help-17

[elfin moon]

I am finding out

Max | n(0)-n(1)|

So here my focus is to get max of it so I'll try to get max value of zeros and minimum values of ones

If it wasn't upper triangular then 25-0 =25

For upper triangular 25-0=25

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[slender sky]

what is D?

[elfin moon]

Mid point

[merry python]

Hint:||Separately draw triangle ABD and then observe two sides are equal and one angle is 60 degrees. This should tell you something||

[slender sky]

which class are you in?

[elfin moon]

Graduated without proper knowledge

Preparing for a teaching exam

[elfin moon]

@merry python

This tells me nothing

[merry python]

Okay did you draw a separate triangle?

[muted vapor]

Try trigonometry

[elfin moon]

Sine formula?

[merry python]

None of sine formula is required

BD is equal to 2 as well as AB=2
angle ABD is 60 deg

angles opposite to equal sides are equal

[elfin moon]

Wait

It's an equilateral triangle

AD=2

[slender sky]

you are indian right?

[merry python]

Yes

[elfin moon]

Ha

[slender sky]

bhai lekin agar tum graduate ho, ye sawal to 10th class ka nahi hai? coordinate geometry ka

[merry python]

Ofc joke tha

[slender sky]

haina

ye ladka 10th ya fir 9th ka hai

[elfin moon]

Jab tum deeply b.sc k topic padj kar 10th ka solve krne aaoge toh tumko basic questions bhi ni niklenge

Should i ask you science questions?

[merry python]

wait tm actually graduate ho

[elfin moon]

Tumko viras ka definition m bhi confusion ho jayega

[slender sky]

virus ya fir viras

[merry python]

my bad

[elfin moon]

Ha virus hi

[slender sky]

computer me ya human me?

dono aate hai

[elfin moon]

Vc aaja me puch leta hu chota chita definition hi puchunga bas

[elfin moon]

Human

[slender sky]

mic nhi hai mere pass desktop par hu

[slender sky]

neetard ho?

[elfin moon]

10th ka hi maths aata hain SSC

Cgl ka exam deke dekh le fir

Pata chal jayega

[slender sky]

mujhe kya mai to jee dunga

[merry python]

CGL me actually hard maths aata hai

[elfin moon]

M level ka bat kar rha hu

[merry python]

oh to govt. job lene ke liye?

[elfin moon]

Topic toh 10th ka hi aata h na ssc cgl ke

[elfin moon]

Yup

[merry python]

accha accha nice

[slender sky]

koi question dena

try kar leta hu

khaali betha hu abhi to

[elfin moon]

Science ya maths?

[slender sky]

@merry python isme madad kar sakte ?

[slender sky]

science (No biology) ya fir maths

[elfin moon]

Langrange laga le

Sum of series wala

[slender sky]

nahi kara

[elfin moon]

JEE ki preparation karne wala sabko lagta h maths bas 11,12th ka hi h

[merry python]

Ye to nhi krna aata \

[elfin moon]

Unko abhi rabbit hole se bahar aayenge 4 sal bad tab malum chalega maths konsa hota h

[slender sky]

Lagrange inversion theorem?

[elfin moon]

Btec wale sab 10th ka maths padh rhe ssc cgl k liye

Even NIT pass out bhi

Last time abhi ka topper jo jodhpur se tha sab NItian

[slender sky]

arey theek hai bhai aap ho college graduate maan gaye

[elfin moon]

Jab 10th m padh lia toh ab kyu padha

B.sc k topics batau kya kya padha h maine?

B.tech level se upr hi h

B.tec m jake tumko bas 3 sem padhna h maths

1,2,7

[slender sky]

iiith jaoge to maths nahi hai btec cse me. sirf projects

konse college me ho?

[elfin moon]

SK govt college pass out

[elfin moon]

Compulsory

1,2 sem

[slender sky]

kaha hai ye

[elfin moon]

Aayega hi aayega

Where are you?

[slender sky]

ggn

[elfin moon]

Then leave

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[odd epoch]

someone explain how they went from 1 to 2

[odd epoch]

ty

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@odd epoch Has your question been resolved?

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[native dagger]

Find the minimum and maximum value of $A = 2x + \sqrt{5-x^2}$

[twin meteor]

ChemicalMendeleev

[sudden compass]

assuming that x is rational, real, natural, or integral?

[native dagger]

real

[sudden compass]

also you could differentiate to find the maxima

[kind light]

to solve this you need to focus on the square root i think

[kind light]

dont think its needed lol

[paper depot]

do you have a calculus-free solution in mind?

[kind light]

wait this involves calculus????

my line of thinking is just that since it has to be real 5-x^2 has to be 0 or more than it

[sudden compass]

...

[brittle minnow]

If it was 2 + sqrt(5-x^2) then no calculus would be required but we have 2x so it's not that simple

[kind light]

oh

[sudden compass]

what if he says that A can be complex?

[kind light]

wait i misread the question nvm

[sudden compass]

can you do that then?

