help-49

[midnight plank]

@quartz sage Has your question been resolved?

[quartz sage]

<@&286206848099549185>, if you'd be so inclined to help me with this problem I encountered?

Question is that I got a triple integral to solve. One of the data I got is xyz = 0. Can I use it as a bottom limiter?

[midnight plank]

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[midnight plank]

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[deep kraken]

really quick question as i cant understand, what can sin(a+b-90) turn into?

[frail burrow]

Let's say x = a + b

So you have sin(x - 90)

Can you tell me how to simplify that?

First remember that sin(90 - x) = sin(x), that's a well known identity

[deep kraken]

um

so cos(-x)?

cuz like i can do cos(-(90-x))

no?

[frail burrow]

Oh i mean cos

Mb

[frail burrow]

Yup

Go on

[deep kraken]

uhhhhh

so like

cos(-x) = -cos(x)?

[frail burrow]

sin(x - 90) = sin(-(90 - x))

No

[deep kraken]

im not sure tho

[frail burrow]

cos(x) is even

[frail burrow]

Continue from here

You have sin(-something)

How would you simplify that

[deep kraken]

i dont remember those identities

they are the only ones i dont rememvber

ummm

hold on

is it -sin(x)?

so like -sin(90-x)?

[frail burrow]

If you are comfortable with the unit circle, you can always draw it and think geometrically

[deep kraken]

and then thats -cos(x)?

[frail burrow]

That is right

Yes

[deep kraken]

ohhhhh yeah thats a good idea

so then what is cos(a+b-90)

cos(-(90-a-b)) = cos(90 -a - b) = sin(a + b)?

is that correct?

[frail burrow]

We said a + b = x

Plug it back in

[deep kraken]

oh so

ok

um

[frail burrow]

There is really no reason to consider the quantity a + b as a sum

It isn't relevant

[deep kraken]

cos(x-90) = cos(-(90-x)) =cos(90-x) = sin(x)?

[frail burrow]

Original question was sin(x - 90)

not cos(x - 90)

[deep kraken]

yes but i meant like another thing

i realized i also need it

sorry

but is that correct for cos(x-90)

[frail burrow]

Yes

[deep kraken]

alr ty

[midnight plank]

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[inner jetty]

why is the zero(s) the numerator?

[fallow scarab]

0/anything= 0

[inner jetty]

makes sense... so if there's a quadtric equation on top it would have more than one 0?

[fallow scarab]

It could yes

[inner jetty]

ok cool

if i had to graph this where x = 7 that means one of the asymptote line crosses through there right? @fallow scarab

[inner jetty]

how would i graph this with the info i have in thie picture?

[fallow scarab]

https://youtu.be/E1fCj5um8_c?si=zS8kSwngCBSvaoX6

[inner jetty]

great video

[inner jetty]

so my question is just leaving out the y-intercept then?

[fallow scarab]

Only your teacher knows what to expect

[inner jetty]

no imean the quetion i posted

[fallow scarab]

If they did examples in class, copy it

Yes I know

"Sketch" is vague

[inner jetty]

i knoow i just wana make sure i understand that y-intercept is not asked for in it correct?

[fallow scarab]

Only your teacher knows that

[inner jetty]

yah

ohh ok

.close

[midnight plank]

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[inner jetty]

.reopen

[midnight plank]

✅

[inner jetty]

.close

[midnight plank]

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[midnight plank]

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[rough monolith]

yo

[rough monolith]

i have had a very long day at school with gcse mocks with lots of every sience and 10 hours of school and my head isnt working can u help me

[jagged saffron]

what does the sine rule say?

[rough monolith]

opposite over hypotonose ?

idk how to spell

[blissful trench]

yes

[rough monolith]

so sin(8/40)?

but i dont have the hypoto

[blissful trench]

you forgot the theta

[rough monolith]

theta?

[blissful trench]

ye

[rough monolith]

whats that

[blissful trench]

look at the image ive sent you

[rough monolith]

tan

[blissful trench]

yep

but since the question asking you to find the x using sine rule I think they mean sine law?

