help-0

[calm tide]

x+ 6 = 0

what is x

[gray isle]

you were forgetting the trivial solution of x=0

[proper lichen]

-6

[calm tide]

yes so the roots are 0 and -6

[proper lichen]

oh

ok

thank u guys

wait

what about

the y intercept

0 = x^2 + 6x

[gray isle]

for y-intercept, you'd sub x=0 instead of y=0

[proper lichen]

oh yeah sorry

so y = 0?

[gray isle]

though by finding that the x-intercept is 0
that also tells you the y-intercept

yes

[calm tide]

y = ax^2 + bx + c

at y intercept x = 0

so y = c

and c is constant term of quadratic equation

in ur question c = 0

therefore, y intercept = 0

[proper lichen]

yep

thanks

.close

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[rustic kettle]

Could anyone solve question 1. (a) and (b)

[vale wigeon]

we don't give out answers here

but if you show your work and/or where you are stuck, we can help you along

[rustic kettle]

Im stuck here

[vale wigeon]

apply exponent laws as normal

you have some x^n factors and some y^n factors

[rustic kettle]

Yeah i bring the Y below and the X above right

[gray isle]

too vague

show don't tell

[vale wigeon]

^

[agile mountain]

can one of you prose help me in channel 28?

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[rustic kettle]

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[proper creek]

in that image what does "Addition formulae for any number of angles" mean? is it just something like sin(x1+x2+x3....) or does it mean something else?

and is this part asking for an expansion on their product?

[lone heart]

@proper creek Has your question been resolved?

[proper creek]

<@&286206848099549185>

i just wanted to confirm whether i was correct in the interpretation or whether it meant something else

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@proper creek Has your question been resolved?

[slate mural]

ayo can yall help with this i havent done trig in a while and im confused

[bronze carbon]

Use sine theorem formula

33/sin 55=x/sin 65

[pseudo lily]

Yeee

[lone heart]

@proper creek Has your question been resolved?

[proper creek]

bruh i just got forgotten wtf

[ornate condor]

LOL

isnt this just a summary

just read thru the part which talks about it

[proper creek]

no like thing is....i dont have the book

i am not even in college yet

this is just the syllabus they will teach and idk what that means

[proper creek]

tbh i just use this as a reference material and study the topics given there

[ornate condor]

lol

[proper creek]

guess i can just give up

[lone heart]

@proper creek Has your question been resolved?

[proper creek]

<@&286206848099549185> anyone?

[proper creek]

this was the question

i got raided in my own help chat while i was away bruh

[tough nova]

hi is this where we ask for help

[proper creek]

better to try asking in a new help channel

[proper creek]

like one of these available ones

[alpine sable]

Help?

[valid island]

star=6
spiral=3
hex=8
rectangle =5

@alpine sable

[alpine sable]

Tysm

[valid island]

@brittle karma 7,2

[brittle karma]

thx

[lone heart]

@proper creek Has your question been resolved?

[agile reef]

\

[alpine sable]

Help anyone?

[distant furnace]

help me Understand Arithmetic sequences

[distant furnace]

Man FUCK DeltaMath

[trim wagon]

bro wtf is this channel

[lone heart]

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[warped gust]

Can someone help me with this other problem?

[lone heart]

Please don't occupy multiple help channels.

[warped gust]

.close

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[alpine sable]

Could anyone help me

Idk where to go from here

[merry depot]

factor the 4 term sum so you can substitute in the 2 term value

[alpine sable]

As in this?

[merry depot]

think more $5 = a(1+r+r^2+r^3) = a(1+r) + a(r^2+r^3)$

[ocean seal]

Zybikron

[alpine sable]

Hm, isn’t that what I technically did before

[merry depot]

well what's a(1+r)?

[alpine sable]

The 2nd term sum

[merry depot]

which is equal to?

[alpine sable]

1

[merry depot]

so you have $5 = 1 + a(r^2+r^3)$

[ocean seal]

Zybikron

[alpine sable]

Yes

[merry depot]

Can you do anything to $a(r^2+r^3)$ to make a similar substitution?

[ocean seal]

Zybikron

[alpine sable]

Hmm I dont see any

[merry depot]

think factoring

[alpine sable]

Oh wait

$ar^2(r + 1)$

Hmm

[ocean seal]

Jared

[merry depot]

yeah

[alpine sable]

Maybe $5r^2$?

[ocean seal]

Jared

[merry depot]

so you have $r^2(a(r+1))$

[ocean seal]

Zybikron

[alpine sable]

Yes

Oh wait

It’s just 1

[merry depot]

yeah

with the substitutions you get 5 = 1 + r^2

[alpine sable]

So just $r^2$

[ocean seal]

Jared

[alpine sable]

I see

And then I solve for r?

r = 2?

