help-4

[ivory tree]

like is there a better solution using some combinatorics trick?
i saw another question that was kind of similar and it used f(x)=f(x-1)+f(x-2)+f(x-3) or something

[distant pulsar]

the answers are all of them factorial * factorial etc, which suggests the best way to do this is by just counting

[ivory tree]

yeah, i guess so

i want to confirm though, is the answer A?

[distant pulsar]

that is correct

if you want you can state how you arrived there and i can say if it is good

[ivory tree]

since it's a circle, lock 1 of the girl's position so the rest of the girls have a 3! amount of arrangements. then I did like a stars and bars thing where I filled each spot with 2 boys leaving 2 left. with the 2 left and 4 spots, there are 10 arrangements of the 2 boys, and just multiplied 10!
then i just rearranged it
10!x3!x10=10!x5!/2!

[vale dock]

@ivory tree Has your question been resolved?

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@ivory tree Has your question been resolved?

[ivory tree]

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[calm jackal]

Can someone please help me with these just need a explanation so I can do it on my own. (Geometry)

[manic igloo]

Hints: 1) Base angles in isosceles trianges; 2) Thales's theorem; 3) Pythagorean theprem and Thales's theorem; 4) Centroid in a triangle divides the medians with ratio 2:1

[calm jackal]

Bro

What is a thales theorem

Its not explained to us

[manic igloo]

In a right triangle, the center of the circumcircle is in the middle of the hypotenuse.

[calm jackal]

I think can we use other because it's not there for us

[manic igloo]

I do not know any other way to solve 2)

[calm jackal]

Oh

[manic igloo]

The median is the line between a corner of the triangle and the midpoint of the corresponding side. So we have calculate the distance to the point opposite of the hypotenuse somehow. And the only thing we have to work with is the fact, that this point is on the circumcircle, and the center of the circumcirle is the midpoint of the hypetenuse.

[normal hollow]

U can do it using similar triangles as well

[normal hollow]

Draw the figure first

[calm jackal]

Figure?

[native rover]

the shapes

draw the shapes from the problem

[calm jackal]

It's a right angle triangle

[normal hollow]

As in draw the triangle as stated with angles,names and all

[normal hollow]

Yea

[native rover]

u see the fig.3.37 here?

[calm jackal]

It's for the 1) one

[native rover]

then we call this is the figure for the 1) problem

u’ll do the same for the 2)

[normal hollow]

Werent u doing 2?

[calm jackal]

The fig should be like this

[native rover]

then draw the median for the seg AB

it’s the complete fig.

[normal hollow]

Alr good

Name the end point of median as well

And the length of given sides

[native rover]

the only given side length is the hypotenuse

[normal hollow]

I m rlly sorry
Cuz i have been reading q no 3

[calm jackal]

Should I use the Pythagoras theorem

[normal hollow]

And not 2

[native rover]

the $a^2+b^2=c^2$ one?

[rocky lotus]

Mei

[calm jackal]

Yea

[normal hollow]

Um i think try proving that the two traingles formed by the median r congruent to eo

[calm jackal]

We will need to use theorem or any formula

[native rover]

it’s gonna be $\sqrt15$ and i dont think it’s gonna lead to somewhere tho im not too sure abt that

[rocky lotus]

Mei

[normal hollow]

We will be using formula after this

[calm jackal]

Guys should I check the answer it's given in the last page

We might get some hint

Because before this questions there was activity all related to Pythagoras theorem I think there is some relation between this

[calm jackal]

Bro it's not √5 i checked

[native rover]

sqrt 15

not 5

[manic igloo]

No, it is 7.5

[calm jackal]

BROOO

Yea that's the answer

[calm jackal]

I placed the symbol before 5

Of sqrt

[native rover]

and have u learnt things like the median’s length is half of the hypotenuse length?

[calm jackal]

Yea

[native rover]

and i’m saying the hypotenuse length is 15, so according to pythagorean theorem, it should be sqrt 15

[native rover]

then just take the 15 divided by 2

[manic igloo]

In a right triangle, the midpoint of the hypotenuse is the center of the circumcirle. Therfore the distance from this midpoint to all corners of the triangle is the same. -> Median = 7.5

[native rover]

and you will get 7.5

no need for the pythagorean theorem (i think)

[calm jackal]

I think lets leave this question for while we should move further

[native rover]

mkay

so have you done q3

[calm jackal]

I am done with the fig

[native rover]

u can use the pythagorean theorem here to find the value of PR

[native rover]

ts one

[calm jackal]

I should find the value of PR first

[native rover]

yes

[native rover]

now yk what to do next, right?

[calm jackal]

Yea

RS and SP will be 6.5

[native rover]

that’s not what i mean

[native rover]

ts

if you have learnt this, just apply into this situation

[calm jackal]

Ohh sorry I forgot

[native rover]

the whole point is to find QS, correct?

[calm jackal]

Yes

QS will be 6.5

[native rover]

6.5

not 6

it’s HALF the hypotenuse

and 13 divided by 2 is 6.5

[calm jackal]

Yea

[native rover]

so yk what to do next with the 4, right?

[calm jackal]

2:1

[native rover]

use ts as hint

[calm jackal]

Ratio

[native rover]

mkay

[calm jackal]

PG is 5.0 right?

[native rover]

yes

[calm jackal]

So PT will be 7.5

[native rover]

yes

[calm jackal]

And about the 1) one
X= 50
Y= 110
Am I correct?

