help-28

[silent sierra]

2/3 ^x

[shrewd hamlet]

Yep

[silent sierra]

ahhh

I see

[shrewd hamlet]

So $(\frac{2}{3})^x = 27$

[glossy valve]

Stephen

[shrewd hamlet]

What do we do from here

[silent sierra]

so x = log 27 / log 2/3

[shrewd hamlet]

Yep

Nice

[silent sierra]

cant simplify further right

also, what was the alternate route you hinted at

[shrewd hamlet]

Where?

Here?

[silent sierra]

here

[shrewd hamlet]

Oh lol instead of dividing by 3^x, we coulda divided by 2^x and then divided both sides by 27

Either method works

[silent sierra]

alr thanks

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[civic veldt]

a

[onyx glen]

@civic veldt is there an image being uploaded?

[civic veldt]

nah just wanted to check my internet connection

[onyx glen]

go to #chill or #discussion for that sort of thing.

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[fair gust]

i need help with discrete and solving pseudocodes

[fair gust]

can someone please help me out

<@&286206848099549185>

[devout valley]

Also don't forget

[full forum]

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.

[devout valley]

ty 🫶

[full forum]

@fair gust Has your question been resolved?

[fair gust]

I understand

but the last time i asked a discrete math question , no one was able to help for a whole hour...

[short siren]

React to the bot

[fair gust]

still need help lol

[short siren]

Okay could you post your question?

[fair gust]

its multiple questions but sure

[short siren]

,rccw

[short siren]

Oh pseudo code

[fair gust]

yea

i get the gist i just need help with the formula portions

and coming up with sigma notation

[short siren]

Hmm

The prints in pseudo code 1 is 2, 3, 4, and 5. They are 4 prints so it's gonna be

Like

You start with 2

That's one print

Then 3

That's another print

[fair gust]

those are the outputs right?

but how do i figure out the fomula

[short siren]

Formula for number of print executions?

[fair gust]

yes

[short siren]

Okay

What sigma formulas do you know?'

[fair gust]

the summation one

[short siren]

Yeah like

What summation formulas do you know?

[fair gust]

isnt there just one?

[short siren]

There are multiple ones

[fair gust]

oh i didnt know that no

i thought there was one for products and summations

[short siren]

Okay here are some

1. $\sum_{i=1}^{n} c = cn$ \
2. $\sum_{i=1}^{n} i = \frac{n(n+1)}{2}$

[glossy valve]

VulcanOne

[short siren]

1. is when you are constantly adding a specific number

Which is just the product of the number and the number of times you're adding it

2. is when you add whole numbers starting from 1 to some whole number n

[fair gust]

can you call and help me

or thats not possible

texting through all this is a bit difficult

[short siren]

Hmm

[fair gust]

That way i can go through everything

[short siren]

Problem is that VC is gone

[fair gust]

ah

[dark moat]

Ayo, what happend to vc??

[fair gust]

can i possibly add you personally on discord then?

[short siren]

Died.

[dark moat]

🥲

Was wondering where it vanished to

[fair gust]

@short siren can i possibly add you personally on discord then?

[short siren]

[short siren]

Hmm

[fair gust]

no?

[short siren]

I'm thinking

I don't usually VC so that's why

[fair gust]

oh ok

:((

[short siren]

VC only

And chats here

@fair gust

Also you didn't tell me what's your confusion with

I gave you the formula

s

https://cdn.discordapp.com/attachments/903486480985489478/1066485149384048650/1000057838007226480.png

You only need those two

[fair gust]

ih

so no vc

[short siren]

I can VC on our DMs

But if we chat, we chat here

1 condition for VCing: we discuss the math problem only

[fair gust]

yup

thank you

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[spring pelican]

I'm trying to figure out if this curve has a "well defined tangent in origo", and if so whats that tangents rate of increase, but I have no clue where to start

[vast fossil]

What do you mean by "origo"?

[spring pelican]

(0,0), thought it was an english word, my bad

[vast fossil]

It's called the origin

[spring pelican]

ahh okey thanks

[vast fossil]

So you wanna find dy/dx at t = 0?

[spring pelican]

thats what I dont understand, wouldnt that just be 0?

[vast fossil]

Generally $\frac{dy}{dx} = \frac{\frac{dy}{dt}}{\frac{dx}{dt}}$

[glossy valve]

A Lonely Bean

[vast fossil]

So in this case you'd have to evaluate 27t^2/(2 - 2cos(2t)) at 0

[spring pelican]

ohhh 0/0

[vast fossil]

But since it's 0/0

[spring pelican]

altiiight didnt see that

[vast fossil]

It's better to solve its limit

[spring pelican]

let me give it a quick try

hmm I got 54/8, but it says its wrong when I try it as an answer, is it the right value or have I just misunderstood what Im looking for or something?