[rough monolith]

hmm maybe

[blissful trench]

,, \frac{\sin(56)}{x}=\frac{sin(40)}{8}

[grand pond]

アキラ (>_<)

[blissful trench]

solve for x

[rough monolith]

0.09

rounded to 1dp

[blissful trench]

you don't need to round it

unless if the question asking you to do it

[rough monolith]

in the thingy it said 2

ye

[blissful trench]

oh yea i see

good job

[rough monolith]

eh it said it was wrong

should it be sin-()

[blissful trench]

i was about to say that lol

,w calc \frac{\sin(56)}{x}=\frac{sin(40)}{8}

[grand pond]

Results provided by WolframAlpha

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

Requested by kensukeken

[blissful trench]

[rough monolith]

tf

[blissful trench]

lmao

are you allowed to use a calculator

[rough monolith]

yep

[blissful trench]

it should gives you the answer

[rough monolith]

but i did it with sin- and the calc said no

[blissful trench]

you finding the length of x so you need inverse of sine

inverse of sine is only used when finding an angle

[rough monolith]

right

but it wasnt 0.09

unless

[blissful trench]

are you sure it's 0.09? cuz i havent checked

[rough monolith]

oh no you should check

ithink it is

0.08715574275 rounded to 1dp it 0.09 or 0.1

[blissful trench]

first you do sin of 56 then multiple by 8 then divide by sin 56

sine 40*

[rough monolith]

this is like learning chinees AHGHHGHGH

[blissful trench]

no its not lol

can i see how you actually got 0.09?

you need to check your calculations again

[rough monolith]

ok sin(40/8)

[blissful trench]

no not like that

[rough monolith]

what should i put in my calc

[blissful trench]

pretty much you need to apply the sine of law rules

[blissful trench]

start putting sin 56 first

tell me what do you get

[rough monolith]

.

[blissful trench]

yeah im showing how to find the number

do you know how to calculate this in general?

[rough monolith]

i got o.8290

i mean i thought i did

[blissful trench]

nice now multiple by 8

what do you get

[rough monolith]

6.632...

[blissful trench]

divide by sin 40

[rough monolith]

10.31

dam so ok

umm

[blissful trench]

can this be rounded?

[rough monolith]

can we go through 1 more together

[blissful trench]

sure

[rough monolith]

10.3

[blissful trench]

10.3 what

you forgot smth

:D

[rough monolith]

for 1dp ?

[blissful trench]

no

just say its 10.3 cm

[blissful trench]

same thing for this

[rough monolith]

oh ye on the answer box it has it

so sin 115

then times 15

then divide by smthing

[blissful trench]

create the equation first

think about this

[rough monolith]

sin(x) * y / ?

[blissful trench]

no

[rough monolith]

o

[craggy phoenix]

opposite/hypotenuse

[blissful trench]

do you know how sine law works in general?

[craggy phoenix]

sohcahtoa

[blissful trench]

we are using the sine law

.-.

[rough monolith]

this thing

[craggy phoenix]

oops

[rough monolith]

xd

[craggy phoenix]

sin a/a=sin b/b=sin c/c

a=BC etc

[blissful trench]

yep

[craggy phoenix]

yeah this

[rough monolith]

right

i find it hard to find what one to pick if its not with a right angle tri

[craggy phoenix]

just write the equation

[blissful trench]

you can pick the ones that works best for you

[craggy phoenix]

and plug in the values you have

[blissful trench]

but don't pick the unknown ones

[rough monolith]

so i have the opposite

[blissful trench]

,, \frac{\sin (115)}{15}=\frac{\sin(28)}{y}

[grand pond]

アキラ (>_<)

[blissful trench]

solve for y

[rough monolith]

28/115?

lol i feel like your loosing all hope

im a lost cause at this point

[blissful trench]

fine lets use sohcahtoa then

[rough monolith]

k

[blissful trench]

so you have sin(28)=y/15

[rough monolith]

yes

[blissful trench]

what did you get?

[rough monolith]

whats y

28?

[blissful trench]

the length of y

[rough monolith]

ah 15

[blissful trench]

^^

are you in 10th class btw?

[rough monolith]

hmm/

year 10/

?

[blissful trench]

ah i see

[rough monolith]

im yr 11

[blissful trench]

then you should learned sine of laws no?

or whatever it was

[rough monolith]

ye but its been a long day

[blissful trench]

about?

[rough monolith]

just school work

[blissful trench]

have you tried watching any yt vids for this

[rough monolith]

not yet

wait i show u smthing

[blissful trench]

ok you should watch then

go for it

[blissful trench]

see told you use sine of laws

excatly what i was doing

[rough monolith]

i never see those in my life on sohcatoa

on;y

[blissful trench]

you learn sine of laws after sohcahtoa

and then cosine of laws

https://cdn.discordapp.com/emojis/1048660781123780749.gif?v=1&size=48&quality=lossless

[rough monolith]

f me

[blissful trench]

this might help

[rough monolith]

tell me the answer and i can see and work back

i learn better like that smthimes

[blissful trench]

we don't give out answers but we can help you learn how to get the answer

[blissful trench]

so start with this

[rough monolith]

shoot me. so sin(115/15) =

[blissful trench]

nope

[rough monolith]

man u gonna be 90 before i get this

[blissful trench]

90 what?