[native rover]

y=60

not 110

it’s an isosceles triangle

[calm jackal]

ohh

ok ok

[native rover]

but it told u to find ABD and ACD, right?

[calm jackal]

Yea

[native rover]

so, found it?

[calm jackal]

I was thinking of using angles in linear pair but it's not possible here

[native rover]

just plus the angle:)

110 is correct for both

firstly i thought u typed 110 bc u messed up the y and the ABD, ACD one

[calm jackal]

Oh

So ∠ABD = 110° and ∠ACD = 110°

[native rover]

yep

[calm jackal]

Got it

I think I will need to research about the 2) one

Else everything is done

[native rover]

not needed much for that

[native rover]

just use ts

[calm jackal]

Oh

[native rover]

u said you’ve learnt it, right?

just need to apply

[calm jackal]

Yea

Ty for the help

[native rover]

ur welcomed

[calm jackal]

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[deft lichen]

Determine the distance from the point P (2|2|1) to the plane E, which runs parallel to the xy plane and passes through the point A (0|1|4).

hello i need help here

[barren hornet]

hey guys can someone help me with alternate angles idk how to find the size for each part

[deft lichen]

so like

do i neeed to take (0/0/1) as the pointing vector

or

[merry crystal]

I mean u can intuit the shortest distance by drawing the graph

[deft lichen]

what about without drawing

[safe fulcrum]

what does a plane parallel to the xy-plane look like?

[deft lichen]

its above the plane

kinda

[safe fulcrum]

as an equation

[deft lichen]

oh

[safe fulcrum]

yeah, so it would be flat right?

[deft lichen]

yes

[safe fulcrum]

it could either be above or below the plane

[deft lichen]

i cant come up with the numbers

thats my problem

[safe fulcrum]

so which coordinate is the same among all the points?

[deft lichen]

but ik how it would look like

[deft lichen]

the z?

[safe fulcrum]

yep! the z-coordinate would be the sam

so you know the point A has z-coordinate 4 then

[deft lichen]

yeah

but

yeah i do so

now what

[merry crystal]

can u imagine a plane parallel to the xy plane passing through z=4

[safe fulcrum]

yeah, so do you agree that the shortest distance from any point to the plane is the vertical distance?

(the perpendicular distance must be the vertical distance for a flat plane)

[deft lichen]

yes but for the distance part

[safe fulcrum]

yes, so which coordinate are we comparing for the distance?

[deft lichen]

2,2,1

[safe fulcrum]

like which one of those

is it the x-coord, y-coord, or z-coord

[deft lichen]

wait bro

this is how we calculate the distance

or like this

wait

no thats for points

were calculating planes tho

[safe fulcrum]

you're really overthinking this

[deft lichen]

its so difficult please oh my god

[safe fulcrum]

the vertical distance is just the change in z-coordinates

[deft lichen]

the z?

yeah

but

[safe fulcrum]

yeah!

[deft lichen]

okay so

[deft lichen]

i need the equation for the plane thats parallel tho

[safe fulcrum]

that's just z = 4 though

[deft lichen]

huhh

i need it in this type of form

and it also passes thorugh the point 0,1,4 it says

[safe fulcrum]

you're really really overcomplicating it

[safe fulcrum]

.

[deft lichen]

uhh

i dont understand

english isnt my first language

wait so

[deft lichen]

ok so 0,0,4 is my first pointing vector

and whats the 2nd one tho

hello

[safe fulcrum]

literally

[deft lichen]

wtf

[thin valley]

What is your first language?

[deft lichen]

now ay

no fucking way

[deft lichen]

german

[deft lichen]

ok but

i need the length of it too

wait

yes

ur so smart holy shit

why cant i fuckign think like this man

[thin valley]

You should learn these two methods this

[thin valley]

and this for the general case

[deft lichen]

ik them already

but

lets say i had to do it the way i wanted to

what would be the 2nd pointing vector of the plane then

[noble raft]

You could attempt an inverse-cross-product of sorts

If yk how to do cross products that is

[deft lichen]

oh

u mean the normal vector?

[thin valley]

If the plane runs parallel to XY then a normal vector is n=(0,0,1) so the equation is z+d=0. Since it passes through (0,1,4) then 4+d=0 → d=-4

so the plane is z-4=0 and
a=0, b=0, c=1, d=-4

The point for the distance is (2,2,1) so xp=2, yp=2, zp=1

|n| = √(0²+0²+1²)=1

[noble raft]

Yeah so the normal vector is the cross product of the 2 direction vectors of the plane

[deft lichen]

yeah

but how does that help me

[noble raft]

You could call ur second direction vector (a,b,c)

cross it with the direction vector u have

The expression u have should be parallel to the normal vector

And then u have a system of equations for a,b,c by equating the ratios of x,y,z components

[thin valley]

Normal vector being n=(0,0,1) is trivial but if you don't see that you can use that since it is parallel to xy then the director vectors are (1,0,0) and (0,1,0) and cross-producted they give (0,0,1).

[thin valley]

and then this

[deft lichen]

im really confused

[noble raft]

so what info do u have, normal and one direction vector?

or have I got it wrong here

[thin valley]

If the plane runs parallel to XY then a normal vector is n=(0,0,1) so the equation is z+d=0. Since it passes through (0,1,4) then 4+d=0 → d=-4

so the plane is z-4=0 and
a=0, b=0, c=1, d=-4

The point for the distance is (2,2,1) so xp=2, yp=2, zp=1

|n| = √(0²+0²+1²)=1

The distance is
dist=|0·2+0·2+1·1+(-4)|/√(0²+0²+1²) = |1-4|/1 = |-3| = 3 units of length

as @safe fulcrum said but using the general formula

[deft lichen]

why z+d=0 tho

i dont understand

[thin valley]

The general formula of a plane with normal vector n=(a,b,c) is

ax+by+cz+d = 0 where d can be calculated with a point of the plane.