[vast fossil]

Try entering that as 27/4 perhaps

[spring pelican]

hmmm weird

[vast fossil]

Does it say the correct answer?

[spring pelican]

no sadly not :/

is there an easy way to plot parametric curves btw? could be useful for later aswell to see what I'm dealing with

[vast fossil]

Well if it's asking for a "well defined" one then it's undefined

Since we solved for the limit, technically plugging t = 0 doesn't work

[spring pelican]

I tried just saying "no" which was the option if there wasnt one which was also incorrect, so I have no clue... I guess I'll just move on to the next one haha

[vast fossil]

Oh damn

I confused y with x

[spring pelican]

ohhh shit hahaha yeahh thats right

[vast fossil]

27t^2/(2 - 2cos(2t)) is dx/dy

[spring pelican]

aaaaa yeah I did the same thing

[vast fossil]

Try entering 4/27 then

[spring pelican]

thanks for the help man 🙂

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[woeful inlet]

I got infinity when I solved, but the answersheet says 1

[woeful inlet]

Can someone explain?

derivative of f(x):
(2x.sinx - x^2.cosx)/(sinx)^2

[lament aurora]

You know about Taylor series?

[woeful inlet]

no

[ebon path]

first of all justify that f is continuous in 0 and that f(0)=0 , then lim x-->0+
f(x)-f(0)/x =limx-->0+ x/sinx = 1

[woeful inlet]

How can I justify that f(x) is continuous in 0?

Well actually I can

Or can I?

lemme

f(0+) = infinity
f(0-) = -infinity

Thus f(0) doesn't exist

But it's continuous

But lim(x --> 0+) then I think x/sinx = infinity?

I mean x would be really small, but sinx would always be smaller thus infinity?

[full forum]

@woeful inlet Has your question been resolved?

[woeful inlet]

<@&286206848099549185>

[woeful inlet]

<@&286206848099549185>

[teal depot]

bruh

[woeful inlet]

I mean I waited 15 minutes before each mention?

[hot herald]

there's a pretty common limit identitiy
$$\lim_{x\to0} \frac{\sin(x)}{x} = 1$$

[glossy valve]

ℝamonov

[hot herald]

(provable with stuff like squeeze/sandwich theorem)

[woeful inlet]

So basically sin(x) = x when lim -> 0?

[hot herald]

So basically sin(x) = x when lim -> 0?
not basically

[woeful inlet]

[hot herald]

although true, that doesn't tell you much about the limit for sin(x)/x

[woeful inlet]

So I should just memorize it for now?

[hot herald]

yes

[woeful inlet]

Alright

[hot herald]

it'll pop up frequently

look up limit sin(x)/x squeeze theorem

[woeful inlet]

I also have 2 more questions (I solved other questions, till I get the answer for this.) should I open a new help channel?

[woeful inlet]

alrighty

[woeful inlet]

I think I'll make a new one

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[woeful inlet]

Thanks for the help with this one

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[torn jolt]

My friend says we have to use a calculator to solve this by saying cos^-1(1/3), and then taking the result and putting it in sin(result) = result.

He says we can't do this without a calculator. Is he right?

( I know technically that most things can be done without a calculator, but in this context, is it ok to expect that we're not supposed to solve without one?)

[torn jolt]

you can do it without a calculator

think about the unit circle

[hot herald]

its expected that you do that without a calc

as well as being able to obtain the simplified exact numerical value

[torn jolt]

Thought so... thanks guys

appreciated

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[hollow grove]

How do i find the equivalent capacitance between A and B

[thorny horizon]

do u see that C1 and C3 are in parallel

[hollow grove]

I thought they were in series

[thorny horizon]

well if u bring that connection to point A

u can see theyre in parallel

[hollow grove]

And c2 and c4 area also parallel

Right?

Or not

[thorny horizon]

no u replace C1 and C3 with their equivalent capacitor

then that capacitor and C2 are in series

[thorny horizon]

replace this again with their equivalent capacitor, and finally that cap and C4 will be in parallel

[hollow grove]

Let me try

Okay got it

I got the answer

But

What i initially did was solve c1 and c3 in parallel and c2 and c4 in parallel then the final result from both in series

[hollow grove]

How will I know if the result will be in series or parallel with the other capacitor

[thorny horizon]

u cant solve C2 and C4 in parallel coz theres something connected to C2

[hollow grove]

What is connected to C2

[thorny horizon]

Ceq is the equivalent capacitance of C1 and C3 in parallel

[hollow grove]

So i add ceq and c2 in series then the result with c4

In parallel

I get it, you mean i cant solve c2 and c4 in parallel and then ceq in series

[thorny horizon]

yes u cant

[thorny horizon]

capacitances dont add in series

[hollow grove]

$\frac{1}{C_{s}} = \frac{1}{C_{1}} +\frac{1}{C_{2}} +....\frac{1}{C_{n}}$$

[thorny horizon]

yes this is right

[glossy valve]

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

[thorny horizon]

so u do this with Ceq and C2

[hollow grove]

Then add normally with c4

[thorny horizon]

that gives u the capacitance of one capcitor that u can replace both Ceq and C2 with

[thorny horizon]

yeah

[hollow grove]

Thanks

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[rugged hound]

I have a tree diagram with 15 branchings, the problem exactly is find the exact probability of 5 families out of 15 buy cheese, when the probability of one family buying cheese is 20%. so i guess a tree diagram is fit for this problem, but 15 levels seem a bit too much, is there an alternative way of doing this?

