help-0

[craggy cradle]

Ill let you know if there are any updates

[mossy field]

I think we should not clutter up this thing, so we're going to close this

.close

[lone heart]

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[mossy field]

.reopen

[lone heart]

✅

[mossy field]

well i guess @craggy cradle thats one wrong answer shot down

https://chat.stackexchange.com/rooms/147115/discussion-between-number-basher-and-user2661923

[craggy cradle]

Welp

Lets give it some time and see

[mossy field]

sure

.close

[lone heart]

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[alpine sable]

Hi, can somebody explain to me first two inequalities?

[lone heart]

@alpine sable Has your question been resolved?

[lone heart]

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[violet spade]

hi

[violet spade]

can you guys solve this ques for me?

i have no problem

[quiet vector]

ur supposed to simplify?

[violet spade]

but just wanna make sure

[violet spade]

thats omega

[quiet vector]

ok?

[violet spade]

not a variable like x

[quiet vector]

hmmm so what u wanna do?

[violet spade]

w³=1

[violet spade]

result

aka simplify

[quiet vector]

wdym

ooh

[violet spade]

have you heard about omega?

its a complex number

[quiet vector]

well first evaluate $\omega^{2}$

[ocean seal]

shah821

[quiet vector]

yes i have

[violet spade]

oh

i have solved it

the result is -4

[quiet vector]

so u want ur solution checked?

[violet spade]

but my teacher solved it and got -12

[quiet vector]

show ur working

[violet spade]

sorry i was a bit fast

@quiet vector

[quiet vector]

seems fine to me

i'll try it once wait

u forgot the square on the denominator

still i got -4/3

not -12

try asking ur teach ig

[alpine sable]

.reopen

[violet spade]

so not -4?

[quiet vector]

#❓how-to-get-help

[quiet vector]

nope

[quiet vector]

see this..

[violet spade]

can you show your work please

[quiet vector]

bro just look at urs; u didnt square the denominator

[violet spade]

gimme time lemme try

[quiet vector]

ofc

[violet spade]

i finished

i think my teacher made mistake

[quiet vector]

ur answer?

[violet spade]

gotta tell him

kept the fraction squared till the end

[quiet vector]

lol

[violet spade]

to make sure i dont make any mistakes

[quiet vector]

great gl

[violet spade]

what

[quiet vector]

nvm me

[violet spade]

what does gl means

[quiet vector]

good luck

[violet spade]

thats new

oh thanks

[quiet vector]

[violet spade]

all the best

thanks my friend

.close

[lone heart]

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[olive oar]

I'm looking at symmetry groups and don't understand the motivation between $D_4$. I know that for $n\geq 3$, the symmetry group $\Sigma(\pi_n) \cong D_{2n}$ which makes sense since it's just reflections and rotations there of. But why do we define the four group to be $${(1), (12)(34), (13)(24), (14)(23)}\subseteq S_4.$$

[ocean seal]

zander_a

[lone heart]

@olive oar Has your question been resolved?

[lone heart]

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[alpine sable]

is this a correct form of pv = nrt?

[lone heart]

@alpine sable Has your question been resolved?

[tight locust]

no

PV = nRT
d(PV) = nR dT + nT dR + RT dn

@alpine sable

[alpine sable]

R is constant

Isn’t R a constant so it reduces to 0?

yes

[tight locust]

yes ok then

Mb

[alpine sable]

thanks

[tight locust]

Been awhile since chem

This is called the product rule

But yeah dR is 0

[alpine sable]

ohh

ty so much

[long axle]

Physics*

[tight locust]

I was taught this in chem back in hs

Guess it's both really

Ideal gas law

[alpine sable]

both

[alpine sable]

ye

[lone heart]

@alpine sable Has your question been resolved?

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[prime sluice]

A circle of radius 5 it's center is the origin point is cut by y=3

How to find volume of the shape that is formed by revolving the shaded part around the x axis

(I suck at drawing circles so assume it's a perfect circle)

[lone heart]

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

[prime sluice]

None no clue how to do this

I would assume it's the area of quarter of the circle minus the area under the straight line

But it seems imperfect

[prime sluice]

The area needed to be revolved*

[rustic coral]

Yk calculus right?

[prime sluice]

Yeah this was on my calculus exam and for the life me I cannot figure it out

[rustic coral]

Hint: Consider what is formed when you rotate a rectangle

[prime sluice]

You mean the area under y=3?

I thought of half of the sphere minus the inner cylidner

But still there is a little smooth part

[prime sluice]

If this is what you meant

A rectangle rotated is a cylinder

[rustic coral]

mhm

Consider drawing in a rectangle somewhere

Once you do it correctly, it becomes very obvious

[prime sluice]

Uhhh

There?

[rustic coral]

Yup

Can you do it from here?