[merry depot]

could be

ah, nvm. all terms are positive

I was going to say r could be negative, but nope.

[alpine sable]

$a = 1/3$

[ocean seal]

Jared

[alpine sable]

Just plugged in r in the $a(r + 1)$ equation

[ocean seal]

Jared

[merry depot]

yep

[alpine sable]

I see

Would this way of solving the question work if it were to be first nth term is x then some random nth term or let’s say last 5 terms

[alpine sable]

Cause this question says first two and first four

[merry depot]

this would be hard to generalize.

[alpine sable]

Right

[merry depot]

you could pull it off in other situations, or something similar, but it's definitely not something you can always do

[alpine sable]

I see

Thanks for the help, nonetheless 🙏

.close

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@zinc cosmos Has your question been resolved?

[lone heart]

@zinc cosmos Has your question been resolved?

[carmine reef]

idk if that's really simplification

are you just trying to classify every possible cross section of a hyperbola of 1 vs 2 sheets?

hmm

so for a hyperboloid of 1 sheet

you can have ellipses, hyperbolas, or empty graphs

as well as single points

(degenerate ellipses?)

2 sheets i think doesn't have single points or empty graphs

but it has crossing lines

ok

i mean if you can picture it

then it's easy to tell the difference

but if you're just given an equation

lol

for equations the difference has to do with the signs

making sure you have 1 (or at least a positive) on one side

no pringles here

or wait yeah

for yours

really it's just 2 parabolas facing opposite directions

on perpendicular axes

the hyperbola doesn't really show up

it's just horizontal cross sections

https://math.libretexts.org/Bookshelves/Calculus/Book%3A_Calculus_(OpenStax)/12%3A_Vectors_in_Space/12.06%3A_Quadric_Surfaces

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[carmine reef]

.reopen

[lone heart]

✅

[carmine reef]

the Dxy, Exz, Fyz terms here you won't have to worry about

they cause the surface to not be aligned with the x,y,z axes

they won't show up

G,H,J might

ah

don't worry about D,E,F

but it's the general equation for these surfaces

idk if your class deals with the G,H,J terms

but if you see them you just need to complete the squares

yea it's not something you need to memorize

it's how the problem will look at the start maybe lol

[unique marten]

Focus on the highest degree of terms so you can get your general shape. Everything else past that just transforms the shape but doesn't change the shape

The highest power

X^n

[carmine reef]

focus on the x^2 y^2 z^2

[unique marten]

Think about it like this

[carmine reef]

and whether they're positive or negative

they're what determines what kind of parabola you have

for the most part

parabola

shape in general

yeah

[unique marten]

Y=x^2 is a parabola, y=x^2+x is still a parabola just with a transformation

[carmine reef]

tho i mean

you will still need to complete squares

first, generally

that can be the difference between a positive and negative constant term

want me to come up with a random example problem

x^2 + y^2 - 4z^2 + 6x = 8

ig just determine what type of surface

idk if you're expected to draw them or not

or what else you're asked

Put it in the nice final equation form too ig if you can

Ah

This is what you meant by classifying cross sections

in that case sadly hyperboloids of one vs two sheets are not distinguishable

By equation they're different

well

x=0 in the yz plane, right

yeah

right

You're solving this by converting it into some standard form, right

for the 2D case?

ik but for each individual 2D

to find all that stuff

But are you thinking about converting to some kind of standard form for conic sections?

like (x-h)^2/a^2 + (y-k)^2/b^2 = 1

I think it is 1 sheet

But so for quadric surfaces as they're apparently called

There's a similar standard form

[unique marten]

Yup, if two planes are negative it'll be two sheets. If two planes are positive it'll be ome sheet

[carmine reef]

$\frac{(x-x_0)^2}{a^2}+\frac{(y-y_0)^2}{b^2}+\frac{(z-z_0)^2}{c^2}=1$

[ocean seal]

monikanicity

[carmine reef]

with some of the + replaced with - for different forms yeah

$\frac{(x-x_0)^2}{a^2} - \frac{(y-y_0)^2}{b^2}=z-z_0$

dont quote me on that

Ah

[ocean seal]

monikanicity

[carmine reef]

nah

I just did what u told me to

[unique marten]

https://www.geogebra.org/3d?lang=en

You can use this and graph a bunch of things and see what it gives you

[carmine reef]

it's hyperbolic instead of elliptic because of the minus

[unique marten]

Lol, I'm rooting for you Marc. Gl with your exam 👍

[carmine reef]

wym?

do you mean why don't we have (z-z0)/c?