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@rugged hound Has your question been resolved?

[rugged hound]

<@&286206848099549185>

[wild sleet]

15 choose 5 is 3003

multiply it by probability of families 1,2,3,4,5 buying cheese

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[worn jackal]

e) Through the intersection of lines
2x +5y -6 = 0
and
x -3y -3 = 0
place the rectangle on the line
4x -y +5 = 0
. Write it down
the equation of a rectangle.

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@worn jackal Has your question been resolved?

[worn jackal]

<@&286206848099549185>

[polar valve]

what have you tried so far?

[torn jolt]

hey i have one doubt here

how can we write equation of a rectangle

i am not getting that point

[worn jackal]

i tried y = y

[torn jolt]

??

can someone tell

[polar valve]

what does this mean?

[torn jolt]

same doubt lmao

please clear my doubt

[torn jolt]

.

is it even possible i mean

equation of rectangle i am not getting

what u mean

[worn jackal]

i need to get this from the firest two equations

[torn jolt]

rectangle is 2 dimensional

[worn jackal]

sow i did y = y

[torn jolt]

line is linear 1 dimension

how tf is it even possible

[worn jackal]

the google translate

[torn jolt]

what

i am not getting u

[worn jackal]

imma draw u

[torn jolt]

wtf

[worn jackal]

what is
rectangle

[torn jolt]

i think u cant speak english properly right?

[worn jackal]

that is rectangle

[torn jolt]

ur question is wrong, a line is one dimension whereas a rectangle is 2 dimension

[torn jolt]

ok

i get it now

[worn jackal]

idk is weird

[torn jolt]

how that is a rectangle

[worn jackal]

idk

[torn jolt]

bruh meh

[worn jackal]

can u help me now

[torn jolt]

i dont think so

sorry

[worn jackal]

damn oke

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[torn jolt]

like rectangle is a closed figure

.reopen

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✅

[torn jolt]

u can keep it opened someone else might help

[worn jackal]

o okey

[torn jolt]

hey i am not sure but ur question is most probably wrong can u verify?

[worn jackal]

let me do the whole question again

1. Given a line p with the equation: 1 = x/2 + y/3

e) Through the intersection of lines
2x +5y -6 = 0
and
x -3y -3 = 0
place the rectangle on the line
4x -y +5 = 0
. Write it down
the equation of a rectangle.

[worn jackal]

@torn jolt can u tell me what is this called

[torn jolt]

this is not a rectangle but a line which is perpendicular to the other line at its foot

if thats the case then m1m2 = -1 formula may come handy

[worn jackal]

okey

imma go ask a friedn

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[sleek quest]

im really stuck

[sleek quest]

i have like no angles to work with

[tulip marlin]

try some angles

with letters

and try writing down some inequalities

and hopefully u can show it

[little prism]

my hint: look at angles BAC compared to BAO (with O a point inside the triangle, like in your exercise).

then, do the same for the angles in the B corner. then, think about the sum of a triangle's angles.

like the previous user suggested, I realise now :).

[sleek quest]

how do i compare them

<BAC > <BAO

[little prism]

usually, by looking at their measures?

[little prism]

yep

how about the angles in the corner B?

there should be a similar inequality there

[sleek quest]

(ABC+BAC)+ACB=180

(BAO+ABO)+AOB=180

ABC+BAC=180-ACB
BAO+ABO=180-AOB

ABC+BAC>BAO+ABO
180-ACB>180-AOB
so ACB must be smaller

[little prism]

remember to make use of what we said earlier

yes 🙂

I believe this should be a sufficient proof.

although if it's university-level studies, there's definitely far more complex proofs, involving affine spaces, if I am not mistaken

[sleek quest]

nice! 🙂

[sleek quest]

no idea what those are lol

[little prism]

haha

then I guess with the tools given, it's all that can be done

[sleek quest]

tysm

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[stuck roost]

how do i prove that -(-a)=a
using only additive identity, inverse of it, multiplicative identity and the reverse of it

[tulip marlin]

have a go playing around with the algebra

have u?

