do not know what is the x.

[tender gate]

12 - something = 12

[naive dirge]

as well as I do not know where the equation comes from

[naive dirge]

how you get that equation

what does it mean

[tender gate]

blurple galaxy take over dawg i'm out lmao

too many questions

[iron basin]

lol

[naive dirge]

I'm trying to understand it.

[iron basin]

uh im assuming you know what series and paraller resistors are?

[naive dirge]

yes

[iron basin]

alright

so across parallel resistors voltage is same

and across series its divided according to how good it can resist

[naive dirge]

So passing a resistor would not reduce the voltage of a electric charge.

[iron basin]

passing a resistor in the sense?

[naive dirge]

is it true

[naive dirge]

yes, does passing a resistor lower the voltage of a electric charge

[iron basin]

no like what do you mean "passing"

[naive dirge]

like A-resistor-B.

some charge traverse from A to B, it passes the resistor.

would the voltage of the charge be reduced by the resistor.

[iron basin]

oh, you mean to ask if electric charge passing through a resistor reduces the voltage?

[naive dirge]

yes

[iron basin]

well, it doesnt reduce the overall voltage

but yes, the voltage gets divided across the resistors if they are in series

and so here we will do some very slight modifications to the diagram

[naive dirge]

would the voltage changes if resistors are parallel

[iron basin]

nope

[naive dirge]

I do not agree with this.

[iron basin]

all the resistors connected in parallel will have the same voltage

[iron basin]

oh

why so

[naive dirge]

ohhh

[naive dirge]

before those electric charges passing through the resistors, their voltages are the same.

[iron basin]

no

[naive dirge]

But, after passing through, their voltages vary.

[iron basin]

AFTER those electric charges pass

uhhhhhh

[naive dirge]

what

[iron basin]

one minute

[naive dirge]

I do not agree

[iron basin]

ill just see if i can find a diagram

this basically

since all resistors are connected from the same endpoints in parallel

the potential difference across those two points will be same for all resistors connected across those points

but in series the potential decreases from 12V to 0V

so the difference is split across the resistors

based on how well they resist

[naive dirge]

I do not like the diagram. It is just memorisation rather than understanding

[iron basin]

memorization??? what memorization??????

oh

[naive dirge]

So were you saying that point A and point B should have same voltage

[iron basin]

that diagram

[naive dirge]

is it your point

[iron basin]

no no

not a single point

the voltage across A and B is same for all resistors

[naive dirge]

then what is it

[iron basin]

connected in parallel

voltage is the potential difference

[naive dirge]

yes

the voltage be reduced when passing through a resistor

do you agree

[iron basin]

i guess so yes

[naive dirge]

If resistors have different ohm, then the voltage would not be the same.

After those charges passing through them.

do you agree

[iron basin]

if they are in series

because in series the same current goes through all resistors

but in parallel the current divides itself and passes through each resistor in different amounts

[naive dirge]

ohhh

[iron basin]

thats why V = IR still holds

[naive dirge]

would they be equally divided.

[iron basin]

not necessarily

depending on its resistance

for example if 1 ohm and 3 ohm are connected in parallel

3/4ths of the current will flow though 1 ohm resistor

and the other 1/4th will pass through 3 ohm

[naive dirge]

what about the voltage, shouldn't the current depend on it?

[iron basin]

yeah V = IR

for each resistor as resistance increases current passing through it decreases

to keep V constant

[naive dirge]

I thought it is the resistance that is constant instead of V to be constant.

I mean each resistor, conductor has a constant resistance, at some temperature.

[iron basin]

uhhhhhh

that is DEFINITELY not true

steel and plastic

at room temperature

one has very high and other has very low resistance

[naive dirge]

I agree

but the resistance of them are fixed

right

[iron basin]

hows that

[naive dirge]

that means it is a false claim

[iron basin]

why so

it makes sense

[naive dirge]

resistance would not "increase"

resistance is a constant given a situation

[iron basin]

resistance is the QUALITY of a substance

for each substance resistance varies

[naive dirge]

I see

[iron basin]

im not saying resistance of a single substance

[naive dirge]

I see

[iron basin]

i meant to say that if the resistance of a substance is higher then the current passing through it will be lower

[naive dirge]

I see now

So you are claiming that point T and point S have same voltage.