[carmine reef]

z0 is just the z coordinate for the center

In this case the "center" is the saddle point

yeah

maybe they moved it to the left side

or didn't consider shapes not centered at the origin

Nah

It would just be a constant + something on the left

ah yeah so they're only looking at shapes centered at the origin

hmm

yes as well

though every surface should have some sort of "center" represented by x0,y0,z0 here

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[alpine sable]

Find the solution of the following initial value problem:
$y'' + y' + \frac{5}{4}y = t - u_{\frac{\pi}{2}} (t) (t - \frac{\pi}{2}); y(0) = 0, y'(0) = 0$

[ocean seal]

CrimsonDevil_Rias

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@alpine sable Has your question been resolved?

[alpine sable]

Never mind. If no one's gonna ehlp me, screw it

.close

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[slender egret]

The COM from O is r/3

I've tried taking moments and resolving forces parallel to the plane but I can't get the answer

Since it's about to topple I suppose it'd look like this

But I'm not too sure since the answer is in terms of theta, and if it was like this, you'd be able to find theta (tan(theta) = 3)

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@slender egret Has your question been resolved?

[slender egret]

<@&286206848099549185>

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@slender egret Has your question been resolved?

[lone heart]

@slender egret Has your question been resolved?

[slender egret]

resolved.

.close

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[glad osprey]

what do i do in this question

[rigid smelt]

what have you tried?

[glad osprey]

times everything by z and conjugate z

and then idk after

[rigid smelt]

ok maybe not that

can you do common denominator for the lhs?

[glad osprey]

wdym

[rigid smelt]

rewrite the lhs as just one fraction

[glad osprey]

oh

yeah

[rigid smelt]

Do it and tell me what you got

[rigid smelt]

Good, now can you tell me what z times zbar would be?

[glad osprey]

difference of two square

[rigid smelt]

no, not quite

i mean, yes, you can apply difference of square to see what it would be

[glad osprey]

yeah ill have a try with it

[rigid smelt]

anyway, $z*\bar{z}=|z|^2$

[ocean seal]

waler

[rigid smelt]

pretty common stuff to remember when doing complex number

[glad osprey]

oh yeh i dont think ive learnt that far yet

[rigid smelt]

alright then, nvm that

so basically we are having $\frac{\bar{z}-z}{z\bar{z}} = i$

[ocean seal]

waler

waler

[rigid smelt]

can you simplify the lhs now with that substitution?

[glad osprey]

o ye

[rigid smelt]

yes, looks good

[ocean seal]

waler

[rigid smelt]

this means that -2y/(x^2+y^2)=1

now can you tell me what this curve would then be?

[glad osprey]

oh

wow

circle

perfect square

[rigid smelt]

yes, but P must not be (0, 0)

as z!=0

[glad osprey]

oh ye undefine

i seeeee ty

.close

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[alpine sable]

hi

[alpine sable]

how do i find the coordinates of the point(s) on the curve for which the normal to the curve is parallel
to the y-axis

[vale wigeon]

find the direction vector of the normal as a function of t

[alpine sable]

what is that

[vale wigeon]

do you know what the direction vector of a straight line is?

[alpine sable]

nope

probably know it in differnet naming

[slender egret]

gradient function? dy/dx?

[alpine sable]

oy ye i know that

[alpine sable]

^

[slender egret]

You can get the gradient function of the normal by using dy/dx * m = -1 where m is the gradient function of the normal

Using that, what it means for a line to be parallel to the y-axis is that its gradient tends to infinity or negative infinity

Most likely you'd have a fraction for the gradient function of the normal, in that case the denominator can be set to equal 0

Because a/x (where as is a constant) as x approaches 0 from either side would go to either infinity or negative infinity which both work for this question

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[scenic mantle]

How do I solve for n :
Abs(2^(-n)-1) < y.

[scenic mantle]

The end game is ro have n > ... , but I cant seem to be able to do it

[frank moat]

Recall what abs do, negates the negative part, try making different conditions

And solve them*

And intersects them

[scenic mantle]

I ll try that.

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@scenic mantle Has your question been resolved?

[scenic mantle]

Ahhh, I cant solve it.

[still finch]

can I see your work?

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@scenic mantle Has your question been resolved?

[alpine sable]

can anyone help me in answering significant figures ?

[lone heart]

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[scenic mantle]

Eyyy I solved it myself.i didnt have to split the abs because I assume previously that the term on the LHS is always positive.

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[floral kindle]

Create a word problem for which the answer is determined by the calculation of
8!/3!2!