!status

[full forum]

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

[stuck roost]

i tried some stuff but didnt rly work

ig im at 1 or 2

i dont rly wanna know the answer i just wanna know where to starrt

[tulip marlin]

use the additive identity to begin with

what does -(-a) satisfy

[stuck roost]

idk

[tulip marlin]

also, I am not sure where the multiplicative identity come into this

[tulip marlin]

are you sure you need all of these?

[tulip marlin]

Ok, what does the additive inverse satisfy. Like write the statement

[stuck roost]

no just the ones i can use

[stuck roost]

tehse are just the ones i can use if i need em

[stuck roost]

well given any number a for example there exists a nomber x such that
a+x=x+a=0

[tulip marlin]

To be precise

for some given a

if a + x = x + a = 0, then x is a's additive inverse

===
Have you proven that additive inverses are unique?

[stuck roost]

no

[tulip marlin]

ah ok

I might be thinking about this the wrong way then

Can I just check then

[stuck roost]

sure

[tulip marlin]

have you defined what the notation -a actually means?

[stuck roost]

nah

[tulip marlin]

well thats very odd then

what course is this

[stuck roost]

idk its just my like tution teacher's course

[tulip marlin]

group theory?

or did they not say

[stuck roost]

didnt say

[tulip marlin]

The question isn't very well defined then ngl

they should have first defined what -x means

It seems you are working in the context of a ring

and so it could either mean the additive inverse of x

or -1 * x

usually it is defined as the additive inverse of x and then you prove it is equal to -1 * x

===
but you cant define -x as the additive inverse of x until you've proven additive inverses are unique

[stuck roost]

yeah

[tulip marlin]

idk if what im saying makes sense to u

[stuck roost]

kinda does

[tulip marlin]

ngl - for this algebra stuff I would generally recommend learning from a book

[tulip marlin]

from what you've said, I don't have much confidence in this

So have they defined what a group or a ring is?

[stuck roost]

nah

[tulip marlin]

Yeah I would really commend reading a book that introduces algebra properly

Not sure what book to recommend maybe you could ask #book-recommendations for an abstract algebra intro book

[stuck roost]

yeah ig ill just ask my teacher if i missed smth or idk

alr ty tho

[tulip marlin]

As for your original question, iirc, a book should usually do this:

Define what a ring is
Prove additive/multiplicative identities are unique
Prove additive/multiplicative inverses are unique
Then define -x to mean the additive inverse of x

Then you can do your question

[stuck roost]

oh

i see

ty

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[austere quartz]

the probability to roll at least one 6 with a six sided die in three total throws is ½ right?

[stable plover]

no

[austere quartz]

im just imagining the ⅙ chance of rolling a six, but since its repeated 3 times and you have the same probability it should logically be 3 in 6 right

[tulip marlin]

Think about the same problem rolled 6 times

are you guaranteed a 6 after 6 throws

or even 7 times

[austere quartz]

theoretically yeah because one in six is a 6

[tulip marlin]

7/6 probability?

[austere quartz]

no no

[stable plover]

the probability you are after is equal to 1 - the probability of three non-6 values in a row, which is 1 - (5/6)^3

[austere quartz]

the probability to get at least one 6

[tulip marlin]

Yes, but can't you see your thinking has a problem

if you consider the case of 6 or 7 total throws

[austere quartz]

ohhh yeah makes sense

[tulip marlin]

The probability to roll at least one 6 in 6 throws is not 1

[austere quartz]

thank you

[grave terrace]

7/6 isn't even probability anymore

[austere quartz]

but isnt the probability ⅙?

meaning theoretically one kn six throws is a 6

[tulip marlin]

how did you get 1/2 here

for 3 throws

you multiplied 1/6 by 3 i assume

[tulip marlin]

so here i do 1/6 * 6 = 1

Which clearly isn't correct

[austere quartz]

that would be getting three 6s

oh wait

[tulip marlin]

[austere quartz]

no

yea

[austere quartz]

yeah so the theoretical probability to get one 6 in six throws is 1

what does the ⅙ probability tell us

[tulip marlin]

really?

so you're telling me 6 throws guarantees me at least a 6

[austere quartz]

theoretically

yes

[tulip marlin]

What does 'theoretically' mean?

Not at all

I could get 6 1's in a row

[stable plover]

you're confusing expectation with probability

[tulip marlin]

i dont thinkt heyve done expectation

[twilit leaf]

A fair die does not mean it will roll a set of 1 through 6 in 6 rolls

[tulip marlin]

Also, consider instead 1/6 * 7 = 7/6

for 7 throws

7/6 needs to be a probability but thats greater than 1

so this is nonsensical

[austere quartz]

oh

wait so what does thr ⅙ actually mean

[tulip marlin]

thats the probability of getting a 6

in 1 throw.

