help-38

[velvet coral]

yup, India

[exotic pine]

how old were you

[velvet coral]

uh, 8?

[exotic pine]

what the hell

[velvet coral]

yeah, its india bro

I did my first integration when i was 10

[limpid fulcrum]

wait how do i get rid of the 25 in y^2

[velvet coral]

and nearly got it right but my arhtemetic wasnt so good

[exotic pine]

what the hell is wrong with your education system lmao

[velvet coral]

exactly, anyways, focus on the question of him

[exotic pine]

actually insane

[velvet coral]

figure it out

[exotic pine]

factor out 25

[velvet coral]

thats math

[velvet coral]

bro... thats too much help

[exotic pine]

oh cmon you solved the first equation for him

[velvet coral]

I mean, wait no, you sure can say factor out

[velvet coral]

I just gave him the idea by 4 - 4

[limpid fulcrum]

it seems like his education system is functional unlike mine where they skipped our 3rd intermediate and 4th highschool grades and crammed it all in 5th and 6th grade

[exotic pine]

what the fuckk 😭

[limpid fulcrum]

we have to relearn this as well as calc 1 2 3 and multivariable

[velvet coral]

no worries, I am trying to get out of here asap

[velvet coral]

that wont help

At least my teachers werent cramming

[limpid fulcrum]

guys im just gonna skip this question

i give up

.close

[velvet coral]

nope

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[exotic pine]

.reopen

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[jovial anchor]

Heyy

[jovial anchor]

I need some help

This is for: y=-3x+27

it's asking me to find X with f(x)=18

No idea how to do that

[nimble stone]

how did you come to -9?

[exotic pine]

f(x) is y

[jovial anchor]

How am I supposed to know 💀

[clear cloud]

So -3x +27 = 18 ?

[jovial anchor]

still tho, how do I solve it?

[exotic pine]

thats the definition

basically*

[jovial anchor]

explain please, I'm kind'a new studying this

[exotic pine]

do you not know how to solve linear equations?

[jovial anchor]

I do, but I've never encountered this f(x) thingy

[frail heron]

take it as y

[limpid belfry]

f(x) tells you what something does with x

[clear cloud]

I told you in the last one

#help-48 message

[jovial anchor]

yeah but it's different cuz it has x in it

I tried to do the same but I got -9 which is wrong..

Lemme try to do it with y instead

[clear cloud]

You know f(x) = -3x + 27

You also know that f(x) = 18

So -3x +27 = 18

[jovial anchor]

so we got
18=-3x+7

ok that's shrimple

we got 11=-3x

so x = -3.6 ?

[clear cloud]

You made an error at first

Look

[jovial anchor]

?

[limpid belfry]

^

[clear cloud]

Look what you wrote

[jovial anchor]

yes I'm looking

oh

[clear cloud]

Its not + 7 its + 27

[jovial anchor]

ohhh

oopsie

so x=3 ?

YESS thank you guys

although, How was I supposed to know y was the f(x) value and not something else? 🤔

[clear cloud]

Website bad, know it now

[jovial anchor]

👍 alright thank uu

[clear cloud]

It should have been precised in course or stuff

[jovial anchor]

I'll make a new one incase I have any trouble.. I'm catching up on tons of stuff lol

so it's just a massive course

big boi

alright, bai

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[rotund grove]

hi

[true kestrel]

your about me ques?

[rotund grove]

If sin(x+y) = sin(a+b), we can't say x+y = a+b but we can say that:
a+b≡ x+y (mod 360)
RIGHT?

[rotund grove]

Solve if you can.

[rotund grove]

yes or nooooo ?

Got it, the answer is no.

[velvet coral]

yes

you are right

[velvet coral]

IT IS YES

[true kestrel]

what does that |360| means

[rotund grove]

it's not modulus

[wind cloak]

It is modular arithmetic

[true kestrel]

oh bite me

my bad

[wind cloak]

bro's trippin' on the tuesday afternoon

[true kestrel]

ok i am cooked

[true sierra]

Can I just use this opportunity to call out mod notation as being weird af

[rotund grove]

sin(80+40) = sin(15+45)

[wind cloak]

fr

[proper talon]

modulo and modulus notation is annoying

[rotund grove]

therefore, 120≡60 (mod 360)

[velvet coral]

see

if there are 2 angles like this

sin = sin

or

$$ sin(\theta_1) = sin(\theta_2) $$

they are coterminal

yeah

oh wait

[rotund grove]

same for cos

[solid kiln]

Greydawn Dewer

[velvet coral]

this is better

[rotund grove]

what is the conclusion?

[velvet coral]

that you are right

[true sierra]

So just give an example, like sin(0° + 90°) = sin(180° + 270°)

[velvet coral]

yeah, sorry, dumb of me

[rotund grove]

So no conclusions can be made between theta 1 and 2

Right?

[true sierra]

The remainder is the same

ah

but not always

[velvet coral]

" the sine function is periodic with a period of 360"

[rotund grove]

Or sin(theta) = sin(180-theta) we can get some sort of relation

[true sierra]

cause wonky circles do be wonky

[velvet coral]

ah leave it

[true sierra]

you can have things like

[velvet coral]

this statement, matters

[rotund grove]

tes

yes

👍

[true sierra]

sin (90° + 45°) = sin(180° + 225°)

[rotund grove]

huh

[velvet coral]

leave that, is your query solved?

