help-49

[lyric charm]

what grade are y'all in btw just so i know what to expect

[blazing geyser]

year 10

[lyric charm]

hm ok

[errant cliff]

i feel like you’ve helped us before

[lyric charm]

i don't remember either of y'all

[blazing geyser]

[errant cliff]

ah

[zenith snow]

Helped too many

[errant cliff]

idk

[lyric charm]

yeah keep going

[errant cliff]

ohh

how

[blazing geyser]

im so confused rn

[lyric charm]

how can x^2 + x^2 be simplified

[errant cliff]

uhmmm

divided by 2?

ohh

[lyric charm]

.....

[errant cliff]

x + x + x + x

x x x x x x

[lyric charm]

no

[errant cliff]

omg

[lyric charm]

both of these are bad but the second one doubly so

did you try to use the letter x for multiplication?

[blazing geyser]

so is it x^4

[lyric charm]

nope

[errant cliff]

omg

[lyric charm]

y'all should not be using the letter x for multiplication btw

[errant cliff]

im about to crashout

[lyric charm]

anyway, x^2 + x^2 simplifies to 2x^2.

[errant cliff]

ohh??

[blazing geyser]

oh ofc

i knew that

[lyric charm]

you knew that but you didn't say it when asked, so...

hindsight is 20/20, as they say in america

[near cliff]

1 = 2x^2
1/2 = x^2
...
continue the rest

[blazing geyser]

[errant cliff]

where did 1/2 come from

[lyric charm]

do you mind taking this channel over actually

i have something else i need to do

[near cliff]

okay sure

[blazing geyser]

[near cliff]

divide both sides by 2

[errant cliff]

okayy

[blazing geyser]

i got 0.5=x^2

[errant cliff]

wait im confised

ohhh

[near cliff]

0.5 is the same as 1/2

[errant cliff]

x = 0.5 x 2^2?

[near cliff]

how did you get this?

[errant cliff]

or is it divided by 2^2

[blazing geyser]

do we square root

[near cliff]

yep

[errant cliff]

omg

[near cliff]

square root both sides

reject the negative x

[blazing geyser]

so x= squaroot(0.5 x 2)

[errant cliff]

ohh

i get it

[near cliff]

nono just x = sqrt(0.5)

[blazing geyser]

O

so x=0.7

[errant cliff]

is each side 0.7

[hushed mauve]

,calc sqrt(0.5)

[grand pond]

Result:

0.70710678118655

[near cliff]

did they specify an exact number of decimal places or significant figures for your answer?

[blazing geyser]

no

[errant cliff]

its probably

2 decimla

[near cliff]

if it's two decimals then you can put 0.71

[lyric charm]

just gonna pop in to say that it did say exact

[near cliff]

oh oops

[blazing geyser]

wait where

[near cliff]

"exact side length" in the question

[errant cliff]

roght there in the questok bro

[errant cliff]

but then are we writing all that

[near cliff]

in that case simplify sqrt(1/2)

[hushed mauve]

nope

[blazing geyser]

sso its basically just 1

[hushed mauve]

this is irrational. you will never finish writing an irrational number in decimals

[near cliff]

rationalise the denominator, that's what i mean

[hushed mauve]

but you don't have to

[near cliff]

@errant cliff @blazing geyser

[errant cliff]

yeah

whats rationalise

[near cliff]

to make rational

[blazing geyser]

whatys rational

[errant cliff]

omg

[near cliff]

basically you want to avoid the sqrt in the denominator and bring it to the numerator

[errant cliff]

did it turn into a fraction

[near cliff]

sqrt(1/2) is 1/sqrt(2)

[errant cliff]

ohh

[hushed mauve]

this is called rationalizing the denominator

[blazing geyser]

i did not learn to do that

[errant cliff]

hmm

soo..

[hushed mauve]

what age is grade 10?

[errant cliff]

like

15-16

here we go again

[near cliff]

so try to bring the sqrt from the denominator the numerator in 1/sqrt(2)

[hushed mauve]

ok, i'm not gonna say anything about your syllabus, but it's a little concerning, imo

[near cliff]

you can do that by multiplying the both sides of the fraction by smth...

[errant cliff]

idk bro were from australia 🥲

[blazing geyser]

dont blame us blame the australian schooling system

[bold peak]

Could it be a language barrier?

[errant cliff]

omg its our own fault

[bold peak]

Nvm Australia

[errant cliff]

lol

[near cliff]

dang aussies...