[kind light]

i thought the question was like "if A is a real number then what is the min and max value of x"

[paper depot]

tell me what order relation on C is intended

[native dagger]

A is real bro

[sudden compass]

what is order relation..?

[sudden compass]

Oh nvm

[paper depot]

a notion of "less than"

[sudden compass]

r u trying to say what part of the question suggests its complex

[paper depot]

by which one could talk about max or min

[sudden compass]

idk

[brittle minnow]

Ann's point is that C is not an ordered field so you can't talk about maximum or minimum

[brittle minnow]

What have you tried so far?

[native dagger]

wdym

[native dagger]

For 1 hour

[brittle minnow]

What have you tried NOT how long have you tried

[paper depot]

question was not addressed to you

it was to show the absurdity of the suggestion that x could be complex given the problem statement

[native dagger]

x is real in this question

[sudden compass]

I meant A but nvm

[paper depot]

anyway we've gone way off track

[native dagger]

Oh, I forgot
I've tried using inequalites

[paper depot]

what inequalities did you use

[native dagger]

AM-GM (maybe)

[brittle minnow]

Chemical do you know calculus? I'm particular differentiation?

[paper depot]

how did you apply AM-GM?

[native dagger]

$2x + \sqrt{5-x^2} ≥ 2\sqrt{2x\sqrt{5-x^2}}$

[twin meteor]

ChemicalMendeleev

[native dagger]

like that

[paper depot]

hm

i don't think that's going to help much.

if you're going to apply an inequality, you want the other side to be a constant or something that is easily boundable by a constant

which i don't think this is

also yeah repeating @brittle minnow's question: do you know calculus?

[native dagger]

No

[paper depot]

then how are you expected to solve this, i wonder

have you done problems like this before?

[native dagger]

Yes, but the easier ones

[woeful cloak]

i suppose you could solve for the minimum by using the fact that sqrt(5-x^2)>=0

not sure how you would find the maximum here though

[paper depot]

how did you do them if not by means of derivatives?

and can you show the ones you did solve?

[native dagger]

And then $A = 2x + \sqrt{5-x^2} ≥ 2x$ ?

[twin meteor]

ChemicalMendeleev

[viscid ore]

The reason by which you can tell whether a < b, a = b or a > b.

[native dagger]

like $|2x - 1| + | - 2x - 7|$

[twin meteor]

ChemicalMendeleev

[nova fulcrum]

If you don't know calculus use geometric intepretation.

[paper depot]

i'll be honest i do not know how to solve this w/o calculus

[native dagger]

just use graph

[paper depot]

like maybe some kind of geometric thing but im not sure what either

[distant eagle]

If you fix A, you get an equation for x. You can solve it, and then see for which values of A there exists a solution. Then you can find the maximum of those values of A

[woeful cloak]

yes, something with this inequality, though haven't exactly figure out a straight foward way, we still need some information about A's behaviour on it's domain

[distant eagle]

However you must be careful because there is a square root and that will probably give some problems if not treated carefully

[native dagger]

how about the maxima

[brittle minnow]

The function isn't a simple increasing one so I don't see how you'd do it without calculus

[vocal sleet]

@native dagger Has your question been resolved?

[native dagger]

No

<@&286206848099549185>

[distant eagle]

This does work, I have just checked it

You only have to solve a quadratic equation and check two values

At least it works for the maximum, not for the minimum

The minimum is very simple, just see that A ≥ 2x ≥ -2sqrt(5) and for x = -sqrt(5), A = -2sqrt(5)

[native dagger]

Because @distant eagle just solve the problem & I have to sleep (it's 10 p.m. at the place where I live) so

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[terse forum]

!status

[vocal sleet]

What step are you on?
1. I don't know where to begin
2. I have begun but got stuck midway
3. I got an answer but I'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above

[terse forum]

Have you tried putting the function on desmos

[inner bloom]

hi

If we have a function called f do you know how to graph f(x-k) (k>0)

or f(x+k)

[summer ore]

The answer should be d if I’m not mistaken, 2 means double and x-1 means it moves one unit to the right

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[vocal sleet]

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.

✅

[pale yoke]

you're doubling y

and therefore "stretching" the graph

if you wanted to double the x value and stretch the graph horizontally you'd say
y = f(2x-1/2) instead of
y = 2f(x-1)

[mild flower]

f(2x) would shrink the graph

f(x/2) would stretch it

[pale yoke]

it's just changing the y intercept

it's not important

or whatever it's called

no, but since it was originally 1, when we stretch it we divide by 2

[karmic imp]

That may be useful

Because x + c = x - - c

Two negatives makes a positive

-c is a shift left

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[fiery raptor]

Distance from $A (i, i, i, i)$ to $B (-i,-i,-i,-i)$? \
My solution:\
$\vec{AB}=(2i,2i,2i,2i). \rho(A,B)=|\vec{AB}|= \sqrt{2i*\overline{2i} + 2i*\overline{2i} + 2i*\overline{2i} + 2i*\overline{2i}} = \sqrt{16} =4$
Is that correct?

