help-23

[safe radish]

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[wild thicket]

hi, is tthis right

[wild thicket]

i need yes or no only

[versed wave]

yesn't

[vale oriole]

no

[wild thicket]

.close

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[loud tusk]

how do you do this?

[loud tusk]

would equal roots mean u can simplify it to smth like (x-1)^2?

[peak estuary]

yes

well, with some factor in front

[loud tusk]

ohhh

thats why

where do i start with it

[peak estuary]

do you know how to tell whether a quadratic equation has 0,1 or 2 solutions?

[loud tusk]

no ..

[peak estuary]

do you know what the discriminant is?

[loud tusk]

is that the part of the sqrt in quad. formuka?

[peak estuary]

yes

[loud tusk]

i think i remember

[peak estuary]

what do you remember?

[loud tusk]

smth abt it being greater than 0?

no wait

if its equal to 0?

[peak estuary]

then what happens

[loud tusk]

it has 1 solution

so

[peak estuary]

yes

[loud tusk]

9a^2 - 4(6a+3) = 0?

[peak estuary]

yes

[loud tusk]

3(3a-2)(a-2) = 0?

oops aait

is it even factorable

[peak estuary]

not nicely, no

you can use the quad formula

[loud tusk]

ohhh ok

but i got -2

for 1/m + 1/n

oops wait

wont it simplify to 3(4+4+2sqrt(7)-2sqrt(7)) / (16-28)?

[peak estuary]

I havent done that part myself, dunno

seems at least somewhat reasonable

[loud tusk]

thank u!

.close

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[warped moat]

Hellloooo i need help in sets, again 😂

[lean otter]

Are you familiar with venn diagrams ?

[warped moat]

UmMm a bittt ya

[glacial cairn]

What's (V u W)²? Cartesian product?

[warped moat]

Whats a cartesian 😂😭

[glacial cairn]

... I'm just asking what this means

If you don't know, I can't guess for you

[warped moat]

hahA yup i dont know 😂

BuT i did made an attempt and im not sure if this is right

[glacial cairn]

That's certainly not true, you're just ignoring the ²

Find what it is in your material first

[warped moat]

HmMmm okaay

[warped moat]

hahaa thought i'd get to skip a bit since its equal to 3x 😂 and well this is only worth 2 marks

2nd attempt 🙄

iS this right?😂

[safe radish]

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[rich dawn]

can anyone explain to me the solution

ahhh never mind its okay

.close

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[languid surge]

sn=3n^2 -4n

[languid surge]

this was given

and in solution he substituted s1=3(1)-4(1)

and got the value of a

since s1 is = a

the part i dont understand is i assumed that it was only true for the nth term

like if i form my own ap
2,5,8,11,14

and say a4=11
and break 11
a4= a*n +4

then if i change n value it wont work

so how does that one?

what make that things value work but this ones doesnt

[vale oriole]

what are u asking?

[languid surge]

like see

the question just gave this an=3n2-4n

and said to find ap

[vale oriole]

is it an? or a_n?

[languid surge]

so in solution he solved it by substituting s1

[languid surge]

whats the difference?

[vale oriole]

an is a multiplied by n, a_n is the nth term of a

[languid surge]

latter

second one

nth term

[vale oriole]

right

show me the whole question

[languid surge]

so he went s1=3(1)-4(1)

ok

[vale oriole]

s_n=3n^2 -4n

this is the question?

[languid surge]

oh wait i read wrong

[languid surge]

this one

[vale oriole]

ok

[languid surge]

but ye my question still remains

[vale oriole]

which is?

[languid surge]

how does changing the value of n still works for equation

[vale oriole]

?

im confused

[languid surge]

wait lemme collect my thoughts

lets say 2,5,8,11..... ap

if i say a4=an+3

its true right

[vale oriole]

no

[languid surge]

well a4=11 and 4*2+3 also =11

so shouldnt it be true

[vale oriole]

no, that equals 12

[languid surge]

oh wait ye

lemme change it

[vale oriole]

well then in this case a_4 = a_3 + 3

[languid surge]

ye so now its true right

[vale oriole]

yes

[languid surge]

but i cant say a_n=an+3

cuz that would be false

[vale oriole]

correct

[languid surge]

so the equation was only true for that sitution

[vale oriole]

by an+3, u mean a_n + 3 right? just clarifying

[languid surge]

umm no

i meant a*n

ok?