[austere quartz]

oh okay i get it now

thank youuu

[tulip marlin]

I hope you do

[austere quartz]

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[empty trail]

i have no clue

wtf this is

[atomic blade]

Rewrite 2 in terms of logs

Remember that a log, universally, defaults to base-10

[empty trail]

i sorta m confused by that

could you give me an example or smthn

[atomic blade]

Well let's take the number 5

We know that log(10^k) = k, right?

[empty trail]

yes

[atomic blade]

So if k = 5

Then 5 = log(10^5)

We also know that the sum of two logarithms with the same base is equal to the logarithm (of the same base) of the product of their arguments

log(a) + log(b) = log(ab)

So:

5 + log(x)
= log(10^5) + log(x)
= log(100000x)

[empty trail]

i see!

so i used this to get the answer D

[atomic blade]

Yes

[empty trail]

thank you!

[atomic blade]

np

[empty trail]

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[worthy reef]

I need to find the intersection point of this but I'm confused since I used y2-y1/x2-x2 to find m then with m I found b leaving me with: y = 1 . x -2 but I don't know what to do next to find the intersection

[devout valley]

Hang on, so g is a linear function with what they said, yea?

[worthy reef]

Yes!

[devout valley]

Alright I agree with the gradient you got

[worthy reef]

It says 'G is the lineal function such that g(2)...

[devout valley]

But you’re saying that the equation of g is x-2, is it?

Surely it should be +2 instead?

[worthy reef]

Hmmm after I found the value of m I did

2=1.4+b
2=4+b
-2=b

[devout valley]

Wrong way round: when x=2, y=4

Similarly when x=4, y=6

[worthy reef]

I'm confused

[devout valley]

Alright so g is a line, yea?

The notation g(x) is basically “what the function gives you at x”

[worthy reef]

yes

[devout valley]

So for example, with the other one you have f, you got f(3) =23, yes?

Put x=3 into there and you get f(3)=3(3)+14

[worthy reef]

So I should replace in f(x) with any of those values of (g) to get the intersection?

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[sleek quest]

how do i prove these things?

[twilit leaf]

The parallelogram is rotationally symmetric

[sleek quest]

so if i draw it vertically

everything it the same?

[sleek quest]

i see how it would help, but why is it true

also how do those angles bisect each other

also not sure how the parts are equal

maybe im misunderstanding?

anyone?

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[sleek quest]

anyone please??

^^^^

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[sleek quest]

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[sleek quest]

.reopen

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✅

[sleek quest]

^^^

[snow obsidian]

What have you tried yet

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[sleek quest]

im not sure what to even do

[snow obsidian]

Do you know what is congruency of triangles ?

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[runic bloom]

studying for a calc ab exam and I haven't seen this exact kinda thing in my notes, but just based on what my teacher has showed in FRQ problems, I "created" this little formula
i just wanted to validate that this is true?

[runic bloom]

$p(c) = p(a) + \int_{a}^{c} v(x)$

[glossy valve]

Kihei

[runic bloom]

where (a, p(a)) is an initial value

idk ive seen this kinda question in frqs a lot

asking p(something)

and then velocity functions given

and an initial position

[fast peak]

in general $f(c) = f(a) + \int_a^c f'(x) dx$ for every differentiable function $f(x)$

[glossy valve]

Denascite

[runic bloom]

okok

tysm

it's weird that this was never explicitly stated anywhere in our notes lol

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[fast peak]

.reopen

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✅

[fast peak]

well it follows quite easily cause $\int_a^c f'(x)dx = f(c)-f(a)$ just by the fundamental theorem of calculus

[glossy valve]

Denascite

[fast peak]

so maybe they didn't think it was worth mentioning

@runic bloom

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[runic bloom]

ohhh

right

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[final topaz]

Can get help 7c

[final topaz]

thanks

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[brave lantern]

matrix transformations

[brave lantern]

letter n)

i don't have an answer sheet and need someone to check if my answer is correct

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[dense edge]

How would I enter the top 2 answers correctly as sqrt values?

[devout valley]

Remember the double angle formula for cos(2t) in terms of cos(t) for the first one

For the second, use the fact that the angle is where it is to find sin(t) then double angle formula for sin(t)

[light sonnet]

How did you solve the first two?

Like do you have your work?

[dense edge]

To be honest I'm lost with this one

I'm gonna start over

any suggestions for a video to watch?

[light sonnet]

Idk if this is helpful https://www.youtube.com/watch?v=Pka2liCES_4&ab_channel=utexascnsquest

[dense edge]

ty 🙂

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[torn jolt]

https://en.wikipedia.org/wiki/Particular_values_of_the_Riemann_zeta_function#Even_positive_integers

[hollow zenith]

thanks!

