help-17

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✅

[gaunt forge]

Can anyone help

[spring tapir]

I mean idk the solution to this or how to do it

But the question itself seems to give hints, as to that it's an iterative process right

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[dusty umbra]

trying to do a mechanics problem, i've got into a pure math part of it that I can't solve. Any help is appricated :)

[flat whale]

well did you use s/a = sinh(u) ?

[dusty umbra]

i don't know how to do u sub 😭. Part of the question gives s/a = sinhu. I'd learn how to do u sub but im gonna be taught it soon ish and i sorta just wanna get this problem done

[flat whale]

https://tutorial.math.lamar.edu/classes/calci/substitutionruleindefinite.aspx

[dusty umbra]

oh that doesnt look too bad

i shall have a go 🫡

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[prime umbra]

i got the first answer

by just graphing and subtracting but what confuses me about the second part is the additional 10 and 6

any help is greatly appreciated

[gaunt sparrow]

You could split the integral up in pieces

[prime umbra]

what would that look like?

[gaunt sparrow]

You'll get say $10 \int_{16}^{13} f(x)dx - \int_{16}^{13}6 dx$

Just with the linear property of the integral

From this, I think you should be able to compute everything

The only other thing you might want to consider is to flip the bounds

[prime umbra]

what happened to the 6\

[gaunt sparrow]

Which changes the sign

Oops sry

Wait

[twin meteor]

Azyrashacorki

[prime umbra]

ok

let me try it real quick

how do i find dx by itself?

without f(x)

[gaunt sparrow]

What is the integral of a constant?

[prime umbra]

ohj lol ok so just 6x

[gaunt sparrow]

Yep

[prime umbra]

ok is the answer 40-6x

or am i supposed to do something different with the left side of the equation

[gaunt sparrow]

Well you still have to plug the bounds into 6x

[prime umbra]

oohhhhhh

yeaaaa

ur right

[gaunt sparrow]

But the first bit seems right

10*-(-4) = 40

[prime umbra]

hohoghe

nice thank you so much

ok that makes way more sense

yea i got it

58

is the answer right?

[gaunt sparrow]

I think so yes

[prime umbra]

ok have a good day

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[gaunt sparrow]

And you

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[gaunt sparrow]

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[upper anchor]

Can some just teach me how to graph in general?

[upper anchor]

I never got to know exactly how to graph and do linear equations

[proven garden]

a graph is just a set of points

so find the points using the equation and plot the points

[flat whale]

https://www.khanacademy.org/math/in-in-grade-9-ncert/xfd53e0255cd302f8:linear-equations-in-two-variables/xfd53e0255cd302f8:graph-of-a-linear-equation-in-two-variables/v/plotting-x-y-relationships

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@upper anchor Has your question been resolved?

[upper anchor]

Thank you rie

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[west rapids]

Good evening I need help with binary subtraction 10000000.1-011011.001 I understand the concept of binary subtraction however this one is super confusing

[west rapids]

all I got so far is .101

[gaunt sparrow]

It's essentially the same thing as with our base 10.

Write them by aligning the decimal points and padding zeros :

1 0 0 0 0 0 0 0. 1 0 0
-0 0 0 1 1 0 1 1. 0 0 1

Then you can just do the subtractions and carry over as you would with base 10

[west rapids]

right but there is only one number which I can carry over with

[gaunt sparrow]

Well yeah, you'll have to borrow ones out until the next 1 to the left.

So say, rightmost digit : 0-1 : need to borrow, see left digit : also 0, so need to borrow from the left of that one which is 1.

Then the 2nd to rightdigit becomes 2 (from the borrow), and 1 is borrowed from that to make the rightmost digit 2 as well.

[west rapids]

Yes I get that part

[gaunt sparrow]

Oh yeah you've already computed the dot bit.

Then you'll just end up borrowing up until the leftmost 1

[west rapids]

however the first number only has ONE 1 which makes it impossible to carry for the rest of the question

[gaunt sparrow]

You can still borrow from it though

It'll just make a trail of borrows up until the dot

Top would become like 0 1 1 1 1 1 1 2

And then you can subtract

[west rapids]

this is confusing but I'll try it out thank you

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[solid sage]

Is the number of (a,b,c,d) solutions to a+b+c+d = r analogous to star barring a set with r-1 bars, r stars and 4 slots so $\binom{4+r-2}{4-1}$

[twin meteor]

annyeong

[glad python]

4+r-1

[solid sage]

r being number of bars right

Although if there are r-1 bars

[glad python]

r is the stars

a_1+a_2+a_3+…+a_n=r is r stars and n-1 bars

[solid sage]

Oh right oops

Alright thanks for clearing up

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[marble tinsel]

how do i

[marble tinsel]

i know i need to find an angle with law of cosine and then proportions with law of sines

but unsure how to find angle B

[buoyant notch]

What

use the law of cosine

That u said

[marble tinsel]

need to solve for cos B, so would i do a^2 + c^2 - 2ac - b^2 = cos B?

[buoyant notch]

no

CosB=(a^2+c^2-b^2)/2ac

I recall

[marble tinsel]

shouldnt it be (a^2 + c^2 - b^2 - 2ac) = cos B?

sub b2 from both sides then div both by cosB

[buoyant notch]

No

b^2=a^2+c^2-2acCosB

b^2-a^2-c^2=-2acCosB

(b^2-a^2-c^2)/-2ac=CosB

(a^2+c^2-b^2)/2ac=CosB

Is how u do it

[marble tinsel]

do you add 2ac CosB to the other side?