[prime sluice]

Uh how to deal with the arc to the right of the dark line I drew

[rustic coral]

You don’t rlly have to

[prime sluice]

Really??

So

If we rotate the entire circle

It's a sphere

The shaded part would be half of the sphere minus the volume of the cylinder from the rectangle

I thought I had to account for the little circular segment

Man I should stop overthinking shit, I literally did this the solid geometry way and the integration way and got the same number but wasn't convinced because of the shitty little extra circular segment bit

[rustic coral]

,w (\int^{4}_{0} (25-x^2) dx-(1)(9)(4))(pi)

[ocean seal]

Results provided by WolframAlpha

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

Requested by civil_service_pigeon#0

[rustic coral]

This is what i got

[lone heart]

@prime sluice Has your question been resolved?

[prime sluice]

What's 9x4

What's the 4 for

9 is the line squared idk what the 4 is for

[rustic coral]

Volume of cylinder is given by $V=\pi r^2 h$

[ocean seal]

civil_service_pigeon

[prime sluice]

Ah you're doing it that way got it

Still

I forgot and rotated on the wrong axis but these are different

Like when do I not take into account these extra areas/volumes

[lone heart]

Channel closed

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[prime sluice]

What

.reopen

[lone heart]

✅

[rustic coral]

Honestly if you're looking for a magic rule, I don't rlly have one

just use some common sense

[prime sluice]

Idk man common sense told me this same answer you provided doesnt work because of that little extra bit

Well anyway thanks for the help

.close

[lone heart]

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[rustic coral]

But you're not rotating this, so why should it be involved in the volume?

It's not particularly advantageous to include like the rectangle

[prime sluice]

Its involved because its involved, I want to uninvolve but the calculation above involves it

[rustic coral]

Do you mean this calculation?

[prime sluice]

Yes

[rustic coral]

How does it involve this?

[prime sluice]

.reopen

[lone heart]

✅

[prime sluice]

Oh my god

I thought the bounds is from 0 to 5

Brooo j never thought if making it to 4

Og my god I am a fucking idiot

Bro I am sorry my brain is made of burnt beans

God damn it and it was a 2 marks question

[rustic coral]

you're fine mate

[prime sluice]

Thanks for helping me regain my sanity

[rustic coral]

cat believes you did well 🙂

[prime sluice]

I hope I really did

Thanks!

.close

[lone heart]

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[warped topaz]

https://i.imgur.com/8bwoIzg.png

[warped topaz]

Im 90% done im just stuck on the last step

I got (+ or - √y) - 5

HI CHARTBIT ❤️

I know that the domain bit means that only 1 of them is valid

[young finch]

you can factor it

[warped topaz]

But i forget how to check which one

[warped topaz]

Wym sry

Factor what

[young finch]

cause you need to find the inverse right

change x out for y and vice versa

then solve for y

you can factor the ys to get the inverse

then find the domain of that

[pseudo ice]

That's what Odie did here tho

[young finch]

or realse that inverse flips the coordinates

[warped topaz]

Yeye pretty much 👆

[young finch]

i see

[warped topaz]

Change the y to x also I forgot about that

(+ or - √x) - 5

Im just not sure about the last bit

How do I decide if its √x - 5 or -√x - 5

[young finch]

you can plug in specific values to see if the equation remains true

[young finch]

using this fact

so if (1,0) was a coordinate on f(x) (0,1) is a coordinate on inverse f(x)

[pseudo ice]

Also bearing in mind they've given you the domain (-♾️, -5], and when you do factor the original f(x) you should "notice the 5" that shows up when you do...

So you would know like the original kind of gets you one side of the quadratic, if that makes sense(?)

[warped topaz]

I dont really understand sry

notice the 5 in (x + 5)^2 = y?

[pseudo ice]

Yea, like that, so like if you e.g. tried to plot it out for the domain they've given, you get only one half of the quadratic

For example, if i like told you to find the inverse of f(x) = x^2 on the domain [0, ♾️), would that be easy to do?

[warped topaz]

It is just the left half right?

Is that what you mean

[warped topaz]

Ohhh yeah its split along y=x

[young finch]

mhm

so you can see that when you reflect it, the -sqrtx part is the part that is in the domain of -inf,-5

[worn fox]

the range of the inverse, should be the domain of the original function

[alpine sable]

is this the same as this because of the product rule?

[lone heart]

Please read #❓how-to-get-help

[warped topaz]

Ok I see what you guys are saying, but how does this help

[warped topaz]

I dont really understand the original point sry

[young finch]

means that inverse f(x) with domain of -inf,-5 is -sqrt(x)-5

[worn fox]

since you know what the range of the inverse has to be, you can reject the option that can give you values outside of that range

[young finch]

thats a more formal way of saying it yeah

[warped topaz]

Do we know the range of the inverse?

