help-17

[topaz swift]

I am assuming this mainly because the top hlaf of the graph is red and so is the equation and my problem is figuring out why that is or why it is not

[vast shale]

yes i think because that equation is for the range "0 <= x <= 10" according to the graph and the problem

[topaz swift]

ty

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[main tapir]

help this thing is making me crazy and i dont now if it rigth the question (sorry my english)

[pale perch]

whats your question

[main tapir]

this

i have to

[pale perch]

prove it?

[main tapir]

yep

the thing

[pale perch]

use induction

[main tapir]

i do it and it doesn't work

[icy spear]

strong induction

[pale perch]

show your work

[main tapir]

i try it in some diferent ways and it dosent equalize the equation and it does not equal the hypothesis

[pale perch]

okay, youre fine to here

everything after is wrong

[main tapir]

what

why

[pale perch]

you wrote that 4(k+1)^3=4k^3+4?

that makes no sense

[vast shale]

Just try it

With 2

Look what happens

[pale perch]

from here, factor out (k+1)^2/4

then try continue

[vast shale]

Nvm it’s +

Why isn’t it written with a sigma 😭

Sum

[main tapir]

latin things

[main tapir]

?

[pale perch]

you wrote that

or at least implied it

its untrue

[main tapir]

let me try

but....

FUCK

you have reason

thankssss

🫶

[pale perch]

no problemo

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@main tapir Has your question been resolved?

[main tapir]

a

men

ammmm how i tell you

that dosent equalize with the hypothesis

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@main tapir Has your question been resolved?

[main tapir]

No

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[burnt gyro]

How should i solve this?

[burnt gyro]

I have some work that i did that ill send in a second

I wasnt sure where to go from here or even if I went the rigth way with the problem (I probably didnt)

would someone mind walking me through the correct way to solve this problem?

i think

thats when youre like u = some part of the intergral

and then you can put the integral in du instead of dx

weve touched on it but im not too familliar

its fine

for refrence this question came from a homework assignment that covered the topics of integration by parts and triganometric integrals

we havent done much of the latter but this question probably involved either one or both of those

do you have any idea on how i would solve this?

ok

[twin meteor]

𖤍

𖤍

[burnt gyro]

yeah

wait shoot i meant to add a negative

also if you want to write cos^2(x) and stuff I get what you mean

if its easier for you to type it out

i see

I get how to do it now

ty :)

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[spiral frost]

I did (2^2)^x+1

[spiral frost]

​Use the properties of exponents and matching bases to solve the following equations.

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[spiral frost]

I need some help with a...

I dont understand what thw question is asking

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[lusty atlas]

Hello

[lusty atlas]

Im a little confused

so my final answer was C(t)=(120+t)^25

that was incorrect

im thinking maybe C(t)=(120+t)25​ / 120^25?

[pale perch]

where did your answers come from

[lusty atlas]

so at first I separated variables and integrated which I think your supposed to do

differential equation = dC/dt = 625 /3000 + 25t

Ill skip some cause its a lot I wrote

I end up with ln |C| = 25ln |120 + t| + K

then to skip a couple of steps I get e^K (120 + t)^25

determine K using the initial condition...

hmmm actually going through that

I put 0 as the initial condition

but its just t

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[thin vale]

This is a practice exam

Since this problem leaves a as an arbitrary field element

Would proving it is not injective suffice to show that for say like a=0

then we can have like

f(x)=x, g(x)=x^2

phi_0(f(x)) = phi_0(g(x))=0

but x != x^2

or do we have to make an argument for arbitrary a

[meager oriole]

you can give a counter example

[thin vale]

I think I just saw the more general argument

phi_a(x-a)=0

and phi_a(0)=0

since x-a != 0

then it isn't injective

Would that also work?

[meager oriole]

how did you reduce that phi_a(x-a)=0

[thin vale]

because phi_a ( f(x))=f(a)

and for f(x)=x-a

f(a)=a-a=0

[meager oriole]

yeah

that works i think

i was being dumb

[random solstice]

That works

[thin vale]

Okay cool

thank you

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[thin vale]

!occupied

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[heavy oar]

can someone help me with this integral?

[twin meteor]

𖤍

[heavy oar]

yeah but whien i. get du it fucks everything u[

[pale perch]

how so

du=0.5e^t (e^t-3)^(-1/2) dt

dt=2/e^t * (e^t-3)^(1/2) du

[viscid lodge]

Did you try u = e^t - 3?

[heavy oar]

shitttt im stupid

its just u * 2u

sry guys

mbmbmb

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[split oyster]

Can someone help w this

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@split oyster Has your question been resolved?

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@split oyster Has your question been resolved?