[buoyant notch]

2acCosB

[marble tinsel]

how does that part get to the other side of the equation

[buoyant notch]

Is multiplication

Therefore you divide to cancel it

that is 2ac times CosB

So you have to divide

[marble tinsel]

ohhh

move a2 and c2 to the left with b2

and then -2ac CosB is on the right and div by -2ac

[buoyant notch]

Yes

[marble tinsel]

ok thanks

one sec

is the answer for B 168.3?

finding B using cos-1

[buoyant notch]

CosB=(100+144-9)/2(10)(12)
CosB=235/240

B=cos^-1(235/240)

I’m on phone so I can’t do

If that’s the steps U did it’s good

[marble tinsel]

divide by -2ac or 2ac

cuz i divided by -2ac instead of 2

[buoyant notch]

Divide by 2

Because we applied the - on top and bottom of the fraction

So it is a positive 2ac now

[marble tinsel]

ohhhh

[buoyant notch]

Ya you can see the signs of a2 b2 c2 have flipped

So that’s why

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[lucid galleon]

What was the rule for this? I need to find X, I did 80=1/2(5X-?) I don't know what to put for the "?"

[karmic forge]

Where is x

Outside the circle

[lucid galleon]

? 5X and I need X value alone

[dim wind]

i cant understand what youre asking

[lucid galleon]

How do I measure X in this photo I sent, and the given is angle f = 80°, and it's arc measure = 5X, and the question is what is the value of X, how do I get it?

[sick owl]

Which formula bro?

[lucid galleon]

What do you mean

[sick owl]

Well it looks tangent

So its perpendiculars at E and G

And sum of all angles in a quadrilateral is 360

So we get EOG

And then we do 360 - EOG(which we found)

To get other arc measure

[lucid galleon]

Ohh and 260 ÷ 5 is 52 so X = 52°, thanks

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[craggy tiger]

N, P € IR^nxn
prove that if P = N*P with P/= O then N has an eigenspace that is at least rank(P)-dimensional.

[craggy tiger]

Could anyone help me to start this proof?

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[craggy tiger]

Consider a,b €IR the matrix
T_(a,b) = (-b 1 b
2a, 0, -a
-2b, 1, 2b)

Show that (1,0,2) is an eigen vector of T_(a,b) for all values of the paramaeters a and b
For what values of the parameters a and b is theT_(a,b) diagonalizable over IR

[craggy tiger]

I have calculated the eigenvalues of the matrix, but now i'm somewhat stuck

[karmic forge]

You don't have to find eigan value

Just matrix enough

[craggy tiger]

?

[karmic forge]

Prove AX=cX

Just multiply this vector to your transformation matrix

[craggy tiger]

oh ok

[karmic forge]

Then if constant come out so it's a eigan vector

[craggy tiger]

i got this after solving it

I also tried this but

[karmic forge]

You don't know how to make transformation matrix

[craggy tiger]

isnt this the transformation matrix

[karmic forge]

And transformation is R^2 to R^3

Matrix is 3 x 2

Show me real question

And how this transformation has eigan vector in R^3

[craggy tiger]

the question is in dutch it translated it into english

[craggy tiger]

.

[karmic forge]

Question is wron bro

Wrong

[craggy tiger]

that can't be

[karmic forge]

Oh so transformation matrix is given

[craggy tiger]

yes

thats the T(a,b)

should is use L(v) = lambda* v

[karmic forge]

Multiple (0,1,2) with this matrix

Simply multiply

Don't use lemda

[craggy tiger]

ok

i get
b
0
2b

[karmic forge]

Take b, comon and b in R

It is a eigan vector

Understood

Lameda is b

[craggy tiger]

yeah

[karmic forge]

b is lameda

https://tenor.com/view/traduun-gif-27169151

[craggy tiger]

so you get b* [
1
0
2
]

which b * eigenvector

[karmic forge]

That's the defination of eigan vector

[craggy tiger]

and so the given eigenvector is indeed an eigenvector ot T(a,b)

[craggy tiger]

yup

so now the second part

for what values of a and b is T(a,b) diagonalizable over IR,

[karmic forge]

You need eigan values for that

[craggy tiger]

i've calculated those

[karmic forge]

What is eigan values

[craggy tiger]

they were b, -sqrt(a) and sqrt(a)

[karmic forge]

They all have to be different for dignolizabilty

Means that satisfy for all b^2 not equal to a

[craggy tiger]

my answer sheet says that a>0 and b € IR

i don't how they got that

[karmic forge]

a>0 is obvious

[craggy tiger]

should i calculate the eigenvectors of the eigenvalues

[karmic forge]

You have to put b^2=a ,and find eiganspace

You know eiganspace

[craggy tiger]

thats the null space right?

