help-33

[novel juniper]

it should be -20

not +20

[ebon depot]

but the online calc det -1

oh

[novel juniper]

I think you've made a few mistakes in the second part too

might want to recheck the entire thing

[ebon depot]

Yeah i give up on that now lmao

-1/7 is the det(A)

so

$\frac{1}{-\frac17}$

[elfin berry]

Merineth

[novel juniper]

||so -7||

[ebon depot]

yeah haha

For my final question

Determine t so that the vectors are all linear independent

doesn't this just mean that

They all only have one solution for the linear combination

that LC = 0

If i write it as a Gaussian elimination

[novel juniper]

I don't know Guassian elimination, sorry, I can't help

[ebon depot]

Okii no worries

[novel juniper]

ok, basically a set of vectors is said to be linearly independent if $v1+v2+v3+v4 \neq 0$

[elfin berry]

Why am. I here

[ebon depot]

Really?

[novel juniper]

wiat

[ebon depot]

It should be = 0 iirc

[novel juniper]

not that

[ebon depot]

$c_1f_1 + c_2f_2 + c_3f_3 + c_4f_4 = 0$

[elfin berry]

Merineth

[ebon depot]

Should be like so right?

Where c is a multiple constant and f_1... f_4 are the vectors

[novel juniper]

that's not 0

not =0

read the defn again please

If there exists no linear combination of vectors that equals teh 0 vector

[ebon depot]

No?

https://youtu.be/X84BzPED3eU?t=163

this guy says

the vectors

u v and w are linear independent if it equals 0

[novel juniper]

ok, I must be misunderstanding something, sorry

go ahead

[ebon depot]

So essentially can't this be written up as gaussian elimination and solve like normal

i'm not sure however

how to determine t

[novel juniper]

ping helpers IMO,you posted your question 25 min ago

[ebon depot]

<@&286206848099549185>

Helpers don't exist

[safe spear]

english pls

[sand fable]

they posted translation

[safe spear]

where?

[ebon depot]

[sand fable]

this is correct

[ebon depot]

But how do i proceed from here?

I got this essentially from the vectors

do i just try and get 1:s from top left down to bottom right

[sand fable]

actually has your class covered properties of matrices yet

[ebon depot]

We don't have a teacher but i would assume that we are past that part of matrices

What properties are you thinking of?

[sand fable]

that the columns of an invertible matrix (i.e. a matrix whose determinant isn't 0) are linearly independent

[ebon depot]

I did not know that

[sand fable]

hm

[ebon depot]

I assume this is essentially what you mean?

.close

[marsh citrus]

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[sinful thistle]

@vapid estuary how old are you

also

<@&268886789983436800>

[marsh citrus]

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[sinful thistle]

LMAO

[vapid estuary]

Snitch

[sinful thistle]

@viscid flame check logs, he was trolling

[stoic slate]

Mods can see deleted mesages btw

[vapid estuary]

Well

[vapid estuary]

Ok

A question is a question

And if u can't answer then that's trolling

[sinful thistle]

LMAO

worst comeback possible

[vapid estuary]

<@&268886789983436800> this guy harassed me for asking question

[wheat rover]

guys, don't waste your time here

[vapid estuary]

.close

[sinful thistle]

lmfao

[sinful thistle]

nah i just love seeing trolls get rekt

[vapid estuary]

You're the one getting rekt

[sinful thistle]

it's rather entertaining

[vapid estuary]

Delulu

[sinful thistle]

fr fr

[wheat rover]

that also works ig

[vapid estuary]

Fighting over a math question

Must be smoking meth

[sinful thistle]

bro fr tried to DM me and cuss

as a wise man once said "mad bc bad"

<@&268886789983436800> ??

^^

check logs

[wheat rover]

even moderators don't wanna waste their time in this shit

[marsh citrus]

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[halcyon crown]

Send what you have done for someone to verify if you need that

[wary eagle]

do i send it in this chat?

[halcyon crown]

Yes

[wary eagle]

oke is a pdf file fine

or

ss?

[marsh citrus]

@wary eagle Has your question been resolved?

[marsh citrus]

@wary eagle Has your question been resolved?

[marsh citrus]

@wary eagle Has your question been resolved?

[feral stratus]

<@&286206848099549185> help this human

[wary eagle]

its quite a lot

so

i think ive done it a bit shit

[feral stratus]

I don't understand a single thing

[wary eagle]

😭

[feral stratus]

What course is that

[wary eagle]

probability

bayesian risk and decision making

[feral stratus]

Oh hell naw

Haven't even learned limits

[wary eagle]

[feral stratus]

[main idol]

don't ping helpers for other people

[feral stratus]

tryna help but ok

[marsh citrus]

@wary eagle Has your question been resolved?

[marsh citrus]

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[twilit arrow]

what is the question

[uneven sparrow]

2nd one

[twilit arrow]

what is your question

[uneven sparrow]

How do u expand this

[marsh citrus]

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[uneven sparrow]

[marsh citrus]

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[quick shard]

Hi. currently working on midpoints and I got a fraction as a midpoint of this question, how would i plot this?

