help-10

[safe stirrup]

Which gives me
2x -y +6z = 0

And thus

y = 2x + 6z

[unreal musk]

(also the reason I chose to solve for y was because I'm lazy and that's the easiest one to do, you could've instead solved for x and it would also get you those)

[safe stirrup]

Honestly I'm very lost after this.

[unreal musk]

Well, your eigenvector was (x, y, z) after all, and you want to see if you can rewrite that, knowing that, say, y = 2x + 6z

From those, there are two "obvious" linearly independent eigenvectors you can find...

[safe stirrup]

Wait where is his vector? I onlyhave ker(E - 2I)

I thought we could forget the vector for now.

[unreal musk]

Remember the eigenvector of 2 is a nonzero vector v such that Ev = 2v, which is equivalent to (E - 2I)v = 0, so v is in the kernel of E - 2I

[safe stirrup]

Oh right.

[pseudo swift]

{(-3,0,1), (1, 2, 0)} is a basis of Ker(E-2I)

as is {(1, 2, 0), (0, 6, 1)}

any of these will do

[safe stirrup]

Ah ok.

[pseudo swift]

and there's a lot infinitely many of them

[safe stirrup]

Hold on I'm getting confused.

I was about to write something like

x [2, 0 ,0] + y [0, -1, 0] + z [0, 0, 6]

But it's so wrong.

The other idea I had was to assume z = r element of R

and maybe y = t element of R

But I'm back at square one.

[pseudo swift]

well you can do that

so that your eigenvectors look like (1/2t - 3r, t, r) for t, r real numbers

i.e. t(1/2, 1, 0) + r(-3, 0, 1)

here's yet another basis

[safe stirrup]

Oh okay, so if I understand well, since I have to give whatever basis I want

I could say z = 1/2

Oooooh I think I remember now.

Wait I,m almost there. I remember something critical, but I'm missing one hurdle.

So I said that Z = s
x = k

and y = 2k + 6

I need twovectors from those, which will be related to s and k.,

I think I got two good vectors. Which are the ones you said earlier.

[safe stirrup]

Here.

I'm only missing one thing.

Hold on will write.

How to go from there

to the two equations.

The two vectors mentionned.

But what is the proper way to transition.

[pseudo swift]

well the trickster way is pick (s=1, k=0) and (s=0, k=1)

which is prolly what chartbit did

it guarantees the two vectors you'll get are linearly independent

[safe stirrup]

Oh I think I know.

Something like this (hold on will write)

Found this somewhere in my notes from some months ago.

About this approach.

That makes total sense.

[pseudo swift]

yeah that's what I did above

[safe stirrup]

I did not realize it was this.

How would I write a basis? inside somes acolades?

[pseudo swift]

sure

[safe stirrup]

Goood.

En prenant le même exemple ci-dessus.
Pour ceci:

Le générateur me donne ceci

donc le k de la valeur de base 2 serait de 1

Mais là notre dimension de la base est... 2?

Ah attends

j'ai une faute de frappe

Nah c'es tbeau c'était une faute de frappe.

[obtuse pebble]

@safe stirrup Has your question been resolved?

[safe stirrup]

It should be fine for now

Merci encore! Très très apprécié.

.close

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[silver ore]

All I want to know is where did the 2 come from

I understand everything but the 2

also the entire problem is:
If the maximum tensile force in any of the truss mem- bers must be limited to 24 kN, and the maximum com- pressive force must be limited to 35 kN, determine the largest permissible mass m which may be supported by the truss.

I have no idea if it makes a difference in whether someone can explain where the 2 came from or not

[tawny copper]

Isnt it sin30 = 0.5

[silver ore]

yes

[tawny copper]

So 0.5*Fbc = mg

[silver ore]

sin30 = 1/2

yes

but where did the 2 come from

[tawny copper]

=> Fbc = mg*2

[silver ore]

wait

hold up

processing

[tawny copper]

LMAO

[silver ore]

OOOOOOOOOOO

aye

I see it

[tawny copper]

💀

[silver ore]

It's been a long day

[tawny copper]

Sleep

[silver ore]

I sadly cannot

I have to constantly study since I'm taking 8 classes and also prepping for grad school and working

I am an insomniac

.close

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[barren nest]

attempt, stuck

[obtuse pebble]

@barren nest Has your question been resolved?

[fresh nymph]

So let's focus on a_i^j (this is a with i as low index and j as high index)

First if i = j then delta_i^j = 1
so a_i^j * a_i^j = 1
so a_i^j = 1 or -1
so |a_i^j - delta_i^j| = 0 or |a_i^j + delta_i^j| = 0

Second case if i != j then delta_i^j = 0
so a_i^j * a_j*j = delta_i^j = 0
so a_i^j = 0 or a_j^j = 0
but a_j^j can't be equal to 0 (we've proven that in the first case it's either 1 or -1)
therefor a_i^j = 0 and we proven what we wanted because remember delta_i^j = 0

@barren nest

ping me if questions but i think this is correct

[obtuse pebble]

@barren nest Has your question been resolved?

