help-0

[brisk lynx]

Lol

[noble sinew]

Post a full question if you want help

[empty ivy]

Ok

[lone heart]

@brisk lynx Has your question been resolved?

[brisk lynx]

What is the answer to 3x+1

Is it not -.333

[noble sinew]

3x+1 isn’t a question

You mean solve for x in an equation don’t you?

So you are missing an equal sign don’t you think?

[echo socket]

State your question in a clear manner

[lone heart]

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[true drum]

hey

[true drum]

i really need help

Binomial distribution

i do not understand this lesson at all

[viscid echo]

.reopen

[true drum]

?

[lone heart]

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[lone heart]

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[sick phoenix]

I don’t know where to start

[severe sluice]

a should be easy with a lil' bit of trig

why am i seeing so many simple trig questions today (checked 5 channels, all are trig)

find XO and OY

[sick phoenix]

Where do I find the other length tho

[severe sluice]

which other length?

[sick phoenix]

Cause if I want to use trigo to find x, wouldn’t I need 2 lengths

[severe sluice]

yes, but which other length do you want to find? (name the segment)

[sick phoenix]

XP

The one between x and p

[severe sluice]

what's x and p?

surely you dont mean the points?

right?

[sick phoenix]

Yes 😭😭😭

[severe sluice]

okay, well, you need to find the angle marked x in your figure (i'll just call it theta to avoid confusing it with point X.)

can you associate theta with a right triangle?

[sick phoenix]

Yea

[severe sluice]

which right triangle will you associate theta with?

[sick phoenix]

Wait I just realised

Can I just do this

[severe sluice]

....do what?

[sick phoenix]

I found the other side

To do trigo

Got 5 and 13

I figured out how to solve it thanks

.close

[lone heart]

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[worldly ether]

I am having doubt rn, isn't the sum of the sequence 4(3^n-2 - 1)/3-1 instead of 3^n-1?

[wanton junco]

there are n-1 terms in that expression

[gray isle]

there are n - 2 + 1 terms in the summation

[worldly ether]

Where did the additional term came from?

[wanton junco]

• 1

[gray isle]

consider 3 = 3^1

from 3^1 to 3^(n-2) there are n-2 terms

and 1 = 3^0 is another term

[worldly ether]

Ah wait I see it now, thanks a lot @wanton junco @gray isle

Thanks a lot once again :3

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[pallid sail]

.close

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[alpine sable]

i need help

[alpine sable]

105 = 5x + 2x - 3x + 5

[echo socket]

What have you tried so far

[alpine sable]

5x + 2x - 3x + 5 = 9

9/105

[polar barn]

whats 9. 9?

i am pretty confused, @alpine sable

[polar barn]

this is equal to 105

[polar barn]

and this one is 9

[alpine sable]

nvm

.close

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[alpine sable]

'someone help me

[wary stream]

More context

You just sent a picture of a triangle

[alpine sable]

How big are the angles in the triangle

[wary stream]

Hint: sum of angles in a triangle equals to 180

[alpine sable]

i know

[wary stream]

Then apply it

That's a big hint to solve the problem

[alpine sable]

i just dont understand

[wary stream]

Sum of angles in a triangle equals 180

[alpine sable]

yes

i dont understand how to solve it

[wary stream]

So then sum up the angles, in the triangle

[gray isle]

start by setting up an equation that represents
the sum of the three angles in that triangle is 180°

[wary stream]

And then sum of angles in a triangle, equals 180

[alpine sable]

if you know the answer then say it i tried to solve this for an hour

[wary stream]

No, we're not here to tell you answers

[gray isle]

what exactly were you trying

start by setting up an equation that represents
the sum of the three angles in that triangle is 180°

were you able to at least do that

[alpine sable]

.close

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[wary stream]

Lol

[lone heart]

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[tidal iron]

I need help please !

[lean spire]

with what

[tidal iron]

In a catalog, a hi-fi system is offered on sale at €255 instead of €300. Calculator file
proposed reduction percentage and round up to the nearest unit.

[lean spire]

sorry

what's the question

I don't get what it's asking

[tidal iron]

I need you to do this exercise

[polar barn]

yes

and the question is

Calculator file
proposed reduction percentage and round up to the nearest unit?

[tidal iron]

proposed reduction percentage and round up to the nearest unit.

Yes

[lean spire]

where is the imperative

what are you supposed to do

[polar barn]

alright ill spend a few minutes to actually figure out what this question means

[tidal iron]

what this it

[lean spire]

an imperative is a command word like describe or eat or relate

[knotty spire]

maybe compute the percentage of the price reduction?

🤷

[polar barn]

i see

[tidal iron]

Calculate the proposed reduction percentage and round up to the nearest unit.

[knotty spire]

But I am mostly guessing

[polar barn]

basically this and round up the result

[polar barn]

learning math in a language that is different from english is extremely painful lol

[knotty spire]

Yeah, I know that feeling.

