help-26

[topaz sinew]

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[topaz sinew]

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[floral rampart]

hi yea im thoroughly confused

[floral rampart]

doesnt he define d(G) in two different ways?

that surely arent the same

d(G) is the smallest natural number with a homomorphism from G to the symmetric group should be less than or equal to degree of G

at least thats what i think should be true

[topaz sinew]

@floral rampart Has your question been resolved?

[floral rampart]

<@&286206848099549185>

[topaz sinew]

@floral rampart Has your question been resolved?

[gleaming thunder]

First he defines d(G) with that homomorphism definition. Then he defines alpha(G) using this definition of d(G). Then he simply names these two values the Cayley Constant and degree of G

[topaz sinew]

@floral rampart Has your question been resolved?

[floral rampart]

so hes dividing by the order of G?

[gleaming thunder]

the cardinal

easy to assume G isn't empty

[floral rampart]

ah i see

thanks

.close

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[torn sky]

can anyone help with this question when f(x)=3x and g(x)=2x+1 If f is a one-to-one function, and g is a many-to-one function, what can you say about
(f ◦g )−1 (x )? (show a mathematical reasoning).

[topaz sinew]

@torn sky Has your question been resolved?

[torn sky]

??

<@&286206848099549185>

just saw how many other help channels there are, my bad guys

@split elbow i'll stop feeding Tom if u help me out

[neon venture]

how is it even possible that 2x+1 is a many-to-one function

[torn sky]

my bad wasnt included in the question

that was the previous questions function

If f is a one-to-one function, and g is a many-to-one function, what can you say about
(f ◦g )−1 (x )? (show a mathematical reasoning).

[torn sky]

everything but that part is the question

damn missed my chance :< 😢

[topaz sinew]

@torn sky Has your question been resolved?

[topaz sinew]

@torn sky Has your question been resolved?

[bright panther]

yeah feels bad man

i cant help

i have no idea what this is about

[topaz sinew]

@torn sky Has your question been resolved?

[sweet shard]

.close

[topaz sinew]

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[mellow spindle]

how did the 3x^(1/2) turn into 3/2(3x)^-(1/2)

[sweet shard]

Chain rule

It's (3x)^(1/2), not what you wrote

[timber valve]

Chain rule cuz d/dx of 3x is 3. But I prefer to just look at it as √3 * √x so that we can use √3 as a constant

[topaz sinew]

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[mellow spindle]

this isn't clicking for me

[mellow spindle]

I don't get it

Im trying chain rule and i'm not getting what my teacher got

^For anyone else who wants to help

im confused as to why its (3/2)(3x)^(-1/2) and not (3/2)(x)^(-1/2)

like why is 3x still there if it was derived

[stiff fossil]

d/dx sqrt(3x)
= sqrt(3) * d/dx sqrt(x) + sqrt(x) * d/dx sqrt(3) --- product rule
= sqrt(3) * 1/2 * 1/sqrt(x) * d/dx (x) + 0 --- derivative of constants are zero
= sqrt(3)/2sqrt(x)

[topaz sinew]

@mellow spindle Has your question been resolved?

[mellow spindle]

so

that's a different answer from what my teacher got (picutre)

[stiff fossil]

it's the same

3 * 1/sqrt(3) = [sqrt(3)]^2 * 1/sqrt(3) = sqrt(3)

[mellow spindle]

ok yeah it is

yeah

mb

i just did the calculations

damn

ok what you did makes alot more sense

ty

[topaz sinew]

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[timber valve]

sorry id help but im in class

[timber valve]

.close

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[ionic thorn]

help

[topaz sinew]

@ionic thorn Has your question been resolved?

[sweet shard]

how are you a helper and you don't know this #help-26 message

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[bold briar]

Hello

[bold briar]

I need help with a geometry problem, i don’t know where to start

[mild bluff]

I will start with 180 - 9x + 16 and use the fact In a triangle, the three interior angles always add to 180°

[bold briar]

I am confused because there are 4 angles in total

I know supplementary = 180

[mild bluff]

horizontal line is 180 degree so the angle that is not lable is 180 - (9x + 16) just a thought

so if we add all the angles and set it equal to 180 and solve for x?

typo

[bold briar]

Yeah, i knew angles that added up to 180.

[mild bluff]

Here is my thought - I could be wrong

180 - (9x + 16) + 6x + 4 + 4x - 2 = 180
x = 14

now plug into x

My calculation came out correct.
4x - 2 = 54
6x + 4 = 88 and 180 - 9x - 16 = 38 when x = 14

[mild bluff]

True.

[bold briar]

.close

[topaz sinew]

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[mild bluff]

180 - (9x + 16) + (6x + 4) + (4x - 2) = 180
x = 14

4x - 2 = 54
6x + 4 = 88 and
180 - 9x - 16 = 38 when x = 14

[topaz sinew]

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[rotund pine]

missed the lesson (was sick)

need help ._.

[still ruin]

don't take calc but i have an idea for a roundabout way to solve the problem

convert polar equation to rectangular

find where curve crosses itself

take integral from 0 to that point

that's definitely not how you're supposed to do those problems but im not smart enough to offer an alternate solution lmao

[lavish musk]

Polar integration formula is $A = \int_\alpha^\beta \frac{1}{2}r^2 : d\theta$.