[rotund grove]

ig

no conclusion can be made

.thanks

[rotund grove]

between the angles 🙂

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[clever thorn]

i have little experience with questions like this. how should i face a similar question when i have limited time.

[limpid belfry]

you could try seeing "If A happens, how many ways can B happen"

[clever thorn]

i feel like i would take too long doing that. im sure theres gotta be a nice solution as this is a past paper for a comp in my country

im tryna look at any blind spots i might have in case i get a question like it

but i need to solve them in a time crunch

[limpid belfry]

most time when you do this its pretty ok though

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[limpid belfry]

"Let ABCD be a square of length 10, point M is on AB such that the diagonal AC intersects DM at point E, if the area MEC is 20 square units, find AM"

[limpid belfry]

so

i got that AEM and DEC are similar

but idk where to go next

[analog shale]

the word should have been "similar"-

[limpid belfry]

oops

idk what it wouldve been in english haha sry

[analog shale]

np :)

[rough goblet]

congruent means same size and shape

similar just means same shape

[analog shale]

oke, I flee

[limpid belfry]

ah okay

[rough goblet]

nah continue am just clarifyin

[analog shale]

as in, I can't do this problem as well LOL

[rough goblet]

LOL

[limpid belfry]

i'm thinking let MB be x? idk

[atomic drum]

AM = x, AE:EC = x : 10 so triangle AME should be 20 x x/10

which is 2x

[limpid belfry]

why is EC 10?

[atomic drum]

its the ratio

AE : EC = AM : DC

[limpid belfry]

oh wait MAE 45 degrees

oh makes sense

lemme try doing it

[atomic drum]

did u get it

[limpid belfry]

i dont understand how you came to the coonclusion ame = 2x

[atomic drum]

because ame and mec have the same height(which is the distance from m to ac)

[limpid belfry]

also using this doesnt give anything..?

[atomic drum]

from this you can get ae : ec = x : 10

[limpid belfry]

yeah?

what next

[atomic drum]

since ame is ae * height and mec is ec * height

triangle ame and mec would be x : 10

[limpid belfry]

ohhh

[atomic drum]

since mec is 20 ame would be 2x in this case

[limpid belfry]

how?

they have same height but different bases

[atomic drum]

the bases are ae and ec which are on the same line ac

[limpid belfry]

yep

and ae : ec = x : 10

[atomic drum]

so the area of ame mec is x:10

[limpid belfry]

ratio of area?

[atomic drum]

yea

[limpid belfry]

ohh

what next?

[atomic drum]

amc = ame + mec = 2x + 20

but amc is also (x) x 10 x 1/2

[limpid belfry]

o

2x +20 = 5x

holy

th

ty

[atomic drum]

np

[limpid belfry]

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[subtle path]

can someone help me solve this?

[true kestrel]

well where are you stuck at?

[subtle path]

uhm idk how to solve this prob only

like idk how to approach to this kind of probs

[true kestrel]

make a diagram for better visualisation

[limpid belfry]

find a function of the x axis (use trigonometry)

[true kestrel]

(it would be a right angle triangle)

[true kestrel]

we can do without it too

[limpid belfry]

oh okay i learned it with haha

[true kestrel]

yup, anything works till you get ans

[subtle path]

the diagram according to question wld be like this

[true kestrel]

ok

[subtle path]

but idk where shld i put tht 4ft value

[true kestrel]

can you name the base as x

[subtle path]

yess

[true kestrel]

and hypotenuse as l

and find the other side using pythogoras

lmk

[subtle path]

u will get the base as

15

[true kestrel]

you mean height

yes

[true kestrel]

what is 4ft/s here?

is it dx/dt or dh/dt

(after we named)

[subtle path]

dx/dt

[true kestrel]

correct

now apply:

x² + h² = l²

differentiate w.r.t time

[subtle path]

2x+2h=2l

[true kestrel]

and l is constant as length of the ladder ain't changing

[subtle path]

oh

then 2x+2h-0

[true kestrel]

it would be

2x(dx/dt) + 2h(dh/dt)=0

you know h, x and dx/dt

find dh/dt

[violet gust]

also, technically, the height would decrease, so dh/dt should be -ve

[dull temple]

well... yes, you'll get a negative number

[true kestrel]

yea

it would become negative

check the eqn

[subtle path]

wht is h over here?

[true kestrel]

h=15 (we got it using pythogoras)

[subtle path]

oh ohhhhh one sec imma try to solve

[true kestrel]

PS: don't keep h=15 in dh/dt

[subtle path]

thenn u will get it as

-64/30

simplified -32/15

[true kestrel]

-32/15

we have to find to dh/dt right

[subtle path]

holyyyyyyy molyyy

yesss

yays

[true kestrel]

yes

[subtle path]

thnkk u

[true kestrel]

that's correct

keypoints to remember:

always assume some variables

make a diagram

use formulas you know and differentiate

and get your ans

ez

[subtle path]

ur method was much more simpler than tht websiite ever suggested

damnn

[subtle path]

notedd!!

