help-23

[lean otter]

Why is it 10x+y??

[eternal carbon]

so let's say i have the number 53, which is made up of the digits 5 and 3

in this case, we have that 53 = 5 * 10 + 3

and, in general, any 2-digit number XY can be expressed as 10X + Y

does this make sense?

[lean otter]

Yeah, I get it so B and C can be 6 and 10

[eternal carbon]

10 is not a digit

the problem specifies that all variables are digits

this means integers from 0 to 9

[lean otter]

But that will make it 60+1=61?

[eternal carbon]

what are you talking about?

[lean otter]

I’m confused for the first one

[eternal carbon]

alright

can you convert the first problem into an equation?

[lean otter]

How??

[eternal carbon]

do you know what an equation is?

[lean otter]

Yes

Oh wait

Since so AB can be 15 right?

[eternal carbon]

i guess? but in general for these kinds of problems you don't want to just plug in values

[lean otter]

So C has to be any integer?

[eternal carbon]

.

digit, not integer

do you know what a digit is?

[lean otter]

Yes

Basically a number

[eternal carbon]

not quite

a digit is one of these numbers:
0
1
2
3
4
5
6
7
8
9

[lean otter]

Oh so from 0-9?

[eternal carbon]

😔

[lean otter]

Sorry 😭

I’m terrible at math

[eternal carbon]

but that's good you got it now 👍

[snow escarp]

me too, you got it dont worry

[lean otter]

This obviously is so simple but I really don’t get the idea

[eternal carbon]

the main idea for problems like this is that you can express numbers in terms of their digits

like

[lean otter]

Oh so anything from 0-9? Meaning that C and B can be 8 and 6?

[eternal carbon]

in theory yes

[eternal carbon]

in the number 53, can you identify the tens digit and the ones digit?

[lean otter]

5 is tens and 3 is ones

[eternal carbon]

yep

so this means that 53 can be written as ten times 5... plus 3

now let's say i have the number XY, can you identify the tens digit and the ones digit?

[lean otter]

X is tens and Y is ones

[eternal carbon]

yep

[lean otter]

Meaning that A is tens?

[eternal carbon]

in this problem yes

[eternal carbon]

and similarly, this means that XY can be written as ten times X... plus Y

algebraically, we say this as 10X + Y

because the 10X means 10 times X, and then we add the Y digit

does this make sense?

[lean otter]

Yeah so it’s the same as A times ten plus B?

[eternal carbon]

that's right

[lean otter]

How about C

[eternal carbon]

in this problem, the C is something else

for the first problem, do you have an idea of how to start converting it into an equation?

[lean otter]

No, but as you said 10x+y?

[eternal carbon]

right so that's when we have a number that looks like XY

[lean otter]

Is there like a time out here?

I have to go eat dinner

I appreciate the help tho

[eternal carbon]

that's fine! although i'm not sure if i'll still be here

[lean otter]

Thank you! I will try to answer it

.close

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[crude lynx]

Topic: Volume of a solid revolving around a line that's not an axis

[crude lynx]

I need help understanding d

I understand the visually what's happening, and where sqrt(y) came from, but not how they set up the expression

mainly I don't get how they got 2-sqrt(y)

[pure agate]

It is the length of the radius.

You always want a positive value so you do that by subtracting the smaller value from the larger value. In this case, the larger value is the axis of rotation, x = 2 and the smaller value is x = sqrt(y).

[crude lynx]

oh, so no matter where the line of rotation is, I always do the larger - smaller value?

[pure agate]

Correct.

So if the curve was on the right side of the axis of rotation, you would subtract the axis of rotation from the curve.

Such a simple explanation that is often never mentioned in books and classes. 🙂

[crude lynx]

thank you for the explanation! makes a lot of sense

I feel though in my mind 2- sqrt(y) would be this yellow part with the sqrt(y) being the green ..?

[pure agate]

One moment, let me make a graph.

[crude lynx]

thank you

[pure agate]

https://www.geogebra.org/classic/qc9hrrfu

[crude lynx]

ooh yeah radius i see

[crude lynx]

ok forget this question I get this now

[crude lynx]

thank you so much for your help

[pure agate]

yw

[crude lynx]

.close

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[timid scroll]

How do you do a stupid question like this

Its just annoying

So you sketch it roughly

Or i guess you just find the Y axis

For both of them

And you take the lowest

[desert pasture]

sketch 5-2x for x<1 and x^2+3 for x>1

[timid scroll]

I got a rough one

Probably like this

Or do I have to make it very very acurate

[desert pasture]

The function is discontinuous at x=1

[timid scroll]

Yea

But for the x^2 is starts at 1

[desert pasture]

x^2+3

not x^2

is what you've been given

[timid scroll]

ok so I guess I have to find y=? when x = 1

to make it more accurate

[desert pasture]

are you familair with the concept of limits?