In this case we have n = (0,0,1) so the general equation is

0x+0y+1z+d=0 → z+d=0

and for calculating the last d we use the fact that the point A=(0,1,4) is in the plane so it satisfies the equation so 4+d must be =0 that is 4+d=0 and d=-4 so the general equation of the plane is z-4=0

Sometimes the simplest examples are the hardest to understand bc many variables vanish in this case x and y. Because the plane is parallel to XY so it is a plane z=something. Everything plane parallel to xy is z=something in this case z=-4 which is equivalent to z+4=0

[vale dock]

@deft lichen Has your question been resolved?

[deft lichen]

OHHHHHH

[deft lichen]

what about the 1 from the point 0,1,4 tho

i understood it man but

yeah what about the 1

[deft lichen]

<@&286206848099549185>

[vale dock]

@deft lichen Has your question been resolved?

[deft lichen]

,stop

.end

[hazy pivot]

Close

[deft lichen]

,close

.close

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[blazing token]

Im trying to derive the identity that stems from integration by parts using eulers number. Can anyone explain to me why they can go to the answer after getting the original integral in the equation?

[blazing token]

Heres the integral calculators method. I calculated myself until before it applied linearity. I dont understand what to do from then on

[distant galleon]

Let the integral be $I$. Then, $$I=\frac{e^{ax} \sin bx}{a}-\left(\frac{be^{bx} \cos bx}{a^2}+\frac{b^2}{a^2} I \right)$$

[rocky lotus]

Civil Service Pigeon

[distant galleon]

and the rest is just algebra bashing

[rocky lotus]

Wolfram Alpha doesn't understand your query!
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Requested by civil_service_pigeon

[distant galleon]

https://www.wolframalpha.com/input?i2d=true&i=Divide[\(40)Divide[Power[e%2Cax]sin\(40)bx\(41)%2Ca]-Divide[b*Power[e%2Cax]cos\(40)bx\(41)%2CPower[a%2C2]]\(41)%2C1%2BDivide[Power[b%2C2]%2CPower[a%2C2]]]

[blazing token]

you are in fact

the goat

im so dumb sometimes

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[rustic knoll]

Can I find the minimum/maximum of a multi-variable expression (with conditions) without using Lagrange?

[jovial edge]

If you're good enough

[brave grail]

if you have an n equation relating to n number of variables then you could write your main expression in terms of 1 variable and then derivative = 0

[primal lava]

You will need to analyse the behaviour of that expression, and apply relevant things

[jovial edge]

That's what inequality made for

[rustic knoll]

For example with a,b,c >0, satisfying 21ab+2bc+8ca≤12 and the expression 1/a+2/b+3/c or whatever, without "trial and error" nor tools

[rustic knoll]

Can you please be a bit more specific?

[primal lava]

I mean, analyse if it's convex or not, if any known inequalities are applicable, etc

And best case, try to understand the functions shape

[rustic knoll]

I'm asking the question to solve inequalities more easily

[primal lava]

Things like bordered hessians exist

[brave grail]

take 1/abc common from the expression and then you could use the inequality

[rustic knoll]

That was just an example, i'm asking for in general though

Also i don't see how taking abc shows you where the equality occurs by the way

[brave grail]

i meant 1/abc but in general you should be making manipulations to implement your inequality

[primal lava]

Also any reason you're avoiding using the lagrangian?

[rustic knoll]

Yeah I got what you meant but I don't see how that works

[rustic knoll]

I barely know about derivatives or such

[jovial edge]

Usually these types of problem use known inequalities, like AM-GM, Cauchy-Schwarz, Minkowski, Holder, etc

[rustic knoll]

I mean i'm willing to learn it (Lagrange) if it's not too advanced

[jovial edge]

Olympic ahhh inequality problem

[primal lava]

It's not too advanced

[rustic knoll]

It does, but I must know where the minima occurs so I can properly apply the inequalities

[jovial edge]

That's why I said you have to be good enough

[rustic knoll]

What knowledge do I need to have before learning it?

[brave grail]

just derivatives really

[primal lava]

Just multivariable calc

That too it's basics

[rustic knoll]

Where can I learn it then?

Any video/document(s) you guys recommend?

[primal lava]

https://youtu.be/5A39Ht9Wcu0?feature=shared

Also there's good vids explaining grad div curl and such

[rustic knoll]

Thank you

[rustic knoll]

What does that stand for?

I mean, what is that short for

[primal lava]

Gradient, Divergence, Curl

[rustic knoll]

Those terms are alien to me (probably partly due to language barrier), so i guess i have things to learn now

Again, thanks

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[sweet tapir]

Is this formula correct? I'm touching up on my notes and trying to find a clear and simple way to on how to get n.

[merry crystal]

n is just the number of elements in your sample set

[vale dock]

@sweet tapir Has your question been resolved?