[worn fox]

.

[young finch]

we find the range of the inverse

with the domain of the oriignal

[warped topaz]

Oh ye haha sry

I think I get it now guys

Thank you so much everyone for your help sorry I was a bit slow haha

❤️

.close

[lone heart]

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[warped topaz]

https://i.imgur.com/20gY0uZ.png

[warped topaz]

Similar question but im stuck at the start this time

I got y^2 = x^2 + 6x + 11
I cannot factorize cause I get a negative in the discriminant so I dont really know what to do next...

[worn fox]

quadratic formula

[warped topaz]

It gave me a negative in the discriminant

So it means no roots right?

[worn fox]

what was your discriminant

[warped topaz]

-44+36

[worn fox]

well you need to rearrange your equation to =0 first

[warped topaz]

How can I do that? I thought I had to factorize first...

[worn fox]

y^2 = x^2 + 6x + 11

make this something = 0

[warped topaz]

You mean like setting y = 0?

I dont really understand sry haha

[worn fox]

rearranging

[warped topaz]

x^2 + 6x + 11 - y^2 = 0

[worn fox]

yes = 0

now you can use the quadratic formula to solve for x in terms of y

[warped topaz]

(-6 (+/-) √(36 - 44))/2 - y^2 ?

[worn fox]

what have you done?

[warped topaz]

I dont know I am so lost hahaha

[worn fox]

x^2 + 6x + 11 - y^2 = 0
solve this using the quadratic formula, whats the coefficient of x^2? whats the coefficient of x? whats the constant term (not involving x)?

those will be your a,b,c in the formula

[warped topaz]

And what is the - y^2

is (11 - y^2) my c?

[worn fox]

yes, because it doesnt involve x

[warped topaz]

https://i.imgur.com/yCQRK3i.png

the +- is supposed to be a plus or minus

I dont know how to use latex so I just took a pic haha

https://i.imgur.com/nsH2yCQ.png
https://i.imgur.com/FnbI5wC.png

So I guess these 2 are the factors ^^ ?

[worn fox]

those are two candidate inverses yes (assuming you did quadratic formula correct)

[warped topaz]

https://i.imgur.com/nPhq92v.png

I got the answer 😄

I think I get how to do it now

Thank you!!

❤️

.close

[lone heart]

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[warped topaz]

https://i.imgur.com/GBoEm5n.png

[warped topaz]

Shouldnt there be 2 asymptotes? y=4 and y=-4?

Oh wait nvm

.close

[lone heart]

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[untold kelp]

Can someone explain how to solve this to me?

[mint robin]

can you tell what the variables in the equation are? as in what is A, A0, t and h?

[untold kelp]

Mhmm

[mint robin]

yeah what are they

[untold kelp]

5=50(05)^t/5730

[mint robin]

yeah. do you know if you're supposed to use log to solve this?

if you divide both sides by A0 just to simplify things

you're left with 0.1 = (0.5)^(t/h)

[untold kelp]

Yeah your supposed to use log

[mint robin]

ok

[untold kelp]

I know that much but where do we go from here??

[mint robin]

so normally you'd use log to find out t/h here

[untold kelp]

How

[mint robin]

if a = b^c

log base b of a is c

base b as in subscript b

that's just how log works

[untold kelp]

So where do I put the log?

[mint robin]

on your calculator?

[untold kelp]

No

do I put the log before 0.5?

[mint robin]

yes

but on a calculator it'll just interpret that as log base 10 of 0.5

base 10 just by default

to do base 0.5, you have to do (log A) / log 0.5

A is the 0.1

[untold kelp]

Ohh

[mint robin]

yeah and then get t from t/h

[untold kelp]

Wait

I got 3.322

[untold kelp]

Wdym

[mint robin]

(log 0.1) / (log 0.5) just gives you the exponent remember

which is t/h

the answer wants t

[untold kelp]

So I do 3.322/5730?

[mint robin]

no 3.322 is t/h

isolate t

[untold kelp]

How

[mint robin]

rearrange it

algebra

t/h = 3.322

t = ?

[untold kelp]

I don’t know

[mint robin]

what grade are you?

you know what h is remember

t/5730 = 3.322

[untold kelp]

19035.06

That good?

[mint robin]

yeah should be

[lone heart]

@untold kelp Has your question been resolved?

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[celest terrace]

in the figure, you’re given the graph of the function, right?

@vague jackal

[vague jackal]

Yes

[celest terrace]

in part a, it's asking when the first derivative of that function is 0

so basically it's asking when the slope of that function is 0, or a flat line

[vague jackal]

So nowhere

[celest terrace]

look at x_2 and x_4

it gets flat at a specific point

[vague jackal]

Heres a better close up of the graph

[celest terrace]

see how it's getting flat at a specific point?