[karmic forge]

Yes

[craggy tiger]

ok

[karmic forge]

And null space is equal to no. Of eigan value repeated then it is dignolizble

You know that algebric multiplicity and geometric multiplicity for eigan values

[craggy tiger]

yes

if they are the same, the matrix i diagonalizable

these are the eigenvectors for each eigenvalue

so both the multiplicity is the same

[karmic forge]

Ya they all different

You can also prove it like that but it long

Eigan space method is good

Ok I think we done

[craggy tiger]

wait

[craggy tiger]

but i don't understand why a>0 and for all b

[karmic forge]

We have found that until all the eigan value same matrix is dignolizble

Right

[craggy tiger]

yes

[karmic forge]

Now -√a and √a cannot be same until a=0

[craggy tiger]

yes

[karmic forge]

If you put a=0 two eigan vector same see

[craggy tiger]

ooohh

[karmic forge]

So a>0

[craggy tiger]

but why not then a € IR without 0

the b one i understand now

[karmic forge]

Ya i think a can be <0

We get different complex eigan values

Do one think take a=-4,and b=1 and see if it dignolizble

[craggy tiger]

we are doint it over IR

not complex

OOOH

thats why a cant be < 0

[karmic forge]

Matrix in R but eigan values can be in Complex

[craggy tiger]

i understand now

thanks very much for helping

[karmic forge]

Oh it stats dignolizble over R

[craggy tiger]

yeah thats why

[karmic forge]

Ok

Bye now i gtg

[craggy tiger]

have a nice day

[craggy tiger]

alrightbye

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[junior citrus]

hey

[junior citrus]

how does a local minimum work?

for y=x^3 where would the local minimum be

Why is 6|3 not a local minimum here but 2|1

[empty frigate]

well presumably the actual function graph continues off to the right forever and that just isn't shown here? it seems pretty plausible that it could extend like this and then (6,3) clearly isn't a local minimum

[mental falcon]

intuitively, you can think of a local maximum as any hill you can walk to the top of and you are higher than the surrounding region around you. even a hill next to everest would be a local maximum but it wouldn't be the maximum for the whole of that mountain range because there are other higher peaks around it. but "locally" its the maximum. i used maximum in the example because it's easier to compare to real world ideas, but minimum is same idea

[junior citrus]

so if there is not curve going up after a local minimum it is not a local minimum since it could continue down forever?

if u understand what i mean

[karmic forge]

No soosh is right

[mental falcon]

yes exactly, that will be a curve going down to it and then a curve going up away from it afterwards (in 2 dimensions it's just two sides)

[scenic ravine]

A local minimum is essentially a point satisfying two conditions 1) The first derivative is zero, 2)the second derivative is positive

[karmic forge]

It is like concept of neighborhood how much neighborhood you taking

[junior citrus]

ok thank you! and for y=x^3 what would the local or global minimum or maximums look like?

[mental falcon]

not quite accurate, the derivative could also be undefined (for example absolute value function at x = 0)

[scenic ravine]

oh yeah, that too, sorry

[junior citrus]

ah ok

[mental falcon]

true for differentiable functions though, what you said

so thats why when you consider "critical points" where you check for local minimums \ maximums, you need to check both points where derivative = 0 and where the derivative is undefined

[junior citrus]

ok thank you

[mental falcon]

is all crystal clear @junior citrus or do you have other q?

[junior citrus]

one more q please

for y=x^3 what would the local or global minimum or maximums look like?

and it would be strictly monoton right

[mental falcon]

also to answer your question about (6,3) here, local extrema (minimums, maximums) are defined on open interval, this function is only defined up to x = 6, so not on any open interval that contains x = 6

[empty frigate]

wait hang on, so are we saying (0,0) is not a local minimum of x^4?

[empty frigate]

(yes it is)

[mental falcon]

when you consider absolute extrema on some closed interval, you need to check all local extreme as well as the END POINTS of the interval

[junior citrus]

but why is it just monotously is not is always rising

[scenic ravine]

doesn;t that require the derivative to be non zero every everywhere

[mental falcon]

derivative of x^4 = 4x^3, that is negative when x < 0 and positive when x > 0 so no it is not monotonic

[empty frigate]

ok wait hang on why are there two different definitions of monotonic here

since the definition i've heard before, and that wikipedia uses, is f is strictly increasing iff x < y implies f(x) < f(y)

[scenic ravine]

Strictly monotonic afaik means the derivative is either >0 or <0 everywhere , at least that's what I learnt

[junior citrus]

what i know strictly monotonic is when it is always rising never staying the same or decreasing

[mental falcon]

thats just strictly increasing, not monotonic

(one type of monotonic), but could also be strictly decreasing

[empty frigate]

well yes, but any function that's strictly increasing is strictly monotonic

[scenic ravine]

yes, but x^3's derivative is 0 at 0, thus it's increasing but not strictly increasing

[junior citrus]

always rising is not it?

[empty frigate]

if x < y then x^3 < y^3, so x^3 is strictly increasing, by the definition on wikipedia

[mental falcon]

i thought you guys were talking about x^4 🤔

[junior citrus]

no 😆 x^3

[mental falcon]

ok hence the confusion

[junior citrus]

so what is it now

[empty frigate]

i would also note that the definition on wikipedia works on non-differentiable functions as well

[mental falcon]

x^3 has a CRITICAL POINT at x = 0 (i.e. a point you need to CHECK for local extrema) but if you do the first derivative test you will see that the sign of the first derivative test is the same on both sides of 0, so there is no local extremum

theres a horizontal tangent, but no local max or min, the first derivative is positive to both sides

[junior citrus]

so, there is no local extremum and also no global extremum and it is strictly monotonic increasing?

[empty frigate]

whether it's strictly monotonic increasing depends on what definition of "monotonic" you're using

[junior citrus]

the rest is true?

(as long it does not say f[-2,4] cause then there would be a global minimum and maximum right?)