[vale oriole]

well a isnt a value

[languid surge]

its 2 right for my case

[languid surge]

.

s1=a

like the formula an=a+(n-1)d

[empty ice]

if the AP is t1, t2, t3, ... tn, then
S(1)=t1
similiarly S(2)=t1+t2
S(3)=S(2)+t3, and so on
find the first three terms, then u can find the first term and common difference

[vale oriole]

i know where ur getting at, but to answer ur question, yes its just specifically for that question

[languid surge]

well

[languid surge]

well i wanted to know how does sn=3n2-4n work for whole ap

but mine doest

[vale oriole]

like i told u, its specifically for this case

[languid surge]

but mine eqution doesnt work for the rest of ap tho

[vale oriole]

its not a general formula for APs

[languid surge]

but why does sn=3n2-4n

work

[empty ice]

its a general formula for a very specific AP

that AP being the one u are asked to deal with in the question

for the AP given in that question, Sn is the function for the Sum of the first n terms of the AP

that isnt the general formula for all APs

[languid surge]

yea i understand

but what makes it work for all values of n in this specific ap

[vale oriole]

that would be what the formula is after subbing in values for a and d

S_n = n/2 * (2a+(n-1)d)

they have the values of a and d

[empty ice]

if u have the common difference and first term of an AP u can find these general values for urself for a soecific AP and such

[vale oriole]

so they can sub it into the formula

[empty ice]

yeah

u can try it for any AP whatsoever

[languid surge]

i dont know how to explain my problem

like

[vale oriole]

u want to know how they got S_n = 3n^2 -4n?

[languid surge]

its accpeted that it works for all the values of n in this specific ap riight

[vale oriole]

yes

[empty ice]

yes

[languid surge]

i wanted to ask what gives it the ability to remain appliable for all values of n but if i make one of my mind it doesnt work for more than 1 case

[empty ice]

ok

to explain it to u

lets take an AP of our own

say

1, 3, 5, 7, ...

[languid surge]

ok

[empty ice]

ie odd numbers starting from 1

the first term a = 1

common difference d = 2

right?

[languid surge]

ye

[empty ice]

now we know the general formula for first n terms of any AP

[languid surge]

a_n=a+(n-1)d

[vale oriole]

wow he died

[languid surge]

ye lol

must have gotten something to do

[vale oriole]

anyways, it wont work for ur case because its built for a specific AP

[empty ice]

no no no

[vale oriole]

he is right tho

[empty ice]

thats the general term for any nth term of an AP

im talking abt the formula for sum of first n terms

[languid surge]

oh

[vale oriole]

yeah the sum is quite different

to first n terms

[languid surge]

n/2{2a+(n-1)d}

[empty ice]

if u apple the values of a and d that we got for the series of odd numbers

[vale oriole]

apple

[empty ice]

u can obtain a general fornula for the sum of first n odd numbers starting from 1

similiarly for the question u had

u can use the formula for sum to get the first term

then use it again to get the second and third term

u can get a and d from there

using that u can get a first few terms of the AP

and also the 12th term of the AP

[languid surge]

so u are saying that formula was also specifically crafted to work for the whole ap like this formula?

[vale oriole]

n/2{2a+(n-1)d}

[empty ice]

yes

[vale oriole]

this formula works for all APs

[empty ice]

the formula for Sn that u were given

in the question that is

[vale oriole]

while that formula works for a specific AP

[empty ice]

is for the AP dealt with in that question

[vale oriole]

their formula

is the same is as n/2{2a+(n-1)d}

except they have a and d

[languid surge]

ok wait

s_n=3n2-4n

thats was only given in question

[vale oriole]

yes

[empty ice]

that is enough to solve it

[languid surge]

so i thought it would work only for the nth term

[vale oriole]

it does only work for the nth term

[empty ice]

u need to apply different values of n

to obtain the terms

S_1 will give u the first term

[vale oriole]

it solves for the sum of the first n terms

[languid surge]

wait

hear me out

i assumed it would work only for the nth term like my created only worked for that specific term

but

it turned out to be not same

[vale oriole]

it works for all values of n

[languid surge]

so i was asking how would ik if it works for all values

[vale oriole]

because it tells u

[languid surge]

like it could be a formula that only works for nth term

[vale oriole]

then thats not a formula

[languid surge]

it just says s_n=3n2-4n

[empty ice]

send the question again

[vale oriole]

no it doesnt

[languid surge]

k

[vale oriole]

read it

[languid surge]

it says that only tho

[vale oriole]

it says the sum of the first n terms of an AP is given by S_n = 3n^2 - 4n

[empty ice]

what do u understand by the first sentence

[empty ice]

wait

i wanna hear what they get from it

[languid surge]

like they use first n terms as a_n so ii assumed some of first n terms as s_n

wait a sec

[vale oriole]

what?

[empty ice]

forget about a_n

just tell me what y get from the first sentence of that question

[vale oriole]

it says sum

[languid surge]

that total of s1 to sn is given by sn=3n2-4n

[vale oriole]

it is

except u got to understand that s_n is the SUM of all terms from a_1 to a_n

[languid surge]

ye i do

[empty ice]

Sn is the sum of the first n yetms

[languid surge]

so i thought the n term is that specific one where this works

[vale oriole]

take the series 1,2,3,4,5,6,... S_3 = the sum of the first 3 terms or 1 + 2 + 3 = 6

[empty ice]

no

the formula u hve been given is for the sum

[vale oriole]

no it would tell u that

[empty ice]

of first n terms

not any nth term

if it were a formula for any nth term it wouldve been written

instead of sum of the first n terms

[languid surge]

how would u write the sum of first nth term?

as s_n right?