Is it your claim

[iron basin]

again

points cant have voltage

voltage ACROSS the two points is same for all resistors

[naive dirge]

electric charges on these points

[tender gate]

see the arrows

you take the tip of the arrow - the end of the arrow and find how much voltage goes across the resistor

and its the same for both since both resistors are connected to the same thing (called node)

[naive dirge]

does the direction of these arrow as the same as the current

[tender gate]

no it opposes the current

so current goes down these arrows go up

because voltage goes from high potential to low potential

[naive dirge]

How do you know the bottom would be 0, or should I say how do you get the voltage of the bottom passage.

[tender gate]

well you know that the top is 12 V

green arrow at the power source on the left

voltage goes from high potential to low

the source is 12V

so since you know that the voltage goes from high potential to low potential

and across the voltage source you have 12 volts

you take high potential (12) - lower potential ( x ) = 12

x is the value of the black line

this equation should not be hard to solve

[naive dirge]

where you get that equation from

how do you know the "high potential - lower potential" would be 12

[tender gate]

because the voltage at the source is 12

bro i legit explained every step i took to find that equation idk what else i could do

[naive dirge]

does it imply "the high potential - the lower potential = 12"

[tender gate]

yes

[naive dirge]

why

[tender gate]

whats the voltage at the source

[naive dirge]

it is 12

[tender gate]

okay

[naive dirge]

I see

I see now

[tender gate]

https://www.multisim.com/

try this

[naive dirge]

I agree with it now that if parallel then the same voltage

[tender gate]

sign up its free you can create circuits and analyse voltage across resistors and currents

[naive dirge]

ohhh

fantastic

[tender gate]

you can make any circuit in here and it would help you if you can't find the correct answer

[naive dirge]

I see

[tender gate]

watch more youtube videos about electric circuits though, if you are interesed in them and you aren't being taught

[naive dirge]

I think the reason that I feel it boring is because I do not actually apply it in real life.

[tender gate]

electric circuits?

[naive dirge]

yes

[tender gate]

well i mean you can always get a small electronics set and play with that

just stay under 12 V or else it would start hurting

[naive dirge]

like if I was running a NASA project that needs me to solve those electric circuits

I would definitely be interested in that.

[tender gate]

well you seem very curious about them with the amout of questions you asked

so you can learn about them alot

if you get familiar with them enough you can start hopping on electronic circuits and using gates and such to power stuff

[naive dirge]

can the "water analogy" be exercised to explain all of these things like if parallel then they have same voltage.

[tender gate]

water analogy is used more for current

voltage you can think of like mountains

higher potential is a high mountain

and lower potential is a smaller mountain

and 0V is sea level

the higher the voltage the higher the mountain

[naive dirge]

I see

I see it now

[iron basin]

the water splits across different streams

but they all descend the same height

thaats how parallel resistors work

[naive dirge]

How do you know they all descend the same height? by the "high potential - low potential" equation?

all the analogy can be applied to justify it.

[tender gate]

can i send files on this server?

[naive dirge]

I suppose so?

[tender gate]

do you have a laptop?

[naive dirge]

sure

[tender gate]

this is a circuit simulation program, you don't have to download it if you don't trust the file but it shows how the voltage moves across the circuit

don't go too deep into it becasue then you have AC circuits which are different than DC which is what you are doing for the moment

[pearl pond]

@naive dirge Has your question been resolved?

[pearl pond]

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[latent quail]

What have you tried?

[pearl pond]

@frozen dagger Has your question been resolved?

[latent quail]

Have you tried moving 5^2 in the denominator to the right side?

Not that fast

Try multiplying the equation by 5^3

[burnt copper]

Is it 4?

[latent quail]

!nosols

[pearl pond]

As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.

[latent quail]

Do you have any idea about the next step?

