help-0

[vague mirage]

Yupp

[hot jewel]

yes

but how would we get it now if we already have the angles

because of it being a diagonal

[vague mirage]

It is given in the question

[hot jewel]

RCA is 35 so is CER is 35 too

CRE

[hot jewel]

oh

[vague mirage]

CRE is 35 yes

[hot jewel]

ohhhhh

okok i get it

so i can just add? to get the angles?

[vague mirage]

Well if you have all angles at the corner then you can just add em

[hot jewel]

o

[vague mirage]

Then use any theorem that would be useful

[hot jewel]

ASA

[vague mirage]

Cause you can do anything here

[vague mirage]

No 🥲

[hot jewel]

o

[vague mirage]

Why you want to prove them congruent

They are already congruent

Btw

[hot jewel]

oh

like same angles

?

congruence means the same right

[vague mirage]

2 triangles that are bisected by the diagonal of a parallelogram are congruent - theorem

[vague mirage]

Yes

[hot jewel]

oh

okok

[vague mirage]

But what will you do by proving them congruent

If you have one side

In a parallelogram

Then opposite side is equal

[hot jewel]

wait what is consecutive angles

[vague mirage]

And the angles which lies in the same transversal there sum would be 180

[hot jewel]

ohh okok

[vague mirage]

A pair of angles formed on each side of the transversal when it interacts with two parallel lines

[hot jewel]

i figured out no. 2

[hot jewel]

how would i solve for this

[vague mirage]

Sum of them would be 180

[hot jewel]

same as earlier?

[vague mirage]

Same concept as the first question

Exactly the same

[hot jewel]

2x + 4x = 6x?

how about square

do i include if its squared

or its squared when only multiplied

[vague mirage]

What do you mean

If the shape is a square

[hot jewel]

2x + 4x is equal to?

[vague mirage]

6x

[hot jewel]

oh

i thought it was squared

okok

-10 + 10 = 0?

[vague mirage]

Only in the case of multiplication

[hot jewel]

oh wait

[hot jewel]

ohh got it

[vague mirage]

What you don't know that?

[hot jewel]

+10 - 10

do i get 0??

[vague mirage]

Yes 🥲

[hot jewel]

oh

[vague mirage]

Anything subtracted by itself is 0 except infinity

[hot jewel]

oh

okok

[vague mirage]

Did I said multiplied 😂

[hot jewel]

yeah

i know subtraction dont worry

im just confused because of 2x + 6x

i thought there was product law

[vague mirage]

2x+4x

2x×4x=8x²

In the case of multiplication

Anyways solve your math

[hot jewel]

yes

i got 30

because 6x / 180

[vague mirage]

Yes

[hot jewel]

ohh okok

thank you for the help

i appreciate

.close

[lone heart]

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[heavy frigate]

ya

[vague mirage]

Any questions?@heavy frigate

[heavy frigate]

wairt

[vague mirage]

Ok

I assume you're saying wait

[heavy frigate]

i need to calculate the intersection with the axes form y= (2x)/(3-x) square root

[open cosmos]

whats inside the square root

(2x)/(3-x) ?

[ornate ginkgo]

I think it is $y = \frac{2x}{\sqrt{3-x}}$

[ocean seal]

ColdTee

[lone heart]

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[heavy frigate]

NOO

[open cosmos]

just ask again lol

[heavy frigate]

i wrong

sorryy

[open cosmos]

or .reopen

.reopen

well i guess i cant

[heavy frigate]

.reopen

[lone heart]

✅

[heavy frigate]

jauiisuudjjjwsjsajka

[open cosmos]

hows the equation exactly

[heavy frigate]

idk

[open cosmos]

i dont get the question here

[heavy frigate]

yes

PLS IDK

my english maths is odd

[open cosmos]

is it on a sheet

paper

you can send the question as an image

[heavy frigate]

yup but its in italian

[open cosmos]

its ok you told whats being asked

i just wanna see the equation

[heavy frigate]

okok

wait

[open cosmos]

ok im google translating

lmao

[heavy frigate]

calculate the domain, sign and intersections with the axes of the following function y= square root of (2x-1)/(3-x)

[heavy frigate]

letteraly me

[open cosmos]

is that this

[heavy frigate]

a

now i need yo calculate the damain

ty

[open cosmos]

it intersects with x axis at 1/2

doesnt intersect with y

oh wait domain is just

ok its [1/2, 3)

[heavy frigate]

THAMK YOU

[open cosmos]

but did u understand why

thats more important

[heavy frigate]

cuz the 2 i will put in the bottom for both

but i dont understand the 3

3-x

[open cosmos]

because then the denominator will be 0

[heavy frigate]

if i move 3 form there to other sile why is not -3?

