help-0

[wary stream]

Where are those angles even coming from?

The ones you used in your work

[azure leaf]

The Southwest is 225° and I see messed up on the northeast and typed down 90° when it should be 45°.

I got the southwest from the unit circle

I think I did the wrong problem in general. Because now see I messed up in the beginning

.close

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[round mica]

I'm not sure how to do question B, I got A right but have no idea where to start on B

[high rapids]

What question?

[high rapids]

,rotate

[round mica]

The value of a is 2

[limpid turret]

I think this is the first time I've seen upside-down

[round mica]

Yeah mb lol

[limpid turret]

b means that, once you expand, you'll have something like 3/x³+b/x²+c/x+d+ex+fx²+gx³+...

Find d, which is the the term with no x. i.e. the "constant term"

[high rapids]

SWR you are based

Doggo > Karl Marx

[round mica]

What do you mean find d

I'm just lost sorry

[ocean seal]

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An unexpected error occurred while processing your command!
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If the error persists, please contact our friendly support team at our support guild!

Exception

AttributeError: 'NoneType' object has no attribute 'remove_reaction'

[limpid turret]

If you multiply this

It'll look like this

The only term without an x factor is d.

That's the constant term

[round mica]

Ohhh thanks

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[high rapids]

Why should it be -1/-7?

[molten pivot]

Because there is no constant term

Lol

[rose rivet]

this one is 12 because its 4*3

[molten pivot]

Yeah

The y intercept is the constant term

The number you get when x=0

[molten pivot]

What happens when x=0 here

[rose rivet]

oh i get it thanks

[molten pivot]

Lol

Gg

[rose rivet]

because its 0 * 7 * -1 = 0

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[steady basin]

is this correct for b?

[last ether]

,w Taylor polynomial sin(x) around x = pi/4

[ocean seal]

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[steady basin]

um

[last ether]

Uh yeah no you goofed up big time

You need to sub pi/4 in for theta

[worn fox]

replace theta with pi/4 not x

[last ether]

You confused yourself by stating that it goes around x = theta

And then putting in pi/4 into x instead of theta

[steady basin]

but it says x is pi/4

[last ether]

x around pi/4

You defined what x goes around as theta

So theta is pi/4

[worn fox]

yeah its which x values you are expanding around, it will still be a function of x

[steady basin]

im so confused

lemme show u my worked examples

[steady basin]

this is my LN examples

[steady basin]

im trying to do this this way^

similar method

[worn fox]

in example 80 they replaced x with 61

[steady basin]

what would theta be here then?

could i say let pi/4 = pi/8 + pi/8

?

[worn fox]

pi/3

is even says in the bottom right

[tough gate]

anyone need a maths tutor for sats or gcse

[steady basin]

no

for the actual question

[worn fox]

well they convert to radians first

theta is pi/4 yes

because thats what you're expanding around

they're not asking you to approximate the value of sin(a particular value) in your question

[steady basin]

i mean like this

[worn fox]

no literally just replace theta with pi/4 in your formula

so it should be sin(x) = stuff involving x and pi/4

[steady basin]

^^

[worn fox]

why have you written at x=4

[worn fox]

you're doing question b

[steady basin]

my brain

ok x = pi/4

anway

is that correct

[worn fox]

but yeah thats right

,w power series sin(x) around pi/4

[ocean seal]

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Requested by iCaird#6258

[steady basin]

so why do we sub pi/4 in theta and not x?

[worn fox]

.

[steady basin]

ight kl

thanks

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[open roost]

how would u solve this algerbrically?

[limpid turret]

logs

[high rapids]

Can you make the 6 2 * 3?

[open roost]

yea

wait so 3(2)^x?

then x+1=x

right?

[strange meadow]

Do you know logarithms

[open roost]

yea but i am reviewing it so it is kind of hazy

[strange meadow]

Well let’s review it now

Take the natural log of both sides

[last ether]

6^x ≠ 2(3^x) ≠ 3(2^x)

[open roost]

k so it would just be log(3(2))^x+1?

= log(3(2))^-x?

right?

(x+1)log(6) = xlog(6)?

[open roost]

something like that ^?

[molten pivot]

2^x × 3^x

Exponents distribute over products

[high rapids]

Yeah this is what I meant

Except -x

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@open roost Has your question been resolved?

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[open roost]

is it right?

[limpid turret]

No

[lone heart]

@open roost Has your question been resolved?

[tacit arch]

https://www.cuemath.com/algebra/properties-of-logarithms/
Use these

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[minor steppe]

where did i mess up? the eigen values are correct and arent shown, i just think i messed up getting P
https://cdn.discordapp.com/attachments/1058567829848334346/1058567852946366464/image.png

[alpine sable]

If the eigenvalues are correct, so are the eigenvectors

[wary stream]

Can you post the original question?