[split oyster]

smh nvm

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[fresh fulcrum]

Given a board of size n x n. The main diagonal of the board is n squares located on a diagonal from top left to bottom right. There are an infinite number of L-triominoes that can be rotated The board will be covered with L triominoes so that no two tiles overlap and no tiles on the main diagonal are covered by L triominoes. Determine all possible values ​​of n>= 2 to fill the board. Each L triomino has 3 squares, and the number of squares that must be filled is n^2 - n

• the picture is one of the 8x8 board example and you only can tilling the white square

[fresh fulcrum]

Help

<@&286206848099549185>

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[half owl]

i need help with one of them, then i can do the rest

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@half owl Has your question been resolved?

[half owl]

<@&286206848099549185>

[polar hinge]

Shall I help with part a?

[half owl]

go ahead

[polar hinge]

Can you continue with part b if I go through with part a?

Ok

[half owl]

yes

[polar hinge]

So, lets take a look at the price of the car in part a. The car, without any discount at all is $35,000

Now, we know that the deposit paid which is $7000 is a a percentage of the overall cost. I hope that makes sense.

We want to know what percentage of the car we have paid already. Think of the deposit as a step towards paying for the overall $35000

So the question we want to answer here is: what percentage of $35000 is equal to $7000

Does that make sense?

[half owl]

20%

[polar hinge]

Yeah, ace. Nice work

So, now the question tells you that the rest of the amount to be paid gets a discount

So we have $35000 - $7000 left to be paid

[half owl]

so 28000 gets discounted

by 1/10 of 20

so 2%

[polar hinge]

We want to discount that by a tenth of the 20%

so the rest is discounted by 2%

[half owl]

that means 28000 x 0.98

[polar hinge]

Exactly, nice work

[half owl]

and then the asnwer is 27440

so is that correct

[polar hinge]

(35000-7000)*0.98

Is that what you did ⬆️ ?

[half owl]

yes

[polar hinge]

Great, youve got it

[half owl]

i thought so

[polar hinge]

27440 is what you should have

Nice work

Hope thats sorted

[half owl]

but the answers in the book have a different answer'

let me send a photo of the answers

[polar hinge]

Ok thank you

[half owl]

so i got confused

and asked for help

[polar hinge]

Give me a minute

[half owl]

could the answers be wrong?

[polar hinge]

I will have a look over this

[half owl]

ok

[polar hinge]

They could be, It might be a mistake

If this is an assignment or for school, you could ask your professor, sometimes the books have mistakes

But nevertheless, I will still check it again

Hang on

[half owl]

yeah, my teacher told me that sometimes they put wrong answers ro see if kids cheat and copy from the answers

that was with my old textbook tho

we recently changed

[polar hinge]

haha - thats also true

Ok i am pretty sure your book is wrong

This is because of the following:

A deposit is always an amount to be paid up front

This is an easy calculation right? Literally the total cost - deposit

[half owl]

yeah

[polar hinge]

The answer in the book is greater than (35000-7000)

So how could this ever be correct?

[half owl]

exactly

[polar hinge]

So I think ask your professor

But you are right

You did the right method and everything

Perhaps its a trick lol

Yeah - you did the right method dw 🙂

[half owl]

ok

thanks

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[rancid iron]

I have got
30x+30y+20z=1300
40x+20y+30z=1700
20x+30y+50=1650

I don't know where I should go from ther

There

[unreal pelican]

Can you solve for x in the first equation?

[rancid iron]

I'm pretty sure I need to solve for any value in any equation

And then i substitute back in

[unreal pelican]

Yes, one start would be to solve for x in the first equation and then use that value in the second equation

[rancid iron]

But to solve for x I need to get rid of y and z

[jagged cargo]

its a three variable simul equation

[unreal pelican]

Just get x on one side and y and z on the other side

[rancid iron]

Yeah

[jagged cargo]

solve for z in terms of x and y

sub that into the remaining 2 equations

[rancid iron]

How do I do that?

[jagged cargo]

you now got a 2 var simul equation

[unreal pelican]

In 30x+30y+20=1300, how do you get x on one side?

[jagged cargo]

pretend x and y are constant, solve for z in the first equation

[rancid iron]

So 1?

[jagged cargo]

he prolly meant 20z

[rancid iron]

Yeah 20z

[unreal pelican]

Oh, good point. You solve for either x or z first, it'll be the same procedure

[rancid iron]

By constant do you mean make it 1

So 30x= 1250?

[unreal pelican]

Well, not quite.

One sec

[rancid iron]

Because when I learnt this a while ago I would multiply equations and then add or take away to get rid of a value

[unreal pelican]

30x + 30y + 20z = 1300 pretend y and z are constants.... try to get this in the form x = something

That also works

[rancid iron]

What do you mean by constants

I'm not the brightest book on the shelf

[jagged cargo]

immutable values

like pi or e

[rancid iron]

I'm just getting more confused icl

[unreal pelican]

Like if you subtract the 3rd equation from the 1st, you eliminate y

[jagged cargo]

you probably also meant 50z

[unreal pelican]

OK, 30x + 30y + 20z = 1300, subtract 30 y from both sides

[rancid iron]

Yes

[rancid iron]

30x + 20=1300- 30y??

