help-10

[timid silo]

ah i see one of them is british stuff and the other is french stuff

makes sense

[umbral nest]

so 1g = 1/100minutes and 1min = 1/100(secs ig?)

i have no idea why its there....

maybe its not important

[timid silo]

like

if 1g = 9/10 degrees

[umbral nest]

but still tho how are they converting 20grade 10/27 into minutes and secs

[timid silo]

then you should have 1g = 54 minutes no?

[umbral nest]

my base is broken ngl i havent done maths in forever

ive no idea how youre getting that....

[timid silo]

[
1^g = \frac{9}{10} \cancel{\text{ degrees }} \cdot \frac{60 \text{ minutes } }{1 \cancel{\text{ degrees}}}
]

[warm shale]

Lixera

[umbral nest]

just doing 9/10 ×100?

[timid silo]

basically that

since from what i read there are 60 minutes in a degree

so i am just applying standard unit conversion

and $\frac{9}{10} \cdot 60 \text{ minutes } = 54 \text{ minutes }$

[warm shale]

Lixera

[timid silo]

,w how many minutes are in one grade

[warm shale]

Results provided by WolframAlpha

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

Requested by Lixera#8529

[timid silo]

okay yeah i am right

i see now, so you want to convert 55/3 degrees to grades plus the other stuff

[umbral nest]

omg

yes

[timid silo]

right so like

[umbral nest]

yes it makes sense

[timid silo]

$\frac{55}{3} \text{ degrees} \cdot \frac{1^g}{0.9 \text{ degrees}}$

[warm shale]

Lixera

[timid silo]

[timid silo]

is it pfft

[umbral nest]

im still thinking

[timid silo]

yeah okay so from that

$\frac{550}{27} \text{ grads}$

[warm shale]

Lixera

[timid silo]

so that part is all well and dandy

whats the point of what they did here tho

[umbral nest]

yeah thats what

im thinking about as well

lmao

like im getting that they got 37 centesimal min

but how are they getting 3.7 centesimal sec

the . was supposed to be after 3

3703.7

[timid silo]

yeaaaa

wish i knew what those measurements meant

but gimme a sec i will try to look it up

[umbral nest]

no but like

why do i write 3.7 sec

centesimal sec*

why not

03.7"

oh mb cuz theres 0 before it

what if it was 1 instead of 0

there cant be more than 2 digits in centesimal secs right

[timid silo]

[umbral nest]

let me go do some more ig

[timid silo]

aighty

it looks like a lot of unit conversions, just not really familiar with the systems you are using

[umbral nest]

ill cry

[timid silo]

lmaooo dont do that

[umbral nest]

ok

i did another one

it makes sense

thank you so much

.close

[obtuse pebble]

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[timid silo]

what i have^

[stark bay]

bruh already occupied

pls send in another help forum

@timid silo

[timid silo]

i see we sent at same time

bruh

[stark bay]

del ur doubt

post it in another forum

@timid silo del ur doubt from here

[timid silo]

it doesnt matter if its deleted or not

scroll up ull see a whole lot of other things people have worked on

[stark bay]

bruh

[timid silo]

bruh

[stark bay]

<@&286206848099549185>

spamming his doubt when one of the forums is already open

[fierce lagoon]

Chill

[daring rock]

🤦‍♂️ And you just did the same thing in his channel. Just post your question again so it's more visible and leave it at that

[umbral nest]

this is a question from probability right

[obtuse pebble]

@stark bay Has your question been resolved?

[umbral nest]

i am not sure but i think it is 29

if the answer is right i can tell how i did it
and if someone else can help please do

[obtuse pebble]

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[junior plank]

how to solve 3^-n=0.2

[frosty goblet]

you can use x^-n = 1/(x^n)

[junior plank]

ok thank you

[obtuse pebble]

@junior plank Has your question been resolved?

[supple quest]

just take logarithm of both sides and then find the value of n

[obtuse pebble]

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[wispy sparrow]

need help on number 9

[obtuse pebble]

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'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above

[wispy sparrow]

im on step number 9

i dont know at all

if some one can explain it would be enough

[high lily]

do you know the formulae for
SA of a sphere
and SA of a cylinder

[bold steppe]

yes

[high lily]

not asking you

[mellow glacier]

lmao

[bold steppe]

we're from the same school and class

so i basically need help too

pls

[high lily]

well then apply those formula here

[wispy sparrow]

ye

[mellow glacier]

If you know the formula for both then just put values in them and then put them in a ratio?