[open cosmos]

move 3 to where

you cant move it because its in the square root

[heavy frigate]

other side

[open cosmos]

also its a fraction

[heavy frigate]

aaaaaaaaaaaa

I UNDERSTAND

[lone heart]

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[lone heart]

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[alpine sable]

Need to solve this

[alpine sable]

Anyone help

[lone heart]

@alpine sable Has your question been resolved?

[tacit arch]

Do you know the formula for focus

[alpine sable]

Yeah

[tacit arch]

Can you show it/type here

[lone heart]

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[lone heart]

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[hoary edge]

Hey can someone help me with this question?

[alpine sable]

Oh my god

[hoary edge]

Ive tried making a quadratic and this is where I got to, since the integral is pi

[alpine sable]

I feel heat in my mind

[hoary edge]

yea im stuck

[alpine sable]

Ur in university?

[hoary edge]

es

yes

only the words after a) really matter

[mortal trellis]

optimal chosen c means that you want the error to be minimal

how do you minimize a function

[hoary edge]

are u asking how to find the minimum of a function

[mortal trellis]

yes

[hoary edge]

using the derivative

o

[mortal trellis]

or well here its a quadratic so you can also just read it off from that

ok derivative

what is the derivative

[hoary edge]

would the integrals disappear

if u derive them

[mortal trellis]

the integrals are constants

after f is fixed

[hoary edge]

oh thats true

so i should derive in terms of c

[mortal trellis]

yes

[hoary edge]

i think this is the derivative

or did i do something wrong

the 2nd term over pi

[mortal trellis]

and then what next?

[hoary edge]

equate to 0

and i get a formula for c

so this would be my cm ?

c_m

[mortal trellis]

yes

[hoary edge]

i see

thank u

[lone heart]

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[round obsidian]

how do u do this

??

is anyone there i dont know how to begin it

.close

[lone heart]

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[empty plover]

is this true for all rotation matrices?

[lone heart]

@empty plover Has your question been resolved?

[empty plover]

A here is a rotation matrix

[lone heart]

@empty plover Has your question been resolved?

[lone heart]

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[clear sparrow]

trying to take this integral, ik sign(x) from 0 to t would just be tx

[clear sparrow]

but i am not sure

what to do here

perhaps u sub?

since sign(x) integral is |x| which is in e^|x|

but

i am a little lost

[lone heart]

@clear sparrow Has your question been resolved?

[clear sparrow]

<@&286206848099549185>

nvm got it

u substittion

[lone heart]

@clear sparrow Has your question been resolved?

[lone heart]

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[topaz grove]

i'm not sure what to do here

depending on what i plug in for n, the Hessian could go back and forth between positive, negative, and zero

i need to figure out if there are relative minima, maxima, and/or saddlepoints

[clever crown]

Can anyone help with these 3 pls

[topaz grove]

why are you posting that here instead of your own help channel?

but yes, i can help...

[clever crown]

Oh sorry I’m new I wasn’t sure where to go

[topaz grove]

when you think of the word "percent", notice that it sounds like "per cent"

yeah?

[clever crown]

Right

[topaz grove]

how many years in a century?

[clever crown]

20

[topaz grove]

no, 100

how many cents in a dollar?

[clever crown]

Oops mb😭

[clever crown]

100

[topaz grove]

good. cent typically means "100"

[clever crown]

Ok

[topaz grove]

so you are trying to figure out, according to the question, with regard to the current ratio of apples to oranges you have out of the total number of fruit, what that ratio would be

so how many total fruit is in the bowl?

[clever crown]

5?

[topaz grove]

yes. and how many of those are oranges?

[clever crown]

3

[topaz grove]

divide 3 by 5

[clever crown]

0.6?

[topaz grove]

now think logically about it, to verify your answer makes sense. if you had 60 cents, would you have over half a dollar?

[clever crown]

Yes

[topaz grove]

remember, $0.60 is the same as 60 cents

good. and the number of oranges in the bowl, is it just over half the number of total fruit in the bowl?

[clever crown]

Yes

So the answer would be 60% right?

[topaz grove]

good. so now, what "percent" is 0.6?

[clever crown]

60

[topaz grove]

yes

[clever crown]

Oh ok that you so much!

[topaz grove]

no worries

you still need help with the other problems?

<@&286206848099549185>

[lone heart]

@topaz grove Has your question been resolved?

[lone heart]

@topaz grove Has your question been resolved?

[lone heart]

@topaz grove Has your question been resolved?

