help-0

[wise jewel]

+4 - 2 = 2
-4 - 2 = -6

ohhh

i see

so how do i know at what point to apply the +-?

should it be from the beginning of my equation?

because its a quadratic?

[glass lichen]

you took a square root...

any even root brings a +/-

[wise jewel]

ok

i will remember that

i get it now

ty all

[brazen shell]

I need some help on this, I have 10 more minutes till i can submit these two questions, if someone can help i would be greatful

transposing is my greatest enemy

[glass lichen]

why the time limit?

[brazen shell]

i only got 10 minutes till the assignment goes late

[alpine sable]

ok obviously apply order of operations

and

how would you

how would you explain how to rearrange an equation verbally

algebraic manipulation

uh

[brazen shell]

sorry i dont really understand

[bitter kite]

hey uh is anyone available to solve my problem?

[alpine sable]

ok you could apply some properties of shapes over here in terms of angles, consider AB||DE you could also apply some angles in parallel lines

and thats about it

[quiet crown]

sqrt(v/pi *h) = r

[alpine sable]

Basic LaTeχ syntaxes include \sqrt[]{} \pi \cdot or \times \qty or \left\right for autoscaling brackets \frac for fractions

[wise jewel]

what about in this example? There are no x-intercepts, so how do they know what the third point is? they say to find one more point, and to determine the point for x = -1, where did the get -1 from? how did they know to make x equal that?

[quiet crown]

Thanks

[quiet crown]

$r = \sqrt{\frac{v}{\pi h}}$

[ocean seal]

Vex

[quiet crown]

$v = \sqrt{\frac{P-mg\times r}{m}}$

I think thats correct

Good way of checking is using https://cymath.com

[alpine sable]

\times for the x and \cdot for the interpunct

[ionic jewel]

just wait until you hear about Wolfram alpha

[quiet crown]

Interpunct?

lol

[alpine sable]

Central dot, middle dot, or whatever you call it

[ocean seal]

Vex

[quiet crown]

oh

Getcha

[ionic jewel]

$\cdot$

[ocean seal]

bunny

[quiet crown]

I was way off lol

[spring harbor]

If you're given two line equations, how can you find the angle they make with each other?

[alpine sable]

wot

[spring harbor]

what?

Is my question unclear?

Let's say you have y= 2x and y=x, how can you find the angle they make with each other?

[alpine sable]

https://math.stackexchange.com/questions/1269050/finding-the-angle-between-two-line-equations/1269620

[spring harbor]

So I am supposed to do arctan(m1)-arctan(m2)?

It's given that it's an acute angle

But m1 is 2/3 and m2 is 3/2. How can I find the arctan of these numbers?

I am not supposed to be using a calculator.

[alpine sable]

hmm

[spring harbor]

and these are the possible answers

[alpine sable]

Trivial Trigonometric Identities maybe?

[spring harbor]

Such as?

[alpine sable]

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

[spring harbor]

Also using the formula I get 0.4 (if my calculator is in rads) which is none of the options

Hmm

[alpine sable]

Then convert them to degs

[spring harbor]

I get 22

[alpine sable]

actually

hmm

convert to gradians 👀

[spring harbor]

Oh wait actually

it's asking for cos alpha

with alpha being the angle

[alpine sable]

Can I look at the question itself

[spring harbor]

nevertheless i still get the wrong answer

Yeah sure wait let me translate it

this is a

[scarlet heath]

can someone helpm e out with this

[spring harbor]

Ren can't you see us talking here?

this is b

we need to find the tangent line of b

which i did

i got 2/3x + 3

[scarlet heath]

mb

[spring harbor]

then i need to find cos alpha of the angle they make

[alpine sable]

ok what does in het punt (3,5) mean

[spring harbor]

in point (3,5)

tangent line at that point

[alpine sable]

mk

wait gimmie a moment

[hardy vault]

can someone help me

[spring harbor]

Channel taken

[alpine sable]

hm i'm unsure

sorry

[spring harbor]

Yeah no worries, thank you regardless.

[alpine sable]

i'll look onto it though

Ok just to make sure

what angle are we looking for

[spring harbor]

But now that I think about it, tanx * tan y = 1, so we can say that cosx cosy = sinx sin y
maybe we have to use that for something

Channel taken

or
cos^2 x cos^2 y - sin^2 x sin^2 y = 0 <=> cos^2 x - sin^2 y = 1 => cosx = sin y => cos y = sinx

hmmm

cos(x-y)=cosxcosy + sinxsiny => 2cosxsinx = 2cos^2(x) tanx

cos^2(x) = 1/(1+tan^2(x)) so we get cos^2(x) = 1/(1+(3/2)^2) = 4/13

so 2 * 4/13 * 3/2 ?

or 12/13

[forest pawn]

Hello everyone, hope you are having a great day, I need help with this solid geometry question

[hardy crest]

is this right?

if not what should i change

<@&286206848099549185>

[forest pawn]

But no one answered my question bro, try another channel please

[spring harbor]

Read #rules dude

[hardy crest]

tough

[hardy crest]

this channel is occupied can u leave please

[alpine sable]

what

[spring harbor]

Don’t start clowning

[alpine sable]

Did you get your question answered

I still don't understand it

but i think your working is fine

[hardy crest]

who

[alpine sable]

Echo

[spring harbor]

Yup I showed the steps above

Did you read them?