[vague jackal]

Yes

[celest terrace]

that's when the first derivative is 0

there's one other point

where it gets flat

[vague jackal]

0

x0

[celest terrace]

yes

[vague jackal]

So that means x3 is f''

[celest terrace]

what do you mean by that?

[vague jackal]

isnt f'' an inflection

[celest terrace]

of the function, yes

when f'' = 0

and it changes signs

before and after the point

[vague jackal]

so is it x4

and not x3

[celest terrace]

no, you were right for x3

f'' looks at concavity

[vague jackal]

so x2 and x3

[celest terrace]

yes

[vague jackal]

Now for point of inflection

Is that x2 and x3

[celest terrace]

yes

[vague jackal]

perfect

thank you so much

.close

[lone heart]

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[lone heart]

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[dreamy magnet]

hi

[ebon sparrow]

Hi

[tacit arch]

[lone heart]

@dreamy magnet Has your question been resolved?

[lone heart]

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[alpine sable]

it's $\sqrt{x^2 + \left(2 + \frac{2}{x-1}\right)^2}$

[ocean seal]

kenfps

[alpine sable]

not $\sqrt{x^2 + \left(\frac{2}{x-1}\right)^2}$

[ocean seal]

kenfps

[vague jackal]

Oh my god

Thats so embarrassing

lol

.close

[lone heart]

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[tender anchor]

ik its chain rule but im kinda confused how to do it

[solemn juniper]

what is h'(x)? using the chain rule ofc

[tender anchor]

f'(g(x)) * g'(x)

[solemn juniper]

and what is g'(x) for all (relevant) x?

[tender anchor]

-3/4

[solemn juniper]

so h'(x) = -3/4 f'(g(x))

[tender anchor]

aha

so h'(1) is = -3/4 (1.75)?

wait no

[solemn juniper]

not quite

[tender anchor]

-3/4 (.25)

[solemn juniper]

perhaps another question to ask is, what is f'(x)?

there are 2 values so you should state it piecewise

[tender anchor]

f'(x) is -1

[solemn juniper]

everywhere?

[tender anchor]

well the slope is -1 right

i think so?

[solemn juniper]

what about on the left side of the "corner"?

that doesn't look like a slope of -1

[tender anchor]

f(x) is positive but the derivative is - i thought

doesnt it go like \

[solemn juniper]

f goes like /\

[tender anchor]

but f' goes like

\ no?

[solemn juniper]

remember f is the black curve, g is the blue one

[solemn juniper]

no

[tender anchor]

o

oih like

/\

no

its straight lines

[solemn juniper]

the slope of g (the blue curve) is constantly negative

the slope of f (the black curve) is not

[tender anchor]

so its like ---- above the x axis and then after x=2 its ---- below x axis

[solemn juniper]

"above" and "below" is a little vague

after x=2 the slope is constant at -1

[tender anchor]

at y=1 and y=-1

[solemn juniper]

what about before x=2?

better

so what I was originally asking for was of the form

$f'(x) = \begin{cases} 1 & x < 2 \ -1 & x>2 \end{cases}$

[ocean seal]

steakanator

[solemn juniper]

(and obviously it's undefined at x=2)

[tender anchor]

ahh gotcha

[solemn juniper]

so when computing f'(g(x)), you just have to ask "is g(x) greater than or less than 2 at x?"

and the computation should afterward be trivial

[tender anchor]

ok so for h'(1) its less than 2 bc its 1 so f'(1) for x<2 is 1 so h'(1) is 1

[solemn juniper]

h'(1) is not 1

[tender anchor]

oh

[solemn juniper]

recall what we derived as the formula for h'(x)

[tender anchor]

o yeah mb

1*(-3/4) so -3/4

[solemn juniper]

better

[tender anchor]

so for h'(2) its undefined

[solemn juniper]

careful

we aren't looking at f'(2), we're looking at f'(g(2))

is g(2) greater than or less than 2?

[tender anchor]

it is 2

oh

blue line

[solemn juniper]

blue line

[tender anchor]

less than

so its 3/4

[solemn juniper]

you sure?

look back, how is f'(x) defined?

[solemn juniper]

(and then also correct this, I missed this error)

[tender anchor]

nope its -3/4 for h'(2)

and h'(1) is 3/4 and h'(3) is -3/4

[solemn juniper]

that looks better

[tender anchor]

thank you for your help

[solemn juniper]

no worries, good luck moving forward

[tender anchor]

ty

.close

[lone heart]

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[steel canyon]

I have a quick quesitn

[steel canyon]

so basically

im working with this function

im confused on how to solve the x intercept and y intercept algebrically

ik if the denomitor exponent is greater then the numerator's exponent, the horizontal asymptote is 0

but in this case they are equal

and also im not sure how to solve vertical asymptotes by using the equation too

[wide marten]

By definition, the x intercept is when y=0. Put your equation equal to 0 and solve it
For the y intercept, by definition once again, it's when x=0. Do the same thing!