[mental falcon]

its not "strictly" monotonic but its monotonic

strictly monotonic and montonic are two diffeent definitions, so be clear on the distinction

[junior citrus]

what are the definitions

[mental falcon]

basically replacing the <= with <

for the strictly

since f(x) = x^3 has a horizontal tangent, it is monotonic but it isn't strictly monotonic

actually im wrong i think 🤔

[empty frigate]

...by this definition, x^3 is strictly monotonic

[junior citrus]

where?

it does not have a horizontal tanget

[mental falcon]

since there aren't two distinct points with same y i guess its still strictly monotonic, my mistake 😄

[empty frigate]

it's only not strictly monotonic if you define "monotonic" in terms of derivatives

[junior citrus]

thank you all

so there is not global maximum or minimum in x^3 neither since it goes on forever?

neither local extremes

[empty frigate]

yep
well more precisely, it's not really that it "goes on forever", the issue is more that it goes up forever

[junior citrus]

ok thank you! so the point 0|0 would not be a local minumum or maximum

it would be the point of inflection tho?

[mental falcon]

i need to pull up a definition of local extremes now 😛

[junior citrus]

y value never decreases after 0|0 so it would not a local maximum

and neither minimum

since it never increased before

[mental falcon]

so in this one book yeah you can see why open interval around the point is required, since it's part of the definition

[junior citrus]

ok thank you

y'all so smart

did u guys study maths

🤣

[mental falcon]

i studied biology 😂

[junior citrus]

oh haha

thanks tho!

[scenic ravine]

I want to let's see lol, sorry for all the mistakes I made

sorry again

[junior citrus]

no you helped me

thanks

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[vapid wedge]

e_1 and e_2 creates a base.
f_1 = 4e_1 + 21e_2
f_2 = e_1 + 5e_2

a) show that e_1 e_2 is a linear combination of f_1 and f_2

[vapid wedge]

Can someone help me understand first of all the formula for Linear combination

I have no idea how to actually read that

[karmic forge]

Put e_1 =af_1+bf_2
Solve for a and b

[worthy citrus]

You just wanna convert this to a matrix equation

[vapid wedge]

Yes i pressumed that but that's not what i asked

[hybrid flicker]

linear combination of (u1,...,un) means that you combine those vectors by adding scaled versions of them together

[vapid wedge]

I want to understand the formula for linear combination

[hybrid flicker]

"linear" has two facets : adding and scaling

and so a linear combination of (u1,...,un) is any vector you get from adding and scaling them together

[vapid wedge]

If i understand linear combination correctly, lmk if i'm wrong.
$v = lambda_1 * u_1 + lambda_2 * u_2 + . . . + lambda_p * u_p$

[twin meteor]

Merineth

[vapid wedge]

Idk how to make vectors with the bot

or lambda

[hybrid flicker]

yes this is what it is

[vapid wedge]

so if the sum of the RHS = the vector on LHS

How come they write it so atrocious ? I can't even read it

It's incomprehensible to me :(

[hybrid flicker]

oh it's just the sum notation, used for abreviating

instead of lazily writing "..." to say the sum continues for a long time

[vapid wedge]

so the LHS actually has

[hybrid flicker]

we write $\sum_{k=1}^na_k$ to indicate that we're summing all the "$a_k$" terms together

[twin meteor]

rafilou2003

[vapid wedge]

a lambdak * uk?

[hybrid flicker]

it sums all those lambdak * uk together

[vapid wedge]

Is it possible to rewrite it without the sum sign? So i can more easily relate and remember it

[hybrid flicker]

and k varies from 1 (bottom index) to n (upper index)

[hybrid flicker]

with "..."

as written on the right

[vapid wedge]

on the right? The trivial LK?

[hybrid flicker]

no

the RHS

[vapid wedge]

$\lambda_1u_1+...+\lambda_nu_n$

[twin meteor]

Merineth

[hybrid flicker]

yes

[vapid wedge]

Okay so this is the LHS or RHS ?

[hybrid flicker]

They're equal

the LHS and the RHS mean the same thing

[vapid wedge]

Oh i see

So in my case i want to figure out if e1 and e2 are are linear combination of $\lambda_1u_1+...+\lambda_nu_n \implies e_1 = \lambda_1f_1 + \lambda_2f_2$

[twin meteor]

Merineth

[vapid wedge]

and the same for e_2?

Do I have to make it into two equations?

$\overline{e_1} = \lambda_1 * (4e_1 + 21e_2) + \lambda_2 * (e_1 + 5e_2) \
\overline{e_2} = \lambda_1 * (4e_1 + 21e_2) + \lambda_2 * (e_1 + 5e_2)$

[twin meteor]

Merineth

[vapid wedge]

Do i have to solve the system of equations for lambda_1 and lambda_2 ?

The question is only "Express the vectors e1_2 as LC of the new basis vectors."

However i'm not sure if i'm done

@dull bear

[vocal sleet]

@vapid wedge Has your question been resolved?

[loud hedge]

(e_1 = (4a_1 + b_1)e_1 + (21a_1 + 5b_1)e_2)

[twin meteor]

nicoco

[vapid wedge]

$\overline{e_1} = \lambda_1 * (4e_1 + 21e_2) + \lambda_2 * (e_1 + 5e_2) \
\overline{e_1} = \lambda_1 4e_1 + \lambda_1 21e_2 + \lambda_2 e_1 + \lambda_2 e_2$

[twin meteor]

Merineth

[vapid wedge]

Det går inte att förenkla mer ^

$\overline{e_1} = \lambda_1u_1+...+\lambda_nu_n$

[twin meteor]

Merineth

[vapid wedge]

@loud hedge

Detta är ju formeln för LK

[dull bear]

[vapid wedge]

for the love of fucking god

help me

like i'm losing my mind over this dogshit

[dull bear]

Awww trying to catch up

[dull bear]

Is it still this one here?