[alpine sable]

Based on what I see

[alpine sable]

I'll use an online calculator to verify the eigenvalues

[minor steppe]

its 2 and -2 lol

[tacit arch]

Why is 4 the bottom right value for both matrices

[alpine sable]

Yes that's correct

[tacit arch]

You didn't subtract correctly for one of them

[minor steppe]

its meant ot be 8 in the second one mb

[alpine sable]

so your matrices with $\lambda_{1, 2}$ are correct too.

[minor steppe]

wrote it down wrong

[ocean seal]

Ø

[alpine sable]

oh yeah, true ^^

[wary stream]

So then the next question is, what's after that?

What was your P matrix?

[minor steppe]

correct one V

[wary stream]

That doesn't answer my question

What is your P matrix?

[minor steppe]

1 1
2 1

[wary stream]

Then you have done nothing wrong

[minor steppe]

alright, think i messed up the multiplication in the later steps, thanks for the help

.close

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[quiet hare]

For this problem, i got the answer 18, but it says i got it wrong and i dont know why. Can anybody help me with this?

[ruby current]

If fewer machines are working, shouldn’t the order take longer?

[wary stream]

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

[quiet hare]

oh ok

so then i would have to do 6 divided by 2, and 36 times 2?

so 3 machines would take 72 hours

ok its correct

thank you!

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[shut basin]

need help solving this

side AB is parallel to side CD

AC = BD

find the area of s1 and s2

[latent swift]

okay if i use chinese?

[shut basin]

sure

i dont mind

[latent swift]

i can still use english to explain if you want to

[shut basin]

nah im fluent in both languages so it wont be a problem

Preferably in english though

[latent swift]

denote the intersect of AD and BC as O

[shut basin]

so point of intersection of AD and BC = 0

[latent swift]

ACD and BCD shares CD, and since AB is parallel to CD, ACD and BCD have the same height

[latent swift]

yes

[shut basin]

ah yes

[latent swift]

ACD-S2 = BCD - S2

[shut basin]

ah ok

how would you find s1 and s2 individually then?

[latent swift]

ah sorry my bad. i just did a mistyping

[latent swift]

so S1 = 7

[shut basin]

oh ok

[latent swift]

and S1:S2 = ABO:DBO

[latent swift]

i'll explain this in more details if you need it

[shut basin]

DBO?

where does the o come from?

[latent swift]

the intersect

[shut basin]

oh yeah sorry

[shut basin]

isnt this just similar triangle ratios?

[latent swift]

no it isn't similar triangles

面积之比等于底之比

[shut basin]

ohhh

ok i get it

[latent swift]

so in china this is a thing called 蝴蝶模型

because it's shaped like a pair of butterfly wings

[shut basin]

ive heard of it before

[latent swift]

ACO ALWAYS equals to BDO in a trapezium

[shut basin]

oh yeah i remember now

[latent swift]

well done

[shut basin]

so BDO also equals to CDO right?

[latent swift]

no

[shut basin]

oh

yep

[latent swift]

wait i'll explain it another way

[shut basin]

OH WAIT

[latent swift]

okay so for the specific problem above, BDO=7 and CDO = 7x(7/4)

[shut basin]

does ABO:ACO = BDO:CDO ?

[latent swift]

correct

[shut basin]

so i can just sub the numbers into the ratio

and solve for s2

[latent swift]

yes

[shut basin]

so s2 would be 49/4

or 12.25

[latent swift]

(my internet connection is really poor so forgive me for not being able to respond immediately even though the response might be only on word)

[shut basin]

oh its alright haha youve already helped me so much

[latent swift]

correct

[shut basin]

wait then how do you prove the butterfly model works?

another problem asks me to prove that it works on any trapezium

[lone heart]

@shut basin Has your question been resolved?

[latent swift]

AE and BF are CD's perpendicular lines

[lone heart]

@shut basin Has your question been resolved?

[lone heart]

@shut basin Has your question been resolved?

[latent swift]

wait how come

[lone heart]

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[hollow thicket]

can someone illustrate what this means?

[hollow thicket]

ah understandable

thanks okisok

.close

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[warped topaz]

https://gyazo.com/14cf648d8fa997639c12392f65d5ce6a.png

[warped topaz]

I put my answer in the blue box, it says im wrong but I dont think I am? 🧐

[tacit arch]

Don't use quotient rule

You are wrong

Use power rule and constant multiple rule

d/dx (af(x)) = af'(x) and write the reciprocal as a power

[warped topaz]

what is af?

[tacit arch]

a is a constant

In your case 6

[warped topaz]

ah

[rose sigil]

af means...

nvm

[tacit arch]

Kids these days

[warped topaz]

So in which situations do I not use quotient rule

just when its sin / cos / tan in the denominator?