[obtuse pebble]

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[valid briar]

Im confused for letter d, how would you even compute f(a) and then graph it?

[sage dagger]

You compute it the same way you would compute any other number

[valid briar]

so its just gona be 2a -1?

well if thats the case, i dont really know how I would put that on a graph

[sage dagger]

Are the only ones you have to graph, 2x-1 and x^2-4?

[valid briar]

well Im assuming I need to graph the answers i get from the ones given in part A

[sage dagger]

It just says evaluate no?

[valid briar]

hmm

[sage dagger]

What does part B say

Is there more

[valid briar]

yeah its just that in the screenshot I sent

[sage dagger]

Evaluate just means you have to compute the value

[valid briar]

yes I alr did that so im not supposed to use it for part B then?

[sage dagger]

Do you know what part B is asking you to do?

[valid briar]

I just thought I would use the values from part A to part B, and if thats not the case, Im not very sure what to do if all I have for part B is those two equations

[sage dagger]

Can you tell me what it’s asking you to do for part B

[valid briar]

yeah that's literally all 😦 the next part is just a whole different question

[sage dagger]

No like

I’m asking you

Do you understand part B

[valid briar]

im thinking id draw a graph on a paper and input the values i got from part A and connect the dots?

[sage dagger]

Well I guess you could do that

Do you know the general shape of 2x-1?

[valid briar]

i forgot certain equations have general shapes oops

so with that i can just like use numbers like -3 to 3 to put in the function for example?

[sage dagger]

well you could

But it helps to have an idea of what the function looks like first

is it a straight line? Will it have curves?

[valid briar]

well Im not very sure for those specific ones I just watched a video explaining a bit of it though all I know x^2 alone produces an upwards curve

[sage dagger]

Does y = mx+b look familiar to you

[valid briar]

Oh yeah i remember that video mentioned that too but yeah not too familiar,

[sage dagger]

well anything in that form is a straight line

the straight line will either have a positive slope (going up) or a negative slope (going down)

[valid briar]

so that applies for the first one? f(x)?

[sage dagger]

Yes since there’s a single x term and it’s highest power is 1

Start by finding it’s y intercept, aka finding f(0) which you seemed to have done in part A)

[valid briar]

yeah I ended up with -1

[sage dagger]

Yea

Now find it’s x intercept

Let 2x -1 = 0 and solve for x

[valid briar]

1/2?

[sage dagger]

Yeah

Plot the points so far on a graph

[valid briar]

like where i should put -1 and 1/2?

[sage dagger]

We found y = -1

so that goes on the y axis

[valid briar]

yeah I put both already

like this?

[sage dagger]

Yes but you might want to put them further apart

[sage dagger]

Yeah

Then since it’s a straight line between those points there’s really only one way you can draw this

[valid briar]

ohh I see

so with the stuff you asked me to do, that's how I would show the process of it?

I got it now, thank you!! I'll just try figuring out what to do with the one with x^2 now, thank you again :))

.close

[obtuse pebble]

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[dense drift]

where can i learn to solve maths like this, like what would be the name of the chapter, that i shuld search in khan academy / youtube

[vague ravine]

ur identifying graphs and trying to match them

like for circles or any sort

you would expect for x and y to be squared

i would probably look at the degree of x and y

[dense drift]

how to find that

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[marsh spoke]

How would this be solved?

[obtuse pebble]

@marsh spoke Has your question been resolved?

[obtuse pebble]

@marsh spoke Has your question been resolved?

[obtuse pebble]

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[azure shoal]

Let A, B be two n × n matrices. If the
answer to any of the following question is yes then give justification otherwise give
an example showing why the question has a negative answer:

[novel knoll]

What have you tried?

[azure shoal]

trying to find an invertible matri

such that PDP^-1 = C

for 2

i thought i could do part 2 first

and then remove conditions which im assuming in part 2 (det A =/= 0 and det B =/= 0)

then based on that ill do part 1

but i really dont know

and i have this due soon so I'm panicking bec of the time constraint

[novel knoll]

If det(A)!=0 then try writing AB as A(BA)A^{-1}

[azure shoal]

for the second part right?

if you don't mind, could you please tell me what i should do for all parts? I actually do not understand, and feel too burnt out to understand

@novel knoll I'm sorry, could you please help?

[novel knoll]

With? I gave a hint. If you just want solutions this is not the server for it (and you can probably find them on stackexchange)

[azure shoal]

I couldn't find it, and that's not clarifying oit either. Will I do soemthing like: det(A) =/=0. We have BA = PDP^-1, where D is diagonalisable and P is invertible. ABA^-1 would be similar to BA, that os they share the same eigenvalues . Since BA is diagpmnalisable, eigenvalues exist.

Since ABA−1 shares the same eigenvalues, and A is invertible, AB must also be diagonalizable.

is that reasoning correct? @novel knoll

[obtuse pebble]

@azure shoal Has your question been resolved?