[high lily]

whats the SA of the sphere here

[wispy sparrow]

4/3 pir3

[high lily]

what's the SA of the cylinder

[wispy sparrow]

pir2h

[mellow glacier]

no

[high lily]

wait,1 sec

no to both

i want SA

NOT volume

[wispy sparrow]

oh

[mellow glacier]

SA = Surface area

[edgy monolith]

Hi!!!

[high lily]

and so does the question

[edgy monolith]

I need a help in a problem

😔

[wispy sparrow]

2pir2+2pir+radius+height

[mellow glacier]

Not giving

[high lily]

no

[mellow glacier]

create your own channel

[wispy sparrow]

for cylinder

[mellow glacier]

read #❓how-to-get-help

[edgy monolith]

Wha

Oh

[wispy sparrow]

for sphere its 4pir2

[high lily]

2pir2+2pir+radius+height
you're adding 1d values with 2d values

where's that even coming from

[wispy sparrow]

so it should be

2pir2+2pirh

[high lily]

also, use ^ to denote exponentiation e.g. r^2

[wispy sparrow]

my bad

[wispy sparrow]

alright

[high lily]

yeh,
2pi * r^2 + 2pi * rh

[wispy sparrow]

yep

[high lily]

and you are also given h here in terms of r

[wispy sparrow]

yes

[mellow glacier]

$2\pi r^2+2\pi rh$

[warm shale]

Shockshwat

[high lily]

sub that in and set up the ratio of your two areas
and simplify

[wispy sparrow]

subtract which one?

[high lily]

sub is short for substitute

and you are also given h here in terms of r
specifically h=2r

[wispy sparrow]

alright

[high lily]

replace h with (2r)

[wispy sparrow]

wait so the r would be considered as

just r itself

[high lily]

the r in the formula represents the radius
which is also represented by r here, so you don't really have to make changes

[wispy sparrow]

so it would be 2 X 3.142 r^2 + 2 X 3.142 x r x 2r?

is it 18.852r^2?

[obtuse pebble]

@wispy sparrow Has your question been resolved?

[obtuse pebble]

@wispy sparrow Has your question been resolved?

[obtuse pebble]

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[brave rune]

stop mass pinging and we will help you

[obtuse pebble]

@fallow zinc Has your question been resolved?

[unreal musk]

.close

[obtuse pebble]

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[obtuse pebble]

Please don't occupy multiple help channels.

[indigo coral]

did i do this right ?

[hybrid steeple]

ye

[indigo coral]

thanks

.close

[obtuse pebble]

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[hybrid steeple]

why

.reopen

[obtuse pebble]

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[indigo coral]

i just wanted to know if i did right

[obtuse pebble]

Please don't occupy multiple help channels.

[hybrid steeple]

k

[indigo coral]

.close

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[plucky lava]

hi

[plucky lava]

need some help with some triangles

[hybrid gull]

[plucky lava]

these are the excercises

if it needs any translating i can

[tardy epoch]

pick one, try it yourself, then ask one

[plucky lava]

i picked nr 1 but i have no idea

how to

[tardy epoch]

take a closer picture for just that problem

[plucky lava]

ok

i just know that i can find DE here

any idea?

<@&286206848099549185> can anyone help?

[worn spruce]

grade lvl\

?

[plucky lava]

well im in albania so

i don really know what that is like

but im 9th

here

[worn spruce]

sorry idk

[plucky lava]

okay

[worn spruce]

@ruby fulcrum

[plucky lava]

thats not the ping

[worn spruce]

oh

mb

<@&286206848099549185>

[bronze osprey]

give names to angles

like a, b or alpha beta etc

[plucky lava]

okay?

[bronze osprey]

do you see anything now?

[plucky lava]

not really

[bronze osprey]

send a pic

[plucky lava]

i cant write on the thing

i only have the pic

[bronze osprey]

okay then

tell me what did you do then

[plucky lava]

isnt adc 30 and acd 60

[bronze osprey]

how is adc 30

[plucky lava]

well because the side that is opposite it is half the hypotenuse

isnt that a thing

[bronze osprey]

isnt it a right angle

adc

[plucky lava]

i mean edc

sorry

[bronze osprey]

okay

[plucky lava]

edc and ecd

[bronze osprey]

yes there is a 30-60-90 triangle there right?

[plucky lava]

well idk im just supossing that

[bronze osprey]

its right

[plucky lava]

okay then what do i do?