[vale oriole]

ur wording is off but yes

[empty ice]

its not thw sum of the first nth term

first n number of terms

[vale oriole]

this

[languid surge]

ye i understand thatt

[vale oriole]

then what dont u get?

[languid surge]

but even if it was given that fiind sum of first nth term

it would still be written same as s_n tho

[vale oriole]

not necessarily, but generally they like to write s_n

[empty ice]

pringles have u solved the question?

[languid surge]

the one i sent?

[empty ice]

yes

[languid surge]

well no

[vale oriole]

but do u understand enought to solve it now?

[languid surge]

well the only thing i didnt understood was the concept of it applying for all the values

and wait

i got questions written here

one of which iis im gonna quote "if sum of first m terms of an ap is the same as sum of first n terms , show that sum of its first m+n terms is zero"

now i dont want its solution

just hear me out

here they didnt specify nth term they said n terms but i cant just assume it works for any right

[empty ice]

what works for any?

[languid surge]

wait

i read ur message wrong

the sm=sn

i cant just assume any value for n

[empty ice]

u cant put any values of n for this case

here n is a constant

same for m

[languid surge]

ye so speification n to nth iisnt required right to assume its a constant

[empty ice]

yes

not assume

it is a constant here

[languid surge]

how u sure?

[empty ice]

u can tell from reading the question?

it says sum of first m terms = sum of first n terms

[languid surge]

so u thought iit wont work unless its a constant right

[empty ice]

for an AP

[empty ice]

i didnt think?

it is a constant here

[languid surge]

but u came to the conclusion that it is a constant because it wont work unles it is right

the s_m=s_n thing

[empty ice]

for the sake of it i'll say yes

and?

my what?

[languid surge]

nvm

[empty ice]

are u unsure whether in the original question that u sent

[empty ice]

this one

if n is a constant or a variable?

[languid surge]

nvm i am tired

thanks for the help

i will look into it myself when i am free

its been 1 hour

[empty ice]

alr np

[languid surge]

ok bye have a good day

.close

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[safe radish]

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[harsh sail]

I remember going over this in class but can’t remember how it works. Could someone give me a refresher on it

[vale oriole]

lol

[harsh sail]

Ok so side C would be hypotenuse and but for the opposite can I just start at any angle?

[vale oriole]

they want u to specifically look at angle A

[harsh sail]

Okay

Thank you both

[safe radish]

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[main mural]

,w taylor series of abs(x)

[flat frigate]

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Requested by arte_m_etra

[main mural]

could someone provide any insight into what 17240 may mean here?

[desert pasture]

wait, |x| has a taylor series?

[main mural]

or rather why wolframalpha spits that out

[desert pasture]

:mood:

[main mural]

nope

i was just curious what it would think

plus it gave it at x=inf

so i guess it's x+something extremely tiny

[vale oriole]

bruh

[main mural]

interestingly 17239 is prime

[vale oriole]

spooky

[main mural]

also bruh 💀

super weird

[desert pasture]

what

[safe radish]

@main mural Has your question been resolved?

[safe radish]

@main mural Has your question been resolved?

[mortal sandal]

WHAT

@toxic stratus

[toxic stratus]

wtf

[main mural]

yeah i am also very confused

if i click on "more terms" it replaces that with just |x|

[mortal sandal]

Wolfram sometimes gives up searching after a while

17240 is just random.

,w largest odd composite number

[flat frigate]

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Requested by a_mog

[main mural]

damn

fair enough ig

[mortal sandal]

There was some significance to this number I think but I forgot it

,w 3^11

[flat frigate]

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Requested by a_mog

[main mural]

i wonder if we can get what wolfram uses by substituting "infinity" and what precision it's looking for by default

[mortal sandal]

,w Taylor series of infinity

[flat frigate]

Results provided by WolframAlpha

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Upgrade to WolframAlpha Pro!

Requested by a_mog

[mortal sandal]

,w Taylor series of x^infinity

[flat frigate]

Wolfram Alpha doesn't understand your query!
Perhaps try rephrasing your question?
Click here to refine your query online

Requested by a_mog

[mortal sandal]

,w round infinity to 2 decimal places

[flat frigate]

Results provided by WolframAlpha

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Requested by a_mog

[mortal sandal]

,w 1^infinity

[flat frigate]

Results provided by WolframAlpha

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Requested by a_mog

[safe radish]

@main mural Has your question been resolved?

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[molten nacelle]

I need to simplify this expression. But I can’t figure out how because I can’t factor any of these. Am I taking the wrong steps or missing something?