[unreal pelican]

Yes... .now subtract 20z from both sides

[rancid iron]

then it's 30x=1300 - 30y -20 z

[unreal pelican]

Now divide both sides by 30

[rancid iron]

X = 43.33 - y -z

[unreal pelican]

That doesn't quite seem right. Also, leave 1300/30 as a fraction. Are you sure -20z/30 is z?

[rancid iron]

Shit your right it's 20

X= 1300/30 - y - 2/3 z

[unreal pelican]

So if you've got x = 1300/30 - y - (20/30)z, you've solved for x, because you've got x by itself on one side

Now, use that value of x in the second equation

[rancid iron]

But how can I use an equation that still has y and z

[unreal pelican]

We'll solve for y next, and then we'll have just zs in the third equation

[rancid iron]

But if I do the same for y will I not just have the same but negatives for X and z

[unreal pelican]

Remember, you've already solved for x, so there won't be any x's in the second equation

[rancid iron]

We don't do it that way

We were taught to substitute the value you find back into the equation

[unreal pelican]

You mean, to check your answer?

[rancid iron]

I dunno that's just how we do it

[unreal pelican]

OK, there's more than one way to solve linear equations. If I'm doing it in a different way, I'll let someone else help since I don't know the way you do it.

[rancid iron]

Need to solve for a value and substitute that value back into an equation to get the other values

I have got
30x+30y+20z=1300
40x+20y+30z=1700
20x+30y+50z=1650

<@&286206848099549185>

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@rancid iron Has your question been resolved?

[true cliff]

ill mog u

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[stark radish]

I didn't get what to do after this

[stark radish]

<@&286206848099549185>

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[summer stone]

can i just delete ln and ln and get as result y = x+cosx+c ?

[jagged cargo]

no lmao

[summer stone]

why

[scenic ravine]

if you express C as ln(K) you could

[jagged cargo]

its lnx + cosx + C, not ln(x + cosx + C)

[summer stone]

this guy shows it here

so if it was lny = lnx i could write y = x ?

but if there is extra stuff i cannot?

[jagged cargo]

still no since theres the cosx

[summer stone]

okay thanks

[summer stone]

no need to be smartass

while having an anime pfp

[jagged cargo]

i wasnt?

[hybrid flicker]

the only thing you can do to simplify is maybe write y = Kxe^(cosx)

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@summer stone Has your question been resolved?

[vast shale]

you may simplify it to
$$ y = k x e^{\cos x} $$

but thats all

where k = ln c

[hybrid flicker]

no that's not how exponential works

[twin meteor]

just panic

[hybrid flicker]

yeah that's what's written here

[vast shale]

mein nahi padha 💀

,align
y = e^{\ln x + \cos x + c} \
y = e^{\ln x + \cos x + \ln k} \
y = e^{\ln x} e^{\cos x} e^{\ln k} \
y = x e^{\cos x} k \
y = kxe^{\cos x}

[twin meteor]

just panic

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[distant girder]

had a question about the definition of a dual map in axler's book:

is a dual map always defined in conjunction with a specific instance phi? or does it refer to all possible phis

[silk comet]

T’ is a map from the dual space of W to the dual space of V, and the elements of the dual space are linear functionals

So phi is a placeholder for any element of the dual space of W

[distant girder]

ok gotcha

tyty

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[gentle lantern]

Hii, I'm stuck at (x+8)^2 and I really want a solution or anything

This is tangent secant power thereom

i know the formula and how it works but the x+8 really boggles my mind, i really dont know how to do it

[outer warren]

do you know what it means to square something?

[gentle lantern]

yeah i think? do i square the 8?

[outer warren]

no

what does it mean to square something?

(in general)

[gentle lantern]

to multiply it with the same number?

[outer warren]

to square something is to
multiply that thing by itself

applying that to (x+8)^2,
that will be (x+8)(x+8)
do you know how to expand that?

[gentle lantern]

no i dont know

[outer warren]

i'd recommend looking up the distributive property

[gentle lantern]

distributive property is a(b+c) goes to ab+ac right?

also i searched (x-8)^2 up and this thing appears, idk how it goes to x(x-8)-8(x-8)

[outer warren]

just treat one of those (x-8) as the "a"

[gentle lantern]

Wait, do I have to create another x-8? So it will be x-8(x-8)(x-8)?

[outer warren]

no

how would you expand
$$a(x-8)$$

[twin meteor]

ℝαμΩℕωⅤ

[gentle lantern]

It becomes ax-8a?

[outer warren]

yes

and what happens to
$$\red{a}x - 8\red{a}$$
when $\red{a} = (x-8)$

[twin meteor]

ℝαμΩℕωⅤ

[gentle lantern]

(x-8)x-8(x-8)?