[timid scroll]

integration?

yes

or differentiation was it?

[desert pasture]

differential calculus . Try finding the left hand and right hand limits

you'll see the LHL is 3 and the RHL is 4

[timid scroll]

how did you get 3

-2 and 2x no if differentiate

Ok i got it

thank you

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[left gyro]

you can go through the first couple of factorials to see which factorial fits this condition

yes

[slender pendant]

Now just prove its not the case for others

27 is 3³

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[slender pendant]

You still have to prove thats the only number that works....

How?

True and did you prove a cube cant end with 3?

[safe radish]

✅

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[lean otter]

Why does the shadow look like that tho…. Just ignore pls

<@&286206848099549185>

[frozen marlin]

!15m

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[lean otter]

Anyone? 😓

[radiant crypt]

what hace you tried

[lean otter]

Ur pfp is cute and funny btw.

I don’t where to start

I only know that it’s 7b+2

[radiant crypt]

let's just forget about the bottom part and work normally

[lean otter]

Ok

[radiant crypt]

what do you get at each digit if you apply this method of multiplication

[lean otter]

Sorry?

[unique salmon]

,work

man damn it

do u have any working?

[lean otter]

??

[radiant crypt]

I mean just working out
AB4
x 7

[unique salmon]

was it show

,show

ion remember

[radiant crypt]

@unique salmon they don't

[unique salmon]

oh alr

[lean otter]

Yeah

It become 4*7=28

And idk after that

[radiant crypt]

ok we got the first digit at far right

let's move to second digit now

[lean otter]

Yeah 7B+2

[unique salmon]

instead of that

we know that AB4 X 7 = B0B8

[lean otter]

Yes

[unique salmon]

try bring the right hand side to the left hand side

[lean otter]

Ok

[radiant crypt]

yah I don't think ik what im doing

[unique salmon]

what do u get?

[timid scroll]

wait no

[terse lichen]

why not just try all the digits 0 - 9 and see which one works

[unique salmon]

i mean

if u do equate it

u get A7=B0

oh wait

hold on

A7 = BO2

sorry, my fault

is it b o 2 or b zero two

[lean otter]

I don’t get it

I will just try 0-9

[unique salmon]

its bo2, right?

[terse lichen]

A and B are digits

not variables

[timid scroll]

(7A00) + (7B0 +2)= BOB0 I think

[unique salmon]

OH

ALR

because i got the value of A as Bo2/7

[terse lichen]

we're not playing with variables here

[unique salmon]

dunno if it helps

[lean otter]

I’ve been stuck in this for too long is there a way?

[terse lichen]

we're trying to find digits

[unique salmon]

hmm

yeah

true

[terse lichen]

ok so we know the carry after 4 * 7 is 2 yes?

[lean otter]

Yes

Since 28

[terse lichen]

so now we're trying to find a digit that when its multiplied by 7 then add 2 we get its right most digit

and tbh idk any other way to do this than brute force 0 to 9

[lean otter]

I will try

Thanks

[frozen marlin]

it's easy...

7x + 2 = x

in mod terms

of 10

so 6x is congruent to 2 mod 10

-2 i mean

[radiant crypt]

i have never used mod

[frozen marlin]

eh

it's 8

[lean otter]

But that becomes -2

[frozen marlin]

yes yes

it's 6x is congruent to -2 mod 10

x is 8

ez

[terse lichen]

3 also works no?

[frozen marlin]

mhm

[lean otter]

What’s going on??

[terse lichen]

man i really should learn modular arithmetic

[frozen marlin]

we're figuring out B

[terse lichen]

eventually i will, maybe

[frozen marlin]

it's fun actually

try brilliant

they have an insanely good course on it

[lean otter]

Yeah

[frozen marlin]

so... we figured it out

[lean otter]

So 7x+2=8??

No

7x+2=x??

[frozen marlin]

no.

what?

no-

@lean otter i'd assumed you knew modular arithmetic

[lean otter]

Or b??

[frozen marlin]

this stuff usually comes up in that.

[frozen marlin]

what???

no-

wh-

forget it

b can be either 8 or 3

now figure out which one it is

[lean otter]

How do I find that tho

[frozen marlin]

...

what kind of a question is that

[lean otter]

Modular Arithmetic??