[thorny flame]

PhenomPlasma

[lavish musk]

Though you need to find the angles $\alpha$ and $\beta$ where $r = 0$.

[thorny flame]

PhenomPlasma

[rotund pine]

wha-

angles?

ok-

[lavish musk]

In polar coordinates, you always need the angle, yes.

[still ruin]

^That's the way I guess lol

[topaz sinew]

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[neon iron]

math is hard and i don't understand how to make two column proofs

[neon iron]

pls ignore the written thing that was just guesswork

how do i create a two column proof 🗿

[topaz sinew]

@neon iron Has your question been resolved?

[wary sun]

@neon iron on the left, like a normal proof, you make statements. these are given as bullet points rather than sentences, as you might see elsewhere. on the right, you give a reason (usuallt used in geometry, so a geometric reason) for each of your statements

[neon iron]

so how do i make statements

[wary sun]

look at the example on your sheet above.

those are all statements, things that you are stating and noting are true; these statements form a sequence that someone can follow, in order, to arrive at a conclusion. the right hand column just gives a justification for each

[neon iron]

oh so i make true statements until i can prove ABC ≅ ADC

[wary sun]

yup, just like any proof. the 2 column idea is just a way to format it

[neon iron]

ohh ok I'll try to make a proof and send it here to check

[wary sun]

👍 close this pls, and when ready make a new channel :)

[neon iron]

oh alright thank you

.close

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[neon iron]

Need help

[neon iron]

i dont get any of it

[topaz sinew]

@neon iron Has your question been resolved?

[topaz sinew]

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[topaz sinew]

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[topaz lynx]

WHY do we work out RMS???

[topaz lynx]

why not just work out average with modulus

why square everything and do dodgy scaling

[marsh mortar]

eh?

[topaz lynx]

i googled it and apparently its something to do with calculus apparently idk

cuz u cant differentiate/integrate absolute functions or something

[marsh mortar]

What is modulus

what is rms

[topaz lynx]

| |

absolute value

rms root mean square

[marsh mortar]

Are you talking about this stuff

[topaz lynx]

well yh but i think i get it now anyway

its just to do with ability to apply calculus to the result

prolly

[marsh mortar]

there is a textbook that explains this very well

uh

it's called Further Pure Mathematics

by bostock and chandler

yellow cover

[topaz lynx]

i'll have a look, thanks.

.close

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[indigo night]

using this

tried reading the example in the book but i could not understand how to do it some help on how to even start solving it would be appreciated

this is the explanation in the book but i for some reason found it hard to understand

<@&286206848099549185>

[topaz sinew]

@indigo night Has your question been resolved?

[indigo night]

<@&286206848099549185>

[topaz sinew]

@indigo night Has your question been resolved?

[indigo night]

<@&286206848099549185>

.close

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[spare marsh]

with the range of values, e.g. 14 <= t < 15

what should my t be

the mid point between 14 and 15?

[pseudo bear]

Yes, use the interval midpoint.

[spare marsh]

okay athanks

.close

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[neon iron]

Help !

[neon iron]

i need the radical

i tried but i cant do it

someone help soon!

<@&286206848099549185>

[wary sun]

@neon iron which one?

[neon iron]

all of them

[mellow venture]

don't ping helpers

[wary sun]

how would you do the first, do u think

[neon iron]

SORRY

im new to this server

[neon iron]

put everything into the therom

slove

then get the answer

then radical it out

but i cant do it right now

i dont have a sheet of paper

[mellow venture]

[wary sun]

well you have answers already, do you need them in sqrt form?

[neon iron]

i dont know if there right

i honestly was quick with my work

[wary sun]

well the first is close, but not correct

how did u do it?

[neon iron]

i just plugged it in i didnt get a radical

[wary sun]

show me how you 'plugged it in'

[neon iron]

like this

but she needs is radical

[wary sun]

do it by hand, without this calculator. write out how you'd find c using the pythagorean theorem

[neon iron]

I Cant

i dont have my piece of paper

thats the issue

[wary sun]

if u don't have paper, and can't do it in your head, you'll have to come back to this later

[neon iron]

DUDE

THIS IS DUE

IN 10 MINUTES

slams into keyboard

[wary sun]

i'll show you how to do one but i'm not doing your homework for you

[neon iron]

i know but cant

[sweet shard]

don't pressure people into helping you

[neon iron]

but i need help

thats literally it

[wary sun]

for this one, the theorem states a^2 + b^2 = c^2, right? in this case, c^2 = 13^2 + 23^3,
so c = sqrt(13^2 + 23^2) = sqrt(698)

[ocean hare]

math rage moment

dw i've raged here too a few times

just use the pythagorean theorem and you'll be fine

[topaz sinew]

@neon iron Has your question been resolved?

