help-23

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[timid surge]

anyone know how to solve this

[safe radish]

@timid surge Has your question been resolved?

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@timid surge Has your question been resolved?

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@timid surge Has your question been resolved?

[fresh inlet]

Maybe we can discuss to solve this problem if you want. Randy ask each of the 21 attendees and because there must be 2 people have the same number of handshakes so Randy must have the same number of handshake with somebody else in the room.

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[lean otter]

i dont know why but i forgot how to get the answer to this i did this like a while ago

but then forgot how to do it again

could someone help

[quasi bison]

Sam travels 126 km in 1.2 hours. what is his speed?

[lean otter]

105km/h

ok i got it

wtf

so does that mean

alisha is travlelling 117km/h

[vapid cove]

yes

[lean otter]

thank you

.close

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[foggy salmon]

wow fast

[quasi bison]

.reopen

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✅

[quasi bison]

@vapid cove @lean otter no

sam is 12km/h faster than alisha

this means alisha is 12km/h SLOWER

[foggy salmon]

lol

[vapid cove]

oh shoot my bad

[lean otter]

oh

i got it

so its 105-12

93km/h

[quasi bison]

yes

[lean otter]

thank you

.close

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[woven urchin]

you know what x/x is?

what is 10/10?

yes

so if you multiply a number by x/x you get the same number back

lol

a little

multiply inside the bracket in the lhs by 10/10 and you have a number with the same denominator

reduce the fractions to the same denominator to as low a factor as possible, then take the logs of both sides

now take the logs of both sides :v

ln((8/10)^(x-1))=ln((165/20)^(6x-5))

$$ln \frac{8}{20}^{x-1} = ln \frac{105}{20}^{6x-5}

$$ln \frac{8}{20}^{x-1} = ln \frac{105}{20}^{6x-5}$$

[flat frigate]

Wraith

[woven urchin]

then you can manipulate until you isolate the x components onto one side

start by removing the exponent....

$$ln x^{z} = z ln x$$

[flat frigate]

Wraith

[woven urchin]

yeh, logs are annoying asf lol

then you can remove the denominators aswell if needed, but you might not have to. Either way, reaarange the equation to get all the x's on one side and find x

all good?

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[slate ridge]

how is this wrong

[slate ridge]

https://gyazo.com/3ac0f4e46d31a6ed089af638d05957c0

[quasi bison]

pretty sure you want a plus sign there, not a minus

,w simplify sin(2x)cos(3x) - (sin(5x)+sin(x))/2

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[tiny marsh]

I think he is right it’s a -

[quasi bison]

ah, no, i was wrong it looks like

wait what. hold on

[tiny marsh]

,w simplify sin(2x)cos(3x) - (sin(5x)-sin(x))/2

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[quasi bison]

ah yes alright

there's a 0 in there

right...

[quasi bison]

try writing $\frac12 \sin(5x) - \frac12 \sin(x)$

[flat frigate]

Ann

[slate ridge]

I did try that earlier and it marked as wrong

[thin bridge]

that fraction in the input looks a bit off,

some weird white space

you could try sin(5x)/2 - sin(x)/2

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[lean otter]

I'm kinda confused by what this is asking

[lean otter]

does "I" mean something specific when talking about matrix algebra because theres been no matrix named I mentioned

[solar hazel]

I_2 is the matrix [1,0\\0,1]

the 2x2 identity matrix

[lean otter]

so does I typically just refer to a identity matrix?

[solar hazel]

yep

[lean otter]

so if it were to be like

I_3 would it be [1,0,0//0,1,0//0,01] ?

[solar hazel]

yep

[lean otter]

surprisingly straightforward it seems

im gonna try n solve the problem ill be back if something comes up that confuses me

[solar hazel]

ok, good luck ^-^

[slate ridge]

thats just how it looks

[safe radish]

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[tranquil fog]

Ok… what now

[safe radish]

@tranquil fog Has your question been resolved?

[tranquil fog]

<@&286206848099549185>

[lusty widget]

aye aye

wassup

so

what’s the

question

Ayo

for the

right hand side

of ur work

why

don’t u just

use

general term

much simpler

[tranquil fog]

Whatchu mean

What’s the general term stuff again?