[median vigil]

unless you have some reason to believe otherwise (e.g. parentheses that were left out), i would interpret [ 3x^2 \divsymbol 4x - 1 = \frac{3x^2}{4x} - 1 ] based on the order of operations

[flat frigate]

cloud

[molten nacelle]

alright, so i may have written it out wrong, i still can't see the next step though. any tips on what to use to find that out?

[grizzled nacelle]

i wish i could explain it in English I can send a photo if u want to

[molten nacelle]

i would appreciate that yea

[grizzled nacelle]

answear or just next step?

[molten nacelle]

ethier or, i would just use the answer to figure out the steps

im trying to understand it more than just get the right answer

[grizzled nacelle]

ok

full one

I guess its correct

[molten nacelle]

where did the x go in the third step? it looks like you factored it out but i don't see how because of that -1 in the brackets

[grizzled nacelle]

1 sec

[molten nacelle]

all good

[molten nacelle]

= 7? we don't know x how did you get 7? sorry im still confused.

i might be looking at this the wrong way.

[grizzled nacelle]

it is ->

[molten nacelle]

oh alright

so you removed the bracket, and then..... removed an x from the neumerator and denominator, how?

just by simplifying it down?

[grizzled nacelle]

i guess? i`m bad at math terminology in english

[molten nacelle]

alright, well ill try this method out. thanks for all your help

ive been having a lot of trouble with this problem

.close

[safe radish]

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[plain summit]

how do you do number 4? i have the numbers of money and stuff i dont ge it tho

[plain summit]

2023 Soul LX: $11,263
2023 Altima: $11,883
2015 Honda CRV: $12,448
this is what i got for number 3

[safe radish]

@plain summit Has your question been resolved?

[safe radish]

@plain summit Has your question been resolved?

[safe radish]

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[crystal hemlock]

Hello

[low vector]

👋

[crystal hemlock]

I know that the following inequality is easy, but I wonder if someone can solve it, because I have some solutions offered in the script that I think are wrong, so I want to make sure of it

[glass carbon]

And what are you getting?

[crystal hemlock]

just a sec

This

but scripture says this

💀

[covert yoke]

You probably just made an arithmetic mistake.

Can you show your work?

[crystal hemlock]

Yes

I got x1/2 via the quadratic formula

[covert yoke]

I get the same answer as you do

[crystal hemlock]

Then solutions from script are wrong?

[covert yoke]

Yes

[crystal hemlock]

it's so relieving to hear that

🙂

[covert yoke]

Moreover it's possible to recreate the error that the solution made

Because they got x between -1 and 4 it means the quadratic they got was x^2 - 3x - 4

In other words they accidentally dropped the + 2 from the FOIL or wrote a 4 in the original problem instead of a 6 by accident.

[crystal hemlock]

Oh

So we are correct actually, i mean our solutions?

And they are not

[covert yoke]

Yes

@crystal hemlock ^

[crystal hemlock]

oh

thats a relief

i got panic attack bc i did the hardest inequalities, and then decided to do a lil revision, did this one and saw wrong answer.... little do i say i was melted

but thank you a lot man

appreciate

.close

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[visual bone]

Hello.

[visual bone]

Sorry for the obvious question but I am confused right now about this one

$\int \sqrt[5]{\tan{x}} , dx$

[flat frigate]

Mary

[visual bone]

any hint to begin with? I know this should be easy

[gusty trench]

you're trolling

[visual bone]

?

[quiet plume]

It's doable, but definitely not easy.

As in the answer probably is several lines long lol

[visual bone]

i know how to do it, i am just having issues with the begining

[gusty trench]

the first step is usually always to let u = tanx

[visual bone]

i was thinking about other lind of sub

[gusty trench]

followed by another substitution like w^5 = u

[visual bone]

ok i got it

thx

.close

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[feral palm]

Hey. The answer should be x^3/8. But i dont know how. Would love for someone to explain.

[median kestrel]

are you simplifying it

[feral palm]

yes. but i end up with x ^ 1/2 too much somehow

[median kestrel]

okay show me your method

[feral palm]

okay to sec. i will take a picture

two

[median kestrel]

check the bottom line

your last surd runs too long

[feral palm]

Oh Hah lol. Thanks i think i got it now. 🙂

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[slate notch]

when graphing transformations of sinosuidol functions, is it best to just make a table of values instead of graphing it one transformation at a time? if not, whats the better method to graph sinosuidol funtcions

[marsh walrus]

usually just look for some easy point you know repeats

[slate notch]

oke dokes

how old are you?

[marsh walrus]

do you have a specific one youre looking at

[slate notch]

nah

[marsh walrus]

theres only so many of these

[slate notch]

just a normal sinosuidal function

[marsh walrus]

i think its 4 variables?

[slate notch]

akdc yeah

[marsh walrus]

$a \sin (bx+c) + d$

[flat frigate]

jan Niku

[marsh walrus]

or something like this

[slate notch]

yeah

usually for any other function thats not sinosuidal I just like making a table of values

is that good?