[outer warren]

just the result after replacement/substitution

yes

which is what they have

its the result of distributing directly, (introduction of "a" wasn't needed)

$\underbrace{\blue{(x-8)}}{\text{this}}(\red{x}-\green{8}) = \red{x}\underbrace{\blue{(x-8)}}{\text{this}} - \green{8}\underbrace{\blue{(x-8)}}_{\text{this}}$

[twin meteor]

ℝαμΩℕωⅤ

[gentle lantern]

So the blue one is a and the red is b and green is c?

[outer warren]

yes

essentially multiply the component outside to each term inside

[gentle lantern]

So it becomes like this?

[outer warren]

yes

[gentle lantern]

Now I'm done with x-8, it should look like this now right?

I'm now more confused on how to solve it

[outer warren]

ideally you'd want everything to one side

instead of subtracting 64 from both sides
subtract 324 from both sides

have you solve quadratic equations before?

[gentle lantern]

Can the AC method work?

Cuz I forgot how to do quadratic equations

[vast shale]

do the (a-b) whole square method

a^2 + b^2 - 2ab

@gentle lantern

[gentle lantern]

Uhhh I don't know what to put on a or b

[outer warren]

ac method will work for factorisation
but its even simpler than that here since a=1

\textbf{Factoring monic quadratics:}\
Consider: \
$$\begin{aligned}
(x+m)(x+n) &= x^2 + mx +nx +mn \
&= x^2 + \underbrace{(m+n)}_b x + \underbrace{mn}_c \end{aligned}$$
finding the pair of values $m,n$ that: \
multiply to $c = mn$ and \
sum to $b = m+n$ \
gives the factorisation: $(x+m)(x+n)$

[twin meteor]

ℝαμΩℕωⅤ

[outer warren]

identifying the pair of values here allows you to jump to the end result directly

[spiral mist]

Need help with this

Reached Till here

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[chilly pawn]

,, \lim_{x \to \pm\infty} \left( \sqrt{x^2 - 2x + 3} - x \right)

[twin meteor]

レナト (renato , ping if reply)

[chilly pawn]

,align
\lim_{x \to \pm\infty} (\sqrt{x^2 - 2x +3} - x) \
&= \lim_{x \to \pm\infty} \left(\sqrt{x^2 - 2x +3} - x\right) \times \frac{\sqrt{x^2 - 2x +3} + x}{\sqrt{x^2 - 2x +3} + x} \
&= \lim_{x \to \pm\infty} \frac{(\sqrt{x^2 - 2x +3} - x)(\sqrt{x^2 - 2x +3} + x)}{\sqrt{x^2 - 2x +3} + x} \
&= \lim_{x \to \pm\infty} \frac{x^2 - 2x + 3 - x^2}{\sqrt{x^2 - 2x +3} + x} \
&= \lim_{x \to \pm\infty} \frac{-2x+3}{\sqrt{x^2 - 2x +3} + x}

[twin meteor]

レナト (renato , ping if reply)

[chilly pawn]

,w limit of x to -inf for sqrt(x^2 -2x + 3) - x

[twin meteor]

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[chilly pawn]

,w limit of x to +inf for sqrt(x^2 -2x + 3) - x

[twin meteor]

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[vocal sleet]

@chilly pawn Has your question been resolved?

[surreal basin]

,align\lim_{x\to-\infty}(\sqrt{x^2-2x+3}-x)&=\lim_{x\to-\infty}x\qty(\frac{\sqrt{x^2-2x+3}}x-1)\
\text{assuming $x<0$, }&x=-\sqrt{x^2}\
&=\lim_{x\to-\infty}x\qty(\frac{\sqrt{x^2-2x+3}}{-\sqrt{x^2}}-1)\
&=\lim_{x\to-\infty}x\qty(-\sqrt{1-\frac2x+\frac3{x^2}}-1)\
&=-\infty\cdot(-\sqrt{1-0+0}-1)\
&=\infty\
\lim_{x\to\infty}(\sqrt{x^2-2x+3}-x)&=\lim_{x\to\infty}\frac{-2x+3}{\sqrt{x^2-2x+3}+x}\
&=\lim_{x\to\infty}\frac{x\qty(-2+\frac3x)}{x\qty(\sqrt{1-\frac2x+\frac3{x^2}}+1)}\
&=\lim_{x\to\infty}\frac{-2+\frac3x}{\sqrt{1-\frac2x+\frac3{x^2}}+1}\
&=\frac{-2+0}{\sqrt{1-0+0}+1}\
&=-1

[twin meteor]

mtt07734

[surreal basin]

@chilly pawn because the -∞ version doesn't go to a number, you can take a shorter route
in all, you might be missing that √(x^2) = |x| and that both limits could require different methods to solve

[vocal sleet]

@chilly pawn Has your question been resolved?

[chilly pawn]

one question

but what is this part assuming x < 0, x = -sqrt(x^2)

oh but x is negative during x approaches -inf so makes sense

the part I still dont understand is why do you

x = -sqrt(x^2)

[flat whale]

When x is negative, what does sqrt(x^2) equal in terms of x?