[frozen marlin]

no!

oh my god

[unique salmon]

relax 😭

[lean otter]

My bad

[radiant crypt]

modular arithmetic, it involves mod operator which gives reminder of division

i think

[frozen marlin]

yes

[frozen marlin]

sighs
it gets annoying it's just basic logic

[unique salmon]

people take time indeed

[lean otter]

Alright then. I guess I shouldn’t ask

.close

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[frozen marlin]

no don't.

@lean otter wait.

[radiant crypt]

[timid scroll]

Wait open

Wait im doing it

[frozen marlin]

all i want is for you to TRY instead of just asking and asking

[timid scroll]

.reopen

[frozen marlin]

that's not how it works

[radiant crypt]

only op can reopen

[timid scroll]

Can tyou just say 10, 100 untis A and B

[frozen marlin]

what?

ok i've solved

[unique salmon]

man

[frozen marlin]

B is 3

A is 4

[unique salmon]

😭

[timid scroll]

how

[unique salmon]

yea

[frozen marlin]

she wasn't trying.

the point of the server is to TEACH

not hand out answers

[terse lichen]

yeah i got the same thing though i got it through brute forcing

[timid scroll]

How did u calc Ren

[frozen marlin]

you don't need to do that

[frozen marlin]

basic logic

mod for b

[timid scroll]

Can you do without mod

[frozen marlin]

yes i mean basic logic

[lean otter]

When did I ever ask for answers lmao 😭

[frozen marlin]

@lean otter you're back?

[unique salmon]

is b=2 or b=3

which one

[frozen marlin]

yk what i seem to be ruining this

imma just go

[frozen marlin]

3

[unique salmon]

howd u get 3

can u explain it

[frozen marlin]

because

4 x 7 = 28

now that carried over

so 7B + 2 mod 10 = B

[unique salmon]

mhm

uh

[frozen marlin]

i mean is congruent to B mod 10

[unique salmon]

ive never

relaly done

[frozen marlin]

basically same remainder

[unique salmon]

mod

[frozen marlin]

when divided by 10

so same unit digit

[unique salmon]

arithematic...

or arithematic at all.....

...

[frozen marlin]

@unique salmon it basically means, in this context, same unit digit

[unique salmon]

mhm

oH

oh

OH

OK

MHM

[frozen marlin]

@unique salmon normal arithmetic is addition, subtraction, etc

anyway

[unique salmon]

oh

right

mb

[frozen marlin]

transferring and stuff

we get -2 and 6B

[unique salmon]

mhm

mhm

[frozen marlin]

so basically 6B ends with 8

so B can be either 3 or 8

so 3038 or 8088 could've been the answers

[unique salmon]

OHH

RIGHT

WOW

[frozen marlin]

now i knew 8088 isn't divisible

[unique salmon]

I GOTTA DO MATHS AGAIN

mhm

[frozen marlin]

lol

so 3038 was the obvious choice

we know it ends with 34... so 4 for the first digit

[unique salmon]

oH

got it

thank u

cutie

:3

[unique salmon]

wait what undergrad are u

[frozen marlin]

??

[unique salmon]

what undergrad course are u doing

[frozen marlin]

calculus 2

[unique salmon]

wow

[frozen marlin]

eh

[unique salmon]

can u help me with my highschool calc

later

[frozen marlin]

not actually doing ungrad

[unique salmon]

i really wanna pass

[frozen marlin]

im self taught

[unique salmon]

oh

[frozen marlin]

i mean sure ig?

[unique salmon]

wow

[unique salmon]

can i add u

[frozen marlin]

eh its a hobby

[unique salmon]

woohoo

[frozen marlin]

you already did lmao

[unique salmon]

oh i did

SORRY

I FORGET

[frozen marlin]

xd

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[lime dust]

What have you tried

[jovial ore]

listen

can i oay you 20 dollars to help me with around 80 questions

full like 3 hour call tho

[lime dust]

No

[jovial ore]

alright thanks

.close

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[lean otter]

Hello

[lean otter]

I want to know why did ABsintheta was used to calculate the vector product

[lean otter]

My failed solution

[rustic goblet]

that’s how you calculate the magnitude of the cross product

[lean otter]

I want to know why that formula was used

It doesn't makes sense

[rustic goblet]

Oh as in, why we calculated the cross product?

or why that formula works?

[lean otter]

The latter

Why that formula works

[rustic goblet]

I’m pretty sure (someone correct me if I’m wrong) that |a||b|sin(theta) is the definition of the cross product actually

At least, the magnitude of it

[lean otter]

Yes, but what does the definition say ?