[polar barn]

haha

[polar barn]

i hope the percentage is 255/300 (of the original price minus the proposed reduction)

which is 85%

which mean the original price is reduced by 15%

[tidal iron]

okay and give me an explanation of how you did it

[polar barn]

well

suppose the original price is 100%

[tidal iron]

ok

[polar barn]

then the offered on sale price will be a% to the original price

and that a is equal to the $\frac{offered on sale price}{original price}$

i hope?

[ocean seal]

alephcomputer

[polar barn]

bad latex

😭

[tidal iron]

I dont understand help me aleph 😭

[polar barn]

lets say you have a cake

and you divide said cake into 10 equal parts

now that cake is 100% of a cake, right?

[tidal iron]

Ok

[polar barn]

so each part will be 100%/10 = 10%

suppose you eat 2 pieces of cake

now the cake is reduced by?

[tidal iron]

20

[polar barn]

20%

so the percentage of the cake after getting eaten is?

[tidal iron]

80

[polar barn]

yea

above is the same thing

probably

[tidal iron]

I understand that

But how do you find 15

[polar barn]

now the above is the same thing but instead of one cake

its 300$

and the sale reduced price is 255$

so the price that has been reduced is 45$

now, that 300$ is 100% right?

@tidal iron

[tidal iron]

yes

[polar barn]

so what do you think is 1%

[tidal iron]

Idk

[polar barn]

300$ is 100%

[tidal iron]

Ok

[polar barn]

so ?$ = 1%?

[tidal iron]

1

[polar barn]

nope

try dividing both side by 100

[tidal iron]

0,4,5

3

[polar barn]

yep

now that we have 3$ = 1%

so 45$ = ?%?

[tidal iron]

I dont know

[polar barn]

multiply by something to make that 3$ into 45$

and when you know how much that something is

multiply that with the right hand side as well

[tidal iron]

15x3

[polar barn]

yep!

now multiply 15 with the right hand side

and you get

[tidal iron]

675

[polar barn]

i mean you have that 3$ x 15 = 1% x 15 now

if you multiply the left hand side, you will have 15%

[tidal iron]

what this the left hand side

[polar barn]

45$

[tidal iron]

45x15?

[polar barn]

nope

now we have 45$ = 15% already

[tidal iron]

but how do you know its 15%

[polar barn]

thats answer this question

[polar barn]

ill write the full thing out

so its easier to understand

[tidal iron]

ok

[polar barn]

First : 300$ is 100%.
=> 300$ = 100%
so 300$ / 100 = 100% / 100
=> 3$ = 1%.

The reduced price is 255$. The price that got reduced is 300$ - 255$ = 45$.

since 3$ = 1% => 3$ x 15 = 1% x 15 => 45$ = 15%.

Hence the reduction is 15%.```

@tidal iron

[tidal iron]

why 3x15=1%?

this is 45%

@polar barn

[polar barn]

3$ x 15 = 1% x 15

[tidal iron]

675%

?

But I have to do what to get 15%

[alpine sable]

I assume they just asked what percentage price was reduced..

aleph explained it already but I am gonna try hoping u understand

Let price be denoted by x.
dx = $300 - $255
hence, difference in price = $300 - $255 = $45 
What percentage of 300 is 45? 
- 45/300 * 100/100 = 15/100 = 15%

[lone heart]

@tidal iron Has your question been resolved?

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[buoyant pebble]

hiiiii i need help with demonstration by recursion to this sum:
Sn = sum(1/n²)
demonstrate that Sn <= 2 - 1/n

[buoyant pebble]

i am stuck at last part for n + 1

[tacit arch]

you mean the induction step?

What have you bounded S_{n+1} by so far?

[buoyant pebble]

yes

S_{n+1} is equal to 1 + 1/4 + 1/9 .... + 1/n + 1/(n+1)

and in the hypothesis we have Sn <= 2 - 1/n

[pale kestrel]

ok, so add 1/n^2 to both sides for starters...

thats what you did right?

[buoyant pebble]

yyes

i think i have to find that S_{n+1} <= 2 - 1/(n+1)

[pale kestrel]

ok .... so what do u get after simplifying this

$$S_{n}+\frac1{1+n}=S_{n+1}\leq 2 - \frac1n + \frac1{1+n}$$

[ocean seal]

Shuri2060

[pale kestrel]

that's what you had right

[buoyant pebble]

wait no my bad

its 1/(n+1)²

[pale kestrel]

sure, didnt notice.

[buoyant pebble]

because Sn is the sum of Un = 1/n²

[pale kestrel]

$$S_{n}+\frac1{(1+n)^2}=S_{n+1}\leq 2 - \frac1{n} + \frac1{(1+n)^2}$$

What's the issue though

[buoyant pebble]

no square in the -1/n

[ocean seal]

Shuri2060

[buoyant pebble]

peeeerfect

[pale kestrel]

Yh ok. And does the result not come out after you simplify

[buoyant pebble]

yes

[pale kestrel]

?

[buoyant pebble]

so i started with the 1st step

for S1 <= 2 - 1/1

can i send a picture of the exercice ?