[surreal basin]

√((-5)^2) = √25 = 5

√(x^2) is -x when x is negative

,,|x|=\begin{cases}x&\text{if }x\ge0\-x&\text{if }x<0\end{cases}

[twin meteor]

mtt07734

[surreal basin]

take a closer look at all of this

[chilly pawn]

i understand this and this is correct

[chilly pawn]

this is incorrect in my opinion

in which case does |x| equals -x?

[chilly pawn]

-x

i’m getting confused

ok I see the -sqrt(x^2) since x approaches negative infinity makes sense

[flat whale]

The answer to my question is -x

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[royal helm]

hoho

[stiff blaze]

What do you need help with?

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[lethal bough]

any help would be appreicated

[lethal bough]

dunno what to do here

basically all we know is that each of them

cant be formed via a lin comb of the otehrs

so is the answer that you end up with yet a new set of 3 unique vecs?

[sly sierra]

try writing a linear combination of v1,v2,v3, set it equal to zero, and show the coefficients have to be zero?

[lethal bough]

hmmm.

will do

what does that do though?

[sly sierra]

what's the definition of linear independence?

[lethal bough]

show the null space is {0}?

uhhhh

[sly sierra]

null space of what?

[lethal bough]

null space of the subspace made by the span of v1 v2 v3?

[sly sierra]

subspaces don't have null spaces
linear maps have null spaces

what linear map do you have in mind?

[lethal bough]

not sure what linear map means, my prof doesnt use that term

oh wait so since the def of linear independence is that the only linear combination of the vectors that = 0 is the trivials olution

okay nvm. i see

thx

!close

.close (thanks again bungo)

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[heady slate]

What is the sum of the values of x that satisfy the equation (x - 2) ^ x^2 + 7x + 12 =1? I need some help understanding this

[patent urchin]

Solve for all values of X, and add up the values.

[heady slate]

how

could x = 3

nvm

i got it

close channel

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.close

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[molten egret]

im a bit lost on how to solve this using substitution.

[molten egret]

wrong one, my bad

[hoary cypress]

add both

write x interms of y

use that in any one of the eqns

[molten egret]

but how would i make for example the second equation be y= or x=

something along the lines of this

[hoary cypress]

hhow did u get this

[molten egret]

this is given in the question

its a diffferent question

im just showing it as a example

[hoary cypress]

oh

yea now u substitue ths y value n the other eqn

[molten egret]

ah i see

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[latent void]

\

[latent void]

i get too

3(x-4)/x+3

but thats wrong

cuz ha=2

so idk

[vocal sleet]

@latent void Has your question been resolved?

[hexed needle]

you're incredibly close

what is the HA of what you wrote, do you know?

[latent void]

ha =3

sadly its supposed to be 2

[hexed needle]

yes...

[latent void]

so would it be 2/3

[hexed needle]

so what if you change the 3 to a 2?

[latent void]

on the bottom

u cant do that

because that changes the y int

i got the 3

by

a(x-4)/x+3=-4

[hexed needle]

oh I was mistaken, i see what you mean

[latent void]

all good no worries

im not sure if is typo or something maybe

[hexed needle]

okay, well i have an idea then

eh maybe not, it could be a typo. but I'm sure this is possible

[latent void]

alright

[hexed needle]

as long as you did your Algebra right, this seems correct

yeah, bc anything else you introduce to the numerator or denominator will give you a different y intercept

[latent void]

yea

thanks for the reassurance i thouight i was going crazy lmfao

[hexed needle]

my only other thought is maybe you could have higher powers

like have (x-4)^2 and (x+3)^2

that could work out, I'd try it

[latent void]

alright

[latent void]

ths would ruin the va tho

i think its a typo

all my friends think so as wel

thanks for ur help tho

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[unique sluice]

im not sure how to di thus

[unique sluice]

im thinking a or d

[inner osprey]

are you familiar with the idea of "separable differential equations"

[mighty nacelle]

you dont even need that

[inner osprey]

ig valid

[mighty nacelle]

just plug in (x,y) = (2,-4)

this is a poorly made multiple choice question

[unique sluice]

thats it?

[inner osprey]

well there's two answer choices that satisfy the constraint (x, y) = (2, -4)

i mean you can reason which one is right but 🤷‍♂️

[mighty nacelle]

right, i just checked to make sure of that too

[inner osprey]

it's more reliable to just know how to do the problem

[unique sluice]

i was thinking a or d beacusse the anti derivatives of the differntial equation is one of those

[mighty nacelle]

agreed

[unique sluice]

im not sure how to know if its 28 or -4

[inner osprey]

that's where the initial condition comes in

[unique sluice]

and no i do not knwo what that is

[inner osprey]

right

is this a problem from school then?

[unique sluice]

yes

[inner osprey]

in other words, do you know what methods you are expected to use to solve this problem?