Not sure if it’s correct though but it seems reasonable

[gusty gorge]

2 is wrong; that's not a proper transformation

[spring harbor]

It seems so far fetched though

[hardy crest]

How can I fix it

[forest pawn]

I will post my question in another channel

[river hearth]

why aren't these parallel?

[gusty gorge]

I fail to understand how that diagram is even possible

[slate monolith]

Lol wtf

Its not

Over 180

[gusty gorge]

Maybe if you bent the ends?

[slate monolith]

No

All straight lines are 180

U cant do more

Plus it doesnt look like 130

Legit is 110

[gusty gorge]

well yeah, but nowhere in the problem does it say that two lines are being cut by a single line

[slate monolith]

It does

I mean thats what the arrows are for

Why would there be multiple lines

[spring harbor]

yeah no that's totally wrong

[gusty gorge]

you could have something like this

[slate monolith]

Well yeah

But thats not gonna happen on a simple quiz

It would be impossible to solve

[spring harbor]

How would you calculate the height of this figure, given that the diameter of one of the circles equals 10?

[queen wigeon]

connect the centers of the circles and use the properties of equilateral triangles

[slate monolith]

Yikes

[spring harbor]

Like this right?

[queen wigeon]

yes

[slate monolith]

How did u come up with that so fast mchen

[spring harbor]

Yeah I kinda already had that, but not sure how to progress

[slate monolith]

Ok so

Its 60 deg

[spring harbor]

yup

[slate monolith]

Height is sqrt3

+1

[spring harbor]

mm?

[slate monolith]

heighr of triangle

306090 triagnle

[spring harbor]

diameter of a circle is 10

Ohh but wait I got it

[slate monolith]

Ye

[spring harbor]

We can split that in half, and use cos 30 = the height of that triangle, then we can add 10cm to it

[slate monolith]

Ye

[spring harbor]

or no we need to use sin 30 = x/20 my bad

[slate monolith]

Wut

Sin60 or cos30 works theyre the same

[spring harbor]

Oh wait yeah i messed up the angles

we get 27.3

thanks

[silk terrace]

Can someone explain this small step for me

why is the equality true?

I mean equal to 0

[slate monolith]

U in calc?

Use integration

[queen wigeon]

or expand $\frac{1}{n^2-1}$ by partial fractions, write it out, and see which terms cancel out

[ocean seal]

mchen10

[slate monolith]

Wut

[silk terrace]

not in calc no

can i use dirichlet*

[slate monolith]

Whst

[silk terrace]

?

[slate monolith]

What is dirichlet

[silk terrace]

nevermind found the answer

[slate monolith]

Oh lol

[alpine sable]

nice handwriting

[hushed pasture]

just wanna know how to prouve it

[hushed pasture]

it's the professor not me😂

[alpine sable]

anyways i am in 9th grade so i am out

[hushed pasture]

ok not a problem dude

[hushed pasture]

<@&286206848099549185>

[solar pebble]

@hushed pasture can I check that that says

$\lim_{n \to +\infty} \frac{|x-a|^{n+?}}{(n+?)!} = 0$

[ocean seal]

Xetrov

[solar pebble]

I don't know what it says in the question marks

[slate monolith]

looks like a 1

[hushed pasture]

well i was doing a calculus exercice and then the prof said that this limit is tend to 0

but I didn't understand it

[slate monolith]

it cant tho

factorial always grows the fastest

[hushed pasture]

yeah that's logical, but there is a way to prove it

[lean flower]

Im starting 8th grade and i suck at algebra

[solar pebble]

@hushed pasture does that say 1?

[lean flower]

not to mention i am asian

[hushed pasture]

no it's 0, it's just the prof said that this limilt is equal to 0

but I didn't get it

[solar pebble]

@hushed pasture No lol, the question marks

[solar pebble]

here

[hushed pasture]

could you prove it like you don't know the output yet?

that's what I'm looking for

[solar pebble]

you're ignoring me lol, I can't read the Profs writing

[hushed pasture]

what is your question, i thought that you didn't ask me

[hushed pasture]

so the fraction is (X-a)^(n+1)/(n+1)!

[solar pebble]

they're 1s?

[hushed pasture]

yeah 1

[solar pebble]

$\lim_{n \to +\infty} \frac{|x-a|^{n+1}}{(n+1)!} = 0$

[ocean seal]

Xetrov

[solar pebble]

unknown x ya?

[hushed pasture]

yeah but the limit is for n not x

[solar pebble]

yes I see xD

[slate monolith]

how is that 0 tho

nvm it is 0

[solar pebble]

yeah it is lol

I'd imagine you substitute the factorial for the gamma function

[hushed pasture]

so you know how to prove it on paper?

[slate monolith]

well so

[solar pebble]

probably L'hopitals but I've not tried it

[slate monolith]

usually u just assume

u cant use LH

[solar pebble]

I'm doing it in my head

[slate monolith]

lmao

[coral pagoda]

Pretty sure this is related to the Taylor Remainder theorem. So yes, the ? Is 1

[slate monolith]

just say that

any factorial is gonna grow faster

[hushed pasture]

exactly

[slate monolith]

and since its in the denom

[coral pagoda]

But tbh, the constant does not matter for the limit (just the theorem).