[quick shard]

i got 11/2, 0

double check if I am correct as well

[fathom sun]

That is correct

[quick shard]

so how would I plot that?

[fathom sun]

Give me one second

[quick shard]

take your time

[fathom sun]

This is the triangle, right?

[quick shard]

L has a point of 7,3

[fathom sun]

Yea thats where it's at

[quick shard]

oh yea, whoops

yea then it's correct

[fathom sun]

So to find the median, we have to find the midpoint, which you already did

(5.5,0)

So we can just plot that

Understand?

[quick shard]

yup, my teacher just doesn't like decimals

[fathom sun]

Then you can convert to fraction

(11/2,0)

[quick shard]

i see

[fathom sun]

So we get this

[quick shard]

alrighty

[fathom sun]

Now, we just have to find the equation of the line that passes through K(-1,-2) and (11/2,0)

[quick shard]

yea, im gonna solve that real quick and get back to you

[fathom sun]

ight ight

[quick shard]

ok so, i got y= 4x-6

my original equastion to get b was -2=4(-1)+b , then i added 4 to both sides but i think thats where i messed up

[fathom sun]

hmm

[quick shard]

haven't masterd that yet because i dont quite understand it

[fathom sun]

your points are (-1,-2) and (11/2,0)

what is your slope?

[quick shard]

i got -6

[fathom sun]

what is the slope formula?

[quick shard]

y=mx+b

[fathom sun]

thats the equation of a line

the fomula for slope is $\frac{y_2 - y_1}{x_2 - x_1}$

[elfin berry]

Dork9399

[fathom sun]

Plugging in the values, we get that slope is (0 - (-2))/(11/2 - (-1))

[quick shard]

uh, for that i wrote m= y2-y1/x2-x1

[fathom sun]

yea

so what is m?

[quick shard]

oh my god

lmao, i forgot b was the intercept

m is the slope

so for my slope i got 4

[fathom sun]

show your work

(plugging into the formula and simplifying)

[quick shard]

m=3-7/-3-4
= 4/-1
= 4

[fathom sun]

What two points are we trying to find the equation of?

[quick shard]

medien of k (-1,-2)

[fathom sun]

So we are trying to find the slope of the line that has the points (-1,-2) and (11/2,0)

[quick shard]

yes

[fathom sun]

so we plug in $y_2 = 0, y_1 = -2, x_2 = 11/2, x_1 = -1$

[elfin berry]

Dork9399

[fathom sun]

understand why?

[quick shard]

i think so

[fathom sun]

Which gives us m as 4/13

Now attempt to find b by yourself

[quick shard]

ok

just wanna double check my equastion 0= 4/13 (11/2) +b

[fathom sun]

yes

[quick shard]

and if thats correct do i find the lcd of the fractions?

or no i dont cuz its multiplication

b= 44/26?

[fathom sun]

you have that 0 = 4/13 * 11/2 + b

which simplifies to 0 = 22/13 + b

So what is b?

[quick shard]

why does it turn into a -?

oh

b= 22/13?

[fathom sun]

How?

[quick shard]

becuase that's the only thing that's left

[fathom sun]

If b = 22/13, will the equation 0 = 22/13 + b be satisfied?

[quick shard]

oh, no

do i add something to both sides?

[fathom sun]

what happens when you subtract 22/13 from both sides?

[quick shard]

22/13 cancels out

and the 0 becomes a negative

-22/13

therefore -22/13=b?

[fathom sun]

yay!

So what is your final equation?

[quick shard]

y= 4/13x+-22/13???

[fathom sun]

What did we say m was?

[fathom sun]

^

still wrong

[quick shard]

there we go

[fathom sun]

you don't need the "+-" but its fine

Good Job!

[quick shard]

ok i need to practice that, but, i got one more question, how does adding and subtracting on equastions work

like when we tried to figure out b

we cancelled out 22/13

and how would i know when to add or subtract

[fathom sun]

If the sign of the term is positive, then you would do the inverse operation, which is subtraction

If it is negative, you would do its inverse, which is subtraction

[quick shard]

which would cancel it out

ok, got it

thank you so much

hope you have a good rest of your day

.close

[marsh citrus]

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[limber merlin]

Question 21 d. Idk what to do...

[marsh citrus]

Please don't occupy multiple help channels.

@limber merlin Has your question been resolved?

[marsh citrus]

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[austere scroll]

How would I solve for tan(pi/2)

[austere scroll]

All i really know is sin/cos = tan

[nova totem]

Do you know sin(pi/2) and cos(pi/2)

[austere scroll]

No

Well

[nova totem]

Use the unit circle.

[austere scroll]

I think that would be

0,1

Because half of it would be like 1pi

And so pi/2

Would be inbetween first and second

[nova totem]

Yeah.