I remember it says the cross product is perpendicular to both of the vectors.

I still dont get it why the formula works

[rustic goblet]

yes, but the formula is just to calculate the magnitude of that vector

the cross product of two vectors returns a vector which is perpendicular to both of the original vectors and has magnitude |a||b|sin(theta)

[lean otter]

How does doing 6 * 4 * sin30 yield me the magnitude of the third vector

[rustic goblet]

.

[lean otter]

Why/How does it have a magnitude of absin(theta)

[rustic goblet]

the magnitude is the same as the area of the parallelogram spanned out by having the two vectors as sides

[rustic goblet]

I actually don’t quite know, it seems to simply be a definition

There’s very likely a motivating reason as to why it was defined as it was, but I unfortunately don’t know it

[lean otter]

Why did they define it that way ?

[rustic goblet]

.

[lean otter]

Okay do you know anyone who might know ? I am new to this server

Or can you query the web, I tried and failed

[rustic goblet]

https://math.stackexchange.com/question

Oh wait

https://math.stackexchange.com/questions/1941044/why-is-cross-product-defined-in-the-way-that-it-is

There we go

[lean otter]

Ah, a rabbit hole

[rustic goblet]

https://math.stackexchange.com/questions/62318/origin-of-the-dot-and-cross-product

Perhaps this is useful too

[safe radish]

@lean otter Has your question been resolved?

[safe radish]

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[bleak remnant]

so why must n be an even number?

and how do i show q(x) is postive for some x

do i just assume a polynomial and and some x and substitute

<@&286206848099549185>

[frozen marlin]

!15m

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[bleak remnant]

ok XD

[safe radish]

@bleak remnant Has your question been resolved?

[safe radish]

@bleak remnant Has your question been resolved?

[bleak remnant]

<@&286206848099549185>

[bleak delta]

@bleak remnant it is necessary to prove that the number n must be even

For example, let it be x²

x² is always greater than 0

But if we add a single degree term next to it like "x"

x²+x it must fall below 0 within a certain range

If we prove that whenever there is any odd degree, we prove that it has even degree

Because we understand that it cannot be odd

[bleak remnant]

so u mean we need n to be even for q(x) to be positive

[bleak delta]

yes

to p(x) to be positive

let me fix it

[bleak remnant]

isnt p(x) postive like that's a given i am a bit confused

[bleak delta]

But we will understand from here that this is a even degree

Doesn't he want us to prove it anyway?

I'm thinking about how we do this

[bleak remnant]

ohhhhhhhhhhh

my mistake

i didnt read that p(x) was of degree n

[bleak delta]

np

[bleak remnant]

i thought its just a number in the sum

yeah n must be even for p(x) to be positive it makes sense

[bleak delta]

ok but not enough

[bleak remnant]

so if i was in that exam

how would i show that n must be even

[bleak delta]

I am thinking about it

[bleak remnant]

if u need the full question

its from the step 2 2023 exam

so it is kind of a journey

(i)(b) is simple i did it on my own

[bleak delta]

understand

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@bleak remnant Has your question been resolved?

[safe radish]

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[jovial nebula]

I am trying to find the max value of this graph. Here is a screenshot of it in GeoGebra, im pretty sure i havn't made any mistakes yet but i don't know how i can derivate the graph with a, b and c

[jovial nebula]

If you don't understand my questions i can try to explain it better

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@jovial nebula Has your question been resolved?

[jovial nebula]

<@&286206848099549185>

[halcyon marsh]

Is there any limit on a,b,c

Like I not know exactly I have never try it but like when we increase c function is increasing we can put maximum value of c ,maybe this can help

[jovial nebula]

Limit for a is 2-8 , b is 0-500, c is 0-300

[halcyon marsh]

Ya put c=300

Then it is 2 variable function

Then we can solve by partial dervitatives

[jovial nebula]

Ok

I don't really know how to solve thos either

[halcyon marsh]

We now get function in a and b right

Partial dervitative function by a and b

Put both equal to zero get the points

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[wild ore]

which one is right

im 99% sure the arctan(1/x) one but idk how to get to that ansswer

[eternal carbon]

they’re online calculators

both are correct

[wild ore]

but arctan(x) does not equal -arctan(1/x)

[eternal carbon]

correct

[wild ore]

right cus arctanx+arctan(1/x)=pi/2

[eternal carbon]

it equals pi/2 - arctan(1/x)

[edgy fjord]

But the c is different

[eternal carbon]

and both of these things have the same derivative

therefore, they are both valid ways of expressing the integral result

[edgy fjord]

The +c in both case is different

[wild ore]

ahhhh

interesting

i was trying to do a harder integral and was trying to find out why i was wrong

turns out its just really weird

ty guys

[edgy fjord]

What's weird

[wild ore]

well nah just interesting

cus of the 2 answers

but ty

.close

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[rough citrus]

hey, im revising some trigonometry and i was watching a youtube video which is illustrating some trig concepts, im having some trouble understanding this part. could someone help me understand?
d is the tangent line and the 1 is the radius of the circle/hypotenuse of the triangle to the left, just to be clear hehe

[rough citrus]

i dont see how that relation holds true

[safe radish]

@rough citrus Has your question been resolved?