[slate monolith]

itll go to 0

[solar pebble]

hmm

[slate monolith]

wait that makes a ton of sense actually

[solar pebble]

yeah 😂

[slate monolith]

the error goes to 0 as the terms go to infinity

[coral pagoda]

Precisely :)

[hushed pasture]

that's the exercice in french, you can easly tanstlate it

[solar pebble]

but we're not French 😅

[hushed pasture]

i don't why the prof use Taylor-Lagrange instead of Young

[solar pebble]

or most of us anyway

[hushed pasture]

ok i'll translate it for you

[ionic jewel]

im extra not french

[solar pebble]

A bit like me giving you a question in Chinese and expecting you to be able to translate it just because I know Chinese

[ionic jewel]

well to be fair french is more readable than chinese to the average english speaker

[solar pebble]

that's a fair point, but similar concept

[ionic jewel]

matter of fact i think i can read that problem

Let f R to R be a function of class c^inf somethign something proper, there exists a polynomial of degree something something n geq 0 for all x in R

close enough

[solar pebble]

I took French in high school. Still can't read much

[ionic jewel]

i speak broken spanish so that probably helps

[solar pebble]

#bilingual gang

[ocean seal]

dackid (jump king +)

[slate monolith]

,w translate soit F une fonction de R vers R tel que F est infiniment derivable. il existe un polynome P impair tel que

[ocean seal]

Results provided by WolframAlpha

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

Requested by Kefir101Awesome#7665

[hushed pasture]

oups my bad hhhhhhhhhhhhh

for every n of N: |F(x)| <= |P(x)|```

[slate monolith]

LMFAO

what is that

[coral pagoda]

It was close

[slate monolith]

very

[hushed pasture]

the 2nd question is to proof that F is null

and you should consider that that what ever the derivative of F, always F(a) = 0

[candid bolt]

For quesiom 17 is the following valid?

Proof by contradiction: assume there exists an int n such that (n^2+2) is divisible by 4. If this is the case it must be that (n^2+2) is even because 4 is a multiple of 2. Further in order for a number plus 2 to be even it must already be even. Thus n^2 is even. It is obvious that if n^2 is even n must also be even. Thus n is even. Thus n can be re-writren as n=2x where x is an int. Meaning n^2+2=(2x)^2+2=4x^2+2 this is not divisible by 4. Since 4x^2+2=4(x^2- 1) +2. Thus (n^2+2) is both divisible by 4 and not divisible by 4

Ie a contradiction

[slate monolith]

what is it asking @candid bolt

all I see is for every n, n^2 + 2

what is the Z

[candid bolt]

I posted the question in the above pictue it is asking for a proof that for every n in the int, that (n^2+2) is not divisible by 4

[slate monolith]

ah

It is obvious that if n^2 is even n must also be even. idk about this

but w/e

Since 4x^2+2=4(x^2- 1) +2 idk what ur doing here

this makes it more compex

[candid bolt]

Sorry that Is just showing it is indivisible it is just how my textbook did similar questions

[remote heron]

i feel like doing just by cases is easier here but idk if you cleaned this up (dont even really have to) i think itd be valid if weird

maybe easier pathway if you wanna just assume the n is odd case doesnt work

is just show that you can factor n^2 + 2 in a fancy way such that it's an odd number + 2

e.g. cant be divided by 4

sorry

[candid bolt]

Oh that would prolly be easier

[remote heron]

2*(m+2)

where m is odd

fuck

i cant type it correctly

maybe ill just scribble it

if you dont get what i mean

lemme scribble

[candid bolt]

Also I checked the proof, I think you can pretty easily prove with contraceptive n^2 even =>n even

That would be appreciated thanks!

[remote heron]

lmao contrapositive* but thats a funny typo

gimme one sec

[candid bolt]

Yeah take your time

[remote heron]

so something like this for even

i guess this should go first

sorry my writing is bad

you can be as pedantic as you want about all this

i probably wrote too much

[candid bolt]

No I can read it w well

I think this makes sense! Thank you so much

[remote heron]

something like "4 divides p implies that at the prime factorization of p includes at least 2 factors of 2..."

np

[candid bolt]

Got it

[alpine sable]

If I'm given (x) = x^2 and I'm told to evaluate f(2+3i) would that mean (2+3i)^2

?

If so I got -5 + 12i

[remote heron]

yea youd just plug the input into the square

[alpine sable]

Ty for clarification :)

[hidden kelp]

How do I start this?

And what does it mean when BM is perpendicular to AC

[remote heron]

they make a 90 degree angle together

its also marked in the image

by that tiny square near where they intersect

[hidden kelp]

So how would I find AB and BC?

[remote heron]

i dont actually know geometry

[slate monolith]

this looks hard

[hidden kelp]

I'm trying to practice for the SATs, but geometry is my weak point

[slate monolith]

this is wayy harder than the sat

[strong furnace]

BAM and BMC are similar to ABC use that

proof would be the right angle and B or C (AA similarity)

[woven pollen]

2 is to x as x is to 18. x = 6. A = (1/2) * 20 * 6.

I should have made x an h. because we are looking for the h of the triangle. but, you know....

[slate monolith]

whats x tho

[hidden kelp]

yeah i got that

thanks!

[spring harbor]

given f(x) = 2x - ln(2x), how can we find the tangent line of f(x) that goes through the origin?

[slate monolith]

i gotchu

itll be when the slope equals the y value

or is a multiple of it

[spring harbor]

Could you explain what you mean a bit further?

I need to find the tangent line equation

[slate monolith]

do u know how to take a derivative

[spring harbor]

Yeah; Df(x)= 2 - 1/x

[slate monolith]

almost

2 - 2/x

[spring harbor]

I believe you're wrong

[slate monolith]

so u gotta set f'(x) to f(x)

,w derivative of 2x - ln(2x)

[spring harbor]

You get 2-2/2x

or 2-1/x

[ocean seal]

Results provided by WolframAlpha

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

Requested by Kefir101Awesome#7665

[slate monolith]

ah mb mb

i forgot

yes

[spring harbor]

no worries

[slate monolith]

set f'(x) to f(x)

[spring harbor]

why would we do this?