[austere scroll]

Ok.

[nova totem]

But sin(pi/2) is not 0

And cos(pi/2) is not 1

[austere scroll]

Well

[nova totem]

You flipped them

[austere scroll]

Yea

I was gonna say that.

[nova totem]

So tan(pi/2) = sin(pi/2) / cos(pi/2)

= 1/0

Which you know cannot happen

[austere scroll]

undefined

[nova totem]

Yup

[austere scroll]

Yes

Yay

Thank you umbraleviathan!

Is it ok to use unit circle to solve things? I feel like its kinda cheating

Idk

[nova totem]

I mean

It's allowed

I don't see why

[austere scroll]

Ok

Idk how my teacher feels

LOL

[nova totem]

I don't use it because I like my 45-45-90 and 30-60-90 triangles

[austere scroll]

Oh

[nova totem]

Like the unit circle's kinda messy

[austere scroll]

I like those too!

[nova totem]

I hate it

I have a smooth brain

Fuck using the circle

But I mean up to you

[austere scroll]

Ummm one more thing

[nova totem]

Ye?

[austere scroll]

So sin(pi/3)

How would i use 306090

ok the hypotenuse would be 1

[nova totem]

Well pi = 180°

So pi/3 is 60°

[austere scroll]

short side is x

hypotenuse is 2x

and medium side is

um

Wait

its like sqrt

xsqrt3

[nova totem]

Yeah

You know the hypotenuse is 1, or rather, you said it was 1

The radius of the circle doesn't matter

The hypotenuse could be anything

[austere scroll]

Okok

[nova totem]

It's easier if it was 2

[austere scroll]

I think i got it

[nova totem]

But going with your 1

Then you'd have 0.5 sqrt(3)

[austere scroll]

Yee

Which is like 1/2*sqrt3/2

And if u multiply its just

wait

sqrt3/1*

So like

Yeah

[nova totem]

Ye

[austere scroll]

sqrt3/2?

[nova totem]

Ye

[austere scroll]

Ok

Thank u

and sin of that would be\

y value

so 1/2?

[nova totem]

Well no

[austere scroll]

Oh

god

[nova totem]

sin(pi/3) is sqrt(3)/2

You already had it

[austere scroll]

sin(pi/3)

1/2?

No?

God

[nova totem]

Sin is opposite/hypotenuse

It is not just the y

[marsh citrus]

@austere scroll Has your question been resolved?

[marsh citrus]

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[wicked crystal]

why does it not equal to $32+4-(-4)$

[elfin berry]

Katanapultti

[wicked crystal]

where do they zeroes come from

[hard gull]

3i + 4j can be written as 3i + 4j + 0k
same with 2i - 4k

[sinful thistle]

because

^^

it's j and k not j and j

[wicked crystal]

ohh that's right

didnt realize hmm

.close

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[velvet elk]

a woman has 12 close friends, im how many ways can she invite 6 of those friends to diner if 2 of them refuse to attend together

[velvet elk]

Can someone help me with this one?

[steel sluice]

wow i have seen the exact same question before

[velvet elk]

can you guide me with this one?

it's a combination one I think

[steel sluice]

yea it is

[steel sluice]

so divide it into 3 cases
when first woman is invited
when 2nd is invitd
when both are not invited

or easiier than this wud be total cases (12C6 ) - cases when both are inviited (2C2 X 10C4)

[velvet elk]

.close

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[bold burrow]

is it possible to pinpoint the exact location of their cross in desmos?
I need the exact value, desmos tells me non-accurate, rounded one

[bold burrow]

https://www.desmos.com/calculator/d38hweude7 graph link

[marsh citrus]

@bold burrow Has your question been resolved?

[marsh citrus]

@bold burrow Has your question been resolved?

[marsh citrus]

@bold burrow Has your question been resolved?

[still temple]

<@&286206848099549185>

[vast grail]

Actually, the one you are looking for is a irrational, non-repeating decimal value.

You can approximate it, but not find the actual value

Or you could use a CAS (Computer Algebra System)

[bold burrow]

thanks for the answer, I guess I just shouldn't mess with factorials haha

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[blissful terrace]

i found it makin a triangle

And the r is at 60°

So i can apply cosine rule in the shorter triangle

r, r-i and i

which gives

and r-i square is the given condition

geometric mean

but somehow this is giving wrong answer

@slate halo u gotta see this i found this dope way by cordinate but its not working for some reason idk

But its not workin

The cosine rule is satisffying for both triangle but when i apply the geometric mean codintion

It gives again r = -1

Ah i think i just made it complex

[slate halo]

uh i don't quite understand ur method

oh okay i understand nvm

well it should work tho xD
maybe calc error

[blissful terrace]

yee it does

had to square both sides

Made it complez

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[vital cypress]

help

[vital cypress]

Hi how do i evaluate

i dont understand

[woven sky]

Sin double-angle formula?