[azure shoal]

no

[obtuse pebble]

@azure shoal Has your question been resolved?

[obtuse pebble]

@azure shoal Has your question been resolved?

[timid silo]

what level maths is this?

university?

[azure shoal]

yes

[obtuse pebble]

@azure shoal Has your question been resolved?

[frank monolith]

you should try asking this in #linear-algebra

[azure shoal]

i did

[meager gale]

Maybe you can try to reason about eigenbasis

Actually for 3 and 4 you don’t need to

[obtuse pebble]

@azure shoal Has your question been resolved?

[obtuse pebble]

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[modest hollow]

can somebody please help?

[ember frost]

,tex .law of cosine

[warm shale]

فطر

[modest hollow]

I just started learning this

[gloomy edge]

You can find the bottom two angles by drawing a triangle comp. to them

[ember frost]

and now you are to use them

[gloomy edge]

Do this for both sides the use law of cosines

[ember frost]

um

[ember frost]

just use alternate interior angle

why draw another triangle

[gloomy edge]

U right

Although either way your assuming parallel

[modest hollow]

I got confuse too because a friend that was helping me said the same thing

I just really dont know how to start

[gloomy edge]

U can find the bottom two angles of the triangle through alt int

[ember frost]

you are also assuming parallel if you do your way

[gloomy edge]

That’s what I said

[modest hollow]

could someone go on a call with me to explain

please

[gloomy edge]

So the angle of depression plus the angle at the base is going to equal 90

[obtuse pebble]

@modest hollow Has your question been resolved?

[obtuse pebble]

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[wide oracle]

how do i do this in a less messy way?

[tranquil depot]

lowk i don't know what they mean by messy

because your work is very clear

oh wait

yeah 🤷‍♂️ ig i don't know whats up with this but other than that looks neat enough

[obtuse pebble]

@wide oracle Has your question been resolved?

[wide oracle]

yeah idk

you would also get 2 different options for b

[obtuse pebble]

@wide oracle Has your question been resolved?

[obtuse pebble]

@wide oracle Has your question been resolved?

[obtuse pebble]

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[light kayak]

hii could i please get help with this question

[safe haven]

!occupied

[obtuse pebble]

Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).

[round rivet]

#❓how-to-get-help Please get yourself a channel

[quiet rapids]

what do you mean

[safe haven]

someone else is already using this channel

[quiet rapids]

oh

sorry

[round rivet]

Are you familiar with using x as an variable to make linear equation and solving it?

[light kayak]

yes

[round rivet]

So do you need help with making the equation?

[light kayak]

yes

[round rivet]

Ok First Lets convert the unit of 40c to $0.4

[light kayak]

would the ham sandwich be x and salad sandwich be x + 0.40

[round rivet]

yes

that is correct

[light kayak]

how would you put it into an equation?

[round rivet]

Now in the problem it is written that the friends bought 4 salad sandwich and 3 ham sandwich

so it will be like 4 times the cost of single salad sandwich

adding that with 3 times the cost of single ham sandwich

[light kayak]

4(0.40+x) + 3(x) = 17?

[round rivet]

will be equal to the total amount they paid

[round rivet]

0.40 it will be

Yes that is correct

now try to do the next steps

[light kayak]

x = 2.20?

[round rivet]

That is correct!

That is the price for ham sandwich

[light kayak]

so the ham sandwhich would be 2.60

[round rivet]

No

[round rivet]

Read this again

[light kayak]

the ham sandwich is 2.20 and the salad sandwich is 2.60

[round rivet]

Yes!

Good job solving it

[light kayak]

thank u so much for your helpp

[round rivet]

You're most welcome

[light kayak]

could i please get your help with other word equations?

[round rivet]

Sure ask ahead

[daring glacier]

simple algebra try thinking in x

[light kayak]

i dont think this is right but would the renovations be 1/6x and the house be 980000 + 1/6x?

[daring glacier]

no let cost of house is x

then what will be the cost of renovation?

[light kayak]

ohhhh

1/6 of 9800000

[round rivet]

No

[daring glacier]

no no

[light kayak]

oh oops

[daring glacier]

9800000 is the gross total amount that is payed

[round rivet]

Let's take cost of house just the house as x

then what is the cost of renovation if the cost of renovation is 1/6th the price of house

[light kayak]

1/6 of 9800000 + the price of the renovations?

[round rivet]

forget the $980k dollars

[daring glacier]

@tim see if price of house is x and ren. cost is 1/6 then what will be the cost of renov.

[light kayak]

would the renovations be 1/6x?

[daring glacier]

yes

now calculate x

[round rivet]

now what if you spent x to buy house and 1/6x to do the renovations

what would your total cost be?

$$
\frac{1}{6}x
$$

[warm shale]

notwish

[round rivet]

also this is 1/6x

[light kayak]

980 000 + 1/6x??

wait no

1/6x + x = 980 000

[round rivet]

Yes

Good job understanding it

Now solve it

[light kayak]

would x be 294 0000

[daring glacier]

no

[oak cape]

what is your working behind this

[light kayak]

help

[oak cape]

dont laugh at it@daring glacier

[round rivet]

no

[oak cape]

yeah, i wanna know your working behind it

[light kayak]

oh i thought u were making fun of it

[oak cape]

no i was genuinely asking... the guy who reacted was making fun

[light kayak]

ok i multiplied 980 000 by 6

[round rivet]

good then

?