[true kestrel]

[subtle path]

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[hollow bolt]

Can someone help me solve this please, the worksheet says the answer is
Area=12sqrt7 cm^2 and perimeter= 12+4sqrt7 cm

[limpid belfry]

use pythagoreom theorum

[hollow bolt]

I tried but im not sure how it wants me to do that with radical form

[limpid belfry]

well, you get the other side is 2sqrt7 long

do you remember the formula for a rectangle's area?

[hollow bolt]

Yea

[limpid belfry]

so, multiply the two sides and you get exactly what the question says

[hollow bolt]

Can u write out ur process please, when i do that i get c as 10 which gives me 60 for the area

[true kestrel]

you got c as 10?

c is the other side right?

[hollow bolt]

Oh wait

[true kestrel]

yea..

check carefully

[hollow bolt]

OH i get it now thank you guys!

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[turbid crow]

Can someone explain me why in laplace we integrate it with e^-st , like why e???

[marble wharf]

how have you encountered the laplace transform but havent seen yet that e^stuff is a nice function

[turbid crow]

Yes ik the reason for angle but why ?

Why it just could not be any other constant

[marble wharf]

well you can always change the base if you put a log into the exponent

a^x = e^(ln(a)x)

but if you choose e as the base it just works out very nice

[turbid crow]

But why

[marble wharf]

well for starters the derivative of e^x is e^x

while the derivative of a^x is ln(a)*a^x

which is more annoying

[turbid crow]

My questions lies why we use e^-st in laplace

[marble wharf]

are you asking why we arent using some completely different function?

then you would get a whole different theory which probably just wouldnt be useful

[mild oxide]

Oh

[vagrant marsh]

it just so happens laplace transforms are really useful for certain problems

[marble wharf]

its not like people havent tried other things

[mild oxide]

Yes for complex circuit analysis

[marble wharf]

but it just turns out that doing this particular thing is very nice

so it stuck

[mild oxide]

Laplace transforms prove to be godly

[vagrant marsh]

whats your background in calculus?

[turbid crow]

Not strong but ok

But why we use e^-st and how it relates with frequency

[marble wharf]

e^ix = cosx+i sinx. so roughly speaking, e^stuff is basically trig stuff. and trig stuff is basically frequency

[turbid crow]

Hmmm ok but how it relates v

[grim sparrow]

are you asking why e^-st shows up in the laplace transform at all, or why e^whatever is nice?

[turbid crow]

Why e^-st

Shows up

The necessity of it

[vagrant marsh]

it just so happens that it was found to be a nice function to use

[turbid crow]

There’s a correlation between them like the frequency etc

[marble wharf]

its not like people thought "hey we have this frequency thing to deal with, lets pick e^-st". the laplace transform was (probably, I dont know the actual history) looked at for other reasons and it just turns out that its nice for these types of things. and also other types of things

just because we use something nowadays for a certain thing does not mean that people actually came up with it at that time for that thing

[turbid crow]

Hmmm

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[wraith hinge]

can someone explain the hence jump?

[grim sparrow]

mhm, if log_10(2^100) = 30.10..., then by definition 10^(30.10...) = 2^100

[wraith hinge]

oh of course

thanks sm

,close

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[hidden lance]

How do you even solve this differential...

[hidden lance]

like ?????

[wraith hinge]

I suspect that you have to change it to polar coordinates

it just looks so "polar"

[hidden lance]

because of the x^2 + y^2 right

but we didn't learn polar coordinates in differentials

iirc

[wraith hinge]

yes. Not only that, x/y is 1/tan(theta) for example

[lusty delta]

have you tested to see if this differential equation is exact?

if not, that would be a good thing to try

[lusty delta]

..no

[hidden lance]

yo that's a good idea

how could i forget

let me try it rn

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[brave pawn]

yo

[brave pawn]

.CLOSE

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[true yoke]

Hello, I was working through this textbook for math in self-study. I was wondering how I could go about solving this using limits to solve the problem?

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@true yoke Has your question been resolved?

[dense breach]

The problem is telling you to use the graph to solve the problem, and just state the answer in terms of limits

[true yoke]

How would I go about doing that?

[dense breach]

Do you know what asymptotic behavior means

[true yoke]

No, I think I need to reread

I can't find it in my textbook. Do you know what it means

@dense breach Are you done with this chat as of now?

[dense breach]

It means like end behavior

As x goes to infinity or negative infinity what happens

[true yoke]

the Asymptote?

[dense breach]

here I'm guessing it specifically means the horizontal asymptote

But maybe it's a good idea to include the vertical one too

Hard to say

[true yoke]

So the problem is asking how to find the limit for the horizontal Asymptote? How would you write that as a limit? I am new to this, sorry

I have the solution if that would be useful

[dense breach]

Well that would be the only thing I can think to type anyways

is there a part of the solution that's confusing

[true yoke]

More like I don't know how they got it in the first place

Why is the limit 0?

[dense breach]

because as x gets "closer" to - infinity or infinity, f(x) gets closer to 0

[true yoke]

So the limit would like be describing the point where the Asymptote won't cross?

[dense breach]

it's the point that the asymptote will get arbitrarily close to

[true yoke]

That makes sense, but then what does the infinity part of the limit refer to then?

at x->2

[dense breach]

as x gets closer to 2, f(x) gets closer to infinity

[true yoke]

Hence why there is a vertical Asymptote? Or am I wrong?