[slate monolith]

basically

if u want it to hit the origin

the slope should be able to reach 0 from the inital value

wait wait

i messed up

it has to hit both

no im right

[spring harbor]

I am sorry I am not following

[woven pollen]

Is this correct?? I guessed.

[slate monolith]

it looks good

idka bout the answer

[woven pollen]

If it's wrong I will delete it.

[slate monolith]

depends on the function

does it have asympotoes

is it piecewise

[spring harbor]

@woven pollen the question is asking me for the slope of that tangent line; these are the options I got

[slate monolith]

any polynomial

[strong furnace]

the answer is not y=2x-1

[slate monolith]

is always continious

[spring harbor]

I assume yours is wrong

[slate monolith]

oof

[strong furnace]

y=2x-1 is the relation between y and x coordinate of the point of tangency

which also lies on the curve

[slate monolith]

well it has a veritcal asympotate at x = 0

so no

[strong furnace]

so y=2x-ln(2x) should satisfy it

[woven pollen]

ah. ok.

[strong furnace]

so you have 2 simultaenous equations y=2x-1 and y=2x-ln(2x) for the point of tangency

[spring harbor]

@alpine sable Could you move to a different channel?

thanks.

[strong furnace]

you have slope in terms of the point

should be easy from here

[spring harbor]

Wait I apologize I am not exactly following

[strong furnace]

ok so if a line passes through origin it is of the form y=mx correct?

[spring harbor]

yup

[slate monolith]

hes asking a diff question not answering urs

[strong furnace]

if the point of tangency is (x1,y1) then line is y=(2-1/x1)x correct?

[spring harbor]

Why 2-1/x1?

[strong furnace]

thats the slope of tangent line you got by differentiating

[spring harbor]

Ohh i see

Yeah I get it sorta

[jagged trout]

$\frac{\Delta y}{\Delta x}$

[strong furnace]

(x1,y1) must lie on this line so y1=2x1-1

and it also lies on the given curve

so y1=2x1-ln(2x1)

solve for x1 get the line equation

[spring harbor]

We get e/2 = x

2-1/2/e = 2-e/2 = (2e-2)/2

which is one of the option

Hmmmmmm yeah I get it now

So basically set f(x) equal to f'(x) * x

Solve for x1 and fill x1 in f(x)

[strong furnace]

this was a problem specific thing you would need to set y=f'(x1)*x+c and then satisfy the given point in this case the point happens to be(0,0) so c=0 is kinda trivial

[spring harbor]

yeah normally it is y-fa = f'a(x-a)

[last sinew]

Hi please excuse me, is this channel soon to be open or should I redirect myself to another channel? Thank you :)

[slate monolith]

wait what

[spring harbor]

I learned that formula

[slate monolith]

so I was close

[woven pollen]

Why does f'(x) go through the origin origin again?

[slate monolith]

I see what they did

[spring harbor]

It's what the question asked for

[slate monolith]

its what ur tryna get

[spring harbor]

Yeah you can post your question

[last sinew]

Thank you!

[spring harbor]

Thanks Sussy & Kefir

[slate monolith]

sure thing

[last sinew]

Will someone kindly explain why sqrt(p(1-p)) must be less than or equal to 0.5? That is all that's troubling me

Any help would be highly appreciated

[slate monolith]

ima guess that

its because u need to be less than 2.5%

[strong furnace]

the function sqrt(x) is monotonically increasing and x(1-x) has maxima at 1/2

[slate monolith]

0.5^2 is 2.5

ah

[last sinew]

I-

Oh my god

[slate monolith]

how did u get that so fast

[last sinew]

Ok thank you 😭

Wait sorry one more thing

[slate monolith]

mhm

[last sinew]

What does z*sqrt((p(1-p)/n) have to do with anything again

So where does the z pop out of 😭

Wait

NEVERMIND

I REMEMBERED

THANK YOU ALL SO MUCH

[strong furnace]

isn't z something in statistics

ohh nm

[last sinew]

Ok im good

Yessir

Thank you

Have a good day everyone :D

[slate monolith]

you too 😄

[sleek elbow]

I literally relate to this feeling so often 😄

[humble anchor]

How would I show that D_vf(0,0) = 0 for all unit vectors v?

[humble anchor]

bruh

<@&286206848099549185>

[slate monolith]

i would ask this in the uni math

this looks like uh

hard calc

or linaer algebra

[simple pond]

Did you cut a part out of the pic?

[red vigil]

Hey yo guys, just came here for an emergency and because my head is going to blow xd, i have hours looking for any calculator and trying to simplify but i do not have found the answers i need.

Is someone available who can help me out?

[slate monolith]

sure

monomial should just be a linear

mb mb

it means one term

so they can be the same

[red vigil]

I know, but also is asking me this

And this is where im stuck

[slate monolith]

u didnt even give the question tho

[slate monolith]

this legit just means

2+ terms divided by 1 term

will have multiple terms

[red vigil]

Is an aleks exercise

[slate monolith]

split it into 3 fractions

simplify each

[old swan]

The graph displays the number of tests given at a particular school over a five-day period. Explain why this graph could be misleading.