[floral kindle]

I would like some assistance for this question

.close

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[quaint schooner]

How do I solve the given set of simultaneous equations using matrix and determinant methods

[lone heart]

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[vocal tapir]

"In right-angled triangle ABC, the smaller cathetus = 10 cm. The radius of the inscribed circle is 3 cm. Find the radius of the circumscribed circle."

[vocal tapir]

so I'm doing something wrong here

the radius of the circumscribed circle is half the hypotenuse

I tried doing

finding the parameter

and I get 11 for c

and I'm wrong

I have no idea what to do

nvm solved it

.close

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[lyric pasture]

how may i prove this please?

[silent parcel]

what does the french say?

[lyric pasture]

x>0 , y>0 two reals with: x+y=1 and n is a natural number

[silent parcel]

I'd probably try and expand out the brackets on either side of the morethan sign first

see where that gets me

then play around with it and see what I get

maybe make an argument on 1 side equal 0, cause then if you know that x and y are greater than 0 you can probably force some kind of conclusion

[last tendon]

A big hint is to use Cauchy-Schwarz

[lyric pasture]

can i find it on youtube?

[trim wagon]

[trim wagon]

sure

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[wide vortex]

where did the 2sinhpi come from?

[harsh girder]

https://en.wikipedia.org/wiki/Hyperbolic_functions

[echo socket]

From the definition of sinh

Hopefully you didn't confuse sinh(pi) with sin(hpi)

[wide vortex]

oh

idk
i dont know much about calculus

.close

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@vale trellis Has your question been resolved?

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[somber spoke]

How do u show

[somber spoke]

d/dx(ln(1+x)/x^2) = 1/1+x

[frigid stream]

Use the division formula for a derivative

[somber spoke]

I did

I can’t get it to simplify

[plain flame]

show your work

[somber spoke]

Okay gimme a sec

This is where I’m at

Oh it should be a minus not plus

Sorry

[lone heart]

@somber spoke Has your question been resolved?

[somber spoke]

<@&286206848099549185>

Nvm the questions is duff

.close

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[crude jungle]

both num and denom is divergent

but num is ocelating between 0and1 and denom is infinite

so that equals 0

?

[echo socket]

Yeah, you can prove that using squeeze theorem

[crude jungle]

got it ty

.close

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[delicate karma]

Can someone help me with this proof:

[delicate karma]

I rlly have no idea how to approach this

Because I’m not aware how to do the sum of i^a

[plain flame]

geometric series no?

[echo socket]

Would be if it was a^i and not i^a

That looks like a Reimann sum though

[delicate karma]

Yeah this is basically reverse power rule

Power rule for integrals*

And it’s easy to show that this is the case if u use the indefinite integral

But I was wondering if u could show just from the sun

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[wise elbow]

How do you graph this?

[somber lantern]

First you draw y = x - 5

Then you mark one side of the line

[wise elbow]

what do you mean mark one side ?

[somber lantern]

Like the inequality is on the whole side.

[wise elbow]

I know its false and the line has to be dashed

but ikd how to plot it

idk*

[wise elbow]

I know that

Idk how to plot y>x-5

[somber lantern]

Which tool are you using?

[wise elbow]

its a site the professor gives out her homework and textbook on]

[somber lantern]

Sorry but I can't help you with a specific question about the site because I don't know the site.

[wise elbow]

I cant type in the equation

It doesn't let me do that

I have to manually put the plot on the graph

[somber lantern]

Sorry but I don't know what you can do.

Maybe ask the professor?

[wise elbow]

is the solution true?

.close

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[dusk mesa]

Need help with long division

[dusk mesa]

<@&286206848099549185>

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@dusk mesa Has your question been resolved?

[mortal trellis]

generally it is a good idea to not make people download random files to help you

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[dawn tusk]

i don't know the fraction 1/3 to put in droite numeric

[lone heart]

@dawn tusk Has your question been resolved?

[fringe lark]

do you mean a number line?

en français?

[lone heart]

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[alpine sable]

Can someone tell me if Im finding the slope of this tangent correctly? Or if Im doing it wrong? This is approaching from the right

[alpine sable]

I dont know if theres a another way to use this formula

[dim oasis]

,w f'(3), f(x) = sqrt[x+1]

[ocean seal]

Results provided by WolframAlpha

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

Requested by lexitorius#4749

[dim oasis]

Looks right to me, all of your limit iterations are approaching 1/4

Also, your handwriting rocks

[alpine sable]

Perfect, thanks

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[lone heart]

@royal quest Has your question been resolved?

[royal quest]

<@&286206848099549185>

[serene junco]

Have you tried anything yet?

You have some similar triangles

Also ABC is a right triangle, in case you didn't notice.