[blazing geyser]

[errant cliff]

its stressing me out how much this gets brung up

[hushed mauve]

i can't comment about that, but moving on

[near cliff]

why are there so many people called mimi

[errant cliff]

sigh

[bold peak]

It is a common nickname tbf

[blazing geyser]

[bold peak]

Anyway how far have we come

[near cliff]

@errant cliff @blazing geyser

[errant cliff]

are we still trynna find the sides

[blazing geyser]

when did we get a fractgion

[errant cliff]

omg

is there really no easier way

[blazing geyser]

[near cliff]

we have already found the sides we're just expressing it in a presentable way

[errant cliff]

ohh

[near cliff]

cause idt they'll accept 1/sqrt(2)

[blazing geyser]

wheres that from

💔

[hushed mauve]

why not

[hushed mauve]

laws of radicals

[errant cliff]

ahh

ofc

[blazing geyser]

this is the answer from the teachers

[near cliff]

idk our school syllabus just taught us to rationalise the denominator for final answers

[hushed mauve]

yeah that sums it up then

[near cliff]

not sure about australia

[hushed mauve]

well i guess if they never said anything it's accepted

[blazing geyser]

whats the m

[errant cliff]

where r u from?? if u dont mind

[near cliff]

hmmmmmm what's that last step that's cropped out 🤨

[hushed mauve]

meters

[blazing geyser]

thats for b

[hushed mauve]

i'm growing more concerned by the hour

[near cliff]

oh

[errant cliff]

im concerned too

[blazing geyser]

OH

[near cliff]

do i really have to say that -_-

[errant cliff]

nvmm 😭

[near cliff]

anyways now that you have a try to solve b

[hushed mauve]

if you were in my school, you'd most likely be in my class and would most likely be my prime target for tutoring

but let's do b if you want to

[blazing geyser]

yes please

[errant cliff]

oo were doing b

ermi said she doesnt get a

i dont get it omg

doesnt matter

[hushed mauve]

what about a) do you not get

[near cliff]

basically this image

if there's a step in there you dont get tell us the line

[blazing geyser]

why is 1^2+1^2=1^2

[near cliff]

Has your school taught you about the Pythagorean theorem yet?

[hushed mauve]

it isn't

[bold peak]

Huh

[hushed mauve]

that's an l, not a 1

[near cliff]

(also that's l not 1)

[hushed mauve]

lowercase l

[blazing geyser]

oh

[blazing geyser]

yea

[near cliff]

yea so the thing is just that

[blazing geyser]

wait i think i get it now

[near cliff]

yay now go do part b

[errant cliff]

wait tell me if u get it bro

[blazing geyser]

ok

after i finish answering ill check with u

[errant cliff]

its 2am im actually tweakingn

[hushed mauve]

my tutoring senses are tingling

[errant cliff]

HELLO

[blazing geyser]

BRO IS THE MEASURMENTS ON THE CYLINDER 1 M OR LOWERCASE L M BRP

[near cliff]

1

[hushed mauve]

no l's in the diagram itself

[blazing geyser]

[near cliff]

helping the guy so i can snipe the problem when it's closed 😈

jkjk

[hushed mauve]

lmao?

[errant cliff]

wait whay

[blazing geyser]

ok so is b v=5.2^3

[errant cliff]

what js lapkercase “

L

hm what is lowercase L

ohhh

nbm

[near cliff]

how did you get that?

[blazing geyser]

i foudn the volume of the cylinder then the cube prism thing then minused the sqaure bottom to it

[hushed mauve]

there's no subtraction involved

[near cliff]

why do you minus the square bottom?

[blazing geyser]

because they r connected

[near cliff]

it's volume

not like surface area

[blazing geyser]

oh

omg

[near cliff]

were you solving for surface area 😭

[blazing geyser]

so its just the cylinder and cube together

[hushed mauve]

the cylinder and the prism

[blazing geyser]

no i just thought we had to

[hushed mauve]

calc them separately

then add

[errant cliff]

are we finding the cylnder and rectangle together??

ohh

[hushed mauve]

it's a prism, not a rectangle, btw

[errant cliff]

0.7 x 10 for the prism??

0.7 x 10 x 0.7

[near cliff]

close but use the exact value of the side length not 0.7

[errant cliff]

oh

[errant cliff]

this??

[hushed mauve]

no*

[blazing geyser]

so is the total volume 5.7

[hushed mauve]

check your rounding

[near cliff]

what does the caution emoji represent btw

[hushed mauve]

i use three emotes to mark helpees' responses

✅ means the helpee is completely correct

⚠️ means that they are half-correct, but there is some misconception, misunderstanding or serious risk of mistakes with their line of thinking or working

[blazing geyser]

i did its still 5.7

[hushed mauve]

❌ is just straight up wrong

[hushed mauve]

what's your final answer, to 4dp?

[near cliff]

what's your exact value for the volume?

[hushed mauve]

specifically, what is the volume of the cylinder?

[blazing geyser]

0.8

[hushed mauve]

the prism?

[blazing geyser]

the cylinder

[hushed mauve]

no

i'm asking you for your volume for the prism

[blazing geyser]

o

4.9

[hushed mauve]

i know you've given the volume of the cylinder alrd

i don't get 4.9

[blazing geyser]

oh

[hushed mauve]

in fact, the volume of the prism should not need to be rounded

[blazing geyser]

it wasnt

[hushed mauve]

then 4.9 is off

how did you get it

[blazing geyser]

0.7 x 0.7 x 10

[hushed mauve]

wrong

you have the exact value for the area of the base

use it

[errant cliff]

how do i find the area for the prism 💔

[near cliff]

gng that's what i said like 15 messages ago

[hushed mauve]

use your result in part a

[errant cliff]

ohh

[errant cliff]

okg im so sorry

[hushed mauve]

the more this conversation goes the more i feel like tutoring lol

[near cliff]

it's okay

[blazing geyser]

it was 0.7

[hushed mauve]

but anyway, you got the side length from part a

it was not

do not round the side length

[near cliff]

yeah

[blazing geyser]

i didnt

[near cliff]

use a scientific calculator for this

[blazing geyser]

wait i did actually

[hushed mauve]

0.7 is not the exact value

a reminder that your side length is 1/sqrt(2)

at least for the prism

[errant cliff]

ermi what are u lookingn for

sre we still doing a

[hushed mauve]

no?