[rough monolith]

90 yrs old lol

[blissful trench]

lmao

[blissful trench]

like i am saying just apply the rule here and already gave you first step

this how sine of laws works

[rough monolith]

アキラ (>_<)

oops

[blissful trench]

if you still don't get it just watch something like vid

here's some examples of it

https://www.mathcentre.ac.uk/resources/Engineering maths first aid kit/latexsource and diagrams/4_6.pdf

[rough monolith]

hmmh i will tmrw

i cant now im fighting to keep my eyes open

[blissful trench]

lol okay

[rough monolith]

is it like a law in this discord u cant give answers

[blissful trench]

!noans I mean its like this

[midnight plank]

The purpose of this server is to help you learn, not to hand out answers. Do not ask someone to give you the answer directly.

[rough monolith]

right

[blissful trench]

!nosols and this

[midnight plank]

As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.

[blissful trench]

you are good now? or still need help?

[rough monolith]

hehe

help

[blissful trench]

I gave you the first step here

did you get how did I get that?

[rough monolith]

nope

[blissful trench]

right here

[rough monolith]

hold on

[blissful trench]

if you understand the rule here then this should be easier for you

[rough monolith]

im getting there

just sit tight

is it 7.8

ok im going now thanks you for your time

if you see this

merci アキラ

[blissful trench]

no worries

happy to help

!done

[midnight plank]

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

[rough monolith]

😍

.Close

. close

[blissful trench]

.close

[rough monolith]

.close

[midnight plank]

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[hazy parrot]

i need to show that ylogy - xlogx <= (y-x)(1+logy) with y > x > 0

I set f(x) = xlogx and f'(x) = 1 + logx

so ylogy - xlogx <= (y-x)(1+logy) is f(y) - f(x) <= (y-x)f'(y)

which is equivalent to: (f(y) - f(x))/(y-x) <= f'(y)

If x -> y then (f(y) - f(x))/(y-x) = f'(y) but idk what to do next...

[harsh marten]

wats the base of log

[hazy parrot]

i suppose it's the natural log

so e

could also say ln

[harsh marten]

but this inequality isnt true

for y = 6 and x = 2

[hazy parrot]

huh?

[harsh marten]

check these values

[hazy parrot]

i made a typo...

i wrote the inequality wrong

[harsh marten]

how should it look

[hazy parrot]

ylogy - xlogx <= (y-x)(1+logy)

now it should be true

[bronze raven]

you can bring this inequality to form log(y/x) <= y/x - 1

and it's equivalent to e^c >= c + 1 for c > 1

[hazy parrot]

and what's with 0 < c <= 1 ?

[bronze raven]

you required y > x > 0 so y/x > 1

[hazy parrot]

ok yeah

i agree with you but it's an exercise about derivatives 😅 (ik i didnt precised it) so i want to make it with derivatives

[midnight plank]

@hazy parrot Has your question been resolved?

[midnight plank]

@hazy parrot Has your question been resolved?

[midnight plank]

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[bleak galleon]

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[bleak galleon]

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[last slate]

division would work i think

[bleak galleon]

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[last slate]

set up a fraction

[bleak galleon]

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[midnight plank]

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[jovial abyss]

How do I do that

[jovial abyss]

Question 7 I’m confused on

Also I’m not sure if I rotated my reflected image 90 degrees counterclockwise

Correctly

[grand falcon]

(-y, x)

so just use that formula with ur original coordinates to find the 90 degree cc points

[grand falcon]

and for number 7

grab one point and count it 7 units to the right

and after that make it go up once

[grand falcon]

btw when u make a new image make sure to make it with the prime symbol

[jovial abyss]

These are the points I’m being asked to rotate 90 degrees counterclockwise

[jovial abyss]

Prime symbol?

[grand falcon]

like the original is named G but the new one will be named G'

' is prime

the more ' it has, means its been copied once more

[jovial abyss]

Oh I see

[grand falcon]

alright, i helped you out a bit i gtg though see ya

[jovial abyss]

Alr thanks

Can someone help?

I changed them from (x,y) to (-y,x) for the 90 degrees counterclockwise. But I don’t think these points will go into quadrant III

These were the original points before I made them (-y,x)

<@&286206848099549185>

[midnight plank]

@jovial abyss Has your question been resolved?

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[pearl idol]

.close

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[sturdy flower]

I've started the process behind the problem, I was just hoping to see how I would format the integral after finding U and du, and if I even chose the right things for u and du?

[twilit field]

!show

[midnight plank]

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

[sturdy flower]

Sorry, forgot to send it- I'm just wondering if I bring the 1/2 out and then put du over the sin(u)

[fallow scarab]

Yea that's fine

[sturdy flower]

Then would I take the integral of 1/sin(u)?

Oh wait

this can change into csc

What's the antiderivative of csc?

[twilit field]

ln(cosec(x)-cot(x))

[sturdy flower]

Is that an identity I should have memorized?