[rose sigil]

f(x) = x/1 is a good situation not to use it 🙃

[woven plaza]

just write down derivative of cosecx

[warped topaz]

Ok thanks everyone!

❤️

.close

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[alpine sable]

there shouldn’t be a -8 if this was quotient rule btw

[warped topaz]

ye typo 😅

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[timid jolt]

Could I get help for question 4

[pseudo ice]

,rccw

[median osprey]

Still need help bro?

[lucid marten]

Yeah I can help him

[median osprey]

That's easy one

[lucid marten]

Its quite simple if you think about it

[lucid marten]

Yeah.... was also overthinking it but lets just help them coz I think this is their third channel

[median osprey]

What's there to overthink lol

[lucid marten]

Nothing as I could not see it. Maybe your solution is simpler than mine

[timid jolt]

Could i see how you guys did the question?

[lucid marten]

Wait a minute I upload

[timid jolt]

thank you

[lucid marten]

Give me a few it will take little while since I dont know how to use this bot

[timid jolt]

sure

[lone heart]

@timid jolt Has your question been resolved?

[median osprey]

You didn't get the answer yet?

[timid jolt]

no im not sure how to do it

[median osprey]

Want hint?

[timid jolt]

yes please

[median osprey]

Find the height of point B and then the height between A and B and then add it

[lucid marten]

Am sending my solution

Let us assume there are imaginary $\triangle AXD$ and $\triangle DCZ$. The $\angle ADX$ = $\angle DCZ$ = $30^\circ$.
new height = XZ = DZ + DX.
DZ = DC $\sin$ $\angle DCZ$ $\implies$ q $\sin$ $30^\circ$.
DX = AD $\cos$ $\angle ADX$ $\implies$ p $\cos$ $30^\circ$.
$\therefore$ XZ = (q * $\frac{1}{2}$) + (p * $\frac{\sqrt{3}}{2}$).
Which becomes $\frac{1}{2}$(q) + $\frac{1}{2}$(p * $\sqrt{3}$)$\implies$ XZ = new height = $\frac{1}{2}$(q+p$\sqrt{3}$)

How do I introduce space between the words?

[pliant cedar]

dont put dollar signs

only enclose the math with dollar signs

[lucid marten]

Thanks

[pliant cedar]

Let us assume there is an imaginary $\triangle AXD.$ The $\angle ADX = \angle DCZ = 30$

etc

[ocean seal]

SilverSoldier

[pliant cedar]

\degree is not valid

[lucid marten]

What should I use?

[pliant cedar]

use $30^\circ$

[ocean seal]

SilverSoldier

[lucid marten]

Thanks a lot

Let me edit

[timid jolt]

thank you so much

[lucid marten]

I think thats understandable and welcome anytime

[ocean seal]

Pyp

[lucid marten]

Is it possible to solve this using rotation transformation @median osprey ?

Assuming it exists on a cartestian place with C being the centre of rotation

Assuming
A(0,q)
B(0,0)
C(p,0)
D(p,q)

[lone heart]

@timid jolt Has your question been resolved?

[lone heart]

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[karmic falcon]

can I multiply -inf by -inf

[karmic falcon]

do they give +inf?

or is it not allowed

[rose sigil]

what's the question from?

[karmic falcon]

wait

i am trying to study behavior of this

as x goes to 3

since 3 is asymptote

so i was trying to find lim to 3-

omg

i think i did a mistake

wait

[rose sigil]

then your original question seems weird :c

[karmic falcon]

so this should be +inf

right

bcs it's $-inf* 3^2/5$

[ocean seal]

lirdi

[rose sigil]

ummm no?

[karmic falcon]

no wait

it's -inf

i got confused

yea yea it's -inf

[rose sigil]

yep

[karmic falcon]

thanks

sorry for confusion

[rose sigil]

welcome ^-^

[karmic falcon]

.close

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[rose sigil]

dw about it!

[lone heart]

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[grizzled zephyr]

How is this possible ? How did cos ( tanx^-1 ) become cosy

[median osprey]

Because it's given that y= tan ^ -1 x

[grizzled zephyr]

wut

[median osprey]

Read the line just below solution 2

[grizzled zephyr]

no line

what u talking abt

[median osprey]

I am saying that it's given that y= tan^-1 x so cosy = cos (tan^-1 x)

And this was your question that how cos y = cos( tan-1 x)

[grizzled zephyr]

iis this like a rule

cuz i dont undertsnad

do u know any videos i can watch?

[median osprey]

You mean why y= tan^-1 x here?

[grizzled zephyr]

i still dont understand why its cos y

[lone heart]

@grizzled zephyr Has your question been resolved?