[vapid wedge]

Yes

It's in swedish but basically it says

We have two vectors, e1 and e2 that has a base in the plane

and then we are given two new vectors f1 and f2

and a asks us

a) Express the vectors e1,2 as LC of the new basis vectors.

And from what i've learned so far LC is done like this:

$\overline{e_1} = \lambda_1u_1+...+\lambda_nu_n$

[twin meteor]

Merineth

[vapid wedge]

Where i only need to replace f1 nad f2 with u1 and u2 respectively

[dull bear]

Cool cool give me one moment to organise some stuff

[vapid wedge]

This is the "answer" he gives us

but i have no ideaaaaaaaaa what he is doing

[dull bear]

Anyways, we basically have that $f_1 = 4e_1 + 21e_2$ and also $f_2 = e_1 + 5e_2$, are you happy with simultaneous equations of two variables?

[twin meteor]

@dull bear

[dull bear]

Arrgghhh gonna get catlove in preamble soon enough

[vapid wedge]

do you refer to making a matrix of the two equations?

Why can't i just utilize the formula for LC?

[dull bear]

You can, that’s one way (and possibly easier!) you could write that in a matrix form

[dull bear]

Alternatively you could solve these for e1 and e2 in terms of f1 and f2

[vapid wedge]

I just don't understand the question

i know how to figure out if a vector is a LC to two other vectors

Is that what he is asking?

[dull bear]

Basically kind of: find the exact linear combination of f1 and f2 that makes e1, and then the one that makes e2

[vapid wedge]

Yes, and isn't that what i have done here?

He isn't even using the formula for LC

Is this correct?

Because this is exactly how i did it

except the last part where it says i should solve a system of equations

[dull bear]

Well sure, that’s fine, you’d just need to find the lambdas from that

[vapid wedge]

How am i supposed to find the lambdas when i don't even know the values of either e_1, f1 or f2

[dull bear]

The idea from here is that you for example know that 4f2 = 4e1 + 20e2, so f1 - 4f2 = e2

Similar to how you would solve simultaneous equations

[dull bear]

You could compare coefficients if you wish

[vapid wedge]

I'm so sorry but i honestly have no idea what we are doing

and i don't know how to compare coefficients

[dull bear]

E.g. this converts to 4a1 + b1 = 1 and 21a1 + 5b1 = 0

[vapid wedge]

Yeah but idk what that is

It wasn't posted by me

$f_1 = 4e_1 + 21e_2 \
f_2 = e_1 + 5e_2$

This is the infromation that i am given

But now they want me to make an expression using the formula for LC to make

[dull bear]

e1 for the second row

[twin meteor]

Merineth

[vapid wedge]

And they ask me now to make a LC by using the formula

and the formula states:

$e_1 = \lambda_1f_1 + \lambda_2f_2$

[twin meteor]

Merineth

[vapid wedge]

now i just replace f_1 and f_2 respectively

and do the same with e_2

$\overline{e_1} = \lambda_1 * (4e_1 + 21e_2) + \lambda_2 * (e_1 + 5e_2) \
\overline{e_2} = \lambda_1 * (4e_1 + 21e_2) + \lambda_2 * (e_1 + 5e_2)$

[twin meteor]

Merineth

[vapid wedge]

Which lands me here ^

Am i not done now?

I've expressed e_1 and e_2 as a LC of f_1 and f_2

[dull bear]

Hmmm

[vapid wedge]

Specifically "Express the vectors e12, as LK of the new basis vectors."

[dull bear]

Well they want you to have $e_1 = \lambda_1 f_1 + \lambda_2 f_2$, with you specifying what the $\lambda$’s are

Similar for e2

[vapid wedge]

huhh

why f1 and f2?

It says e1 and e2

[dull bear]

Ah yea got mixed up

[vapid wedge]

[twin meteor]

@dull bear

[dull bear]

But you want f1 and f2 to be there explicitly as they are

[vapid wedge]

But how am i supposed to determine the lambda

We aren't given enough information

[dull bear]

You are: rearrange these is what I was saying you could do

Alright, a slightly different task, if I asked you to solve something like
$2x + y = 6$ and $4x + 3y = 22$, could you do that?

[twin meteor]

@dull bear

[vapid wedge]

Literally no clue

or ig i could multiply the 1st equation byu -3?

to get rid of y

and then solve for x

Am i supposed to use the same method to find lambda?

[dull bear]

A good idea

[vapid wedge]

But they are equal?

[dull bear]

That’s one way you can use: starting from…

[dull bear]

…these, multiply the second equation by 4, which allows you to eliminate the e1’s

[dull bear]

I mean they would be, the e1 on the left being the same, but then of course those are just more simultaneous equations anyway, through the comparing coefficients thing

[vapid wedge]

multiply by -4? or 4

[dull bear]

Either: by 4 and subtract that from the first one, or -4 and add that to the first one

[vapid wedge]

$f_1 - 4f_2 = e_2$

[twin meteor]

Merineth

[vapid wedge]

This is what i get if i mult på -4 and add the two equations together

and now the same to find e1?