If it is then, that's just on me

My bad

[fallow scarab]

https://www.cuemath.com/calculus/integral-of-cosec-x/

[sturdy flower]

Thank you!

I'm doing a review rn for a quiz tomorrow, so I'll definitely have more questions, buuut I'll do what the rules say and just send it in another channel when I do

Thanks again!

.close

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[sturdy flower]

.reopen

[midnight plank]

✅

[sturdy flower]

Haha, okay, yeah, this ones, odd to me too

I chose 4x+2 as my u

[twilit field]

wait, don't

[sturdy flower]

Would I choose x^2+x instead?

Or, just x^2?

[twilit field]

factorise 2 out of the numerator first

[sturdy flower]

Oh.

[twilit field]

then take x^2+x as u

[sturdy flower]

would it turn out to be 1/2du= x+1 dx?

because du=2x+1

[twilit field]

du=2x+1 , yes. That;s what you'd get if you factorise 2 out of the numerator

[sturdy flower]

I see my mistake now

When I factorized, I wrote 4x into just x

Rather than 2x

would it be 2du/u?

[twilit field]

yup

[sturdy flower]

I now have 2 integral du/u

I'm gonna separate the du and u

Ah, now I see

1/u turns into ln

ln u i mean

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[round palm]

hi, maybe a dumb question but if i need a matrix to denote a "vertical stretch/shrink by a factor of c"

[round palm]

,, \begin{pmatrix}1&0\ :0&c\end{pmatrix}

[grand pond]

kanna

[round palm]

then only this suffices right?

i don't have to consider the 1/c case?

[fallow scarab]

Yea as long as you say c>0

Well depends what your vector convention is

[round palm]

but isn't squeezing 1/c though?

[fallow scarab]

if c > 1 yes

[fallow scarab]

But also this

[round palm]

(1 x 2)?

idk if that's what you meant

it's (x y) * that matrix

[fallow scarab]

Oh

[round palm]

not the conventional T(x) = A * x

[fallow scarab]

Yea that convention

Yea just wrote down a couple equations for 0<c<1 and 1<c and compare the initial line with the resulting one from matrix multiplication

[round palm]

so the question had to specify the interval for c?

since it just says "by a factor of c"

[fallow scarab]

What question

[fallow scarab]

,tex .transformation rules

[grand pond]

riemann

[fallow scarab]

Yea just this

[round palm]

oh lol it always maps to (x,y) -> (x,cy)

[round palm]

i don't get what you mean here

[fallow scarab]

You could specify stretch is for some values of c and compression is for another set of values

[fallow scarab]

Yes just like your matrix

[round palm]

oh no i mean it was an actual question i saw somewhere

and not me actually trying to find a matrix that does that

so was just curious

[round palm]

right okay, thanks

.close

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[pine kernel]

i simply just dont get where to start

[twilit jetty]

this is 5 + 5 * 10 + 5 * 10^2 + 5 * 10^3 + 5 * 10^4 + ... + 5 * 10^(n-1), right

[pine kernel]

what does that mean

i thought you use the Sn formular

[fallow scarab]

Yea that's the same thing

You said you didn't know where to start so they were giving you a start

But if you have a formula use it

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[midnight plank]

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[calm atlas]

.close

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[chrome hill]

int (1-3x)/(3+2x ) dx

[worthy wing]

What did you tried?

[chrome hill]

Frational derivative?

Seperate derivative

[worthy wing]

And what fractions did u get

[chrome hill]

I didn't get actually

I took minus common

[worthy wing]

Ok good idea and what do u think it’s next

There is a way to make the fractions easier to find

[chrome hill]

I don't know what i am doing 😆

Not sure about why rationals??

[worthy wing]

I see xd

Look at your integral after u take negative out

[last slate]

Just take partial fractions and then solve, you'll get the answer in ln(...)

[tribal temple]

This isn't partial fractions but polynomial division

[last slate]

I mean 1/(3+2x) -3x/(3+2x) and then solve

It shld make it easy right

[worthy wing]

If you are gonna do that, you better using 2x+3 first

Usub

[last slate]

But I got the answer

[tribal temple]

not any easier than just dividing (which was done correctly!)

[last slate]

Yeah that's crct too

[chrome hill]

I am confused at writing it

[worthy wing]

Show your writing first

What do you think it is

[chrome hill]

I got it

[tribal temple]

Basically, what you've written tells you that
[
\frac{3x - 1}{3 + 2x} = \frac32 - \frac{11/2}{3 + 2x}
]

[grand pond]

@tribal temple

[chrome hill]

Wait lemme show

Yes

I got it now

I was missing denominator

[worthy wing]

Cool

[chrome hill]

I got the answer in 3rd step

Both of you thanks 😀

[tribal temple]

One thing to comment is that you should put it as $\log\abs{3 + 2x}$ - reason being to allow you to put in values where $3 + 2x$ is negative as well

[grand pond]

@tribal temple

[tribal temple]

The original function is defined for all values except when 3 + 2x = 0 after all

[chrome hill]

Log property

Thanks

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[wet escarp]

im bottom set

help would be nice

[brittle shoal]

The sum of all sides of a quadrilateral is 360°

Use it to find angle A

[slender walrus]

sum of angles, not sides

[midnight plank]

@wet escarp Has your question been resolved?