[sweet tapir]

n = total number of values I think this is as basic as can be. I'm wondering if it can be further symbolized.
n = sum1 is what I have attempted to use because 1+1+1+1 etc... but it doesn't explain where I am getting my values from. It's obvious to us, but not to a complete beginner.
n = sum1 total number values this combination is a little more direct on including the set while using the sum1.
Is sum1 even correct? or does it complicate things? I guess I would have to be really direct with the description by saying total number in set?
Sorry I'm rambling. My thoughts on this is to figure out different type of approaches or directions, what they actually mean and if its appropriate

[steady charm]

it's implied that all sums are summed over all values (so the bounds are always 1 to n), so Σ1 = n is just saying if you sum 1 to itself n times you will get n

so a more complete equation would be
[ n = \sum_{i = 1}^n 1 ]

[rocky lotus]

cloud

[sweet tapir]

Hey I like this! This makes sense thank you 😄 My teachers lesson/notes is incoherent so this helps clarify the approach for n ❤️

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[north scarab]

Do we need to use sine rule, which is x/sin60 = y/sin45

and try to get x and y

alone?

[tawny moon]

yes

[north scarab]

wait do I need to sub in the exact values in for sin45 and sin60?

from the exact values triangles

[tawny moon]

i mean yeah

i suppose?

[north scarab]

,rotate

[tawny moon]

otherwise this is just a one-step question

[north scarab]

this is what I have done

[tawny moon]

ok, you're not done yet though

[north scarab]

hmm

Idk if I’m on the right track

😭

[tawny moon]

you overcomplicated things a lot

the whole question just wanted you to find x/y

[sinful obsidian]

this starting point looks perfect

[sinful obsidian]

you look close at the end

[tawny moon]

from here it was just one more step to get the right thing

[sinful obsidian]

x = y * blah

so x / y = ???

[north scarab]

ohhh

[north scarab]

Divide by y

[tawny moon]

you didn't need to find x and y individually (not like you can - the expression for x will have y and vice versa)

[north scarab]

But where’s the x= y*blah

[sinful obsidian]

your last line

$x = y \frac{\sqrt{6}}{2}$

[rocky lotus]

back to ginger

[sinful obsidian]

sorry if i'm giving away the answer

but you basically did it yourself

[north scarab]

You replied to the wrong image

I think

[sinful obsidian]

oh yeah

[sinful obsidian]

this image, last line

[north scarab]

but hana said the other image only needed one step

to get the answer

[tawny moon]

both can be true, you know

[sinful obsidian]

that is also true (other than evaluating trig functions)

you were just even closer in your second image, at the end lol

[north scarab]

,rotate

[sinful obsidian]

you're futher away now :p

that's ok though, it happens

[tawny moon]

you didn't need to bring the 2 to the left

you're asked for x/y, not 2x/y

[sinful obsidian]

$x = \frac{y \sqrt{6}}{2} = y \frac{\sqrt{6}}{2} = y \times \text{blah}$

[rocky lotus]

back to ginger

back to ginger

[tawny moon]

i guess since ginger is here i'll let them take over

[sinful obsidian]

nono i might not be here

[north scarab]

x/y = sqrt6/2

[sinful obsidian]

i can try

[sinful obsidian]

🎉

let's see if it's right

[north scarab]

alrigjty

[sinful obsidian]

,w x/sin(60deg) = y/sin(45deg), a = x/y, solve for a

[rocky lotus]

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[sinful obsidian]

ok it gave it as sqrt(3/2)

,w sqrt(3/2) = sqrt(6)/2

[rocky lotus]

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[sinful obsidian]

perfect @north scarab

[north scarab]

yep it is right

thannk you

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[deep apex]

honestly not sure what I am doing wrong? had two other friends redo the problem and we all get the same answer?

[vale dock]

Show your work, and if possible, explain where you are stuck.

[jovial edge]

Oh wiat

[deep apex]

my work is the third image

I am not sure where i am stuck honestly, I got the charges for Q1 and Q4, but for some reason the answer is wrong? I am just confused if I am interpreting the question wrong or not because I am so lost on what is being asked atp

[copper stump]

initially, the three capacitors were in series, and they were fully charged before the switch was flipped

[deep apex]

Yes but isnt the question refering to after the switch is closed?

[copper stump]

So, only charge that flows thru P is the difference

I see that you have C_eq, and from that Q_eq

[deep apex]

Yes

[copper stump]

does that mean you directly used Q_eq as V*C_eq?

that would not be the difference

thats the total charge stored

but a part of that was already present in the capacitors 1, 2 and 3

[deep apex]

ok so they want the difference between closed and open switch?

[copper stump]

indeed

[deep apex]

essentially this?

[copper stump]

if the calculations are correct, then yea

the steps look good

[deep apex]

but im so confused on the wording, which part asks for the difference lol

[copper stump]

you have to calculate when the switch is closed

[deep apex]

OH

[copper stump]

so that directly tells you to calculate the difference

coz thats the extra charge that the circuit can accumulate

also, you should notice that the voltages across the capacitors change once the C4 gets added to the circuit, so the charges on the rest of the capacitors also change, so part b gets different answer

[deep apex]

So my question is, when the switch is closed, should I have treated C2 and C4 as a parallel and then combine everything into a series? or I should have right off the bat went with series and then make that all into a parallel

[copper stump]

c2, c4 in parallel, and the combo in series with c1 and c3

[deep apex]

which is what I did

ok ok

sec let me try and solve it

[copper stump]

sorry, I gotta dip, irl stuff

[deep apex]

you good man thanks for hte help

hmmmmmmmmmmmmmm

[woeful rover]

Ouchies this looks tough

[deep apex]

lol

im struggling

but

I might have a breakthrough now

im just confused as to how to treat q1 now

do I now treat it as the difference between open and closed or do I just ball it

hmmmmmmmmm

Is this the right way to approach part b then after part a?