[vital cypress]

what

its actually a formula for projectile motion horizontal range

[wheat rover]

sin(2x)=2sinxcosx

[vital cypress]

is that a formula

[wheat rover]

yes

the double angle formula

the v is just multiplied separately

[vital cypress]

yeah

[wheat rover]

done?

[vital cypress]

ok i think thats all for now

thx everyone

.close

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[lyric kelp]

does tan^2 (x) = sin^2(x) / cos^2(x)

[steel sluice]

tanx = sinx/cosx

square both sides

[lyric kelp]

ah so it is

okay ty

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[shell yoke]

haii im confused should i be using 2 for a?

[main idol]

draw a picture

[shell yoke]

do i find the area between -4 and 2?

[main idol]

-infinity and 2

but by paritioning, i think they mean -infinity to 0, then add that to the area between 0 and 2

the second one is much easier than the first

[shell yoke]

so should i integrate by parts and for one do -inf to 0 then 0 to 2 then add it

[main idol]

no integration by parts is needed for either

integral (2e^x) dx = 2 * integral (e^x) dx

and uhhhh, area of triangle is 1/2 * base * height

[shell yoke]

LOL

bye

that went over my head

[shell yoke]

so is the final answer 2\int (e^x) dx + 2

[main idol]

well the integral converges to a number

you don't need integration by parts, but you do need to integrate

[shell yoke]

i got 2e^2

[main idol]

that's a no

,w 2 * int -inf to 0 e^x dx

[elfin berry]

Results provided by WolframAlpha

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

Requested by rie.mann

[shell yoke]

aw man

so shouldnt it be

2 + 2

but

4 is wrong

[main idol]

i messed up

you want that area above the green and below the blue

i missed this

try finding the intersection and use that in your limits and then set up the integrand with those limits

[shell yoke]

oh

well

honestly idrk what that means so ill try

.close

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[hardy smelt]

If the scalar product is not the usual one, does the norm change?

[hardy smelt]

In other words is the norm dependant on the scalar product?

[static quarry]

yes

in an inner (scalar) product space, the norm induced by the inner product is ||x|| = <x,x>

er, square root of that

so it is completely dependent on the inner product

[hardy smelt]

Damn

Ty

.close

[marsh citrus]

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[marsh citrus]

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[sharp gull]

Can someone help?

[marsh citrus]

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[south goblet]

this should be 4 right?

[south goblet]

this is the question

[crimson osprey]

could you guys help me?

please?

[main idol]

!1c

[marsh citrus]

Please stick to your channel.

[crimson osprey]

no one is ansewring me

[main idol]

!vol

[marsh citrus]

Helpers are just people volunteering their time to help you. Be polite and patient.

[main idol]

do you know what R is in eqn (b)

[south goblet]

well I drawed it

and I think it should be the same lket me double check

[main idol]

same as D?

[south goblet]

ye I think so but let me check agian

so if u put in x = -u and y = -v

the requirements stays the same right?

[main idol]

oh yes it does stay the same

so R = D

[main idol]

yea that red underlined 2 should be a 4

[south goblet]

my second question is how do u know the substiution x = -u and y = - v works

[main idol]

works for what

[south goblet]

like to solve this

how do u know it will work outt

like I wouldn't come up with this substiution

what would the thought process be finding the substitution

[main idol]

then memorize it and redo the problem again and repeat until you can

[south goblet]

so like this is a trick I gotta memorize?

[marsh citrus]

@south goblet Has your question been resolved?

[marsh citrus]

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[worldly dome]

Can someone tell me what I did wrong the first time I tried to solve this problem

The first time I made u = sin2theta and turned cos^2 into (1-sin^2)

The 2nd time I made u= cos theta and directly got the answer

[shy gust]

Reading

Ok, so

If you make u = sin, then du is cos.. but du only takes care of one of your cos

And yeah, you can use trig identities to get rid of the rest

[worldly dome]

Yea that’s what I did?

I isolated 1 cosine

Then I turned the cos^2 into 1-sin^2

[shy gust]

keeps reading - Bear in mind, the answer you get will differ from the "textbook" answer when you opt for a different u sub

But "different" is not necessarily wrong

(unless there were other instructions that specified which u sub you should make)

So.. why was your first answer marked wrong? Do you know?

Or is this a website/program that just spits back "correct"/"incorrect"?

[worldly dome]

Just checked on mathway and they are not equivalent

Oh I got this problem from a text book

I used integral-calculator.com to check my answer

[shy gust]

integral-calculator is good, but sometimes it goes in really weird directions

Are you aware of https://www.symbolab.com/solver/integral-calculator

[worldly dome]

Yea I had that experience before

[shy gust]

Also free.. I tend to use them in tandem

[worldly dome]

I never used symbolab before

[shy gust]

O

I'm not seeing anything that's jumping out as incorrect, tbh

to be fair, though? I run into this as well.. I pick a different u-sub that should be valid, and my end result is considered incorrect

it's infurating and without a clear pattern, it's hard to figure out why it's wrong

[worldly dome]

Yeah

Like if I got the wrong answer there should be a point in my work that I could identify as incorrect

[shy gust]

sometimes integral-calculator has the option of choosing a different u-sub in the Steps

Did it offer that for you on this one? Or do you recall?