[blazing geyser]

0.7071067812

[hushed mauve]

that's also not exact enough

[errant cliff]

hmmm

[hushed mauve]

^

[blazing geyser]

thats all it showed

[hushed mauve]

^^^^^^^^

[hushed mauve]

^

[near cliff]

use your calculator for this

[hushed mauve]

use 1/sqrt(2) as your side length

[near cliff]

(1/sqrt2)^2 times 10

[hushed mauve]

the final volume for the prism is literally a single-digit number

[errant cliff]

ohh thats the side length, i thought it was 0.7

[blazing geyser]

0.7071067812

[errant cliff]

whats 0.7 then

omg

[hushed mauve]

you rounded the side length

[errant cliff]

oh

[near cliff]

it's the side length that's rounded

[hushed mauve]

and this is not exact

[hushed mauve]

for the third time

[blazing geyser]

5

[hushed mauve]

there we go.

now add the volume of the cylinder

[errant cliff]

this..?

[hushed mauve]

the bottom is an approximation. the top is the exact form

use the top one

[errant cliff]

ohh i see

okayy

[hushed mauve]

as i have mentioned, you can't fully write the decimal form of irrational numbers

so have we gotten the final ans?

[blazing geyser]

78.54

[hushed mauve]

this is just wildly off

where did this come from

earlier you had 5.7

[errant cliff]

are we finding the area of the cylnder now

[blazing geyser]

pie x 5^2 x 1

[hushed mauve]

no?? why are we doing that

[hushed mauve]

wait!

the radius of the cylinder is not 5!!

[errant cliff]

isnt it 0.5

[blazing geyser]

oh yea

[hushed mauve]

yes!!

[errant cliff]

YES???

[blazing geyser]

so its 0.79

[hushed mauve]

earlier you got your cylinder correct already

why recalculate it

[hushed mauve]

to 1dp

[blazing geyser]

0.8

[hushed mauve]

then add it to the vol. of the prism you got earlier

[blazing geyser]

250.8

[hushed mauve]

....how?

[errant cliff]

what are we doign rn

[hushed mauve]

idk. you tell me.

[errant cliff]

volume of the cylnder??

[blazing geyser]

4

[hushed mauve]

ok look

the volume of the cylinder is 0.8m^3

the volume of the prism is 5m^3

so the total volume is?

[blazing geyser]

5.3

[errant cliff]

im sorry where is 0.8 coming fromm:,)

[hushed mauve]

how???

[blazing geyser]

thats what my calculator says

[hushed mauve]

formula of vol. for cylinder

[hushed mauve]

what did you try to add?

[blazing geyser]

5+0.8

[hushed mauve]

5+0.8 is 5.3????????

[blazing geyser]

oh yea its 5.8

the rooms to dark

[errant cliff]

0.8 is the cylnder volume, 5 is the prism

[hushed mauve]

turn on some lights or something

[blazing geyser]

im good

ok so is that the answer

[hushed mauve]

yes

[errant cliff]

is 5.8 rhe totol volume

[hushed mauve]

...yes. just literally answered right above you lol

[blazing geyser]

thank you

[errant cliff]

ohhh

omg

[hushed mauve]

so you girls are both 15-16?

[errant cliff]

im 15

[blazing geyser]

yeea

[errant cliff]

ermi turns 16 december

[blazing geyser]

BRO WE r tired

[hushed mauve]

i see. i'm quite a bit concerned as your peer

[blazing geyser]

i swear we aint that dumb

[errant cliff]

PEER

omg

omg

wdym

peee

peer

💔💔💔

[hushed mauve]

i'm your age

[errant cliff]

im tweakingout

OMG

[hushed mauve]

anyway

[blazing geyser]

its 3 am

we r tweaking rn

[errant cliff]

we study tikk the sun rises!

[hushed mauve]

glhf

!done

[midnight plank]

If you are done with this channel, please mark your problem as solved by typing .close

[errant cliff]

ay

1/10 yay

[blazing geyser]

omds

[hushed mauve]

also, i don't mind answering some of the more concerning questions you two might have, i guess

[errant cliff]

i still dodnt get it ermi SHOW ME UR BOOK

[blazing geyser]

ok stay here ok

[hushed mauve]

i can't continue this session

[errant cliff]

omg

its upside down

[hushed mauve]

but i am available for future sessions

i'm already dead tired from a 13+ hour study session earlier

[errant cliff]

13 hours is crayz

[hushed mauve]

good luck!
(also, if your questions are somehow unanswered, the two of you and only the two of you can drop me dms)

[errant cliff]

ermi what did u say again

[blazing geyser]

thank you

[errant cliff]

u need to calm down dndi

[blazing geyser]

[errant cliff]

yk maybe if we just studdied 13+ hours

wenwouldnntbe sturkfigjnhere

[hushed mauve]

i had friends to help. let's not be crazy here.

