#help-23

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safe radishBOT
#
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wild thicket
#

hi, is tthis right

safe radishBOT
wild thicket
#

i need yes or no only

versed wave
#

yesn't

vale oriole
#

no

wild thicket
#

.close

safe radishBOT
#
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safe radishBOT
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loud tusk
#

how do you do this?

safe radishBOT
loud tusk
#

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

peak estuary
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yes

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well, with some factor in front

loud tusk
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ohhh

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thats why

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where do i start with it

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

loud tusk
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no ..

peak estuary
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do you know what the discriminant is?

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

peak estuary
#

yes

loud tusk
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i think i remember

peak estuary
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what do you remember?

loud tusk
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smth abt it being greater than 0?

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no wait

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if its equal to 0?

peak estuary
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then what happens

loud tusk
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it has 1 solution

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so

peak estuary
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yes

loud tusk
#

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

peak estuary
#

yes

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

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oops aait

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is it even factorable

peak estuary
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not nicely, no

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you can use the quad formula

loud tusk
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ohhh ok

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but i got -2

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for 1/m + 1/n

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oops wait

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

peak estuary
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I havent done that part myself, dunno

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seems at least somewhat reasonable

loud tusk
#

thank u!

#

.close

safe radishBOT
#
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safe radishBOT
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warped moat
#

Hellloooo i need help in sets, again ๐Ÿ˜‚

lean otter
#

Are you familiar with venn diagrams ?

warped moat
glacial cairn
#

What's (V u W)ยฒ? Cartesian product?

warped moat
#

Whats a cartesian ๐Ÿ˜‚๐Ÿ˜ญ

glacial cairn
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... I'm just asking what this means

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

warped moat
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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 ยฒ

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Find what it is in your material first

warped moat
#

HmMmm okaay

warped moat
#

2nd attempt ๐Ÿ™„

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iS this right?๐Ÿ˜‚

safe radishBOT
#

@warped moat Has your question been resolved?

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rich dawn
safe radishBOT
rich dawn
#

can anyone explain to me the solution

#

ahhh never mind its okay

#

.close

safe radishBOT
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languid surge
#

sn=3n^2 -4n

safe radishBOT
languid surge
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this was given

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

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and got the value of a

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since s1 is = a

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

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

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

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then if i change n value it wont work

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so how does that one?

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what make that things value work but this ones doesnt

vale oriole
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what are u asking?

languid surge
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like see

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

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and said to find ap

vale oriole
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is it an? or a_n?

languid surge
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so in solution he solved it by substituting s1

languid surge
vale oriole
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an is a multiplied by n, a_n is the nth term of a

languid surge
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latter

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second one

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nth term

vale oriole
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right

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show me the whole question

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

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ok

vale oriole
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s_n=3n^2 -4n

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this is the question?

languid surge
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oh wait i read wrong

languid surge
vale oriole
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ok

languid surge
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but ye my question still remains

vale oriole
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which is?

languid surge
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how does changing the value of n still works for equation

vale oriole
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?

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im confused

languid surge
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wait lemme collect my thoughts

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

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if i say a4=an+3

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its true right

vale oriole
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no

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

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so shouldnt it be true

vale oriole
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no, that equals 12

languid surge
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oh wait ye

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lemme change it

vale oriole
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well then in this case a_4 = a_3 + 3

languid surge
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ye so now its true right

vale oriole
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yes

languid surge
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but i cant say a_n=an+3

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cuz that would be false

vale oriole
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correct

languid surge
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so the equation was only true for that sitution

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

languid surge
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umm no

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i meant a*n

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ok?

vale oriole
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well a isnt a value

languid surge
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its 2 right for my case

languid surge
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s1=a

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

empty ice
# languid surge

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
#

but mine doest

vale oriole
#

like i told u, its specifically for this case

languid surge
vale oriole
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its not a general formula for APs

languid surge
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but why does sn=3n2-4n

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work

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

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

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that isnt the general formula for all APs

languid surge
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yea i understand

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

vale oriole
#

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

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they have the values of a and d

empty ice
vale oriole
empty ice
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yeah

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u can try it for any AP whatsoever

languid surge
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i dont know how to explain my problem

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like

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

languid surge
vale oriole
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yes

languid surge
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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
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to explain it to u

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lets take an AP of our own

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say

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1, 3, 5, 7, ...

languid surge
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ok

empty ice
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ie odd numbers starting from 1

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the first term a = 1

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common difference d = 2

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right?

languid surge
#

ye

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

languid surge
#

a_n=a+(n-1)d

vale oriole
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wow he died

languid surge
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ye lol

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must have gotten something to do

vale oriole
#

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

empty ice
vale oriole
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he is right tho

empty ice
#

thats the general term for any nth term of an AP

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im talking abt the formula for sum of first n terms

languid surge
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oh

vale oriole
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yeah the sum is quite different