The goal is essentially just to find the length of XY. The things about p and r being relatively prime and q square-free just means that it's in simplest radical form.

@royal quest

[royal quest]

I am aware of the similar triangles, i just feel like i need a hint, to guide me to the solution

[serene junco]

Since DX is parallel to AB
and DY is parallel to AC,
That means DXY is also a right triangle

If you can find DX and DY, you can find XY by pythag

[royal quest]

Ok thanks i got

.close

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[ornate roost]

82% of all adults think gambling should be illegal. In a sample of 50 Adults:

Calculate the mean and standard deviation of adults who think gambling should be legal

[ornate roost]

nvm figured it out lol

.close

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[gusty cedar]

"three more than the value of x is at least eight."

i forgot how to make this into a equation

how do i get help

[lone heart]

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[low gyro]

<@&286206848099549185> can someone explain the chain rule to me

[worthy relic]

the chain rule

is a method of differentiation where youve got a function inside a function

or a graph inside a graph

such as ln(x^2 + 2)

i will post an example

[low gyro]

Ok can you explain tan(x+3)^2

[worthy relic]

ok

first function = tan(x)^2
second function = x+3

[low gyro]

But the squared is on the outside.. you can move it?

[worthy relic]

you are doing a harder chain rule question where you have to do it twice

[low gyro]

Ohh ok

[worthy relic]

so

the derivative of tan(x)^2 is 2sec(x)^2 * tan(x)

[low gyro]

Yes but when i add the other on it gets extremely confusing and i get a really long thing

[worthy relic]

ok

I forgot to explain the chain rule

basically derive the outside function and leave the inside function and then multiply by the derivative of the inside function

in this case

multiplied by the derivative of the inside function which is just 1

[low gyro]

Wait is that the answer?

[worthy relic]

yes

[low gyro]

I’m still a little stumped sorry, how did you get tan(x+3)

[worthy relic]

ok lets do an easier chain rule question to explain

[low gyro]

Ok

[worthy relic]

y = (x^2 + 3x)^2

lets split the question into 2 functions

f(x) = x^2
g(x) = x^2 + 3x

[low gyro]

I got 2(x^2+3x)2x+3

[worthy relic]

right

[low gyro]

Yess

Thanks

[worthy relic]

so

[low gyro]

I just figured it out

Oh my god thank you so much

[worthy relic]

you are welcome

[lone heart]

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[slow dirge]

Can someone help me w 7?

[slow dirge]

I've tried plugging it in f(x)-f(a)/x-a and it doesnt seem to work

.close

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[unique marten]

If my bounds is from -l to l in integration can I just multiply by two and change the bounds

[ruby current]

if the function is even, yes

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[alpine sable]

https://cdn.discordapp.com/attachments/903486478049488936/1029575114641117225/F89F549F-6C24-430A-9EEA-514EFEFB2CCE.jpg

[alpine sable]

can i get help with 1 or 2 questions

Mostly the imperfect squares

[lethal pelican]

like?

[alpine sable]

1 c and 4 a

[lethal pelican]

ok they are pretty similar

so i assume you know how to factor something like

$a^2 - 2ab + b^2$?

[ocean seal]

bmeoa

[alpine sable]

yeah

[lethal pelican]

ok, lets go with 4a

what if i rewrote it like this

$3^2 x^4 - 49x^2 y^2 + 4^2 y^4$

[ocean seal]

bmeoa

[alpine sable]

um

can't we also write it like

$9x^4 - 24x^2y^2 +16y^4 - 25x^2y^2$

[ocean seal]

xzc

[alpine sable]

can we do it like this?

[lethal pelican]

i guess, but how would you continue that

also i think its overcomplicated it. this is honestly simpler than you think

[alpine sable]

🤔

[lethal pelican]

wait maybe i am pretty stupid

1 sec o.o

[alpine sable]

alright

[lethal pelican]

eh the way i was originally planning to do still works

[lethal pelican]

but yes, i see what you are doing here

so then how would you continue that

[alpine sable]

thats where i get confused in imperfect squares, all i know is how to split the middle terms into 2 terms

[lethal pelican]

well, we can first ignore the -25 x^2 y^2

[alpine sable]

alr

[lethal pelican]

$9x^4 - 24x^2y^2 +16y^4$ so can you first just factor this part?

[ocean seal]

bmeoa

[alpine sable]

yeah

3x^2(3x^2 -8y^2 + 6y^4)

[lethal pelican]

wat. if you expand that its not the same

[alpine sable]

o

[lethal pelican]

you know (a-b)^2 = a^2 - 2ab + b^2 though

[alpine sable]

yea

[lethal pelican]

just take a closer look i guess? idk

[lethal pelican]

this is pretty much the same

[alpine sable]

um

[lethal pelican]

$(3x^2)^2 - 2(12x^2 y^2) + (4y^2)^2$?