Oh, look at that

That is a valid solution

So don't beat yourself up too much, eh

If you're wondering how it "simplified" the original input, it looks like double-angle formulae

@worldly dome

[marsh citrus]

@worldly dome Has your question been resolved?

[marsh citrus]

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[minor verge]

someone help please

[minor verge]

im so lost

[whole sleet]

I suggest constructing change of basis matrices. Let's start with a matrix that takes a vector with coordinate B, and moves it into coordinate E

(1,0) in B, is the same as (2,3) in E

Can you construct that change of basis matrix? Or should we focus on this part

(Where I'm using E as the standard basis, as the question seems to)

[minor verge]

wouldnt we want it to happen the other way though?

cuz we have [S]_EE

[whole sleet]

You're correct, we would!

It's pretty easy to go the other direction after we have it, though

Just take the inverse

And the change of basis from B to E is pretty easy to get here

[minor verge]

oh ok right
so we would have the matrix
2 3
3 5

for E to B right?

[whole sleet]

Bingo

The inverse of that is then a change of basis from E to B

[minor verge]

right

that makes sense

idk what to do freom there though

i got
5 -3
-3 2

as the inverse

[whole sleet]

[S]B,E should take a vector in B, and output a vector in E.

We instead have [S]E,E, which takes a vector in E, and outputs a vector in E.

We can replicate [S]B,E by first taking a vector in B, moving it to E, then performing [S]E,E on that

Actually wait, does [S]B,E take a vector from B, and outputs in E? Or am I mixing that up? I always forget how this notation works

[minor verge]

yeah im pretty sure thats hwat it is

[minor verge]

oh

yeah that make ssense

[whole sleet]

Anyway if I'm right, then
[S]B,E = S[E,E]M(B,E)

[minor verge]

M(B,E)?

[whole sleet]

Where M(B,E) is that change of basis matrix

[minor verge]

oh

ohhh

[whole sleet]

There's definitely a better notation you should be using

[minor verge]

wait so would this just work for anything like
[S]A,C = S[E,E]M(A,C)?

a c are just random bases

[whole sleet]

No. Acting with the change of basis matrix on the right will change the origin basis

[minor verge]

wait what

then how would we do something like part c where there is no E

[whole sleet]

So [S]A,C = S[B,C]M(A,B)

As M moves from A to B, and S[B,C] moves from B to C

[minor verge]

ohh

[whole sleet]

Creating a new matrix that has the exact same info as S, but moves from A to C

Then post-multiplying can change the destination basis

Wait mb, I am lying directly to you.

I apologize, it's been a while

You will still need to compute the change of basis matrices, but you'll use that formula instead

[minor verge]

yeah i just tried it on this
for practice,cuz i have the answers to this one
but i got somehting different from the answer

[minor verge]

could u explain what that formula means? if possible? cuz i dont really get it

the answer to get S_BE
seems to just be S_EE* matrix B where each column is the basis in order

idk though

[whole sleet]

,w matrix multiply {{0,1},{3,-3},{4,-8}}*{{5,-3},{-3,2}}

[elfin berry]

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Requested by kaynex

[whole sleet]

Yeah that doesn't seem right

[minor verge]

no because the bases are different int this question

5 -3
-3 2 isnt for this question

for paart a i did

,w matrix multiply {{0,1},{3,-3},{4,-8}}*{{2,1},{1,1}}

[elfin berry]

Results provided by WolframAlpha

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Requested by notshrey

[minor verge]

bbut idk why it works

[whole sleet]

That's just:
S[E,E]M(B,E)

Which is S[B,E]

I was right the first time lol. Oof.

[whole sleet]

You'd follow this when you want to change S[E,E] to S[B,B]

But we're not doing that here

[minor verge]

i dont see how i would do like
S[E,E] to S[E,C] though

[whole sleet]

S[E,E] takes a vector in E, and produces a new vector in E.

S[E,C] takes a vector in E, and produces that new vector, but in C.

We can mimic S[E,C] by producing the new vector with S[E,E] and then move it to C with M(E,C).