[opaque current]

if you use y as the angle, tan(y) = x/1 = x, so with that, we can do y = arctan(x), with that, we do cos(arctan(x)) = cos(y)

[grizzled zephyr]

omg i dont get it

nvm i got it

[worn fox]

you need to read #❓how-to-get-help

and claim an available channel

read carefully

[alpine sable]

How can I know its occupied ?

[alpine sable]

Oh thank you !

[grizzled zephyr]

.close

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[vast sonnet]

how come is he doing something to ythe right side

but not to the left aswell?

[lone heart]

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[vast sonnet]

f

.close

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[civic ice]

can someone explain why f^-1( f(x) ) is equal to x?

[worn fox]

by definition

f^(-1) is the function that "undoes" whatever f does

[civic ice]

mhm

[vague coral]

there are inverse functions

its like 3*(1/3)
1/3 is the inverse of 3, so it will give 1

for function it gives identity

[echo socket]

By definition

[alpine sable]

$\sqrt{x}^2 = x$

[ocean seal]

rbit ✨

[alpine sable]

now f is the sqrt, and ² is f^-1

[civic ice]

right cuz the x is on the output's side for the inverse function

alr thanks

[alpine sable]

$\ln(e^x) = x$

[ocean seal]

rbit ✨

[alpine sable]

now f is e^x and f^-1 is ln

[lone heart]

@civic ice Has your question been resolved?

[lone heart]

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[pulsar laurel]

Wait can someone just tell me complex numbers when they are roots in polynomial they come in a complex conjugate pair meaning if one root is 2+i the other is 2-i

[alpine sable]

huh i don't understand this question

but yes

there is always a conjugate zero

if you know a zero is an imaginary number

[pulsar laurel]

Wait I'll get an example

Wait it's just loading

For the question at the top all the roots are real right because you can't get a complex root on its own

[alpine sable]

yep

[pulsar laurel]

K thanks

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[indigo thorn]

The equation in ist pic and in 2nd pic are also the same equation but in a different form
how do they right in different form explain please ??

[sharp sail]

just multiply with i j and k and factor out t's and s-s

[indigo thorn]

can you explain step by step if possible please

[sharp sail]

Just multiply like
(1-t) i = i - ti

[indigo thorn]

umm ok

thanks understood

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[dim matrix]

Does the given expression mean that A inv = 1/6 B and B inv = 1/6 A ?

[lone heart]

@dim matrix Has your question been resolved?

[dim matrix]

<@&286206848099549185>

[waxen osprey]

yes

[dim matrix]

Thanks @waxen osprey 🙂

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[open pumice]

,_,

[alpine sable]

$\frac{3-\sqrt{x+9}}{x}$

[ocean seal]

rbit ✨

[alpine sable]

lets write it this way

[open pumice]

okey

[alpine sable]

do you know about the trick of multiplying the numerator and denominator by the conjugate?

[open pumice]

not really

but show me

that

[alpine sable]

multiply them by 3 + √(x+9)

notice the plus

[open pumice]

ah yeah

ahhhhh

but why not 3-

√(x+9)

[median osprey]

Because you won't achieve anything by that

[open pumice]

okey

[alpine sable]

you know about the difference of squares?

[open pumice]

thanks a lot for that

yeahh

i finally understand it

[median osprey]

Ok

[opaque current]

i'd just lhopital'd it right off the bat

[median osprey]

That is also a way

[limpid spade]

I would just taylor it

[alpine sable]

pls not

[opaque current]

why not

[alpine sable]

you can, but he might not have been introduced to that yet

[opaque current]

ig

[open pumice]

anyone have a limit calculator with steps?

[alpine sable]

,w lim x to 0 of (-sqrt(x+9)+3)/x

[ocean seal]

Results provided by WolframAlpha

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

Requested by Toby#2275

[open pumice]

need for steps

[alpine sable]

click

[alpine sable]

basically, do this ^

[alpine sable]

you want to prove this?

[open pumice]

do you know reccurence?

proving this reccurence

by reccurence

[alpine sable]

you mean by induction?

[open pumice]

yes

[late mango]

prove the same thing but replace the n's with n+1's

normally by using the given proposal

[lone heart]

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[frank basalt]

hello

[frank basalt]

i need help with a question

what is the inverse of f(x)=4x+e^6x

[half tusk]

what have you tried

[vale wigeon]

... have you been instructed to find the inverse? or do you need this for something else?

[frank basalt]

do i send the full question?

[keen mason]

tf is that formula

[frank basalt]

it requires me to use domain f(x) = range f(x)^-1

[vale wigeon]

bad wording

[vale wigeon]

yes, as you ALWAYS should.

[frank basalt]

my bad g

[vale wigeon]

no, it does not.

you only need to know the value of f^-1(1).

it is not hard to see that f^-1(1) = 0, as f(0) = 1
and you do not need to know anything more

certainly not a formula for f^-1, because such a formula does not exist

[frank basalt]

so it would be 1/10 yes?