[topaz grove]

.close

[lone heart]

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[rotund crater]

someone can explain me this for step step

[uneven isle]

from step 1 to step 2

they multiplied by 1

but reexpressed it in the form of −2sqrt(c+h + 2sqrt(c)

step 2 to 3, they expanded the top brackets

step 3 to 4, they expanded brackets again and collecected like terms where applicable

from step 4 to the answer

they divided both top side and bottom side by h

so that u get −4/2(sqrt(c+h) + sqrt(c) )

then as h approaches o

*0

sqrt(c+h) in turn becomes sqrt c as h is approaching towards 0

thus u collect the like term and form 2 sqrt(c), divide both top and bottom by 2 and u would yield ur final answer

@rotund crater

[rotund crater]

multiplied by 1 explain

[uneven isle]

well

a/a = 1

b/b = 1

[rotund crater]

but why dont using conjugate

[uneven isle]

u could use conjugate

if u wish

makes no difference afaik

[rotund crater]

the 2 came out of the bracket I did not understand that part

@uneven isle

[rotund crater]

the conjugate is -2sqrt(c+h) - 2sqrt(c)?

[lone heart]

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[ember flax]

What is the difference between multiplying two vectors and the dot product?

[ember flax]

.close

[lone heart]

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[lilac trench]

Mr Julia equation
x^3+y^3=z^3 ,
what the solution of x, y, z, but with the use of Géométrie Fractale

[lilac trench]

I think i found the solution with use of géométrie fractale x=0, y=0, z=0 , please correct me if i am wrong

[lone heart]

@lilac trench Has your question been resolved?

Please read #❓how-to-get-help

[wary stream]

Then read #❓how-to-get-help

[lone heart]

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[fringe lotus]

can anyone help me?

[manic moat]

differential eq

i have trouble on how they got the C

[rustic coral]

#❓how-to-get-help

[rustic coral]

Substitute $y(0)=-1$ and solve for $C$

[ocean seal]

Civil Service Pigeon

[manic moat]

i understand that part, but just to make sure

that i integrated this correctly and it is ready to let t=0, and y=-1

but i cannot do ln(-1)

[rustic coral]

Absolute value

[manic moat]

so it would be 0

my bad

0=e^(4(0)+C)?

i get C=-1?

but why is the answer -e^(4e^t-4)?

[rustic coral]

It should probably be $e^{4(t+C)}$

[ocean seal]

Civil Service Pigeon

[manic moat]

are you talking about the final answer? thats what it should be?

[rustic coral]

Just send all your work for the exercise.

[manic moat]

ok

thank you, .close

.close

[lone heart]

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[blissful river]

How to solve this

[lone heart]

Please don't occupy multiple help channels.

[alpine sable]

First notice that gold fishes living 10 times longer than betta fishes implies that betta fishes live 10 times shorter than gold fishes

And that 3 decades is 30 years

And since gold fishes live 30 years, betta fishes must live 10 times shorter than 30 years

From there it should be trivial, but feel free to ask if you have any further questions

[pseudo ice]

Also could you move your other questions to this thread and close #help-13 please @blissful river?

[lone heart]

@blissful river Has your question been resolved?

[blissful river]

thx

I'll try to solve it for now

[lone heart]

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[old nest]

Hello
How do i find the a_1 and the value of An if n= 5, Sn= 220 and r=-2

[old nest]

Here we go

F my internet

[lone heart]

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'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above

@old nest Has your question been resolved?

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[old nest]

.close

[lone heart]

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[flint pecan]

Anybody care to check if I got this right?

[lone heart]

@flint pecan Has your question been resolved?

[flint pecan]

<@&286206848099549185> I just need it checked

[ornate ginkgo]

I suck at optics 😭

[flint pecan]

Lmao that's alright

It's basically a question on similarities though

[flint pecan]

.close

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[dusky wraith]

Can someone check my work

[dusky wraith]

For 1(f)

[alpine sable]

The last part is wrong

[dusky wraith]

k(x)

[alpine sable]

[
3^- {\c r {}\neq{}} -3
]

[dusky wraith]

the first two are right tho?

[alpine sable]

wait nvm that's not what you did, but why is k(x) defined with +8 and +6

Oh I see now

Okay

Yeah sorry, your work is fine

As far as I see

[sudden igloo]

in h(x) isnt there should be +1

[dusky wraith]

like equal to +1?

[sudden igloo]

-2x + 7 + 1

[dusky wraith]

there needs to be an additional one?

[sudden igloo]

(x-3)/(x-3) = 1

[dusky wraith]

Oh

bc its absolute value

so the final answer should be 2?

[sudden igloo]

yes i think so

[dusky wraith]

kk ur def right

wait should it be minus two

wait no

it should be 2

okay

thanks

.close

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[smoky quest]

Does anybody understand why this process is wrong? I understand the reasoning for the solution but I can't find the problem with my solution.