[ocean seal]

bmeoa

[alpine sable]

oh

[lethal pelican]

you see it?

[alpine sable]

yeah

wait why woudn't my way work?

like the 3x*2

[lethal pelican]

cause if you expanded it, the last term would be 18x^2 y^4

so it isnt the same equation

[alpine sable]

ohh

ok

[lethal pelican]

so this factored is?

[alpine sable]

3(x^2) -2 * 3x^2 * 4y^2 +(4y^2)^2

?

[lethal pelican]

and then?

its like the a^2 - 2ab + b^2 right?

[alpine sable]

yeah

[lethal pelican]

so?

[alpine sable]

um

3x^2 - 4y^2

?

that don't seem right

uh

[lethal pelican]

ok first, tell me what this factored would be

[alpine sable]

(a-b)^2

[lethal pelican]

good

[lethal pelican]

so here, our a would be 3x^2 and our b would be 4y^2

[alpine sable]

ohh

(3x^2 - 4y^2)^2

[lethal pelican]

yes

and we still have the 25 x^2 y^2 that we ignored at the start if you remember

[alpine sable]

yeah

[lethal pelican]

so right now, we have (3x^2 - 4y^2)^2 - 25 x^2 y^2

do you know how to factor difference of squares?

[alpine sable]

kinda

litte confuesing

[lethal pelican]

something like $a^2 - b^2$

[ocean seal]

bmeoa

[alpine sable]

oh alrihgt

would we just split the 25 in half?

put in 2 brakets

?

[lethal pelican]

wdym

[alpine sable]

like

$(3x^2 - 4y^2 + 5xy)(3x^2 - 4y^2 - 5xy)$

[ocean seal]

xzc

[alpine sable]

?

[lethal pelican]

yes, very good

so that is the final factored form

[alpine sable]

I don't think so

i think we can go more?

[lethal pelican]

oh maybe youre right

eh, im not really seeing a way on how to factor it more with integers

[alpine sable]

would this make sense

(3x +4y)(x-y)(3x -4y)(x+y)

?

[lethal pelican]

i dont believe so

if you expanded it, you would get something like (9x^2 - 16y^2)(x^2 -y^2), and expanding that wouldn't be the same

[alpine sable]

yeah maybe ur right

[alpine sable]

This is probably it

@lethal pelican I have a questions for thesde type of questions if there was a even number in the middle would you interrupt it the same way

or would there be some difference

or if there were 4 digits

[lethal pelican]

idrk i wouldn't really look at it if it was even or odd. I would say to try take a square number out of the middle term, if that makes sense. In this case, the 49 x^2 y^2, we took 25 x^2 y^2, which is a perfect square.

[alpine sable]

yeah

[lethal pelican]

we want the square number because the last step was to use difference of squares, which only applies to square numbers

[alpine sable]

so would if the middle term was -12

would u use -6 -6 or diffretnt numbers like 18 and -6

[lethal pelican]

well like i said, i would try get a square number out of 12. maybe like -9 and -3, or -4 and -8.

[alpine sable]

oh alright

[alpine sable]

and what if there was umm 4 temrs?

[lethal pelican]

4 terms, splitting wouldnt really work cause there would be a lot of trial and error, since you have to split 2 terms. it depends a lot on the context, but i think maybe grouping the first and third, second and fourth terms together could work, then doing difference of squares

[alpine sable]

oh alright, can we try it or are you busy? is up to u ig

[lethal pelican]

i gtg sleep, so no ig. you should definitely try it yourself first though

[alpine sable]

Alright

thanks for your help

[lone heart]

@alpine sable Has your question been resolved?

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[dense apex]

Hello

[dense apex]

Anyone

Any1

I need some help

With a little thing

[ornate condor]

lol

just ask ur q

[dense apex]

Whos my q

[ornate condor]

LOL

your question

[dense apex]

Alr xd

So

164

That has 8 sqrts on it

Ima send u a pic 1s

[ornate condor]

ye plz fdo

do

[dense apex]

Like this one

Do i just keep the 8

[ornate condor]

wot

so lost

like

[dense apex]

Do i add anything/is it like 8000 now?

[ornate condor]

$\sqrt{\sqrt{8}}^8$

[dense apex]

Yes

Without the one

[ornate condor]

like this?