@frozen dagger

Move one to the right side

🪵

And move 3 to the right side, end

🪵

Log

🪵 5

Yes

Rmb, log base 5

and that’s all, that’s the entire process

What is this for?

@frozen dagger have you gotten my point?

If does, give me an affirmative reply. On the contrary, tell me where you are stuck at.

[burnt copper]

Can u help me with mine

[latent quail]

Which channel?

[burnt copper]

11

[latent quail]

You cannot take out 7 from the exponent

I know what you mean now

yes

Just move 3 from the left to the right

That’s all

Correct

That’s all

That’s x

Aren’t you supposed to find x?

@frozen dagger

You don’t need to deal with it

Do you actually believe the answer is rational?

No it’s not

[errant cedar]

it’s in between 1.5 and 2

are you able to isolate 5^x on one side of the equation?

imo that’s the first step then we’ll talk about logs

are you able to move the 5 squared on the denominator to the other side?

[latent quail]

[latent quail]

Your equation has a few flaw

All the bases in the equation are 5

[errant cedar]

ah yes sorry godam

i’ll leave you this

[latent quail]

Nah

I don’t know how to convince them that the answer is irrational

I’ve guided him through the entire process

@errant cedar

[errant cedar]

yeah i’m reading that

[latent quail]

That’s the current issue

[errant cedar]

wait

but when you zoom in it’s not exactly 4

it’s a bit less

[pearl pond]

@frozen dagger Has your question been resolved?

[pearl pond]

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• Show your work, and if possible, explain where you are stuck.
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[midnight haven]

is the numerator odd?

thats a hinr

hint

[scenic hedge]

Odd ?

No, f(-x) is not equal to -f(x)

If that's what u mean

[pearl pond]

@scenic hedge Has your question been resolved?

[pearl pond]

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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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[junior token]

Yo

[brisk steeple]

.

[junior token]

Hi

Wait a sec

[brisk steeple]

!da2a

[pearl pond]

No need to ask “Can I ask…?” or “Does anyone know about…?”—it’s faster for everyone if you just ask your question! See https://dontasktoask.com/

[junior token]

Plz check my question 16

Did I do it wrong?

[candid harbor]

no its correct

[junior token]

Ok thank you so much

.close

[pearl pond]

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[arctic roost]

Can someone help me tell which graph has a vertical asymptote at x=0
x=0, and passes through the point (1,7)

[cosmic raptor]

mark where point (1,7) is on each of the graphs

its ok if it's not on the scale for some of them

[arctic roost]

is this the correct graph?

[cosmic raptor]

yep

[arctic roost]

thanks

.close

[pearl pond]

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[pearl pond]

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[forest sun]

could someone explain how they got to that answer? I got the right tangent line eq, y=1/2(x) +2 but my answer is always wrong

[lime river]

Just use the formula f(r) = f(a) + delx (derivative of f(x) at x = a)
Here delx is. 4 and a is 27

[leaden wadi]

What are you using for (x-a) in the approximation?

[forest sun]

so f(27) +4(1/((3x)^(2/3))

[lime river]

Ye

[forest sun]

hmm

[lime river]

Btw cube root of 27 is 3 how tf did you get 2.11

[forest sun]

no idea

i saw a vid where they made us find the tangent line

and use that to approx

[lime river]

U don't need the eq of tangent to approx u can directly use the derivative at that point

[forest sun]

so in here 1/((3x)^(2/3))

can i just put the 27.4 instead of x?

wait no

that would be wrong

[leaden wadi]

a is the value you use to approximate some value near a. In thise case, a = 27.

[forest sun]

right

[leaden wadi]

It is the nearest cube value to 27.4.

[forest sun]

f(a) would be 3

[leaden wadi]

In the above equation, you plug in all of the values for a and use 27.4 for x.

The above equation is the non-reduce form of y = mx + b.

[forest sun]

right

so would be something like this

[leaden wadi]

No, the 3 in (3)^(2/3) should be 27.

[forest sun]

sorry, wdym?

ohh

like instead of 3 its 27

[leaden wadi]

You're trying to cube the 27 before you need to.