[smoky quest]

I chose 30 possibilites by first starting with choosing one woman, and then choosing the leftovers from the whole group (59, 58 . . . 51) and then multiplying the possibilities

[upbeat arch]

The problem with your solution is there are multiple ways to reach the same outcome, and your method counts each one separately

I made this same mistake a couple weeks ago

[prime badge]

every time you end up with 2 women, you overcount twice

every time you end up with 6 women you make 6 copies of each

etc.

[upbeat arch]

basically the problem is: if Alice and Brooke are the only two women on the committee, then Alice could have gotten the designated seat and Brooke was chosen randomly, or vice versa

your solution counts those as different outcomes

[smoky quest]

So I did a permutation instead of a combination

[prime badge]

that doesn't sound right

you did something

[smoky quest]

okay I see now thanks

[prime badge]

oh yes, you did a permutation on the remaining people the way you described it

[smoky quest]

.close

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[balmy zodiac]

https://i.imgur.com/znxGQ61.png

[balmy zodiac]

can we try to get this x in the sinx by itself?

how do I do that (obviously using arcsin)

[alpine sable]

Taylor's expansion ?

[balmy zodiac]

How do i do that?

My calculus/algebra is very very rough when it comes to doing this time of isolation

https://i.imgur.com/JBP2bJ9.png

This is what I got @alpine sable

Is that right?

[lone heart]

@balmy zodiac Has your question been resolved?

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[blissful river]

How to solve this

[alpine sable]

This is the fourth time you're asking this... Did the previous explanations not suffice?

First notice that gold fishes living 10 times longer than betta fishes implies that betta fishes live 10 times shorter than gold fishes
And that 3 decades is 30 years
And since gold fishes live 30 years, betta fishes must live 10 times shorter than 30 years
From there it should be trivial, but feel free to ask if you have any further questions
This was my explanation

And as stated you can ask further questions if you still have any

That would be more practical than resending the question each time you failed to solve it

[lone heart]

@blissful river Has your question been resolved?

[blissful river]

soo...20 is the answer?

how will i write this in an equation

[lone heart]

@blissful river Has your question been resolved?

[gusty gorge]

ok do you know what it means when someone says "the life expectancy of A is ten times as long as that of B"?

[blissful river]

10 multiplied to the life expectancy of B?

[gusty gorge]

it just means that A lives 10 times longer than B

[gusty gorge]

this isn't an English sentence

so if I say that a gnome has a life expectancy ten times longer as that of a human

what I mean is that a gnome lives ten times longer on average

does that makes sense?

[blissful river]

so 30 x 10? or 10 + 30?

[gusty gorge]

those are just numbers

I'm talking about

if you're talking to someone else about how long something lives

we don't talk to each other by writing random math symbols and numbers

like you would think I'm a nut if I just said 9x2 59x3 29-49 5109+4

do you understand what I mean if I say humans live ten times longer than dogs on average?

[blissful river]

yes

[gusty gorge]

so if told you that

and then I said a dog lives 7 years on average

how long does a human live on average?

[blissful river]

70

[gusty gorge]

okay now if I told you that a human lives 75 years on average, could you figure out how many years a dog lives on average?

[blissful river]

7.5

years

or 7 and a half

[gusty gorge]

okay now let's imagine we're in some crazy world, and I tell you that women live three times longer than men on average

if a woman lives on average for 30 years

how many years does a man live?

[blissful river]

3

years

[gusty gorge]

okay now let's say

that we're in a normal world, and I tell you that gold fishes live ten times longer than betta fishes

and gold fishes live for 30 years

how many years does a betta fish live?

[blissful river]

3

[gusty gorge]

now if I say "the life expectancy of gold fishes is ten times as long as that of betta fishes, and gold fishes live as long as 30 years," how long do betta fishes live?

[blissful river]

Betta fishes live for 3 years

[gusty gorge]

are you aware that 3 decades means 30 years

[blissful river]

yes

[gusty gorge]

so now if I ask you the question: "The life expectancy of gold fishes is ten times as long as betta fishes. How long can betta fishes live if gold fishes can live as long as 3 decades?" can you answer that?

[blissful river]

40 years

[gusty gorge]

rnijshakjhdsd;hkgsajfas

bruh

what

[blissful river]

Sorry. I'm just so bad at word problems😓

[gusty gorge]

this isn't word problems this is more like English

[blissful river]

ha?

[gusty gorge]

now if I say "the life expectancy of gold fishes is ten times as long as that of betta fishes, and gold fishes live as long as 30 years," how long do betta fishes live?

so now if I ask you the question: "The life expectancy of gold fishes is ten times as long as betta fishes. How long can betta fishes live if gold fishes can live as long as 3 decades?" can you answer that?

would you say that I said the same thing in these messages but in a slightly different order of words?

[blissful river]

yes

[gusty gorge]

so why would you change your answer from 3 years to 40 years

[blissful river]

oh

so 3 years is the right answer...or not?