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to first n terms

languid surge
#

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

empty ice
vale oriole
#

apple

empty ice
#

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

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similiarly for the question u had

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

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then use it again to get the second and third term

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u can get a and d from there

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

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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}

vale oriole
#

this formula works for all APs

empty ice
#

the formula for Sn that u were given

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in the question that is

vale oriole
#

while that formula works for a specific AP

empty ice
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is for the AP dealt with in that question

vale oriole
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their formula

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

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except they have a and d

languid surge
#

ok wait

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s_n=3n2-4n

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thats was only given in question

vale oriole
#

yes

empty ice
languid surge
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so i thought it would work only for the nth term

vale oriole
#

it does only work for the nth term

empty ice
#

to obtain the terms

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S_1 will give u the first term

vale oriole
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it solves for the sum of the first n terms

languid surge
#

wait

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hear me out

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

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but

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it turned out to be not same

vale oriole
#

it works for all values of n

languid surge
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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
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
empty ice
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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

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wait a sec

vale oriole
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what?

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

vale oriole
#

it says sum

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

vale oriole
#

it is

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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
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
#

the formula u hve been given is for the sum

vale oriole
empty ice
#

of first n terms

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not any nth term

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

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instead of sum of the first n terms

languid surge
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how would u write the sum of first nth term?

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as s_n right?

vale oriole
#

ur wording is off but yes

empty ice
#

first n number of terms

languid surge
vale oriole
#

then what dont u get?

languid surge
#

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

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

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and wait

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i got questions written here

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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"

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now i dont want its solution

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just hear me out

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

languid surge
#

wait

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i read ur message wrong

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the sm=sn

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i cant just assume any value for n

empty ice
#

u cant put any values of n for this case

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here n is a constant

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same for m

languid surge
#

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

empty ice
#

yes

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not assume

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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
#

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
#

and?

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my what?

languid surge
#

nvm

empty ice
#

are u unsure whether in the original question that u sent

empty ice
#

if n is a constant or a variable?

languid surge
#

nvm i am tired

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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

safe radishBOT
#
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safe radishBOT
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harsh sail
#

I remember going over this in class but canโ€™t remember how it works. Could someone give me a refresher on it

flat frigateBOT
vale oriole
#

lol

flat frigateBOT
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 radishBOT
#

@harsh sail Has your question been resolved?

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main mural
#

,w taylor series of abs(x)

safe radishBOT
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
#

i was just curious what it would think

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plus it gave it at x=inf

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so i guess it's x+something extremely tiny

vale oriole
main mural
vale oriole
#

spooky

main mural
#

also bruh ๐Ÿ’€

#

super weird

desert pasture
#

what

safe radishBOT
#

@main mural Has your question been resolved?

safe radishBOT
#

@main mural Has your question been resolved?

mortal sandal
#

@toxic stratus

toxic stratus
#

wtf

main mural
#

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

mortal sandal
#

Wolfram sometimes gives up searching after a while

#

17240 is just random.

#

,w largest odd composite number

main mural
#

damn

#

fair enough ig

mortal sandal
#

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

#

,w 3^11

main mural
mortal sandal
#

,w Taylor series of infinity

mortal sandal
#

,w Taylor series of x^infinity

flat frigateBOT
mortal sandal
#

,w round infinity to 2 decimal places

mortal sandal
#

,w 1^infinity

safe radishBOT
#

@main mural Has your question been resolved?

#
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molten nacelle
#

I need to simplify this expression. But I canโ€™t figure out how because I canโ€™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 frigateBOT
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
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 meeku

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

grizzled nacelle
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 radishBOT
#
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safe radishBOT
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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 radishBOT
#

@plain summit Has your question been resolved?

safe radishBOT
#

@plain summit Has your question been resolved?

safe radishBOT
#
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safe radishBOT
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crystal hemlock
#

Hello

safe radishBOT
low vector
#

๐Ÿ‘‹

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

#

๐Ÿ’€

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
#

๐Ÿ™‚

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

safe radishBOT
#
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visual bone
#

Hello.

safe radishBOT
visual bone
#

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

#

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

flat frigateBOT
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
safe radishBOT
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. ๐Ÿ™‚

safe radishBOT
#

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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
#

how old are you?

marsh walrus
#

do you have a specific one youre looking at

slate notch
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 frigateBOT
#

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

#

.close

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#
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loud tusk
#

where do i start solving this

safe radishBOT
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

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
marsh walrus
#

so what that gets us down to

#

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

flat frigateBOT
#

jan Niku

limber moth
marsh walrus
#

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

flat frigateBOT
#

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 frigateBOT
#

jan Niku

marsh walrus
#

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

safe radishBOT
#

@loud tusk Has your question been resolved?