[twin meteor]

feniksovich

[fiery raptor]

Sorry for bad latex layout

[flat whale]

what is i

$i = \sqrt{-1}$ ?

[twin meteor]

rie.mann

[fiery raptor]

Imaginary unit, yea

[flat whale]

what is $\rho$ in your solution

[twin meteor]

rie.mann

[fiery raptor]

Letter to define operation "find distance from A to B" or smth like this

Actually distance between two points

[flat whale]

Yea the answer looks right

[fiery raptor]

cool 😎

thank you

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[terse valve]

Possibly stupid question but is there an equation to calculate how much oxygen a flame consumes?

[terse valve]

couldnt find anything of it online

[full hatch]

You could probably do some assumptions to (over)simplify the problem, but I am not fimiliar with one

Measureing should be best here

[terse valve]

alright ill try to create on myself worst case scenario

ty though

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[lilac rock]

how did they get perimeter as 20?

[lilac rock]

but how does that represent the perimeter

[flat whale]

what else would be on the perimeter besides the wire

[lilac rock]

oh im getting confused with the wording

[flat whale]

"form a wire into a rectangle"

[lilac rock]

also why are we finding if there are no zeroes how does that correspond to it being impossible

im not sure what the quadratic formula here represents

[flat whale]

this is a proof by contradiction

suppose such a wire exists

then the width = w satisfies w^2 - 10w + 30 = 0

width is a physical measurement so it's a real number

but the contradiction arises from there being no real solutions to w^2 - 10w + 30 = 0

,w roots w^2 - 10w + 30

[twin meteor]

Results provided by WolframAlpha

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Requested by rie.mann#0

[lilac rock]

why is the formula set to 0 what does the 0 represent

[flat whale]

it's just algebra

[flat whale]

which step here didn't you follow?

[lilac rock]

right sorry

so use perim to set the formula for area

then see if w can be a real number by finding discriminant

if negative no answer so there cannot be the wire

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[pseudo peak]

very simple quick question

[pseudo peak]

given 2 points

to find the normal

is it just a x b

or AB

and if there are different solutions depending on whats given please inform me

[rugged orchid]

Normal to what

[pseudo peak]

in a vector equation

[rugged orchid]

Also a x b isn’t defined for all a and b

[pseudo peak]

heres an example

would i find AB

or cross them to find the equation

[rugged orchid]

Honestly I’ve not learned this before so my method is gonna be scuffed

Also where does it say we need to normal

[pseudo peak]

shoot your shot

[rugged orchid]

Id first find the equation of the line defined by 2 points

[pseudo peak]

i mean i just figured, how else could i solve?

does that not include the normal?

[rugged orchid]

Then solve the 2x3 matrix of the 2 lines

There’s 2 lines

The one given and the one that passes through the 2 points on line 2

[rugged orchid]

This will be an augmented matrix

[pseudo peak]

have not learnt that

[rugged orchid]

Hmm

It’s just a system of equations

[pseudo peak]

okok

basically

the error was in my wording

what i meant was a direction vector but nvm figured it out

ty

[rugged orchid]

Ah lol

[pseudo peak]

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[trim walrus]

Hi

[trim walrus]

Well I'm stuck here and idk how to proceed...

This is my attempt.

I feel like this will connect me to proving (n+2) can't divide the "series" without leaving the remainder...but idk how...

[twin meteor]

_basudev

[trim walrus]

I used this

[paper depot]

what's epsilon?

[trim walrus]

That's E, sry for my bad writing

I let the seires to be E

[paper depot]

okay so like

you showed the sum is divisible by n+1

so what

do you claim that if the sum is divisible by n+1 then it is definitely not divisible by n+2?

[trim walrus]

No no, not like that, I felt like it can go some where... like (n+2) and (n+1) are consecutive so they're co prime so i feel like I should connect it that way.....but idk

How

[paper depot]

there is in fact no connection between divisibility by n+1 and by n+2

[trim walrus]

Alr then

[paper depot]

this problem looks nontrivial

[trim walrus]

So how should I proceed

[paper depot]

i can't immediately think of anything

[trim walrus]

Alr

[paper depot]

try looking at sums of smaller powers

maybe some idea will appear

[trim walrus]

Hmm alr

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[bold hound]

Functions like f:R^2->R

[bold hound]

I want to show that f is continuous

For example

$f(x,y)=\frac{xy^2}{x^2+y^2}$

[twin meteor]

Machmut

[bold hound]

And f(0,0) is defined as 0

If we say x and y approach 0 equally, so we can say x=y this becomes easy. But i dont think that is how i should do it

Got it

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[dusk mantle]

In the isosceles triangle ABC, B=120 CD is the height of the triangle,

Find AD if the length of the altitude through the vertex B is 10.