[gusty gorge]

you tell me

what is the English meaning of the question

and does your answer align with that meaning

[blissful river]

20 years final answer

[gusty gorge]

you have to be trolling

this can't be real

okay so you're saying that betta fishes live 20 years, right?

[blissful river]

yes...

[gusty gorge]

so if I say that the life expectancy of gold fishes is ten times as long as that of betta fishes

then how long do gold fishes live?

if you say that betta fishes live 20 years

[blissful river]

30 years

20 + 10=30 ???

[gusty gorge]

ten TIMES as long

didn't we go ove rthis

[blissful river]

200

[gusty gorge]

if a human lives for ten times longer than a doggo

[gusty gorge]

okay so does the question say that gold fishes live for 200 years?

[blissful river]

no

they can live for 30 years

[gusty gorge]

so clearly betta fishes don't live for 20 years, because that would mean that gold fishes live for 200

and the question says they don't

do you understand that logic?

[blissful river]

so 300

[alpine sable]

yo

help me pls

[gusty gorge]

stop writing random numbers

I'm asking you to use some common sense and logic here

not guess random numbers or try random things on the calculator

[blissful river]

okay

,close

[alpine sable]

.close

[lone heart]

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[lone heart]

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[wild pebble]

How do I solve this square?

[mint wadi]

wdym "solve the square"

[wild pebble]

I mean solve x

For x

I need the value of x

<@&286206848099549185>

[modern imp]

so how do you think we can solve this problem?

we'll construct? or

check smthn we can get with the given data

!status

[lone heart]

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'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above

@wild pebble Has your question been resolved?

[lone heart]

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[dapper river]

Hello! does P() mean power set or something else?

[dapper river]

I was originally thinking probability

[tacit bobcat]

Probability.

[dapper river]

alright

.close

[lone heart]

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[waxen plinth]

$cot\theta = \frac{1}{\sqrt{3}}$

[waxen plinth]

How do I calc theta in deg and rads

[pliant cedar]

\sqrt{3} by the way

[waxen plinth]

I know that cot = 1/tan

[pliant cedar]

enclose all of it within { }

[waxen plinth]

thx

[ocean seal]

OceanBro

[waxen plinth]

do I like 1/arctan ?

[pliant cedar]

okay if u know that $\cot\theta=\frac{1}{\tan\theta}$

[ocean seal]

𝕾ilver𝕾oldier

[waxen plinth]

yes

[pliant cedar]

you can just replace the $\cot\theta$ with it

[ocean seal]

𝕾ilver𝕾oldier

[waxen plinth]

true!

I can say 1/ sin\theta/cos\theta ?

[pliant cedar]

u can but that is not necessary

[vague mirage]

$\theta=\cot^{-1}(\frac{1}{\sqrt{3}})$

[waxen plinth]

Fair, keep going

[ocean seal]

Arnab

[waxen plinth]

How do I solve this manually tho

[vague mirage]

Well $\frac{1}{\tan\theta}=\frac{1}{√3}$

[ocean seal]

Arnab

[waxen plinth]

true

[pliant cedar]

you would have $\frac{1}{\tan\theta}=\frac{1}{\sqrt{3}}$, so $\tan\theta=\sqrt{3}$

[ocean seal]

𝕾ilver𝕾oldier

[pliant cedar]

yes

[vague mirage]

More true

True ×100

[waxen plinth]

uh huh

[pliant cedar]

and u probably know the anlge

[waxen plinth]

do I have to brute force the unit circle

[pliant cedar]

that has a tangent of sqrt(3)

[waxen plinth]

I.. don't

[vague mirage]

But tan 60°=√3

[pliant cedar]

oh

[vague mirage]

Oh

Sad

[waxen plinth]

1/2/sqrt(3)/2

that's for 30

[vague mirage]

You have to know the angles at least

[waxen plinth]

for 60, it'll be sqrt(3)/2 / 1/2

[pliant cedar]

well u r usually supposed to know the sines cosines and tangents of angles like 30, 60, 45, 90 deg

[vague mirage]

There's a finger trick to learn it

[waxen plinth]

Well, I know the sin and cos of them

but not the tangents

[vague mirage]

$\frac{\sin\theta}{\cos\theta}=\tan\theta$

[pliant cedar]

well you could have found out by dividing the sines and cosines then but ig its still better to know them off the top of ur head

[ocean seal]

Arnab

[waxen plinth]

@vague mirage

[waxen plinth]

yeah, but I'm imagining myself in a test position and I'm brute forcing all the combinations

that's kinda dumb

Imagine it's sec

[pliant cedar]

well if its a sec that is just a 1/cos

[waxen plinth]

$sec \theta = 2$

[ocean seal]

OceanBro

[pliant cedar]

btw prefix ur trig ratios with \

so \sec

[waxen plinth]

$\sec\theta = 2$

[ocean seal]

OceanBro

[waxen plinth]

Smart!