[urban yew]

see the bigger triangle , the other angle apart from theta would be 90- theta
tan 90- theta will be 1/d
since tan 90- theta = cot theta
cot theta = 1/d
which means tan theta = d/1 and tan theta also equals sin theta /cos theta

thats why sin theta/ cos theta = d/1 here

[rough citrus]

i dont understand what you mean by the bigger triangle

the both green ones combined?

or do you mean the triangle that is formed if we extend the tangent until it meets the y axis

[safe radish]

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[quaint aspen]

am not sure what how to go about solving this problem

[slender pendant]

Do you know the power rule?

[quaint aspen]

i do

[empty gyro]

,rotate

[quaint aspen]

am not sure which solution is right

<@&286206848099549185>

[empty gyro]

$\pi^{18}$ is just constant

[flat frigate]

SWR

[quaint aspen]

oh

[empty gyro]

So it would be the second one

I see the confusion, but yeah, you don't need to do power rule on $\pi^{18}$ itself.

[flat frigate]

SWR

[quaint aspen]

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[humble sequoia]

I need help

[humble sequoia]

Number 2

[hearty egret]

[sinful basalt]

What are you stuck on with number 2?

[humble sequoia]

i'm not stuck

just got a different answer

and i put the same equation in chat gpt

it's giving me a different answer

[patent flame]

Chatgpt is often wrong

[sinful basalt]

Don’t use ChatGPT for math, simple as

[hearty egret]

because chat gpt sucks lol

[humble sequoia]

lmao

but first

Is that correct for number 1?

[plucky elk]

Isn't it the solution the book gave

Why would you think that's wrong

[hearty egret]

you should compute f'(2) instead of f'(4) because $\frac{d f^{-1}(y)}{dy}=\left[\frac{d f(x)}{dx}_{|x=f^{-1}(y)}\right]^{-1}$

[humble sequoia]

it's not a book

[hearty egret]

1

[humble sequoia]

it's my lecturer's notes

[flat frigate]

everg

[humble sequoia]

cause why did he use f'(4) instead of f'(2)?

[plucky elk]

Yes ever pointed it out

[plucky elk]

If you already knew, why didn't you say so

[humble sequoia]

i knew but i wasn't sure

that's why i'm asking if it's correct

[plucky elk]

Then say it next time and save everyone some time

[eternal carbon]

this sounds a bit critical

they asked a simple yes-or-no question

[humble sequoia]

exactly

[humble sequoia]

but sure i'll do that next time

[plucky elk]

They already had an idea and didn't say so. Could have saved everyone the time if they just said it from the start

[plucky elk]

That's part of the "show work" here

[humble sequoia]

Oh okay

So can I get help with 2?

How do i get the equation?

I already differentiated and I got -2e^-2x - 27x^2

[safe radish]

@humble sequoia Has your question been resolved?

[humble sequoia]

.close

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[lean otter]

i need help

[ionic dove]

send the question

[lean otter]

how am I wrong here

arent I suppose to put the left side or then in the middle or then on the right side or

[inner parrot]

it says or

[drowsy moss]

the or means you need only one of those things to be true at a time

[inner parrot]

meaning either inequality can be true

[lean otter]

what does true mean

?

[lean otter]

What does true mean?

For this equation

[drowsy moss]

the value of x you pick makes either
11x + 4 < 15 a true inequality
or
12x - 7 > -25 a true inequality

as in, it is correct

[safe radish]

@lean otter Has your question been resolved?

[lean otter]

No

[lean otter]

How do you find if its true

can you show me

an example

and I think ill be good

[drowsy moss]

like, if x = 2
11(2) + 4 = 26 < 15 is false
but
12(2) - 7 = 17 > -25 is true
so 2 is a solution value for x because it makes one of the inequalities true.

similarly, x = 0
11(0) + 4 = 0 < 15 is true, so x = 0 is a solution because it makes one of the inequalities true

I don't need to check the second one, because this one is already true.