Isnt that what im doing

Or

[lusty widget]

I have

no clue

what ure doing

wait nvm

alr so

[tranquil fog]

Hold on lemme specific

[lusty widget]

I can see

[tranquil fog]

Specific

[lusty widget]

u attempted I think

but

better to

separate

the x

from the a

[tranquil fog]

Question 5. Find ‘p’ and ‘a’

How so

[lusty widget]

so

$C^6_r \cdot{2^{6-r}}\cdot{(-a)^r}\cdot{x^r}$

oops

forgot the r

one sec

[flat frigate]

Springsskateboard

[lusty widget]

the p

is attached

to the x

with power 1

so let r=1

and find the coefficient

of x

in terms of a

and equate to p

next

they gave u

coefficient

of x^2

so let r=2

and find ur a

[lusty widget]

then plug a value into this

and find p

[tranquil fog]

Aight hold up

Lemme read

[tranquil fog]

How do i do that

I got (6C1)*(2)ˆ5 so far

Then what?

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[kind dove]

Construct context-free grammar such that languague generated by the grammar is L = ${ucv \vert u,v \in {a,b}^*; #_a(u) = #_b(v)}$

[flat frigate]

Michal

[still talon]

.w factorise 5y^2+5y-10

[kind dove]

does anybody have an idea? I constructed a grammar but i'm not sure if it's correct

[quasi bison]

@still talon #bots

@kind dove show us your grammar

[kind dove]

$\sigma \mapsto a \sigma b\
\sigma \mapsto b \sigma\
\sigma \mapsto \sigma a\
\sigma \mapsto c$

[flat frigate]

Michal

[quasi bison]

hmm... no, this will not do

i think so, anyway

or maybe i'm wrong, hang on

we want the same amount of a's to the left of c as b's to the right of c

ok then this actually works i think

[kind dove]

yes

[quasi bison]

any word of this language can be constructed "from the middle" using your rules

[kind dove]

ok thanks, i will try to prove it by induction

.close

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[lean otter]

Why does my prof call alpha the angle between lines n and m and L and K? how can you have the angle between these two lines be the same

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@lean otter Has your question been resolved?

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[marsh granite]

is this true?

[halcyon carbon]

Yes

[marsh granite]

ok thanks

.close

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[devout peak]

how would i solve this?

[maiden jetty]

$\log_{25}x = \frac{\log_5 x}{\log_5 25}$

[flat frigate]

秋水

[devout peak]

thats the answer?

[thin bridge]

no, that's just the first step

the final answer should be in terms of y only

[devout peak]

how would i do that?

[foggy salmon]

well

,w log5(25)

[flat frigate]

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[foggy salmon]

and u know log5(x)

[devout peak]

1/2y

[foggy salmon]

so

[devout peak]

right?

y/2

[foggy salmon]

umm

no

yes

y/2

[devout peak]

thanks

eveyone

.closee

.close

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[wild trout]

How do you get the turning points in cubic and quartic graphs?

[wild trout]

<@&286206848099549185>

[halcyon carbon]

set gradient = 0

[wild trout]

M=0?

[halcyon carbon]

[halcyon carbon]

Do you know how to find the gradient function of a function?

Derivatives?

[wild trout]

No

[proud grove]

Hi, what is the question?

[wild trout]

Maybe I've heard it before but I'm confused

[fossil vine]

Go to https://discord.gg/QwSdffq

[halcyon carbon]

Look it up maybe on YouTube

[wild trout]

ALSO, how can I tell how long a cubic graph will rest on the x axis

(x+3)³ means it's roots are 3, 3, 3

But how can I tell how long the line rests on the x axis for

Like this

It's a terrible example but yeah

[thin bridge]

<@&268886789983436800> inappropriate behaviour from @lean otter

[halcyon carbon]

Yes

RIP

[wild trout]

I mean -3, -3, -3

[halcyon carbon]

Roots would be at -3

Yeah ok

[halcyon carbon]

What do you mean by this

,w plot y=(x+3)^3

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[wild trout]

How do I know how long I should drawn the line on the x acis

It's going from -3.25 to -3.75

<@&286206848099549185>

What's stopping me from drawing it from -infinity to infinity?

[proud grove]

I don't fully understand your question

The plots shown in the attachment have a limit on domain

You can do -infinity to infinity

Since (x+3)^3 has no restriction on x

[wild trout]

Whatever is in the middle of the line shown is the root?