[bronze osprey]

it says that dec is a right angle

[plucky lava]

yes

[bronze osprey]

so edc is 30 and ecd is 60

[plucky lava]

yes

then what do i do

i can find the angles of ade triangle

[bronze osprey]

can you tell me dae and ade

[plucky lava]

dae is 30

ade is 60

[bronze osprey]

that is correct

then can you find the other sides

[plucky lava]

Ac is 8

[bronze osprey]

dc is given 4

[plucky lava]

yes

[bronze osprey]

find ed first

[plucky lava]

i foumd Ac is 8 and i can find ad and ed

let me find ed

[bronze osprey]

you have 30-60-90 and two sides given

you know the rule right?

[plucky lava]

Ed is 2 square 3

[bronze osprey]

yes

[plucky lava]

now

[bronze osprey]

2√3

[plucky lava]

i can find AD

[plucky lava]

yes

[bronze osprey]

we know that dae is 30

[plucky lava]

if i find Ad isnt it half AB?

because abd=dae

so abd is 30 and in front is AD ad is half the hypotenuse which we need

so i didnt even need ED

[bronze osprey]

yep

[plucky lava]

👍

[bronze osprey]

but, to gain speed

find all sides and angles

[plucky lava]

👍

[bronze osprey]

imo

[plucky lava]

So Ad is square root pf 84

oh no

sorry

[bronze osprey]

we have dc 4

[plucky lava]

yes yes sorry

ac is 8

i got it 10

[bronze osprey]

we found dac 30

ad is 4√3 right

[plucky lava]

can u help with others?

or u have stuff to do

[bronze osprey]

maybe one more

but then i have to go

choose one

[bronze osprey]

hmm

we can draw a line from d to f

if that helps

[plucky lava]

ye

how can it help doe

[bronze osprey]

i think there was a rule for this type

but i dont remember

hmm

we can look for some similarity things

[plucky lava]

hmm

[bronze osprey]

its hard to do it from screen fr

[plucky lava]

i wrote it on my notebook but i aint seein anything

[bronze osprey]

i couldnt find anything helpful

[plucky lava]

okay nw

i can get other helper or smth

<@&286206848099549185>

anyone can help?

.close

[obtuse pebble]

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[bronze osprey]

.reopen

[obtuse pebble]

✅

[bronze osprey]

wait i am still looking

give me a few mins

[plucky lava]

nono dw i opened new thing

.close

[obtuse pebble]

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[swift dawn]

if the composite function of two functions f ∘ g is given and f is also given how can I determine what g is?

[misty iron]

Probably by comparing f(x) with f(g(x)).

[bronze osprey]

(fog)(x)=f(g(x)) you know?

you take g(x) as x basicly and put it in f(x)

like, if f(x)=3x+2, then (fog)(x)=3g(x)+2

hey

[swift dawn]

ohh alright thank you

[bronze osprey]

you are welcome

[swift dawn]

.close

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[tall tusk]

its not from putnam bruh

anyway, how do u continue

[tardy epoch]

lmao just throw the whole link

[tall tusk]

on

like

no

theres some werid exponent here in the real question

i wanna solve it without the weird exponent

without the weird exponent, its just a calc 1 question

[misty iron]

I am pretty sure it is not an exponent. What it probably means here is that (n+1)th term of this sequence is given by adding e to the nth term of the sequence.

[tall tusk]

eh yeh i know, the ss is cut off

[warm canopy]

their point is they've changed the putnam question

[misty iron]

o

[tall tusk]

@mint tendon help

[mint tendon]

What.

[tall tusk]

see the quesrtion pinned

[mint tendon]

Lintahlo, do you wish to know the answer or the methodology

i gotta bike home be back later

[warm canopy]

this boils down to $\lim_{n \to \infty} (1 + ne - \ln(n))$

[warm shale]

ΣAC

[tall tusk]

method

[tall tusk]

yeh

ik that

[warm canopy]

!work

show what you've done then

[tall tusk]

^

dont know how to evaluate

[warm canopy]

what ways have you tried to evaluate it

[tall tusk]

idk ig 1 is negligible

ne-ln(n). maybe change ne to ln base

and divide

not sure

[warm canopy]

try factoring an n out

[tall tusk]

i see

this is 0 because xe approaches infinity faster?

[warm canopy]

vague but sure

[tall tusk]

ok lemme try the real putnam

[warm canopy]

you can lhoptial it

[obtuse pebble]

@tall tusk Has your question been resolved?

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[cursive mirage]

In this question it does not matter if I can remove the 0 on the denomerator?

[cursive mirage]

Every function is continuous on its domain.
A. True
B. False

is this True?

[obtuse pebble]

@cursive mirage Has your question been resolved?

[lethal egret]

if the denominator is 0 for any x

[lethal egret]

no of course not there are a lot of functions that are discontinuous

if every function was continuous why would we even talk about discontinuous functions

[cursive mirage]

What if I said Any function f is continuious on its domain

[lethal egret]

no?

you can think of an example like this

the domain is R

but its not continuous on R

[cursive mirage]

So 5 should've been False?