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[chrome hill]

7^-1 mod 9

[chrome hill]

How to start this?

[visual tiger]

general method : use euclid's extended algorithm to find a bezout couple for (9,7)

[chrome hill]

9=7+2

7=2×3+1

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[midnight plank]

Please don't occupy multiple help channels.

[barren trench]

help

[dense latch]

What have you tried so far?

[barren trench]

plugged z for w

[dense latch]

can you transform $\frac{1}{1+i}$ into $a+bi$ form?

[grand pond]

Dri111

[barren trench]

i dont know how to

[dense latch]

you can do it by multiplying conjugate of denominator into both denominator&numerator

[barren trench]

ohhh

wait let me try

[small rapids]

is this right 💀

[dense latch]

where does denominator goes

[small rapids]

just skipped it

[dense latch]

and $i\ne\frac{1+i^2}{1+i}$

[grand pond]

Dri111

[dense latch]

RHS is just 0 as numerator becomes 0

[barren trench]

got this

is this correct

?

[dense latch]

yes

[barren trench]

but whats the exact value

[dense latch]

make it as a+bi form

[barren trench]

how

[dense latch]

$\frac{1-i}{2}=\frac{1}{2}+\frac{-1}{2}i$

[grand pond]

Dri111

[dense latch]

distributing denominator

[barren trench]

so

[chrome hill]

1/1+i + i
(1+1+i)/(1+i)

[barren trench]

this is the exact value?

[dense latch]

so this is $\frac{1}{1+i}$

[grand pond]

Dri111

[dense latch]

and $\omega=\frac{1}{1+i}+i$

[grand pond]

Dri111

[dense latch]

so finally you can make $\omega$ into a+bi form

[grand pond]

Dri111

[barren trench]

im so lost

.close

[midnight plank]

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[barren trench]

.reopen

[midnight plank]

✅

[dense latch]

are you ok with $\frac{1}{z}=\frac{1}{1+i}=\frac{1}{2}+\frac{-1}{2}i$?

[grand pond]

Dri111

[barren trench]

yea

[dense latch]

and $\omega=\frac{1}{z}+i$ right?

[grand pond]

Dri111

[barren trench]

yes

[dense latch]

therefore $\omega=\frac{1}{z}+i=\frac{1}{2}+\frac{-1}{2}i+i=\frac{1}{2}+\frac{1}{2}i$

[grand pond]

Dri111

[barren trench]

yes

how do we change into a+bi

[dense latch]

a=1/2 and b=1/2

[barren trench]

ohhhh

Thank u so much

[dense latch]

solved now?

[barren trench]

solved

thank u so much

[dense latch]

np

[barren trench]

one last question

so far i distributed

the two

idk what to do doe

[dense latch]

the idea is to make LHS into a+bi and compare it to RHS

[barren trench]

right

[dense latch]

you are making LHS into a+bi form, where a and b is real number

[barren trench]

right

[dense latch]

in other word you are separating real part and imaginary part

[barren trench]

right

[dense latch]

can you give it a try?

[barren trench]

the left side?

[dense latch]

yes

[barren trench]

like this?

[dense latch]

yes!!

[barren trench]

then?

[dense latch]

Then use the fact that real part of LHS is same of it on RHS, and vise versa on imaginary part

[barren trench]

okok wait

this?

[dense latch]

only real part on both side

[barren trench]

ohh

?

[dense latch]

nice

[barren trench]

then what

make it equal to

p or q

and substitue?

[dense latch]

yep

[barren trench]

then answer it?

[dense latch]

Sorry I found mistake here

[barren trench]

where

[dense latch]

while binding real part

you wrote 2p+q as 2(p+q)

[barren trench]

oh woops

how would it be

[dense latch]

(2p+q)

so just (2p+q)=5 and (2q+p)=1

[barren trench]

got it

[dense latch]

solved?

[barren trench]

thank u so much again

.close

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[simple terrace]

Is this question even sane? We know nothing about a_n other than the fact that it’s infinitesimal and bounded

[simple terrace]

a_n isn’t even all guaranteed to have the same sign, so leibniz test is out of question, absolute convergence seems to be the only hope, but I can only show that |a_n| * b_n is infinitesimal

[midnight plank]

@simple terrace Has your question been resolved?