[steel canyon]

then i get weird square root numbers

i plugged in the equation on desmos and the x intercepts were 2 and -2

im confused on how it got that from this equation

[wide marten]

Do you have some work to show @steel canyon? Trying to guide you to the answer without actually giving you the steps

[steel canyon]

so basically im trying to make a graph

i finished with the denomiator

but i have no clue on how to work with recriptocal fucntions sadly

[wide marten]

You don't need to make a graph, as it would be too complicated

Here's the graph

But, as I said: to find the x intercept, you need to make your equation equal to 0

But you have a fraction. That being said, with fractions, what does it take for them to be equal to 0?

(idk if I'm clear)

[lone heart]

@steel canyon Has your question been resolved?

[wide marten]

@steel canyon let's say you have a fraction, what could the numerator and denominator be if you want the fraction to be equal to 0?

[steel canyon]

OHHH I GET IT NOW

THANK U BRO UR A LEGEND

[wide marten]

What's the answer then? It's actually so hard to bring someone to think in the right direction xD

[steel canyon]

the numberator would be x = 2

[wide marten]

For the fraction be equal 0?

[steel canyon]

yeah for the numerator

-2 and 2

[wide marten]

That's not right

[steel canyon]

wdym

[wide marten]

For a fraction be equal 0, what does the numerator must be

[steel canyon]

look at the graph on demos

its right

the graph x intercepts are 2 and negative 2

[wide marten]

Yes

And you get that by making your fraction equal to 0

[steel canyon]

yea

[wide marten]

Algebraically, to solve for your fraction equal to 0, you just have to take the numerator equal to 0

You don't have to worry about the denominator

Because for a fraction to equal 0, only the numerator matters

That's what I was trying to get you realize

[steel canyon]

got itt

[wide marten]

Work from there!

From there, you should find x=+-2

[steel canyon]

what i did was i factored the numbetor

[wide marten]

As the graph shows

[steel canyon]

numerator

and then i found out

[wide marten]

Yeah

That work too

[steel canyon]

yea thanks man

how would i find the horizontal asymptote though

i heard its just b

[wide marten]

Full work

horizontal is just x=0

So find f(0)

[steel canyon]

for numerator or denominator

[wide marten]

For botgh

both*

[steel canyon]

i dont think thats right

cuz the horizontal is y=3 on the graph

on desmos

but then if i set to 0 it is different

[wide marten]

Just to make sure, for the y intercept, you just take your f(x)=(3x^2-12)/(x^2-1) and sub every x for 0

That's what f(0) means

[wide marten]

It's not y=3 on my graph

[steel canyon]

here

isnt the horizontal y=3

[wide marten]

That's not the y intercept

[steel canyon]

i was talking about horizontal asymptote

[wide marten]

Oh

Do you know limits?

[steel canyon]

but for y intercept i got (0,12)

[wide marten]

That's good

[steel canyon]

nope

[wide marten]

Tbh, idk how to find an horizontal asymptotes without limits. I can't think of something else than limits

[wide marten]

You sure they want horizontal asymptotes? Cause you were talking about x and y intercept in your question here

[steel canyon]

Here

[steel canyon]

I'll just learn lims

[wide marten]

Are you learning them next?

[wide marten]

I'm going to sleep, so good luck finishing your stuff! If you need more help, feel free to DM me 😄

[lone heart]

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@low depot Has your question been resolved?

[lone heart]

@low depot Has your question been resolved?

[lone heart]

@low depot Has your question been resolved?

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[indigo anchor]

hi! how do I solve this using null factor law?

[indigo anchor]

i forgot how to do it over the holidays

[upbeat hornet]

You can factor the left side first

[upbeat hornet]

do you remember how to factor the left side?

[indigo anchor]

ahhh sorta

i know different ways to

i tried one way

kinda forgot what its called

"Factorising non-monic quadratic trinomials"

i tried that and it didnt work

[upbeat hornet]

What did you do?

[indigo anchor]

cross method

if you know?

[upbeat hornet]

Can you show your work?

[indigo anchor]

my teacher taught us two ways and i used the cross method

ill rewrite it

then that gives you two factors

and i tried it but got the wrong answers?