[topaz sinew]

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[young violet]

can anyone help with this

[young violet]

for fx i got 3x^2 y^2 e^x^3

for fy i got 2ye^x^3

not sure how to do fxx and fyy

[sage cliff]

Take the derivative with respect to x

Again

[young violet]

do i use chain rule

there's 3 terms so its a bit confusing

[sage cliff]

Well if needed yes

[young violet]

thats what im stuck on im not sure how to differentiate with 3 terms

if they're all multiplied together

[sage cliff]

Product rule

And chain rule

And like the classic power rule

That’s all you need

[young violet]

ok ill try it

[sage cliff]

Do you know what the product rule is ?

If you have two function u(x) and v(x)

d/dx(uv) = u’v + v’u

[young violet]

ah yeah

[sage cliff]

Yeah use that

[young violet]

alright

ty

[sage cliff]

Np

[topaz sinew]

@young violet Has your question been resolved?

[topaz sinew]

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[heavy stag]

having difficulty with this one. I don't know how to find what it's asking for. I don't see how it is related to the limit either. I've found out that (5/6)^(log(p)/log(5/6)), not sure if that is relevant.

[wooden matrix]

find a natural number N such that when $n\geq N$, you have that $(5/6)^n<p$ for any $p>0$

[thorny flame]

Mosh

[wooden matrix]

this is the literal definition of a limit, that's how it's related

[heavy stag]

oh ok. why is it written as lim n->inf (5/6)^n = 0 though? where is the "inf" and "0" coming from?

[wooden matrix]

Formally: If $\lim_{n\to\infty}a_n=A$, then for all $p>0$, there exists $N\in\mathbb{N}$ such that, when $n\geq N$, we have that $|a_n-A|<p$

[thorny flame]

Mosh

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[azure osprey]

hello

[azure osprey]

this is my question:

im wrong on the integral part

but im not sure why

since biggest r is y^2 function- (-4)

and inner r is y-(-4)

i checked desmos too for radius

i feel like i missed something in the equation, or applied something wrong

<@&286206848099549185>

.close

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[leaden trail]

I am trying to test the rates of rewards from apex packs in apex legends, however im not sure how to convert the % of total items to chance to receive the item.

I have a spreadsheet with the results of 570 packs

[pulsar falcon]

wdym convert? You have % right there

[leaden trail]

but thats the % of total items but each pack gives you 3 items

in my head i feel like the 2.2% is different i just cant prove why

[pulsar falcon]

as long as you are comparing to 570*3

that is the correct probabilities

[leaden trail]

so EA is lying about the probability?

because 2.2 is awfully low

[pulsar falcon]

there might be some dependency thing

check how many times you got 1 on legendary

[leaden trail]

36 times, one was 2

[pulsar falcon]

35 you mean then

[leaden trail]

no 37 total, one was 2

[pulsar falcon]

35 * 1 + 1 * 2=37?

[leaden trail]

yes

[pulsar falcon]

so 35

but anyway 36/570

[leaden trail]

6.3%

so thats the number i need to compare

[pulsar falcon]

si

[leaden trail]

danke

i knew something was wrong just didnt know where

.close

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[willow wedge]

Any help is greatly appreciated

[willow wedge]

How do I do number 4

<@&286206848099549185>

[topaz sinew]

@willow wedge Has your question been resolved?

[willow wedge]

<@&286206848099549185>

[sweet shard]

sounds like a physics question

go look in #old-network for physics server

[stuck lintel]

Nah

Look at 3

This is probably stats

This is definitely probability theory

[mellow venture]

it is political stats in the formal of magma

[stuck lintel]

I guess this is becoming a meme now

[sweet shard]

ah my bad for only reading the first two sentences

[stuck lintel]

Eh no worries

I had the same reaction.

[sweet shard]

Use z-score with
$z = (X-\mu)/\sigma$

[thorny flame]

riemann

[sweet shard]

$\sigma$ = square root of variance

[thorny flame]

riemann

[willow wedge]

Ahhh okay

So when I do this, I get standard deviation

How do I calculate the probability from this?

[sweet shard]

have you ever used z score?

[willow wedge]

No I haven’t

[sweet shard]

https://www.youtube.com/watch?v=HCrYy1vNtHI

[willow wedge]

Ah, so I use this to tell me the probability of it being an outlier

Thanks, I’ll give this a go

.close

[topaz sinew]

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[bright dagger]

How can I find the angle?

[topaz sinew]

@bright dagger Has your question been resolved?

[bright dagger]

<@&286206848099549185>

[topaz sinew]

@bright dagger Has your question been resolved?

[bright dagger]

<@&286206848099549185> can u just come here and say something?

I ll take also a f off if u want

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@bright dagger Has your question been resolved?

[tardy nebula]

sine law

[topaz sinew]

@bright dagger Has your question been resolved?

[topaz sinew]

@bright dagger Has your question been resolved?

[hot wren]

I mean, you have a formula for theta in terms of x, and a value for x at which theta is maximised. Assuming your value of x is correct, you should be able to plug that into your formula to get the correct answer

[topaz sinew]

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[raven canyon]

becomes 2x/0 therefore 0?

[raven canyon]

or do they cancel out during division?

[leaden tusk]

the old division sign

hate that thing

you should apply PEMDAS/BEDMAS or whatever you learned

[leaden tusk]

they wouldn't "cancel" but they would reduce

[raven canyon]

yeah we use BEDMAS

wdym by reduce?