[marsh walrus]

you can do whatevers easy

[slate notch]

but for sinosuidal I just find 3 values and a period?

a trough, peak, and the equation of axis

[marsh walrus]

yea basically

[slate notch]

oke dokes

.cloes

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[loud tusk]

where do i start solving this

[loud tusk]

i dont have much know,edge when it comes to these kinds of questions

[marsh walrus]

hmm well i guess you could start with just all the arrangements

and then start removing some

and ...

does this mean that the smallest two factors are 2^5 and 5^2?

,w pfactor 800

[flat frigate]

Results provided by WolframAlpha

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Requested by janniku

[loud tusk]

mathventure has 11 letters so 11! ?

i forgot what ur suppsoed to do with the duplicate letters

[median kestrel]

do i count four vowels?

[brave matrix]

divide by the number of duplicates of each letter factorialed

[marsh walrus]

divide by (# of duplicates)!

so what that gets us down to

$2^3 \cdot 7 \cdot 2 \cdot 3 \cdot 5 \cdot 2^2 \cdot 3$

[flat frigate]

jan Niku

[limber moth]

2520 no?

[marsh walrus]

thats $2^6 \cdot 3^2 \cdot 5 \cdot 7$

[flat frigate]

jan Niku

[marsh walrus]

so i guess that means we wanna find a factor of $\frac{5}{2 \cdot 3^2}$? but im not sure i understand the method

[flat frigate]

jan Niku

[marsh walrus]

oh this isnt true is it 😭

honestly, id just solve it

who cares if theres some super fast method of finding the last 3

just solve for the actual number

[loud tusk]

iicic

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[lean otter]

max i found to be (-3,...) and min (-1,...)

but apparently only my min is right

the max is apparently (1,...)

makes sense from a pure number standpoint but then was my first der test wrong?

probably was honestly

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[tender vector]

Could someone help me with this problem ?

[plush mulch]

Find the area of the semicircle (connecting the points on (1,4) and (5,1)), and then divide the resultant quadrilateral into triangles and find their areas

[tender vector]

so would it be divided like that?

[plush mulch]

Yep you can do it like that

[tender vector]

okay thank you

So the area for the semicircle would be 6.28 right?

[plush mulch]

what did you use for the radius

[tender vector]

2

[plush mulch]

it's not exactly 2, you can use the distance formula to find the distance between (1,4) and (5,1), which is the diameter, and then divide it by 2 to get the radius

[tender vector]

OH

so 5

[plush mulch]

yeah that's the diameter

you need the radius for area

[tender vector]

24.53

[plush mulch]

is that the area you got?

[tender vector]

yes thats what i got

[plush mulch]

may have been a miscalculation, the diameter is 5 so the radius is 2.5, and then you use the formula pi*r^2 to find the area

[tender vector]

19.625?

[plush mulch]

yeah so that's the area of a circle

but notice you have a semicircle

[tender vector]

yes, i would divide by 2 right?

[plush mulch]

Yes

and that would be the area of the semicircle

[tender vector]

ohhh okay

so how would i do the distance formula on the triangles? theres three points

[plush mulch]

What dimensions do you need to find the area of a triangle?

[tender vector]

bxh

[plush mulch]

yeah so can you identify the base and height for the two triangles

right one is a lil tricky because the height is inside the triangle

[tender vector]

So for the base i got 7.812 and the height i got 7

i dont think i got it right

[thin bridge]

where's 7.812 coming from

[tender vector]

idk

hold on lol lemme redo this

6.70...i think

omg im dumb the height is7

[plush mulch]

i'm guessing you also know the base

[tender vector]

Im not completely sure on that

[plush mulch]

the base is just the length of the bottom part of the triangle, which you can just count using the squares

[tender vector]

its 6.70 or 7.81 i think im not sure

OH

omg

Ok so that triangle is 17.5

Would the other triangle 7 * 5/2 ? since we already found the diameter of the semi circle?

[plush mulch]

the diameter of the semicircle isn't the height of the right triangle

the height has to be perpendicular to the base

the base of the triangle is 7 you're right about that

that's the actual height of a triangle

[tender vector]

so that is 7 for both of them correct

sorry if im not making sense

[plush mulch]

7 is the height of the left triangle yes

and it's also the base of the right triangle

[plush mulch]

this is correct btw

you just need to find the height of the right triangle

[tender vector]

Ohh ok

so what side would I find?

[plush mulch]

it would actually be neither of those

you see the h

[tender vector]

yes

[plush mulch]

take the point on (5,1) and draw it so that it crosses the line that you marked with 7

connect them

[tender vector]

so like that??

would i make a square or something im confused

[plush mulch]

connect the points (5,1) and (1,1). That would be your height

it's not easy to see

but that would be the height because it's perpendicular to the base

[tender vector]

?