[dull bear]

Yep, or you can put that into, say, that f2 = e1 + 5e2 = e1 + 5(f1 - 4f2) and rearrange

[vapid wedge]

$f_2 = e_1 + 5(f_1 - 4f_2) \
\implies e_1 = f_2 -5(f_1 - f_2) \
\implies e_1 = -5f_1 +6f_2$

[twin meteor]

Merineth

[vapid wedge]

$e_1 = -5f_1 +6f_2 \
e_2 = f_1 - 4f_2$

[twin meteor]

Merineth

[vapid wedge]

I have no idea why we found e1 and e2

[dull bear]

he's got something else

[vapid wedge]

yeah his numbers are different

His is just a general solution

every student gets different values

[dull bear]

,w [[4, 21], [1, 5]]^(-1)

[dull bear]

Ohh fairs, thought it was for the same question, would have said

[twin meteor]

Results provided by WolframAlpha

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

Requested by chartbit

[dull bear]

You forgot the 4 here middle line should be f2 - 5(f1 - 4f2)

[vapid wedge]

i'll redo..

$e_2 = f_1 - 4f_2 \
e_1 = -5f_1 + 21f_2$

[twin meteor]

Merineth

[dull bear]

Yep

[vapid wedge]

Is that the answer?

[dull bear]

Yep, it is

[vapid wedge]

It's really bad when i don't even know that it's the answer

i would've never figured this out on my own

even tho i studied hard

Like what am i supposed ot do

there is something wrong with me

[dull bear]

There's also converting it into matrix form too, notice you have the rows forming your coefficients!

[dull bear]

Awww

Some of it is understanding what they're asking for

[vapid wedge]

Yeah but more often than not i don't understand what he is asking for

the vast majority of times*

I'm at a loss

Having no1 in class to ask and the teacher can't help me

[dull bear]

Awww sorry to hear that

Definitely makes it more difficult to keep up

[vapid wedge]

I’m done with this and life

.close

[vocal sleet]

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[rigid laurel]

I think c is 65 deg

CE

[cedar kernel]

are you reffering to angle ECB or angle ECD

[rigid laurel]

I mean inside the parallelorgam

BCE

[magic wasp]

Correct

[cedar kernel]

can you find angle cea

[rigid laurel]

Is it 115?

[cedar kernel]

yeah!

so from that can you find angle ced

[rigid laurel]

again 65

[cedar kernel]

basically because cd= ce condition is give , can you tell me what type of triangle it is

(triangle ced)

[rigid laurel]

isosceles

triangle

[cedar kernel]

yeah can you find angle bcd now

[rigid laurel]

So is it like 65 +65 -180 = 50

[cedar kernel]

50 would be the measurement of ecd right?

[rigid laurel]

yes

[cedar kernel]

now can you see it

[rigid laurel]

Now 50+65 =115

[cedar kernel]

sounds good

wait

wait

[rigid laurel]

yes

[cedar kernel]

yeah ok

[rigid laurel]

So answer is 115

[cedar kernel]

i think yeah

isocells trapezium

[rigid laurel]

can you take a look at this

[cedar kernel]

i gtg rn

sorry

[rigid laurel]

okay

.close

[vocal sleet]

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Remember:
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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.

[coarse ridge]

this sequence is positive and decreasing (observing first few terms suggests that) now we can take 0 as a lower bound, thus {x_n} is monotonically decreasing and bounded below thus by MCT, the sequence converges to a value, hence limit_n->inf x_n exists. Now how do I prove that is sequence is actually monotonically decreasing (after certain value of n), also how to find this limit?

[lucid bane]

seems like you could use induction

[coarse ridge]

Induction to show that x${n+1} \leq x{n} \forall n \geq c ; c \in \mathbb{N}$?

[twin meteor]

Normed

[lucid bane]

well if you have a good guess of the c, yea

[coarse ridge]

c = 2 ig

[lucid bane]

base case would be showing $x_3 \leq x_2$, then showing given $x_{k+1} \leq x_k$ that must necessarily mean $x_{k+2} \leq x_{k+1}$

[twin meteor]

🫎 ムウスィイ 🫎

[vocal sleet]

@coarse ridge Has your question been resolved?

[vocal sleet]

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[vocal sleet]

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

[pale arch]

I need some help

[pale arch]

How can i solve?

[karmic forge]

Inverse the B matrix

You know how to inverse ?

[vocal sleet]

@pale arch Has your question been resolved?

[vocal sleet]

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[vocal sleet]

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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[analog oak]

help!

don’t send answer please explain

[karmic forge]

Put 4 as 2 square and 9 as 3 sqaure

[analog oak]

Ok

[karmic forge]

Then take 2^x=u
And 3^y =v

Make 2 equation solve for u and v

[analog oak]

In the second one?

[karmic forge]

Both

Equation

Put in. Both

[analog oak]

u raised -1.

[karmic forge]

Multiply one 2 inside you got 2 x 2^x

[analog oak]

2sq (u raised -1) + 3sq(v raised -1) = 17
2(u) -2(v)=6

[karmic forge]

First one is wrong

[analog oak]

ok

[karmic forge]

It will be 2u+3v =17

[analog oak]

First?

ok

[karmic forge]

Ya

Solve both equations

What you get

[analog oak]

ok I am new to solving 2 equation as I haven’t been taught but I have done some questions I’ll try

let me do

[karmic forge]

Try

Take your time

Second one also wrong bro

[karmic forge]

3u-2v=6

2u+3v=17

Is right equations

[analog oak]

Just wait

I have put in 2nd equation

I see it wrong

26/3

let me give you the one I have put in 2nd

2u-2(17-2u/3)=6

Is this wrong

you there?