[leaden tusk]

well what does x/x simplify to?

[raven canyon]

0?

h

1

[leaden tusk]

there ya go

1

so you'd be left with x+1-x

and i take it you can do it from here?

[raven canyon]

oh shit true

omg ty

i thought x+x was bracketed and x-x was bracketed

.close

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[neon iron]

Hi i would like to ask, how would you prove this is a subspace?

.close

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[raven charm]

.reopen

[raven charm]

Uhh how did this work again?

20-.5-15

[restive inlet]

what's with the - between the 20 and the .5

[raven charm]

messed up

[restive inlet]

20.5-15 gives you the length of the circled segment
from properties of rectangles and segment addition/subtraction

[raven charm]

properties of rectangles

Yea I would have never figured that out

make with 4 hours of thinking I would’ve gotten that shape

to figure that out another 2

long before that I would have given up

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[frail palm]

Hello, i do not understand, how do you find the midsection here? Also, AB = 40cm and AC = 60cm, Find CE

[unique viper]

You can use sine rule to fine angle ACB

[frail palm]

I found it, 25 degrees ?

I assumed BAC was 90 degrees

But I still couldn't find CE

[unique viper]

It’s 37.17°

[frail palm]

From that, how do you find the length of CE ?

[unique viper]

Ye, with that you can find angle BDE because it’s 360 - the other 3 angles

[frail palm]

Uhh idon't think its that complicated, it's about congruence

[unique viper]

What are you trying to actually find?

[frail palm]

The length of CE

The length of AC is 60cm

And AB = 40cm

It's about congruence and similarity

[unique viper]

I’ve got that it’s 12.36cm the complicated way but I don’t know what the actual thing it wants you to do

[frail palm]

I just started learning about congruence and similarity, I don't think there is decimals

[unique viper]

So are the 2 triangles similar?

[frail palm]

No

From the image the line wasn't symetrical

[unique viper]

Ok I think it wants you to do, 32/20=1.6
40/1.6=25 (AE)
40-25=15

So CE = 15

If I was doing it I’d say it was 12.36cm but I think if you are doing congruence and similarly it will probably be 15cm

[topaz sinew]

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[frail palm]

Alright, i'll look into it, thank you

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[rapid hull]

Can someone just tell me the process

Like don’t even need to go in depth with the numbers just tell me every loose step of how to solve it

And I should be good

Just having a brain fart

[topaz sinew]

@rapid hull Has your question been resolved?

[rich karma]

X=fum

[rapid hull]

😦

<@&286206848099549185>

[narrow torrent]

ok. let's start by recalling the definition of a line in 3D

the most helpful one is this:

$L = <x,y,z> + t<a,b,c>$

[rapid hull]

okay

[thorny flame]

EndTimes

[narrow torrent]

sure ok

[rapid hull]

im really tired lol if you could tell me the parts i think i could piece it together

[narrow torrent]

$= (x_0+at, y_0+bt, z_0+ct)$

[rapid hull]

alright

[thorny flame]

EndTimes

[narrow torrent]

it should be (x_0, y_0, z_0) not (x,y,z) my bad

[rapid hull]

that looks correct no?

what the bot sent was correct?

ohhhhh

i see what ur saying

ok

what i do now

[rapid hull]

wow

thank you so much

thats so helpful

@narrow torrent

saved my life

thank u

.close

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[topaz sinew]

@violet cove Has your question been resolved?

[drifting swift]

do you know the relationship between arc length and angle?

@violet cove

it's pi, not pie. also don't use the letter x for multiplication.

i can't see if the angle is marked in any way for part b.

if it isn't, then you do not have enough information.

if it is, then please tell me what it's marked as.

okay

so it appears the relationship between arc length and the angle in radians didn't occur to you for part a.

otherwise you would not be complaining about part b being much harder than a, which it isn't.

[sweet shard]

Because that's what you were solving for?

theta is measured in radians / degrees. The useful unit is radians because that's what gives you area

So how did you solve part a without knowing that?

Go through the formulas in your notes until you find one that gives you the answer when you plug in the given information in the problem

It's the same formula

[topaz sinew]

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[drifting swift]

you mean that it didn't have directions for you to use one unit or the other?

.reopen

[topaz sinew]

✅

[drifting swift]

it's kind of the definition of radians as a unit

https://upload.wikimedia.org/wikipedia/commons/4/4e/Circle_radians.gif

here, this gif may be of use

the point is arc length is proportional to both radius and angle

[neat lantern]

Can someone help me with a quick problem

[drifting swift]

@neat lantern read #❓how-to-get-help

okay, so?