[pale kestrel]

Base case is trivial

[pale kestrel]

It's just this that's the problem

But I don't get what's the issue

Is it that the result doesn't come out after simplifying?

[buoyant pebble]

the issue is that i don't know what to do after simplifying

[pale kestrel]

I haven't done the question so I wouldn't know.

Show what the simplified result is then.

[buoyant pebble]

because i have to find that Sn+1 <= 2 - 1/n + 1

[pale kestrel]

If u dont show working we wont know where ur stuck

[buoyant pebble]

its in french that's why 😦

wait gimmi one sec i take a picture

am sorry for it might not be very clear and IN french

[lone heart]

@buoyant pebble Has your question been resolved?

[pale kestrel]

$$S_{n}+\frac1{(1+n)^2}=S_{n+1}\leq 2 - \frac1{n} + \frac1{(1+n)^2} = 2 - \frac{1 + n + n^2}{n(1+n)^2}$$

[lone heart]

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[ocean seal]

Shuri2060

[pale kestrel]

ur missing the important bit

which is this

???

And then you want to show the top of that fraction is greater than n+n^2

then ur done.

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[prisma prawn]

any help on this one

[prisma prawn]

Derivatives

[echo socket]

What have you tried

[prisma prawn]

solved

i solved it 😐

thanks for the help tho

what about this one @echo socket

[echo socket]

Just use the chain rule

[lone heart]

@prisma prawn Has your question been resolved?

[prisma prawn]

this is the answer i got

but the answer on my sheet is this

are these 2 the same thing ? and if they are how do i convert mine to this

@echo socket

[echo socket]

Do you know the quotient rule?

[lone heart]

@prisma prawn Has your question been resolved?

[prisma prawn]

yes

[echo socket]

Just use the quotient rule here

[weak oasis]

does anyone know how to not make small mistakes in math

like forgetting the signs?

i just got an 80 on the math test because of that

every single time i’m forgetting to keep the answer or some of the work negative from my work to the paper

[echo socket]

This help channel is occupied

[weak oasis]

oh my bad didn’t mean to send that here

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[gentle abyss]

What is it

Which one

<@&286206848099549185>

[glass lichen]

#❓how-to-get-help

dont ping right away.

[gentle abyss]

Sorry but

Which one is it

Really need help here

[barren glade]

what do u think

[wary stream]

Do you know how to complete the square?

[barren glade]

yes what he said

[wary stream]

Also, very much like a test

[barren glade]

yeah is this a test?

[gentle abyss]

No

[barren glade]

do u know how to complete the square?

[gentle abyss]

Nope

Just want the answer

[barren glade]

well help channels don't work that way man

i suggest watching this

and coming back to your question

https://www.youtube.com/watch?v=9_2DYOfHxyk&t=991s

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[ocean seal]

sweetgrass160

[buoyant kayak]

just do partial fractions like normal

note that the denominator is factorable

oo yknow that's a solid point

LMAO

try swallowing your pride and doing long division then friend :)

If your question has not been answered for a minimum of 15 minutes, you may use the @Helpers tag once. Do not abuse this ping.

[wary stream]

You should apply long division

[buoyant kayak]

but they don't wanna

[lone heart]

@wide forum Has your question been resolved?

[little drum]

Just do long division lol

The smarter way is just using long division in your brains as you write out the factors but that just comes with practice lol

[buoyant kayak]

no but you see

they don't wanna

[sly mantle]

@wide forum cut it out

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@wide forum Has your question been resolved?

[lone heart]

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[hollow flare]

someone plz explain

[lone heart]

@hollow flare Has your question been resolved?

[naive valley]

Have you tried substituting the first three x = 2 - 2t, y = 3t, z = 1 + t into the fourth? This should enable you to solve for t, which you can then substitute back into the first three equations.

[native tide]

e

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[amber jackal]

Honestly I don’t know how to find the side

[boreal flare]

well the perimeter is the sum of all the sides

so the lenght of the 1 side + the lenght of the 2 side plus x(which is the lenght of the 3rd side), is equal to the perimeter

[pale kestrel]

It's not going to be an explicity number.

[boreal flare]

well i guess so in some circumstances; but you just have to set up the formula correctly

[amber jackal]

I forgot the formula😅

[wary stream]

Perimeter is sum of side lengths

[boreal flare]

I suppose you know what to do @amber jackal

[amber jackal]

Yeah

I do

[boreal flare]

great!

[amber jackal]

.close

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[waxen tartan]

no idea how to do this

[lone heart]

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[magic terrace]

I used the pythagorean theorem

but this practice is on law of cosines

So I must be missing something

ping me if you reply

[lone heart]

@magic terrace Has your question been resolved?

[lone heart]

@magic terrace Has your question been resolved?

[magic terrace]

<@&286206848099549185>

[magic terrace]

<@&286206848099549185>

[daring coral]

Are you certain BC=820?