[dense apex]

On the leftye

Ye

[ornate condor]

so um

whats ur issue

[dense apex]

Idk how to solve it

[ornate condor]

well

[dense apex]

Do i make it a 4 by 2

Like divide by 2

[ornate condor]

firt u go rid of the outermost sqrt

[dense apex]

Ye

[ornate condor]

ye u make it 4 first

then u repeat it then u get 8^2

[dense apex]

Ye

[ornate condor]

ye

[dense apex]

Then we get 8x8

[ornate condor]

think thats all

ye

[dense apex]

Alright then

Thanks alot

Problem solved

[ornate condor]

np

💕

[lone heart]

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[inner birch]

Really need help on this

[lone heart]

@inner birch Has your question been resolved?

[alpine sable]

!rotate

.rotate

[alpine sable]

.rotate

[lone heart]

@inner birch Has your question been resolved?

[carmine reef]

I don't think it works after 20 minutes but it's ,rotate I believe

[carmine reef]

In a problem like this you probably need to start by coming up with names for the important variables

[alpine sable]

ty

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[urban spear]

Hi! im looking for help on this problem. I know the answer but i dont know how to get to the answer.

[urban spear]

ive tried with both of these and cant seem to get it correctly

the answer is 98.010.000 but i got 192.119.400 and i have no idea what went wrong

[gilded citrus]

its not an arithmetic or geometric series

the sum of cubes of first n natural numbers if (n(n+1)/2)^2

[urban spear]

do you have an example of some sort?

[lone heart]

@urban spear Has your question been resolved?

[stable pecan]

You can prove this using induction if you want

[lone heart]

@urban spear Has your question been resolved?

[gilded citrus]

$$\sum_{n=1}^{5} n^3 = \left(\frac{5(5+1)}{2}\right)^2$$

[ocean seal]

hsp

[lone heart]

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[alpine sable]

$$
\text{find the first integer n such that n}!>10^{10}
$$

[ocean seal]

Zermelon

[gray isle]

log_10 both sides

[alpine sable]

i forgot to add: you must use combinatorics

because the book where i got this from does not cover logarithms

and the exercise comes directly after a chapter on counting

[last tendon]

You're just going to have to guess and check to some extent

[dense apex]

It does depend on the size tho also the mecanisum

Wrong channel

[alpine sable]

is there no "right way" to do it?

[last tendon]

You can rearrange 10! to be (2x5)(3x7)(4x6)(8x9)10 > 10x20x20x70x10 = 2x2x7x(10^5) so that 10! is around 10^6

and then play similar games to reduce the search space drastically

[alpine sable]

binary search

would make it easy

[last tendon]

But you're not going to get very far without techniques from Calculus otherwise

[alpine sable]

i see

thanks then

[last tendon]

You then know that 14x13x12x11 = 24024

[alpine sable]

are you 100% sure there's no way to do it with comb?

[last tendon]

so it's probably something like n = 15

[keen plinth]

,w xlnx - x = 10ln10

useless

[alpine sable]

this is very clear

lol

[keen plinth]

,w table xlnx - x - 10ln10 for x from 10 to 15

[alpine sable]

i think the author wants you to brute force it

[keen plinth]

bruh

[last tendon]

I don't know what more you expect, I basically showed that it boils down to either n = 14 or n = 15

[alpine sable]

brute force it is

[last tendon]

If you want something better you're going to need Calculus

[alpine sable]

i dunno i thought there was a correct way to deduce it

what amount of calculus

[keen plinth]

writing the prime factors for n! might help

but its not really that great

[alpine sable]

,w plot n! and 10^n

,w plot n! and 10^10

[ocean seal]

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[alpine sable]

,w n!>10^10

[keen plinth]

,w e^(1 + ProductLog((10 (log(2) + log(5)))/e))

[ocean seal]

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[last tendon]

One way off would be to construct an upper and lower riemann sum by looking at the logarithm, another way would involve expanding the factorial using stirling's formula and then try to reduce it to so that you could use something like Euler' method or some other fixed point iteration.

[alpine sable]

alright

thank you both

[last tendon]

It is easier to just use the initial guess I constructed and ask Wolfram to compute 13! - 10^10, 14! -10^10 etc and you immediately see the answer is n = 14.

[alpine sable]

care for another problem ?

[last tendon]

You know, despite having read hundreds of papers in combinatorics and have worked with many top mathematicians in that area. I hate combinatorics and want nothing to do with it.

[alpine sable]

very well

thanks again

[keen plinth]

this shouldnt be very hard

like

the last letter is fixed

and then you already got an O

so you just choose the rest and permute

[alpine sable]

$$
4^5-(4\cdot 3\cdot 2 \cdot 1)- (1\cdot 4\cdot 3\cdot 2)-(4\cdot 1\cdot 3\cdot 2)\dots=4^5-(4\cdot 3\cdot 2\cdot 1)\cdot 5=4^5-5!
$$

is this it

[ocean seal]

Zermelon

[alpine sable]

@keen plinth

[keen plinth]

on second thought this looks kinda terrible

[lone heart]

@alpine sable Has your question been resolved?