[dense breach]

More or less

There can be a vertical asymptote without a limit too, like in y=1/x

[true yoke]

let me put that in desmos, do you mind telling me where the limit in that would be

[dense breach]

I just said there isn't one at the vertical asymptote

[true yoke]

Sorry I misread, why wouldn't there be an limit in the vertical one?

[dense breach]

Because there's nothing that f(x) approaches as x approaches 0

[true yoke]

Wouldn't it approach 0 itself? Or does that not count

[dense breach]

It doesn't approach 0

[true yoke]

I see, thanks for your help. I am new to this

[dense breach]

As x goes to infinity f(x) would approach 0 but that's not what we're talking about here

[true yoke]

I plan to close the channel. Is that okay?

[dense breach]

Yes

[true yoke]

have a good one

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[dense breach]

You too

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[uncut aspen]

remember the second fundamental theorem of calculus

[winter egret]

I remember

e^(-t^2)

[vagrant marsh]

let F(x) be the antiderivative of the integrand

write your problem that way

[winter egret]

(e^(-(alpha+h)^2+alpha^2)/h

e^(-alpha^2+alpha^2=1

@vagrant marsh @uncut aspen

[uncut aspen]

you'd have to use the antiderivative of e^(-t^2)

but that's not possible with normal integration techniques

so instead, substitute the antiderivative as F(t)

such that $\frac{d}{dt} F(t) = e^{-t^{2}}$

[solid kiln]

890s

[winter egret]

Wait a moment let me think

actually tried but goy no good antiderivative

e^(-t^2)(-2t)

But i felt it will not work out

[uncut aspen]

you don't actually have to find the antiderivative

you can use an unknown so that you can continue with the rest of the problem

[winter egret]

What unknown?

[winter egret]

I didn't get it

[uncut aspen]

we could say that e^{-t^2} equals f(t)

and it's antiderivative is F(t)

[winter egret]

Hmm so

[uncut aspen]

now, instead of trying to find the actual antiderivative, we can use F(t) instead

[winter egret]

d/dt (F(alpha+h)-F(alpha)?

.close

[trim jolt]

Channel closed

Closed by @winter egret

Use .reopen if this was a mistake.

[winter egret]

.reopen

[trim jolt]

✅

[winter egret]

@uncut aspen check

[uncut aspen]

yep

[winter egret]

And next?

F'(alpha+h)-F'(alpha)?

@uncut aspen

Bro let me alone

2 minute problem taking 2 hours

[uncut aspen]

yes

and what is F'(alpha)?

actually no

[uncut aspen]

not this

since this is part of the limit definition of the derivative

[uncut aspen]

this is not the same as the limit definition

it's d/dt F(t) at alpha

[winter egret]

There would be -c?

[uncut aspen]

nope, that's only when you integrate

[vagrant marsh]

well F(t) includes the +C, but you find F'(t) which gets rid of the +C

[trim jolt]

@winter egret Has your question been resolved?

[trim jolt]

@winter egret Has your question been resolved?

Channel closed

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• After 15 minutes, feel free to ping <@&286206848099549185>.
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[spiral garnet]

yo

[spiral garnet]

i already tried negative

and its wrong

[west pine]

web assign 💀

[spiral garnet]

i just evaluated the integral t^3/3 +t^2-15t over 0 to 5

ik

[west pine]

pain

[spiral garnet]

any1

[keen shoal]

its -25/3 yeah

,w int((t^2 +2t-15)dt) t = 0 to 5

[solid kiln]

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[west pine]

I see a slight problem with this

[spiral garnet]

omg bro

[west pine]

it's asking for total distance

[orchid wagon]

you forgot the absolute value

[west pine]

whilst the integral

yeah

that

[spiral garnet]

i tried 25/3

[orchid wagon]

$\int_0^5 |t^2+2t-15|\dd t$

[orchid wagon]

should be this

[keen shoal]

yeah

,w int((|t^2 +2t-15|)dt) t = 0 to 5

[solid kiln]

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Upgrade to WolframAlpha Pro!

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[keen shoal]

change everything lol

[spiral garnet]

oh my gyatt

,w int((|t^2 +4t-5|)dt) t = 0 to 5

[solid kiln]

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Upgrade to WolframAlpha Pro!

Requested by mwb117

[spiral garnet]

i put /2 instead of /3 so it got randomized to that

bruh?

[keen shoal]

forgot the t^2

wait

mb

you tried 137/3

[west pine]

problem changed

it's from 0 to 4 now

[keen shoal]

oh lol

[spiral garnet]

oof

,w int((|t^2 +4t-5|)dt) t = 0 to 4

[solid kiln]

Results provided by WolframAlpha

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Upgrade to WolframAlpha Pro!

Requested by mwb117

[spiral garnet]

finally

thanks

.close

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[azure smelt]

it says that china is adjacent to two 4 stars countries, algeria and laos have 3 stars which makes only spain and saudi the ones eligible to have 4 stars, however when I put 4 in saudi it's a mistake, any help pls

[trim jolt]

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@azure smelt Has your question been resolved?

[trim jolt]

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• After 15 minutes, feel free to ping <@&286206848099549185>.
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[loud orbit]

Can someone let me know if I did these right?

[hallow cliff]

H(36) is incorrect

[loud orbit]

So then how do I do it?