[lethal egret]

yes

[cursive mirage]

thank you

.close

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[quaint umbra]

to confirm it is any double right?

cause I have a higher chance of getting doubles if it is any of them

[strange belfry]

yeah

[quaint umbra]

ty

.close

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[quaint umbra]

so there is a 94% chance that the components arent faulty

so can I do 94/100 to get 1%

0.94 = 1%

and then 0.94*0.94 = 0.8836

and thats if I use 2 components

0.8836*0.94 = 0.830584

and thats if I use 3 components

0.830584*0.94 = 0.78074896

for 4 components

then I times it by 100

so its 78%?

is that correct?

[dark stirrup]

,w (1-.06)^4

[warm shale]

Results provided by WolframAlpha

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

Requested by SWR#8588

[quaint umbra]

.close

[obtuse pebble]

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[rugged oak]

?

[rugged oak]

uhhhhh

[sharp pecan]

nah uh

[rugged oak]

?

.close

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[cursive mirage]

The function f(x) = sin−1(e^x − 1) is

A. discontinuous on (−∞, ln 2)
B. continuous on (−∞, ln 2)
C. continuous on [0, 2]
D. discontinuous on R − {ln 2}

[cursive mirage]

when I tried to find the domain

-1 <= e^x - 1 <= 1

0 <= e^x <= 2

but then ln0 is undefined what should I do

[brave ore]

What is the domain of sin-1

[cursive mirage]

[-1,1]

[brave ore]

Ok

give me a second im getting it's graph

OH

Ok so it goes on forever to the left

[brave ore]

I don't think you need to ln it

It passes through point 0,0

It's b

tell me if you want me to explain

[cursive mirage]

I got it by testing values in the domains

random values

[brave ore]

Yea you can do that too

Like since the domain of sin^-1 is [-1,1] you can find out the value that makes it 1

[cursive mirage]

thank you

.close

[obtuse pebble]

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[drowsy carbon]

I keep getting the wrong answer, and I am not sure if am I doing this right

[drowsy carbon]

Could someone please help me figure out my problem? This is my second try and I got the same equation

[knotty crow]

y = m(x-x1) + y1
m = 1/2, x1 = 0, y1 = ln(6)

y = 1/2(x-0) + ln(6) = 1/2x + ln(6)

[drowsy carbon]

I just need the value of m and the value of b

I have the right m value

Im pretty sure

but Im not sure if my b is right

[strange belfry]

yes you do

and your b is not right

recall that "b" is the y-intercept for a linear line

[drowsy carbon]

Ohh

So it would be 0?

[strange belfry]

no

the line you are taking the derivative of intercepts the y axis at (0, ln6) right

[drowsy carbon]

Yes

[strange belfry]

and you are taking the derivative at the point (0, ln6)

remember that the derivative and the original function are tangent to each other

and touch at the point of that you tske the derivative of, that what makes the derivative at that point, the derivative of that point

[drowsy carbon]

Yeah I understand that

So how would I calculate the b value

I thought all I was supposed to do but sub in all the values and then solve for b

Would it just be ln 6

[strange belfry]

yeh

[strange belfry]

you can manipulate the equation for the slope to derive the top equation too

$\frac{y - y_1}{x - x_1} = m$

[warm shale]

biggboy

[strange belfry]

which can be written lile this because it should be correct for all (x,y) for any chosen (x1,x2)

that what makes the line linear

[drowsy carbon]

Ohhh

[strange belfry]

having the same slope everywhere

[drowsy carbon]

That makes a lot more sense now I am gonna try to use that

Thank you for all your help

[strange belfry]

glad to do so

[obtuse pebble]

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[obtuse harness]

Anyone know how this is Found?

I understand that's it's a solution but idk how to like compute/ come up with it

[wise talon]

x = x-1+1

[obtuse harness]

I don't understand what this changes?

[wise talon]

its a hint

[obtuse harness]

I found it thanks :)

Very clever trick

[wise talon]

np

use it too often in real analysis for triangle inequalities

[obtuse pebble]

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[spice chasm]

hello

[spice chasm]

can somebody explain how the domain restrictions work

[trail musk]

The range of f is the domain of the inverse

Because it is only an inverse over that interval

Understood?

[spice chasm]

wait

[trail musk]

What

Please.