The scale in the vertical axis is broken. It appears as if half as many tests were

given on Monday as on Wednesday, but actually twice as many tests were given on
Monday than on Wednesday.
The axes of the graph are wrong. The number of tests should be on the horizontal axis, and the days should be on the vertical axis. It appears as if there are fewer
days than the number of tests.
The scale in the vertical axis is broken. It appears as if 5 times as many tests were given on Monday as on Wednesday, but actually only 4 more tests were given on
Monday than on Wednesday.
The scale of the graph is wrong. The vertical axis should represent equal intervals of numbers. It appears as if 5 times as many tests were given on Wednesday as on Monday, but actually only 4 more tests were given on Wednesday than on Monday.

[slate monolith]

? whats ur q

[old swan]

?

[slate monolith]

are those options for the answer

[old swan]

yes

[slate monolith]

or is that ur work

ah

well what do u think

[old swan]

im not sure all ik is it isnt the axis one

[slate monolith]

3 left

reread them carefully

[old swan]

ok

i have no idea tbh

[minor crypt]

bye

[jagged trout]

What was that?

[slate monolith]

two of them are similar

only 1 word diff

[old swan]

The scale in the vertical axis is broken. It appears as if half as many tests were
given on Monday as on Wednesday, but actually twice as many tests were given on
Monday than on Wednesday.

is it that one?

[slate monolith]

how would it be that one

[old swan]

idk how to explain it-

[slate monolith]

that one says half as many tests on M than on W

where is that on the grap

[old swan]

it shows it on Tuesday

[slate monolith]

what

[old swan]

please just say the answer

[slate monolith]

i cant, thats not the point

its not a or b tho

thats my hint

[old swan]

The scale in the vertical axis is broken. It appears as if 5 times as many tests were given on Monday as on Wednesday, but actually only 4 more tests were given on
Monday than on Wednesday.

that?

[slate monolith]

what do u think

ik its tiring

take a break if u want

[old swan]

i want to get it done i just have no clue how to do it

[slate monolith]

taka break tbh

[humble anchor]

nah theres just irrelvant info below it

ill send it again cuz i still dont know what to do

How would I show that D_vf(0,0) = 0 for all unit vectors v?

my initial approach was using the limit formula with f(0 + hv1, 0 + hv2) - f(0,0)/h

and then subbing in the values and cancelling h out

but i end up with v1^2 v2^4/3 / (v1^10 + v2^2)

so idk how to show that equals zero

<@&286206848099549185> still struggling here! would appreciate help

[humble anchor]

pls someone i have pain

[slate monolith]

it could be impossible

looks very hard

[humble anchor]

this is calc 3 tho

[slate monolith]

big brains tuff

@humble anchorask it in calc

or uni

[simple pond]

Send the full pic please. Even if it’s irrelevant. Just want to see

[woven pollen]

What does the D_u operator do?

[simple pond]

You’re looking for how to do question a?

[humble anchor]

yep'

i can tell u what i have so far but i think its wrong

[woven pollen]

Does D_u take the derivative of f(.) with respect to u?

[simple pond]

Yes send a pic of your work please

[glass lichen]

my guess is directional derivative in the direction of u

[humble anchor]

^ yea its directional deriavtive

so obvisouly this isnt 0 so idk what to od

[woven pollen]

did you divide by h ok? it looks off.

[old swan]

k im off my break

[slate monolith]

lol

[humble anchor]

i factored out h from both top and bottom

so it should cancel out

[old swan]

can you just tell me the answer this assignment is already 2 hours late

[simple pond]

I don’t think that the question is asking for it to be equal to zero. All its asking is for the directional derivative of Du (f(0,0))

[old swan]

can you please give me the answer

[woven pollen]

e.g. (h · v_1)^10 = h^10 · v_1^10. how did you cancel 10 h's?

[slate monolith]

either one

read this

[humble anchor]

uhhh then is what i did fine?

[old swan]

thats the one i chose

[humble anchor]

and wait tensor

lemme doublecheck

[old swan]

which one though

[humble anchor]

also can u guys use a different channel

cat girl

[old swan]

I was here first-

[humble anchor]

haha no u werent

[old swan]

yea i was...

[slate monolith]

lmfao

[old swan]

look though the chat

[slate monolith]

u were 1.5 hrs later @old swan

[old swan]

idgaf

[slate monolith]

read it

cmon

its not hard

[humble anchor]

kefir

do u know how to do my stuff

plz

[old swan]

it is hard

[woven pollen]

The graph could be misleading because y = (1 .. 4) is cut off.

[humble anchor]

tensor do u know

ik i messed up with the cancelling

but i still dont know what to do

[woven pollen]

I'm working on it. gimme a few minute.

[humble anchor]

thank u

[old swan]

dude just give me the answer please

[humble anchor]

haha cathlene

ik hwo to do it

but nah

lol!

xd!

[old swan]

im not talking to you

[slate monolith]

;-;

i cant

thats not the point of this server

[old swan]

well i dont get it

[slate monolith]

what dont u get

[velvet oyster]

Hi. I want to know how to sold question5 in this photo.

[humble anchor]

@simple pond @woven pollen uhh i thought of another method to solve this questions

so i know this is true

[woven pollen]

I was just reading that! on a webpage.

[humble anchor]

i mightve messed fx up

and fy

cuz this doesnt make sense

ideally fx and fy should be 0, then that would make sense

maybe i cant math

[woven pollen]

yay. I'm trying to get my head around the correct way to make the substitutions

[humble anchor]

wait isnt that for a different equation

[wise jewel]

Hey guys does 9t^2 + 25t + 6 represent a soccer ball after being kicked off an initial height of 6 ft?