[runic hamlet]

in questions like this I would first start with some examples a_n of very easy obviously convergent sequences and see what happens with those

there is a nice candidate to choose here

[simple terrace]

Hm, but how does that help? Things that hold for trivial sequences don’t always hold for non-trivial ones. a_n = 1/n^2 comes to mind, or a_n = 0 is another very trivial one

[runic hamlet]

a_n=0 is a good one

what about 1/n^3 instead of 1/n^2

wait

fuck me I made a stupid mistake

[midnight plank]

@simple terrace Has your question been resolved?

[midnight plank]

@simple terrace Has your question been resolved?

[midnight plank]

@simple terrace Has your question been resolved?

[midnight plank]

@simple terrace Has your question been resolved?

[frail burrow]

i can't image how this doesn't converge, but i haven't been able to prove it

[west iron]

find bounds on the sizes of a and b and then use comparison

look at "eventual sizes", so exists N such that for all n>N we have ...

[midnight plank]

@simple terrace Has your question been resolved?

[simple terrace]

For b, sure. But what could even bound a? Eventually it will be in a neighbourhood of 0 and that's all I can say from what's given

[simple terrace]

Mh, again. I did not really have trouble bounding b_n. But don't we also need a bound on a_n if you are heading towards using the comparison theorem?

[honest kelp]

I'd study the modules of the product, that is product of the modules

we also know that a_n --> 0

[simple terrace]

Module as in the absolute value?

[honest kelp]

yes it is

[simple terrace]

This is so far the only thing I have about a_n

a_n * b_n also -> 0 so it's not not convergent outright 😄

[honest kelp]

how about this:

[simple terrace]

Oh, hm that might work actually

[lusty hearth]

hi guys

[midnight plank]

@simple terrace Has your question been resolved?

[midnight plank]

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[thick shoal]

why cant we assume that since x^2 grows more rapidly than 5x that the 5x becomes irrelevant here?

[nova yoke]

and conclude what?

[thick shoal]

to get x - x

= 0

[nova yoke]

nope, sadly that won't work

[thick shoal]

ik it is 5/2

[nova yoke]

turns out that 5x matters

[thick shoal]

but idk why its different from this:

where you can

to get 2x

[nova yoke]

aren't these identical

[slender walrus]

• instead of -

[nova yoke]

oh thx

[slender walrus]

you don't have an indet form there

[nova yoke]

that's just gonna go to infinity

[slender walrus]

5x doesn't grow as fast, but its still relevant

[thick shoal]

you multiply top and bottom by this to get the answer

it becomes (5x - 3)/this lim

which is 2x

and the -3 becomes irrelevant so it jsut becomes

5x/(2x)

or 5/2

[nova yoke]

yea, the num behaves like 5x and the denom like 2x

which shows you why the 5x matters!

[thick shoal]

i just dont know why it works for adding but not subtracting

[nova yoke]

well you can make it a bit more formal by dividing num and denom by x

then you get:

$$\frac{5}{\sqrt{1 + 5/x} + \sqrt{1 - 3/x^2}}$$

now it's no longer indeterminate

now use the fact that sqrt is continuous and the usual limit laws to conclude that the denom goes to 1 + 1 = 2

[thick shoal]

oh wait ive realized

[grand pond]

Bungo

[nova yoke]

just fixed a typo btw

[thick shoal]

lol you get 0 multiplied by infinity

[nova yoke]

where

[thick shoal]

yeah now i get why you cant do that for subtraction

[nova yoke]

yea, there's just not really a comparable manipulation you can do with the difference

that's why converting it to a sum like this is useful

[thick shoal]

factoring out an x which is how the irrelevancy works lol

you get the x that was factored and 1 - 1 which is 0

[nova yoke]

yep

but x -> infty

still indeterminate

[thick shoal]

yeah now ik why it doesnt work lol

thanks

[nova yoke]

sure, cheers

[thick shoal]

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[inner pilot]

i tried solving this but i doesn't want to be solve can i get some help

[civic moth]

Which one

[inner pilot]

the third one with A-(B-C)=A-(BUC)

[civic moth]

I suggest you a trick to solve, draw vein diagram of problem and then analyze, you will definitely get the idea to solve

[inner pilot]

i did it in my mind and its right but the way to get to it with writing is pretty hard

[civic moth]

Y u r right

Lemme solve

[midnight plank]

@inner pilot Has your question been resolved?

[civic moth]

Here
x€ A and (B-C)
x€ A and x€ (B Or C)
From here u will get 3 cases
Compere that to make rhs

[inner pilot]

okthx a loooot

.close

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[floral plank]

Sup, does anybody know the answers to these? I did a little bit of solving but i think the answers may be wrong

[floral plank]

More clearer pic

[summer remnant]

Is it given to be a parallelogram?