[magic terrace]

well it says 820ft. it would be partway through C though

halfway

also the B label is for the drawn triangle

All of the lettersare for the drawn triangle they're just far away so I could write values in

the red line is 820ft

[daring coral]

read the question carefully, from the base of the mountain is from where to where?

[magic terrace]

is it asking from the middle or the side of the base

Because every other problem we've had like this has it coming from the middle

[daring coral]

i think it might be from the side of the base

[magic terrace]

why are these math problems so badly worded

Also this

How do I get the area from 3 side lengths and an angle

the other side is 14.2914

nvm

.close

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[waxen tartan]

if a_n/b_n = the thing

[waxen tartan]

yeah

[tacit arch]

what's your question

[remote heron]

the thing

[waxen tartan]

like how would i evaluate that limit

$\frac{a_n}{b_n}=\frac{a_{n-1}+b_{n-2}}{b_{n-1}+2a_{n-2}+b_{n-2}}$ then how would i evaluate $\lim_{n\to\infty}\frac{a_n}{b_n}$

with those startinv values

[ocean seal]

AlephNull

[waxen tartan]

or like does it nto make sense to prove it algebraically

i tested it in the calculator and it looks like 1/2 but i wanted to see if i could prove it algebraically

<@&286206848099549185>

[lone heart]

@waxen tartan Has your question been resolved?

[vast inlet]

@waxen tartan u got no idea how much ur username confused me

[waxen tartan]

lmaoaoaoa

[lone heart]

@waxen tartan Has your question been resolved?

[tacit arch]

post the original question

[waxen tartan]

a_1=b_1 = 0.5

a_2=b_2=1

@tacit arch

[tacit arch]

Not your interpretation.

Original

A clear photo or screenshot usually

[waxen tartan]

its not original

like i just want to see if i can get anywhere with this approach

[tacit arch]

Where did you get it from?

[lone heart]

@waxen tartan Has your question been resolved?

[little drum]

Ganyuuuuuu >_<
unfortunately, <@&268886789983436800> Quiz

[tall wing]

interesing

bannde

.close

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[serene kernel]

Use the relation tthe limit as x approaches 0, sinx/x = 1 to determine the limit. Question: The limit as x approaches 0, of 1-cosx/sin22x

[echo socket]

sin(22x) or what?

[serene kernel]

Sorry if I didn't explain the question thoroughly, I attached a screenshot of the problem if that helps.

[echo socket]

No, I just thought there'd be sin^2 or something

One moment

[alpine sable]

Yeah

Maybe sin²(2x)

[echo socket]

Consider multiplying denominator and nominator by 1 + cos

[echo socket]

It's still solvable for sin(22x), I see it now

I think*

Yeah it is

[serene kernel]

I get 1-cos^2x/sin22xcosx. I could turn the 1-cos^2x into sin^2x but them I'm not sure where I would go from there

[echo socket]

Is this clear?

(I removed 1/(1 + cosx) because its limit is 1)

Oh nvm

It's 1/2

The limit is still the same tho

[serene kernel]

.close

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[alpine sable]

Hii can I message here?

[alpine sable]

Oww sorry umm about my assignment I'm having hard time in answering my homework can anyone help me? Thanks a lot:>

[severe sluice]

can you send a screenshot (windows+shift+s on windows, cmd+shift+4 on mac)

[slender gull]

He has the questions written on a paper.

Probably can't.

[buoyant kayak]

it's a pic of a computer screen lmao

[alpine sable]

That:>

[severe sluice]

arc BAC is basically the measure of this angle

[alpine sable]

Im sorry I'm not good at math because my math teacher always pressure me everytime he ask me. I cannot relate in every math problems I'd encounter at school

[alpine sable]

Ohhhh

Wait a minute

Umm did you know how to answer this one?

<@&286206848099549185>

Btw thanks a lot guys:>

Byee! Keep safe everyone

.closed

Hahaha

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[digital junco]

It's a square with side 10 . There are 2 semi circle in figure and a quadrant find area of shaded part

[severe sluice]

buncho law of cosines and circular segment areas

[lone heart]

@digital junco Has your question been resolved?

[little drum]

cosines? >_<

[little drum]

mark up all areas out there with letters and show the diagram

only the constituent areas... no need to mark areas of square, semicircle, etc. seperately

[digital junco]

To find : area of shaded part

[little drum]

nooooo (╯°□°）╯︵ ┻━┻

I literally meant to mark up the area

not the vertices

aaah

[digital junco]

Yeah

There you go

[little drum]

nvm my bad (╯°□°）╯︵ ┻━┻
I should just do it myself

[digital junco]

Sorry 😔

[digital junco]

Oh my bad

You meant areas

🤦

[little drum]

Just frame equations from here and figure c

there isn't much really though

[alpine sable]

U see A and B form a semi circle

[digital junco]

Yes

[alpine sable]

The diameter of the semi circle is 10 right?

[alpine sable]

assuming from here

[digital junco]

Yes

[alpine sable]

i in year 5

shhes

h

i smartest in class

i did oc

[lone heart]

@digital junco Has your question been resolved?