[slate monolith]

no

[wise jewel]

Why? @slate monolith

Ahhh

Probably because it doesn’t make sense for a ball to be 157 feet in the air after 3 seconds?

[slate monolith]

no, because it would keep going up foreever

[wise jewel]

Ohhh

Ok

Ty!!!

[old swan]

A factory produces 15,000 computer monitors per day. The manager of the factory claims that fewer than 800 defective computer monitors are produced each day. In a random sample of 220 computer monitors, there are 5 defective computer monitors. Determine whether the manager's claim is likely to be true. Explain.
No, the manager's claim is not likely to be true. Based on the data, you can predict that there are 805 defective computer monitors produced per day.
No, the manager's claim is not likely to be true. Based on the data, you can predict that there are 810 defective computer monitors produced per day.
Yes, the manager's claim is likely to be true. Based on the data, you can predict that there are 346 defective computer monitors produced per day.
Yes, the manager's claim is likely to be true. Based on the data, you can predict that there are 341 defective computer monitors produced per day.

[jagged imp]

this channel just exploded lmao

2 of you post in different channels

[old swan]

lmao ikr

[main panther]

I’ll switch

[jagged imp]

looks like they're reflections of each other in the x axis

[old swan]

mine is the easiest in the chat i need halp

[jagged imp]

Every point (x,y) has been changed to (x,-y) so like on the blue graph, you can see (0,3) on the blue and (0,-3) happens to be on the black graph. This is true of every point, which means its a reflection in the x axis if you want ig an "empirical" justification

but i just looked at it and it looked like a reflection in the x axis

[alpine sable]

thank u

!

@jagged imp

could u please explain how its 1/n?

[jagged imp]

wait so you want to understand why the image of a dilation of 1/n from the y-axis gives you f(nx)?

[sullen nova]

Yoooooo

Halllllp

[alpine sable]

yes

u could give me an example of a graph if u wish

[sullen nova]

Pls halp

[jagged imp]

I mean i can give you an example here of the dilation in action here, but I'm not sure if that's quite what you're looking for. I'm finding it hard to explain at your level since when I was at your level all i was told to do was memorise the rules so my intuition for this is based on some higher level maths(kinda higher level)

[alpine sable]

Best way is to pick a simple f (say a line), pick a value of n (say 2). Then graph it and see what's happening.

@jagged imp it makes perfect sense thank u

parabola was the best choice of functions to explain the concept

[surreal merlin]

People still have school?

[nova widget]

you could try obtaining the perimeter of each rectangle, then add them together.
the formula for the perimeter of a rectangle is $2(l + b)$, where $l$ is the length and $b$ is the breadth

[ocean seal]

g-e-o-m-e-t-r-i-c

[jagged imp]

some countries handled the pandemic better than others

or just coincidentally or for whatever reason aren't bad enough affected to have schools closed down

[surreal merlin]

Ima need this server in august

[velvet oyster]

Ok. I'll try. Thanks

[inner token]

i don't understand how to do this

[hybrid furnace]

theres still math summer classes and camps i guess

[quick dew]

https://tenor.com/view/sorry-stitch-史迪奇-sad-gif-10399341

[tough hatch]

graph the region bounded first

use the bounds of the first triple integral

[sullen nova]

Hello

Can someone halp me?

[tough hatch]

@sullen nova

no need to ask if someone can help

[inner token]

i need help setting up this triple integral

I can solve em fine I just never know how to set em up

[wise jewel]

1. (x + 9)^2
2. x^3 - 9
3. (x - 9)^2
4. x^2 - 9

None of these are examples of the difference of two square right?

@tough hatch why the reaction?? Lol

[simple pond]

This is just the start

[alpine sable]

Is the derivative of natural log x³ = 3/x ?

[inner token]

well at least I had the same order lol....

[inner token]

thanks

[alpine sable]

🤔

[wise jewel]

Anyone know?

Nvm

[tough hatch]

u sure?

[wise jewel]

Wdym

[tough hatch]

have u checked everything?

[alpine sable]

Is it correct? @tough hatch

[wise jewel]

Well a difference of two squares, a^2 - b^2 = (a + b) (a - b)

[alpine sable]

Thanks

[wise jewel]

But none of those equal (a + b) (a - b)

[tough hatch]

well (x+9)^2 is just one square by itself

[tough hatch]

why not look for the ones that look like a^2 - b^2 instead

[wise jewel]

(x + 9)^2 = (x + 9) (x + 9)

[tough hatch]

a^2 - b^2 is what difference of two squares looks like

[wise jewel]

Right..

[tough hatch]

it's not a difference of two squares, it's just one square by itself

how about x^3-9

it's a difference right?

[wise jewel]

No?

-9 isn’t being squared

Right?

Idk lol

[tough hatch]

im asking if $x^3-9$ is a DIFFERENCE

[wise jewel]

Yes

It is

[nova widget]

sure it's a difference but it's not a difference of squares

[wise jewel]

You’re subtracting

[tough hatch]

there we go

is 9 a square?

[nova widget]

yes

[tough hatch]

is x^3 a square?

[nova widget]

9 = 3^2

[tough hatch]

@nova widget stop answering the questions not intended for u

[nova widget]

sure

[tough hatch]

u keep trolling around lol

[tough hatch]

@wise jewel

[wise jewel]

What

How am I trolling

[tough hatch]

not u

[wise jewel]

Oh

[tough hatch]

geometric

is x^3 a square?