$L = r \theta$

[thorny flame]

Ann

[drifting swift]

that's legit all there is to it

arc length

r * 4.15

yes, that's the whole point

the degree version of this formula is L = rθ*π/180

[warm kraken]

notice what sqrt3/2 is

wait 18 a ryt

just to confirm

part a

ok so try dividing both sides by 2 cos phi

yeah so it's done ryt

oh

wait

hyp is 1 not 2

so cos 30 = sqrt3/2

yes

but u gotta look at all sol

yeah in 1st n 4th quadrants

see cosphi cd be 0

too

whenever u divide both sides of n equation by something see if that itself is possibly 0

a common mistake i make too lol

r the answers pi/6 , 11pi/6, pi/2 , 3pi/2?

yeah so cospi/2=0

take cosphi=0

the angle(variable) given

ok so see solve cos(a)=0

what do u get?

yeah that's the mistake

cos0=1

sin0=0

ig u confused there

lol it's fine

[empty sail]

Why are you dividing?

[warm kraken]

for simplification

assuming cos phi !=0

that case is separate

[empty sail]

The problem is $2\cos^2 \theta = \sqrt{3} \cos \theta$, right?

[thorny flame]

dldh06

[warm kraken]

just rem that when the angle is 0 hyp=base so cos0=base/hyp=1

[warm kraken]

yup

[empty sail]

There is no need to divide at all

[warm kraken]

yeah obvio there r more ways to do

[empty sail]

You shouldn't really be dividing at all

[warm kraken]

y not?

[empty sail]

If you divide, you get $\frac{2 \cos \theta}{\sqrt{3}} = 1$

[thorny flame]

dldh06

[warm kraken]

yeah so cos theta =sqrt3/2

try taking the sin as 'x' n solve quadratic

[empty sail]

If you divide, you making it only have one solution, when in fact it has 2

[warm kraken]

noo

[empty sail]

You subtract first to set it equal to zero

[warm kraken]

4 sol

ok bro u can do it that way too but cosx = sqrt3/2 doesn't mean x is only pi/6

[empty sail]

So you get $2 \cos^2 \theta - \sqrt{3} \cos \theta = 0$

[thorny flame]

dldh06

[empty sail]

Factor

[warm kraken]

yeah

[empty sail]

Using quadratic formula or any factoring method you know

Multiplies to -2

[empty sail]

Bro your method is wrong, you should not divide. You set that equation equal to 0, then factor, like what I have showing

Then use the quadratic formula

[warm kraken]

ok any reason for y that's wrong?

[empty sail]

Because solving equations, you don't normally set the equation to a non zero number, especially in that problem because it was originally it was a 2 solution answer, but when you divided by cos, you made it 1

[warm kraken]

bruh

[empty sail]

You didn't need to use the quadratic formula

[warm kraken]

.

[empty sail]

You don't assuming that, that's why you set it equal to 0 and solve

It was a suggestion. Either use the quadratic formula or use any factoring method

[warm kraken]

ok bro see ax^2=bx is an eq. if we assume x is not 0 we can cancel the x n write ax=b

so the sol are x=b/a n x=0

[empty sail]

You going from ax^2 = bx to ax = b loses a solution which will confuse people more which is exactly the reason why you set it equal to zero instead, to make it ax^2 - bx = 0 which then becomes x(ax - b) = 0, which you then then obviously see that x = 0 and ax - b = 0

[warm kraken]

man ur answers' right

[empty sail]

You are doing it in a much more confusing way that makes it seem like you are losing information

[warm kraken]

but this procedure is useful for simplifying

ok nvm man

[empty sail]

When it says solve, it's normally setting the equation equal to 0

Not to a non zero number

You did not do something right

Then how did you factor 2x^2 + 3x - 2 = 0?

And that gave you?

You did something wrong

Because 2x^2 + 3x - 2 is factorable, you should factor it

You are missing something

It's multiply to be -4

Because A times C

How would you solve x^2 - x - 2 = 0?

Where is -1 * -1 from?

In my example, x^2 - x - 2 = 0, how would you factor it?

No

It's multiply to -2 and add to -1

It looks like you need to touch up on factoring

No one asked for your option, x^2 - x - 2 = 0 isn't hard to factor. It has factors that are pretty simple to find

https://youtu.be/qeByhTF8WEw?t=182
From there to around the 5 minute mark is factoring the way you need to use

https://www.youtube.com/watch?v=4v-EQIxqpMQ&ab_channel=TheOrganicChemistryTutor

Did you guess these two or did you actually factor?

Well, you do A times C first, then find two values that multiplies to AC but add up to B

Now you can do apply factor by grouping

Factor the GCF from the first 2 terms and the GCF from the last 2 terms

Start with the first two terms

What should you factor out?

And you get?

Stop getting ahead

All I said was factor the GCF from the first 2 terms

No

The first two terms are 2x^2 - 4x, right?

Now the readjusted equation is 2x(x-2) + 1x - 2 = 0, right?

You still messed up, because you initially picked the wrong values

It's 2x^2 + 3x - 2 = 0
You then said 2x^2 - 4x + 1x - 2 = 0
Does that equal +3x?

Resting helps

Staying up all night to study for a test is not good. You will be mentally and physically exhausted by the time you take your test, if you stay up all night

And this is a learning experience, it means you should review much more earlier than you expected

Your teacher most likely told you that you had a test after spring break, sometime before spring break

Well, you can solve for x first, then turn x back into sin

Zero product property

If you have something in the form of AB = 0 then either A = 0 or B = 0

That's what it is

You do x + 2 = 0 or 2x - 1 = 0

Solve for x

Properly written, it's x = -2 and x = 1/2

Now you can replace x with sin

No

It's x = -2 and x = 1/2

It's now pretty much two separate equations

You don't divide

Yes

Now solve for theta

Because it doesn't

You should know that the domain or sin^-1 is between [-1, 1]

Where is this question?