[lone heart]

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[lone charm]

Hello I am asked:
"The Polynomial P(x) = x^3-kx-2 has roots α, α and β. Find the value of 2α + β." I have tried watching some videos on polynomial roots but cant find anything to help. Thank you!

[lone charm]

<@&286206848099549185>

[echo socket]

By Vieta's theorem, sum of roots of a polynomial with degree n is equal to the negative coefficient of x^(n - 1) (divided by the leading coefficient, which is 1 in this case)

[lone charm]

so 2α + β would equal 0?

[echo socket]

Yes, because there's no x^2, thus its coefficient is 0

[lone charm]

how come 1? isn't it zero because there is no term x^2

yeah

so how come you edited it to be 1? imconfused

[echo socket]

I stated that the leading coefficient is 1

(leading coefficient is the coefficient of x^n)

[lone charm]

oh

yes my bad

thank you

[echo socket]

Np, feel free to .close if you don't have further questions

[lone charm]

I have a followup question if you don't mind, how would I find the value of α^2 * β?

[echo socket]

Vieta's theorem also states that the product of roots of a polynomial with degree n is (-1)^n multiplied by the constant coefficient

(which is again divided by the leading coefficient)

So here we have n = 3

And the constant coefficient is -2

So the product of coefficients will be (-2)(-1)^3 = 2

[lone charm]

multiplied by the constant coefficient
what is the constant coefficient?

[echo socket]

Consider visiting this wiki page if you're curious about Vieta's theorem

https://en.wikipedia.org/wiki/Vieta's_formulas

[echo socket]

The last coefficient, the one without x

Here it's -2

[lone charm]

oh yes

aaaaaaaahhhhh yes i understand thank you

i will check out that wikipedia page

thanks so much

.close

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[vale pulsar]

AB and CD are perpendicular to each other. What is the diameter of the circle?

[little drum]

Do you know MC?

[vale pulsar]

4

MC = 4

[little drum]

Exactly

Now draw the center O.

[vale pulsar]

How?

[little drum]

Idk how... just draw any point in the circle that's close to looking like a center

[vale pulsar]

Ok then?

[little drum]

then drop perpendicular to CD

or AB

doesn't matter

Let's drop on CD

[vale pulsar]

OK did it

[little drum]

now mark the point $OP \perp CD$ and apply pythagoras on triangle $\Delta OPC$

[ocean seal]

Ansh

[vale pulsar]

How?

[little drum]

You know OP now

Hint: ||OP is perpendicular with CD and AB parallel to CD as well||

[vale pulsar]

I know that!

How can I apply pythagoras on triangle OPC?

[little drum]

OP^2 + PC^2 = r^2

and you get your R

[vale pulsar]

How much is OP?

And PC?

[little drum]

You said you knew OP is perpendicular bisector of CD 👀

obviously that gives PC

And since OP || AB, you have OP if you put some thoughts into it

That's enough hint tbh, ping me after 10 mins if you still can't figure

[lone heart]

@vale pulsar Has your question been resolved?

[vale pulsar]

I didn't get how I can get OP...

[little drum]

Okay drop perpendicular from O to AB

say it intersects at point Q

OQ is perpendicular bisector of AB

QA = (6+2)/2 = 4

AM = 2 given

so OP = QM = QA - AM = 2

[vale pulsar]

How did you get that......

[little drum]

You know AB right?

and OQ is perpendicular bisector

so QA = 1/2 AB

[little drum]

Perfect! thanks

[tawny orchid]

No problem

[little drum]

So RM = OQ yes?

And OR perpendicular bisector of AB

[tawny orchid]

It's M and yes

[tawny orchid]

Yup

[little drum]

Hence, OQ = RM = (RA - AM) = (AB/2 - AM) = (6+2)/2 - 2 = 2

[tawny orchid]

Yes

Oh sorry you can explain him

[little drum]

And OQ is perpendicular bisector to CD to CQ = (4+3)/2 = 3.5

Hence, apply pythagoras and CQ² + OQ² = r²

[tawny orchid]

Same for ORB

[little drum]

Not really necessary, cause CQ and OQ are both known here, in numbers

[vale pulsar]

R = √20?

[tawny orchid]

I got $\frac{\sqrt{65}}{2}$

[ocean seal]

kirby your mom

[vale pulsar]

It's not in the options

[vale pulsar]

What did you get @little drum ?

[tawny orchid]

I did a mistake I guess

[little drum]

I got √65 diameter

,calc sqrt(3.5^2 + 4)

[ocean seal]

Result:

4.0311288741493

[little drum]

,calc sqrt(65/4)

[ocean seal]

Result:

4.0311288741493

[tawny orchid]

d = 8.062

[little drum]

Yeah

[little drum]

mention what that number is as well lol : the diameter

[tawny orchid]

Lol forgot that 😅

[vale pulsar]

QO = 2 right?