[spice chasm]

the domain of f is x≥4 but range of inverse is only y≥0

[knotty crow]

domain of f is given (x >= 4)

[spice chasm]

but the range of the inverse isn’t y≥4

[knotty crow]

range of the inverse is domain of f

so yeah it's y >= 4

(for x = 0 we have y = 4)

[spice chasm]

the range of √(x²+16) is y≥0 tho

wait it isn’t

[spice chasm]

why do you pick the positive version instead of negative

[knotty crow]

because question restricted domain

[spice chasm]

so you look at the domain of the original and choose which solution based off of that

.close

[obtuse pebble]

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[hard minnow]

How would I solve this?

It's saying the answer isn't 7...

?

[zenith crest]

is it -3

[hard minnow]

Yes, but how did you get it?

[zenith crest]

we take the integral from 3 to 10

so we ignore A1

so its -4 + 2 - 1

= -3

[hard minnow]

one last question

[hard minnow]

why would I be wrong here?

[zenith crest]

uh

is this the same question as the one above

or does it refer to it

[hard minnow]

It doesnt

Thank you for help on the other one

it makes sense

[zenith crest]

i mean i would think its -7 to 5 but the last integral is kinda throwing me off

[hard minnow]

b = 5

a not -7, not sure how you got this

[hard minnow]

why was it b=5?

[zenith crest]

im not sure yet

like if it was just like this

then it would make more sense

but idk what integral -7 to -1 does

[hard minnow]

No problem. My final question is, how do we understand a problem like this graphically?

[zenith crest]

well all a bound of integration is

is literally abound

so 0 to 2 means

when x is from 0 to 2

it itll be the area under the curve

[hard minnow]

So 1?

[zenith crest]

6

its just the are of the rectangle

2*3

[hard minnow]

So how would 9 2 work?

[zenith crest]

think about it

its the same thing

[hard minnow]

would it just be

[zenith crest]

but from 2 to 9

[hard minnow]

is it -1 times something?

[zenith crest]

uh

find this area

[hard minnow]

This one is four times something, right?

[zenith crest]

uh

you know how to cualculate area right

its just a triangle, triangle, rectangle

[hard minnow]

Wow I'm lost.

[obtuse pebble]

@hard minnow Has your question been resolved?

[obtuse pebble]

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[obtuse pebble]

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[solemn needle]

hi

[solemn needle]

whats a good way to solve this integral

$\int_{-\pi}^{\pi}x\sin(x)\cos(nx)\dd{x}$

[warm shale]

RickyDicky

[solemn needle]

i already solved it without the limits

but im having trouble when i plug in the limits

[ruby path]

What's the matter

[solemn needle]

$\frac1{2\pi}\left[\frac{-x\cos(x-nx)}{1-n} + \frac{\sin(x-nx)}{(1-n)^2} - \frac{-x\cos(x+nx)}{1+n} + \frac{\sin(x+nx)}{(1-n)^2}\right]_{-\pi}^{\pi}$

[warm shale]

RickyDicky

[solemn needle]

figuring out some trig stuff

like

the equations get so long

how do i know what cos(pi - n*pi) would turn out

without using formulas to expand it even further

[ruby path]

Oh damn 💀

[solemn needle]

its literally just a matter of substituting in the limits

but im confused

[ruby path]

,w cos (pi - x)

[warm shale]

Results provided by WolframAlpha

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

Requested by NEONPerseus#2128

[solemn needle]

i know how to ask wolfram for it

but i wanna learn it myself

[ruby path]

Well do you know the formulae

[solemn needle]

its like cos(pi)*cos(npi)+sin(pi)sin(npi)

so thats -cos(n*pi)

but i dont want to have to write all these long formulas

is there a more intuitive way to figure it out

[solar trellis]

Is n an integer

[solemn needle]

yea

[solar trellis]

You can then simplify cos npi and sin npi

[solemn needle]

how

[solar trellis]

What's sin pi

[solemn needle]

0

sin(npi) = 0

[solar trellis]

Yes

Cos npi?

[solemn needle]

sin(pi + npi) tho?

[ruby path]

Did you try using Kings Property

[solemn needle]

cos(pi) = -1, cos(npi) = ..?