[last slate]

Opposite angles in a parallelogram are equal so you have to set up an equation

[floral plank]

Opposite angles are congruent

And also supplementary

[last slate]

for the opposite angles

[floral plank]

Basically its the properties of the parallelograms

Im more confused on how to get the y part and why there are 3 given x's

[last slate]

Have you found x yet?

[floral plank]

I did find the values of x

If 3x+11 and 5x-1 then 85/4

If 5x-1 and 4x-3 then 184/9

[last slate]

Those angles aren’t opposite

[floral plank]

What i did was used the supplementary thereom and basically did 3x+11+5x-1=180

And did the same to 5x-1 and 4x-3

Should i instead do 3x+11 and 7y+5?

I tried to find the value of x by doing 5x-1+4x-3=180 then what i got was x=184/9
Then used that value to my 3x+11+7y+5=180 equation (3(184/9)+11+7y+5=180)

Man im so bad at explaining

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[sturdy plank]

Why would 1/2 r^2 theta be used here if the formula for integration with polar curves is 1/2 r^2 dtheta

[sturdy plank]

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[stable dawn]

$4m^5 + 4m^4 - 9m^3 - 11m^2 + m + 3 = 0$

[stable dawn]

How do I solve this

[slender walrus]

approach with rational root theorem

there seems to be one rational solution
and the other solutions are ugly

[stable dawn]

I got -1

Then I did synthetic division

[slender walrus]

,w 4m^5 + 4m^4 - 9m^3 - 11m^2 + m + 2 when m=-1

[grand pond]

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[slender walrus]

-1 isn't a solution

[stable dawn]

That's weird

,w 4m^5 + 4m^4 - 9m^3 - 11m^2 + m + 2 when m=1

[grand pond]

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[stable dawn]

,w 4m^5 + 4m^4 - 9m^3 - 11m^2 + m + 2 = 0

[grand pond]

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[stable dawn]

Ahh

Its 3

My bad

[grand pond]

ColdTee

[stable dawn]

,w 4m^5 + 4m^4 - 9m^3 - 11m^2 + m + 3 when m=-1

[grand pond]

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[stable dawn]

Is this right till here

[slender walrus]

yeh

[stable dawn]

Now what do I do?

[slender walrus]

repeat

rat root again

[stable dawn]

I check for other values and found 1/2 was a root

So I just keep doing this?

[slender walrus]

yeh

though depending on your ability to recognise things

[stable dawn]

,w 4m^5 + 4m^4 - 9m^3 - 11m^2 + m + 3 = 0

[slender walrus]

factorsation by grouping is viable here

[grand pond]

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[stable dawn]

Why only 3 roots

[slender walrus]

repeated roots probably

[stable dawn]

How do I know which one

[slender walrus]

the factorisation will tell you

[stable dawn]

I see so I just gotta

Keep doing rat theorem

[stable dawn]

I didn't pay much attention to it 🥲

I'll try that out too i guess

[slender walrus]

note that 4m^4 - 9m^2 is a difference of two squares

[stable dawn]

Ohhhh

Yeah

[slender walrus]

m^2 ca also be factored out of that first

[stable dawn]

m^2(2m+3)(2m-3) - (2m-3)

(1+m)(2m-3)(2m^3+3m^2-1)

[midnight plank]

@stable dawn Has your question been resolved?

[stable dawn]

,w 2m^3 + 3m^2 - 1

[grand pond]

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[stable dawn]

,w 2m^2 + m - 1

[grand pond]

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[stable dawn]

(1+m)(1+m)(1+m)(2m-3)(m-1/2)

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[chrome hill]

-3 to 3 integration x^2/(1+3^x) dx

[hearty rune]

is it really a 3^x, ew

[orchid vault]

$\int_{-a}^a f(x) \dd x = \int_0^a \pl f(x) + f(-x) \pr \dd x$

[grand pond]

! What the hell am I doing here?

[orchid vault]

Use this@chrome hill

[chrome hill]

is this called kings property?

[orchid vault]

I don't know a property called that.

But thf, I do not know names of any properties.

Might wanna Google that.

[left pagoda]

That's a different thing

[chrome hill]

this made this problem too easy

i got x^2

[olive matrix]

you should get a number

[orchid vault]

[marsh agate]

😭

[chrome hill]

x^3/3= 9

thanks

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[stiff escarp]

quick question on proofs

[stiff escarp]

Is proof by contradiction the same and proof by negation

relating to "If P then Q terms"

<@&286206848099549185>

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[plush prism]

hey

[plush prism]

ah nvm

.close

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[eternal idol]

Prove that if φ is a contradictory formula, then for any formulas ψ1,...,ψn the formula: φ ⇒ ψ1 ⇒...⇒ ψn is a tautology.