That's just:
M(E,C)S[E,E]

Remember of course that matrix multiplication counts from right to left. You should think of S acting first, M acting second

[minor verge]

,w matrix multiply {{1,0,1},{3,2,0},{0,3,-4}}*{{0,1},{3,-3},{4,-8}}

[elfin berry]

Results provided by WolframAlpha

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Requested by notshrey

[minor verge]

but thats not the right answer

[whole sleet]

That's M(C,E)

[minor verge]

ohh

[whole sleet]

You'll need to get the inverse of that left one

[minor verge]

,w matrix multiply {{-8,3,-2},{12,-4,3},{9,-3,2}}*{{0,1},{3,-3},{4,-8}}

[elfin berry]

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Requested by notshrey

[minor verge]

ohhhh

ok that works

thankj you sooo much

[whole sleet]

Does it make sense? Haha. I'm admittedly poor with change of basis notation, you might want to look through your notes for what M(A,B) should be called

[minor verge]

wait but isnt that E,C?

why it is C,E

[whole sleet]

(1,0,0) in C is the same as (1,3,0) in E

So the change of basis matrix from C to E, when acting on (1,0,0), should produce (1,3,0)

The matrix you made does this. It's M(C,E)

[minor verge]

oh i see

[minor verge]

do you think you could explain why M(E,C)*S(E,E) gives S(E,C)?

[whole sleet]

This is that. Have any questions about this explanation?

[minor verge]

OHHH wait i see, i wasnt treating them as linear maps so i was getting confused

thgis is true right

c is a matrix that takes bases in C and makes them to E

wait no it takes E and makes them C

[whole sleet]

It's handy to think of each vector as "carrying its basis information" and each matrix here changes that basis

[minor verge]

wait

if we take C is a matrix that takes values in E and converts them to c
to find [S]EC
wouldnt we have
C * S = S

why would it be the inverse

@whole sleet

[minor verge]

isnt it EC because ur that*a vector in E gives the same vector in C

?

[whole sleet]

C is a matrix that takes values in C, converts them to E

Assuming you mean C as "the basis vectors of C, but aligned into a matrix"

[whole sleet]

I personally just do this every time to reason out which direction a matrix goes

Like, if I want to ensure I have M(A,B), I think about what (1,0,0) in A would be when converted to B

[minor verge]

oh i had this the wrong way in my head

[whole sleet]

That should be the first column in the matrix

[whole sleet]

It's very easy to mix the directions haha

[minor verge]

OHHH its all starting to make sense now

thank you soooo much

[marsh citrus]

@minor verge Has your question been resolved?

[marsh citrus]

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[warm knoll]

how to do number 7

[warm knoll]

it does not have fl or gl

[wheat rover]

find ke by doing ge - gk

[warm knoll]

yeah i got 3

idk how to do the gf=25

cause thats the whole side

[wheat rover]

take gl = 25-x

[warm knoll]

i got 75-3x=12LF

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[ocean lily]

I did the first part

and computed the partial derivative with respect to y to try and find the Lipschitz constant

But I don't know how to find the sup of the mod of the partial derivative as the domain hasn't been specified

[marsh citrus]

@ocean lily Has your question been resolved?

[ocean lily]

<@&286206848099549185>

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@ocean lily Has your question been resolved?

[main idol]

looks like you have to find the rectangle using t=0 and y=1

i suppose you can find the behavior of the solution for small t >0 for y(t)

[marsh citrus]

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[maiden latch]

this is not a subspace because it's not linearly independent right?

[main idol]

try u = (1, 1, 0), v = (0, 1, 1)

[maiden latch]

in what form? I don't really know what to do with those or where to put/subsitute

[marsh citrus]

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[spark vale]

hey can someone help me with the first question? the second pic is all the new identities we learned today but i have no idea how to apply them

[stark trail]

So since the problem says without a calculator, you're going to need to get it into the form of something on the unit circle

that you know of

right?

[glossy flint]

You have 1 - 2sin²x as one of your formulas, use that

[still temple]

you should be able to do it with 1-sin^2 x = cos^2 x and cos(x)cos(y)-sin(x)sin(y) = cos(x+y)

[spark vale]

so first cos2x(22.5) ?

[glossy flint]

Yes

That's cos(45°) which is a well known value

[spark vale]

wait why 45

[glossy flint]

2 × 22.5° = 45°

Because 1 - 2sin²(x) = cos(2x)

[spark vale]

oooh

okok

ok so cosx(45)

then would one value be rad2/2

[glossy flint]

Yes

[spark vale]

it says it's wrong when i put it in ?

[glossy flint]

Well, I don't know why they have two boxes for the answer, maybe put it on the box below

[spark vale]

oh the bottom box is right but the top no

oh i got it

it wanted cos(45)

[glossy flint]

Very weird, maybe on the top they want you to type cos(45°)

[spark vale]

okokawesome

[glossy flint]

Right, I just figured it out now lol

[spark vale]

tyyysm

[glossy flint]

You're welcome

[spark vale]

.close

[marsh citrus]

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[spark vale]

.reopen

[marsh citrus]

✅

[spark vale]

ok idk if you're already gone but i have another question😭😭

how do i start this ?

[glossy flint]

Remember what csc is, from that you can calculate the values of sin(x) and cos(x), hence the value of tangent

And finally using double angle formula for tangent, tan(2x)

[spark vale]

oh so cos is 4 and sin 3

[glossy flint]

Nope

[spark vale]

oh

😭

OH

[glossy flint]

How can they be greater than 1 ?😅

[spark vale]

csc is 1/sin ?