[solar trellis]

0

[ruby path]

The a + b - x thing

[solar trellis]

it alternates between 1 and -1

[solemn needle]

i can swear wolfram was giving me a diff answer to that, further increasing my confusion

,w sin(pi + n*pi)

[warm shale]

Results provided by WolframAlpha

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

Requested by RickyDicky#2484

[solemn needle]

-sin(npi)

[solar trellis]

You can express this as (-1)^n

[solemn needle]

oh

its not taking n as an integer

thats why it gives that answer

[solemn needle]

okay also sin (pi-npi) is 0

so we just cancel out all those sines?

because its all gonna be 0

[solar trellis]

Yes because that's just sin ((n-1)pi) and n-1 is also an integer

[solemn needle]

$\frac1{2\pi}\left[\frac{-x\cos(x-nx)}{1-n}- \frac{-x\cos(x+nx)}{1+n} \right]_{-\pi}^{\pi}$

[warm shale]

RickyDicky

[solemn needle]

so its just this

[solar trellis]

0×a = 0

Haven't checked

[solemn needle]

$\frac1{2\pi}\left[\frac{-x\cos(x-nx)}{1-n} + \frac{\sin(x-nx)}{(1-n)^2} - \frac{-x\cos(x+nx)}{1+n} + \frac{\sin(x+nx)}{(1-n)^2}\right]_{-\pi}^{\pi}$

[warm shale]

RickyDicky

[solemn needle]

this was previous

if we cancel out those sines

we're left with only the cosine funcs

[solar trellis]

Yes

[solemn needle]

so cos(pi-n*pi) = (-1)^n

but also cos(pi + n*pi) = (-1)^n?

are these right? @solar trellis

[solar trellis]

No

[solemn needle]

hm

so only cos(npi) = (-1)^n

how do we find out cos(pi-n*pi) and cos(pi+n*pi)

@solar trellis sorry for the ping, but mind helping me some more here?

cos(pi + npi) = (-1)^(n+1)

cos(-npi) = 1^n
cos(pi-npi) = -(1)^n?

[tardy epoch]

Just plug a few n into a calculator and see

[solemn needle]

yea it keeps repeating

alternating

1 to -1

doesnt that make both

cos(pi+npi) and cos(pi-npi) = (-1)^n

[tardy epoch]

Cosine is an even function

[solemn needle]

yea and

[tardy epoch]

And has period 2pi

[solemn needle]

its 5 AM i cant make sense of it

[tardy epoch]

Then revisit it when you wake up

[solemn needle]

so its not (-1)^n?

[solemn needle]

just trying to get it now so i can work on smth else tomorrow

[tardy epoch]

Use this

[tardy epoch]

And this

[tardy epoch]

To see how these two relate

[solemn needle]

so its value repeats every 2pi

i really dont get it

[tardy epoch]

.

[solemn needle]

it should be -(-1)^n

i plugged in some values

cos(pi + 0pi) = -1
cos(pi + pi) = 1
cos(pi + 2pi) = -1

so if for n = 0 we need to get -1

cos(pi+npi) = -(-1)^n

and if i plug in values for cos(pi - npi)
cos(pi - 0) = -1
cos(pi - pi) = 1
cos(pi - 2pi) = -1

same

cos(pi - npi) = -(-1)^n

[solemn needle]

did i get it right?

[tardy epoch]

If that's enough to convince you, then you're done

[solemn needle]

it does convince me

[obtuse pebble]

@solemn needle Has your question been resolved?

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[solemn needle]

actually

[solemn needle]

i might have a few more questions

I solved the fourier series of x*sin(x) from [-pi, pi]

$f(x) = \frac{1}{2} + 2\sum_{n=1}^{\infty}\frac{(-1)^{n+1}}{n^2-1}\cdot\cos(nx)$

[warm shale]

RickyDicky

[solemn needle]

i have to use this series to find out the value of this sum:

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

[warm shale]

RickyDicky

[solemn needle]

any ideas how to proceed about this? @tardy epoch

[tardy epoch]

Just ping helpers

After 15min

[solemn needle]

alright

[solemn needle]

maybe i need to substitute f(x) = x*sin(x) here

and plug in f(0)

yeah

thats it

.close

[obtuse pebble]

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[obtuse pebble]

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[obtuse pebble]

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[cursive prairie]

I am not sure how to do this question, find the derivative of: cos(sin(x))^3, I tried it, and got -3*sin(sin(x))^2 * cos(x) * 1 but the correct answer is -3 * cos(x) * sin(sin(x)) * cos(x)^2. How would I arrive at that answer?

[obtuse pebble]

@cursive prairie Has your question been resolved?

[tardy epoch]

Write your function as f(g(h(x)))

h(x) = sin(x)

What's g(x) and f(x)?

[obtuse pebble]

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[queen mica]

To prove multiple points are collinear i would show they have the same gradient and have the same equation which meets all the said coordinates, right?

[next reef]

You can also show that area of the triangle formed by those points are 0 and hence they are collinear.

[queen mica]

I will try that, that sounds interesting

Thank you

.close

[obtuse pebble]

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[queen mica]

.reopen

[obtuse pebble]

✅

[queen mica]

@next reef can you elaborate why this works?