Show me part b

B in this picture here?

Where is part B?

Because you assumed that it's a 45 45 90 triangle

You're using a unit circle, correct?

So you don't need to draw a triangle

You have sin theta = 1/2 therefore theta = sin^-1(1/2), right?

How would you solve for theta?

Given $\sin \theta = \frac{1}{2}$

[thorny flame]

dldh06

[empty sail]

Inverse trig function

Does that ring any bells?

Here's another thing that shows that it's not a 45 45 90. For sin, it's opp/hyp. So hyp = 2 based on 1/2, if you applied pythgorean theorem on this triangle you drew, you don't get this triangle

No

You drew the triangle wrong

Yes

And it's wrong because it's not a 45 45 90 triangle

If you drew the hyp and opp, you have 2 sides of a triangle, applying pythgorean theorem to get the last side, it does not equal 1

You're assuming that the missing side is 1

Which it is not

If you did pythgorean theorem on that triangle, you will not get 2 as the hyp

I know, I'm saying this triangle you drew is invalid

Because if you checked the work, using pythgorean theorem, you will not get 2 as the hyp

You will get sqrt(2)

Yes

It wasn't that much work. It's taking you a long time because you did not remember how to factor properly

Yes

Now you should see that your answer does result in pi/6

Alright, if you're done, you can close the channel using .close

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[rocky radish]

if a condom has a 98 percent to prevent pregnancy, how many times do you have to have sex (with a new condom every time) for it to reach a 50/50 chance of pregnancy?

[mellow venture]

nice

I need to know too

[celest glade]

how many times do you have to multiply 98/100 by itself to get 50/100

[rocky radish]

You can’t?

[celest glade]

you can

[rocky radish]

How?

[celest glade]

$\frac{50}{100} = \left(\frac{98}{100}\right)^n$

[thorny flame]

illuminator3

[celest glade]

there's an n for which this is works

[rocky radish]

What does the n stand for?

[celest glade]

the number of times you have to have sex

[rocky radish]

So then you have to use the logarithm to find it?

Since we don’t know n?

[celest glade]

yes

[rocky radish]

thanks mate

[topaz sinew]

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[gray basin]

I want help with part b)

[drifting swift]

have you done part a?

[gray basin]

Yes

[topaz sinew]

@gray basin Has your question been resolved?

[gray basin]

So what should I do?

[drifting swift]

so you know how much sand falls through the hourglass

and you know how long it takes

surely you know how many seconds there are in an hour, and how to find the flow rate given total volume and total time?

[gray basin]

Ok yh I got it

Thanks

.close

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[fresh sun]

How many pairs of parallel diagonals does a decagon have?

[fresh sun]

I'm kind of confused

is a pair of diagonals a diagonal or two diagonals that are parallel?

4C2x5+3C2x5?

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[dim seal]

Are all whole numbers integers?

[mellow venture]

yes

[dim seal]

Another question what number set does -2 go into

[mellow venture]

complex mumbers

[dim seal]

/close

.close

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[languid viper]

hi

[languid viper]

probably really basic but i just want a reminder how this is done

1a

[fallen wind]

Translate

[languid viper]

using power rule or something i think it is called in english

[fallen wind]

Please 😂

[languid viper]

yes i know

it says

determine f’(x) for f with

a: f(x)=x^4

b: f(x)=x^7

like how would this be done

[thorny flame]

Couldn't find an attached image in the last 10 messages.

Mar 30, 2022, 11:50 AM

[fallen wind]

Okay I have no idea what does ’’ mean

[languid viper]

i donot

[thorny flame]

WhipStreak23

[topaz sinew]

@languid viper Has your question been resolved?

[topaz sinew]

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[grim swift]

guys

so i got this on test right

and i was confused because i was trying to factorise it but then i thought maybe i cant factorise it because its a 2 degree polynom

so I did x^+2(x-1) / x(x-1)

removed the brackets and limes x-->1 put 1 instead of all x's

end result -1

or maybe not in this case because i might have not remembered task completely

but its overall the idea

[restive inlet]

the question as written in the image is nonsense

you should've also encountered quadratics before doing pre-calc/calculus

and what you attempted to do also violated multiple algebraic laws

[grim swift]

hmm

😦

ye like its insane

[restive inlet]

we you being asked to evaluate:
$$\lim_{x\to1} \frac{x^2+2x-1}{x^2-1}$$

[thorny flame]

ℝamonov

[grim swift]

yeah

so i had to appyl quadratic equation formula?