[dusk mantle]

<@&286206848099549185>

<@&286206848099549185>

[vague mortar]

#geometry-and-trigonometry message

[dusk mantle]

why

i need help

and nobody's helpin

him

[merry python]

Draw a diagram and send a pic

[dusk mantle]

k

[merry python]

@dusk mantle you there?

[vocal sleet]

@dusk mantle Has your question been resolved?

[dusk mantle]

ye

[dusk mantle]

i cant 😭

[vocal sleet]

@dusk mantle Has your question been resolved?

[merry python]

send what you infer

it may be wrong

nothing to worry

@dusk mantle

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@dusk mantle Has your question been resolved?

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[fading forum]

I have a A =
[[2, 4, -2],
[0, 1, 1],
[0, 0, 4]] and a B= [2, 4, 8]

[fading forum]

I want to solve X for AX =B

How can I find this?

[paper depot]

so you have a linear system

do you know in general how to solve those?

[fading forum]

Like equations?

[paper depot]

systems of linear equations yes

[fading forum]

2x+4y-2z = 2

I do

[paper depot]

ok then whats the problem

did you run into some difficulty with this one in particular

[fading forum]

Can I do a linear calculation to return the solution array?

I am working on Matlab, just wondering if there's a linear function to solve such systems, if I happen to come across a larger system

[paper depot]

what's a "linear function" as opposed to a different type of function

also if youre working w matlab you should be using matlab notation

A = [2, 4, -2; 0, 1, 1; 0, 0, 4] and B = [2; 4; 8]

and what you're looking for is A\B

[fading forum]

What's \

[paper depot]

it's matlab left-division

https://www.mathworks.com/help/matlab/ref/mldivide.html

[fading forum]

Oh, that's the function I was seeking, I reckon

There it is

Thanks @paper depot

.close

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[trim walrus]

Helo

[trim walrus]

Any help with this ??

I tired smth but it let no where

I'm pretty sure I've to pair the number but idk in what manner

[patent nymph]

n = n + 2 - 2

[patent nymph]

Then, notice that (-a)^n = -(a^n) if n is odd since the integers mod (n + 2) are a ring

[trim walrus]

But -a can't be it says for every natural number?? Isn't it??

[patent nymph]

a can be any natural number

[trim walrus]

Alr alr

[twin meteor]

_basudev

[patent nymph]

You can make pairs here with 2^1987 and n^1987

[trim walrus]

Hmm alr so smth like
$n + 2 | n^{1987} + 2^1987$

[twin meteor]

_basudev

[patent nymph]

By the way, how is that proven

[trim walrus]

Wait let me share the screen shot

[astral shadow]

Binomial theorem.

Should prove that.

[astral shadow]

This is a result concluded using binomial expansion.

[trim walrus]

Ye

[trim walrus]

Any help with this

?

[astral shadow]

well you're making pairs aren't you

2,n

3,n-1

...

[trim walrus]

Ye

I should leave 1

Alr

[woeful cloak]

before that, you should divde this into 2 cases first

[astral shadow]

I mean consider 2 cases.

[trim walrus]

Even and odd

[astral shadow]

yes, n could be odd or even.

[trim walrus]

??

[woeful cloak]

there is an uncertainty whether there is a mean between 2 and n

which is why you need to divide it into 2 cases

[trim walrus]

I tried this

Wait

[woeful cloak]

then post your work

[trim walrus]

The circle part is just a marker

I felt like

there's a connection between n+1 and n+2, as they are co prime but it didn't let anywhere

[woeful cloak]

you actually had the opposite for each cases, when n is even. There IS a mean between 2 and n

you can prove this by just letting n=2k where k is a natural number. This means that (2k+2)/2 is also natural

implying that there is a mean between 2 and n

for example, n=4, that mean is 3

[patent nymph]

Here was my approach: Reduce the entire expression by taking modulo (n + 2)

Then, n becomes -2

then (-2)^1987 + 2^1987 is congruent to 0, and the whole expression becomes 1

And in this way we get that the remainder is always 1

Never 0

[trim walrus]

I've just attended just 1 lec, and the concept of modulo and congruence has not been introduced to me

[patent nymph]

Are you allowed to use it in your proof

You could prove that n^1987 has the same remainder as (-2)^1987 under division by (n + 2) then

[trim walrus]

Hmm I think I get but I dont have pen paper rn I'll show my work tmwr

See ya

.close

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[solid sage]

in order to differentiate this equation, I made it in terms of y^2=something

and then using product rule i think, i did d/dy (y^2) x dy/dx

[dim quail]

take the 9x^2 to the right

[solid sage]

which is 2yy'

but im not sure how to find just y'

[outer warren]

again, solve for y'

[dim quail]

divide both sides by y

[outer warren]

its fine to have the derivative in terms of x and y

[dim quail]

your answer can have y in it

[outer warren]

don't really need product rule since its a constant that's being multiplied to y^2

differentiating that is just power+chain

[solid sage]

Would this seem right

[outer warren]

no

[solid sage]

hmm

[outer warren]

derivative of the right side of your equation isn't 0

[dim quail]

differenciate the third step

[solid sage]

ah yikes

[outer warren]

also y isn't quite a function of x,

[solid sage]

would it be a relation?