[vale wigeon]

seems so.

[frank basalt]

you are an angel id give u a kiss on the cheek

thank you very much

[median osprey]

lol

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[safe mountain]

how do i solve tan(x-45)=-2cosx

[safe mountain]

ive used the compound angle formula

and ive gotten as far as tanx - 1 = -2cosx - 2sinx

[ornate ginkgo]

$tan(x-y) = \frac{tan(x) - tan(y)}{1+tan(x)tan(y)}$

[ocean seal]

ColdTee

[marsh rapids]

according to WA, you don't

the exact solutions are a pain

it also makes you wonder how it comes up with those

[safe mountain]

yea you get stuck past a certain point which is what i wrote

[safe mountain]

will the computer always do the easiest solution

[marsh rapids]

usually yes

if WA doesn't find it, usually you don't

I have yet to see a counter-example to that

[median osprey]

Well this statement is wrong

[marsh rapids]

I plugged in the original question

[safe mountain]

what did you get

[safe mountain]

the original question didnt ask for the solutions, it wanted me to draw a graph to see if the 2 equations intersected at one point

[marsh rapids]

they do

[safe mountain]

but my graphs are never accurate

between 0 and 180 degrees

[marsh rapids]

you should know how to roughly plot tan and cos

here roughly is enough

[safe mountain]

yea my tan slightly overlaps the cos

but theres no solutions between 0-180

would i need to do x and y coordinate box to make sure i was correct ?

[marsh rapids]

when it's actually about being accurate (here around 110°) either you make sure it's accurate by drawing better or you do more math

[safe mountain]

how would i draw better ?

and wdym by do more math

[marsh rapids]

1. sample values and try to have reasonable slopes between them
2. requires more knowledge, in that case I was thinking about a convexity argument, which would require quite a bit of work

[lone heart]

@safe mountain Has your question been resolved?

[safe mountain]

ill look into it, thanks

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[leaden bobcat]

can someone help me with this?

[leaden bobcat]

i need to derive

[keen mason]

u mean get derivitive?

[woven plaza]

use product rule

[keen mason]

u=x^4 v = (5x-1)^3

[leaden bobcat]

idk gang english not my first language

y'

idk whats it called in english

[keen mason]

u' = 4x^3 v' = 15(5x-1)^2

[leaden bobcat]

yea i got that

[keen mason]

yea its derivitve

[leaden bobcat]

but what next

[keen mason]

use rule

[leaden bobcat]

what does that mena

[keen mason]

(uv)' = uv' + vu'

[leaden bobcat]

aight thx

[modern topaz]

derive

vative

derivevative

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[wanton jolt]

Translation : If x+ y = 5 then the numerical value of the expression x2 + 2xy + y2 =

[wanton nova]

you could write x in terms of y and then solve the equation

[viscid pawn]

il faut reconnaître la forme de ta formule à droite

[viscid pawn]

not needed

the answer is 25 it's easy

c'est une identité remarquable

[wanton nova]

yeah but he probably has to prove it

[wanton jolt]

Yes

[viscid pawn]

easy

[viscid pawn]

tu reconnaît la forme de x² + 2xy + y² ?

[wanton nova]

just do what i said it will be done in 30 seconds

[viscid pawn]

what i'm giving him as a solution is like 3s to do lmao

[wanton nova]

omg

wait

ur right

omg im so stupid

[viscid pawn]

(x+y)²

[wanton nova]

yes

[viscid pawn]

since x+y = 5

the result is 25

👍 no worries dude

[wanton nova]

yup

[viscid pawn]

this is how french ppl would have solved it

[wanton jolt]

😂

[viscid pawn]

i reckon this is because we are so used to this things like ( a + b )² = a² + 2ab + b²

[viscid pawn]

tu as compris là ?

[wanton nova]

do french people ever type without accents?

i always see you guys putting accents

[viscid pawn]

we have lots of accents

[wanton nova]

why cant you write

tu as compris la

or reconnait

[viscid pawn]

because it's not the same

[wanton nova]

it's weird

[viscid pawn]

accents gives another meaning to the word

yeah french is weird and difficult

[orchid topaz]

Maybe an accent gives a different meaning

Uea

It does in spanish sometims

[viscid pawn]

yeah it often changes the meaning

like you use la femme to say " the women " whereas you say " je suis là femme " for i'm here women and not i'm the woman

[wanton jolt]

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[idle sand]

Can someone tell me what type of distribution this is and what formula i have to use to get the probabilities of X

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[empty plover]

yo

[empty plover]

why when minimal and characteristic polynomials are equal the geometric multiplicity of each eigen value is one

.close

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[royal plank]

yes

[alpine sable]

yes

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[open roost]

why would it turn to 13/6

would it not be 3x^2/6?