[upbeat hornet]

-1 * 6 ≠ 12 at the top

You didn’t apply it correctly

[fringe turret]

i dont know ur style so according to mine this is hw its done

so we look at the x'2 coeficient which is 2 and multiply it with 12 to get 24

then the x coefficient determines the sum so its 11 nd we find 2 numbers that give a sum of 11 and a product of 24

[fringe turret]

can u show me the crossmethod

[indigo anchor]

its a bit hard to explain

but ill try my best

you find two factors of each term on either side

so its ax + bx + c

youre finding two factors for ax and two for c

and you need to x the terms

so what i did

2x = 2x and 1x

12 = 1 and 6

so 2x * 6 = 12x

1x * 1 = x

but we need 11x

so make the 1 -

so 1x * -1 = -x

12x - x = 11x

shit this part is so hard to explain

basically you see how i did the X

and i put arrows

the terms that you ARENT multiplying go in the brackets together

so for this one it is (2x -1) and (x + 6)

and thats ur answer

[fringe turret]

thats kinda of hard i learn easily like in person thanks anyway

[indigo anchor]

ahaahha i can only learn irl

its too hard to explain without like live video

BUT ANYWAY

[indigo anchor]

show me how you did this

[fringe turret]

yeah

[indigo anchor]

ive never seen your way

maybe i have and i forgot

[fringe turret]

ill try

ok

so 2*12=24 and the middle no = the sum

then we find 2 numbers that give us sum and product

so 8*3=24 and 8+3=11

[indigo anchor]

ok

i see i see

[fringe turret]

u got it

[indigo anchor]

yeah

[fringe turret]

can u make a video or an audio for your method

[fringe turret]

sure

[indigo anchor]

https://www.youtube.com/watch?v=zps8H3snx78

thats for my method

[fringe turret]

ok thanks

[indigo anchor]

no problem

[fringe turret]

i got it a bit

here is yours

[lone heart]

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[floral vault]

I need help with question 4, using u-sub I see that the answer is -1/2ln(1-x^2). When I use partial fracionts I get -1/2(1/x+1+1/x-1)

[fringe turret]

above my level

[floral vault]

lol

[fringe turret]

im schooling so its rational

[floral vault]

huh

[fringe turret]

nothin discord is cool

[floral vault]

<@&286206848099549185>

[noble sky]

can someone help me on math

im dumb

[fringe turret]

no one is dumb its just that ur processing speed is lower than average

[noble sky]

but can u help me

with my grade

[floral vault]

go to the other help room the unocupied ones and ask your question there

[noble sky]

ok ty

ummm where that room

[floral vault]

under the avaliable tab so try help-3

can someone help me wiht question 5

[lone heart]

@floral vault Has your question been resolved?

[floral vault]

<@&286206848099549185>

[floral vault]

.close

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[ebon heath]

0

[ebon heath]

example 8

how do I start? ive only learnt the two identities of trigonometric

that is, tan theta = sin theta divided by cosine theta

cosine square theta + sine square theta = 1

does this have anything to do with the unit circle? and how does the property of the angle (reflex vs obtuse etc) affect things?

never mind I think I get it

,close

.close

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[loud sage]

How do I find the nature of the stationary points of the function x/(1+x^2+y^2)?

[lone heart]

@loud sage Has your question been resolved?

[loud sage]

<@&286206848099549185>

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@loud sage Has your question been resolved?

[dense blaze]

You can use second derivative test?

[lone heart]

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[vivid heath]

trying to understand orders of magnitude

[young finch]

if its 10 times it should only be $10^{n+1}$ of whatever it is bigger than

[ocean seal]

Arctic

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[young finch]

it essentially turns everything to 0

plug in -infinity

[vivid heath]

so if the proton is 10^-27 the atom is 10^-26?

[harsh swallow]

the text below is for the step above

the simpliefied knowing that for lim

[young finch]

i would assume so

get a new channel if you want continued help

[harsh swallow]

it's x goes to - infinity

[vivid heath]

so now that i have the mass of the atom how do i decide the mass of the bacterium?

[young finch]

@vivid heath

[harsh swallow]

the calculated

is for the step towards - infinity

and the step

simplified knowing

is for the step before that

the degree of q(x) here is 2

so x^2 should be factored out

so it's -2x + 2/ -6

x going to infinity

yes

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[dusty iris]

i am stuck on part ii, the answer to part i is: (k(k+1))/2

[dusty iris]

answer:

from MAT 2019

im a bit confused on the inequality they set up in part ii when solving it

[echo socket]

Each coefficient is <= a_max, right?