[errant cliff]

ahhh

omg it took

4 people to doa single trinagke

ermi stop talking to urself

[blazing geyser]

[errant cliff]

what are we sojgn ehdy

nezt

[hushed mauve]

if you have nothing else, i suggest closing this channel and taking a rest

you are NOT doing math in this condition.

[errant cliff]

@blazing geyser

WE MUSTT

continue

[hushed mauve]

either way, if there are no further questions

!done

[midnight plank]

If you are done with this channel, please mark your problem as solved by typing .close

[errant cliff]

.close

sigh

[blazing geyser]

.close

[midnight plank]

Channel closed

Closed by @blazing geyser

Use .reopen if this was a mistake.

[midnight plank]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[keen heart]

I've looked at this question for a while and im just wondering what exactly happens with the slopes of secant and tan lines?
This question is ungraded extra practice homework

[keen heart]

it's not just 1,2 and 5

gave me a .8/1

[shell wigeon]

If it's 2 then surely it's also 3

[astral canyon]

I think it's also 3. as the deltax in the secant line decreases, it gets closer and closer to the tangent line. When the distance between the two points that make up the secant line is infinitesimal, it turns into a tangent line

gif: https://personal.morris.umn.edu/~mcquarrb/teachingarchive/SUFE/Resources/Lecture2.1.html

[keen heart]

🥀

[shell wigeon]

The wording is weird

[keen heart]

i lowk don't get it

[shell wigeon]

The slopes of tangent lines to a point?

There's only one tangent

Well, if the function is differentiable at that point I guess

But also, the slope of the tangent line to a point doesn't really estimate the rate of change, it is the rate of change (at that point)

[keen heart]

i can't even retry the question 😭

is there a simple definition of what happens so i can just know that for the future?

[midnight plank]

@keen heart Has your question been resolved?

Channel closed

Closed by @keen heart

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[prime swallow]

Im describing the graph and was wondering if each line has 2 asymptotes cause im trying to figure out the x intercepts but what if the bottom line has one

[prime swallow]

<@&286206848099549185>

[tiny inlet]

hey

wait i don't understand the problem

can you explain where' you're stucl

[tiny inlet]

oh

if we have y = 1/(x - h), the graph cannot have any x-intercepts

since no reciprocal of a number can be 0

[prime swallow]

Im bad with vocab can you explain it dofferently?

[tiny inlet]

so

if we have any number, and we flip it (like express it as a fraction, then flip the top and bottom) it can't be zero

like, think about 1/a

if we want 1/a = 0, then a ≠ 0. then we multiply by a on both sides, getting 1 = 0, which is untrue

so there are no x-intercepts

[prime swallow]

Can i check in the equation by making it equal to 0

@tiny inlet

And better off do both of those lines have 2 acendtotes

[mortal mirage]

what do you mean by check in the equation?

also, for future reference, if you question has not been answered for at least 15 minutes, please don't ping helpers. thanks c:

[midnight plank]

@prime swallow Has your question been resolved?

[prime swallow]

I mean by making it 0=1/x_4

[mortal mirage]

but as @tiny inlet stated, that simply isnt possible

[prime swallow]

Ik that but when i wait for 15 min its never answered its usually an hour which would

[prime swallow]

See when i make that equation idk how to solve it could you show me?

[mortal mirage]

how to solve $0=\frac{1}{x-4}$?

[grand pond]

Mathemusician

[prime swallow]

Yes

[mortal mirage]

well...

its just not possible

[midnight plank]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[mortal mirage]

huh?

[prime swallow]

.reopen

[midnight plank]

✅

[mortal mirage]

ok

[prime swallow]

So like when you would solve it to get 1=0 or whatever ik its not possible but what are the steps that get you there

[mortal mirage]

assume x=/=4 first, so we dont get a syntax error

and/or undefined

then, so we have x-4=a for some real a

following?

[prime swallow]

Uh not really

[mortal mirage]

oof sorry i made a typo

[prime swallow]

If its 0=1/x-4

[mortal mirage]

x is NOT equal to 4

if x is not equal to 4, the right hand side is equal to some real number, right?

[prime swallow]

Yea

[mortal mirage]

mk, and also we have that x-4 is some other real number right?

[prime swallow]

Yes

[mortal mirage]

lets call x-4 "a"

so $0=\frac{1}{x-4}$ becomes $0=\frac{1}{a}$

[grand pond]

Mathemusician

[mortal mirage]

for some real number a

got that?

[prime swallow]

Ye

[mortal mirage]

then we can multiply both sides of an eq by a real number right?

so lets mult both sides by a

lhs becomes 0*a which is 0, and rhs becomes 1

so we get 0=1

which is obvi not true

[prime swallow]

Ohhhhh ok got it

And is this true for every rational function?

[mortal mirage]

imma go sleep, someone else should be here to help soon

[mortal mirage]

no, only for those with constant/positive numerators

so for instance, any real number, or something like x^2+1

[prime swallow]

Can you explain? Sorry my teacher doesnt teach us

[hushed mauve]

where are we rn

[prime swallow]

Its all good i get it but i have another question

@hushed mauve

[hushed mauve]

you don't have to ping me. just ask

[prime swallow]

So since theres 2 lines wouldnt there be a maximum for the line below?