[forest sun]

okay now that makes more sense since the answer is right

thanks

.solved

[pearl pond]

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[tawny drift]

Can someone explain how this answer was achieved?

[tawny drift]

I know it's a very simple problem in multivariable calc, but it has been a while, and I am definitely missing something

not to mention my brain is fried today

[tawny drift]

In the first pair of brackets, would the partial derivatives not reduce the x. 2y, and 3z to 1, 2, and 3 respectively?

Or do I have to multiply out both pairs of brackets? Since the x, 2y, and 3z, are in the wrong place to be partial differentiated?

[ocean hornet]

the notation is a little weird, but i believe the inner brackets is the divergence of A, which is then scalar multiplied with B

so assuming A=(x, 2y, 3z) and B=(3y, -2x, 0), then that expression is div(A)*B

[tawny drift]

Yes, that is correct

Well, I have always seen divergence to mean $\nabla \dotproduct v$

[jolly parrot]

Adam

[tawny drift]

where v is a vector function

but those should mean the same thing

because dot product is commutative

[ocean hornet]

wait but then im confused because the divergence should be 6, so then it is 6(3y, -2x,0) = (18y,-12x,0)

so i don't know how they got that

[tawny drift]

That is exactly what I thought

So are they incorrect?

[ocean hornet]

i think so

[tawny drift]

Hmm

Problem is, this is part of a proof for one of the product rules which I have attempted, but in the textbook, this step is done, and after a few more steps, they reach the correct conclusion

Here, the same possible mistake is done too

[ocean hornet]

ok in that case i think what they are distributing and then applying the partials to the term on the right

so for example you get $3y\frac{\partial}{\partial x} x = 3y$

[jolly parrot]

Bair

[tawny drift]

oh yeah

[ocean hornet]

very bizarre

[tawny drift]

so 3y is treated as an outside constant, rather than something being differentiated

but anyways, once you distribute, you can bring the 3y in like normal, then differentiate

[tawny drift]

yeah, it is

well, thank you very much for helping, this was giving me a headache!

.close

[pearl pond]

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[weak cipher]

what is wrong with this

[weak cipher]

eveyrhting looks good, am i missing something

[cosmic raptor]

the last part is a line segment, not a ray

so it needs an upper bound

[weak cipher]

the one on the right needs to be bound?

oh

yes

welp nvm

how was this right

and this wrong

nvm

ill come back later with stuff i need help w

.close

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[weak cipher]

.reopen

[pearl pond]

✅

[weak cipher]

how is the bottom function supposed to be graphed on this plot

[summer imp]

You can't draw the y intercept, but it'll still touch the x axis at x=5

[weak cipher]

is it this?

ok nevermind that answer didnt go thru

[summer imp]

Well at x=2 it should be -10

So connect those two points

[weak cipher]

wym?

[summer imp]

It shouldn't be passing through (2,-9)

[weak cipher]

oh

then where should it be starting

i dont understand how im wrong

that should be the answer

[summer imp]

I can't count

[weak cipher]

im so confused lol

[golden fjord]

relatable

[summer imp]

Just forget everything I said I think I'm tired I'll look over your graph again one sec

[weak cipher]

ok

[weak cipher]

do u see anything

[summer imp]

Maybe it's just because the line doesn't really look like it goes through (5,0)? How picky is this graph question?

[weak cipher]

has to be

pretty picky

i give up

this was right

[summer imp]

Oh

[weak cipher]

this was wrong

like wtf

[summer imp]

Isn't it because of that point up top? Does it just pop up there?

[weak cipher]

i have another one sec

look good?

i feel i may have messed up the bottom

but overall it looks good i think

@summer imp

my god

it was wrong

wtf

[summer imp]

Bottom line doesn't have a slope of 1/3

[weak cipher]

good?

[summer imp]

And top line you seem to have drawn from (-1,10) to (2,6), but it doesn't go through (-1,10), try (0,9)

[summer imp]

No it's 1/4 now

[weak cipher]

its impossible to do 1/3

because i move it up and its 1/2

[summer imp]

Start from the first point, go up 1 and right 3

[weak cipher]

ok, from here?