[unique sluice]

uh

no

antideriative?

i did that

[inner osprey]

the whole "plugging in derivative" and "checking initial value" method works i guess but if the problem wasn't multiple choice you would have issues

[urban edge]

can you show your work?

[unique sluice]

sure but i was just wondering how to figure out if it is 28 or -4

[inner osprey]

.

[mighty nacelle]

plug in (x,y)=(2,-4)

[inner osprey]

to solve an initial value problem, you make use of the constraint the problem gives you

in this case, f(2) = -4

[unique sluice]

it doesent make sense tho, becasue isnt the equation we just solve for the anti derivative but we are pluggin in the normal f function (2,-4)

.close

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[feral sentinel]

how to get m and d?

[feral sentinel]

first of all, i don't know if Null(A) is the number of free variables in the general solution

or something else

if Null(A) = set of free variables (or free variable in parametric form), then I'm confused. I thought column space is R^2, which means at least 2 columns are not free variables (have pivots).

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@feral sentinel Has your question been resolved?

[feral sentinel]

whatever

.close

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[sonic gale]

where to start?

[flat whale]

plot the first one for x in [0, 1]

[sonic gale]

yeah ive got that

[flat whale]

then you've started

[sonic gale]

whats next

i dont understand the 2nd and 3rd conditions

[flat whale]

f(-x) = f(x)

plug in a few known values of x until you get the pattern

[sonic gale]

right so it reflected on the y axis

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[queen wadi]

Hi, I want to find focii and directrices of (x-1)(y-2) = 2

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[waxen hawk]

I have been asked to prove that angle A is equals to angle 1.

[jagged cargo]

its cyclic quadrilateral

so A + C = 180

[waxen hawk]

Can someone check my work, also the grammar and usage of words

[jagged cargo]

guess what else + C also 180?

[jagged cargo]

angle 1 and angle BCD are supplementary angles

[waxen hawk]

^

[jagged cargo]

complement is 90, supplement is 180

[waxen hawk]

I didn’t know that

Let me check on the definition of these words

[vast shale]

you know abt cyclic quad?

[waxen hawk]

Except the misuse of words, I suppose the proof is fine?

[jagged cargo]

yes

[vast shale]

of course

[waxen hawk]

So I mixed up these two words, supplement and complement.

What are the similar expression for “mix up” but in noun form?

SOS

[jagged cargo]

confusion?

[waxen hawk]

That’s a little bit different in connotation, I suppose?

Emm

I think confusion is fine

[hushed pewter]

Confusion is perfectly fine.

Or even just "mixed up"

[waxen hawk]

How do I use it to express that I had mixed up these words supplement and complement

I made a confusion between the words supplement and complement.

[hushed pewter]

This is the ideal way to say it

Or "there was some confusion over my understating of these words"

[waxen hawk]

People commit confusion when being asked to distinguish between supplement and complement.

Can I commit confusion.

[waxen hawk]

I see

[hushed pewter]

People confuse the definitions of these words

[waxen hawk]

I see

[hushed pewter]

But, "mix up" would be slightly better

[waxen hawk]

Yes, as it is more specific

[hushed pewter]

Either is fine though

People would understand what you are saying

[waxen hawk]

I see now thank you so much!

.close

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[indigo warren]

Can somebody explain why 6y + 9 not = to 15y
but (y+3)^2?

[indigo warren]

This might sound stupid. But I really want to know..

[hushed pewter]

Sorry. What?

[indigo warren]

um what?..

[hushed pewter]

Where are you getting all this from?

[indigo warren]

im trying to write an equation in standard form for the circle

[hushed pewter]

What circle?

!xy

[vocal sleet]

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

[indigo warren]

wait i lost the thing

[indigo warren]

( x − h )^2 + ( y − k )^2 = r^2

x^2 + y^2 +6y = -24. I have to turn it into standard form for the circle

[jolly lava]

you sure it is -24 on RHS?

[hushed pewter]

Ohh. Ok

[indigo warren]

Sorry.. what is RHS?.

[jolly lava]

right hand side

right side of =

[indigo warren]

oh

in the sheet yes

or..

that's like

what chatgpt said..

I ask for some explanation but he just keep repeating the thing

so I think asking real people might help

[jolly lava]

wdym chatgpt said it?

Are there original question you want to solve?

[indigo warren]

this

[indigo warren]

I finished it but I just dont understand.

I want to understand not just like know the solution

[jolly lava]

for why 6y+9 is not 15y is

because there is no y multiplied to 9

9 is not similar terms with 6y

[indigo warren]

oh okay

[flint escarp]

.close

bruh

[indigo warren]

wait

[jolly lava]

any more questions?