[unique spear]

Let me ask

what is the area

if a line

of a line*

just draw a straight line

tell us what the area of that straight line is

[neon eagle]

^

[unique spear]

when you try to find the area of collinear points

it’s the same as the area of a straigtt HR line

[obtuse pebble]

@queen mica Has your question been resolved?

[obtuse pebble]

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[timid silo]

Can anyone help me in that question

[sharp pecan]

,rccw

[sharp pecan]

you can write this as 3 boolean statements and then combine them

[timid silo]

Can you tell me how

it's valid i think.

[sharp pecan]

lets say that there are statements I like discrete math=A and I studied=B and I failed the course=C
then find equations

like, A implies B would be one

[timid silo]

I think doing this programmatically would make u understand

What will be the second equation

[sharp pecan]

but thats not how to test validity right

[sharp pecan]

well, a clear 'or' right

exclusive

[timid silo]

Yup

I will explain why i think it is valid.

[timid silo]

Explain

[timid silo]

Second equation might be A or C

If I like math ==> i will study
If study_discrete ==> Pass the course
else ==> Fail the course

If fail_course ==> didn't study ==> don't like math

[sharp pecan]

$A\implies B$\
$B=!C$\
$C\implies !A$\

you can combine this to $C \implies C$

[warm shale]

Jigglyproff

[timid silo]

Why you write !C

[timid silo]

!C means $\lnot C$

[warm shale]

! matthewzz

[timid silo]

do you know what that means?

!C means basically NOT C

[neon eagle]

Fail course implies DIDNT study implies don’t like discrete (contra positive of first statement)

[timid silo]

i dont think they teach contrapositive in discrete

[sharp pecan]

its just subsitution lol

$A\implies B$
$B=!C$
$C\implies !A$\

place 2nd in first to get \
$A\implies !C$\

then you either know the rule or you make the validity table for $C\implies !A$ ~ $A\implies !C$\

[warm shale]

Jigglyproff

[timid silo]

Ok

[obtuse pebble]

@timid silo Has your question been resolved?

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[timid silo]

Hey is D) x is tripled mean 3x

[timid silo]

can someone help me with the bottom questions please

[thick oracle]

All of them?

I'm sure you can do most

[timid silo]

idk what 7 more than y even means

[thick oracle]

Rly

Cmon

[timid silo]

yes

what even is y

[thick oracle]

Whats 2+7

[timid silo]

9

[thick oracle]

Whats 7 more than 2

[timid silo]

9

[thick oracle]

Whats 7 more than y

[timid silo]

what is y

[thick oracle]

A number

[timid silo]

what number?

im guessing 2

[thick oracle]

You dont guess

y is a variable

It can have any value

It can be 2

Or 17

[timid silo]

how do i know what number it is

[thick oracle]

You dont need to know

The question isnt : Find y

[spring sandal]

It's asking you to write an expression - not get a number as a solution

[timid silo]

but then how would i know what 7 more than y means

[thick oracle]

Ok i'l tell you

Cuz you re not getting it

It's y+7

7 more than y

Thats it

[timid silo]

that = 7y tho

but where did you get 2 from

7 more than y = 9 how?

[spring sandal]

Bro

Ok

think of it like

this

y is any number that can exist

but it hasnt been given a number in the question

so...

[timid silo]

so i can say any number i want

[spring sandal]

No.

You leave it as y

y is just a pronumeral

that stands for an unknown value

[timid silo]

but then its still 7

[spring sandal]

no its y +7

[timid silo]

i need to make it more than 7

[loud tangle]

any number that satisfies the condition imposed

[spring sandal]

no.

its asking

what is 7 more than Y

not make y more than 7

[timid silo]

this is so confusing

what numbers y

[thick oracle]

Bruv

[spring sandal]

r u trolling

[thick oracle]

This is grade 0 or 1 magh

[spring sandal]

did u learn this in class

[thick oracle]

Math

[spring sandal]

💀

[timid silo]

no im being serious

[spring sandal]

bro its a pronumeral

[thick oracle]

Bro go back to grade 1

[spring sandal]

it can represent anything

[thick oracle]

Pls

[loud tangle]

its any number that satisfies the thing youre asked to do

which is literally anything

[timid silo]

so 3+7 = 10

that is y+7?

[loud tangle]

youre not asked to find y

[spring sandal]

It's not asking to find y

Its asking to write the expression where its 7 more than y

[timid silo]

bro im sorry how am i meant to know whats 7 more than y when i dont know what number is y

I did 3+7 = 10

isnt that it

[spring sandal]

BRO

its not a number

get that out of your head now

[loud tangle]

leave it as y

just

[spring sandal]

its not asking u to get an answer

its asking u to write an expression

just leave y as the pronumeral

[timid silo]

okay so the answer is 7+y = 7y?