The top part was a waste of time I just fumbled

[vale dock]

@deep apex Has your question been resolved?

[deep apex]

nah

not yetttt

almost tho

nvm i think that is wrong

UGH

ye ima redo the entire problem rn lol

[copper stump]

Oki, Im bac
Firstly, you gotta calculate the accumulated charge at the start

[deep apex]

at q1?

[copper stump]

no, the entire circuit

c1, c2 and c3 combined

[deep apex]

Ah

just c1 c2 and c3

?

[copper stump]

yea

we are looking at some point of time before we flip the switch

[deep apex]

nooo i got part a

its 7.6

i meant part b

[copper stump]

oh good

then for this its simple, all you gotta do is find the voltage across c4

[deep apex]

yes switch open = 29 micro C, closed is 21.39 micro C, difference is 7.59 or wtv

wait.

voltageE?

like

V?

as in vector

not Q??????????????????????????

😮

[copper stump]

potential difference

[copper stump]

not vector

[deep apex]

but i thought part b asked for the charge that shows up on capacitor 4

[copper stump]

the magnitude

[copper stump]

yea, it does

and you have formula that relate the potential difference acorss capacitors to the charge stored within them

[deep apex]

wouldnt it be 10.4 then

[copper stump]

Q = CV

10.4 is across the entire circuit

each component in the series has only a part of it across its terminals

only the components in parallel have the same potential difference

cmon dude, this is same as what happens in resistance circuits

[deep apex]

lol

here

let me do it rq

i see what you mean and ye

I know that

I was just having a dum dum moment

[copper stump]

yea, I get that, sometimes ppl need a jolt in memory to remember stuff

[deep apex]

Hopefully I did it right this time

[copper stump]

steps are good, I trust the numbers you calculated are right

wait, whyis your q_tot same as q_24?

[deep apex]

series?

qtot = q1 = q3 = q24

right

[copper stump]

q_tot is q_1+q_24+q_3

[deep apex]

0.0

ill take myself out the door now~

LOL

ok ok

well thats one thing i didn tknow

sec

[copper stump]

oh wait, me dumdum

you are right, they should be equal

[deep apex]

AYYYYY

[copper stump]

[deep apex]

ight last attempt

lets hope I actually got this right

hmmm

oh well

[copper stump]

you seem to have rounded the numbers a lot

[deep apex]

actually no my calculator is still spitting 1.1

I got the same answer as the answer keyu

for v

hmm

[copper stump]

wel,, C_24 is 7.44+4.78 which is indeed 12.22

[deep apex]

yes i got the same answer as all of that

[copper stump]

keep more sigfigs in your calculated values so you dont get roundoff errors and different answers

[deep apex]

alright

thanks for the help!!!!!!!!!!!!!!!!!!!!!!!!

[copper stump]

np

[deep apex]

.clsoe

.close

[vale dock]

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[vale dock]

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[olive grove]

this question is from memory so i apologise if its too hard to work out pls tell me

solve for all real value(s) of p where one root is 4x the other y = 3x^2 -px + 2

[olive grove]

i forgot if its 3x^2 or just x^2

im just curious as to how a question like that would be solved

[stark wedge]

if you forgor the question data then we can't be certain of the answer

but anyway you say one root is 4 times the other?

[olive grove]

yea i dont want the exact answer im just curious how i would solve a question like that

[olive grove]

yes

[stark wedge]

so the roots are r and 4r

[olive grove]

yea

[stark wedge]

vieta these fuckers

[olive grove]

ok

whats vieta

🥀

i heard of it before

[stark wedge]

sum and product of roots?

[olive grove]

oh yeah this thing i never learnt it in school but i seen it online

[stark wedge]

how did you never learn it at school

did you miss 5 months of class

[olive grove]

no

i have NEVER touched that

in my whole life

at school

[stark wedge]

what kinda shitass school did you go to that they didn't teach you this in math class

[olive grove]

idk bru

i dont learn anything in class anyway

its past papers youtube and mathcord

😭

5r = -p/3
is ts what were supposed to do now

[stark wedge]

use the other one as well

[olive grove]

4r^2 = 2/3

oh

lemme get my calc

r = ±sqrt6/6

5±(sqrt6/6) = -p/3

15±(sqrt6/6) = -p

[stark wedge]

±

[olive grove]

ah

u right mb

-15±(sqrt6/6) = p

ill do the plus one first

[stark wedge]

15 ± sqrt(6)/6 is incorrect

[olive grove]

wait why

[stark wedge]

"15 plus or minus something"

it's not the same as 15*(±sqrt(6)/6)

you meant ±15sqrt(6)/6 for sure

[olive grove]

ohh

cuz we multiplying it

-15(±(sqrt(6))/6)) = p

does this work?

[stark wedge]

yes but it's ugly as hell

[olive grove]

im just gonna put it into the calc

😭

then boom 2 values for p

ngl gng i jus wanna say tysm for helping

u helped me so many times

i saw this one question today

OH WOW I JUST GOT ACTIVE RAHHHH

[olive grove]

that i wouldnt be able to do if i didnt come here and u didnt explain

so thank you

p = -6.12 or p = 6.12

ty!

.close

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[terse plinth]

The greatest integer function is defined by [x] = n, where n is the unique integer such that n=< x < n+1. How do i find the graph of y=[x] and find a limit?

[stark wedge]

a limit
limit at what point

[tawny moon]

!xy

[vale dock]

Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.

[stark wedge]

anyway, consider this:

[x] = 0 when 0 ≤ x < 1,
and [x] = 1 when 1 ≤ x < 2,
and [x] = 2 when 2 ≤ x < 3,
and so on...