[restive inlet]

the polynomial in denominator is very common

you should've encountered it countless times
and you should know the factorisation for it

[grim swift]

ye like i did that ages ago

but like the below part of the fraction

[restive inlet]

actually,

[grim swift]

i couldnt imagine how to factorise it

because if x(x-1) then 1 turns to 1x

[restive inlet]

did you copy down the numerator properly?

x(x-1) expands to x^2- x

not x^2 - 1

[grim swift]

yeah but i did it like that because i had no other idea

and if 1(x-1)

x wouldnt be x^

[restive inlet]

x^2 - 1 is a difference of two squares

[grim swift]

oh

now i remember

[restive inlet]

and

did you copy down the numerator properly?

[grim swift]

i did x^ * 2(x-1

man i failed completely

now i get it

its frustrating cos i was learning for 5 days for test but never did limits with polynom 2

[restive inlet]

and
did you copy down the numerator properly?

[topaz sinew]

@grim swift Has your question been resolved?

[topaz sinew]

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[barren sundial]

For part b)
I have the curl, but I don't see how to get the unit vector n
So, does anybody know how to get the unit vector n and what the final bounds should be?

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[barren sundial]

<@&286206848099549185>

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[obsidian oak]

Yo

[storm monolith]

Alright

[storm monolith]

We’re getting followed 😐

[obsidian oak]

wtf

nvm

[storm monolith]

Oh maybe he was banned

Nvm

[teal burrow]

a user spamming images?

[storm monolith]

Alright anyway

Yeah

[obsidian oak]

yeah

He just left

guess he was banned or something

[teal burrow]

yeah, banned them. in the future, please don't delete mod pings

[storm monolith]

Alright thanks

[obsidian oak]

Ty @teal burrow

[storm monolith]

So just to reflect, $sin{u} = 1 when u = \frac{\pi}{4}$, and when each of $sin{x} = 1, x = \frac{\pi}{4}, sin{x^2} = 1 when x = root \frac{\pi}{4}, and sin{x^3} = 1 when x = cube root \frac{\pi}{4}$

Uh

Hold on

Oh I see

[thorny flame]

dk.dkn

[storm monolith]

Sorry about that

Idk what package they use for latex where

here*

Anyway that should be reasonable enough

[obsidian oak]

ok yeah

[storm monolith]

Basically pi/4 > sqrt(pi/4) > cbroot(pi/4)

So what does that suggest about the shape of the graphs?

[obsidian oak]

that sin(x^2) is higher than sin(x^3)

has bigger values

and they start and end at the same point

if sin(x^2) is bigger

[storm monolith]

Exactly

[obsidian oak]

than the integral of sin(x^2) is bigger as well

[storm monolith]

To make it a bit more formal

[obsidian oak]

yeah

idk how to lol

it must be foraml

formal

I need to prove that sin(x^2) is bigger

[storm monolith]

When x is between 0 and 1, x^2 > x^3 and sin(x^2) > sin(x^3)

Because as you said previously sin(u) is increasing here and so is larger for larger inputs

From that try to produce a decent enough sketch

That’s formal enough

[wide berry]

Sorry to interrupt, just wanted to share my idea: let $g(x) = \int_0^1 \sin(x^3) dx - \int_0^x \sin(t^2) dt$. Note that $g$ is continuous. $g(0) = \int_0^1 \sin(x^3) dx > 0$ as $\sin(x^3)>0$ on $(0,1]$. Note that $g(1)=\int_0^1 \sin(x^3) - \sin(x^2) dx.$ Now, on $[0,1]$, $x^3 \leq x^2$ and $\sin$ is increasing. So $\sin(x^3) \leq \sin(x^2)$. Then, from monoticity of integration, we deduce $\int_0^1 sin(x^3) dx < \int_0^1 sin(x^2) dx$, i.e $g(1)<0$. The intermediate value theorem gives the answer.

[storm monolith]

Yeah that’s basically a formal way of saying what I’m getting at

With the fact that sin(x^2) > sin(x^3) but I’m assuming they haven’t done anything that formal yet

[thorny flame]

1345631

[wide berry]

Oh okay. Thanks for your comment. Btw @obsidian oak , for interest, WolframAlpha gives c=Gamma(1/3)=0.9...

[storm monolith]

Yep I checked that and realised that’s a very very inefficient way to go about it

[obsidian oak]

g is continuous

just because its sin is continuous

?

or because it is a constant

sorry for the dumb question

[storm monolith]

It’s not a constant but and yes it’s because sin(x) is continuous

And x^2 and x^3

[wide berry]

Sum of a constant function and a continuous function. Note that $\sin(x^2)$ is continuous since it is the composition of continuous functions. The FToC says $\int_0^x sin(t^2) dt$ is differentiable. So it must also be continuous

[thorny flame]

1345631

[wide berry]

Integral of continuous function is continuous (holds for both Riemann and Lebesgue-integrable functions)

[storm monolith]

@obsidian oak Have you got a sketch yet?

[obsidian oak]

yeah

[storm monolith]

Alright let’s see it

[obsidian oak]

I am just wondering how to write this formaly

[storm monolith]

Once you work out the answer and how you got it you can think about that

‘Formality’ is an abstract concept, they’re method seemed ‘more’ formal, and to most people it is, but as long as we explain all the necessary parts effectively it doesn’t matter

[obsidian oak]

Monoticity of Integrations works for <=? Can you conclude from sin(x^3) <= sin(x^2) that the integrals inequality is with < and not <=?