I'm assuming

So

Are these two the same?

When both of their roots are all 3

They can't be because of the intercept right?

Oh wait, did I just solve this on my own...

[safe radish]

@wild trout Has your question been resolved?

[wild trout]

I'm still not sure about this

[plucky dew]

the roots of an equations would give an output of 0

so for eg the root is 3

the graph is 0 only at x=3

the curves near this point may seem like its touching the graph but its not, its just really close to it

[plucky dew]

so here if u only have a one distinct root, the curve only cuts the x-axis at one point

[wild trout]

Yea

So the y intercept determines how long I can draw this line

It appears to be lying on the x

But it ain't

Equal roots of -3

I mean 3 for the one I drew

Because there isn't really a rule stopping me from drawing it to thy kingdom come

[plucky dew]

well no

its just that we cant really accurately draw graphs w our hands

so if you did have to, just try to draw it so the graph only touches x-axis at roots, and label the points

[wild trout]

Mhm

Wait, must the line be balanced between a range

Let's say the equal roots are 5

And the y increases by 1 at 6

And decreases by 1 at 4

Must all graphs be drawn like that?

How do I say it... inverted range?

3 and -3

4 and -4

Is the one on the right Incorrect ?

Must be mirrored right?

At the equal roots

That picture is blurry...

If my statement is true, then the y intercept truly does determine how to draw the line

This is just extremely confusing

It can't still because nothing can stop you from drawing the sharpest turn to touch the y axis

The difference between humans and computers making these graphs is that the computers will check ALL VALUES possible until they cant

And humans get lazy and do it with integers

[safe radish]

@wild trout Has your question been resolved?

[safe radish]

@wild trout Has your question been resolved?

[safe radish]

@wild trout Has your question been resolved?

[wild trout]

.close

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[latent umbra]

is it just by a factor of 3 to the left?

not by a factor, just to the left by 3?

for c

[neat kiln]

Yes

[latent umbra]

oh got it thank you lol i was so confused idk why ;-;

.close

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[fallen scroll]

All above is one question

h e l p D;

[safe radish]

@fallen scroll Has your question been resolved?

[fallen scroll]

<@&286206848099549185>

.

no one ?

[fallen scroll]

hello ?

@meager igloo

ANYONE

?

.close

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[elder lichen]

How do I solve

[bold sedge]

16*2 for dimes

Since it’s twice as many

10*16 for value of dimes

With that we can set up our equation

[elder lichen]

What it says is that Colin and David has 2.50 in total each

[elder lichen]

Can we solve the solution together

[bold sedge]

Wait where does it say that

[elder lichen]

No the answer I got

On Photomath

It knows my textbook

So the answer is from the textbook

[worthy hemlock]

Don't do the work for people or give out answers

[bold sedge]

My bad I thought It was fine if I walked them through it

[elder lichen]

@bold sedge is what u got that David and Colin have $2.50 each

Cuz that’s the answer

[bold sedge]

Uh nope that’s not what I got and that’s not what the questing is asking for

[elder lichen]

The textbook says it’s 2.50 each for each boy

[bold sedge]

For the amount of money maybe but it wants to know how many quarters and dime each boy has not what they are worth

[elder lichen]

Well would ur equation tell us what they are worth

[bold sedge]

No the equation I set up tells you how many quarters the boys have

My bad I made a mistake let me rewrite the equation

[elder lichen]

Oh

[bold sedge]

Alright I wrote it out now walk me through the steps

I’ll tell you if your write or wrong

Here’s a hint for David q+d=16

[elder lichen]

I already got it

Plug in y on both sides and work it out from there

I did the steps below if u wanna see but it’s messy

[bold sedge]

I also did the steps so sure show me

[elder lichen]

The result is x = 10

[bold sedge]

Nope

Wait for quarters or dimes?

Oh wait for dimes then yeah that’s right

I solved for quarters

[elder lichen]

What’s for quarters

[bold sedge]

^

[elder lichen]

Him I’ll try it

[bold sedge]

you already have what you need to know how many quarters there are

[bold sedge]

You solved for dimes you have dimes

quarters + dimes = 16

[elder lichen]

I get 2.50

D is David

[bold sedge]

if you have 10 dimes how many quarters do you have?