[wise jewel]

Yes

It’s Bringen squared by 3

[tough hatch]

wtf is bringen

[wise jewel]

LOL sorry

Autocorrect

Being*

[tough hatch]

Being squared by 3

what exactly is ur definition of "squared"?

[alpine sable]

x^3 is cubed

[wise jewel]

Oh right

Sorry

It’s cubed*

[tough hatch]

squared is different from raised to the exponent ___

[wise jewel]

Right

Squared is to the power of 2

[tough hatch]

so its not squared

[tough hatch]

redundant

if it's squared then it's raised to the power of 2

[alpine sable]

lol

[tough hatch]

so B is also not ur answer

in general u can check if

1. it's a difference
2. of BOTH SQUARES?
   OR
3. it's a product
4. in the form (a PLUS b)(a MINUS b)

@wise jewel

that's what we've been doing so far

now how about 3)?

NOTE: if it's a single square, it's not a difference of two squares

[wise jewel]

Well

#3 is just (x - 9) (x - 9)

[tough hatch]

note what i said

since it's already a single square it's just in the form (a+b)^2

no a-b factor there

[wise jewel]

Sooo not correct

[tough hatch]

follow?

mhm

how bout the last one

x^2-9

[wise jewel]

Wait when you say single square

[tough hatch]

^

[wise jewel]

Wdym

[tough hatch]

by single square i mean (a+b)^2

[tough hatch]

use this

x^2 - 9

[wise jewel]

Oh ok

[tough hatch]

is it a product or difference?

[wise jewel]

Difference

So that’s a check

[tough hatch]

ok,

of both squares?

[wise jewel]

Nnnnno?

-9 doesn’t have an exponent

[tough hatch]

i.e. is x^2 a square AND is 9 a square?

[wise jewel]

Well 9 has a square root

[tough hatch]

no think of it as c-d

[wise jewel]

Of 3

[tough hatch]

soooo?

[wise jewel]

Ohhhh wait so this is after the square root has already been applied

[tough hatch]

9 IS the square of 3

[wise jewel]

Right

[tough hatch]

so now?

[wise jewel]

That means that $x^2 - 9$

[tough hatch]

is?

[ocean seal]

¿Black Hat? ͜..

[wise jewel]

Is indeed a difference of 2 squares

[tough hatch]

yep

[wise jewel]

YAYYYY

Ty!!!!

Do I have to know how to factor by grouping when I can just use the slide n’ divide method to factor?

[tough hatch]

what is this slide n' divide

[wise jewel]

One second

A trick for factoring, I’ll post the steps here

^^ @tough hatch

It’s way easier than grouping IMO and does the same thing

[tough hatch]

factoring by grouping applies to more polynomials

u can probably use this when it's not possible to factor (let alone by grouping)

[wise jewel]

Oh ok

So if I’m factoring 6x^2 - 7x - 20

The middle term should be rewritten as -2x - 5x right? @tough hatch

[lusty pewter]

can someone help me with 7f

@wise jewel

[wise jewel]

?

[lusty pewter]

can u help with my question

[tough hatch]

uhhh

this channel is clearly busy

u may post on another #question- channel

[lusty pewter]

uhhh this channel is clearly busy SHUT UP MAN U WANNA GO ME

lmao jk

[wise jewel]

…

[lusty pewter]

ok

[wise jewel]

But yeah if I’m factoring 6x^2 - 7x - 20

The middle term should be rewritten as -2x - 5x right?

[lusty pewter]

yepp

i have no clue

[wise jewel]

…

@tough hatch any clue?

[ionic jewel]

idk what ur doing but I'd just throw that into the quadratic eqn tbh

[queen wigeon]

have you tried setting up an equation?

[tough hatch]

factoring

not solving for x

i doubt they only factor second-degree polynomials

[ionic jewel]

could use the quadratic eqn to factor

idk whatever trick he's doing

[small holly]

how do i factorise this

[tough hatch]

ur goal is to get a common term out

[tough hatch]

why not factor by grouping

m^2 - mn = ?
3n - 3m = ?

[small holly]

i have to factorise it in pairs

like binomial pairs

[ionic jewel]

yes

[thorn kindle]

Good job!

[tough hatch]

so u good?

[small holly]

no

[ionic jewel]

pull a -m out of the first two and a 3 out of the second two

[tough hatch]

so ?

factor these

[small holly]

m(m-n)

and

3(n-m)

[toxic sleet]

i was thinking it became (m-3)(m-n)

[tough hatch]

yes

so now
m^2 - mn + 3n - 3m becomes
m(m-n) + 3(n-m) or
m(m-n) - 3(m-n)

[alpine sable]

how do i learn 7 times tables

[tough hatch]

u follow?

[small holly]

yeah

[tough hatch]

@alpine sable channel is busy, u may post on another #questions- channel

[small holly]

wait why is there a + in the first one then a - on the second

im so confused

[tough hatch]

n-m = -(m-n)

[small holly]

yeah

[toxic sleet]

can you help me out with parabolic quadratic essays bro?

[small holly]

sheeeeesh ur big brained

[tough hatch]

channel is busy

[small holly]

wait so it becomes (m-3)(m-n)?

[tough hatch]

yes

[small holly]

but if i factorise that it becomes m^2 - mn - 3m + 3n not m^2 - mn + 3n - 3m

or is there no difference?