[hushed mauve]

so $f(x) = \frac{1}{x-4}$ is your function?

[grand pond]

Seia

[prime swallow]

Or is it one of those types of inf where it can be maximum cause it keeps going to 0

Yes

[hushed mauve]

by line below, you mean to the left of x = 4?

[prime swallow]

Yes

[hushed mauve]

ok so what do you mean by this whole thing?

[prime swallow]

So

With the line left of 4, there wouldnt be a max point for it because its inf close to 0 but never 0 so lets say -0.1 couldnt be a maximum point because there would be -0.9 and that is inf

I should say that continues forever

[hushed mauve]

could you please draw what you mean?

[prime swallow]

ye

This arrow grows increasingly to 0

But will never reach it

So even if you find a point such as 0.0000001 that wont be the max point because there will always be a number closer

[jaunty ivy]

the function wont admit any maxima, if that is what ur question is

[prime swallow]

Yes for the left side

[jaunty ivy]

nor on the right side

[prime swallow]

Ok and is it like one whole, for example if there is a maximum for the left side but also the right side, would there only be one maximum?

[jaunty ivy]

we would classify them as local maximas

a function can admit multiple local maximas / minimas on an interval

if you have done calculus, by fermat's theorem, a necessary condition for any extremum located at x_0 is for f'(x_0) = 0

[prime swallow]

So if theres two lines there can be two maximums?

Or for rational functions because both lines are part of the same function there can only be one maximum?

[jaunty ivy]

the number of maximas depend on the derivative

you cant put blatant generalizations for classes of functions without an analysis of the derivative and its sign around the critical point

This is a rational function with a maxima (at x = 0.27...) and the other one is minima

[prime swallow]

Ok but in this scenario would it be possible to have 2 or one max points?

[jaunty ivy]

yes

[prime swallow]

Which one?

[jaunty ivy]

ah u mean in the f(x) = 1/(x-4)

no, there isnt any max point

[prime swallow]

Ah ok

[jaunty ivy]

we can use your logic here. we can pick any point close to 0 but there will be a point that is closer to 0 than the previously chosen point

[prime swallow]

Ahhh and its the same for the minimum?

[jaunty ivy]

yes

[prime swallow]

It also has 2 lines of symetry?

[jaunty ivy]

how do u define a line of symmetry again

[prime swallow]

It reflects across itself perfectly

[jaunty ivy]

ah -f(x) = f(-x)?

well it isnt the case

in fact, f(-x) = -f(x) so it has rotational symmetry

nevermind, it doesnt have rotational symmetry

f(-x) ≠ -f(x)

[prime swallow]

It cuts in half so like lemme draw it

Like this

Where it can reflect

[jaunty ivy]

like this?

[prime swallow]

yes

and also the other way right? the other diagnal?

[jaunty ivy]

yes

it is a reflection about the line y=x-4 and y=-x+4

[prime swallow]

Ye

the asymptotes are x=4 and y=0 correct?

[jaunty ivy]

yes

[prime swallow]

Ok and the final thing, im doing integrated 3 this year for math idk if yk what that is but its all graphs and its the class before precalc, is there any advice that i should know?

[jaunty ivy]

i dont have any

[prime swallow]

ah ok tysm for the help

[hushed mauve]

this might be a better question for #study-discussion

[prime swallow]

ah ok thx

[midnight plank]

@prime swallow Has your question been resolved?

[midnight plank]

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[ruby dust]

which one's sum is to be determined?

[tidal turret]

wdym?

[ruby dust]

uh i asked a simple question

which queston has a doubt

[tidal turret]

my english is bad, im sorry

I wanted to do the 1ia)

[ruby dust]

ok

do you understand basic english?

[tidal turret]

only very basic eng, yeah

[ruby dust]

ok

so, u must've learnt the sum of 1 till n, right?

like if n=5, S=1+2+3+4+5

isn't it?

[tidal turret]

wdym?

[ruby dust]

i wanted you to realize that the 1a problem works/hinges on the princliple of sum of 1 to n, where n=100

now just plug it into the formula and obtain the answer

[ruby burrow]

i dont think this is basic english for them to understand

[ruby dust]

translate it then

[ruby burrow]

my spanish is very limited

[ruby dust]

i am nice in english, uk

[ruby burrow]

i could try but dont know most math words

[ruby dust]

i know only two languages...

english and my native speech

[tidal turret]

you are from the usa?

[ruby dust]

nah

southeast asia

[tidal turret]

india

[ruby burrow]

ok im gonna try to tell them how to do the problem

[ruby dust]

yes

sure

[ruby dust]

try

[ruby burrow]

india is in south asia-

[ruby dust]

i tried but his weak english ia a barrier for me

[ruby burrow]

renato, you see how the problem is saying 1+2+3+4+...+100, this is the sum of the numbers 1 to 100

sum=ma(acento)s

[tidal turret]

yes

so what?