[light kayak]

then added 1x +x

2x

[round rivet]

ok that was a mistake

$$
\frac{x}{6} + x = 980000
$$

[warm shale]

notwish

[oak cape]

why

[round rivet]

@light kayak Does the equation you wrote look like this?

[light kayak]

ohhh my

nooo

[oak cape]

no what how is that good

[light kayak]

i forgot to multiply 1 by x

[daring glacier]

@light kayak you should also try to work on LCM

algebra's base

[round rivet]

I thought she did the fractional addition

[light kayak]

oh okay thank uu

[daring glacier]

@light kayak if you dont mind me asking are you in high school or in university?

[light kayak]

highschool

[round rivet]

1st year?

[light kayak]

wdym like 7th or 9th

im not american so

[round rivet]

so are you in 7th?

[daring glacier]

you should really work on LCM and basics of algebra. althought dont take this the wrong way this question was of an aptitude. but keep trying you ll be able to solve once you grasp the knowledge

[oak cape]

have you understood it in the first place @light kayak

did you get an answer

[light kayak]

okay thank u

[light kayak]

no

okk im gonna do it again

[warm shale]

TheRuleOfEngineering

TheRuleOfEngineering

[light kayak]

980 000 x 6?

[round rivet]

no you can't multiply directly

since x/6 and x are in addition

you first gotta make their denominator same

[light kayak]

ohhh oops

[round rivet]

yes

[oak cape]

add $\frac {x}{6}$ and $x$

[warm shale]

TheRuleOfEngineering

[oak cape]

fraction addition

[oak cape]

then you can do this

[light kayak]

so would it be 140000?

[round rivet]

no

[light kayak]

boy

[round rivet]

did you first add the fractions?

[oak cape]

always state your working behind your answers

[round rivet]

what did you get on adding them?

[warm shale]

TheRuleOfEngineering

[oak cape]

in your case, what would A, B, C and D be

[light kayak]

a is x

b is 6 and c is x

would d be x

[oak cape]

d would be 1

[round rivet]

no

[light kayak]

okay

[warm shale]

TheRuleOfEngineering

[round rivet]

always remember if there is any number or variable with no denominator it means the denominator of that number is 1
Okay?

[light kayak]

yeah makes sense other wise itd be

1

so would it be 2x/x

[oak cape]

would what be 2x/x

[round rivet]

kind of reminding me of how my dad used to beat tf outta me doing my maths hw 😭 the thing should be in CAPS for that ngl

[oak cape]

i still remember the belt lmfao

[round rivet]

fr

[light kayak]

no wait would it be 2x/7

[round rivet]

no can you try again ?

[round rivet]

Check this one more time

[oak cape]

how do you add those fractions

[warm shale]

TheRuleOfEngineering

[oak cape]

how do you add these fractions

[light kayak]

oh i forgot

the formula

[oak cape]

...

[round rivet]

the formula

[oak cape]

AD = A * D (A multiplied by D)

just in case

[light kayak]

x+6x/6

7x/6??

[oak cape]

yep

[round rivet]

yes

good job

:D

[oak cape]

now you can finally do what your idea in the beginning was

[round rivet]

[warm shale]

TheRuleOfEngineering

TheRuleOfEngineering

[light kayak]

ok so 6 multiplied by 980000

5880000 divided by 7

840 000

[round rivet]

yeah

good job

[oak cape]

this is the price of the house

[round rivet]

Now what is this you got?

[oak cape]

you can also cross-check your answer

[light kayak]

omggg yess guyss

it just took me 3 ppl but i made it

[round rivet]

this is important @light kayak

[light kayak]

okay so

[oak cape]

$840000 + \frac{1}{6}840000$

[warm shale]

TheRuleOfEngineering

[oak cape]

since renovation price was 1/6th of the house

idk what kind of renovation they're doing with 140 grand

but yes hope you understand the logic tim

[light kayak]

thank you sosososooo much for the help and your paitence

would the equation for this be: 40 + x = 3x?

[chrome crypt]

40 + x = 3x

Yep that seems reasonable.

[light kayak]

x = 10?

wait no

x= 20

[chrome crypt]

Yeah,

20 mb.

[light kayak]

thank u smm

[chrome crypt]

Aye np.

[light kayak]

.close

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[graceful kestrel]

need some help with simplification of this integral

[hollow badger]

yeah sure

so what integration technique do u think we should use

[graceful kestrel]

i didnt learn how to deal with this sort of things.

[hollow badger]

have you done integration by subsitution?

u sub?