[outer warren]

yes

[solid sage]

my thought process i needed y on its own to complete the equation

[outer warren]

its fine to have the derivative in terms of x and y

[solid sage]

for y+xy', wouldn't i need y on its own?

[outer warren]

you ultimately want y' on its own

y' = stuff with x and/or y

[dim quail]

$y^2 = \frac{144}{16} - \frac{9x^2}{16}$

[twin meteor]

bettimsucks

[dim quail]

try differenciating this

[outer warren]

the convenience of doing implicit differentiation is so that you DON'T have to / need to isolate y

[solid sage]

I see

[outer warren]

having
y' in terms of x and y,
allows you to determine the slope at a certain location as you'd know both x,y coords at that point

[solid sage]

y+xy'=-9/8 x

[dim quail]

no?

[solid sage]

oh right cuz if you know x then you know y by subbing into the relation

oh oops

[outer warren]

not quite,

[dim quail]

what is $\frac{d(y^2)}{dx}$

[twin meteor]

bettimsucks

[solid sage]

y+xy'

[outer warren]

no,

[solid sage]

oh

[outer warren]

that was d/dx of (xy)

[dim quail]

okay that isnt right

[solid sage]

ah yep sorry was looking at the wrong one

2yy'

[dim quail]

yes

now

differenciate the right side

[solid sage]

ohh so y' would be the right side derivative over 2y

[dim quail]

yep

[solid sage]

do i need to do anything like sub in y or

[dim quail]

||2 gets cancelled in the process||

[solid sage]

just leave it as that

[dim quail]

just leave it

as it is

[solid sage]

oh

so does that mean for every question like this where you try find y' given an elipse

oh wait nvm

thanks!

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[solid sage]

Im not sure what b) means

[solid sage]

sorry why are the images like so bad

if y=12, wouldnt the second deriv be 0?

[fossil ginkgo]

y'' + y = 0, y = 12, so y'' + 12 = 0

[mild flower]

it means when y(x) = 12, like at the point at which y = 12

[solid sage]

but I thought that was if y=sinx, does it work for all x?

[fossil ginkgo]

"When y = 12" is a bit ambiguous

It doesnt mean y = 12 for all values of x

I think it just means when y = 12 like at a point where y = 12

On a function that satisfies that diffeq

[solid sage]

oh is it saying 12=sinx ?

[fossil ginkgo]

No

[solid sage]

wait no thats like impossible

[fossil ginkgo]

It doesnt have to do with sin x

[solid sage]

is it related to a) in any way?

[fossil ginkgo]

No

[solid sage]

oh

to me, it doesnt make any sense if im being honest

[fossil ginkgo]

b) is asking: lets say you have some y(x) such that y'' + y = 0. Let's also say that at some value of x, y = 12. What is the second derivative of y at that point?

[solid sage]

oh so y=12 isnt a function its referring to the y coord of a point

[fossil ginkgo]

Yeas

the function y = 12 would not satisfy that diffeq

[solid sage]

oh i c

.cloes

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[vast shale]

what does C[a, b] mean

[hard atlas]

probably continuous functions with domain [a,b]

i.e., f:[a,b]->R continuous

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[rocky fox]

Can someone help me with this question?

[rocky fox]

I honestly just need some checking on the last two blanks

[vocal sleet]

@rocky fox Has your question been resolved?

[outer warren]

what triangles are we looking at

[vocal sleet]

@rocky fox Has your question been resolved?

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[wispy lotus]

plz help

[fierce shale]

usually when you are trying to prove there isnt something you can do it by contradiction

so

supp for the sake of contradiction that there is a pos int n such that...

[wispy lotus]

oh ok

how i do that tho

[regal bane]

That's basically a quadratic, so you can find all of the solutions

There might be a more elegant way, but that comes to mind

[wispy lotus]

so do i set it = 0

then just quadratic equation it

like

[regal bane]

Ye

[wispy lotus]

n^2+n^4-200=0

[fierce shale]

oh lol that is way easier

[regal bane]

Also can't help but notice the left is just n²(n² + 1)

Does 200 factor like that?

[wispy lotus]

hm idk

so like

i dont rly get why doing quadratic equation solves it tbh

can some1 explain to me plz

[regal bane]

You can get all solutions. None of them are integers.

[wispy lotus]

so

if its

not a whole number

its not a integer

like 25.5 would be a no

how do i even put this in the quadratic formula wut

[regal bane]

(n²)² + (n²) - 200 = 0

u² + u - 200 = 0

[wispy lotus]

wut y it become u

[regal bane]

Substitution

I felt like it looked better that way

[wispy lotus]

oh ok

but like

where did the ^2 go

[regal bane]

u = n²

[wispy lotus]

u factored them out?

oh

ohhhh

thats smart

then i just sub that alr

bruh

this looks like a mess

i sub it in but get nowhere

idk wut to do

do i sub in u as a negative number?