#
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#
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lean otter
safe radishBOT
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

#

.close

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#
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tender vector
#

Could someone help me with this problem ?

plush mulch
tender vector
#

so would it be divided like that?

plush mulch
tender vector
#

okay thank you

#

So the area for the semicircle would be 6.28 right?

plush mulch
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
#

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 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
#

you just need to find the height of the right triangle

tender vector
#

so what side would I find?

plush mulch
#

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

safe radishBOT
#
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safe radishBOT
#
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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
thin bridge
#

yes

tidal otter
# thin bridge yes

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
thin bridge
#

not drop x on the 4x

#

actually ou've made a mistake before that as wll

#

how are you getting

tidal otter
thin bridge
#

no

tidal otter
thin bridge
#

what rule are you applying

#

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

tidal otter
#

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 frigateBOT
#

โ„ฮฑฮผฮฉโ„•ฯ‰โ…ค

tidal otter
#

o

#

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

thin bridge
#

yes

tidal otter
#

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

thin bridge
#

you didnt' distribute the 6 properly

tidal otter
#

so far am i correct?

thin bridge
#

yes

tidal otter
thin bridge
#

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

tidal otter
thin bridge
#

no

tidal otter
thin bridge
#

no

tidal otter
#

so -10x?

thin bridge
#

yes

tidal otter
#

ah

tidal otter
#

what should I do for the next step ๐Ÿ’€

verbal sonnet
#

2 - 4 = -10x

tidal otter
verbal sonnet
#
  • 2 = -10x
#

,tex -2 = - 10x

flat frigateBOT
#

WhatsApp

verbal sonnet
#

damn

#

-2/-10 = x

#

1/5 = x

tidal otter
#

alright thanks

#

.close

safe radishBOT
#
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slate notch
safe radishBOT
slate notch
#

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

rough storm
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)

safe radishBOT
#

@slate notch Has your question been resolved?

#
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slate notch
#

also

#

thats uh

#

second one is

#

associative

#

communitive is when ab = ba

safe radishBOT
#
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slate notch
#

associative is with brackets

safe radishBOT
slate notch
#

so a(b) = b(a)

#

pretty suire

rustic goblet
#

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

safe radishBOT
#

@slate notch Has your question been resolved?

#
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solemn reef
safe radishBOT
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
# solemn reef oh okay

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

safe radishBOT
#
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flat frigateBOT
#

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

#

kisnar
Compile Error! Click the errors reaction for more information.
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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
#

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

safe radishBOT
#
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devout shale
light shoal
devout shale
#

its a genus 4 embedding of the graph

safe radishBOT
#
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wintry elm
safe radishBOT
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
#

k and K are constant

desert iris
#

wait

royal kiln
lean otter
#

ok

desert iris
#

where are you from?

lean otter
wintry elm
# lean otter how

you go into one of these channels and send ur question there then people will help you ๐Ÿ˜Š

desert iris
#

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

wintry elm
#

its alright!!

desert iris
#

sorry

wintry elm
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
limber moth
#

now ill do the calculations one second

wintry elm
desert iris
#

you are welcome

limber moth
wintry elm
#

ahahh ๐Ÿ˜ญ

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
desert iris
#

i haven't agood friends

wintry elm
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
desert iris
#

it is solve for a problem in top ?

wintry elm
#

okay wait i think i get it

limber moth
#

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

desert iris
#

it is solve okay

royal kiln
#

30 was the lucky number

limber moth
#

im just dumb at explainig

wintry elm
limber moth
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 ๐Ÿ˜ญ

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

safe radishBOT
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safe radishBOT
#
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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 frigateBOT
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
midnight prairie
#

ALWAYS

raw pivot
#

always

surreal fable
midnight prairie
#

Nope always

raw pivot
#

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

surreal fable
raw pivot
#

which will go away, when you re substitute

midnight prairie
surreal fable
raw pivot
midnight prairie
#

He says you have to change the bounds

midnight prairie
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 frigateBOT
#

โ„ฮฑฮผฮฉโ„•ฯ‰โ…ค

surreal fable
thin bridge
#

yeh. but its more tedious that way

midnight prairie
#

It's just way more confusing

midnight prairie
safe radishBOT
#

@surreal fable Has your question been resolved?

#
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flint moat
#

can anyone teach me exterior angles of triangles

flint moat
#

.close

safe radishBOT
#
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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 frigateBOT
safe radishBOT
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safe radishBOT
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 radishBOT
#

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 radishBOT
#

@loud oar Has your question been resolved?

safe radishBOT
#
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grim plover
#

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

flat frigateBOT
#

rakยณen

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
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 frigateBOT
#

ฦ’(Why am. I here)=I don't Know

grim plover
grim plover
desert pasture
#

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

flat frigateBOT
#

ฦ’(Why am. I here)=I don't Know

desert pasture
#

use that I guess?

#

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

#

right

flat frigateBOT
#

ฦ’(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
grim plover
#

thats kinda tough then ๐Ÿ˜