[alpine sable]

Product of exponents

Equal sum of powers

$a^m(a^n) =a^{m+n}$

[ocean seal]

Taka shi

[open roost]

oh right ur supposed to add

[alpine sable]

Yh

[open roost]

mb

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[crisp root]

can any one solve this:
f(x)=x² : |x| <=3.

[tacit arch]

Are you supposed to graph?

[crisp root]

no find the range of x and y.

[lone heart]

@crisp root Has your question been resolved?

[royal plank]

so what do you know about ranges of x and y?

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[vapid stirrup]

Hi there, the unit I am working on is Rational Expressions

My question is, is there some rule of thumb for the form that final answers should be left as?
( should they be expanded or factored)

Does it not make a difference?

[vapid stirrup]

Highlighted in yellow is the final answer from the solutions

[wary stream]

Depends on what your teacher wants

[tacit arch]

Distribute your x(2x-3)

[wary stream]

Both are valid

[wanton nova]

Why am i attracted to that writing

[vapid stirrup]

Is there a reason... why

?

Or is that just

how it goes

[tacit arch]

Only to get the answers to match

[vapid stirrup]

Ohh lol

[tacit arch]

Like dld said, both are valid answers and it depends on your teacher what they accept

[vapid stirrup]

Ok thanks

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[loud thorn]

Is this proof right?

[last ether]

You cannot use alternative interior and any other parallel-transversal without stating the transversal I'm pretty sure

So for 3) just state that GC is also a transversal to the parallel lines

[loud thorn]

Changed to this

[last ether]

For 8, what's the congruent side

[loud thorn]

@last ether do I need to also write that angle EDF = ADB bc of vertical angle thm

[loud thorn]

DE and DA

[last ether]

Yes

[last ether]

Oh because of CPCTC

you need to state that too

[loud thorn]

what is cpctc lol

[last ether]

Corresponding parts of congruent triangles are congruent

[loud thorn]

ah

do i need to say that about all sides of the big traingles before saying theyre congurent

oh wait no

[last ether]

Just before 8

[loud thorn]

yeah makes sense

So this basically

[last ether]

Vertical angle before 7

[loud thorn]

ah yes

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@loud thorn Has your question been resolved?

[loud thorn]

Final answer

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[near moth]

HAPPY NEW YEAR

[abstract fractal]

Do you have a question?

[wary stream]

.close

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[rigid zodiac]

Hello

[rigid zodiac]

How would I integrate this?

[rocky grove]

Ooo

Numerical integration

You use either Trapezoidal method

Or Simpson's

And Simpson's is more accurate when it comes to curved functions

[rigid zodiac]

hmm

how to do that? 😂

[rocky grove]

Pick a method first

[rigid zodiac]

simpsons

[rocky grove]

Trapezoidal is easier

[rigid zodiac]

oh then trapezodial

[rocky grove]

Okay

[rigid zodiac]

so where do i start?

[rocky grove]

First, decide on a $\Delta x$

[ocean seal]

VulcanOne

[rocky grove]

And this is based on the error you get from trapezoidal method

[rigid zodiac]

hm

[rocky grove]

And you calculate the error from this

[rigid zodiac]

ok

what would you decide

i looked at the answer key, and the author of the book had a very long and almost convoluted solution

[rocky grove]

Hmm

What did the author use?

[rigid zodiac]

idk what its called

that's one part

second part is

[rocky grove]

Oooo

[rigid zodiac]

so what method did they use?

[rocky grove]

They made the dx into $\Delta x$ and assume that it =0.1

[ocean seal]

VulcanOne

[rigid zodiac]

oh i see

but what about the trapezodial method you introduced

[rocky grove]

Which is another way to use Riemann sum

[rigid zodiac]

ohhhh

yeah but the riemann sum for that is too long

[rocky grove]

That's a bit more accurate way to numerically integrate

There is a nice compact formula to use Trapezoidal method

[rigid zodiac]

show me plz

like is the trapezodial method in calc ab

or in calc bc/c

[rocky grove]

Should in the integral calculus

Lemme write it

$\int_a^b f(x)\mathrm{d}x \approx \frac{\Delta x}{2} (f(x_0) + f(x_n) + 2\sum_{j=1}^{n-1} f(x_j) )$ where $x_j = a + j\Delta x$

[ocean seal]

VulcanOne

[rocky grove]

Step by step

[rigid zodiac]

yknow whata

how about you teach me how to solve it

according to the textbook

is the textbook's solution just riemann sums from an integral

[rocky grove]

Whatever you want but trapezoidal method is pretty simple

[rigid zodiac]

alright then continue

[rocky grove]

It's like 2 lines

[rigid zodiac]

ok

[rocky grove]

First thing though, you should find how much error you want

[rigid zodiac]

how much would you suggest

[rocky grove]