[elder lichen]

6

[bold sedge]

yes

[elder lichen]

The formula is y = 16 - x

X is 10

[bold sedge]

Now I can show my work

Since you have all the answers

[elder lichen]

Oh ok

That’s much appreciated because this will be in the test for sure

[elder lichen]

Thank you

[bold sedge]

Np

[elder lichen]

.close

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[polar pumice]

any assistance

[bold sedge]

4pi doesn’t do anything since it loops

[polar pumice]

would it be possible to hop in a vc to explain how it works?

[bold sedge]

No but I can explain it to you pretty easily

[polar pumice]

ok

[bold sedge]

sec(x) = 1/cos(x)

cosine and sine waves work with angles a lot

[polar pumice]

why are we using this?

[bold sedge]

breaking it down to basics

cosine loops after 2pi as that’s when the wave ends

so 2pi is the same as 0

For cosine

And sec

which is why 4pi doesn’t change the graph

[polar pumice]

ohh ok

[bold sedge]

It loops twice

What do you think the -2 does?

[polar pumice]

makes the graph stretch

[bold sedge]

let me rewrite the equation for you

-2-1/2sec(x)=-1/2sec(x)-2

That help a bit?

[polar pumice]

a little im a visual learner so its kinda hard to understand it through messages

[bold sedge]

Think of y=mx+b

b=-2 in this case

[polar pumice]

? would be be x

[bold sedge]

sec(x)

[polar pumice]

so is this different from sin or cos instead of sec

[bold sedge]

think of x as a generalized thing like f(x)

It applies to pretty much all functions

Think like x+b
x^2+b
log(x)+b

They all do the same thing

It’s no different for sec(x)

[polar pumice]

ok

[bold sedge]

So what does -2 do?

[polar pumice]

it causes the graph to shift verically

[bold sedge]

Yeee

up or down?

[polar pumice]

down

[bold sedge]

yep last thing -1/2

What does that do?

[polar pumice]

causes the graph to shift horizontally

[bold sedge]

-1/2 is your slope

[polar pumice]

actually nvm it causes the graph to strectch/Compress vertically

[bold sedge]

Yes and it does one more thing

Think -x vs x

[polar pumice]

im not sure

what else it does

[bold sedge]

What’s the difference between-x and x

[polar pumice]

the negative sign

[bold sedge]

yeah if slope was -1 what would that do?

[polar pumice]

cause it to shift

[polar pumice]

so it would be the point where they cross

[bold sedge]

-x is a reflection of x

[polar pumice]

so in this case there would not be an x-axis reflection

[bold sedge]

-1/2

[polar pumice]

?

i know the basics i just need help answering the questions

[bold sedge]

-1/2sec(x) is it reflected?

[polar pumice]

yes

bc of the - in front of 1/2

[bold sedge]

Ye

and 1/2 < 1 right

[polar pumice]

ok so to find the phase shift i need to do bx-c

[bold sedge]

well first is it expanding or compressing

[polar pumice]

expanding

[bold sedge]

it only expands if m > 1

1/2<1

1/2sec(x)=sec(x)/2

[polar pumice]

ohhhh

[bold sedge]

So is it expanding or contracting?

[polar pumice]

contracting / compressing

[bold sedge]

Ye

so with that all in mind you should be able you answer the questions now

[polar pumice]

so for the phase shift i do i find it if there is there is no b

[bold sedge]

Let me show you all the important factors

v(hx+h_s)^n+v_s

[polar pumice]

ok i think i got it

this is the final answers i got

[bold sedge]

v=vertical expansion/contraction
h= horizontal expansion/contraction
h_s = horizontal shift left or right
n = exponent
v_s= vertical shift up or down

-1/2

But yeah I think you got it

[safe radish]

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[frozen quail]

How do i do e

[foggy salmon]

dark theme with dark letters

[frozen quail]

Confusibg cause subtract and add

[foggy salmon]

hm its alternating series

but not to inf

[foggy salmon]

u can consider them as 2 series ig

[quasi bison]

what is Euclid's method?

[frozen quail]

Thus

[foggy salmon]

oh crap i didnt see that euc method

[frozen quail]

This

[foggy salmon]

,rccw

oh ye bots down

[quasi bison]

like, this is just a geometric series with common ratio -1/2. there's not really a need to break it into two.