[ruby burrow]

there is a formula

do you know the formula

[tidal turret]

not really no

what formul

[ruby burrow]

there is a formula for the sum of numbers 1 to k

$\sum_{n=1}^k n=\frac{k(k+1)}{2}$

[grand pond]

ava 💕

[ruby burrow]

this is the formula

[tidal turret]

it was found by gauss

[ruby burrow]

did your teacher teach this method

this is how your class taught you right

if not there is another way

[clever igloo]

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

[tidal turret]

!nospoilers

[ruby burrow]

send the spanish article

[still flax]

a= your first number/term d=the difference between numbers and n=how many terms you are adding

[clever igloo]

https://es.wikipedia.org/wiki/Progresión_aritmética

Espanol

[tidal turret]

what is the name of this thingy

[ruby burrow]

en espanol:
a = el numero primero
d = la differencia (menos) en los numeros
n = cuanto numeros hay

[ruby dust]

@ruby burrow how did you manage to explain him???

[ruby burrow]

thats probably not right

[ruby dust]

i tried my best

[still flax]

this is the formula for sum of arithmetic sequences

[tidal turret]

how do I use it?

[clever igloo]

We plug in the values

[clever igloo]

We take the values and put it

[tidal turret]

can you give examples

[still flax]

you must plug in your numbers into the formula so the a= your first term in your case for a) it would be the number 1 . then d=the difference between each number, so it is going up by 1 so it is just 1 as well. n=how many terms you want to add which you want 1 to 100 so n=100

[ruby burrow]

por ejemple:
1+3+5 (muy simple)
a = 1 (el numero primero)
d = 2 (3-1=2, es la diferencia)
n = 3 (hay 3 numeros)

[still flax]

100/2 (2 x 1 + (100 - 1) x 1 )

since you are given the last term you can also use this formula where l is the last term

100/2 (1+100)

[tidal turret]

what now

?

,calc 50 * 101

[grand pond]

Result:

5050

[ruby burrow]

yea

[still flax]

that is your answer 👍

[tidal turret]

what about the one that is next to this one

is like twice the previous one

[still flax]

so for b) that is a geometric sequence because you are x2 everytime so you now have to use the formula for sum of geometric sequences

[ruby burrow]

$\sum_{n=0}^k 2^n=2^{k+1}-1$

[grand pond]

ava 💕

[ruby burrow]

i think thats right

[tidal turret]

how did you noticced it was a gp

[ruby burrow]

iirc

[still flax]

because for the a) you can see you are adding 1 everytime no exceptions 1,2,3,4 right? but for b) it goes 1,2,4,8 thats because 1 times 2 = 2 then 2 times 2 = 4 then 4 times 2 = 8 .

[tidal turret]

we dont need to find the actual value

[ruby burrow]

oh wait

the question

its saying "usando el simbolo de sumatoria"

which means using summation symbol

we're not finding the actual sums-

[still flax]

bro 😭

[ruby burrow]

how did i just notice 😭

[still flax]

the summation symbol is

[ruby burrow]

the big sigma symbol

the weird looking "E" for beginerrs

[still flax]

not sure if I can tell you the actual answer but lets say we had 1+2+3+.....50 then it would look like this

[tidal turret]

how does it work?

[ruby burrow]

$\sum_{n=1}^3 n=1+2+3$

[grand pond]

ava 💕

[ruby burrow]

youre basically plugging the values as n=1,2,3 for the equation (n) and adding it all up

[still flax]

so sigma means sum which tells you to add up the numbers in the sequence. under the sigma sign is n=1 which tells you where to start and above that is the number 50 telling you when to stop

[ruby burrow]

$\Sigma$ es el simbolo de sumatoria

[grand pond]

ava 💕

[tidal turret]

how do I do my exercise tho?

[ruby burrow]

es similar a:
$$f(x)=x$$
$$\sum_{n=1}^k f(x)=f(1)+f(2)+f(3)+...+f(k-1)+f(k)$$

[grand pond]

ava 💕

[ruby burrow]

ok lets do the first one

i kinda already gave the answer but how would you write it using sumatoria

[tidal turret]

,, \sum_{n = 1}^{100} n

[grand pond]

Renato

[ruby burrow]

yes

good job

[tidal turret]

second one?

[ruby burrow]

ok lets do the 2nd one

what do you notice about 1+2+4+8+...

what can they be written as

or well the pattern

[tidal turret]

unsure

[ruby burrow]

ok lets do 2+4+8+16+32

what are these numbers?

do you see that 4=2*2

[tidal turret]

ok ok

2^0

[ruby burrow]

that is 1 yes

so how about the other numbers

[tidal turret]

,calc 2^10

[ruby burrow]

2^10=1024

[grand pond]

Result:

1024

[tidal turret]

easy

[ruby burrow]

so how would you write using sumation?

[tidal turret]

,, \sum_{k=0}^{10} 2^k

[grand pond]

Renato

[ruby burrow]

yes

[tidal turret]

third is getting tricky

[ruby burrow]

ok there is a pattern

first try to see what numbers are 1, 4, 9, 16, ...

what are they called?

[tidal turret]

perfect squares

[ruby burrow]

yes

[tidal turret]

ofcourse

[ruby burrow]

now notice some are negative

[tidal turret]

👅

you from india?