[summer imp]

This is such a weird tool how does it draw the arrows and full lines

[weak cipher]

ikr

you plot the points

and drag a line

and its not flexible

its hard to explain

[summer imp]

And it puts an arrow at the end when?

Because that bottom one needs an arroe

[weak cipher]

on a specific point, so no inbetween action

[summer imp]

If you need to draw it up to the edge of the graph for it to show an arrowhead then put a point on the edge of the graph such that then line passes through that point you just added

[weak cipher]

alright ima start a new opne

thanks fo rthe help

ima starta new one

[summer imp]

It needs to look like that. The thing is I just don’t know how your software works. It might just be put put off t=by the extra points you seem to have on top of the arrowheads here

[weak cipher]

ok HOW TF IS THIS WRONG

[weak cipher]

ye, i skipped it

[summer imp]

But you still have the same thing

[summer imp]

And the bottom line doesn’t have slope 1/4

[weak cipher]

this is so dumb

its not letting me put it at the half part

[weak cipher]

the top left is right

[summer imp]

Are you sure you need to draw the two points? Can’t you just start from the point you drew say at (4,-3) and drag a line ensuring it passes through (8,-4)?

[weak cipher]

ok i can drag from there but it locks onto one of the points

so i cant just lay it in the middle

it keeps doing it on the right answers tho, i dont know how to

im so done

i can put it in the middle and it keep shows up in the examples on the fucking middle

[summer imp]

You might want to ask clarifications with your instructor then because it looks like it’s either really poorly made or you’re doing something wrong drawing the lines

[weak cipher]

yh

sadly

it is summer homework and due tomorrow

💀

it was like one of my last problems

[summer imp]

Ah shoot

[weak cipher]

i figured it out

it was bs

.close

[pearl pond]

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[weak cipher]

i have 3 questions i need help on

[weak cipher]

i can do the long division

but

i need some assitance

3 more of these and then i can sleep for next day of school id really appreciate the help

[pearl pond]

@weak cipher Has your question been resolved?

[weak cipher]

.close

[pearl pond]

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[winged karma]

Does anyone have any tips for when you are stuck reading a proof for an hour and you still can’t understand?

[vital estuary]

ask for help

no shame in that

[winged karma]

Thing is, is summer and I’m just reading on my own.

There isn’t a professor or upperclassman to ask. I google it but I barely find clear explanations, instead I find the same proof or longer again

[tough depot]

well uh

there's always here

[winged karma]

Okey thank you, I’ll share the proof

Also anytime I share a picture of a page, do I have to to edit it and cut it? I just want to know for next time.

Btw I’m not sure what the name of this proof is but it is related to something called the Ramsey game

Which is a bit related to graph theory and the nodes having either odd or even degree

I think

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[clear orchid]

I’m struggling with a show that question

[merry carbon]

Well then, show that question you're struggling with

[clear orchid]

they say i can use the result and technique used in a prior question

[vital crescent]

their technique is on the finite case: $$\sum_{i=1}^n$$

[jolly parrot]

qwertytrewq

[vital crescent]

now let us do the finite case first: what is $$\sum_{i=1}^n ix^i$$

[jolly parrot]

qwertytrewq

[clear orchid]

are you asking what it equals?

[vital crescent]

yeah

follow the technique from the second img step by step

[clear orchid]

x+2x^2 + 3x^3 + … + (n-1)x^(n-1) + n*x^n

this is what i had previously tried

[vital crescent]

good, now notice we have a formula for $$1+x+x^2+\cdots+x^{n-1}$$

[jolly parrot]

qwertytrewq

[vital crescent]

precisely from the previous pic

[clear orchid]

yeah

[vital crescent]

so can you simplify further?

[clear orchid]

yeah

[vital crescent]

using the formula?

[clear orchid]

one sec

Yeah i got it thank you

[vital crescent]

the light is covering some part i cant see

[pearl pond]

@clear orchid Has your question been resolved?