[hollow zenith]

just found this https://arxiv.org/pdf/math/0609775v4.pdf

[vivid aurora]

both are toby

name sounds same

[hollow zenith]

Its still an open problem lol

[torn jolt]

.yeah, a lot of things to do with riemann is open

[hollow zenith]

I just wonderd why 1/n^3 shouldnt be a multiple of pi^3 then

it would fit in the pattern

[torn jolt]

the evens are multiples of pi^n due to bernoulli (I dont think its too hard of a proof)

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[torn jolt]

but odd ones are much harder

[hollow zenith]

I only understand like 20% of this paper

[tidal swan]

How mathematical integrals work?

[clear lily]

which one 🤓

its basically you sum the area of a bunch of rectangles

you approximate the area by rectangles

and then you make the approximation exactly accurate by taking a limit to infinity

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[autumn sierra]

I need help on the bracket one

[silk flame]

What have you tried

[autumn sierra]

Only the first one

[thick minnow]

Show your work

[autumn sierra]

I didn't do any working out

[silk flame]

That’s what I meant by “what have you tried”

[golden furnace]

expanding the binomial squared is a start

[late fable]

Yes

[thick minnow]

Do you have any idea on how to approach the problem or are you clueless?

[late fable]

Actually

[late fable]

You don’t have to do that

[autumn sierra]

I'm clueles

[thick minnow]

Alright, do you know mathematical induction?

[late fable]

Is induction necessary?

There’s no need for it

[torn jolt]

i don't think induction is necessary

[rose rain]

sure you can try considering 2 cases instead, n being even and n being odd

[golden furnace]

lots of way to do it

[late fable]

No

[rose rain]

induction is easier tho

[flat mural]

Nah

[late fable]

Is 2n+2 even

2n+1 is odd

[torn jolt]

you just need to use the knowledge that an even number multiplied by any number odd or even is even

[thick minnow]

That is true but it is easier and more systematic

[late fable]

Yes

[flat mural]

It can be done in two seconds without induction.

[late fable]

Yes

[rose rain]

proof?

[late fable]

2n+2 is even

Even ^2 is even

[autumn sierra]

Can u explain how they got the answer then

[torn jolt]

if you quickly expand it, it becomes 4n^2+6n+3, you know it's odd bc 4n^2+6n has to be even

[flat mural]

||2n + 2 is even => (2n+2)² is even
2n + 1 is odd => (2n+2)² - (2n+1) is odd||

[autumn sierra]

H ow is there 8n

[rose rain]

and now you have left this unproven

[late fable]

They expanded the binomial

[golden furnace]

I don't think this paper asks for a formal all-inclusive proof

[late fable]

They factored out a 2 from as many terms as possible

[golden furnace]

seeing as the questions are rather "basic"

[late fable]

Very easy to prove

[rose rain]

this is a fair point

[torn jolt]

an even number x even number = even number is not really necessary to be proven

[thick minnow]

There's multiple ways to do it, one using mathematical induction and another as written by Silfer

[flat mural]

Even number * any number is even without needing any justification, stop hypocrisy

[golden furnace]

hypocrisy is rather rude

[flat mural]

Indeed

[autumn sierra]

Ok thx I definitely understand the whole thing

[flat mural]

I try to find another word but I dont know it in english

Sorry for that

[golden furnace]

oh, it's okay

[thick minnow]

It's not a hypocrisy, you have to prove anything that you're not already taught

[golden furnace]

anyway

[rose rain]

you can prove it, but we should move that to #math-discussion if you want to talk about it since it will be offtopic

[golden furnace]

seems that the situation needlessly escalated

[thick minnow]

Good, let us know if you get stuck

[rose rain]

I will retract my comment of induction being easier, it's not in this case

[autumn sierra]

Can u help me understand the graph one

[rose rain]

do you know how graph transformations work?

[thick minnow]

Is that the shifted graph one?

[autumn sierra]

Should I watch a video about it

[autumn sierra]

Yes

[thick minnow]

I mean it's not hard if you think about it. Like say you have value y0 = f(0) which is f(x), x = 0

[autumn sierra]

Ohhh ok

[thick minnow]

Now for f(x+1), to get the same value of y0, you'll need x=(-1) cause f(x+1) = f(0) = y0

So, basically everything needs to be adjusted by 1

Thus the whole graph shifts left by 1

[autumn sierra]

Ok I understand how about the bottom one

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[hollow zenith]

,rotate

[golden furnace]

$\frac{\left(3\sqrt{2}\right)^2}{6 + 3\sqrt{2}}$

[glossy valve]

biggboy

[hollow zenith]

you sure that its a plus?