[dapper condor]

Even after finding the non-integer solutions, if the question is cruel, you might have to prove that it is not an integer (I.e. prove that it is irrational)

[regal bane]

Yeah let's go with a better method. Note that the equation is also
n²(n² + 1) = 200

If there's an integer n, then this provides a factorization of 200. What is that factorization?

[wispy lotus]

uh

idk

plz help

@grand frigate

<@&286206848099549185>

[flat whale]

do you know what factorization is?

[wispy lotus]

ya

u factor out something

like factors of 12 r 2 2 3

like that right

[flat whale]

yes. can you do the same process with 200

[wispy lotus]

oh so which numbers

like 10 10 2

[grand frigate]

?

[flat whale]

compare that with the factorization kaynex gave you

[wispy lotus]

idk tbh

im confusd

[flat whale]

n^2 * (n^2 + 1) = 200 = 10^2 * 2

but you should first write 10 = 5 * 2

can you rearrange the prime factors of 200 in anyway such that it equals
n^2 (n^2 + 1) ?

[wispy lotus]

hm

divide it by 2

5^2 +1

or wait

idk

ugh im so tired

im so sorry

can some1 help with this question instead its easier

i did 3 cases

x=0
x>0
x<0

i alredy did the x=0 case since it is ez to prove that

[vast shale]

if x > 0, can u tell what |x| is?

[wispy lotus]

wym

[vast shale]

if x > 0, what does |x| equal to?

,tex abs def

[twin meteor]

mist9912

[vast shale]

urgh i never remember the demand

lemme type the definition of |x|

$|x|=\begin{cases}x&\text{if }x\geq0\-x&\text{if }x<0\end{cases}$

[twin meteor]

mist9912

[vast shale]

do u know this?

[wispy lotus]

nope

first time seeing it

[vast shale]

this is the definition of |x| for real x

[wispy lotus]

oh

i thought abs x always equals positive

[vast shale]

wait hold on

ah yes

when x < 0, |x| = -x > 0

[tough valve]

Yeah it is always +ve

[vast shale]

if u learned |x| in the context of complex x

think of it this way

if x is real, Im(x) = 0

so $|x| = \sqrt{(\Re(x))^2+(\Im(x))^2}=\sqrt{x^2+0^2}$

[twin meteor]

mist9912

[vast shale]

do u see why?

[wispy lotus]

what is re

also im sorry but i think we making the question more complicated

my prof never taught me this

[vast shale]

how did your prof define |x|

[wispy lotus]

he never did

[vast shale]

oh

[wispy lotus]

i go to every lecture

[vast shale]

this is what's important for the question now

[wispy lotus]

ok

[vast shale]

so, u already shown that if x = 0, |x| = 0 = x

this is good

so, now let's move on to if x > 0

from the definition i gave, can u tell what |x| equal to if x > 0?

[wispy lotus]

it will equal

just

x

[vast shale]

yes

so now the last case, if x < 0, what does |x| equal to?

[wispy lotus]

-x

[vast shale]

yes, now we have |x| = -x

hmm we need to show |x| ≥ x

[vast shale]

this is a hint

|x| > 0 is always true for all x

so now we have two things we know

|x| = -x and |x| > 0

try to figure out the last fact we already know

[wispy lotus]

hm

idk sorry

[vast shale]

nw, remember we are considering the case x < 0?

this is the third fact

now we have |x| = -x, |x| > 0 and 0 > x

do u see how we show that |x| ≥ x?

[wispy lotus]

uhh

not rlyy

[vast shale]

it's okay, i'll just show it

u should think it through again to see if u can reconstruct the proof yourself

|x| = -x > 0 > x

$|x|&=-x&\text{ (from the definition of }|x|\text{ and }x < 0\text{)}\&>0&\text{ (}x < 0 \text{ implies }-x > 0\text{ )}\&>x\text{ (}x < 0\text{)}$

[twin meteor]

mist9912
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[vast shale]

sry the latex is a bit tricky lol

do u follow this proof?

[wispy lotus]

yep brb just gota use washroom

alr back

[vast shale]

yea read through the proof to see if it's reproducible

[wispy lotus]

i dont get it sorry

ima try to understand it tmrw

im too sleepy rn

its 4am for me lol

[vast shale]

alright i hope u'd get the proof eventually

[viscid ore]

Good night

[vocal sleet]

@wispy lotus Has your question been resolved?

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[solid sage]

write them i nthe form

.close

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[zenith pagoda]

What is twelve hundredths in scientific notation?

[paper depot]

what is twelve hundredths in any kind of notation you're familiar with?

[zenith pagoda]

I know how to do scientific notation

I just don't know how many 0's is before

[mint turret]

scientific notation is a*10^b

[zenith pagoda]

Thanks

[mint turret]

10^b where b is a positive number is 10 with b amount of zeroes

10^-b where -b is a negative number is 1/10 with b amount of zeroes on the bottom

[zenith pagoda]

So is it 1.2*10^-3?