[lean otter]

@drowsy moss

Yeah

So can you solve it

though too

and explain when you solve it

not just write the whole equation

[drowsy moss]

solve the first inequality: 11x + 4 < 15
solve the second inequality: 12x - 7 > -25
tell me what you get.

[lean otter]

ok

11x/11 | 18/12x

now explain from here on forward

Because I have some problems

that dont always get the same format of the answer

@drowsy moss

[drowsy moss]

what are those numbers?

[lean otter]

from the inequality

problem

both problems

[drowsy moss]

11x/11 isn't a solution. its just x

[drowsy moss]

how did you get these answers?

[lean otter]

okay

x=1

x=18/12

true? @drowsy moss

this is compound inequalities by the way

[drowsy moss]

no, x doesn't =1

solving 11x + 4 < 15 gives you x < 1

[lean otter]

oh yeah

not with the equal

my incorrect

let me solve the last part then can you explain please

[lean otter]

x<18/12

[drowsy moss]

something went wrong with that one

that's not correct

[lean otter]

x<-32/12

I think youre incorrect @drowsy moss

Due to the fact

its correct

re check it

because +7 on both sides

then after

x<18/12

[drowsy moss]

x =-10 is less than 18/12
12(-10) - 7 =-127 is not greater than -25

[lean otter]

woah

were are we getting the -10 from

[drowsy moss]

what do you get when you add 7?

[lean otter]

18

[drowsy moss]

you said x < 18/12 is the solution to the inequality. This means I can pick any value smaller than 18/12 for x and the inequality should be true.
I chose x = -10

[drowsy moss]

what are you adding 7 to?

[lean otter]

to -25

-18

oh

I see

its a -18

-18/12

okay go on

can you give me the definitions of no solution and all values of x are solutions

[drowsy moss]

the next problem is that your inequality changed direction for no reason

[lean otter]

can you show me a example

[lean otter]

of these both and a definition

@drowsy moss

sorry for pinging you

I just need to really hurry up

.close

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[simple drift]

is this answer correct?

and the steps?

[desert pasture]

looks right to me

don't take my word for it though

[simple drift]

oh then I will wait for a second opinion..

<@&286206848099549185>

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[devout shale]

I am trying to understand this solution

and so far everything above the green line makes good sense

but I'm not sure about the remaining part

T(vk)=bkw1+....bnwn sure because it has to map to some element of W which can be expressed as the basis vectors times constants b_i

but then the part where it redefines it to be vk=vk-bkv1

T(vk)=T(vk-bkv1)=0w1+....+bnwn

is the only 0 attached to the w1 basis vector? So our M(T) will have just zeroes in the first row?

the rest of the b_iw_i+...b_nw_n still remain possibly non-zero?

nvm I think I get it

🐺

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[whole coral]

hey i need some clarification on this

[safe radish]

Please don't occupy multiple help channels.

[whole coral]

ok now i’m lost omgosh 😭😭

[plucky elk]

!1c

[safe radish]

Please stick to your channel.

[plucky elk]

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[brazen parrot]

hello

[brazen parrot]

how does this prove that x+y/2 is greater than sqrt(xy)?

it only prove dat (x-y)^2 is greater than or equal 0?

[median vigil]

the point that the example is making is that it doesn't prove that

[ruby bolt]

AM GM

[brazen parrot]

hmm it doesnt but i worked backwards and it does

which is wat the thingy told me tod o

oh.

i see.

hahahahahahahah

ok thanks anyways 👍👍

[median vigil]

working backwards isn't the same thing, though. even though the equations are the same, it's different to say that the equation below shows the equation above rather than the other way around

[brazen parrot]

is this wrong then

[median vigil]

you should probably add arrows to show which statements imply which other statements, but the proof is valid

[brazen parrot]

what do u mean arrows?

can u please teach me how to use them

they are confusing to me

these?

[median vigil]

yes

[brazen parrot]

what is am gm inequality?

[ruby bolt]

Well what you are proving is am gm inequality

I would suggest using cauchy induction

[brazen parrot]

what is cacuhy induction?

[median vigil]

the left side is called the "arithmetic mean" of a and b, and the right side is called the "geometric mean" of a and b. the inequality is called the "am-gm" inequality for that reason

[brazen parrot]

wait

so i just put an arrow

on every line

[median vigil]

in this case, yes. you may also want to add a small statement of why one equation being true means the next equation is also true (if it isn't obvious)

[ruby bolt]

did you do this on your own?