[tawny orchid]

yeah

[little drum]

QO = 2 yes

[vale pulsar]

CQ = 4

[tawny orchid]

Where is P

3.5

Changed it

[tawny orchid]

(3 + 4) / 2

[little drum]

Nope.. MC = 4

[vale pulsar]

Oh right!

[little drum]

MD = 3

CQ = CD / 2

[vale pulsar]

R ^ 2 = 16.25?

[tawny orchid]

Yes

16.25 is 65/4

[vale pulsar]

Whatttt!?

[tawny orchid]

Multiply 16.25 by 4 and see what you get

4 because .25 * 4 = 1

[vale pulsar]

Oh 16.25 is the radius !

[tawny orchid]

What are the options by the way?

[tawny orchid]

16.25 is the square of the radius

[vale pulsar]

4√5 / √65 / 2√17 / 3√7

[tawny orchid]

Alright

[little drum]

btw what's your name though 👀

Is it read *curvy ... or kirby

[tawny orchid]

kirby your mom

[vale pulsar]

Thank you very much both of you for helping me with this question! @little drum & @tawny orchid

[tawny orchid]

kirby 😂

[tawny orchid]

You're welcome

[tawny orchid]

🙂

[little drum]

kawaiii kowai

[tawny orchid]

Knife was near

[vale pulsar]

.close

[lone heart]

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[barren glade]

this is not a test or anything just a book of past question papers

i need help with 3b

[lone heart]

@barren glade Has your question been resolved?

[barren glade]

<@&286206848099549185>

<@&286206848099549185>

[barren glade]

@digital junco ??

wyd

this channel is taken

find an unoccupied channel

[digital junco]

Sorry 😔

[barren glade]

@digital junco

<@&286206848099549185>

[lone heart]

@barren glade Has your question been resolved?

[lone heart]

@barren glade Has your question been resolved?

[lone heart]

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[warped spruce]

claim

[warped spruce]

how to I simplify this?

it should be this in the end

can you show me it solved please?

[wary stream]

Expand it first, then you will notice things will cancel out

Then simplify

[warped spruce]

I got it, but like how can you reduce the x that is on top with the button and you will still have x^3 in the button

[wary stream]

What do you have so far?

[warped spruce]

2x(-1) / (x^2)^2

[proven rune]

it must be +1 , check properly

[warped spruce]

wdum?

it should be -1 no?

[proven rune]

nope

[wary stream]

You didn't distribute correctly

[proven rune]

-2x(x^2-1) = -2x^3 + 1

• x - = +

[warped spruce]

you right 🙂

now I got it

[wary stream]

Also exponent rule for the denominator

[proven rune]

nice

[warped spruce]

and then you reduce the The x in denominator and numerator

right?

[proven rune]

yes

[warped spruce]

thank you so much my friend 🙂

have a nice day!

[proven rune]

np dude
thank @wary stream too !
gl

@warped spruce m8 close channel if ur done

[warped spruce]

thank you too @wary stream, you helped a lot m8

how do I close chanel?

[wary stream]

.close

[warped spruce]

.close

[lone heart]

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[warped spruce]

close

[lone heart]

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[peak owl]

Claim

[buoyant kayak]

solid claim

[peak owl]

I have to take a math diagnostic test but this one question I don't really understand. I think I'm just a little slow and can't process the question, but regardless I need a little help on how to solve it

[wary stream]

But it's a test?

[peak owl]

Not really a test

It's not for a grade

[buoyant kayak]

diagnostic tests are to test your knowledge lol

[wary stream]

If it's a diagnostic test, that's used to see your math level, right?

[peak owl]

Is that still against the rules?

Ah ok

[wary stream]

So it's testing knowledge

[peak owl]

Fair enough then

.close

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[bold venture]

help me plz

[bold venture]

<@&286206848099549185>

[wary stream]

You have to wait at least 15 minutes before pinging helpers

No

[bold venture]

.close

[lone heart]

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[tacit arch]

FTOC

[icy raft]

Huh

I know it has to do with that but I’m not sure how to apply it

My second picture is after i tried it

I probably did something wrong

[placid zinc]

The fundamental theorem says that if x were on the top, and some constant on the bottom, you could simply replace u with x

That's not what you've got though. x is on the bottom instead

Second FToC is a better fit for odd cases like this

But you can still fix it by swapping the bounds

[lone heart]

@icy raft Has your question been resolved?

[last tendon]

It involves a tiny bit more work than just swapping the bounds since you need to justify how the ftc still works with an improper integral too

[little drum]

the second expression is also incorrect: should be $\frac{e^{-\infty}}{\infty}\dv{\infty}{x} - \frac{e^{-x}}{x}$

[ocean seal]

Ansh

[vague coral]

if it was this easy to apply the fundamental theorem to an improper integral...

[little drum]

:O

[vague coral]

that looks wrong tho

[little drum]

Yes, it's wrong in many ways

[vague coral]

I don't know how you would take the derivative of infinity

there is more work to do when we are dealing with improper integral

[little drum]

Exactly.. but they said they're doing it their way and got it like that... so I added on it

[vague coral]

?