[foggy salmon]

oh ye mb

[quasi bison]

but the instructions say to apply a particular method to find the sum

[quasi bison]

ok so it's basically the rederivation of the sum formula got it

yeah as i said the common ratio for your GP is -1/2 so thats what youll want to multiply it by

really your sum can be written as 1 + (-1/2) + (-1/2)^2 + (-1/2)^3 + ... + (-1/2)^7

[frozen quail]

Good start ty

Ill type in ehat i get

I goy

I got

0 644

0.644

Im not sure about c do i think i got it wring

I mean d

[thin bridge]

how are you getting 0.644

[frozen quail]

Lemme send a pic

I just did euclids method

[thin bridge]

ideally you'd keep your value exact

simplify you fraction without using a calculator/ given a decimal approximation

[frozen quail]

Ok

[safe radish]

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[hoary dirge]

why when you intergrate a fraction with the x on the top does it become a whole number?

[hoary dirge]

like if you intergrate sec^2 x/3 it becomes 3tanx/3

wait nevermind

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[lean otter]

given this formula

so what I first did was convert them into fraction form

which amkes

4 x 7! 9!
------- = -----------------------------
(k-1)(7-(k-1))! k!(9-k)!

I don't think we're about to cancel out factorials

[quasi bison]

4 * 7!/[(k-1)! * (8-k)!] = 9!/[k! (9-k)!]

to make this look less ugly if you can't LaTeX

[lean otter]

alright

[quasi bison]

taking the reciprocal of both sides and unraveling some factorials you get $$\frac{(8-k)! (k-1)!}{7! \cdot 4} = \frac{[k \cdot (k-1)!] \cdot [(9-k) \cdot (8-k)!]}{9 \cdot 8 \cdot 7!}$$

[flat frigate]

Ann

[lean otter]

ah i see

and then you can remove the 7 factorial

so it becomes

[lean otter]

what i don't get though is where the 8-k comes from

[quasi bison]

7-(k-1)

[lean otter]

right

but i see the k-1 again before

and there is only 1

so if the k-1 is used to sipmlify for 7-(k-1)

where is the other k-1 coming from

wait a sec, just gonna take shit

[quasi bison]

k! = k*(k-1)!

[lean otter]

ah yes that's true

and then you can simplify by removing that from both sides

i think

[quasi bison]

there's a bunch of stuff you can cancel out of both sides

[lean otter]

right

so i'm guessing 7!, k-1,, 8-k

[quasi bison]

you will get k(9-k)/72 = 1/4

[lean otter]

yep and from that point it's fairly

simple

thank you @quasi bison

oop

hve a good day

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[abstract kayak]

how do u do this

[void plank]

What do you understand by "stationary point"?

[abstract kayak]

occurs when f'(x) = 0

when a function stops increasing / decreasing and changes its direction

[void plank]

Good

What's f'(x) here?

[abstract kayak]

36x - 4ax^3

[void plank]

That's correct

You know that it is equal to zero at x=-3/(sqrt(5))

Try and use that now

[abstract kayak]

how would i use that

[void plank]

Form that as an equation

So that you can solve for a

[abstract kayak]

what plug -3/sqrt5 into f'(x)

[void plank]

Yes

[abstract kayak]

is this valid?

[void plank]

Yes

That's correct

Good work

[abstract kayak]

thanks!

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[main lynx]

This is what i did

Is this the way?

[delicate bobcat]

I think you're most of the way there the method you used seems good

You need to show more clearly though that the thing on the left is divisible by 5

[main lynx]

But that was just so easy, I thought I missed something

[delicate bobcat]

Or that it's a multiple of 5

[main lynx]

Ohhh ohh so should i rearrange the terms?

[delicate bobcat]

Factor a 5 out

And rewrite

[main lynx]

The terms of RHS

[delicate bobcat]

5* (ak*5^k-1 + ......)

[lean otter]

bro...💀

[delicate bobcat]

Then you can say the thing in the parentheses is an integer

And 5*an integer is something divisible by 5

[main lynx]

Ohhh got it thanku sm

[delicate bobcat]

You have to show everything very clearly except justification for basic arithmetic

And depending on the class sometimes that too

[main lynx]

So i should take 5 common and i have to show that the thing inside parentheses is an integer

[delicate bobcat]

Yea which you have enough info for that

[main lynx]

Yea I'm asked to explain every single steps

[delicate bobcat]

5^n is integer for any value n in integers

Coefficients are all integers

Integer * integer is integer

Sum of integers is integer

[main lynx]

Yesss you meant 5*n

?