[brazen parrot]

i have a tutor next to me

LOL

but im scared hes gonna scream at me

[ruby bolt]

bruh

[brazen parrot]

but i undersatdnw aht he did

i did it for the next questions too

[brazen parrot]

what...

am i supposed to know it ...

i started proofs yesterday

[ruby bolt]

Well its been used here Cauchy induction

[brazen parrot]

idk the name it just makes sense lol

working backward is cauchy induction?

[ruby bolt]

I would suggest having a discussion with your teacher rather than being here.

He would really help you and not scream at you

[brazen parrot]

no.

he is chinese

...

i quit in grade 5 because he made me cry

but then my mum forced me to have him again

[ruby bolt]

Where you from?

[ruby bolt]

He must be very good at math

[brazen parrot]

australia

HAHAHAHA

[brazen parrot]

he is..... he teaches calculus at a university

[ruby bolt]

He must be great

Look you have Wikipedia or your tutor whom you can discuss with.

[brazen parrot]

NO HES SCARY

i need to find a young tutor

😭

[ruby bolt]

How old are you?

[brazen parrot]

15

why?

[ruby bolt]

You could just use wikipedia etc to learn stuff,

[brazen parrot]

i was taught my whole life wikipedia can lie

[ruby bolt]

whut

Use AOPS

Brilliant

[brazen parrot]

what is this

another wikipedia?

[ruby bolt]

instead of asking use the web browser

[brazen parrot]

ok i quit proofs im movng onto vectors

.close

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[pliant fossil]

not sure where i went wrong

[pliant fossil]

the guide video says "multiply through to clear the fraction)", where did he pull 24 from??

[upper rivet]

24 is the smallest positive number that you need to multiply both sides to clear fractions

notice that the RHS of the equation is effectively ( .....)/24 when you take the LCM

[upper rivet]

you've written +83/72 here and -ve in your website

[pliant fossil]

ve?

[upper rivet]

negative (-ve)

its a common abbreviation

[pliant fossil]

ohhh i see

[pliant fossil]

fixed it thank you. i honestly cant visualize how to "clear" those fractions with the lcm. of 3/4 and 5/3?

i just had the signs flipped haha

just ran everything through my calculator, maybe made a mistake somewhere, guess i dont need to clear the fractions if i can multiply straight out

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[pliant fossil]

hello, how would I do the third one? I substitute 3r for r but dont know how to get rid of the r

[plucky elk]

You don't get rid of it

r = r

[pliant fossil]

so i break it down until r is left?

not sure where to go next

[plucky elk]

You can simplify a tiny bit, but that's the answer

[pliant fossil]

okay ill try that

got it

thought i had to distribute pi itself and not 4/3pi together

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[dark marlin]

i don't understand the process

so must i find something where

f(-3) < 1/2 < f(3)?

[median vigil]

yes, or the other way around

[dark marlin]

ok

wouldn't that just be 3/x?

since -3 < 1/2 < 3

or do i have to think about continuity

where that would be continuous within -3, 3

limiting my options to only c and e

the polynomials?

[median vigil]

it would need to be continuous, yes

although the polynomials aren't the only functions that are continuous on the interval

[dark marlin]

hmm

would the square root be continuous

since -3 ^2 = 9

no neg

but that wouldn't work since same outputs

for -3 and 3

well i got it right

thank you

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[mellow mountain]

how would i complete this?

[safe radish]

@mellow mountain Has your question been resolved?

[mellow mountain]

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[sleek hornet]

for 2e why is it only one answer

what about 1-i

<@&286206848099549185>

[frozen marlin]

!15m

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[sleek hornet]

o

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[next oar]

this is what i tried to get a but i don't have much confidence

like i don't know what form the equations are suppsoed to take

[safe radish]

@next oar Has your question been resolved?

[vague urchin]

I'm guessing the ball is moving in a circle while the mass is restricted to the y-axis?

[next oar]

yes

i sorta thought the equation for the mass would be y = sint or something

but it is accelerating down

[vague urchin]

There's a lot of different kinds of motion that would enable the mass to meet the ball at the bottom

I'm guessing the question's assumption is that the mass is undergoing constant acceleration

[next oar]

i think assuming constant acceleration

[vague urchin]

Okay, so given a unit circle, it needs to fall by 2 units (the diameter). I think we can assume it starts from rest. And since the ball has speed 1, it takes π seconds to reach the bottom (halfway around the circle)

So we can use x = x0 + v0t + 0.5at²

Have you seen something like that before

[next oar]

i don't think so

is that a physics thing

[vague urchin]

Yes

I mean if we're talking about accelerations, surely you've met the kinematics equations right?