[keen plinth]

do you have the solution to this

[alpine sable]

In the book, no

I provided an answer tho

I can explain it

[keen plinth]

im not sure thats correct

im getting 841 by brute forcing it

[alpine sable]

4^5 is the universe of all possible strings besides the s

4*3*2*1 is every non repeating strings

Then 4*3*2*1 is every string that contains o in a certain position

Thus we are left with a set with no repeating symbol with at least two o's

@keen plinth

[keen plinth]

the thing is

there is only 1 string that is PROOFS

not 2

the O is repeated

[alpine sable]

Where does PROOFS fall?

Wait i found the mistake

It was below the programs output right

[keen plinth]

maybe im tripping

you get 5^5 strings in total

[alpine sable]

Yup

That was the mistake

[keen plinth]

and then

[alpine sable]

No i was right

It is 4 because i excluded the s

There are 5 symbols

Remove the s

Now i work with the substring

Length of 5 from 4 symbols

That is the universe

Thus 4^5

Am i making sense

[keen plinth]

5^5 - 5*(4^4) - 4^5

im definitely tripping

[alpine sable]

Snow

I will work on it later and if i find a solution ill ping you is that ok

Or if i verify that im correct

[keen plinth]

no i know the solution

its 821

[alpine sable]

How did you get it

[keen plinth]

but your idea is fine

,w 5^5 - 5*(4^4) - 4^5

typo

[ocean seal]

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[lone heart]

@alpine sable Has your question been resolved?

[blissful meadow]

can you guyss help me which is the odd number

[lone heart]

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[strange fractal]

Hi i need help with this

[runic trench]

1. simplify the left and right side
2. move all terms and rearrange them
3. use quadratic formula

[strange fractal]

whats the quadratic formula

[golden canyon]

sry

[strange fractal]

WTF

ive never seen that in my life

[calm tide]

thats quadratic formula

[strange fractal]

how do i do this?

[calm tide]

u can also derive it, its not that hard

[calm tide]

open the brackets and bring all the terms to one side

then reply to me

[strange fractal]

i keep getting this

[calm tide]

what you got

12x - 3x^2 = 0

factorize it

see if something is common

[strange fractal]

idk how to do that i just know how to use null factor law

[calm tide]

r u sure u got -3x^2 + 12x?

[strange fractal]

yes

[modest saddle]

Are you using the quadratic formula for this?

[calm tide]

its wrong

[calm tide]

do it again

[strange fractal]

idk the chapter is called quadratic equations but ive never seen quadratic formula

[modest saddle]

Quadratic equations will need the quadratic formula.

[calm tide]

not necessarily

[runic trench]

na not rly

[calm tide]

u can factorize them

[runic trench]

lmoa

[lone heart]

@strange fractal Has your question been resolved?

[lone heart]

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[alpine sable]

I have a set of points all rotating about a common axis, is there a way to compute the curl here without regressing a vector field onto this data?

[daring patrol]

#❓how-to-get-help

[lime cedar]

oh, sorry, thanks for reminding me

[pulsar aspen]

So, you have a finite sample of data?

[lone heart]

@alpine sable Has your question been resolved?

[lone heart]

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[flat saddle]

Hi, I need some help with graphs

[flat saddle]

,rcw

[flat saddle]

I'm trying to figure out if what I did was right

whoops

even number

[runic trench]

ayo lemme try this

btw is that a macbook pro

ok so
A graph is said to be a 3-regular graph if all of its vertices have degree 3

Any 3-regular graph must have an even order because we know that : degree of a graph = 2* number of vertices

I will be showing the proof using mathematical induction

consider n=4

We will need to show if there is a graph that is 3-regular of order k where k is even, which in that case, there is a 3-regular graph of order k+2

[flat saddle]

Huawei matebook lol

[runic trench]

continuing from the top

construct a new graph G' from G as follows:

add 2 new vertices m and n , so now the number of vertices :

[flat saddle]

,rcw

I tested with 6 just to see if I understand what it does

[runic trench]

Okie

[flat saddle]

How would I do induction on this?

kind of lost

Proof by Induction is when you start with n=1 and then change n to k and then prove it right?

[runic trench]

i did this using induction tho?

[flat saddle]

I mean I am lost

.close

[lone heart]

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[ivory sleet]

help

[ivory sleet]

Find the surface area of the following solid. The cubical blocks has a side of length 4 cm.

[karmic solstice]

aye aye