[delicate bobcat]

(Integers are closed under multiplication and addition)

No i mean 5^n

[main lynx]

Yes I got that

[delicate bobcat]

Because when you plug 5 into the polynomial you are still taking powers of 5 even after factoring one 5 out

[main lynx]

Yeah that helped

Got it

[delicate bobcat]

GL enjoy

[main lynx]

I'll close this then? Isn't that how it works?

[delicate bobcat]

Yea it can close automatically too if youre not sure you want to close yet

[main lynx]

Okay got it

[safe radish]

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[acoustic goblet]

Topic: Exponential functions
Specific part: The initial value

[acoustic goblet]

In f(x) = a • b^×
a and b ≠ 0
but x can

how? exactly can x be 0? wouldn't it be a constant function just like if a and b were 0?

I just saw an explanation on initial value and it said...
if x = 0

f(0) = a • b⁰

then

f(0) = a

[gilded mountain]

b^0 = 1

since b =/= 0

[acoustic goblet]

Wait so it's just the basics power of zero thing?

[gilded mountain]

yeah

and its not a constant function, since f(0) = a not f(x) = a

[acoustic goblet]

Ah... i may have forgotten about the power of zero rule ahshahaa

welp thanks for helping me sir ^ ^

byebye

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[hoary dirge]

I've done (2x+2)^-1/2 x 1/2

[hoary dirge]

but the answers are asking for 2-root2

since the formula is (ax+b)^n = 1/a x (ax+b)n+1 / n+1

i tried to apply it but i'm now left with (2x+2)^1/2

[lean otter]

are you familiar with u-substitution?

[hoary dirge]

yes

[teal skiff]

https://www.symbolab.com/solver/step-by-step/\int_{0}^{1} \frac{1}{\sqrt{2x%2B2}}?or=input @hoary dirge

[lean otter]

okay basically, take u = 2x+2

[hoary dirge]

OHHHH

[lean otter]

yeah

[hoary dirge]

i think i got it from here

thank you!!!

[lean otter]

change the bounds of the integrals based on the 'u' you get too, or just convert u back to x

same result

[hoary dirge]

thank you again

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[remote kernel]

Can anyone help me with the math here?

[remote kernel]

Whats the width and height of each cell?

For info, the canvas size 1920 x 1280

There is a outer border of 50px thick

Oh wait...

364...

364 x 590....

Got it nvm

.close

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[true estuary]

for intersection would i write it as (6, 12, 18, ... where the ... would show infinition ?

oh wait

would i say multiples of 6?

[prime nacelle]

ye

[true estuary]

wat about union

sry the multiples of 6 was for intersection not union

so what would union be?

[foggy salmon]

yesh

[foggy salmon]

its just all numbers 2>

=2

ints

[true estuary]

how

wat about 5

[foggy salmon]

well

OH WAIT

sry

:c

[true estuary]

yh lol

7 as well

[wind stream]

The union is just all numbers that are divisible by 6

[true estuary]

thats intersection

[wind stream]

Or you could say numbers that divides 2 and 3

[wind stream]

No, the union of those two sets are numbers that divides 2, and those that divides 3

Actually, numbers that divides 6 also does not fully describe the union

[true estuary]

'The union is just all numbers that are divisible by 6
this should say The intersection is just all numbers that are divisible by 6

[foggy salmon]

intersect no?

[wind stream]

Yes, because they divides 6, they divides 2 and 3

[true estuary]

yh

[foggy salmon]

ye think thats what they said

they corrected after

[foggy salmon]

^

[true estuary]

can i not write union as (2,3,4,6,8,9 ...

[foggy salmon]

i think u just write in set notation

[foggy salmon]

no

that looks so sus

[true estuary]

idk how to write it then

[foggy salmon]

u can write like

[wind stream]

You can just write integers n that divides 2 and 3, seems good for me

[foggy salmon]

{x|k in N0, x = 2,3,4+6k}

[foggy salmon]

or this

[true estuary]

just like that?

in normal english?