[clear orchid]

.close

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[versed estuary]

I have a uniform distribution D between T-E and T+E where E is known but T is unknown.
I can sample random values from D and average them to try and approximate T, Let's call this approximation T_a. However, I'd like to know how close T_a is to the true value of T.
How could can I define a function F(E, W, P) where E≥0 W≥0 0≤P≤1 and where P is the probability that |T_a-T|≤W is true?
As an example: F(5, 2, 0.5) would tell me how many samples I'd need to take of D to be 50% sure that T_a is within 2 units of T.

Any help is appreciated ^^

[pearl pond]

@versed estuary Has your question been resolved?

[versed estuary]

<@&286206848099549185> Would anyone be willing to help me? If I phrased the question poorly, feel free to ask for clarification 😄

[midnight haven]

High school diploma but ask away

[versed estuary]

i wrote the question here ^

if anything is unclear, just ask and i'll see if i can explain better

[versed estuary]

is anything unclear?

[last moth]

Btw if you don't get an answer here, you might be able to get an answer in #probability-statistics

[midnight haven]

Ngl I don’t know. Kinda rusty might need to change my roles

Ask a higher up im new

( and I’ve been drinking )

[versed estuary]

oh, alright. is it fine to ask questions there as well? i assumed only the help section was dedicated to that.

[last moth]

Yup the topics channels are also fine to ask for help in

Just try not to have the same question active in multiple different places at the same time

[versed estuary]

should i close this first then?

@last moth ?

[last moth]

Yeah, if you want to ask the q in #probability-statistics instead

Hope you find someone able to help!

[versed estuary]

i might give that a try in a bit then!

[versed estuary]

thanks!

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[elfin wyvern]

Hello

[elfin wyvern]

I need help

[latent quail]

[elfin wyvern]

I will not show the other questions since it's basically the same idea

I just want to know how you can tell if a graph is a polynominal function

like what are the characteristics of it

I can search it up in like other places but like I thought it would be faster if I just asked it here

[dapper kraken]

a polynomial function will shoot up to infinity like a

not sure how to specify it tho

[latent quail]

A polynomial function will approach ♾️/ - ♾️ when x is getting extremely big or small

[elfin wyvern]

hmm

so I'm guessing that the first one IS a polynomial function

[iron stream]

Yeah it is

[elfin wyvern]

and it would be considered a quadratic function since it has 2 zeroes

[iron stream]

No

[elfin wyvern]

but the second one would not be since it has no zeroes

[iron stream]

It has f'x = 0 at three points

[iron stream]

It is not a quadratic

[elfin wyvern]

oh

[iron stream]

A higher order with complex roots

[elfin wyvern]

ohh

is it because the graph looks like broken?

a regular quadatric function would look normal

like no bends

is that why

[iron stream]

A quadratic function will always be a parabola

[elfin wyvern]

alright

so the first one IS a polynomial function but it's just a higher degree one?

[iron stream]

Yeah

[elfin wyvern]

interesting..

further question

[iron stream]

2nd one is just observation

[elfin wyvern]

So in order for it to be a polynomianl function, is it required for it to have zeroes?

[iron stream]

I'm giving an example

[elfin wyvern]

for example like the second one wouldn't be a polynominal function since it doesn't have any zeroes

[iron stream]

,w graph x²+x+1= 0

[elfin wyvern]

and it's an exponential function

[jolly parrot]

Results provided by WolframAlpha

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Upgrade to WolframAlpha Pro!

Requested by xor_11

[elfin wyvern]

hmm

[iron stream]

Is x² +x +1 polynomial?

[elfin wyvern]

oh that one doesn't have any zeroes

Yeah, I guess

It seems to be

[iron stream]

It has zeroes

But imaginary

[elfin wyvern]

oh

oh

[iron stream]

We call them complex roots

[elfin wyvern]

wait so since it is imaginary, it would not be considerd a polynomial function?

Do the zeroes have to be real in order for it to be a polynomial function

[iron stream]

No it is a polynomial function

[elfin wyvern]

ah

[verbal whale]

No

[elfin wyvern]

I see

[iron stream]

Basically polynomial functions are continuous in their domain of definition

[elfin wyvern]

I see..