[plush mulch]

yes that's the base and height

of the triangle

so the base you said was 7

what's the height

[tender vector]

yes

I would use the distance formula on 1,1 and 5,1?

[plush mulch]

yeah

that's the height

[tender vector]

4?

[plush mulch]

yes

now find the area of the triangle

[tender vector]

okay thats 14

[plush mulch]

yes

now you have the three areas

the total area is the sum of those three

[tender vector]

ohhh

okay thank you so much

[plush mulch]

yw

if you're done you can write .close to close this channel @tender vector

[tender vector]

Okay, thanks!

I can still look back at what we did though after i close it right?

[plush mulch]

yeah you can

[tender vector]

okay ty

.close

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[tidal otter]

A little confused on this question, should I change to to base index to 2 or 4?

[thin bridge]

doesn't matter much here

[tidal otter]

so the answer should be the same whether I changed to either 2 or 4 right?

[thin bridge]

yes

[tidal otter]

I made them the same base of 2 which the next step could apply laws of indices, but I kinda stuck on the steps to find x, mind helping a little?

[thin bridge]

last step is incorrect

[tidal otter]

what should I do for the last step?

[thin bridge]

not drop x on the 4x

actually ou've made a mistake before that as wll

how are you getting

[tidal otter]

2 + 4x = 6 + 2 -x - 8
is this one correct?

[thin bridge]

no

[tidal otter]

basically copying down the power on the top?

[thin bridge]

what rule are you applying

because the first power is 6(2-x), not 6+2-x

[tidal otter]

I applied rule 1 and rule 2

I kinda confused, I guess for that need to apply rule 3?

[thin bridge]

no

you just apply rule 2

on the right you don't have rule 1

$2^{\red{6(2-x)}}$ is of the form $a^{\red{m}}$, NOT $a^{m} \times a^{n}$

[flat frigate]

ℝαμΩℕωⅤ

[tidal otter]

o

so the 2 + 4x = 6(2-x) - 8 is the correct one?

[thin bridge]

yes

[tidal otter]

2+4x = 12-12x -8
2+4x = 12-8-12x
2+4x = 4 - 12x

now should I bring the 4 to the right side or the 2?

[thin bridge]

you didnt' distribute the 6 properly

[tidal otter]

2+4x = 12-6x -8
2+4x = 12-8-6x
2+4x = 4 - 6x

so far am i correct?

[thin bridge]

yes

[tidal otter]

then now should I bring 2 to the right or 4x?

[thin bridge]

up to you,
as long as you work towards separating the variable

[tidal otter]

x - x = x right?

[thin bridge]

no

[tidal otter]

if I go -6x-4x, will the x be completely eliminated?

[thin bridge]

no

[tidal otter]

so -10x?

[thin bridge]

yes

[tidal otter]

ah

[tidal otter]

2 + 4x = 4 - 6x
2 = 4 - 6x -4x
2 = 4 - 10x

what should I do for the next step 💀

[verbal sonnet]

2 - 4 = -10x

[tidal otter]

then how to find the value of x since later it will become -10x + 2

[verbal sonnet]

• 2 = -10x

,tex -2 = - 10x

[flat frigate]

WhatsApp

[verbal sonnet]

damn

-2/-10 = x

1/5 = x

[tidal otter]

alright thanks

.close

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[slate notch]

how does applying these transformations in order of operations order versus any order I want make it any different

[slate notch]

@rough storm

for questions like a

order of operations

doesnt matter

and for b

100% botted

[rough storm]

some do, some don't

[slate notch]

oke dokes

[rough storm]

like regular order of operations

some are commutative

[slate notch]

ig

which one is communitive/

@rough storm

[rough storm]

f(ax)->f(ax+b)
f(x+b)->f(a(x+b))->f(ax+ab)
f(ax+b) not equal to f(ax+ab)

https://www.studysmarter.co.uk/explanations/math/calculus/function-transformations/

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[slate notch]

yo

also

thats uh

second one is

associative

communitive is when ab = ba

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[slate notch]

associative is with brackets

[slate notch]

so a(b) = b(a)

pretty suire

[rustic goblet]

this is commutativity

associativity is (ab)c = a(bc)

commutativity is ab = ba

[slate notch]

i see

thak you very very mcuh

I learned this like 2 months ago but forgor

im speedrunning grade 11 math

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[solemn reef]

i cannot understand the highlighted one

[mortal sandal]

the first 2 vectors alone have a span dimension of at least 2

adding more vectors wont decrease that

[solemn reef]

oh

okay

is "~cannot have dimension larger than two because dimF2,1 = 2" part came from this?

Also i thought that it has dimension at least four because 4 element of this list is not scalar multiple of the other

[light shoal]

that characterization of linear dependency only holds for a list of 2 vectors

if you have 3 vectors, they can be linearly dependent even if no two of them are scalar multiples of each other

[solemn reef]

oh okay

thanks

[light shoal]

example: (1,0) (0,1) (1,1)

[solemn reef]

thank you

[quiet plume]

Moreover, in this case, it's a transformation from 4D to 2D. There wouldn't be a way for four 2d vectors to be linearly independent.