[vale dock]

@terse plinth Has your question been resolved?

[terse plinth]

ohh so a step function

[vale dock]

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

😭

[vagrant glen]

What did I doooo

[woeful rover]

The question asks

"What got increased by 2% to give $2040?"

[native rover]

u still need to keep that 1+0.02

[vagrant glen]

Oh I get it

Because 2040 is a different whole than the one before

So a 2% decrease from 2040 is different than a 2% increase from a lesser whole

[woeful rover]

Yeah exactly

[vagrant glen]

I don't think I have the original noted

Notes

[tawny moon]

the hint tells you what you need to do.

[native rover]

what note:)?

[vagrant glen]

I don't understand random equations :p

[vagrant glen]

This one WOOHOO I FOUND IT :D

[tawny moon]

,rccw

[woeful rover]

If it tells you "increase by x percent" then you write the equation as : A(1+ x/100) = B

If it tells you "decrease by x percent" then you write the equation as: A(1- x/100) = B

[vagrant glen]

I thought it was searching for percent decrease tho XP

That's why I did the 1-yknow

[tawny moon]

Kenny got a pay increase, not a pay cut.

[vagrant glen]

Ya

I recognize that now

[woeful rover]

Yeah that happened with me a lot when I first learned that lesson

[vagrant glen]

I just saw it wanted me to find the original price

Which I misinterpretted as finding the decrease

[woeful rover]

But that distinction in equation form is what made me understand it

[vagrant glen]

Yehhh

It seems simpler now

Ima keep this open cuz I'm on the hardest question rn

😭

[stark wedge]

just to not have to deal with the black background that makes up about half your photo

@vagrant glen do you have something specific to ask about this or are you just doing it right now until you get stuck

[vagrant glen]

I'm sorry

I had to block out the top of the screen by angling my phone down cuz they're was personal stuff there XP

[vagrant glen]

Doing it til I get stuck

Theres 4 available channels so I thought it'd be chill

If not I can close it

[stark wedge]

no i was just wondering if you had something to ask already or not

[vagrant glen]

I have a smol questions

So to find the 73% you need to do 15(x/100) which is 0.15

To make an equation

And just

I got that for my second number

It'll be 71.995+0.15x=73 tho right?

[stark wedge]

yes

[vagrant glen]

It was not 6.7

[stark wedge]

wait hold on

i misread your message, sorry.

[vagrant glen]

Did I mess up at the 85(84.7/100)?

[stark wedge]

it should be 71.995 + 15x = 73 scratch that

[vagrant glen]

Lol I did the equation before doin this

[stark wedge]

err

wait a minute

did i confuse myself?

[vagrant glen]

Oh wait

Hold on

[stark wedge]

sorry, no, your equation was correct and your x value should also be correct.

6.7 is rejected bc you didnt round as they say

[slender veldt]

0.15 is right

[stark wedge]

they want you to round up to the nearest whole %

[vagrant glen]

😭

[stark wedge]

yes like that

[vagrant glen]

I swear I know math

[stark wedge]

you should read questions carefully

[vagrant glen]

I just always miss that lil bit

[stark wedge]

misreads are a very embarrassing thing to lose points over

[vagrant glen]

ACTUALLY THO AAAAA

Especially when the teacher has to manually grade them cuz they'll write "read the question carefully" 😭

I hate rounding

ALRIGHT IM DONE

Thank you all for the help X3

.Close

.close

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• Show your work, and if possible, explain where you are stuck.
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Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[mental sierra]

I’m stuck on Monic Quadratic equations

[stark wedge]

!da2a

[vale dock]

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/

[stark wedge]

send your specific question(s) here

[mental sierra]

I have a test and this is the notification for it but I need help with the whole test

I need study notes and what to study

[stark wedge]

you need help with the test?

we can't help you during the test, just so you know

[mental sierra]

Yesss

Not during the tes

Tes

I need like reversion notes and stuff

[stark wedge]

• khan academy
• the organic chemistry tutor (on youtube)

[mental sierra]

What videos

[stark wedge]

look up "organic chemistry tutor quadratics" and an entire playlist should pop up

so look among those

[mental sierra]

Ohhhhh

Okay

Thankss

[vale dock]

@mental sierra Has your question been resolved?

[vale dock]

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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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• Be polite and have a nice day!

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

[muted bridge]

hi

[muted bridge]

oh i see

i shouldve subtracted 2

i dont even know actually

i just need help

😭

[lyric sundial]

,rccw

[tidal swift]

this is a quadratic in sin x

[muted bridge]

im so lost

[tidal swift]

replace sin x with y

[muted bridge]

is this some special thing?

[tidal swift]

nope, not really. just to help you see the quadratic

[muted bridge]

my teacher gave this with no instructions

[tidal swift]

it's not necessary

[muted bridge]

okay

done

yeah its a quadratic

[tidal swift]

mhm

solve the quadratic with whichever technique you prefer

[muted bridge]

i see

i wasnt aware it was different

[tidal swift]

different? in what sense?

[muted bridge]

what did i do wrong

[lyric sundial]

Using x to replace sinx, first of all

x is the input of sinx, so you can't say x = sinx

[tidal swift]

i don't recommend using x to replace sin x, yeah

use something like y instead

[lyric sundial]

@muted bridge

[muted bridge]

just for visualization purposes for now

is it fine to keep it

but other than that

whatd i do wrong

[lyric sundial]

2x² - 4x = 2x(x - 2)

[tidal swift]

also

if you decide to put a bracket around x+2, that + becomes a -

because there's a - sign outside

[lyric sundial]

But please, do not use x. If it's wrong it's wrong...