[hallow cliff]

You have written $h(x)=-3/2 \sqrt{x} -1$, but when evaluating h(36), you have written $h(36)=-3/2 \sqrt{36-1}$

[solid kiln]

daddymorphism

[loud orbit]

What sorry so I have to write it

The first way?

[hallow cliff]

You have written it the first way over here, in the question

Look at what you have written in the question. Is it the first way or the second way?

[loud orbit]

First

[hallow cliff]

Yes, so when you find h(36), you should also use the first way

[loud orbit]

Could you write it out for me please for h(36) I’m just confused still

[hallow cliff]

$h(36)=\frac{-3}{2} \sqrt{36} - 1$

[solid kiln]

daddymorphism

[hallow cliff]

Do you understand why its not $h(36)= \frac{-3}{2} \sqrt{36-1}$?

[loud orbit]

Ohhh

How come it’s -3

[solid kiln]

daddymorphism

[loud orbit]

Yes

I understand now

[hallow cliff]

Oh sorry, i read the = as a -

[loud orbit]

All good

[loud orbit]

So this is correctly written

[hallow cliff]

Yes

[loud orbit]

Ahhh

Does it change the end answer ?

[hallow cliff]

It does

$3/2 \sqrt{35}$ is not equal to $3/2 \sqrt{36} -1$

[solid kiln]

daddymorphism

[loud orbit]

That’s right

[exotic pine]

use \frac{}{} smh

[hallow cliff]

Second one is fine (although technically that quadratic function doesnt have an inverse. it seems like you are taking a class in basic algebra and the term inverse function is loosely used. Had you used the quadratic formula, youd get the same expression for f^(-1).)

[loud orbit]

Okay okay

So just to confirm

It is h(36)=3/2 sqrt 36 - 1

[hallow cliff]

Do you mean
h(36)= 3/2 sqrt(36) - 1 or
h(36)=3/2 sqrt(36-1)?

[loud orbit]

First one

[hallow cliff]

Yes

[loud orbit]

What’s after that

[hallow cliff]

Well, do the rest of the steps

[loud orbit]

3/2 sqrt 35?

[solid kiln]

daddymorphism

[loud orbit]

Oh

[hallow cliff]

We had just discussed it here and you said yes too.

[solid kiln]

daddymorphism

[hallow cliff]

Have you heard of BODMAS, or GEMA? If you apply those rules correctly you will get the right result.

[loud orbit]

Bedmas?

[tall kernel]

its like pemdas

[hallow cliff]

Yes, that is another name for it

[loud orbit]

Brackets exponents division multiplication adding subtraction

[hallow cliff]

Sqrt(x) = x^(1/2)

[solid kiln]

daddymorphism

[loud orbit]

OHHHH

[hallow cliff]

I hope you can apply the rest of the rules, yourself

[loud orbit]

The answer has to be one number right

3/2 • (6) - 1

It’s 8

[hallow cliff]

Yes

[loud orbit]

3/2 • 6 is 9

9-1 = 8

[hallow cliff]

So what is (1/7)*g(f(-1))-h(36)

[loud orbit]

Which is my final answer?

[hallow cliff]

Yes

In your question you have been asked to find (1/7)*g(f(-1))-h(36)

[loud orbit]

Yes

Is that wrong how I did it

[hallow cliff]

no its correct

You have found h(36)=8

[hallow cliff]

Now find the value of this

[loud orbit]

Is it not 7

[hallow cliff]

Is what not 7?

[loud orbit]

1/7 x 49 = 7

[hallow cliff]

Yes

So 7-8=-1

[loud orbit]

And then that’s the value of

[hallow cliff]

I am not understanding you

[loud orbit]

7 - 8 = -1 correct

[hallow cliff]

Yes

[loud orbit]

-1 = (1/7)*g(f(-1))-h(36)

[hallow cliff]

Yes

[loud orbit]

And therefore -1 is the value of (1/7)*g(f(-1))-h(36)

[hallow cliff]

Yes it is

[loud orbit]

Okay

Another thing

I need help with this question

Is the inverse of f(x) a function?
If not, restrict the domain of f(x) such that its inverse is a function, include all possibilities

I’m trying to get all my practice questions done currently

[hallow cliff]

You should open a new help channel for a new question

[loud orbit]

Okay

.close

[trim jolt]

Channel closed

Closed by @loud orbit

Use .reopen if this was a mistake.

[loud orbit]

Thank you

[trim jolt]

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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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[echo linden]

Guys I have a few maths question a need a bit of help with

[clear cloud]

Sure, post your problem

[echo linden]

A 20 sided shape has 10 right angles in it and order 10 rotational symmetry. There are 10 obtuse angles on the outside of the shape where the two sides meet. What angles are they?

[worldly wing]

What will be the sum of the internal angles of a 20 sided polygon?

[echo linden]

2880°?

[latent iron]

The interior angle sum will be (n-2)*180 for an n-gon

We can use that formula for n=20 for the sum of the internal angles

[echo linden]

So how would we start

Do I have to do like a diagram of some sort

I don’t think I can draw an icosahedron though

Is it like a star shape?