[solemn reef]

i see

thanks

.close

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[flat frigate]

kisnar
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

kisnar
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[devout shale]

you have a good taste in sirs I must say

[light shoal]

well x2 is unconstrained

it doesn't have to be 0

your only constraint is x1 + x3 = 0

[light shoal]

ABCD!

wasn't (x 0 -x) the eigenvector for lambda=2?

how can it also be an eigenvector for lambda=0

unless this is for a different matrix

what is the original matrix?

oh wait the other one had (x 0 x) as an eigenvector, not (x 0 -x)

all's well

your A - 2I matrix was wrong

assuming A is the one above

A - 2I would be

    -1     0     1
     0    -2     0
     1     0    -1

i'm not right, matlab is right haha

i'm just typing it in

i can't do this shit in my head

(not without making mistakes)

oh right i see

yea I should be the identity matrix

ha, fair

nw, have a good night

damn i can't type

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[light shoal]

i have no idea what it means but it looks cool

[devout shale]

🫡

its a genus 4 embedding of the graph

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[wintry elm]

how would you go about answering that? ive never done a question like it before

[desert iris]

hi

i am here

[lean otter]

M = maximum {| k |, | K |}

k and K are constant

[desert iris]

wait

[royal kiln]

get your own channel, guy

[lean otter]

ok

[desert iris]

where are you from?

[lean otter]

how

[wintry elm]

you go into one of these channels and send ur question there then people will help you 😊

[lean otter]

thanks

[desert iris]

oh i ask because my english not good some words i can't translat it

[wintry elm]

its alright!!

[desert iris]

sorry

[lean otter]

it's ok

[wintry elm]

does anyone know how to do this?

[limber moth]

1. Find the number of teenagers:
2. Calculate the proportion of teenagers:
3. Apply the proportion to the sample size
   these are the three steps id do

[desert iris]

it is good

try this

[limber moth]

now ill do the calculations one second

[wintry elm]

okay thank you so much

[desert iris]

you are welcome

[limber moth]

😭

[wintry elm]

ahahh 😭

[desert iris]

what ?

[wintry elm]

its okay dwdw

[desert iris]

why you cry ?

[wintry elm]

maths is just so hard yk

[limber moth]

i no cry iron man im great! you should go to your friend

[royal kiln]

maria...they're just trolls. stop feeding them

[desert iris]

i haven't agood friends

[wintry elm]

i dont catch onto that stuff adhuekhjfhem,d

[desert iris]

so i search about who i can friend him

[limber moth]

basically just do 180-70 = 110 (cumulative frequency of ages 13-19), then do the proportion of teenagers in the population 110/300, 11/30 and since the proportion size should be 30 you just multiply it by 30 and therefore 11 teenagers should be in the sample

idk if i explained it alright

[wintry elm]

ohh okay

[desert iris]

it is solve for a problem in top ?

[wintry elm]

okay wait i think i get it

[limber moth]

just get the cumulative frequency between 13-19

and subract it

[desert iris]

or you talking with me ?

[limber moth]

then just divide the subtraction between the rest of the people remaining

[royal kiln]

Child: 70/300 -> 7/30,
Teenager: 110/300 -> 11/30,
Adult: 120/300 -> 12/30

[limber moth]

yeah

this

[desert iris]

it is solve okay

[royal kiln]

30 was the lucky number

[limber moth]

im just dumb at explainig

[wintry elm]

okay

[limber moth]

good job my dude🙏

[wintry elm]

thank you alottt

[royal kiln]

stratified samples require that you retain the population proportion for each group in the sample you take.

[wintry elm]

wait so what would i do for this one then its worded compeltely differently 😭

[wintry elm]

okay

[royal kiln]

when converting ratios to a fraction, the denominator is the sum of both quanitities

[limber moth]

yeps

[wintry elm]

yeah

[desert iris]

good bay guys

[limber moth]

goodbye ironman youve been great

[wintry elm]

would you find the lcm of the 2 ratios to work out the adults?

oh yeah i did it

[limber moth]

oh okay

nice

[wintry elm]

ty guys for the helppp

[limber moth]

np

[wintry elm]

.close

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[surreal fable]

$\int_0^{\frac{\pi}{2}} 7^{\cos t} \sin t \ dt \$
$u = \cos t \$
$du = -\sin dt \$
$\frac{du}{-\sin} = dt \$
$\int 7^{u} du \$
$[\frac{7^{\cos x}}{\ln 7} + c] \Big|_0^\frac{\pi}{2}] \ $

[flat frigate]

Tomi

[surreal fable]

what is wrong with the way I find this definite integral? it should work out if the upper bound would evaluate to one instead of zero

if I plug back the value of u, I don't have to change the bounds

[midnight prairie]

You forgot the minus no?

du=-sindt

And

when using substitution you should change the bounds too

Put the bounds in the u=cost(t)

[surreal fable]

not always, right?