[indigo warren]

wait lemme

analyse what you said first

[jolly lava]

take your time

[indigo warren]

ty

[indigo warren]

so what's the reason for like 6y + (6/2)^2?

yea 9 comes from (6/2)^2

[jolly lava]

to make $(y-k)^2$ part

[twin meteor]

Dri111

[jolly lava]

in standard form of circle

[indigo warren]

wait if im not mistaken.. is it like (y^2 + 6y +9)?

[jolly lava]

yes it is

[indigo warren]

so how did the 6y gone?

[jolly lava]

$(y^2+6y+9)=(y+3)^2$

[twin meteor]

Dri111

[jolly lava]

you get this?

[indigo warren]

i dont

[jolly lava]

do you know $(a+b)^2=a^2+2ab+b^2$?

[twin meteor]

Dri111

[indigo warren]

oh yes

[jolly lava]

a=y and b=3 in your situation

[indigo warren]

If I close this channel will all this gone?

[jolly lava]

you can still see

but not will be able to ask

otherwise make new help channel

[indigo warren]

Okay, thank you so much.

.close

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[jolly lava]

!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 was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

[clear cipher]

hmm, so according to the answer

it becomes this

i highlighted the only part i understood

but the rest i've got not a clue

[vast shale]

you understood that you divide the numerator and the denominator by cos²x?

[clear cipher]

uhh nope, why do we have to do that

[jolly lava]

to say the intention would be by doing that it becomes easier to integrate

[clear cipher]

i see

[jolly lava]

Also as question told you to use substitution t=tanx, answer is trying to make tanx

[clear cipher]

then how come sec^2x becomes 1?

[clear cipher]

yeah

[jolly lava]

substitution of t=tanx

[clear cipher]

how does this make sec^2x 1?

[jolly lava]

t=tanx so dt/dx=sec^2(1)

so sec^2x and dx altogether becomes dt

do you know how to integrate by substitution?

[clear cipher]

ohh yeah

[clear cipher]

yep

but sometimes the differentiation part is confusing for me

[jolly lava]

so problem solved then?

or do you have more questions?

[clear cipher]

hmm

yep

understood it

thank you!

.close

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[hardy cargo]

did i do it right?

i am curious because the question says "prove why it must converge" while the series diverges (according to my solution).

oh sh i see where i am wrong

.close

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[late orbit]

to write the number 20 as a sum of two positive terms, so that the sum of the cube of one term and the square of the other term is minimal

[jolly lava]

so $a^2+b^2=20$

nvm

[late orbit]

.close

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[vast shale]

crossposted in groups-rings-fields:

[vast shale]

Let $R$ be a commutative ring. Let $I$ and $J$ be ideals of $R$ and let $\mathfrak{p} \in \text{Spec}(R)$ with $I \cap J \subset \mathfrak{p}$. Prove that either $I$ or $J$ is contained in $\mathfrak{p}$.
\begin{proof}
Let $i \in I$ and $j \in J$. Then $ij \in I$ and $ij \in J$, i.e. $ij \in I \cap J \subset \mathfrak{p}$. Therefore $i \in \mathfrak{p}$ or $j \in \mathfrak{p}$. Hence $I \subset \mathfrak{p}$ or $J \subset \mathfrak{p}$.
\end{proof}

[twin meteor]

gian

[vast shale]

where p is a prime ideal

not sure if my proof is fine

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@vast shale Has your question been resolved?

[hard atlas]

well right now some i of I could be in p and some j in J could be in p

but nothing says that all of I or all of J is in p

[vast shale]

thank you, this discussion is continued in groups-rings-fields

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[half summit]

I need help with factoring this.

[livid horizon]

Are you familiar with the expansion of (a-b)³?

[wide sundial]

well it's conveniently (x-3)^3

[half summit]

yeah but how..

[hoary cypress]

a more general way to solve it would be to try and guess a root

and then factorize the quadratic

[finite hatch]

thats not how u got dat thats just working backwards

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[arctic gazelle]

help

[arctic gazelle]

x^2 -8x +16

factorise

pls

[scenic ravine]

!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 was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

[arctic gazelle]

1

[scenic ravine]

heard of the quadratic formula?

[arctic gazelle]

no

(x-4)^2

but I dont understand where the 16 goes

[scenic ravine]

yeah, that works better

use the formula for $(x-y)^2$

[twin meteor]

Why am. I here

[arctic gazelle]

yeah but what happens with the 16

[scenic ravine]

$(x-4)^2= x^2-8x+16$

[twin meteor]

Why am. I here

[arctic gazelle]

4^2 = 16 yes

and xx = x2

but now where does the 8x come from

[elfin surge]

(x-y)^2 = x^2+y^2+2ab and you have x^2-8x+16 you could do some comparision here

@arctic gazelle

or try splitting the middle term 8x

[grim oasis]

distribute properly:

$(x-4)(x-4) $

$= (x-4)x - (x-4)4$

$= x^2 - 4x - (4x - 16)$

$= x^2 - 4x - 4x + 16$

[vast shale]

i know texit is hard to master

[twin meteor]

CosmoVibe

[grim oasis]

i just dont know how to do newlines here

i can do newlines in latex fine lol

[vast shale]

same, Im also used to latex

[vast shale]

This is crazy

[vast shale]

Why?