[latent iron]

We know we have 10 right angles and 10 obtuse angles, and that we have 10 ways positions we can rotate it that will result in the same diagram correct? Does that give you any initial information on relationship between any 2 chosen obtuse angles

I would personally find a diagram very hectic, I recommend trying to break it out into a few fundamental facts and seeing what relationships emerge in this case.

[echo linden]

So is there like an easier way to do it

Maybe an equation

[latent iron]

Yup!!

Does any formula jump to mind when you think of the interior angle calculation?

[echo linden]

Are you able to tell me the answer and I’ll see how I can get to it

I think I know now

I’ll try the formula and see what I can do

[latent iron]

The main formula I had in mind was this one

(n-2)*180= sum of interior angles

[echo linden]

Would this help?

[latent iron]

I do know how to solve this question, I’m mostly trying to make sure I don’t give away too much to you. I personally don’t use many visual diagrams, but I know for a lot of people they are super useful, so if it helps you please use them.

[echo linden]

I used the formula here and I didn’t seem to get anywhere with it

[latent iron]

We know we have 10 right angles, and 10 other angles, each of the others corresponds to an obtuse on it’s other side

[velvet coral]

@latent iron the sum of the interior angles of the 20 sided gon is (20−2)×180°=18×180°=3240° right?

I mean, yeah?

[latent iron]

Unless I’m very wrong, that’s correct

[echo linden]

Can anyone else help with this

[velvet coral]

I dont know exactly, but its not too much to give up to radiance

[latent iron]

Try taking the sum of the 2 groups of interior angles

The right and others

[velvet coral]

ah, I am coping up, lets see if anyone else comes up

one more thing

[latent iron]

We have 3240=10*90+ 10X

If we can justify all other angles are the same

[velvet coral]

the rotianal symmetry is 10

so after 36 degree rotation its still same

[echo linden]

Right

[velvet coral]

if there are 10 right angles

give them a specfic degree

say, if 1 right angle is 90, how much are 10 of those?

[echo linden]

900

Then what do I do?

[velvet coral]

then

if the total is 3240 is the total angle

[echo linden]

A 20 sided shape has 10 right angles in it and order 10 rotational symmetry. There are 10 obtuse angles on the outside of the shape where the two sides meet. What angles are they?

Just to make it easier to see

[velvet coral]

wait so the obtuse angles are not the interior angles?

@latent iron is this right?

[velvet coral]

.

and one more thing

"At each vertex, the interior and exterior angles sum to 180°"

[latent iron]

When I check it out I find

X=(3240-900)/10=234

Which suggest that it should be the interior angle, but the visual and description above describes the outside angle as the obtuse angle

So that makes me inclined to believe I’ve misunderstood the question at some level, or that I made a mistake, but I don’t know where that would be

[velvet coral]

that should be the logical angle

[echo linden]

How would I figure out how big each of the angles are with these numbers now

[velvet coral]

hm

[latent iron]

360 not 180, the interior and exterior together make a circle

[velvet coral]

for this problem yeah

[latent iron]

We know
obtuse angle+234=360

So this should be enough, and I feel very silly now lol

[velvet coral]

it takes not adjacent angles

then

[latent iron]

What do you mean?

[velvet coral]

@echo linden the answer is 360-234

[echo linden]

For each of them?

[velvet coral]

the 180 rule which I said talks about adjacent angles

[echo linden]

Let me check

[velvet coral]

as, the angles make a sum

then 234 is the angle of 1 verter interior

then one outside angle must be the diff

[echo linden]

Ohhh it does make sense

[velvet coral]

my rule applies here

[echo linden]

Oh that’s smart

[velvet coral]

but the 360 rule is for your question so yeah

[velvet coral]

math

[echo linden]

Wait

I had another question

[velvet coral]

check the answer then if you are satisfied

[echo linden]

Is it fine if I ask that?

[velvet coral]

different channel

[velvet coral]

different question diff channel

[echo linden]

Oh ok

[velvet coral]

first check the answer for this

[echo linden]

.close

[trim jolt]

Channel closed

Closed by @echo linden

Use .reopen if this was a mistake.

[velvet coral]

wait

[echo linden]

.reopen

[trim jolt]

✅

[velvet coral]

lol

[echo linden]

Oops

[velvet coral]

so yeah

check the answer if you are satisfied

or make any attempts

well first, 360-234 is?

[echo linden]

126°

[velvet coral]

yup

is it the answer?

[echo linden]

It looks correct

I’m not sure

lmao

[velvet coral]

answer key?

[echo linden]

I’ll find out next week

Sorry

[velvet coral]

hm ok then

next question ig

close now

[echo linden]

.close

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Channel closed

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

(a^n)(a^m)=100000
(a^n)/(a^m) = 10
Find a

[wooden hornet]

Im am stuck on this problem for like an hour help

[candid sluice]

what are the restrictions on a,m,n?

[mild oxide]

@wooden hornet

Why don't u try manipulating both equation

[wooden hornet]

No restriction i guess since it doesnt say

[wooden hornet]

a^n+m = 100000
a^n-m = 10

Thats farthest ive gotten idk what else to do now

[candid sluice]

try multiplying them

and dividing them

[nova spire]

please a,n and m are integers?

at least

[wooden hornet]

Yeah i think so

[nova spire]

ok so at least this is solvable

a^(n-m) = 10

do you know many integers that when raised to some power give you 10?