[foggy salmon]

idk that might work

if they dont want it super formally

[wind stream]

Yeah, your choice basically

We are just giving out suggestions

[true estuary]

acc wait

no

it should say integers n that divides 2 OR 3

[wind stream]

You could also do something like
{$n \in \mathbb{Z} | n|2 \ \verb|or| \ \ n|3$}

[wind stream]

And yes, i was wrong there

[true estuary]

this looks a bit odd

2orn?

[wind stream]

sorry latexing on phone is not easy

Bruh

[true estuary]

lmao

do it without latex

and just use letters

ill understand

[wind stream]

| basically denotes divides

[true estuary]

apart from the first I

where that means where

right?

[wind stream]

Yes

[true estuary]

cool cheers man

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[true estuary]

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[rich jacinth]

From the product rule we get p(x, Ck) = p(Ck|x)p(x)

But do we also get p(x, Ck) = p(x|Ck)p(Ck)

Or does order matter in the first p(x, Ck)

[safe radish]

@rich jacinth Has your question been resolved?

[toxic stratus]

the conditional probability formula can be used both ways

[safe radish]

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[safe radish]

@spice lantern Has your question been resolved?

[spice lantern]

<@&286206848099549185>

[spice lantern]

.close

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[stoic robin]

how can i find the x and y intercepts for this function

[stoic garden]

x intercept : root
y intercept : f(0)

[stoic robin]

so y = 50

do i need to factor it to find the roots

x²(x²-18)+50

still quite hard : |

[thin bridge]

you have a quadratic in disguise

it you are struggling to see it, consider a substitution like t =x^2

[stoic robin]

oh snap, thanks

[stoic robin]

but when i find the roots for t²-18t + 50 what do i do with them? how do i substitute back

[thin bridge]

well sub x^2 back in

[stoic robin]

alright!

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[rich jacinth]

Why do we take a step into the direction of the gradient if we want to maximize?

[quasi bison]

if you want to get high up, you go uphill

@rich jacinth

[rich jacinth]

But here for example

I want to minimize the value

[quasi bison]

then you go downhill instead

[rich jacinth]

And if I start at 100, 100 and take a step in the direction of the gradient

Then it gets minimized

But that contrasts this sentence

In my case taking a step in the direction of the gradient minimizes the value

[safe radish]

@rich jacinth Has your question been resolved?

[rich jacinth]

Aha

This is where it goes wrong no?

I get the negative gradient where it should be positive

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[gray barn]

The problem is as follows:

Let f and g be two functions such that their composition f ◦ g is defined for
all x in the domain of g. Suppose that g is periodic with period T . Show that f ◦ g is also
periodic with period T .

I'm not sure how I would show that f ◦ g is also periodic. I know g(x) can be written as g(x + T), but I don't think that helps here. I would appreciate a hint

[gray barn]

Maybe to consider that the range of g is fixed between a certain interval, so the domain of f can only be in that interval

hm yes I guess so, since the inputs to f are always periodic, it means f's outputs must also be

[cinder viper]

(fog)(x+t) = ?

[gray barn]

(fog) would be f(g(x))

"f composition g"

[cinder viper]

Yes

and then?

[gray barn]

sorry i dont follow

[cinder viper]

(fog)(x+t) = f(g(x+t)) = ?

[gray barn]

!close

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[runic matrix]

N \ {0} does this mean every postive number

[cinder viper]

Probably

[runic matrix]

n e N{0 , 1}

that what does this mean

[cinder viper]

Whats this?

[runic matrix]

n element of N

[cinder viper]

Oh

and is there anything before {0,1}?

[runic matrix]

sorry

[cinder viper]

Okay so im assuming N is the set {0,1,2,3....} here

so N \ {0,1} means {2,3,4,....}

[runic matrix]

thats what i thout too

but

this is the full picture

Tell whether the following subsets ofR are bounded from above and/or below,
specifying upper and lower bounds, plus maximum and minimum (if existent)

this is the question

this means that min is -1

right

no wait

min is 0

[cinder viper]

try putting some values of n in and maybe see if u get a pattern or something

[runic matrix]

so if i put 2

[cinder viper]

for x=(2n-3)/(n-1)

[runic matrix]

whihc is the smallest

i get 1

[cinder viper]

okay, and for n=3?