[glossy flint]

Yes

[spark vale]

i got it mixed up with cot 😭😭

wait so how do i use that to find sin and cos

[glossy flint]

Even if it was cot, you couldn't say that sin is 3 and cos is 4

[spark vale]

ooh okay

wait so if csc is H/O, do i js draw a triangle relative to x

like

[glossy flint]

Well, sin(x) = 3/4 do you agree? (By definition of csc)

[spark vale]

yes

[glossy flint]

No you don't need to do it

[spark vale]

okok

[glossy flint]

Ok, so cos(x) would be what?

Remember the fundamental relation btw sin and cos

||sin²x + cos²x = 1||

[spark vale]

ooh right

so 1-(3/4)^2 is cos^2x ?

[glossy flint]

Exactly

[spark vale]

okok

then is tan (3/4) / (1-(3/4)^2)

[glossy flint]

No, wait

[spark vale]

😭

[glossy flint]

You have cos²x = 7/16

So cosx is either √7/4 or -√7/4, right?

[spark vale]

oh wait

[glossy flint]

Which one do you choose? Given that the angle is in the 1st quadrant

[spark vale]

wait where did you get 7/14

/16*

[glossy flint]

Square root of 7/16

$\sqrt{\frac{7}{16}} = \frac{\sqrt{7}}{4}$

[elfin berry]

Alberto Z.

[spark vale]

wait but where'd you get 7/16

[glossy flint]

From $1 - {\left(\frac{3}{4}\right)}^2$

[elfin berry]

Alberto Z.

[spark vale]

ooooh ok i js got it

why'd you square root 7/16 ?

oh cause cos^2x = 7/16

[glossy flint]

Exactly

[spark vale]

is it rad7/4 ?

[glossy flint]

Yes right 👍

[spark vale]

ok so that's cos

[glossy flint]

So now know both sin and cos, hence we can find what tanx is

[spark vale]

(rad7/4) / (3/4) ?

wait opposite

3/4 / rad7/4

[glossy flint]

Yep

Simplifying the 4s we have: $\tan(x) = \frac{3}{\sqrt{7}}$

[elfin berry]

Alberto Z.

[spark vale]

right

[glossy flint]

Now, recall that $$\tan(2x) = \frac{2 \tan(x)}{1 - \tan^2(x)}$$

[elfin berry]

Alberto Z.

[spark vale]

so is it tan(3/4 / rad7/4) or tanx=3/4 / rad7/4 ?

[glossy flint]

The second one

[spark vale]

okok

so would the thing be 2(3/4 / rad7/4) / 1 - (3/4 / rad7/4)^2

wait pretend the fours aren't there

[glossy flint]

Therefore you have: $$\tan(2x) = \frac{2 \cdot \frac{3}{\sqrt{7}}}{1 - {\left( \frac{3}{\sqrt{7}} \right)}^2}$$

[elfin berry]

Alberto Z.

[spark vale]

right

ok let me try to simplify it

is rad7 times rad7 rad 14 ?

wait

is this right so far

[glossy flint]

Which is: $$\tan(2x) = \frac{\frac{6}{\sqrt{7}}}{1 - \frac{9}{7}}$$

[elfin berry]

Alberto Z.

[spark vale]

why did the rad 14 become 7 ?

[glossy flint]

Because it's not rad 14

[glossy flint]

There's no 14 here

[spark vale]

OH

the square root and squared cancel out

ok

then does the denominator become -2/7

[glossy flint]

Yep

So in the end: $$\tan(2x) = \frac{6}{\sqrt{7}} \cdot \frac{-7}{2} = -3\sqrt{7}$$

[elfin berry]

Alberto Z.

[glossy flint]

And this should be the final answer, unless I did some wrong calculations

[spark vale]

yes that's correct

tysm

.close

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[rustic fox]

i have determined the distance travelled is 4 meters by integrating Vx and putting it into the Y and solving for the triangle, but i am stuck on the acceleration

[marsh citrus]

@rustic fox Has your question been resolved?

[marsh citrus]

@rustic fox Has your question been resolved?

[rustic fox]

<@&286206848099549185>

[marsh citrus]

@rustic fox Has your question been resolved?

[marsh citrus]

@rustic fox Has your question been resolved?

[marsh citrus]

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[waxen nest]

Help plz

[marsh citrus]

No need to ask “Can I ask…?” or “Does anyone know about…?”—it’s faster for everyone if you just ask your question! See https://dontasktoask.com/

[waxen nest]

I keep getting 49kg*m/s opposite to direction of travel

I think im right

Answer key is 3.5*10^2

Plz double check for me

[steel sluice]

yea shud be 49

[waxen nest]

Alr awesome thx

[steel sluice]

but really i wish i cud feel an exact numerical value of coeff of friction just while walking

[waxen nest]

?