[graceful kestrel]

yeah

[hollow badger]

okay cool so u can do this

[lost otter]

think about this

[hollow badger]

sin i got this one

[lost otter]

what differential gives u

oh ok

[graceful kestrel]

but this isnt the case, im not supose to calculate F(x)

[hollow badger]

@lost otter go help florida with ordering decimals

[lost otter]

he had his test today

i think

hope he did well

[graceful kestrel]

😐

[hollow badger]

oh damn same

anyways

[hollow badger]

u are supposed to find F(x)

u find F(x) then sub in the bounds

[lost otter]

even i wanna know the answer

at first i thought its ln(f(x)) but thats not it

[hollow badger]

we should find F(x) first

[graceful kestrel]

im supose to get to this, without the need to intergrate

[hollow badger]

we need to use integration by substitution

[graceful rapids]

let $u = f(x)$

[warm shale]

b

[graceful kestrel]

and

[hollow badger]

so let u = f(x)

then find du/dx which is straightforward

[graceful kestrel]

i haven't learnt this method, so its not straightforward for me, can you show me the steps?

[lost otter]

are u in math adv lol

[hollow badger]

u said u knew u sub?

[lost otter]

even i havent learn substitution

[hollow badger]

i can show you the steps

[graceful kestrel]

i now see we mean different things

[lost otter]

LMAO

[hollow badger]

okay so our question:

you can see we are integrating a product here i.e f’(x) f(x)

[graceful kestrel]

yes

[hollow badger]

to integrate a product we can use a technique called u substitution

so we let u equal to one of the functions

in this case, let u = f(x)

do you understand so far?

[lost otter]

do you differentiate u

[graceful kestrel]

yes

[hollow badger]

okay so u= f(x)

du/dx = f’(x)

u understand that step?

[graceful kestrel]

yeah

[hollow badger]

so we can rewrite the integral now

[lost otter]

O I GOT IT

omg

[hollow badger]

from f’(x) f(x)

we replace f’(x) with du/dx

so its integral of du/dx f(x)

[lost otter]

and f(x) is u

[hollow badger]

u got it yoni?

[lost otter]

:0

[graceful kestrel]

yea, but how does that help us?

[hollow badger]

watch

so integral of du/dx f(x) dx

as f(x) is u, we replace it with u

integral of du/dx u dx

the dx will cancel out

so now we have integral of u du

[graceful kestrel]

and thats exactly f(x) * f'(x) isnt it?

[hollow badger]

yes

its the same thing but with respect to u

instead of x

so we transformed the integral to one we can actually evaluate

so integral of u du is…

[graceful kestrel]

u^2?

[hollow badger]

u^2/2

[lost otter]

:0

[hollow badger]

now sub u back in

u was f(x)

so its (f(x)^2)/2

[graceful kestrel]

ok

[hollow badger]

now evaluate the definite integral by subbing in the bounds

[graceful kestrel]

i dont understand why do we need to integrate if we removed the dx

[hollow badger]

the dx just means “with respect to x”

i replaced the dx with du

so its an integral with respect to u

[graceful kestrel]

oh

[hollow badger]

so we still integrate

[graceful kestrel]

ok

thanks!

[hollow badger]

np

[graceful kestrel]

.close

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[graceful kestrel]

.reopen

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✅

[graceful kestrel]

@hollow badgerafter i did it, i got a negative result, but i am given a photo of f(x) and the area is above the x axies

[hollow badger]

are you given f(x)?

[graceful kestrel]

yes

[hollow badger]

show me

[graceful kestrel]

one sec

[hollow badger]

remember that we integrated f’(x) f(x) not f(x)

[hollow badger]

this is a graph of f(x)

[graceful kestrel]

so what i got is true?

[hollow badger]

yeah

[hollow badger]

u understand what i mean?

[graceful kestrel]

yes, its not the same graph

[hollow badger]

yeah cool

any other questions?

[graceful kestrel]

not 4 now

thanks again

[hollow badger]

yeah no prob

[graceful kestrel]

.close

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[hollow badger]

reopen if u need help

[graceful kestrel]

.reopen

[obtuse pebble]

✅

[graceful kestrel]

need some help with calculating the sum of the second sequence in order to find q

[obtuse pebble]

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[full oriole]

How can I find f'

If i can find f' then i can find f

But idk how to find f'

[deep skiff]

so you have (x^2 + 1) * f'(x) + x * f'(x) = f(x) right?

[sage geode]

It's f''(x) next to x^2 + 1

[deep skiff]

ah

let's replace f(x) with y

(x^2 + 1) * y'' + x * y' = y

this is a second order differential equation

you familiar with solving those?

[full oriole]

I know them as "Mean Value's Theorem consequences"

@deep skiff but i suppose they are the same thing because I heard my teacher saying that they are basically differential equations or something

But the book doesn't mention them as diff equations

[deep skiff]

solving these is a bit of a chore

here are some resources

https://tutorial.math.lamar.edu/classes/de/introsecondorder.aspx

https://tutorial.math.lamar.edu/classes/de/VariationofParameters.aspx

look at this second link, this algorithm should work for you

[full oriole]

Oh ok

I think I got it @deep skiff

Does this seem about right?