[iron stream]

Your 2nd Q is although not a polynomial

[elfin wyvern]

hmm

[iron stream]

It is an exponential function

,w graph y= e^x +3

[elfin wyvern]

ah yes

[iron stream]

Wait one moment

[verbal whale]

This is a polynomial function:
$$y = a_{n}x^n + a_{n-1}x^{n-1} + ... + a_2x^2 + a_1x + a_0$$
(with a_n≠0)
@elfin wyvern

[elfin wyvern]

yep

I recognize that

[jolly parrot]

Alberto Z.
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[elfin wyvern]

I mean I understand how you can tell from the equation but I just don't understand how you can tell from the graph

[jolly parrot]

Results provided by WolframAlpha

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Upgrade to WolframAlpha Pro!

Requested by xor_11

[verbal whale]

If you do the limits at x → ±∞ what do you get?

[iron stream]

Your exact graph

[verbal whale]

Or you haven't studied limits yet?

[elfin wyvern]

we're not learning about limits yet

we are still at the very start

[verbal whale]

Alright

[elfin wyvern]

Right now, we just have to determine whether a graph is a polynomial function or not

based on the equation which I understand and based on the graph

[iron stream]

It's recommended you look at graphs of various functions, logarithmic, exponential, trigonometric, polynomial, you will soon understand

[elfin wyvern]

alright

I'll check it out

[iron stream]

Use Desmos to try how various graphs look like

[elfin wyvern]

Okay

[iron stream]

One moment

https://www.purplemath.com/modules/polyends4.htm

Without going in detail

See how graphs can be of polynomial function of various degrees

[elfin wyvern]

Yep

[iron stream]

Just look at the images , it's quite beginner friendly kind

[elfin wyvern]

I can see that

[elfin wyvern]

Is there any good site I can practice?

I'm learning Advanced Functions right now

[iron stream]

What ?

[elfin wyvern]

I mean practice problems

[iron stream]

Idk such site but you can think of a random function in mind , plot it's rough graph and cheçk from desmos

[elfin wyvern]

alright, thanks for the help

I'll look into it

[iron stream]

Yeah 👍

[elfin wyvern]

Yeah, I found this definition:

To tell if a graph represents a polynomial function based on its appearance, you can look for the following characteristics:

1. Smooth and Continuous Curve: The graph of a polynomial function is always smooth and continuous, meaning there are no sharp corners or breaks.

2. End Behavior:

   • If the degree of the polynomial is even, both ends of the graph will either go up or down.
   • If the degree is odd, one end of the graph will go up and the other end will go down.

3. Number of Turning Points:

   • A polynomial function of degree ( n ) can have up to ( n-1 ) turning points (local maxima or minima). For example, a cubic function (degree 3) can have up to 2 turning points.

4. Symmetry:

   • If the polynomial function has only even powers, the graph will be symmetric about the y-axis (even function).
   • If it has only odd powers and no constant term, it may be symmetric about the origin (odd function).

5. No Asymptotes: Polynomial functions do not have asymptotes. If the graph has vertical or horizontal asymptotes, it is not a polynomial function.

6. Behavior Near the x-axis: The graph may touch or cross the x-axis at the roots. It may cross at an angle or just touch the axis if the corresponding root has even multiplicity (e.g., the graph of ( y = (x-1)^2 ) just touches the x-axis at ( x = 1 )).

By checking for these features, you can usually determine if a graph represents a polynomial function.

[jolly parrot]

Ene

[elfin wyvern]

it makes a lot of sense now

the second graph would not be a polynomial function since it has an asymptote

[iron stream]

I mean

Point 5 is not correct

[elfin wyvern]

oh

I see

[iron stream]

Hmm !

[elfin wyvern]

"We should know that the only polynomial functions that have asymptotes are the ones whose degree is 0 (horizontal asymptote) and 1 (oblique asymptote). i.e. functions whose graphs are straight lines. Therefore, we can say that a polynomial function has an asymptote."