[little drum]

Anyways... do you know what to do with it?

[vague coral]

sadly no, but all I could say is that we should prove that this integral exists

[lone heart]

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[little drum]

Is it okay to write $\dv{y}{x}=\lim \limits_{b \to \infty} \dv{}{x} C_1 \int_x^{b} \frac{e^{-u}}{u} \dd{u}$?

[ocean seal]

Ansh

[last tendon]

All you do is split it up. To be a bit lazy about my notation: $\int_{x}^{\infty} = \int_{x}^{a} + \int_{a}^{\infty}$. The second term clearly has a zero derivative. You don't need to do any dominated convergence, swapping of limits.

[ocean seal]

Hexicle

[little drum]

Ohhhh right! wow that was smart lmao

the second term is clearly some area independent of "x" so derivative is 0.

Is it okay to take the limit the way I said tho?

[last tendon]

You need to justify the interchange of limits but yes

[little drum]

because I read: $\int_x^{\infty} \frac{e^{-u}}{u} \dd{u} =\lim \limits_{b \to \infty} \int_x^{b} \frac{e^{-u}}{u} \dd{u}$

[ocean seal]

Ansh

[vague coral]

well it's true

[little drum]

so I was wondering if it's okay to just differentiate w.r.t. x here, and then apply lim b tends to infinity

[vague coral]

wrt ?

[little drum]

with respect to

[vague coral]

but you guys chose to split the integral right ?

[little drum]

Anyways... I should've thought about what Hexicle said Splitting works

[vague coral]

indeed

[pale kestrel]

b is constant

this justified the swap?

[little drum]

Shuri joins with no context >_<

[pale kestrel]

And then you could FTC2?

[pale kestrel]

I mean here 👀

[little drum]

Ah

Idk FTC

[pale kestrel]

nvm FTC

how do we justify limit switch?

[vague coral]

you can swap the derivative and the limit I think

[pale kestrel]

constant b right

i was curious

[little drum]

this is the previous step

[pale kestrel]

Splitting the limit is smart

[little drum]

btw quick question: if integral is the area under the curve, of a function... the anti-derivative is the family of curves which have the same area under curve +/- some constant?

[pale kestrel]

was gonna say. yes

$$\int^b_a f(x) \dd{x} = F(b) - F(a)$$

[ocean seal]

Shuri2060

[pale kestrel]

For antiderivative F

We can apply this to above

$$\int^b_x f(u) \dd{u} = F(b) - F(x)$$

[ocean seal]

Shuri2060

[pale kestrel]

$$\dv{x}\int^b_x f(u) \dd{u} = \dv{x}(F(b) - F(x))$$

[ocean seal]

Shuri2060

[little drum]

yep got it

[pale kestrel]

Then the right side becomes -F'(x)

yh

[little drum]

UwU

thanks Shuri !!!

.close

[lone heart]

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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[hollow zephyr]

how to approximate $0.99^{2.02}$?

[ocean seal]

Erzis エルジス

[buoyant kayak]

well .99 is pretty close to 1 and 2.02 is pretty close to 2

[little drum]

$(1-0.01)^{2(1+0.01)}$

[ocean seal]

Ansh

[little drum]

_< I'm sure the question probably asks for something like "up to 2 decimals" or something lol

[buoyant kayak]

lo siento mi amigo

[hollow zephyr]

that's true but I don't think that's the answer I'm looking for because I need calculator to calculate that, no?

[little drum]

Yep.. so you can do something else that makes your life a bit easier

[little drum]

$= \qty(( 1-\Delta)^2)^{(1+\Delta)}$

[ocean seal]

Ansh

[little drum]

where $\Delta$ is just $0.01$ and we assume $(\Delta)^x << 1$ for $x \geq 2$

[ocean seal]

Ansh

[little drum]

Okay? 👀

[hollow zephyr]

bruuh

[little drum]

$= \qty( 1-2\Delta)^{(1+\Delta)}$

[ocean seal]

Ansh

[hollow zephyr]

what's the approximation then?

don't use the calculator

[alpine sable]

We can set the answer to be A
Then take natural log on both sides
And bring power to the front 🤔

[little drum]

$= \qty( 1-2\Delta) = 0.98$

[ocean seal]

Ansh

[little drum]

:/ that's the approximation

[hollow zephyr]

hmm

okay, thank you

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[hardy quail]

I'

[hardy quail]

I'm trying to simplify 11k/6 -1/7+1/7 = -1+1/7, the worksheet tells me it ends up as 11k/6=-6/7 but I really don't understand how it got there

[vague coral]

-1/7 + 1/7 = 0

and -6/7 is just the result of -1+1/7

[hardy quail]

might be a silly question but how does -1+1/7 give you -6/7? The -6 seems wild to me

[daring coral]

multiply -1*7/7 to get similar fractions

[wary stream]

Get a common denominator

[mystic hamlet]

@hardy quail so -1+1/7=-1+0.142857... so it equals -6/7

[wary stream]

Combine fractions

[gray isle]

don't use a calculator

[hardy quail]

im trying really hard but still not really getting where that -6 is coming from. If I expand the equation solver I use to help me it turns -1/1+1/7 which I understand, but no idea how it then gets -7/7 + 1/7

[daring coral]

what is -7/7?