[ruby burrow]

it goes like:
positive, negative, positive, negative, etc

[ruby burrow]

yes

i dont live here tho

[ruby burrow]

now think: how would you write this using sumation?

hint: (-1)

[tidal turret]

(-1)^(n+1)

[ruby burrow]

almost

think about how you get the first term

the first term is positive

so you would need (-1)^2

yes

now how would you write using summation

[tidal turret]

im more worried about the perfect squares

[ruby burrow]

you can write them as n^2

n^2 is perfect squares

[tidal turret]

ok

,, \sum_{n=1}^{12} n^2 \cdot (-1)^{n+1}

[grand pond]

Renato

[ruby burrow]

yes

[ruby burrow]

do you know how to do 1id?

[tidal turret]

yes ofc

[ruby burrow]

what are the numbers?

ok try it

[tidal turret]

(2n + 1)^2

[ruby burrow]

yes

now write using summation

[tidal turret]

,calc sqrt(441)

[grand pond]

Result:

21

[tidal turret]

,, \sum_{k = 0}^{21} (2n + 1)^2

[ruby burrow]

uh no

[grand pond]

Renato

[ruby burrow]

you need the last term to be =21

so try to solve for n in 2n+1=21

[tidal turret]

10

[ruby burrow]

yes

it should go to ^10

not 21

[tidal turret]

,, \sum_{k = 0}^{10} (2n + 1)^2

[grand pond]

Renato

[ruby burrow]

yes

[ruby burrow]

the 1ie is kinda what you did

but it goes infinitely

[tidal turret]

,, \sum_{n = 0}^{\infty} (2n + 1)

[ruby burrow]

the first term is 1

yes

[grand pond]

Renato

[brave stag]

This is wrong

[ruby burrow]

now 1if

[brave stag]

It doesn't

[ruby burrow]

it goes to 2n+1

[tidal turret]

goes up to n

[brave stag]

Correct.

[ruby burrow]

that implies its odd numbers

or im slow i should probably go to sleep

[tidal turret]

care to elaborate

?

[brave stag]

You didn't define n anywhere in the summation

k is also defined but not used

[tidal turret]

dude

[ruby burrow]

oh shoot i see the problem

[brave stag]

It should be
$$\sum_{k = 0}^{10} (2k + 1)^2$$

[grand pond]

Catgod

[tidal turret]

I appreciate it :D

[ruby burrow]

ye

[tidal turret]

what about the infinite one?

[ruby burrow]

make sure ur variables are right

[tidal turret]

what about infinite one?

[ruby burrow]

it is only odd numbers

[tidal turret]

WTF

[tidal turret]

whats the summation limit

[ruby burrow]

so yeah this is right

[tidal turret]

goes up to infty @brave stag

?

[ruby burrow]

im pretty sure thats how the quetion wants

[tidal turret]

or not ?

[brave stag]

It does NOT go up to infinity

Notice how the last term is 2n+1

So it should be
$$\sum_{k = 0}^{n} (2k + 1)^2$$

[tidal turret]

it goes up to n

[grand pond]

Catgod

[brave stag]

Yess

[ruby burrow]

yeah i need to go to sleep 😭

[tidal turret]

ok now what?

[ruby burrow]

this next one is similar

try to use the same method

the coefficients are increasing by 1 and go to n (the last term is n^2=n*n)

[tidal turret]

wdym?

[ruby burrow]

oh dear idk how to translate coefficient to spanish

the number before variable

3x, 3 is coefficient

[tidal turret]

,, \sum_{k=1}^{n} n \cdot k

[grand pond]

Renato

[ruby burrow]

yea

ok now 1ii

do you know el simbolo de productoria is

[tidal turret]

,, \prod

[grand pond]

Renato

[ruby burrow]

yes

[ruby burrow]

so lets do the first one

it goes from 5 to 100

how would you write this using that symbol

[tidal turret]

,, \prod_{n=5}^{100} n

[grand pond]

Renato

[ruby burrow]

yes

ok now 1iib

what do you notice about the numbers (again)

[ruby burrow]

what is the pattern

it is the same for 1ib

[tidal turret]

the multiplication with the previous

idk how to explain it

[ruby burrow]

uh what

it is powers of 2

[tidal turret]

right

my bad

[ruby burrow]

2^0=1
2^1=2
2^2=4
and so on

[tidal turret]

,calc 2^10

[grand pond]

Result:

1024

[tidal turret]

,, \prod_{k=0}^{10} 2^k

[grand pond]

Renato

[ruby burrow]

yes

[ruby burrow]

ok the last one

it is similar to 1if

[steel crest]

it's a bit confusing at first, but

the variable below the symbol is the index

and the variable above the symbol is a constant

[tidal turret]

,, \prod_{k=1}^{n} n \cdot k

[grand pond]

Renato

[ruby burrow]

yes

[steel crest]

so you can also write that as

$n \prod_{k=1}^n k$

[grand pond]

gfauxpas

[ruby burrow]

or well that yeah

alr im going to sleep i wake up in 4 hours buenas noches

[tidal turret]

I thank you guys, i need to visit india one day

[steel crest]

you like racecars?