[mint turret]

thats 1.2/1000

which is 12/10000

do you think that is correct?

[zenith pagoda]

no

so is it -1?

[mint turret]

thats 1.2/10

which is 12/100

[zenith pagoda]

wait if 12 hundredths is 0.12 than shouldn't it be 1.2*10^-1?

[mint turret]

yeah

[zenith pagoda]

Ok thanks

sorry, my question is kinda dumb

[mint turret]

its fine

[urban edge]

No dumb questions if theyre honest

[zenith pagoda]

so how do I resolve this help thing

thanks guys

[urban edge]

Use ".close"

[zenith pagoda]

ok, I'm new to the server

[urban edge]

Have a good one

[zenith pagoda]

you too

.close

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[native dagger]

a/Prove that the 2 colored triangles are similar to each other
b/Prove that IG ⊥ HK

[vocal sleet]

Please don't occupy multiple help channels.

[sudden compass]

this figure 💀

[urban edge]

So are you gonna give us more information about the construction?

[sudden compass]

why so many unnecessarly lines..?

like the red and green ones can all be removed

[urban edge]

Im assuming its for the construction

[sudden compass]

i think the thingies (symbols) are enough it would be helpful

[urban edge]

It would be nice if we didnt have to parse it though

[sudden compass]

but we just have to prove similarity, so we care only about the triangles. if we need to use any of these constructions we can construct them

[sudden compass]

thats correct

[karmic imp]

It'd be nice if OP answered back

[urban edge]

Sure would

[native dagger]

You will need those thing (maybe)

[urban edge]

soooo

Are you gonna tell us the instructions of construction

Or are you just gonna say theyre necessary

I think those are congruent marking because they ran out of tick marks 💀💀

[vocal sleet]

@native dagger Has your question been resolved?

[native dagger]

No

[sudden compass]

bruh @native dagger

[urban edge]

Im not giving help until that happens btw

Dont you know how to get help by now

Oh ok

[vocal sleet]

@native dagger Has your question been resolved?

[native dagger]

<@&286206848099549185>

[native dagger]

<@&286206848099549185>

[fossil ginkgo]

bro😭

[vocal sleet]

@native dagger Has your question been resolved?

[native dagger]

<@&286206848099549185>

[native dagger]

<@&286206848099549185>

[fossil ginkgo]

Bruh

tell us the instructions of construction

they asked u about it like 4 hours ago 😭

[native dagger]

oh i forgot & i have to sleep . sorry

.close

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[trim walrus]

Hi

[trim walrus]

Anyhelp with this..?

Well my attempt was

a²+b²+c² it has no minimun under the given constraints a²+b²+c² so it can be as minimum as it can be that won't affect 2 so 4/2 = 2

So the minimum should be 2... isn't it ??

[errant briar]

maybe take
a,b,c once and apply, am gm
Then take 1-a, 1-b, 1-c and apply am gm and then divide

[gray yarrow]

im gonna try something in python to get the answer, cant help you with the math proof tho

[errant briar]

It will be 4

[errant briar]

Try applying this, it is easier

[trim walrus]

Alr

Minimum is 4??

[errant briar]

Yeah

[trim walrus]

And key says 8

[errant briar]

Wait

[trim walrus]

,w min{a/(1-a) * b/(1-b) * c/(1-c)}, 0<a<1, 0<b<1, 0<c<1

[twin meteor]

Results provided by WolframAlpha

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

Requested by _basudev#0

[trim walrus]

[astral shadow]

i think it has something to do with f(x) = (x-a)(x-b)(x-c)

you need minimum for f(0)/f(1)

[trim walrus]

I think like am and gm + cacuhy is involves

*involved

[astral shadow]

and you'll have to set up certain conditions so that all the roots are in interval (0,1)

[trim walrus]

[astral shadow]

cauchy might get you somewhere, but a pure algebra approach such as mine ought to work. Then again, I'm not thinking much into it rn.

[trim walrus]

,w min{ab+bc+ca}, 0<a<1, 0<b<1, 0<c<1

Well I've a manipulation let me type it in latex..

[errant briar]

I got it

It will be 8

Apply the method i told

I squared instead of cubing lol

@trim walrus

[trim walrus]

[errant briar]

Follow this

[trim walrus]

8/27 >= abc

1/3 >= \cbrt{-1-(ab+bc+ca)-abc}

[astral shadow]

a. It's +1/3

b. There's no \cbrt command

[errant briar]

Don't simplify this

1/3>= cbrt((1-a)(1-b)(1-c))

[trim walrus]

Alr

1/27 >= (1-a)(1-b)(1-c)

[astral shadow]

27

[errant briar]

1/27

[trim walrus]

F

Ye

37

*37

*27

[astral shadow]

...

[trim walrus]

Bruh

$8 (1-b)(1-a)(1-c) \geq abc$
$$8 >= \frac{abc}{(1-b)(1-c)(1-a)}$$

[twin meteor]

_basudev

[trim walrus]

Wait what??