[wooden hornet]

10^1

[candid sluice]

if you multiply them

the m cancels

if you divide the n cancels

[wooden hornet]

Hmm?

Multiply what with what

[candid sluice]

the 2 equations

[wooden hornet]

What would happen to the 10 and 100000

[candid sluice]

well multiply them

[wooden hornet]

Sooo... (a^(n+m))(a^(n-m))=(a^(2n) = 1000000

[candid sluice]

ye

now divide them

[wooden hornet]

(a^-2m)

[candid sluice]

what about rhs

[wooden hornet]

rhs?

[candid sluice]

right hand side

of equation

[wooden hornet]

(a^-2m)=10000

[candid sluice]

its a^2m

not -

[wooden hornet]

Ah right cause positive number minus a negative number

[candid sluice]

can you do the rest

a^2m = 10^4

a^2n = 10^6

thats what you have

[wooden hornet]

Yes

[candid sluice]

👌

[wooden hornet]

I still dont know how im gonna cancel out the exponents to get a

[candid sluice]

if u say they are integers

a = 10, -10

right

otherwise you cant get a factor of 10 on rhs

[wooden hornet]

Howd you arrive at this

My inital answer was that too but i couldnt prove it

[candid sluice]

if rhs divides by 10

left hand must also

if a,m,n are int

then a must have a factor of 10

let a = |10k|

if k >1 then

rhs has a factor of k

which is contradiction

so a = 10, -10

[mild oxide]

See

[wooden hornet]

Dam i dont understands that.
Glad to see my intial hunch was right though

[mild oxide]

U need to find a or m and n

Here is a solution for it a=10, n=3 and m=2

By seeing the question

[wooden hornet]

But then I would prove that how i got those values

[mild oxide]

Simple prove

As all are integers

A m and n

a^(m+n) can only come in the form of power of 10

If a is itself 10

💀🙂

See the first expression

a^(m+n)=10^5

All a m and n are integrrs

Integers

it's only possible if base is 10

[wooden hornet]

Yeha it fulfills the two equations.

[mild oxide]

See

Like I want to say

a^(p+q)=64

Only possible if base is 2

This is true only bcz

All a p and q are integers

2^(2+1)=8

[wooden hornet]

How do i say it in mathematics forms.
Cause is it acceptable to juat write it like that

" a= 10 because no other base can fulfill both equations"

[mild oxide]

Wait let's look into it then

[mild oxide]

Na bruh 💀

[wooden hornet]

💀

[mild oxide]

Bro srsly

Even if u can say

Clearly

The answers

U can't convince them that it's the proof

💀

fr

Wait

A can't be -10

Don't u think we will get a -

[wooden hornet]

If the expoment is odd yez

[wooden hornet]

Thats what im having trouble with

Anyways im just gonna write something like that as the explaination though a bit more formally and mathematically.

.close

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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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[quick mango]

Hello guys I need help with a question

[clear cloud]

Sure post it

[quick mango]

A machine has a probability of 0.1 of manufacturing a defective part. The parts are packed in boxes of 20.
a) What is the expected number of defective parts in a box
b) what is the probability that the number of defective parts in the box is less than the expected number? Express answer in the form ab^19/c^20

🙏🙏pleease help

[clear cloud]

It is a binomial distribution

[quick mango]

yesss

[clear cloud]

With which parameters ?

[quick mango]

aye im really sorry but what do you mean by parameters

[clear cloud]

X~Ɓ(n,p)

The n and p

[quick mango]

like what their values is

n = 20 p = 0.1

[clear cloud]

Indeed

And what is the mathematical esperance of a binomial ?

I mean the formula

[quick mango]

hereee

is this what you meant

[clear cloud]

Not this one

[quick mango]

WHICH ONEE

WHOOPS

SORRY

[clear cloud]

But keep it, we'll need it

E(X) = ?

[quick mango]

OHHH

e(x)=np

[clear cloud]

So ?

[quick mango]

I’m kinda confused how to solve for part b mostly sorry i should’ve said that from the start

[clear cloud]

Dw ima explain it

[quick mango]

like from the formula i thought the probability when you sub in for ‘p’ in the other formula would be 0.1 but in the worked solutions it said 19/20

[clear cloud]

Wait we havent ended the a)

E(X) = np = ?

[quick mango]

2

[clear cloud]

Yes

So the expected amount of defectives machines is 2 in a box of 20

[quick mango]

yuss

[clear cloud]

So

For b)

We want to know P(X<2)

(wait, striclty less or less and equal ?)

[quick mango]

it is just less than

no equal

[clear cloud]

Ok so all good

P(X<2)

$P(X<2) = P(X\le1) = P(X=0) + P(X=1)$

Do you agree?