[golden furnace]

nope

a bit blurry

wanted to confirm

[young storm]

It is

Yeah

[golden furnace]

is it an asterisk

[young storm]

This is correct

[golden furnace]

oh

confused the OP lol sorry

so I guess first rationalise the denominator

do you know how to do that

[young storm]

Not with multiple terms

[golden furnace]

how about the conjugate of 6 + 3√2

[young storm]

No clue what that means lol

[golden furnace]

hmm

do you recall the difference of squares

[young storm]

Yeah

Know that

[golden furnace]

if we were to "enlarge" the fravtion with 6 - 3√2 the denominator becomes a difference of squares right

it other words multiplying by (6-3√2)/(6-3√2)

[young storm]

I’m lost

I’ve got to go tho so thanks for the help I’ll come back later

[golden furnace]

sure

[young storm]

,close

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[rare pasture]

find a positive number so that subtracting the number itself from its triple cube gives the smallest difference

[golden furnace]

triple cube?

[rare pasture]

3a^3 i assume

[golden furnace]

27x³ or 3x³

I see

so you have 3x³ - x right

[rare pasture]

YA

is it 3x³ -x=y by any chance

[golden furnace]

sure

you can use a function such as f(x) = 3x³ - x

which describes the difference that we need to find the minumum of

notice that you can factor out a "x"

[rare pasture]

x(3x^2-1)?

[golden furnace]

yep

[rare pasture]

oh wait i think i got it

x=0 and 3x^2-1=0?

[golden furnace]

yeah I think so

[rare pasture]

gee thanks

[frosty geyser]

triple cube sounds like 3 times a cube tough, not 3 times x^3

[golden furnace]

you mean 3 times a all cubed

[rare pasture]

I believe I translated it wrong because in my language it should be 3a^3

though i will try both

[golden furnace]

27x³ - x is similar

[frosty geyser]

well then do that

[rare pasture]

(X³)³ ?

[frosty geyser]

3x^2 lol

[rare pasture]

But tripe cube not square

Wait im so confused

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[frosty geyser]

ah right, ok

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[spice orchid]

yes?

speak to us we are humans

[light sonnet]

I think they need help

[torn jolt]

i need help

[spice orchid]

!status

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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

[torn jolt]

I got an answer but I'm told it's wrong

[light sonnet]

Post your work

[torn jolt]

I got an answer but I'm told it's wrong

[hasty bramble]

For 7x + 44 = 24, x = -2. For 3x + 2y = 10, x = 5 and y = 0.

[light sonnet]

Don't give out answers

[torn jolt]

it was wrong

[full forum]

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

[light sonnet]

That's not work

Post your work

[hasty bramble]

Sorry

[torn jolt]

i cant im on pc and im doing on paper

[gritty rose]

work is something that you've written in attempt to solving the problem

type it here

[hasty bramble]

Use the systems of equations

[gritty rose]

7x + 4y = 24, ...

[weak marlin]

x = 4

[hasty bramble]

Wait what is the question asking though

[light sonnet]

No one asked you. If you look above, they attempted but got something wrong, hence the show work part

[hasty bramble]

Send that as well

[weak marlin]

y = -1

[light sonnet]

Don't give out answers

[weak marlin]

oh sorry

[light sonnet]

Use paint if you have a windows pc

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[frail geode]

Which variable would I remove first idk why I’m confused about this one

[worthy tree]

y or z are the easiest ones

[frail geode]

aok so I can do the first equation and the third and then 2nd and 3rd and that would work?

removing z variable

[worthy tree]

just multiply the third equation by -5 and add it the second equation to remove the variable

[frail geode]

aok thanks

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[worthy tree]

do the same thing to remove the z from the first equation

[frail geode]

ok first one and the third

after I remove the second and third

makes sense

[worthy tree]

multiply the third equation by 7 then add the result to the first equation

[frail geode]

Ty

[worthy tree]

anytime

[frail geode]

.close

I guess it’s closed already

[worthy tree]

yep

[unreal pecan]

js reopen it

[worthy tree]

he want to close it

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[small jewel]

How would I solve a problem like this

[small jewel]

God I hate android photo quality

[gritty rose]

any picture of a monitor is gonna be bad

[small jewel]

Lemme try to retake it

[slate zenith]

no its fine

[gritty rose]

Volume of cone is 1/3 volume of cylinder

https://www.mathsisfun.com/geometry/cone-sphere-cylinder.html

[small jewel]

0-0

Wait

If a cone is 1/3rd of a cylinder

Would I just add it 3 times then?

bruh y'all can't just leave me hanging like that : (

[gritty rose]

?

[gritty rose]

did you try using this in your problem

[small jewel]

Think so

since 96 is 1/3 of the cylinder

A full cylinder would be 288

Oh.....

I see..

Ok so uh

I ran into another question

Ik you can barely see the answers but

If I try to find the volume of the cylinder using the method I just used

It doesn't match up any of the answers

[full forum]

@small jewel Has your question been resolved?