[midnight prairie]

ALWAYS

[raw pivot]

always

[surreal fable]

only if I introduce new variableshttps://www.youtube.com/watch?v=FJoyIAIC1Ag&t=319s

[midnight prairie]

Nope always

[raw pivot]

you can also write u(0) and u(pi/2)

[surreal fable]

then he's wrong in the video?

[raw pivot]

which will go away, when you re substitute

[midnight prairie]

how far in the video

[surreal fable]

6:15

[midnight prairie]

He says you have to change the bounds

[midnight prairie]

He made my point

[raw pivot]

he says its incorrect

[midnight prairie]

Just put t=1 and t=2 in the formula u=cos(t)

And you get the new bounds

[thin bridge]

he says its incorrect to change the variable while keeping the old bounds like that
technically you don't have to update the bounds like that,
but you'd need to go in a roundabout way to write it to make the work valid

unless specified the bounds are for the variable of integration, so you could write
$$=\int_{x=1}^{x=2} \frac{1}{\sqrt{u}} \dd{u}$$
explicitly stating those bounds are for $x$

[flat frigate]

ℝαμΩℕωⅤ

[surreal fable]

so that it could still work out without changing the bounds?

[thin bridge]

yeh. but its more tedious that way

[midnight prairie]

It's just way more confusing

[midnight prairie]

Just change the bounds by doing this it's simple

[safe radish]

@surreal fable Has your question been resolved?

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[flint moat]

can anyone teach me exterior angles of triangles

[flint moat]

.close

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[surreal fable]

Could someone help me derive the integral of x^{2x}?

$\int _0^{4} x^{2x} (1 + \ln x) dx$

[flat frigate]

Tomi

[safe radish]

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[little blade]

they probably expect the chips to take the size of the container

so you need to find the container that has the highest volume for the smallest surface area

[wild copper]

Yeah, I think the question is super unclear here.

[little blade]

but yeah wait

only weight isnt enough

do you have the density?

[wild copper]

!source

[little blade]

then it looks impossible?

because you cant find the volume even

[wild copper]

!original

[safe radish]

Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.

[little blade]

i was thinking of that but it sounds stupid

and you have no idea how big a chip is or what its density is

well actually, you could do that keeping the density as an unknown but then it becomes extremely tedious

and it sounds strange

i feel like they forgot to tell you something in the question

because you could find the proportions to find the best shape you need, but you cant find the exact dimension cause you lack informations

well first find the best shape then

you can do it, just not with actual lenghts for the sides

no for the package

you keep the lenghts as x

you can find the shape at least

but it sounds very annoying

doesnt matter much since there is still no relation to the weight

that weight alone doesnt give you any information about the acrtual volume of your container

therefore it's like they didnt give you anything

it's strange

the only reasonable thing would be to go check the density of the chips but your teacher said you have everything there which doesnt make sense

it would but why wouldnt they give you the number already

[grim plover]

they might want u to assume they are perfect circles?

[safe radish]

@loud oar Has your question been resolved?

[safe radish]

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[grim plover]

why isnt ${ x + y } = { x } + { y }$ true $ \forall x , y \in \mathbb{Q}^{+}$

[flat frigate]

rak³en

[grim plover]

i mean

[pseudo scroll]

1.5 and 2.7

[grim plover]

1.5+2.7 = 4.2

hmm

it definitely feels true for positive rationals

[pseudo scroll]

uh the range of the left would be [0, 1) and the right would be [0, 2)

[grim plover]

[pseudo scroll]

yeah

[grim plover]

so thats 0.2

[pseudo scroll]

so on the left its 0.2

[grim plover]

Oh

yes

mb

[pseudo scroll]

and on the right its 1.2

[grim plover]

hmm

[vapid glen]

x=y=.5 I think works

[grim plover]

ig its \leq in that case?

[desert pasture]

is ${x}$ the fractional part function?

[flat frigate]

ƒ(Why am. I here)=I don't Know

[grim plover]

more importantly, if its not always true, when is it true?

[grim plover]

yes, standard notation

[desert pasture]

ok so ${x}= x-[x]$

[flat frigate]

ƒ(Why am. I here)=I don't Know

[desert pasture]

use that I guess?

you know that $[x+y] \neq [x]+[y]$

right

[flat frigate]

ƒ(Why am. I here)=I don't Know

[desert pasture]

except at integers

[grim plover]

Hmmm

but it works with x=1.3, y=2.5

[desert pasture]

it does?

[x+y]=3

[pseudo scroll]

the sum of the fractional parts shouldn't exceed 1

then the original equality holds

[desert pasture]

excellent insight

[grim plover]

i see

thats kinda tough then 😐