[spring sandal]

troll ?

[timid silo]

what

[spring sandal]

is this guy trolling ?

like actual

[timid silo]

I literally dont get it

[loud tangle]

i have no idea

[timid silo]

you just said its not a number seriously im not trolling bro

[loud tangle]

how old are you

[timid silo]

almost 16

[spring sandal]

💀

you ain't learnt this yet ?

[loud tangle]

wait is this english homework of some sort

are you a native speaker

[timid silo]

if its saying to write an expression it means y + 7 which is the expression and it equals 7y bro isnt that it?

[spring sandal]

lowkey looks like cambridge textbook

idk

[loud tangle]

answer the question

[timid silo]

its math homework

language of algebra is the title

[spring sandal]

what grade are you in?

[timid silo]

10

[spring sandal]

Australia?

[timid silo]

yeah

[spring sandal]

ok so its cambridge

nice

how have you not learnt this yet?

[timid silo]

idk...

i forgot it all

[dark stirrup]

Falcon my poor child. I'm sorry these people are mistreating you

[spring sandal]

Ok so lets say y is any number in the universe

it literally does not matter what it is

[dark stirrup]

There's nothing wrong with not having learned it yet

[spring sandal]

what does it mean by 7 more

[dark stirrup]

Or even having forgotten

[timid silo]

anything more than 7

[spring sandal]

no

what does 7 more than 6 mean

it means 7+6 correct?

[loud tangle]

i was just tryna make sense because if it were english homework i could have treated it differently

[dark stirrup]

Everyone learns at their own pace and as long as you try, that's what's important

[timid silo]

7+7?

[spring sandal]

No.

y itself is any number

like

leave it as y

so whats 7 more than y

[timid silo]

7

[loud tangle]

it could be 3 it could be 108 it could be -82719 it doesnt matter

[spring sandal]

No

[timid silo]

8?

[spring sandal]

7 MORE than y

ok guys this is a troll

just kick

[timid silo]

bro whats y

WHAT NUMBER IS IT

[loud tangle]

but instead of writing every number possible you leave it as y, implying it can be anything

[dark stirrup]

Saying you're unsure if he's a troll isn't helpful. But you've been the most minor offender

Hello falcon

I will help you

[timid silo]

hey

okay thanks

[loud tangle]

ill leave it to swr

[dark stirrup]

I apologize for my less patient colleagues

I know it's hard to feel like you don't know something

And it can be intimidating to ask for help and it's even worse to be told you're a troll

I'm sorry that happened

No one deserves that

[timid silo]

yeah its fine tho

[dark stirrup]

Anyway, let's take a look

So you're goal is "write an expression for each of the following"

It then gives you some math terms in words

And your goal is to write it in the language of mathematics

[timid silo]

ohh okay yeah

[dark stirrup]

You're learning the language of algebra now, which will be pretty different from the standard arithmetic you may have learned in the past

In beginning maths, you learn how to evaluate expressions and find their final results

Stuff like 9*9 or 25-13

These would be evaluated to 81 and 12, respectively

But there's a big difference between evaluating the expression and just the expression itself

For example 9*9 is an expression, not 81 is its evaluation

In your assignment here, you're only writing the expression. You don't need to evaluate them

So if I said "nine times nine" then you only need to write "9*9"

[timid silo]

isnt it 9x9

?

[dark stirrup]

• and x mean the same thing

[timid silo]

oh okay

so the evaluation (answer) of 7 more than y doesnt matter

[dark stirrup]

Yeah sorry. Kind of a habit. Once you get to algebra, you'll likely see * more than x

[dark stirrup]

Yes this is exactly right!

You don't care what it's equal to

In fact, we have no way of knowing

[timid silo]

so we only need to write the expression in mathematical way

[dark stirrup]

Yes exactly right

[timid silo]

so what would 7 more than y mean

7 + y

thats an expression

[dark stirrup]

Yup

[tawny sail]

yes!

sorry was watching until that point

[timid silo]

is that it

[tawny sail]

😄

[dark stirrup]

It's an expression and it's the **correct ** expression too

[timid silo]

it was so easy

thank you so muchh

[dark stirrup]

Np

Happy to help

[timid silo]

also one more thing if you dont mind

for five term expression

3a + 5x + 2y + 6c + 8b

is this it?

thats 5 terms

[tawny sail]

yes

[dark stirrup]

Yes