[tidal swift]

also, one of these two solutions are a little... "special".

and by special i mean inconsequential trash extraneous

[muted bridge]

@tidal swift

@lyric sundial

[tidal swift]

something went wrong with your factoring

[muted bridge]

am i tweaking

!nogpt

[vale dock]

Please do not trust ChatGPT or similar AI tools for mathematical tasks, as they often generate output which "sounds correct" but has numerous factual or logical errors. Use of these AI tools to answer other people's help questions is strictly against server rules (see #rules).

[muted bridge]

bad boy

[tidal swift]

there we go, and yes

grats on using your first factoid (i presume). shame it has to be on yourself

[muted bridge]

broo im so confused

help seia

whatd i factor wrong

[tidal swift]

in line 3 the + in between the two () should not have been a +

it should have been a -

[muted bridge]

but other than that its good?

[tidal swift]

yes

[muted bridge]

(2z-1) (z-2)

[craggy girder]

nogpting yourself is crazy

[vale dock]

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[plucky arrow]

hi im trying to solve this limit, but i have no idea what to do,

I've tried the trick with doing e^ln(f(x)), didnt work. and now im stuck, helpless and sad

[craggy girder]

e^ln(f(x)) should work imo

pls send your working

[plucky arrow]

this is what im getting into, and id ont know where to continue from here

don't think i can use lhopital because it's not looking like f(x) / g(x)

[craggy girder]

$x ln(x + x^2) = \frac{ln(x + x^2)}{1/x}$

[rocky lotus]

Wumpus Man

[craggy girder]

now you have inf/inf so you can use lh

[plucky arrow]

ive forgot to add another fraction so i got inf/0

TY

[craggy girder]

[vale dock]

@plucky arrow Has your question been resolved?

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

How do I claim a channel

[tidal swift]

you just did

[onyx tusk]

Epoc

I would like to know the answer for b and c

Because the answer sheet got different answer than mine

[tidal swift]

show your answer and those of the answer sheet's.

bonus: show your working

[onyx tusk]

I've been triple checking if I substitute the wrong value but I don't think I did

[tidal swift]

think you flipped the m and n around when calculating P

let me check this one

yeah looks like it.

[onyx tusk]

Which part issit

[tidal swift]

2AP:PB suggests that PB is twice the length of AP

yet P is at 0 - the x-distance of AP is 2 times the x-distance of PB, the wrong way round

this part. all of your m and n are flipped

[onyx tusk]

Wait pb is twice the length of ap me and like

Means like*

1:2...?

Sorry I'm slow

[tidal swift]

think of 2AP : PB as 2AP = PB

so AP should be the shorter part, not the longer one

[onyx tusk]

Ooooowahhh I think I get itt noww

Wait gimme a while

This is so epic thank u

[tidal swift]

i suspect the other one has the same mistake

[onyx tusk]

Probably

How do I read the ratio of it tho

[tidal swift]

3AP : 2PB => 3AP = 2PB

then it's the same thing as before

[onyx tusk]

Oooo

It basically flipped?

3AP:2PB = 2:3?

[tidal swift]

i'll give you a hint for this kind of stuff

3AP : 2PB means that 3 lengths of AP is the same as 2 lengths of PB.
when this kind of situation happens, the longer part is always the part with the lower ratio. why? because it needs less "lengths" to equal the other part's ratio.

[onyx tusk]

Oooo okok

I'll keep tht in mind

Thanks btw ur soo cool

[tidal swift]

nah i'm just doing my job

[onyx tusk]

How do I close this channel

.close

[vale dock]

Channel closed

Closed by @onyx tusk

Use .reopen if this was a mistake.

[tidal swift]

there you go

[vale dock]

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[midnight pier]

Hii @true coyote

[midnight pier]

Remember me?

[tidal swift]

please don't chat in help channels.

!redir

[green urchin]

?

[vale dock]

This channel is only for on-topic discussion. Please take casual conversation to #discussion or #chill.

[tidal swift]

do you have a question? if not, please close this channel.

[vale dock]

@midnight pier Has your question been resolved?

[tidal swift]

.close (OP opened channel to chat, left channel hanging with no question)

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

[sterile apex]

Hi teachers

[sterile apex]

I have a question about a proof

the limit told us: convergent sequence has a limit and by definition, we know: for all epsilon we can find ...... etc.

but i'm confused, why we can choose A epsilon to prove the lemma instead of using FOR ALL epsilon

[echo rampart]

Consider a proposition of the form: for all values of x, T(x) is true

• if you're proving the proposition, you must FIX an arbitrary x and prove T(x)

• if you're using the proposition, you can take whatever x you want and you will have a guarantee that T(x) is true

[sterile apex]

is that not depending on the circumstance where we knew the statement T(x) true is?

[echo rampart]

?

[sterile apex]

every people could die, i'm a human, i would die

[sterile apex]

there the epsilon is not arbitrary

isn't it?