Thank you again

[vague mirage]

https://youtu.be/PF2nmCVSUEs

@waxen plinth

[pliant cedar]

if $\sec\theta=2$, $\frac{1}{\cos\theta}=2$, so $\cos\theta=\frac{1}{2}$

[ocean seal]

𝕾ilver𝕾oldier

[vague mirage]

I'm going to sleep

[waxen plinth]

$\frac{1}{\frac{1}{2}} \rightarrow \frac{2x1}{\frac{1}{2}} \rightarrow \frac{2}{\frac{1}{1}$
@pliant cedar correct?

[ocean seal]

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

[waxen plinth]

jesus

$\frac{1}{\frac{1}{2}} \rightarrow \frac{2x1}{\frac{1}{2}} \rightarrow \frac{2}{\frac{1}{1}}$

[ocean seal]

OceanBro

[waxen plinth]

omg my x

hm ok

I got it

Thank you!

.close

[lone heart]

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[alpine sable]

by checking records a carpenter find that joel can build a small shed in 12hr sam can do the same job in 16hr how long would it take if they worked together round yor answer to 2 decimal places

[alpine sable]

$\frac{t}{12}+\frac{t}{16}=1$

4t + 3t = 48

7t=48

t=48/7

=6.85

how do i get it into minutes

[quasi vector]

how did you get this equation

oh

should it be t in the numerator of both fractions?

then it's correct

[ocean seal]

okokok

[alpine sable]

yeah typo

[quasi vector]

well

you have it in hours

so

just multiply by 60

since there are 60 minutes in an hour

[alpine sable]

so 6.85 times 60 ?

[quasi vector]

yes

you could also

multiply before diving

48x60/7

[lone heart]

@alpine sable Has your question been resolved?

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[split tundra]

What does sigmaXi represent/mean

[split tundra]

[mint wadi]

sigma Xi is the sum of the observations from a sample of size n

from the description

[whole shell]

Xi are the data

So X1 , X2, X3..

[split tundra]

The context is central limit theorem

[whole shell]

Sigma Xi means summing up all these data

[split tundra]

Mm okay

Let me show the question

[whole shell]

Further stats 1 right? @split tundra

[split tundra]

Yeah

[split tundra]

I have a test this Wednesday on it

[whole shell]

What does this have to do with sigma Xi

[split tundra]

I think part c

The part I'm not 100% on is "if T 1150 then X_ 1150/60"

[whole shell]

It's because

T is for 1 hour

Or 60 minutes

In this case each minute is a sample size

[split tundra]

X bar is the mean value of T

[whole shell]

Yh

[split tundra]

So you're working out the mean

[whole shell]

Across 60 samples/minutes

[split tundra]

What does 1150 represent

sum of X?

[whole shell]

Sorta yh

[split tundra]

And then 60 is number of X or n

[whole shell]

n

[split tundra]

Yeah

Thanks

It makes sense now

Have a good day bro

.close

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[thorny raptor]

when i got a function to differentiate

[thorny raptor]

can i do the a^2+2ab+b^2 and then differentiate it?

is it possible?

[limpid spade]

?

[whole shell]

What is a and b?

[thorny raptor]

a formula

like

(a+b)^2

=

[whole shell]

Use x and y

[quasi vector]

yes

[thorny raptor]

a^2+2ab+b^2

[limpid spade]

That or chain rule

[whole shell]

Or do you mean a(x), b(x)

[thorny raptor]

that's the same

[quasi vector]

i think he means two expressions a and b

[limpid spade]

For (a+b)^n higher n values chain rule would be preferred unless u have time

[quasi vector]

like (x+2)^2

[thorny raptor]

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

[whole shell]

Implicit differentiation

Is what you're thinking

[limpid spade]

I don't think so

[harsh swallow]

You can first multiple out an expression and then take the derivative

You can try doing both

[thorny raptor]

yeah that's what i meant

[harsh swallow]

You will get the same thing

Afaik

Lemme try to make sure

You can

Although i imagine there are some crazy expressions where it wont work

[thorny raptor]

alright

thanks

🙏

[lone heart]

@thorny raptor Has your question been resolved?

[lone heart]

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[warped topaz]

https://i.gyazo.com/c1a8f04d319d27b821e7a42cfaa143f1.png

[warped topaz]

https://i.gyazo.com/6cf5bb235df9a9af4dcddbe5ad3cb51c.png

These are the questions and the answers to them

They said to use 'but' instead of 'and', but I forgot to do this, so for c) I put 'Today is Tuesday and its not belgium' and for d) I put 'You pass the final exam and you dont pass the course'

Do you think I would lose marks in an exam if I did this?