[tidal turret]

wdym?

[ruby burrow]

why visit 😭

[tidal turret]

never been to india

[steel crest]

races with super fast cars

the cars are called race cars

[tidal turret]

what about them

I dont think I follow?

[steel crest]

https://en.wikipedia.org/wiki/Indianapolis_500 why else would you want to visit India?

[ruby burrow]

i think theyre talking about the country india

not sure tho

[steel crest]

same thing

[ruby burrow]

no its not

india is not the same as indiana

[steel crest]

it's spelled almost the same

[tidal turret]

guys dont fight

[ruby burrow]

are you trolling or something

[tidal turret]

its fine ava, just want to visit there one day

[ruby burrow]

ok well

[tidal turret]

I have seen they have huge elephants

true or false?

[ruby burrow]

cows*

[tidal turret]

wdym cows?

[ruby burrow]

la cava

i think

[tidal turret]

vaca jaja

[ruby burrow]

oh

close enough

ok im going to dormir now

[tidal turret]

nice, see you later, ty for the help

.solved

[midnight plank]

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[ruby dust]

ah heck, here we go again.

which one?

[tidal turret]

i

[ruby dust]

S=2(6-5)+2(7-5)+2(8-5)+....+2(n-5)
=2(1+2+3+4+5+6+7+...+n-1-2-3-4-5-5n)
=2[(n)(n+1)/2-15-5n]

[steel crest]

you don't need to do all that

[ruby dust]

=(n)(n+1)-30-10n

[steel crest]

it's not askingj for the sum

[ruby dust]

idk the language man

ik english

nothin else

[steel crest]

write the two first terms and the two last terms of these summations

[tidal turret]

i don't have exercises in hindu man

[steel crest]

is what the instructions say

[ruby dust]

idk mate

its not my mistake

[steel crest]

what do you mean you doint know

im telling you

[ruby dust]

first of all idk the language

[steel crest]

Spanish

[ruby dust]

i meant to say that

[steel crest]

but i translated it

now it's in English

[ruby dust]

fine

@steel crest expalin him

[steel crest]

im about to go to sleep

[tidal turret]

why do you have a lorenz attractor

in the pfp

[ruby dust]

i found it interesting

thats why

[tidal turret]

can you help me with my shit?

[ruby dust]

which shit mate? this?

[tidal turret]

ye

[ruby dust]

which one now

[tidal turret]

i

[ruby dust]

2(6-5), 2(7-5) are the first 2 terms and 2(n-6), 2(n-5) are last 2 terms

@tidal turret understood?

[midnight plank]

@tidal turret Has your question been resolved?

[midnight plank]

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

How does that implies $|b_n| > \frac{|b|}{2}$?

[grand pond]

Ænema

[midnight plank]

@steel cedar Has your question been resolved?

[tribal temple]

You have that $\abs{b} = \abs{b - b_n + b_n} \leq \abs{b - b_n} + \abs{b_n}$, the former is strictly less than $\frac{\abs{b}}2$, then subtract from both sides

[grand pond]

@tribal temple

[steel cedar]

ah, thanks!

.close

[midnight plank]

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[midnight plank]

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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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[polar nexus]

Need help

[graceful drum]

do it step by step

square it first

[lyric charm]

!status

[midnight plank]

What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

[polar nexus]

Idk where to begin

It's my first time solving this

[lyric charm]

$a^{12} = ((a^3)^2)^2$

[grand pond]

Ann

[mystic condor]

Do you know binomial expansion?

[keen saddle]

!original

[midnight plank]

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.

[polar nexus]

It's the original

[midnight plank]

@polar nexus Has your question been resolved?

[lyric charm]

you're not suggesting that OP should expand a twelfth power are you 💀

@polar nexus still here?

[midnight plank]

Channel closed

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[lyric charm]

.reopen

[midnight plank]

✅

@polar nexus Has your question been resolved?

[deft elk]

yeah I think binomial expansion is the way to go here

[bold peak]

Are all of you crazy

[frozen lake]

only 13 terms... not that hard

[bold peak]

Binomial expansion for 12 power?

[bold peak]

Yes but there's easier ways

[lyric charm]

and still unnecessary

also OP is just gone now

[bold peak]

Case in point

[frozen lake]

bro despawned 😭

[frozen lake]

isnt this just the same?

binomial a few times?

[bold peak]

Yes but the numbers are smaller, and you'll only ever deal with two terms

[frozen lake]

ah

IC

smart

[bold peak]

At no point do you have to calculate 12C6

[deft elk]

nah, ur just dumb

[bold peak]

Hey be nice smh

[frozen lake]

hmm ig

[deft elk]

no thnx, nothing to be nice to in this guy

[frozen lake]

kbai, hope OP comes back soon

[midnight plank]

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[frozen lake]

ma'am, stop following me everywhere if u hate me, this is a help channel

[bold peak]

This is a help channel, take your personal issues with people to other places please

[midnight plank]

Available help channel!

Send your question here to claim the channel.

Remember:
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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[slender walrus]

.Don't harass others.

[azure bolt]

<@&286206848099549185>

[past jay]

!15m

[midnight plank]

Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.

[azure bolt]

sorry

[past jay]

What did you try?