[eternal idol]

I have already answer to(image) that but i don't understand it. Why can you put brackets in place where they weren't in the command?

[midnight plank]

@eternal idol Has your question been resolved?

[eternal idol]

<@&286206848099549185>

can someone help pls <@&286206848099549185>

[midnight plank]

@eternal idol Has your question been resolved?

[midnight plank]

@eternal idol Has your question been resolved?

[midnight plank]

@eternal idol Has your question been resolved?

[eternal idol]

.close

[midnight plank]

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[muted mica]

is a laplace probability space the same thing as a uniform distribution in a probability measure

[fallow scarab]

What is the definition of Laplace probability space

[muted mica]

P(A) = |A|/|Omega|

and for uniform distribution its 1/N right

in both cases, say a dice roll, both would have even probabilities for each outcome so 1/6 and 1/6

[fallow scarab]

Yes they're the same in the dice roll

[muted mica]

they can be different?

[fallow scarab]

Well you've only defined it for finite sample space |Omega| < infinity

Probability measure usually refers to continuous probabilities densities

[muted mica]

oh so LPPS can only take on countibly infinite sums and the uniform distribution infinite ones?

.close

[midnight plank]

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[humble lance]

can someone pls help me out here : How many permutations of {0, 1, 2, 3, 4, 5, 6} have no adjacent even digits? For example,
a permutation like 5034216 is not allowed because 4 and 2 are adjacent

[midnight plank]

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[onyx grove]

hello! I want to factor 6x^2−19x−10, i've tried brute forcing it and nothing really works, but symbolab gives this crazy answer which I don't think is correct. How to factor 6x^2−19x−10?

[fresh sparrow]

the answer is wrong

but

the actual one is not much prettier

just use the quadratic formula

[onyx grove]

alr

didnt learn that yet but will explore it next

thanks

!

.close

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[waxen willow]

6x^2 - 19x + 10 can be factored very nicely

Maybe you read the question wrong?

[midnight plank]

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[topaz pier]

please help me solve the table

[midnight plank]

Please don't occupy multiple help channels.

[daring cairn]

(f o g)(x) = f(g(x))

(f o g)(-8) = f(g(-8)) = f(1) = 10

[topaz pier]

i got that one already

i need help with the rest

[topaz pier]

can u please help with the rest

[daring cairn]

reminder: people are not here to answer questions for you

[topaz pier]

ok but can u help

[daring cairn]

I think you have enough info to work out the rest

[topaz pier]

well ive been stuck on this question for like an hour

so i could really use some help

[midnight plank]

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[pearl tulip]

how do you factor this

[pearl tulip]

because i have a similar problem

6x^2 - 13x - 63

[waxen willow]

You find two numbers that add to $-19$ and multiply to $6\times 10$

[grand pond]

casework

[pearl tulip]

oh

OH YEAHHHHH

OMG

WAIT

HOLY COOK

ok wai tnvm

it doesnt work for my problem

[waxen willow]

Here it looks like $-15$ and $-4$ satisfy it

[grand pond]

casework

[pearl tulip]

thats coiio

i sitll dont kno whow to do

$6x^2 - 13x - 63$

[grand pond]

probablycrashing

[pearl tulip]

do i split 6?

or what

[waxen willow]

I mean you have to find 2 numbers that multiply to $-63 \times 6$ and add to $-13$

[grand pond]

casework

[pearl tulip]

two numbers that mulitply to -378

and add to -13

....\

is that even posible

OH WAIT

no

this is imposible!

[waxen willow]

14 and -27

[pearl tulip]

what the hell how

[waxen willow]

,calc 14 *-27

[grand pond]

Result:

-378

[waxen willow]

,calc 14 - 27

[grand pond]

Result:

-13

[waxen willow]

Its pretty dumb question if you ask me

[pearl tulip]

yeah it is very stuped

holy cook

[waxen willow]

Who would try every combination just to find that

(I used a calculator btw)

[pearl tulip]

okay so then what do i have

all good

so

14 and -27

nowwhat

[waxen willow]

Now you factor by grouping

[pearl tulip]

wat

da

fook

[waxen willow]

$6x^2 - 27x + 14x - 63$

[grand pond]

casework

[pearl tulip]

OHH YEAHH\

BRO

UR A GENIUS

TJEN I SPLIT THE TWO EQUATIONS

FACTOR OUT x FROM THE FIRST ONE

FACTOR OUT 7 FROM THE SEOND

DUDE

UR A GENIUS

so now

$x(6x-27) 7(2x - 9)

whoops

$x(6x-27) 7(2x - 9)$

[grand pond]

probablycrashing

[pearl tulip]

@waxen willow

and i make the original equation equal to that one