[lilac harness]

Where’s geometry at

Who knows Spanish

[hardy quail]

I follow until step 2 but get lost at step 3

[daring coral]

what is -7/7 simplified?

[hardy quail]

-1?

[wary stream]

Do you know how to add/subtract fractions?

That's the process that's happening

[hardy quail]

I could definitely use a refresher

[wary stream]

https://youtube.com/watch?v=52ZlXsFJULI

Refresher video

[hardy quail]

roger. will watch and comeback

@wary stream thanks for the video and mentioning the adding subtracting thing. I now understnd where it came from 🙂

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@hardy quail Has your question been resolved?

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[fickle dock]

Alright so after getting some sleep I finally read up a bit on this but I'm still getting it wrong, does anyone know what I'm doing wrong here?

[fickle dock]

I changed my answer to "Yes" for 9) and it's saying that only one of them is incorrect now

[glass lichen]

10 is No cause they assumed AB=BA

9 you also assumed commutativity @fickle dock

$(AB)^n\neq A^nB^n$

[ocean seal]

Mosh

[fickle dock]

I figured you change B with A, then undo those changes with A^-1?

[glass lichen]

No, that's commutativity

$AB\neq BA$ always

[ocean seal]

Mosh

[fickle dock]

hmm okay then, so 9 and 10 are the same cases

thank you!

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[fickle dock]

actually changing 9 and 10 to No is still wrong

[fickle dock]

9 is Yes

now I got it

but I don't understand why

[glass lichen]

Write it out in full w/o assuming commutativity

[fickle dock]

okay I'll do that once I get back then, it might be a bit so I will open another channel

I appreciate the help

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[rugged pebble]

when you divide it moves?

[bright hedge]

What?

[rugged pebble]

when you divide it flips correct?

[buoyant kayak]

if it's positive? no

[rugged pebble]

oh

so it flips if its a negative and you times or divide?

[buoyant kayak]

yep

[rugged pebble]

thanks

this is why i was asking

google said wrong stuff

[buoyant kayak]

it's probably from an article about dividing negative numbers

those little snippets can be misleading

[rugged pebble]

thanks

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[placid kindle]

Hello everyone! I'm having some trouble with trigonometry. I have an autocovariance function Sigma_(t, t-1) = sigma^2 * cos(ct-c)sin(ct). If c = kpi and k is an integer, the process should no longer depend on t but I do not know how I get there.

[placid kindle]

c = k * pi

And the function in reality is X(t) = cos(ct-c) * sin(ct)

<@&286206848099549185>

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[dusk panther]

How do I do b?

[daring coral]

try drawing a triangle

[dusk panther]

Oh

[dusk panther]

x^2+y^2=128?

[daring coral]

this is an equation of a circle. the question asks for the line passing through OM. Where is M located?

[dusk panther]

In between AB.

(4,4)

[torpid star]

how would you work out the equation of a line going through 2 points?

[dusk panther]

y=mx+c

[torpid star]

ye

you know the line goes through O and M

you worked out the coordinates of M as (4, 4)
and O is just the origin, so its coordinates are (0, 0)
you want to work out the equation of a line going through those 2 points

[dusk panther]

What is the y intercept?

4?

[daring coral]

where does the line intersect the y-axis?

[dusk panther]

y=x+8

[wary stream]

Hint: you need to find m before you use that equation

[dusk panther]

I got the answer

[daring coral]

what is y at x=0? does that point lie on OM?

[dusk panther]

Or 8

It isn't on OM tho

[daring coral]

so why do you have the equation for OM as y=x+8

[dusk panther]

Wait why doesn't c=0

I don't get how I got 8 actually

[daring coral]

i don't understand how it accepted that answer

,w plot y=x+8, x^2+y^2=64

[ocean seal]

Results provided by WolframAlpha

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

Requested by Taltost#8448

[dusk panther]

Wait isn't that the answer then

Wait you could just square root x^2+y^2=64 then rearrange.

But it would be y=-x+8

[daring coral]

no, O is the origin correct? the line must pass through the origin

[dusk panther]

You know what I give up

All of a sudden I cant do maths

I should sleep

Thanks for the help anyways

.close

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[faint thicket]

Our team had won 60% of football games. After that point we won 8 more games and lost 2, to finish the season having won 65% of games. How many games did Our team play during the season? (There were no ties.) I'm stuck on this question, I dont know how to find it.

[long iris]

If you say x to number of games your team played number of games that your team won is 60x/100

Ill contuine but do you know the math bot

[faint thicket]

what's the math bot?

[long iris]

It shows fractions better

[faint thicket]

oh

pls continue

[long iris]

Ok

Your team won 8 and lose 2 more games so team played 10 games more

[faint thicket]

yap