Not in a bad way

It’s just cool

Oh

Never seen it distributed like that

New way to visualize FOIL ig

this is also $(x-4)^2$

[twin meteor]

EinPest

[vast shale]

Yup

You can expand more easily if you know $(a-b)^2=$a^2-2ab+b^2

[twin meteor]

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

[grim oasis]

i generally dislike this approach if someone already doesnt know it

because they wont understand why the 2ab is there

deriving it from first principles gives them more intuition

[vast shale]

Oh, if he doesn't know it then thats fine

true

[grim oasis]

also the geometry method also works

https://2.bp.blogspot.com/_PnLYRqe0k9g/S0nZrwyLyCI/AAAAAAAAAQ8/PUoKC5qRbR8/s320/binomial-squared.png

if they dont get why 2ab is there, they will continue to forget its there

[vast shale]

Yeah

I mean this must help a beginner to start off

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[neon jay]

I got pi(6x-x^2)^2dx

as the integral

but it says its not correct

I got all the other parts of the question correct

just went wrong on setting up the integral apparently

I need a little help with that

not sure where I went wrong

V = integral of pi*[f(x)]^2 dx

<@&286206848099549185>

[grizzled swift]

Damn bro that’s crazy

[neon jay]

😭

[grizzled swift]

What’s the question my n word

[neon jay]

what about this is wrong

its just asking to setup the integral

[grizzled swift]

Is it definite or indefinite

Oh

Hm

I’m unable to understand the question

Mb bro

[neon jay]

all g

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@neon jay Has your question been resolved?

[neon jay]

<@&286206848099549185>

I’ve already pinged but I’ve been unable to get help

[river kettle]

Hi, I think I can help you here

Although I haven’t done this in a bit so I might be rusty

You should try drawing a diagram first, it helps @neon jay

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[shy token]

I need assistance with this shape

[civic drift]

Looks like a really bad cursor

[sharp lynx]

need assistance with doing what

[shy token]

Working out what shape it is

[sharp lynx]

[sharp lynx]

is there a list of shape names you've been given?

because I can think of a few names for this shape (correct or otherwise)

[shy token]

no

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[viscid root]

What i dont understand is how 5 1/16 is 81/16....

As i know that if its to the power of 1/4 it'll be quad root

[tight sonnet]

5 1/16 means 5+1/16=5*16/16 +1/16 = 80/16+1/16=81/16

[viscid root]

oh my god im such an idiot man

I didnt realize it was mixed fraction

Thank youuu

[tight sonnet]

np

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[deep python]

Hi

Can someone explain where I went wrong here

The actual answer is 2+2ln(2/3)

Im p sure I've made a mistake in the 3rd line

[pale perch]

your integration is wrong

this

[deep python]

Isn't the integral of 1/x --> ln(x) + c

[pale perch]

you dont have 1/x though

[deep python]

Ooooh

Bruh in my mind u thought I'll use substitution again but I neglected doing the du thing

Alr thanks man

❤️

[pale perch]

try u^2=x-1 maybe

[deep python]

Yes I should have done that

That's what the solution does

But I didn't think of that

Anyway thanks

[pale perch]

nw

[deep python]

,close

.close

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[lavish ridge]

How can I solve this?

[dawn kestrel]

If I remember correctly

Long division

And then the remainder will be some function of x

And then that is your equation for the slant asymptote

[toxic lion]

you are correct its long division

[lavish ridge]

I don't understand this part

[dawn kestrel]

When you do long division you will get some remainder

That remainder is the slant asymptote

[lavish ridge]

Finally, where do I put that value?

[dawn kestrel]

Wdym that value

Start by doing long division and see where it leads you

[toxic lion]

Nothing. Here, watch this video

https://www.youtube.com/watch?app=desktop&v=--vh9zgZZmQ

Explains it well

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[vast shale]

but how is this a question

[left kraken]

It's not, they're advertising

not sure who to message about this though

!done

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If you are done with this channel, please mark your problem as solved by typing .close

[left kraken]

.close

:/

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[eternal glacier]

How are these all wrong exactly?

I thought “elementary” means one row operation difference? Am I supposed to only do that row operation on A and B identity matrix?

[hard atlas]

you arent supposed to do anything to A

read the question again

[misty belfry]

you are finding the product of E and A not E

[eternal glacier]

Ahh OK

Would these look correct? Mainly question d

Also, when multiplying E with A, elementary ALWAYS comes first?

I’m getting the same answers only when I put E on the left side, not the right side, and doing matrix multiplication in that order

[flat whale]

left = row, right = column

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

[eternal glacier]

Oh I see

Ty

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[fallen sand]

.

[fallen sand]

is my solution correct?

[silk hollow]

yes

@fallen sand