Like is it wrong because its not really natural English? Or is it ok because the sentence is technically correct?

[cedar hearth]

I think it's fine tbh.

I don't see the issue...I think.

[warped topaz]

Ok awesome!

Thats all I wanted to ask

Thank you!!

❤️

.close

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[alpine sable]

an airplane maintaining a constant airspeed takes as long to go 450 mi with the wind as it does to go 375 mi against the wind if the wind is blowing at 15 mph what is the rate of the plane in still air

[alpine sable]

$\frac{375}{x-15}=\frac{450}{x+15}$

[ocean seal]

okokok

[alpine sable]

375(x+15)=450(x-15)

375x+5625 = 450x-6750

12375=75x

x=165

so is that the final answer or do I need to write something else

.close

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[humble cedar]

Hey can you help me with this equation.
My teacher said that we should solve it by prove that the left hand side is greater or equal/ smaller or equal to a number and then do the same thing to the right hand side, then find x so that both side equal to that number
Can u help me solve that way

[lone heart]

@humble cedar Has your question been resolved?

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[tidal ingot]

if we have this matrix

[tidal ingot]

and we were given that trace of it is different than 1

is it possible to conclude that it is not invertible?

here is the full exercise, im trying to solve the second part

[mortal trellis]

multiply (I-A) times the RHS and check whether it is equal to I

[tidal ingot]

whats the RHS?

[mortal trellis]

right hand side

[tidal ingot]

Ohhh thank you

hmm where do we use part (a) tho

thats what confused me

oh wait got it where we use part A

but we first need to prove that A is not invertible to use part A no ?

can we do that from the trace?

[mortal trellis]

no

clearly trace(2*I)=4 is not 1

but 2*I is invertible

hmm

[tidal ingot]

yeah

[mortal trellis]

maybe they want casework, not sure

[tidal ingot]

in first part we proved that ad has to equal bc for it to be non invertible

because if it is det(A) = 0

at least thats how i did it

used contrapositive

for A^2 = (a+d)A ad has to equal bc

and if that happens its det is 0 so it is not invertible

[mortal trellis]

phrased like that technically you proved the other direction

not contrapositive

[tidal ingot]

i need to review my terminology

if p -> q, contrapositive is ~q ---> ~p no ?

[mortal trellis]

you proved A^2=(a+d)A => A not invertible

[tidal ingot]

ah

[mortal trellis]

contrapositive would be A^2 != (a+d)A => A invertible

[tidal ingot]

ic ic

[tidal ingot]

this is the inverse ?

ah its converse

i got it

i just got sent the solution

they did use part a like A is invertible

idk how they proved it tho its not written

[mortal trellis]

maybe they just assumed that A is again not invertible

but didnt write it into the question

[tidal ingot]

hm

thats weird since this is a previous exam

[mortal trellis]

badly written questions also happen in exams

[tidal ingot]

true

ig ill keep this open for another 10 mins or so if someone can bring in an input

[mortal trellis]

for A invertible the claim is false. again choose A=2I, then LHS is equal to -I, RHS is equal to 1/3 I

which is expected cause you proved that (a) is actually an iff

so if we try to use (a) then some part in that fraction will still be left over and it doesnt cancel cleanly

[tidal ingot]

hmm

its weird we will get A - A -A TR(A) +A TR(A)

so a 0

idk ill just skip over this one

ah wait we do need it a 0

so we get the identity

ah i get

[lone heart]

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[errant dagger]

I was also stuck on this question

[errant dagger]

for a is my method actually just to manually calculate

[errant dagger]

sorry gang

[lone heart]

Please read #❓how-to-get-help

[mortal trellis]

that's probably the intended way for (a)

and while doing it you get a feel for the sets A_k

[errant dagger]

and then for b is it just looking for a pattern?

[mortal trellis]

and then can do (b) more easily

[errant dagger]

for c i got no idea

[mortal trellis]

you hopefully will after doing b

[sage token]

sorry, may you know fuction

[errant dagger]

its like the biggest number from the previous

is in the next

[errant dagger]

find a new chat sorry mines been claimed and itll be way harder to help u

wait i think im fcuking stupid

lemme just do from the top

[ruby current]

compute the intersection of A1 and A7

[errant dagger]

zilch

{}

empty set

[ruby current]

yes

and intersecting more sets can only make the set smaller

[errant dagger]

wait why isnt b

the empty set

[ruby current]

i can give you an element in all of the sets in the intersection

90, for example, is in each of A_{10}, ... A_{90}

therefore 90 is contained in the intersection

[errant dagger]

yeaah

wait so there will be a point

where the highest number of A_(k-1) < the lowest element of A_(k)

@ruby current

in which there is no interesection anymore?

agh

i dont real,ly get it

[ruby current]

you can think of the sets as intervals of natural numbers

so (b) can be thought of as [[10, 105] \cap [11, 126] \cap [12, 149] \cap \cdots \cap [90, 8105]]

[ocean seal]

tushar

[errant dagger]

yeeap

ohhhhh

so

a_10 will not intersect with a_106?