Just added +xf'(x) to every part

[deep skiff]

oh.... looks ok I guess, I didn't think of that approach

[full oriole]

Oh lol, well our book doesn't have the differential equations approach lol

[deep skiff]

I'm not sure if it's fully mathematically correct, but like, if it works it works

just make sure to check your answer

[full oriole]

I will, thank you very much

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[graceful marten]

Im having a problem with trig identities,
I dont know where to start

[graceful marten]

Prove.
sin x / 1+ cos x = tan x/2

I dont know what im missing

I dont know how to do it

i thought sin x / cos x = tan x

so sin x/2 / cos x/2 = tan x/2

is that wrong ^? if so how?

ty tyty

[round rivet]

yes

you need make it sin x/2 divided by cos x/2

there is an identity to convert sin2x to 2sinxcosx

and another one cos2x = (cosx)^2 - 1

hope this helps you to approach further

[graceful marten]

Ohhhhh

I see

smart

no that makes sense

[graceful marten]

I wasnt very sure if this part was 100% correct

Yeah its just playing around with it

[graceful marten]

Thank you Veryyy Much

wishnot

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[gaunt gyro]

Any german-speaking here who'd like to explain "Faktorräume" (LinA) to me?

[obtuse pebble]

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[median scarab]

this is the solution for this question, i don't understand why iii must be true?? how can we determine convergence based of an??

[gaunt gyro]

what exactly do you mean? It says if $\sum a_n$ were to converge, $\sum b_n$ also converges.

[warm shale]

Sheymes

[unreal musk]

See limit comparison and its conditions

tl;dr this limit being finite and nonzero implies both series behave the same

[median scarab]

OHH i see, okayyy. the thing that threw me off was it basing the conditions off of an by saying "if an"

[median scarab]

don't we determine convergence or divergence by bn??

[unreal musk]

You can swap the places of a(n) and b(n) really, doesn't really make a difference which one you use
If the limit of a(n)/b(n) is finite and nonzero, so is the limit of b(n)/a(n)

,w limit comparison test

[warm shale]

Results provided by WolframAlpha

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Requested by chartbit

[unreal musk]

bruh-

[obtuse pebble]

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[blissful bane]

can you show how this is established?

[obtuse pebble]

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[prisma shale]

<@&286206848099549185>

[river falcon]

what have you tried till now?

[prisma shale]

answer pls

[distant shadow]

6/30 = 1/5

[dark osprey]

which one do you need answer for?

all of them?

[dark osprey]

so I think that they mean that
6 - Iced & C Chip
2 - Iced & No C Chip
18 - C Chip & No Iced
4 - Neither

[obtuse pebble]

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[midnight dust]

the given answer is option a

[midnight dust]

isnt it wrong?

since g is onto and f is said to be one-one, should not h be both?

so i am using this proposition. Or am i wrong?

[molten grove]

f isn't onto

so gf won't necessarily be a well defined function

Youre using the converse of the proposition

[obtuse pebble]

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[wheat lance]

need to integrate this by parts

looking for someone familiar with the DI method to help

i can do it the long way but wanna learn DI method

[river falcon]

what DI method

tabular method?

[wheat lance]

yes thats it i believe

2x^2 goes in the D column right

[river falcon]

yes

[wheat lance]

essentially im struggling to integrate sec^2 (x) * tan(x)

[timid silo]

take tan(x) as t

dt would be

[wheat lance]

sec^2(x)

[timid silo]

yes

so it's integral would be ....

[wheat lance]

............

1/2 sec^2(x)

maybe

dk

idk

[timid silo]

no

what is integral of t dt ?

[wheat lance]

not sure sorry

[river falcon]

t^2/2

[timid silo]

t^2 / 2 + c

you can ignore the c in DI method

[wheat lance]

This is what I did

I dont think its correct

[river falcon]

it is

[wheat lance]

i thought u said /2

[river falcon]

nvm

i just saw the table

[wheat lance]

yeah..

im cooked

i see i am wrong

it is 1/2 tan^2 (x) ??

[river falcon]

yes

[wheat lance]

ty

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[agile scarab]

can someone point me in the right direction, idk where to start with this question

[agile scarab]

i have this, but im not exactly sure how to apply it

[karmic yarrow]

what series best fits the question

[agile scarab]

-ln(1-x)

im confused on how to make it work with ln(1+5x)

[slim lake]

$-x\rightarrow 5x$

[warm shale]

Max

[agile scarab]

so i can replace all instances of x with 5x in the expanded version?

like 5x + 5x^2/2 + 5x^3/3 + ...

[karmic yarrow]

Do you know what the maclaurin series of ln(1 + 5x) be using the formula -ln (1 - x)

Thats what the question is asking

[agile scarab]

no

yeah im just confused how to apply the formula

[karmic yarrow]

Have u done another question like this before were u basically convering something into a power series or nah

[agile scarab]

nope 🤣 the final is in 4 hours

ill try watching some youtube video on it to figure it out

[karmic yarrow]

Damn

Ok the maclaurin series is -sum((-5x)^n/n))

I think

u understand how I got there

[obtuse pebble]

@agile scarab Has your question been resolved?