[runic matrix]

it is greater than 1

so it goes to infinity

as n increases

[cinder viper]

how do u know?

keep going till like n=5

[runic matrix]

it s like 7/4

[cinder viper]

what happens if n goes to infinity

[runic matrix]

approaches 2?

[cinder viper]

Yep

[runic matrix]

so sup2?

no maximum

min 0

and inf0

[cinder viper]

Yes

[runic matrix]

thanks a lot mate

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[brittle dust]

how do I do this?

actually give me a min

actually I have no idea how to do this

someone help

[dusk vapor]

so its bounded by 4 and 8

and is increasing

u set up the equation

l=8-12/l

and u solve for l

[dusk vapor]

this by taking n to infinity

the limit must lie in the range between 4 and 8 btw

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@brittle dust Has your question been resolved?

[brittle dust]

alright thanks

.close

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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[lean otter]

,rotate

[silver pond]

Pls quickly

[lean otter]

Is this a test?

[silver pond]

نو

No

Man we r in night

[lean otter]

Did you try something?

[lean otter]

I think a proof by contradiction may works

[silver pond]

Pls do it if u can

[lean otter]

Let's say B is not in C

A N B is in A N C and B is not in C so A is in A N C so A is in C

A U B is in A U C and B is not in C so..

[silver pond]

Is N mean includ ?

I mean instraction

[lean otter]

Let me do it properly

[silver pond]

Write it pls

So

[lean otter]

Do you agree on this?

A and B are in A and C but B is not in C so A is in C

[silver pond]

Look

[lean otter]

ok

We're doing a proof by contradiction

Do you know how that works?

[silver pond]

Yup

[lean otter]

Let's suppose B is not in C

Then the left part is wrong so B is in C

[silver pond]

Okk

[lean otter]

So now you can try to do a diagram with B not in C

[silver pond]

Doesnt work

[lean otter]

Well then B is in C and we're done

[silver pond]

Thats it ?

[lean otter]

I think it's clearer with A U B is in A U C, B not in C

[silver pond]

So i should make it with the two

[lean otter]

yeah

A U B is in A U C means A is in A U C => A is in A or C and B is in A or C so B is in A or C but B is not in C so B is in A

[silver pond]

The last is false so the main is true

Like that ?

[lean otter]

,rotate

[lean otter]

More like not q => not R^S so R^S=>q

[silver pond]

I made first proposition bar

[lean otter]

what you wrote is

**Not ** (p=>q) is p & Not q?

I'm confused

Just take B not in C and show that the left part R & S are wrong

$R\wedge S\Rightarrow q\Leftrightarrow \overline{q}\Rightarrow \overline{R\wedge S}$

[flat frigate]

Zamarus

[silver pond]

Thank uu

[lean otter]

Wlc

[safe radish]

@silver pond Has your question been resolved?

Channel closed

Closed by @silver pond

Use .reopen if this was a mistake.

[safe radish]

Available help channel!

Send your question here to claim the channel.

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

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

[lean otter]

what am I doing wrong here

[lean otter]

For the second part, I am aware that it should be the gradient / || gradient||

so the numerator is the gradient that I got

the unit vector for the direction, I got < 1/sqrt(10), -3/sqrt(10)>

<@&286206848099549185>

[safe radish]

@lean otter Has your question been resolved?

[lean otter]

.close

[safe radish]

Channel closed

Closed by @tired cradle

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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

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

[lean otter]

Ron made 155 000$ of sales

How much did he made with the first 80 000

How much did he made from the 80 000 to 100 000

How much did he made from the more than 100 000

Then you add it all

[misty bay]

this is pretty important when figuring out your taxes lol

guess the tax authorities do a lot of it for you though

[mighty garden]

$80,000 * 2% =1600
155,000-80,000= 75000

[lean otter]

[mighty garden]

After that where I get confused

[lean otter]

You're going too fast

$80,000 * 2% =1600 OK

100,000-80,000=?

[mighty garden]

20,000

Do I subtract 20,000 from 150,000

[lean otter]

no no no

How much did he made with the first 80 000
How much did he made from the 80 000 to 100 000
How much did he made from the more than 100 000

How much did he made with the first 80 000 you found 1600$

now from 80 000 to 100 000

Then 100 000 to 155 000

[mighty garden]

So next I do 20,000 * 3.5% = $700