Should be within 2% of the actual answer

[rigid zodiac]

alrighty then

2%

[rocky grove]

Now 2% of an answer that we don't know is not gonna give us much info

To get a sense of what we are playing with here

We try the function at a point between the intervals

[rigid zodiac]

ok

[rocky grove]

Let's say at x =20

[rigid zodiac]

alright

[rocky grove]

I got 0.046

And we will integrate this supposedly

So 2% of 0.046 = 0.0009

[rigid zodiac]

alright im following along

[rocky grove]

So let's say our error is at 0.001

[rigid zodiac]

ok

[rocky grove]

Now we use this formula to get a $\Delta x$ suggestion

[ocean seal]

VulcanOne

[rigid zodiac]

ok

[rocky grove]

$\epsilon \le \frac{\Delta x^2}{3}$

[ocean seal]

VulcanOne

[rocky grove]

$\epsilon$ is our error

[ocean seal]

VulcanOne

[rigid zodiac]

ok

i see

[rocky grove]

Do some algebra

[rigid zodiac]

alright

[rocky grove]

And you get $\Delta x$ should be at most 0.05

[ocean seal]

VulcanOne

[rocky grove]

1 more step to get to our last formula

We find the number of divisions

[rigid zodiac]

alright

[rocky grove]

$\Delta x = \frac{b-a}{n}$

[ocean seal]

VulcanOne

[rocky grove]

We get n from here

[rigid zodiac]

wait

[rigid zodiac]

how did you get 0.05 again

what was delta x equal to

0.46?

[rocky grove]

$\epsilon \ge \frac{\Delta x^2}{3}$ (Oops I made a mistake here) \
$3\epsilon \ge \Delta x^2 \
\Delta x \le \sqrt{3\epsilon} \ \le 0.05$

[rigid zodiac]

ok

[ocean seal]

VulcanOne

[rocky grove]

We got 0.046 when we plugged x=20 into our function

[rigid zodiac]

ok

[rigid zodiac]

what about this part

[rocky grove]

Anyways we get n from this formula

We plug in our Delta x

And our a and b

$\Delta x = 0.05 = \frac{23.7-12.8}{n} \
0.05n = 10.9 \
n = 218$

[ocean seal]

VulcanOne

[rocky grove]

218 divisions

This seems like a lot

But you'll plug it in your calculator

So no big deal about it

Anyways we have our number of divisions and our delta x

All we need is to plugin

$\frac{0.05}{2} (\frac{375}{12.8^3 +3.75(12.8)} + \frac{375}{23.7^3 +3.75(23.7)} + 2\sum_{j=1}^{218 - 1} \frac{375}{(12.8 +j(0.05))^3 +3.75(12.8 +j(0.05))}$

[ocean seal]

VulcanOne

[rigid zodiac]

nice

what does this equal to?

[rocky grove]

Lemme write this rq

0.798811958544

[rigid zodiac]

pretty much accurate

[rocky grove]

Yep

Simpsons will need less divisions

[rigid zodiac]

alright thanks

i might look back at this again

[rocky grove]

But will need more typing into the calculator

[rocky grove]

Wait

[rigid zodiac]

alright

[rocky grove]

I'll explain rq how to do Riemann sums

[rigid zodiac]

i know how to do riemann sums

[rocky grove]

If you want

[rocky grove]

Oh

Hmm

Wanna go over it though?

[rigid zodiac]

i think i might look over it again tho sometime soon

nah

thanks tho

[rocky grove]

Sorry it took long to explain

[rigid zodiac]

np

[rocky grove]

Hopefully you understood it

It will need some practice

[rigid zodiac]

yeah ik

[rocky grove]

Yeah hopefully you'll master it quickly

[rigid zodiac]

.close

[lone heart]

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[warped topaz]

when getting the length of a vector from 2 points (a,b) (c,d) I know you need to do (c-a) and (d-b) but how do I tell which point is (a,b) and which is (c,d)?

[warped topaz]

is it the one with the higher x value (c,d) and the one with the lower x value (a,b)?

or higher y value?

or something else

[wary stream]

Are you referring to the magnitude?

Liked based on that

[warped topaz]

nah something else

to get a over b idk how to type it

[last ether]

Create the vector

Define the vector as V

[warped topaz]

https://gyazo.com/f7564d5977ec1de04ebd11cd4ec5f020.png

like this ^^

[last ether]

$$||V|| = \sqrt{V\cdot V}$$

[ocean seal]

Umbraleviathan

[warped topaz]

nah this isnt what im looking for

from 2 points on a graph

to get the formula of a vector

[warped topaz]

to get it into this form ^^

[last ether]

Depends on the direction of the vector

Where does it start and where does it end

Well

[rocky grove]

For the length, it doesn't really matter which is point 1 and which is point 2

[last ether]

If you're looking for a magnitude

Tehn it ain't gonna matter

[rocky grove]

It will get squared anyways

[last ether]

Reflexive property goes crazy

[warped topaz]

im not looking for magnitude

[rocky grove]

And it will lose its sign

[last ether]

Length is magnitude

[rocky grove]

Magnitude = length

[warped topaz]

ok then im not looking for length 😅

[rocky grove]

Hmm

You're looking for which point is which?