[echo rampart]

if you're proving that the sequence (a_n) has a certain limit, you have to consider every possible epsilon > 0

[sterile apex]

maybe i got something

[echo rampart]

it's a little bit like you must provide to someone every possible epsilon

but if it is given to you that the sequence (a_n) has a certain limit, it's like somebody must provide to you every possible epsilon

it is then up to you which epsilon you will take and use

I don't know how much sense this analogy makes 😁

[sterile apex]

so a_n is a convergent sequence, and by definition it works forall epsilon, so epsilon = 1 works too, and if for 1 works, then forall works

[echo rampart]

so a_n is a convergent sequence, and by definition it works forall epsilon, so epsilon = 1 works too - yes

and if for 1 works, then forall works - no

[sterile apex]

uhmmm

then how can i imply: every convergent sequence are bounded

[echo rampart]

uh, like on the screenshot

you are given a convergent sequence

since this sequence is convergent, it comes with a certificate

that whatever epsilon > 0 you will use

it will work with the rest of the limit definition

so as a human being with free will you take epsilon = 1

and the rest follows

this is different from if you were to PROVE that the sequence is convergent

then you would have to provide some fact for every possible value of epsilon

when you're proving, you're the provider

when you're using an assumption, you are the recipient

[sterile apex]

is that like: you take a random convergent sequence, it could be proved: it is bounded, so every convergent sequences are bounded?

[echo rampart]

I'm not sure I understand, but doesn't sound false

[sterile apex]

alright, at least sounds reasonable

thank you@echo rampart

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[left quest]

What’s wrong..? 🥲

[last comet]

Wdym

[stark wedge]

the horizontal asymptote

[last comet]

Yep

As x--> inf, f(x) -->-5/3

[left quest]

The graph is wrong..

[left quest]

The graph is wrong

[last comet]

Ya understood

[left quest]

I had that..

😭 or did I place it in the wrong place?

[last comet]

Ya

[stark wedge]

your HA should be y=-5/3 but you have it somewhere above -1

that's what's wrong with it

[left quest]

😭 oh

Lmao, thank you! 🙏

Like this? @stark wedge

[stark wedge]

yeah that looks good now

[left quest]

Tysm! 🙏

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[gleaming niche]

Heya, I'm doing some research into a topic and I've come across a notation I've not yet seen and I'm having issues finding out what it means exactly:

[gleaming niche]

$L_s(x' \rightarrow x, t)$

[rocky lotus]

JohnyTheCarrot

[gleaming niche]

specifically, that right arrow

$L(x' \rightarrow x, t)=L_{0}(x' \rightarrow x, t)\ + \int_{\Omega}L_s(x' \rightarrow x, t) \circledast M(x'' \leftrightarrow x', t)dA_{x''}$

similarly, what's with the double arrow

[rocky lotus]

JohnyTheCarrot

[gleaming niche]

full def ^

is x' the item after x or smtn?

[neat locust]

It would also help to mention where you are seeing this notation.

[gleaming niche]

sec

this paper

under point 3.1 background

x is defined as the position, omega as the direction, t as time.
plus the following:

For the conve-
nience of analysis in a path tracing framework, we use L(x′ →
x, t) to represent L(x′, ω(x′ → x), t) so that the relationship
between the transportation formula and path nodes is expressed
clearly.

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[wraith heart]

just screenshot

[wraith heart]

should read teh siltanen 2007 paper

$*$ could be just multiplication

[rocky lotus]

riemann

[wraith heart]

which is different from what you used here

[gleaming niche]

it's defined as convolution

[wraith heart]

great it's defined here:
https://mathworld.wolfram.com/Convolution.html

[gleaming niche]

convolution to my knowledge can be represented as both * and (*)

[gleaming niche]

yee ik what convolution is

[wraith heart]

[gleaming niche]

ah yes, the siltanen paper does clarify

I thought it was some standard notation

perhaps not

where L
x →
 is the outgoing radiance from x in the direc-
tion
.

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[stone acorn]

multivar/calc 3 question

all i can think is that this is a paraboloid

what am i supposed to even start with here, distance formula? ok D = root x-4) square + y^2 +z^2

then im lost

[jade ivy]

You should check your notes on how to write a Lagrangian. It'll make it a little easier if you use the squared distance instead.

[stone acorn]

?

[stone acorn]

lagrange multipliers?

this simply is in noody notes?, nor book

its some wierd abstract question ive never seen

[desert knot]

it's a hyberbola

since there's no y, it's just extruded through the y axis

[stone acorn]

i see

how do i solve this?

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@stone acorn Has your question been resolved?

[zinc spear]

maybe start by sketching x^2=1+z^2 to have intuition for the shape and the point (0,0,4) in R^3.

then i agree with the other helpers lagrange multipliers seem by far the simplest way of dealing with this problem

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[spark burrow]

(I made the substitution x = e^(-u))

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@spark burrow Has your question been resolved?

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@spark burrow Has your question been resolved?

[thin valley]

Yes, not.

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@spark burrow Has your question been resolved?

[spark burrow]

Thanks

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[undone crane]

I'm super stuck on Part C of this question for my geology class. I feel like I'm missing information to get the answer?

[undone crane]

I've calculated the rate of change over seven days and now I have a massive number 2,327,875,200 cfs but I cannot move onto how I would use that to find the inch change over the area of the lake

[stable parcel]

OK, so you have the surface area and the problem says that the lake's beach suddenly drops straight down when it meets the water.

You can divide the volume change by the surface area to get the height change.

That only works because it has walls like a swimming pool.

[undone crane]

Yeaaaap I think I was over complicating that and confused myself. Thank you so much

So with converting to inches I'm looking at 5510367596.71 inches. That seems incorrect to me I'm getting lost in the units. If I divide the rate of change by the surface area I have 3,188,870.137 cfs/m^2. Where do I go from there?

[stable parcel]

What did you get for b?

[undone crane]

-3849 cfs