[vale wigeon]

there is no difference between these

-3m + 3n = 3n - 3m

[small holly]

oh okay

[lusty pewter]

What is the value of n if n is the largest of 5 consecutive numbers that multiply to give 95040?

@tough hatch

yo superficialsicko

i need help :]

[tough hatch]

@lusty pewter don't ping me as if i'm the only one who can help u

lol

[lusty pewter]

ok sorry

[tough hatch]

[lusty pewter]

ok lol

[vale wigeon]

have you made any progress on this?

[lusty pewter]

alll i know is:

(n-4) x (n-3) x (n-2) x (n-1) x (n)

[vale wigeon]

you should not use x for multiplication

but yes, n(n-1)(n-2)(n-3)(n-4) = 95040

[lusty pewter]

yeah

i am a bit confused

[vale wigeon]

confused at what, exactly?

[lusty pewter]

how to get 95040

[vale wigeon]

what do you mean by "get 95040"?

[lusty pewter]

like what does n have to be to get 95040

[vale wigeon]

"i'm a bit confused at how to solve this problem" in other words

which is not very informative unfortunately

[lusty pewter]

i literally said that

[vale wigeon]

i was attempting to narrow down where the confusion was

and failed

[lusty pewter]

what do you want me to stay instead when i have no clue how to solve it

[vale wigeon]

"i have no clue how to solve it"

[lusty pewter]

THATS BECAUSE I DONT

lmao

[vale wigeon]

anyway, if you treat this as an algebraic equation, it's going to be hard to solve, as it's 5th-degree
however, since we know n must be an integer, we can look at what 95040 is divisible by

you may notice that 95040 is divisible by 9 and by 10

[lusty pewter]

how did you figure that out

so fast

[vale wigeon]

figure what out

[lusty pewter]

like how it was divisible by 9 and 10

[vale wigeon]

these both have simple to check divisibility rules

a number is divisible by 10 iff it ends in a zero

and by 9 iff the sum of its digits is divisible by 9

[lusty pewter]

oh ok

[vale wigeon]

you know your divisibility rules, right?

[lusty pewter]

no

[vale wigeon]

[lusty pewter]

ill learn after this

what

[vale wigeon]

i mean ok

in any case

[lusty pewter]

lmao i am being bullied

[vale wigeon]

........

are you accusing me of bullying you, in complete seriousness?

[lusty pewter]

lmao

no

its joke

[vale wigeon]

and how exactly was i meant to know it's a joke?

[lusty pewter]

y do we need to find what it is divisible by

[lusty pewter]

OMG

r u trolling me

[vale wigeon]

i never said we 'need' to do anything

no, i am not trolling you.

[lusty pewter]

ok

[vale wigeon]

try writing down some products of 5 consecutive numbers that involve 9 and 10

there aren't many options for that

maybe you'll be lucky.

[lusty pewter]

y do they involve 9 and 10

[vale wigeon]

well 95040 is divisible by 9 and 10. maybe 9 and 10 could appear in the product directly

you know

when a number is divisible by 9, it can be written as 9 times something

[lusty pewter]

yeah

oh thanks so 9 is n

[vale wigeon]

it isn't

and i didn't say that

[lusty pewter]

oh so its 10

[vale wigeon]

it's not 10 either

,calc 9 * 8 * 7 * 6 * 5

[ocean seal]

Result:

15120

[vale wigeon]

,calc 10 * 9 * 8 * 7 * 6

[ocean seal]

Result:

30240

[lusty pewter]

close enough

[vale wigeon]

no

these are not 95040

[lusty pewter]

quiet close though

ill take that

[vale wigeon]

no, not nearly.

no.

at your level in math, you cannot get away with "close enough".

[lusty pewter]

what is my level

[vale wigeon]

from what i can see, you're studying basic algebra.

[lusty pewter]

yeah

[vale wigeon]

and right now, you're being stubborn.

[lusty pewter]

what is stubborn

oh i searched it up

ok

[vale wigeon]

bet you haven't actually done this

seeing as all i got from you were two incorrect guesses

[lusty pewter]

i did

19 18 17 16 15

[vale wigeon]

......

fine

,calc 19 * 18 * 17 * 16 * 15

[ocean seal]

Result:

1.39536e+6

[lusty pewter]

yikes

[vale wigeon]

1395360 is too big

[lusty pewter]

im on the right track

[vale wigeon]

no you're not

[lusty pewter]

oh

[vale wigeon]

this list of numbers includes neither 9 nor 10

[lusty pewter]

9 is in 19

[vale wigeon]

it feels as if you're deliberately not following my instructions

[lusty pewter]

dude what

can you give me an example

idk what u mean

[vale wigeon]

13 * 12 * 11 * 10 * 9

like this

[lusty pewter]

wow spoiler

alert

[vale wigeon]

no lol

[lusty pewter]

is that answer

[vale wigeon]

no

it is not

[lusty pewter]

oh

[vale wigeon]

you can see for yourself

(unless you are unable to multiply five numbers together)

[lusty pewter]

oh i get it

so like 11, 10 , 9, 8 ,7

as an example

[vale wigeon]

yes that's an example of the kind of list i wanted you to write out

but this particular one won't give you 95040

it is but that's of no use here

[lusty pewter]

wow

[ocean seal]

Result:

55440

[lusty pewter]

do i need to know that

[ionic jewel]

no

[vale wigeon]

no you don't, you can ignore what bunny said up there

[lusty pewter]

factorial

[vale wigeon]

yknow what. fuck it.

,calc 12 * 11 * 10 * 9 * 8