[storm monolith]

You don’t really need to think about that

[obsidian oak]

wdym?

[storm monolith]

This question has lots of methods

You had a much simpler method going with the graph sketch, you don’t need to reference different theorems and formalise everything heavily to deliver a correct answer

People who are very comfortable with this stuff will, but if you’re not then it doesn’t make sense to try and write it like that

There is a very simple way of writing this without that

If you want to, you can, but it’s not really the right time and it’s the ‘long’ way if you will

[obsidian oak]

yeah

you're totally right

[storm monolith]

So

Let’s see the graph you sketched

[obsidian oak]

I am so sorry a friend waits for me now

And I am going to have to continioue later

is that fine?

ill ping you?

[storm monolith]

Yeah that’s alright

[obsidian oak]

thank you so much!

[wide berry]

Monoticity means that the inequality is preserved. The < stays <, <= stays <= etc.
g(1)<0, and not equal to 0, because that would imply sin(x^3) = sin(x^2) on [0,1], which isn't true, e.g sin(1/2^2)=/=sin(1/2^3)

[storm monolith]

Yea np

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[fierce talon]

Hello

[fierce talon]

I am wondering how to find the roots of this equation

[sweet shard]

,w solve x^2=sin(x)

[thorny flame]

Results provided by WolframAlpha

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

Requested by riemann#2529

[fierce talon]

that doesnt help

[sweet shard]

what exactly are you looking for

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[sweet shard]

.close

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[royal lichen]

hi

[olive plume]

hi

[rotund osprey]

hi

[loud dock]

hi

[royal lichen]

what is the integral of the function $f(x)=3e^{-4x}$ if $F(0)=-1$

[thorny flame]

AuHasard

[rotund osprey]

https://tenor.com/view/homer-leave-simpsons-gif-11461058

[royal lichen]

so I was thinking

$F(x)=\frac{3e^{-4x}}{-4}$

[thorny flame]

AuHasard

[royal lichen]

right?

$F(0)=\frac{3e^{-4(0)}}{-4} =\frac{3}{-4} =1$

[thorny flame]

AuHasard

[royal lichen]

I know I am missing a key detail, can someone explain what I should do?

And by that I meant the fact that 3 divided by minus 4 doesn't equal 1.

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[viral badge]

Mathematics discrete anyone?

[sweet shard]

Try to come up with a counterexample

[wary oak]

And draw a Venn diagram of two random sets to get some intuition

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[toxic marsh]

ok step one is obviously to take the derivative first, question is did I do that correctly?

[keen venture]

Did that 5 become a 6?

[toxic marsh]

yes on the exponent

[keen venture]

Derivative of e^u is u'(e^u)

[toxic marsh]

ohhh so no power rule just chain rule

[neon iron]

uh can someon ehelp me pls

[keen venture]

No power rule when the variable is in the exponent

[toxic marsh]

read the rules

[keen venture]

You're close after that. You multiplied by -5x, should have multiplied by the derivative of that instead, -5

[neon iron]

whats wrong?

[toxic marsh]

oh ok

yea cuz of chain rule

.close

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[timber lantern]

did i do this question right, ive struggled with z scores for awhile and I wasnt too sure what to do about the settings of my ti84. You can see i added my steps on the calculator as well but i wasnt sure if the left tail was right or not. Left tail being everything below the 90th percentile is shaded correct?

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[timber lantern]

<@&286206848099549185>

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[pulsar falcon]

Find the z such that P(Z<=z)=0.9

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[distant urchin]

I’m stuck on this, I’ve been trying to get old work done and I found this stuff, and I forgot how to even start this

[prime hollow]

https://www.mathsisfun.com/algebra/polynomials-division-long.html

maybe this will be helpful?

as a refresher?

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[orchid geyser]

Danish Opløs i hvert af nedenstående tilfælde
English Dissolve in each of the cases below,

Danish vektorerne således at
does not make sense in my head

[stuck lintel]

What does the text below the task say?

[orchid geyser]

ohh sorry, draw a coordinate system and illustrate the calculations

[stuck lintel]

Ah, alright

As I understand it, you need to find the s and t, for which $\vec{c} = s\vec{a} + t\vec{b}$

[thorny flame]

Remavas

[orchid geyser]

and how do i find them?

[stuck lintel]

Well, let's take the first one

[orchid geyser]

ohh wait

[stuck lintel]

$\mqty(-3 \ 13) = s\mqty(-2\6) + t\mqty(1\-5)$

[orchid geyser]

nvm

ohh

[thorny flame]

Remavas

[stuck lintel]

(had to quickly refer to texdoc for this)

[stuck lintel]

How would you go about solving this for s and t?

[orchid geyser]

isnt it a^1 + b^1 over a^2 + b^2?

[stuck lintel]

what is?

[orchid geyser]

dont really know, if i need to plus them

[stuck lintel]

Let's do something else

Let's do the scalar multiplication of the vectors first

$\mqty(-3 \ 13) = \mqty(-2s\6s) + \mqty(1t\-5t)$

[thorny flame]

Remavas