By the definition of a_max

[dusty iris]

yeah each coefficient is less than a_max

however im not sure why theyre multiplying it by (N+1)

[echo socket]

Right, so, since a_0 <= a_max, a_1 <= a_max and so on, the sum of these inequalities yields
a_0 + a_1 + ... + a_N <= a_max + ... + a_max

And the right hand side is just a_max multiplied by the amount of coefficients, which is N+1

[dusty iris]

wait does it mean the degree N or is it just the number of terms - 1

because they use N for the power of x

in the question above

[echo socket]

By N I meant the degree, yeah

Which is also the number of terms - 1

[dusty iris]

the degree is the sum up to the number of terms

as it shows N = (k(k+1))/2

[echo socket]

Sure but why are you bringing that up

[dusty iris]

idk im rlly confused xD

idk what they mean

like they used N for both the degree and the term number

[tardy stag]

they're the same
try doing an example for k = 3

[dusty iris]

hmm

N = 3x4/2 = 6

wait

sp

so

omds

[tardy stag]

okay, that's the calculation for N, now expand out the polynomial

[dusty iris]

yeah

[tardy stag]

and verify that that's actually the highest degree

[dusty iris]

ahhh yeah that makes a lot more sense that N would be the same

i thought that they were just being silly by using N more than once

tyy

how do i close this channel

[buoyant storm]

type ".close"

[dusty iris]

.close

[lone heart]

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[dusty iris]

.reopen

[lone heart]

✅

[dusty iris]

ok ok

so i was taking a look at the answers and now im rlly confused why 2^k equals the sum of all the coefficients

[dusty iris]

^^^

[tardy stag]

have you done the example for k=3?

try doing it but don't combine like terms

[dusty iris]

dont combine?

[tardy stag]

like if you have x^2 + x^2 don't combine them into 2x^2

[dusty iris]

ok

ohhh

so theres only as many terms as 2^k

is that why?

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[tardy stag]

what a weird way to phrase that; I think they mean "f(x) is non-differentiable at its maximum points"?

[wet nest]

Can you elaborate please?

[tardy stag]

i think they mean like "at the points where f achieves its maximum value, it is non-differentiable"

[wet nest]

Are you sure, this is what the question means?

[tardy stag]

honestly no

[wet nest]

I think the question means that f(x) has the maximum points of non differentiability for n≠k

<@&286206848099549185>

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[wet nest]

.close

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[tall shuttle]

Is there a generalization for $(A\cdot v) \cdot (A \cdot w)$

[ocean seal]

talestitan

[tall shuttle]

Where A is a nxn matrix and v ,w are vectors of size n

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@tall shuttle Has your question been resolved?

[tacit arch]

this is just dot product?

[tacit arch]

inner product could be one generalize

https://en.wikipedia.org/wiki/Inner_product_space

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[dusty iris]

i am very stuck on the solution for part iii (*), about showing the areas are equal:

[dusty iris]

from MAT 2019

idek any of the steps theyre doing in part iii

[tardy stag]

do you understand the first equation they wrote down?

it comes from problem (i)

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@dusty iris Has your question been resolved?

[dusty iris]

sry was having food

ive setup the equation

the same one theyve done

but cant follow the next bits of part iii

[tacit arch]

Which equation exactly

[dusty iris]

ive got no clue what the markschemes done

[lone heart]

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[proper vine]

Anwser- Common characteristics 2 parabolas will have are the same x roots which are 4 and 8. Both will have the same vertex of x which is the middle number of 4 and 8 which is 6.

how many characterisitcs can be found?

[ebon sparrow]

5

[proper vine]

mmm

im assuming chararestics such as

shape and how they open are not apart

since it all relies on the a constant

so what other chararestics can it be?

same horizontal and vertical translation

both start at the vertex

have the same horizontal stretch

[proper vine]

are these the rest?

same horizontal and vertical translation
both start at the vertex
have the same horizontal stretch

[placid zinc]

You've nailed the question with "roots are 4 and 8"

If you start looking for an exhaustive list, you're opening yourself up to stuff like "they're both parabolas" and "they're both functions"

[proper vine]

so its gonna be a long list

of stuff that seem very obvious

[placid zinc]

They want to see if you can recognize what the factored form tells you about the parabola, haha

Roots! Vertex is a good touch.

Maybe say that the only thing that can change is the vertical stretch factor, which creates the family of functions

[proper vine]

thats very good

since it combine the three ideas

uptop

to one specific thing

[proper vine]

so i ended up with this answer

Common characteristics 2 parabolas will have are the same x roots which are 4 and 8. Both will have the same vertex of x which is the middle number of 4 and 8 which is 6.
They're both parabolas
They're both functions
The only thing that can change is the vertical stretch factor, which creates the family of functions because the 2 parabolas have the same horizontal, vertical translation,
both start at the vertex, and have the same horizontal stretch.

this answers the question pretty well

.close

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[proper vine]

we all good here?

wait replace the y at the end with f(X)

since its a quadratic function

[tacit arch]

show the original question

[proper vine]

k

[proper vine]

The quadratic function that passes through the points (-3, 0)​, (5, 0)​, and (4, -3)​.

[tacit arch]

,calc 3/7(4 + 3)(4-5)

[ocean seal]

Result:

-3

[tacit arch]

looks good

[proper vine]

The quadratic function with zeros 0​ and 8​ that passes through the point (-3, -6)​.

for this

does

the 0

turn to a(x)(x-8)

or

ax(x-8)?