[gritty rose]

show your math

[full forum]

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[rotund delta]

At the bulk food store, almonds sell for $7.20/kg and cashews sell for $9.20/kg. Find the mass of each type of nut in a 100 kg bin with an almond-cashew mixture that sells for $8.80/kg

[rotund delta]

idk how to do this question

[brittle steeple]

it'll be a system of equations

to set it up we need variables that represent the amount of almonds and the amount of cashews

[rotund delta]

so like let a=almonds?

c=cashews

[brittle steeple]

yeah

then try to look for the parts of the word problem that give you the equations

[rotund delta]

thats the hard part

I suck at word problem

[brittle steeple]

ah

so just thinking like if it was an english comprehension problem

what parts of the problem represent "constraints"?

[rotund delta]

we have to find the mass

omggg im so confussed

ya idk dude

ohh wait so 100kg bin

for each type of nut

so almonds are $7.20/kg

so $7.20x100?

[full forum]

@rotund delta Has your question been resolved?

[rotund delta]

no this guy left me💀

[dusty karma]

ok i think i can help

so we start with our variables, C for cashews and A for almonds

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[finite axle]

can someone help

[finite axle]

are these right

[kind siren]

theyre right you can turn it in

[finite axle]

i need a helper to make sure

[kind siren]

i got you my boy

[sly frigate]

No the second one is wrong

[finite axle]

<@&286206848099549185>

[finite axle]

oh

[tulip beacon]

Bro just called you stupid nicely

[sly frigate]

The third one is also wrong

[finite axle]

lol

[finite axle]

oh..

[cosmic canopy]

is this an assignment thats graded?

it sure looks like one

[tulip beacon]

Naa not to me

[finite axle]

nope

[cosmic canopy]

ok ok

[tulip beacon]

Looks like he just likes to do things in his free time

[finite axle]

im just asking if their right

[tardy verge]

no you don’t

[sly frigate]

Well they're wrong

[tardy verge]

helpers don’t always have the right answer, and they could be busy

[finite axle]

ok

[tardy verge]

we can still help

despite not being helpers

[finite axle]

what about these

[sly frigate]

Those are fine

[finite axle]

i think this is good

[sly frigate]

Those are also fine

[finite axle]

ok

this?

[sly frigate]

This isn't a test, isn't it?

It's just an assignment?

[finite axle]

yea its an assignment

[sly frigate]

Wrong

[finite axle]

oh

hmm

uhh

what about these

[sly frigate]

Seems fine

[finite axle]

ok

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[ancient idol]

can someone explain how I would factor and simplify this problem? i'm not sure what to do with the negative exponents

[sharp flame]

I mean you can still factor it with negative exponents

[sly frigate]

You group it by a common factor

[ancient idol]

i'm not supposed to have negative exponents in the answer

[sharp flame]

Write it as a fraction :P

[sly frigate]

Well if ur unfamiliar with negative exponents you can write is as a fraction

[ancient idol]

would i then just take out fractions like a normal problem without negatives

wait let me write it

[sharp flame]

Yeah

That's what you'd have to do

[sly frigate]

No

It's not 7(x-7)

It's just 7

[ancient idol]

i didn't multiply it yet cause i was wondering if i could pull out x+7

wait

i'm dumb

i really thought i had it this time but it still says it's incorrect, idk what's wrong

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@ancient idol Has your question been resolved?

[full forum]

@ancient idol Has your question been resolved?

[full forum]

@ancient idol Has your question been resolved?

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[arctic kernel]

how to solve it

[old hamlet]

Try putting the value of x as 0 in the equation first

[grave elm]

Doesn't work

I think he knows that

[old hamlet]

Mb

[arctic kernel]

yup

[covert wing]

It'll become indeterminate

[arctic kernel]

it gives ln2/0

[covert wing]

On x = 0

[grave elm]

Oh yes, you are right, sorry

[grave elm]

When you plug x=0 in it, it becomes ln(2)/0.

[old hamlet]

Can't think of any simplification either

[arctic kernel]

why are you repeating me

[grave elm]

Oh sorry, it was you

I am pretty sure it's undefined

[old hamlet]

In the unlikely event that the question is wrong

[arctic kernel]

I also feel same becuase answer is given ln2

[old hamlet]

There should be a 1 left in the denominator then I'd say

Can you verify the question from somewhere

[arctic kernel]

It is a online practise question

I have just pasted screenshot

[covert wing]

Wait

A min

Let's try a different thing

[arctic kernel]

no @grave elm

[grave elm]

Which one?

[grave elm]

oh well :/

[covert wing]

Uhm.

Kinda doesnt work but still

[arctic kernel]

.close

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[gloomy warren]

Number 8

How to get equation of straight line

[hazy wedge]

try to reform the second line to also be like L2=v1+t*vector2

then you have the origins basically given, and u can get the intersection by equating both line functions

[worldly drum]

@gloomy warren

[gloomy warren]

Thanks

Lemme read it rq

[worldly drum]

ok