@karmic forge

[karmic forge]

3u in start

[analog oak]

ooo

[karmic forge]

See these equations are right

Try again

[analog oak]

@karmic forge

I have the answer

u=4, v=3

[karmic forge]

Yeah

[analog oak]

ok finally

now question is saying

[karmic forge]

Now find x and y

[analog oak]

hmm

how we do that

[karmic forge]

What is u and v

Equal

[analog oak]

2raised y-1

Is u

[karmic forge]

No

[analog oak]

3 raised y-1 is v

[karmic forge]

What we take u equal to

[analog oak]

2 raised x-1 is u

[karmic forge]

No

[analog oak]

ok

we take it 4

v is 3

7 is their sum

[karmic forge]

Yes now we need x and y

We not need u and v sum

[analog oak]

hm

yes

[karmic forge]

We need x and y sum

[analog oak]

we need x and y

[karmic forge]

How u and x related

[analog oak]

2 raised x-1 is u?

or no

[karmic forge]

See this is u

Rembeber

[analog oak]

oo

ok

2 raised x

[karmic forge]

Can you solve it now

[analog oak]

ok

Let me try

[karmic forge]

Give me x and y

[analog oak]

X is 2?

[karmic forge]

And y

[analog oak]

It is

Uhm

y is

1?

[karmic forge]

Yeah what is the answer

[analog oak]

3

[karmic forge]

https://tenor.com/view/high-five-patrick-star-spongebob-squarepants-the-patrick-star-show-yes-gif-22559195

[analog oak]

That took holy hours of time

[karmic forge]

https://tenor.com/view/messi-yes-wink-thumbs-up-gif-14443123

[analog oak]

hey man let me get the solving properly it was in rough

lm10

[karmic forge]

Ok bye

[analog oak]

Thanks

[vocal sleet]

@analog oak Has your question been resolved?

[analog oak]

@karmic forge

U is 2

I guess

I resolved

It

Something is wrong

If you can give me solved one that would be helpful

[karmic forge]

Why you think that

You got the equations right ??

[analog oak]

Second time writing I got it wrong

It’s coming 2 idk

let me see

I’ll send

[karmic forge]

Ya everything is perfect

[analog oak]

no

[analog oak]

Check the solved 50. One

[karmic forge]

Problem in solving equations

Try one more time

Equation are right

[analog oak]

Is the 3rd last step good

[karmic forge]

Do it all again

You make a mistake when you start solving equations

Equations are right try one more time

[analog oak]

Which

equation

[karmic forge]

Equations are right

[analog oak]

3u-2v=6
2u+3v=17

is it correct

[karmic forge]

Ya solve it

They are correct

You took v=(6-2u)/3

But v=(3u-6)/2

[analog oak]

@karmic forge

man

I am

clearly

new

To this

I know what is wrong

2 raised x is 16

x is 4 then

?

no

[karmic forge]

2 raised x is 4

[analog oak]

Wait

[karmic forge]

x is 2

[analog oak]

Ok look

u = 16

[karmic forge]

u=4

[analog oak]

no

[karmic forge]

No 16

[analog oak]

2u+3(6-3u/2) = 17

is this correct

[karmic forge]

Not correct

[analog oak]

ok found the problem

v is put has 6-3u/2

[karmic forge]

v=(3u-6)/2

3u-6 not 6 -3u

Try it now fast

I have to go

[analog oak]

If you look here 3rd last step has 3u-2v= 6 if we shift it becomes 6-3u

[karmic forge]

Ya then -v=(6-3u)/2

You forget -

-v

[analog oak]

I see

[karmic forge]

Multiply both sides with minus

Now solve it

https://tenor.com/view/don’t-make-me-beg-gif-18284150441593567102

[analog oak]

Doing

nope

It’s coming incorrect

[karmic forge]

Ok I have to sleep you DM me I will send you answer tomorrow

[analog oak]

Is it 12?

Midnight

For ya

?

[karmic forge]

Ya

[analog oak]

Same

[karmic forge]

12 o clock

[analog oak]

yes

[karmic forge]

India

[analog oak]

yes

I will study till the morning or maybe 2-3

[karmic forge]

Yeah sleep now don't worry

[analog oak]

ok

[karmic forge]

Which class are you in

[analog oak]

you?

I am in 8th

Still

[karmic forge]

I completed my masters

[analog oak]

masters in mathematics?

[karmic forge]

Yeah

[analog oak]

from

?

iit?

[karmic forge]

Rajasthan

[analog oak]

ok

[karmic forge]

No just some private colleges

[analog oak]

well ok

[karmic forge]

Why you study at night

[analog oak]

I am studying class 9th, 10th

[analog oak]

Uhm

[karmic forge]

Ya it's hard

[analog oak]

to

[karmic forge]

Morning studies are better

[analog oak]

Make things much easier

in future

They are

[karmic forge]

Should I solve the equation in chat

[analog oak]

Dm me

[analog oak]

.close

[vocal sleet]

Channel closed

Closed by @analog oak

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Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• 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.

[tropic anchor]

Solve
9x⁴-42x²-x+46=0

[tropic anchor]

Dont know where to start i only know quadratic and cubic polynomial how do i do this one

[desert hornet]

are you sure you gave us the exact correct equation?