[agile scarab]

kind of

im started to get it

prob will just watch video to fully understand tyvm anyways

[obtuse pebble]

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[winged estuary]

I did this but it's wrong

[obtuse pebble]

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[weary magnet]

Losing my mind over this integral

[weary magnet]

I need help

Anyone?

this is what i manage to work out
let u = 2x^2+x
(du)^-2 = (4x+1)^-2 dx
1/2 int (u^2)/2 (du)^-2

then i'm stuck cuz i dunno how to solve (du)^-2

[timid silo]

Well you need to split the integral bc The function isn’t continuous at -1/4

I think that’s how that works

Somebody correct me if I’m wrong

I think I’m confusing myself

Ignore me possibly

[obtuse pebble]

@weary magnet Has your question been resolved?

[weary magnet]

<@&286206848099549185>

[cosmic grotto]

The interior of this integral is the formula of a derivative function

Hint: ||Distribute x in and take 1/2 out||

@weary magnet

Then i should give hint 2

[weary magnet]

How would u approach it

I need to find a good approach

Already did that method the final result is this

i'm stuck i dunno how to solve (du)^-2

[cosmic grotto]

Uh lets give me 1 min

[cosmic grotto]

I think answer is -infinity

[obtuse pebble]

@weary magnet Has your question been resolved?

[obtuse pebble]

@weary magnet Has your question been resolved?

[obtuse pebble]

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[timid silo]

please help i don't know where to get started

[plain stag]

How have you been taught to find intervals of convergence in general?

[timid silo]

no

[plain stag]

The question was how, not yes or no

If you haven't been taught, and you're being asked questions about the topic, you should go to your instructor and let them know about this discrepancy

[timid silo]

now im gonna fail the class

[obtuse pebble]

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[marsh spoke]

How would this be solved?

im thinking of using p/x^q where if q>1 it converges

is that the right approach and how would i make it work

[viral blade]

often x = ln(u) is a useful substitution in these types of situations

idk how well it works here

[viral blade]

this unfortunately isn't helpful here because the power on x in the denominator is always 1

[brisk grove]

Compare it with 1/(x * (lnx)^(1-p)) at infinity

[viral blade]

oh my bad it's x = e^u

[obtuse pebble]

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[shell cove]

How can I take the derivative of this

[gritty vessel]

quotient rule

[shell cove]

i think im doing it wrong

[gritty vessel]

what's the derivative of e^(-x)

[river falcon]

-e^(-x)

[gritty vessel]

yeah so you need to fix that

[shell cove]

ok, thx

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[obtuse pebble]

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[shell cove]

whattt

derivative of -e^-x

its -e^-x. ln(-e) . -1 ?

ln(-e)

its log (-e) = -1 (?)
e

im confused, how ist it gon be +e^-x

[timid silo]

chain rule

[crude coral]

$$\frac{d}{dx} -e^{-x} = -\frac{d}{dx} e^{-x} = - (e^{-x} \frac{d}{dx} -x) = -e^{-x} \cdot -1 = e^{-x}$$

[warm shale]

JustToPro

[crude coral]

yeah chain rule

[shell cove]

isn't that kind of situation ?

i mean i just don't see the ln a

[crude coral]

a here is a constant

also if u use a = e in here , lne is just 1

[shell cove]

yes but wasnt a -e

i just dont known whats ln (-e) isn't it -1

?

[rough marten]

lna where a >0

[crude coral]

how do u have ln(-e) btw?

[shell cove]

wait

[crude coral]

$$\frac{d}{dx} -e^{-x} = -\frac{d}{dx} e^{-x}$$ u can just keep the - outside while u do all derivatios

[warm shale]

JustToPro

[shell cove]

hmmm

but then this "-" wont come back?

its this exercise

first line, second part -> d/dx (e^x-e^-x)

[crude coral]

$$\frac{d}{dx} e^x = e^x$$ if u want i can prove this to u

[warm shale]

JustToPro

[crude coral]

also proof available on google

[shell cove]

wait im gonna send a better picture

the [] is where im confused

its like

ln (e) = 1
ln (-e) = 1

[shell cove]

soo, is that it?

I will accept this for my life

❤️

[crude coral]

no

lna is only defined when a > 0

its undefined when a is negative or 0

[crude coral]

just use chain rule

[shell cove]

okay so clearing up, when I want to do the derivative of (e^x - e^-x) i must do the chain rule and not use the exponential derivatives formula cuz ln a cant be negative < 0

[crude coral]

yeah

cuz power rule is when x is the base

e^x rule is when u have e as base

and a^x rule is when a constant is a base with x as power

[shell cove]

I see... that was mmm, a lot. thank you very much!