[wary stream]

Alright, can you post an image of the problem you are doing?

[last ether]

h u h

[warped topaz]

https://gyazo.com/c4be5c41669ebe4dc2cf18a1bd3356b2.png

[wary stream]

Or something with more context

[last ether]

Okay yeah

Checks out

[warped topaz]

How do I tell which is (a,b) and which is (c,d)

[rocky grove]

Well here it's assumed that c and d are larger than a and b respectively

[warped topaz]

but what if x is larger and y is smaller

[last ether]

From the wording:

Vector from (a,b) ... to (c, d)

[rocky grove]

If a is bigger than c then the x direction is negative

[warped topaz]

sometimes it dosent say from which to which it just gives 2 points

[wary stream]

The head minus tail

[rocky grove]

And if b is bigger than d than the y direction is negative

[wary stream]

The point where the arrow minus the other end

[warped topaz]

Ok I understand now

thanks guys!!

❤️

.close

[lone heart]

Channel closed

Closed by @warped topaz

Use .reopen if this was a mistake.

[rocky grove]

[last ether]

[lone heart]

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[alpine sable]

Wouldn't one of the parts be x(sqrt(9))

sqrt(9)=3

so x^y=3.

please help for z

$x^y = \sqrt{9} \ x = 1/2 , y = 9 \ x(x^y) = 1/2 ((1/2)^9)$ ?

[rose sigil]

why must x = 1/2 and y = 9?

[alpine sable]

No reason, it doesn't have to but it seemed like easiest given the condition, we could have chosen other values as long as they suit the condition that x^y = √9

y = 1, x = 3 also satisfies the condition

So does y = 2 , x = √3

And this can keep going on forever

so 1/2(1/512)=z

[rose sigil]

in other words there is not enough information given

[alpine sable]

There are multiple solutions to that question tho

[alpine sable]

Yep

ok

i'll close this

[rocky grove]

,w graph x^y = sqrt(9)

[ocean seal]

Results provided by WolframAlpha

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Requested by VulcanOne#5806

[rocky grove]

Infinite solutions

[alpine sable]

oh shoot, I accidently unfollowed the occupied channel.

[rocky grove]

??

[lone heart]

Channel closed

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• Show your work, and if possible, explain where you are stuck.
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[alpine sable]

Need help again. If x^3=4. Y=sqrt(x)^2. And Z=Y/x^2, What is Z?

[rocky grove]

Okay

Solve for x

By taking cube root

Or raising both sides by 1/3 power

[alpine sable]

So basically x= cube root(4)

[rocky grove]

Yep

Then you solve for y

[alpine sable]

Then Y= Sqrt(Cube root(4))^2

[rocky grove]

Mhm

Wait

Do you mean

$\sqrt{x^2}$ or $(\sqrt{x})^2$?

[ocean seal]

VulcanOne

[alpine sable]

yea

[rocky grove]

Hmm

Doesn't matter here lol

[alpine sable]

How do you use that?

[rocky grove]

Which one?

[alpine sable]

The picture thing

[rocky grove]

$\sqrt{x}$

[ocean seal]

VulcanOne

[rocky grove]

Dollar signs at the beginning and end

Square root is \sqrt

And to include what's inside I use {}

[alpine sable]

$\sqrt{x^2}$

[rocky grove]

To add powers I use ^ or ^{}

[ocean seal]

Piggy

[alpine sable]

$\frac{y}{x^2}$

[ocean seal]

Piggy

[rocky grove]

\sqrt

Edit

It's gonna pick it up

$\sqrt{x}$

[ocean seal]

VulcanOne

[alpine sable]

$\frac{y}{x^2}$

[ocean seal]

Piggy

[rocky grove]

$\frac{y}{x^2} = \frac{(\sqrt{\sqrt[3]{4}})^2}{(\sqrt[3]{4})^2} = \frac{\sqrt[3]{4}}{4^{\frac{2}{3}}} = 4^{\frac{1}{3} - \frac{2}{3}}$

[alpine sable]

So Z= that

One sec, ima get my calculator

uhh

[ocean seal]

VulcanOne

[alpine sable]

Aprox 0.629960525

[rocky grove]

$=\frac{1}{\sqrt[3]{4}}$

[ocean seal]

VulcanOne

[rocky grove]

Should give the same result

Simplifying is essential

[alpine sable]

yes