<@&286206848099549185>

[tacit arch]

oh yes

x - 0 = x

[proper vine]

so both are right?

[tacit arch]

they're the same expression

[proper vine]

k thanks

.close

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[fierce cloud]

Isn't this like 1/7?

[fierce cloud]

I'll send the next photo in a min

[tawny condor]

it's not

I would suggest trying to simplify first

[fierce cloud]

$\lim_{n \to \infty } \frac{n^2(-1)^n(6)^n}{6^n(7n^2+2)}$

What if i do this?

And cancell the 6^n

[ocean seal]

totomc

[fierce cloud]

oh the (-1)^n is the thing that wont let me get a result

right?

thanks

.close

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[vital bear]

"You have a craving for Mrs. Fields gourmet cookies. You have a choice of oatmeal raisin, macadamia nut, triple chocolate, cinnamon sugar, chocolate chip, and peanut butter. If you must choose at least one cookie: How many ways is this possible?"

[vital bear]

i'm pretty sure the answer is 64, but I am not sure how to explain it

[void sinew]

6c1=6
6c2=15
6c3=20
6c4=15
6c5=6
6c6=1

add them up and you get 63

and you can choose from 1 to 6 cookies so that's why theres those equations

[vital bear]

ah ok

thank you

[void sinew]

np

[vital bear]

.close

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[random sable]

Hi. I had a question. Let's say a business gets a average of 50 calls a min. We want to find the standard deviation of the number of calls between 3pm and 4pm. How do I find it?

[random sable]

I am confused between two answers: $sqrt{50*60}$ and $sqrt{50}$

I think so becuase if im right it's a poisson distribution with parameter 50. And this is the way to find the standard deviation

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@random sable Has your question been resolved?

[random sable]

<@&286206848099549185>

[keen plinth]

a poisson distribution with rate 50 would describe the number of calls received over a period of a minute

but you are asked to model the number of calls over an hour )60 minutes)

so this rate is not 50

it would be 50 * 60, where 60 is the length of the time interval in minutes

[visual quest]

Help

[random sable]

@visual quest please visit #❓how-to-get-help

[fair current]

who is smartest in the server

[random sable]

so the stadard deviation would be sqrt(3000)?

[random sable]

I'm sorry did i do something wrong?

[fair current]

no im just asking

who is it

[keen plinth]

seems like it

[visual quest]

Youre occupying channel help-0

[random sable]

No no buddy that was just an example in the image. As of now , Help 11 , 19 , 23 , and 24 are vacant. Msg there and it will be all yours!

[visual quest]

Oh ok

[random sable]

alright thanks so much

.close

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[prime sluice]

How does this work

[lone heart]

@prime sluice Has your question been resolved?

[dusk canyon]

For the whole 5kg object, you have only one force acting on it, so:
F = ma
20 = 5a
Find a, then apply Newton's second law to the 3kg object only.

[prime sluice]

Got it thanks

.close

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[raven narwhal]

Hi.

[vale wigeon]

@raven narwhal hello, these channels are for math help. if you have a question to ask, then ask it now. if you are just looking to chat, go to #discussion or #chill

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[gritty wing]

is my proof correct?

[noble dome]

Im confused on how to use arc cos and arcsin

[ebon sparrow]

!help

[lone heart]

Please read #❓how-to-get-help

[noble dome]

Im new to discord and I’m not sure where to tsp to see the attachment

I did read how to get help though. Did I do it incorrectly.

*?

[ebon sparrow]

are you using phone

[noble dome]

Yeah I’m at work rn

[ebon sparrow]

okay

[tacit arch]

pick any help-n channel, not just help-0

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[shy salmon]

If there are 7 distinct objects then the most ways to arrange them is 7! how is the answer 864?

I get all the work they did in the video:

https://www.youtube.com/watch?v=RldWnL4-BfI&t=87s

But it still doesnt make sense how there are more than 7! ways?

[shy salmon]

it just doesnt make sense how there are more than 7! ways

how is the answer 864

[tawny condor]

,w 7!

[ocean seal]

Results provided by WolframAlpha

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

Requested by redstoneplayz09#0

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@shy salmon Has your question been resolved?

[tawny condor]

(864 is not bigger than 7!)

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[craggy spire]

What methods

[craggy spire]

Are needed to solve the first problem

Im completely lost

Img loading

Help

[young finch]

first find an equation that has the points given

[steep pendant]

well, consider the conditions of the question separately; your answer must:
-be perpendicular to the segment AK (its slope is equal to the negative reciprocal of the slope of AK)
-bisect AK (the line in question must also pass through the average of the points A and K)

simplest way to get to the answer is to build a line in slope-point form

then check if that line corresponds to any of the answers

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@craggy spire Has your question been resolved?