.close

[obtuse pebble]

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[obtuse pebble]

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[timid silo]

Hello

[daring glacier]

POST your question

[timid silo]

Im wiriting the question here

What Is the arm of ql/2 in s in respect of the line AC?

[obtuse pebble]

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[timid silo]

Do you Need more information ?

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[shell moth]

lets say f(x) is equal to this

intuitively, if I want to shift this function to the right one, shouldn't I do f(x+1)

which is equal to (x+1)* -x, but this actually shifts it to the left

so in reality, you have to do f(x-1) to shift it to the right

which isnt intuitive

so why is it right?

[river falcon]

one way to think about it is

if you're subtracting something from x, you'll need to begin with higher value of x than you did when it was just x

lets say you have x = 4

now if you want x-1 to be 4

x would have to be 5

which is higher than the previous value

so it shifts the graph to right

[shell moth]

ok alright

that does make sense

[near jackal]

I took the derivative to prove part b is that sufficient

[river falcon]

!occupied

[obtuse pebble]

Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).

[near jackal]

oh sorry

[shell moth]

its fine

im done anyway

thanks

.close

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[visual path]

how do we get the SA here

[visual path]

<@&286206848099549185>

[stiff glade]

Hello

[visual path]

hi

[polar fossil]

just find the area of each side

there are 6 total

and they're all rectangles

[river falcon]

or use volume = lbh = 972

get h in terms of x

suface area = 2(lb + bh + hl)

substitute values and simplify

[visual path]

oh right nvm i get it thanks yall

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[gray verge]

anyone know why this is wrong?

[obtuse pebble]

Please don't occupy multiple help channels.

[gray verge]

answer should be 233m

[polar fossil]

,calc t = 3.75; 9t^5 / 156250 - 2t^6 / 15625

[warm shale]

Result:

[-0.3132421875]

[polar fossil]

,w 30t^4 - 8t^5 = 0

[warm shale]

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[polar fossil]

,w 9.6e-6 * int[0, 3.75] of 30t^4 - 8t^5 dt

[warm shale]

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[polar fossil]

,w plot 9.6e-6 (30t^4 - 8t^5) from 0 to 3.75

[warm shale]

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[polar fossil]

yeah idk that seems like such a low velocity, not sure how you could ever travel 233m on that

[gray verge]

hm weird

maybe mark scheme wrong

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[hollow berry]

Hi! I'm studying statistics and i don't know how to solve this question. Any advice?

A new drug is being tested in 18 patients. The process consists of measuring the level of a certain component in the blood before and after the application of the treatment, in order to study the increase in that level in each individual. If the sample quasi-variance is equal to 26.35, how many patients would it take to estimate, with 95% confidence, the mean increase with an error of less than 1?

[obtuse pebble]

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.close

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[pearl bobcat]

Hello, could someone help me see what’s going on with the underlined area? I can’t see if (based on the equation until now) this is supposed to be -3x4 or -3x to the power of something that’s been removed.

Someone earlier said it’s just -3x and 4 goes on the other side but is this something you do later or is it simply supposed to be -3x alone there where it’s underlined?

[obtuse pebble]

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[pearl bobcat]

<@&286206848099549185>

[timid silo]

sorry can u put it clearly

[timid silo]

see you equate the powers

and since the bases are not integers,

the inequality is reversed like you did

and u can subtract 4 from both sides, doesnt make a difference

u can keep -3x and 4 on the same side to solve the quadratic, doesnt matter.. ull get the same answer considering all your signs are correct

,w plot (x^2-3x-4>=0) from -5 to 5

[warm shale]

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[timid silo]

see

[obtuse pebble]

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[torn bough]

How would I solve this?

[rain forge]

What is A ?

[runic void]

@torn bough

recall each coloumn represents variables

can you tell the corresponding reduced system of equations from the rref matrix?

[obtuse pebble]

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[safe stirrup]

Hello friends, I have a quick question

[safe stirrup]

Is this an example of a passage matrix?

For changing coordinates of a basis to an another basis?

Here is what I have for a passage matrix :

Sorry if this is french, if you aren't french... The low quantity of text should be fine.

[rain forge]

Pour une fois qu'il y a un français que je ne peux pas aider merde, t'es en quelle année ?

[safe stirrup]

Universitaire, introduction en algèbre linéaire ahah.

[rain forge]

1 ère année ?

J'adore l'algèbre linéaire mais j'ai pas encore vu ça

[safe stirrup]

Rendu à l'université, premi`re année, deuxiène années n'existent plus vraiment, car c'est ma... 8e année universitaire en théorie ahah.

J'ai fait 7 ans dans un autre programme.

[rain forge]

Ah d'accord

J'ai vu que tu postais pas mal sur ça faudra que je m'y intéresse justement je prépare un devoir sur les quaternions et les matrices de rotation yavait des trucs assez semblable

[safe stirrup]

Ouais je suis un peu désespér avec mes études ahah. Les notes de cours laissent à désirer un petit peu.

Au moins je comprends mieux là.

[rain forge]

Bonne chance alors 👍