What did I just do here

[errant briar]

Divide both the inequality

[trim walrus]

Alr

8/81 >= abc/(1-b)(1-c)(1-a)

Them??

[errant briar]

How you got 81?

[trim walrus]

,w 8/27 ÷ 1/3

[twin meteor]

Results provided by WolframAlpha

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

Requested by _basudev#0

[trim walrus]

See

[errant briar]

Bruh

[trim walrus]

No??

[errant briar]

Why won't you cube 1/3?

[trim walrus]

F

[errant briar]

This

[trim walrus]

8 >= abc/(1-b)(1-c)(1-a)

Correct??

[errant briar]

Yes

[trim walrus]

But question is saying is always greater than or equal too

I showed is always less than or equal to

We showed its maximum value

Isn't it??

[errant briar]

Wait

[trim walrus]

Or I maybe high or smth

I have a approach from cauchy but idk if it's right or wrong

[errant briar]

I think the inequality has to change when dividing

[trim walrus]

They're all positive

So no change... ??

[errant briar]

Yeah the inequality will change

See 0<a,b,c<1

Remember if
a<b and 0<a,b<1
Then 1/a>1/b

0.2>0.1
but 1/0.2< 1/0.1

[trim walrus]

1/3 < 1/2

3 > 2

Make sense

Alr thanks mate I appreciate your help

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[undone sleet]

Triangle $ABC$ has altitudes $\overline{AD},$ $\overline{BE},$ and $\overline{CF}.$ If $AD = 12,$ $BE = 16,$ and $CF$ is a positive integer, then find the largest possible value of $CF.$

[twin meteor]

funwiththepros

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Please don't occupy multiple help channels.

[undone sleet]

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[finite saddle]

https://www.wolframalpha.com/input?i2d=true&i=Integrate[arcsinh\(40)sin\(40)x\(41)\(41)%2C{x%2C0%2CDivide[pi%2C2]}] I’ve done something wrong but I can’t tell what

[patent nymph]

What is G

[patent nymph]

I think the first step is wrong, you put the power inside the integral immediately

[finite saddle]

Catalans constant

[patent nymph]

and also moved the sigma outside the integral, are you allowed to do that?

[finite saddle]

Lemme check the convergence of the series

Yeah it is

Cuz it’s valid for | x | less than 1

[patent nymph]

Are you allowed to move the sigma outside the integral?

[finite saddle]

Yeah it’s convergent across the domain

So should be fine

I think

[patent nymph]

Is there a theorem that lets you move the terms in the sigma outside the integral, and switch the order of the sums?

[finite saddle]

Dominated convergence

Fubini/Tonelli theorems applies here too

[patent nymph]

I don’t know enough about analysis to say if the first step is wrong so I’ll leave it to another helper/helpful

[finite saddle]

And all conditions are met (I think)

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[peak matrix]

In context of sets, is $\mathbb{R} \times \mathbb{R}^2 = \mathbb{R}^3$?

[twin meteor]

methisalwaysright

[river minnow]

I don't think they are equal, but they are definitely isomorphic

[peak matrix]

Ah, okay so they're not. Tysm

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[prisma imp]

Need help pls

Anyone

??

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[summer river]

Here's my work:

Here's their answer:

can they just plug in r into r^2 without deriving it first???

[flat whale]

Your formula for volume looks wrong

[summer river]

ahhhhh

thank you

Thank you for the good eyes!

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[coarse yoke]

can someone help me understand how t is 2

[coarse yoke]

can someone help me understand how t is 2

[sharp lynx]

,calc 360/(6000*0.03)

[twin meteor]

Result:

2

[coarse yoke]

i get 0.0018

[sharp lynx]

i imagine you've dropped a bracket

,calc 360/6000*0.03

[twin meteor]

Result:

0.0018

[coarse yoke]

oh

oh ok

thanks

[sharp lynx]

[coarse yoke]

pemdas right

[sharp lynx]

yep

[coarse yoke]

awesome sauce thanks boss

[sharp lynx]

np

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[soft arch]

hey! I have to take linear algebra soon, within a 6 week time span. I am freaking out because 6 weeks to take linear algebra is/sounds super stressful. Can someone give me a breakdown of the major topics so I can go study it myself. If not, can someone give me any references? youtube? anything?

[sudden compass]

Search 'essence of linear algebra 3b1b' on youtube (I found the link, here: https://youtube.com/playlist?list=PLZHQObOWTQDPD3MizzM2xVFitgF8hE_ab)

[merry python]

https://www.khanacademy.org/math/linear-algebra

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[trim walrus]

Hi

[trim walrus]

I found the maximum value if the expression which is 1

But I've no idea for the minimum value

Any help??

[split wind]

try start with (a+b+c)²≥0

[trim walrus]

Ye I did that and go the max value

[split wind]

i see

[trim walrus]

Qait

Wait