[next oar]

true

ive forgot them

[vague urchin]

Okay well

Hm

[next oar]

but yeah i can see how this one would work

what about solving by finding the equation of the mass

[vague urchin]

This kinda is the equation of the mass

Its position as a function of time

[next oar]

ohh right

ill just plug it in and see what i get

[vague urchin]

Sure

[next oar]

i got similar answer to what i had in my working out

but there was a mistake in my working out

i think

[vague urchin]

So what do you get for acceleration in the end?

[next oar]

not sure

i got pi^2 on 2

[vague urchin]

Hmm

[next oar]

i mean my initial workiing out was wrong

[vague urchin]

Well assuming v0=0, we have x=at²/2

So a=2x/t²

And x=2, t=π

[next oar]

oh wait my bad

2/pi^2?

[vague urchin]

2*2/π²

Please open a new help thread

[next oar]

i forgot the half in the equation

[harsh dove]

Oh i'm so sorry

[next oar]

so its 4/pi^2

[vague urchin]

Yeah

Unless I'm missing something

[next oar]

thats roughly 4/9

i guess that seems in the ball park

i thank you for your assistance

[vague urchin]

Np

[harsh dove]

Hey can anyone help i'm new here i don't know anything

[next oar]

click the help threads underneath help forum

[safe radish]

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[mighty plover]

I got an answer for a question my teacher gave me, but I’m not confident about the answer. Could someone tell me if I made a mistake somewhere or if my work is correct

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@mighty plover Has your question been resolved?

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@mighty plover Has your question been resolved?

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[shrewd hedge]

im finishing this PA=LU factorization and im trying to match the solution of x to what im doing by hand but i cannot get the same result.

[shrewd hedge]

am i missing some steps?

[charred saffron]

Let me check

-y = -2
2*1 + g + 3ty = 0
1 - t + 3 = 6

The first equation is already in standard form.
The second equation is not clear since there are missing terms and it is not clear what "ty" represents.
The third equation has an error in the mathematical operations as 1 - t + 3 = 4, not 6.

[proper salmon]

A car track has six lanes. You have a task to find the four fastest cars out of 36. How many races would you conduct to find the fastest four cars?

[shrewd hedge]

?

[frozen marlin]

!occupied

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[frozen marlin]

@proper salmon

[charred saffron]

we would need 10 races in total

[frozen marlin]

@charred saffron not here

in their channel please

!topic

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[shrewd hedge]

im sorry but i do not understand what you're saying. this is an LU factorization or decomposition for linear systems.

you start with the system and decompose it in matrix form

[proper salmon]

The answer is 8 can Someone explain

[shrewd hedge]

go in your channel bruh

[frozen marlin]

@proper salmon like i said, occupied

[shrewd hedge]

<@&286206848099549185>

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[hardy lion]

whats your question

[full yarrow]

i got as far as understanding and doing like -1< x-2 < 1 and (x-2)(2x+1) but i don’t know what to do with the 2x+1

[lean otter]

i think he just posted his question

[full yarrow]

unsure how to proceed

[hardy lion]

what you can do is find the axis of symmetry of the parabola and make sure the extreme values are less than 7

[full yarrow]

how is that proved by the existence of |x-2|<1 ?

[hardy lion]

what if i told you instead to find the absolute minimum and maximum of 2x²-3x-2 on the interval (1,3)

[hardy lion]

basically this is just giving you an interval

[full yarrow]

well with calc id find the critical points and such but obv i cant do that for this so could i jsut plug in the values 1,2, and 3 to see which has the absolute max/min?

[full yarrow]

that makes sense but i dont get how it proves it proof wise 😭 sorry

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[crude bear]

https://math.stackexchange.com/questions/1146808/prove-s-is-a-supremum-iff-for-all-epsilon0-there-exists-a-in-a-such-that

[crude bear]

I'm having trouble seeing why s is a upper bound for A

(Assuming we remove the hypothesis's)

I should reword that.

If For all epsilon> 0, there is an a in A such that a> s-e.

Can we say that s is a upper bound?

For A

[light shoal]

not just from that

seems to be one of the hypotheses in that MSE question

[crude bear]

Yeah

But if we remove that

Can we still prove that?

[crude bear]

I guess no

[light shoal]

no, all you could prove is that sup(A) >= s in that case

[crude bear]

Thanks

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[steep gust]

someone can help me with eposilon delta

[steep gust]

I see a trick , why i can choose last interval (6) and after evaluate epsilon
|(4(6) + 3) -23|
|24 - 20|
|4| < e
delta = e/4

Other exercises work for me why?

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