[ruby current]

correct

[errant dagger]

ahhhhh i gotcha

that makes sense in my mind now

thanks vbery much for youe je;p[

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[lone heart]

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[chilly dove]

Can anyone help me do this question

[mint wadi]

@chilly dove

[chilly dove]

yes

[mint wadi]

notice that you can be able to find the distance between town p and town R

[chilly dove]

mhm

[mint wadi]

through "ella left ... at 60 mph" and "ella had traveled 3/5 of the journey"

and "at 10:30"

so that means that 3/5 of the journey takes ella 1h 30mins to complete in 60 mph

1h 30min = 1.5 h

60 * 1.5 = 90

[chilly dove]

mhm looks good

[mint wadi]

3/5 of the journey = 90km -> the journey is 150 mi long

and pablo is 10 mph slower -> pablo drives at 50 mph

[chilly dove]

mhm

[mint wadi]

and 150 mi will take him 150/50 = 3 hrs

and he left at 10:00

so it means he will reach town p at 1:00 pm

[chilly dove]

ahh ok let me reread what you wrote

[mint wadi]

hope this is helpful

[chilly dove]

yep it is

[mint wadi]

oh yes

[chilly dove]

ye

[mint wadi]

i use 150 mi when i calculated pablo's time because the distance between town p to town r is the same as town r to town p

[chilly dove]

oh ok

wait i have one more problem

[mint wadi]

so

let tony's average speed be x+15, and sumin's average speed be x

[chilly dove]

sounds good

[mint wadi]

so the total distance between a and b is equal to 3.5(x+15) = 3.5x+3.5*15
(5:00~8:30 = 3.5h, and recall distance = speed * time)

and sumin has traveled 3.5x

and sumin has traveled 3.5x (since sumin's speed is x)

so 3.5x + 3.5*15 - 3.5x = 3.5*15

(tony has reached town b already)

[chilly dove]

yep

[mint wadi]

so there u go

the answer should be 3.5*15

you understand how i got this?

[chilly dove]

yea

[mint wadi]

nice

good luck on your homework :)

[chilly dove]

thanks 🙂

[mint wadi]

hope these formulae help

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[lone heart]

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[steel carbon]

hi i need help with more 8th grade math

[steel carbon]

one step, two step and three step equations

[wild trail]

[steel carbon]

ok so in one step equation, the first question is
x + 5 = 12

[last ether]

Yeah

[lone heart]

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

[steel carbon]

what do i have to do in order to find the answer

[vale wigeon]

have you solved equations before, in general?

[steel carbon]

no we just started

[vale wigeon]

mkay

[last ether]

What did you do

To solve for x?

[steel carbon]

i haven’t done anything, since i don’t know where to start

[vale wigeon]

might want to (re)read your textbook on equations in general like conceptually

for a simple equation like this you can get your bearings a bit by rephrasing it as a question in plain english

"What number added to 5 yields 12?"

[steel carbon]

okay

7 ?

[vale wigeon]

correct

[steel carbon]

so x = 7 ?

[vale wigeon]

indeed.

you understand that this number could also have been found as 12 - 5, yes?

[steel carbon]

oh okay! but what if the number is a fraction

[steel carbon]

yes i understand now

[vale wigeon]

well it makes no difference if they're fractions or not

so long as they are things you can do arithmetic to (specifically addition and subtraction)

[steel carbon]

so y/4 = 9

i just have to find add and find the ans ?

[vale wigeon]

"find add and find the ans" is wonky at best and nonsensical at worst.

[steel carbon]

oh sorry

[vale wigeon]

maybe you should try rephrasing this other equation as a plain-english question as well

after you've managed to get your bearings on what equations are in general you may want to do some reading or video-watching on algebraic techniques such as "adding the same thing to both sides" or "multiplying by the same thing on both sides"

khanacademy has a decent set of lectures about this and others

[steel carbon]

okay!

i’ll reread my text book then

i think I’ll be able to handle it from here by myself

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[lone heart]

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[alpine sable]

i tried doing it with l'hospital but its really painful

[long axle]

Hmm, it doesn’t look that painful

Could u show ur work

[alpine sable]

Sure

I haven't done the denominator cuz it's just ridiculous

And the numerator still yields 0

[wind cloak]

Split the limit first I suppose

[alpine sable]

I did that too

[wind cloak]

Ah yeah you did

[alpine sable]

Nono not here

I tried it like just now