[tropic anchor]

its not the original question but i ended up with that equation

[desert hornet]

!xy

[tropic anchor]

3x²-7= square root of x+3

[desert hornet]

the equation is probably wrong, it doesn't have any simple solutions

[desert hornet]

$3x^2+7=\sqrt{x}+3$ or $3x^2+7=\sqrt{x+3}$?

[twin meteor]

kheerii

[tropic anchor]

Second one

[desert hornet]

ah, okay

hmm is this the ORIGINAL question you are given?

can you provide us with an image of the question

[tropic anchor]

its from a test but its really messy 😭

my writing

[desert hornet]

it's okay

you can show me the question

[tropic anchor]

okay wait i gotta erase sum

[desert hornet]

hmm, weird.

f^(-1)(x) doesn't exist, since f(x) is not a one-to-one function

[tropic anchor]

ummm

then what am i supposed to do

[desert hornet]

question your teacher

a function is only invertible when it is a one-to-one function, which f(x) is not

since f(x)=f(-x)

also, even if you somehow assume that there exists an inverse function, like you did

it leads to an irreducible quartic (the same one that you wrote)

[tropic anchor]

ah well

okay then ty for trying

[desert hornet]

i did not "try" the question. I am telling you that the question is wrong

you should talk to your teacher about this

[tropic anchor]

what really??? This was from my math final

damn

[desert hornet]

unless I'm being incredibly stupid right now, I really don't see a way how this question is correct

[serene parrot]

your teache is chatgpt

[desert hornet]

maybe some other helpers can corroborate my thinking

[tropic anchor]

?

[serene parrot]

how many marks does the question have and how many did you get?

[tropic anchor]

6 marks, part a i got 2 part b i got 2

😭

[desert hornet]

it doesn't make sense.

there literally does not exist an inverse function

[serene parrot]

my first thought was restricting the domain, but not sure how correct that is

[desert hornet]

it is clearly stated that the domain is all reals

[vocal sleet]

@tropic anchor Has your question been resolved?

[vocal sleet]

Channel closed

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[marble harbor]

how to do this

[marble harbor]

wtf

😭

[urban laurel]

<@&268886789983436800>

[night sequoia]

ooh mods

[gaunt sparrow]

No one cares, I don't know who hurt you but ppl come here for help and you're just being awful.

[viral copper]

write it in cis form

use 1 + cos t = 2cos^2(t/2)

and rewrite isint as 2isin(t/2)cos(t/2)

[upbeat bronze]

@viral copper after you finish with him can you help me in #1198716695615897763

[urban laurel]

i think writing the expression inside () in exponential form is easier

[viral copper]

just open a help channel

[night sequoia]

don't advertise your channel in other's help channels

[marble harbor]

wdym how do i use that here

[upbeat bronze]

Sorry

[upbeat bronze]

i did

[viral copper]

first rewrite the exponential term in terms of cost + isint

[viral copper]

you opened a forum thread

[upbeat bronze]

oh mb

[viral copper]

@marble harbor

[marble harbor]

how do i find t tho

[viral copper]

it's π/3 is it not

[marble harbor]

i dont know

[viral copper]

do you know $e^{ix} = \cos x + i\sin x$

[twin meteor]

NEON

[marble harbor]

oh yea

re^itheta

[viral copper]

yeah that's what i meant

should have been clearer

so after doing that

you would have

$(1 + \cos x) + i\sin x$

[twin meteor]

NEON

[viral copper]

where x is π/3

[marble harbor]

yes

[viral copper]

do you agree so far?

alright

[marble harbor]

yea i do

raised 2 5 right

[viral copper]

yup that too

now you can write 1 + cos x as 2cos^2(x/2)

do you agree to that?

[marble harbor]

yes

[viral copper]

alright cool

and sin x as 2sin(x/2)cos(x/2)

$\left [ 2\cos \frac{\pi}6e^{i\pi / 6}\right ]^5$

[marble harbor]

yes

[twin meteor]

NEON

[upbeat bronze]

@viral copper i forgot how to open a room

[viral copper]

go type in one of the unoccupied ones

[marble harbor]

go to one of these and ask for help

[viral copper]

so what's the modulus of this complex number?

[upbeat bronze]

ight

[marble harbor]

how do i find that

[upbeat bronze]

Thank you

[viral copper]

now you can just distribute the power

$\left ( 2\cos \frac{\pi}6 \right )^5 e^{5\pi i/6}$

[twin meteor]

NEON

[viral copper]

can you compare this with re^(iθ) and tell me what the modulus is?

[twin meteor]

Adam Chebil

[marble harbor]

how do u find the modulus

[viral copper]

do you not know what the modulus is for z = re^(iθ)

[marble harbor]

no

[viral copper]

= but yeah that

[twin meteor]

Adam Chebil

[marble harbor]

im still not sure aboutt his

[viral copper]

he wrote it out for you as well

are you not familiar with the notation

[marble harbor]

nope

well

ive seen it

but idk what it implies

[viral copper]

well

do you know what modulus is

at the very least

[marble harbor]

from what i know i think itmeans remainder

but idt

that makes

sense here

ok wait

it means

absolute

[viral copper]

that's a different modulus

[marble harbor]

value

makes more sense

now

[viral copper]

yes what's the absolute value of a number

[marble harbor]

its disstance away from 0

[viral copper]

yes exactly

do you know about the polar form of a complex number

[marble harbor]

yea

[viral copper]

what's r and what θ

[marble harbor]

of this equation?

[marble harbor]

of this?

[viral copper]

of

this

just trying to make sure you know what the symbols are