[quick mango]

Yes i agreee

[solid kiln]

YakuBros

[clear cloud]

Perfect

[clear cloud]

So now, you apply the formula here to the P(X=0) AND to the P(X=1)

[quick mango]

yuss

[clear cloud]

$P(X=0) = \binom{20}{0} \cdot (0.1)^0 \cdot (1-0.1)^{20-0}$

[quick mango]

the textbook solutions put 19/20 instead of (0.1)^0

WAIT WHOOPS I MEANT 1/20

[clear cloud]

$P(X=0) = 1 \cdot 1 \cdot(0.9)^{20}$

[clear cloud]

Wait mb

[solid kiln]

YakuBros

YakuBros

[clear cloud]

$P(X=1) = 20 \cdot 0.1 \cdot (0.9)^{19}$

$P(X=1) = 2 \cdot (0.9)^{19}$

[solid kiln]

YakuBros

YakuBros

[quick mango]

hey sorry the answers had P(x=0) as (20,0) x (1/20)^0 x (19/20)^20

im not sure why the book wrote it like that

[clear cloud]

Ok ic why

Its in one box

So yeah

[quick mango]

why wouldnt it be 0.1 but instead 1/20

[harsh prism]

.open

[clear cloud]

!occupied

[trim jolt]

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).

[clear cloud]

And the same for P(X=1) ?

Changing 0 to 1 ?

[quick mango]

Yess

[clear cloud]

I dont see how they get it

They dont explain ?

That would meant that E(X) = 20*1/20 = 1

Which is absurd

[quick mango]

thats trueee

it is weird

[quick mango]

nopee

[clear cloud]

Thats what they say for a) ?

Like E(X)= 1?

[quick mango]

they said part a was just 2

so n had to be 20 and p be 0.1

[clear cloud]

Yeah

[quick mango]

so if like a question like this comes up should i go by your method

[clear cloud]

Where do they take out the 1/20

[quick mango]

Im not too sure…

do u want a pic of the solutions?

[clear cloud]

Yes please

[candid sluice]

this is incorrect

yaku did it right

[clear cloud]

Well, they once again dont understand that the most important is the justification and text in maths, not only the calcul and furthermore its incorrect

[quick mango]

TRUE TRUE

so it should be 0.1 then

[clear cloud]

Do you want me to continue where we were ?

[quick mango]

Yes pleasee

[clear cloud]

So we have $P(X=0) + P(X=1) = (0.9)^{20} + 2 \cdot (0.9)^{19}$

[solid kiln]

YakuBros

[quick mango]

yess

[lunar linden]

Binomcdf

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[quick mango]

yepp

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[orchid sun]

Topic: conic sections circle
How do I find a point which is not quadrantal point?

[twin storm]

what is that

[marsh forum]

,w quadrantal point

[solid kiln]

Results provided by WolframAlpha

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Requested by physicsrocks

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[upbeat dome]

I have created a program, which makes random noise pic rel. I would like to make a demo app, which will utilize it. Do you have an idea what would look good with noise like this?

[upbeat dome]

idk some fire texture or smth?

screw it, nobody will answer it anyway
.close

.close

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[shrewd obsidian]

im given the problem: for $an \geq 0$ if $\sum{n=1}^{\infty} an$ diverges, does the $\sum{n=1}^{\infty} \frac{a_n}{1+na_n}$ converge. i tried some tests but all were inconclusive. any hints appreciated

[solid kiln]

atif

[shrewd obsidian]

do i need to consider cases if a_n is monotonic or not?

[limpid dawn]

I'm given the problem: For $a_n \geq 0$ if $\sum_{n=1}^{\infty} a_n$ diverges, does the $\sum_{n=1}^{\infty} \frac{a_n}{1+na_n}$ converge? I tried some tests but all were inconclusive. any hints appreciated.

[solid kiln]

𝔸dωn𝓲²s

[limpid dawn]

We can assume that a_n doesn't go to 0 as n -> inf

[shrewd obsidian]

can we though?

[limpid dawn]

The series diverges right

[shrewd obsidian]

afaik if \sum a_n converges then a_n goes to 0

so the contrapositive is

[limpid dawn]

so the necessary condition that a_n -> 0 is not the case

[shrewd obsidian]

but it doesn't go both ways

[limpid dawn]

If the series diverges then that implies a_n -> not 0

[shrewd obsidian]

i m not sure that's true

i thought the same but upon thinking more it seemed false

[limpid dawn]

yea you are right mb

[wraith hinge]

sum 1/n diverges but 1/n -> 0

[shrewd obsidian]

yeah good one

[wraith hinge]

and actually, to answer the original problem, let a_n = 1/n, then we know that (sum 1/n) diverges, and (sum a_n / (1 + n a_n) )= (1/2) sum 1/n which is divergent as well.

[shrewd obsidian]

but that's only for a_n = 1/n, no?

i need to check for any a_n sequence

[safe leaf]

wait...

[limpid dawn]

$\sum_{n=1}^{\infty} \frac{a_n}{1+na_n} = \sum_{n=1}^{\infty} \frac{1}{\frac{1}{a_n}+n}$

[solid kiln]

𝔸dωn𝓲²s

[limpid dawn]

If a_n >= 0

[wraith hinge]

do a comparison test might work. Haven't looked at the problem very carefully

[shrewd obsidian]

i tried that, and limit comparison test

[shrewd obsidian]

yes im given this condition, ok let me see. thx

[limpid dawn]

i am trying to see myself

[safe leaf]

if a_n decreases, then the series must diverge fs

[shrewd obsidian]

any hints as to why?

[safe leaf]

actually lemme think

im trippin

mb @shrewd obsidian

[shrewd obsidian]

np, im thinking if we should consider cases whether a_n is monotonic or not

[limpid dawn]

great idea

[safe leaf]

i am still trippin

disregard what i am saying rn lmao