Wdym

[steel sluice]

no the questions says the person was able to feel the coeff of friction was exactly 0.05 between the ice and skates which is funny

[waxen nest]

O lol

I see

.close

[marsh citrus]

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[sinful thistle]

the heck

[marsh citrus]

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• After 15 minutes, feel free to ping <@&286206848099549185>.
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• 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.

[copper comet]

Is there a fast way to simplify a fraction?

[sinful thistle]

??

as in

like give me an example

[copper comet]

Ive got a question that tells me to simply a fraction

[sinful thistle]

@copper comet how old are you

[copper comet]

but im not sure how ill simplify it

13

[sinful thistle]

grade?

[copper comet]

9

[sinful thistle]

(just asking)

...

send

!xy

[marsh citrus]

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

[copper comet]

uh wait rq

[sinful thistle]

probably rationalisation

[copper comet]

for example 42/100

its a simple number

[sinful thistle]

...

how is that 9th grade mathematics

[copper comet]

But i dont know the technique to do it

[sinful thistle]

...

42/100 = 42 bits out of 100 bits

[copper comet]

i was never taught this

[sinful thistle]

that's simply not possible

but i won't judge

[copper comet]

but u can do 21/50?

[sinful thistle]

yes

[copper comet]

thats what im trying to ask

coz surely thats not the simplest form

[sinful thistle]

that is...?

[copper comet]

bro

[sinful thistle]

@copper comet are you really in 9th

[copper comet]

wait

wait

[sinful thistle]

please answer honestly

[copper comet]

ok what about this

19.9% rec

im simplest fraction

[sinful thistle]

?

[dire spire]

how are you 13 and in 9th grade

[sinful thistle]

might have skipped one, is fine i did too

[copper comet]

well, in my country its years

year 9 i think is grade 8

idk

[copper comet]

but still

19.9% rec how am i supposed to know what it is in simplest form

[sinful thistle]

what is rec?

[copper comet]

reoccuring

[sinful thistle]

oh i see

[copper comet]

its in one of the questions

[sinful thistle]

so 19.9999999999.../

show me, please

[copper comet]

but what if there was a simpler form

[sinful thistle]

!xy

[marsh citrus]

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

[delicate sphinx]

u cant simplify 21/50

[copper comet]

bro ffs

ik, but how am i suppsed to know if its simplest form

thats just a example question

if its alot bigger, im asking how im supposed to find if its the simplest form

im not allowed a calculator

[sinful thistle]

my god

factorization is a thing

you do realize

[delicate sphinx]

if u cant devide both numbers with a same different number its the most simplified form

[sinful thistle]

example

[copper comet]

oh i see

[sinful thistle]

@copper comet could you show me the question

like the original thing

[delicate sphinx]

if its big numbers use the primary number technique

[copper comet]

hmm?

[delicate sphinx]

21/50=37/25*5

[sinful thistle]

im assuming you mean prime factorization

what

[delicate sphinx]

3 * 7

[sinful thistle]

OH

[delicate sphinx]

discord is wank

[sinful thistle]

$\frac{21}{50} = \frac{3\cdot 7}{2\cdot 5\cdot 5}$

[copper comet]

🧠 malufunction

[delicate sphinx]

@copper comet use prime factorization or whatever and if u dont have any same number at the top and at the bottom

its simplified

[copper comet]

alright

[elfin berry]

ren

[sinful thistle]

this is what he meant

[delicate sphinx]

yes

[sinful thistle]

@copper comet u got any other questions

[copper comet]

yes, that was like the least of my problems

that was the easiest lemme get my book rq

[sinful thistle]

well then SEND the questions

picture/ss best

[copper comet]

i cant

im on my computer rn

[delicate sphinx]

@sinful thistle u any good in trigonometry?

[copper comet]

Heres the question

What is 32% of 42600

im taught to do 32/100 x 42600/1

but im not sure how to simplfy that

[delicate sphinx]

/1 😭

[copper comet]

its the same

[delicate sphinx]

devide 42600 by 100

and then multiply the remaining by 32

[copper comet]

but why

[delicate sphinx]

x/yz=xz/y

[sinful thistle]

why not

[delicate sphinx]

fiuck

fuck

wait

bro

its /100

[sinful thistle]

tf

[delicate sphinx]

doiscord

is bugging

[sinful thistle]

!noadvert

[delicate sphinx]

discord*

[marsh citrus]

Please do not advertise your help channel or thread in other parts of the server. There are many people who need help, so advertising can quickly turn into spam.

[delicate sphinx]

i cant use * normally

[delicate sphinx]

just asked a question bro

[copper comet]

oh wait i see what u mean

but how does that apply with 25/100 x 480/1

[delicate sphinx]

huh

[copper comet]

am i supposed to do 25x4.8?

[delicate sphinx]

no

25/100 is 1/4

1/4 times 480 is 480/4 which is 120

[copper comet]

ohhhh

aight lemme get big numbers