Yeah, I can see why

[elfin wyvern]

I just looked at the answer key.

It says:

1. a) "This represents a polynomial function because the domain is a set of all real numbers, the range does not have a lower bound, and the graph does not have horizontal or vertical asymptotes."

ah yes yes

I found a good definition:

In any polynomial expression, the exponents on the variable must be whole numbers.

• A polynomial function is any function that contains a polynomial expression in one variable. The degree of the function is the highest exponent in

the expression. For example, f{x) = 6x^ - 3x^ + 4x - 9 has a degree of 3.

• The nth finite differences of a polynomial function of degree n are constant.

• The domain of a polynomial function is the set of real numbers, {xgR}.

• The range of a polynomial function may be all real numbers, or it may have a lower bound or an upper bound (but not both).

• The graphs of polynomial functions do not have horizontal or vertical asymptotes.

• The graphs of polynomial functions of degree zero are horizontal lines. The shape of other graphs depends on the degree of the function. Five typical shapes are shown for various degrees:

[pearl pond]

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[jolly parrot]

x

[pearl pond]

@minor ferry Has your question been resolved?

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[humble tinsel]

Lets say u: N(1,2)
Then how is Var[-2u] = 16 ?

[humble tinsel]

This is the explanation we got, but i dont get it

[pearl pond]

@humble tinsel Has your question been resolved?

[humble tinsel]

.close

[pearl pond]

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Use .reopen if this was a mistake.

[pearl pond]

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[midnight haven]

so we know that there are total 91 medals

distributed among 60

each one of them atleast got 1 medal; right?
so 91 -60 = 31

now how do i proceed

and now there are 5 people who got three medals

we have to subtract 5*2 medals since these 5 have 1 already

31-10 =21

21 medals!!! were given to those who won in exactly two events

correct me if i am wrong, or suggest some other method to solve it ( venn diagram highly suggested)

[vital crescent]

how many people recieved all medal? (single them out)

oh wait i didn't see you cook afterwards

[midnight haven]

yeah

[vital crescent]

good job

[midnight haven]

yeah i think the answer is correct, but the question is meant to be solved using venn, idk how to

[vital crescent]

oh i see lemme take a look

[vital crescent]

draw an venn diagram with the events A,B,C

where the region A is the people who won A, region B is the people who won B,...

[midnight haven]

mhm

[vital crescent]

and the conditions/the problem statement all traslate to "how many elements are in a certain region"

[midnight haven]

oh yeah, i think i got it

[vital crescent]

cooking

🔥

[midnight haven]

so we got three intersecting circles

we know the thing by which we can calculate n( A u B u C)

[vital crescent]

^this is given since there are 60 people

[midnight haven]

that equation has the thing for two intersecting circle too

[midnight haven]

yeah

and we know n( A n B n C) which is 5

awesome

thanks a lot

.close

[pearl pond]

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[pearl pond]

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[lean orbit]

normally when doing practice problems, i have atleast some idea on how i'd do them, but with this one, i have absolutely no idea
heck, i have negative idea

[lean orbit]

question no. 53, please

(grade 8)

where am i stuck: i can't even understand the question

[drowsy adder]

holy cow- im a 10th grader and its hard

[lean orbit]

🥲

anyone help <@&286206848099549185>

[olive plinth]

stupid!

[stone portal]

Which question

[drowsy adder]

53

[lean orbit]

yes

[drowsy adder]

by any chance ru an indian-

[lean orbit]

how

did

u

know

:o

[onyx kernel]

2nd case must be even

It must be in the form of 2n

[lean orbit]

mhm

[onyx kernel]

420 is the answer

[lean orbit]

let me check

[onyx kernel]

It is in the form of 2k

[midnight haven]

the last leaf has numbers 31 and 32

[lean orbit]

Level 3
52. (b) 53. (c) 54. (a) 55. (c) 56. (d) 57. (b) 58. (b) 59. (a) 60. (b

[midnight haven]

i don’t quite understand what a “case” is

[lean orbit]

same