help-13

[thick heath]

the fraction must be positive, you can get two cases

x>0
and
x-1>0

the other case is

x<0
and
x-1<0

you can intercept the solutions of each case and then create the domain with all the cases

[undone star]

sevchenko just suggested the same thing

u have a problem with dealing with 0s

it is hard to do this algebraically

u have to do it analytically

[vapid otter]

x > 0, x > 1 & x < 0, x < 1

so set interval notation

wpould be

$(-\infinity, 0)\union(0, 1)\union(1, \infinity)$

[wraith dagger]

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

[vapid otter]

well you get it

unions in between

and infinities at the end

is it right

[undone star]

assuming u meant x<0 and x>1 yes

[vapid otter]

?

its set interval notation

[undone star]

im not sure what (0,1) is in middle

[vapid otter]

i just said there are unions in between

[undone star]

sure then i guess

[vapid otter]

yes?

so its correct?

[undone star]

yes

[vapid otter]

THANKS

.close

[cedar kiln]

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[thick heath]

the interval 0-1 is not a solution

[undone star]

they meant union

x<0 union x>1

[cedar kiln]

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[timber urchin]

The frame of a painting has the form of a 10500 by 10500 square with a 9500 by 9500 square removed from its center. The frame is built out of congruent isosceles trapezoids with angles measuring 45 deg and 135 deg. Each trapezoid has one base on the frame’s outer edge and one base on the frame’s inner edge. Each outer edge of the frame contains an odd number of trapezoid bases that alternate long, short, long, short, etc. What is the maximum possible number of trapezoids in the frame?

[timber urchin]

.close

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[primal wigeon]

hi

can i ask a question

[frozen rune]

what is your inquiry young one

[cerulean sail]

In your own channel though, this one might lock

[primal wigeon]

alreight

[primal wigeon]

can u check opal

#help-0

[cedar kiln]

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[stray vine]

is it correct?

[reef mantle]

hi

[cedar kiln]

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[ionic wolf]

idk how to do 11

[zenith sail]

Do you understand how you got numbers 9 and 10? You can do this the same way

[ionic wolf]

idk the middle one looks weird

[zenith sail]

actually you should double check your solution for k in number 10 as well

[ionic wolf]

oh k=5

[zenith sail]

yeah

Still, if you try doing what you did for 9 and 10, what equations do you get?

[ionic wolf]

idk

[zenith sail]

oh is it the 0 ≤ x ≤ 1 that's tripping you up?

[ionic wolf]

yes

there like 0 and 1 on there instead of just 1 or 0

idk

[zenith sail]

The function switches from the top rule to the middle one at x=0, and then switches from the middle rule to the bottom one at x=1

So in order to be continuous, the top and middle have to be the same when you plug in x=0

the middle and bottom have to be the same when you plug in x=1

[cedar kiln]

@ionic wolf Has your question been resolved?

[cedar kiln]

@ionic wolf Has your question been resolved?

[ionic wolf]

OK

b=π

I got 10-π=a

[zenith sail]

Nice 👍

[ionic wolf]

maybe like -1 from pos and neg direction

idk

[zenith sail]

Yeah exactly

That's basically what you did on the other problems

Just without specifically mentioning the limits

[ionic wolf]

is it same for B

[zenith sail]

yeah

[ionic wolf]

Yayaya

[ionic wolf]

how to do C

[cedar kiln]

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[hexed vortex]

is anyone able to check these

[hexed vortex]

I didnt really understand much from 17 and below

besides on 17 that is has something to do with the uniqueness theorem

[humble marsh]

If it is true, explain why. If it is false, provide a counterexample or an explanation.
can you provide your reasoning for each?

[hexed vortex]

well I'm confident in pretty much everything above 17 and could provide reasoning

but 17 and after I cant

I kinda just whimmed it

for 17 though

I believe it has something to do with the uniqueness theorem

and the fact that

if the dy/dy is continous

and partial of dy/dt is continous

then on some sub-interval on its continous interval it will have a unique solution

sin and cos are continous

along with the polynomial so multiplying and adding them gives us a continous function still right

we also have an equilbrium solution at y = 3

[humble marsh]

mhm, that's important

[hexed vortex]

but what I dont really understand is

[humble marsh]

can the solution with y(0) = 4 ever touch the equilibrium solution?

[hexed vortex]

how does the uniqueness theorem say that y(t) has to be above that equilibrium solution

no since it has to be unique

right

[humble marsh]

if y(t) = 3 for any t, then y(t) = 3 for every t

so if y(0) = 4 then y(t) is never 3

[hexed vortex]

oh

oh is y(t)

talking about the same solution of y(0)

I was thinking of like the family of solutions

and I was confused on why there werent any solutions below the equilibrium

but I think it makes sense now if y(t) is just one solution and its the solution from y(0)

[humble marsh]

there are solutions below the equilibrium

and solutions above

but never the twain shall meet

because if any solution touches the equilibrium, it would become the equilibrium

if that makes sense

[hexed vortex]

yeah

[cedar kiln]

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[hollow dagger]

@old ridge Is there someone that could help me with digital system ?

[hollow dagger]

I cannot understand what does the exercise 3 want me to do

[slim birch]

the same way u did the previous questions i assume

assume A is always high (??)

however in that case the or gate will always output high as well

@hollow dagger

[hollow dagger]

really ?

I thought +5V _ VCC is a special case or something

if so thank you so much

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[slim birch]

you can almost always assume pulling to vcc means logic high (A=1 as they said) np

[hollow dagger]

the x of this diagram should be 0 always, right ?

these exercises is a bit bland and weird

[slim birch]

.reopen

^ ahh u need to do this lol

[hollow dagger]

.reopen

[cedar kiln]

✅

[slim birch]

no it's not always 0

whenever at least one of the lines is high it will output high

[hollow dagger]

but that is AND gate

[hollow dagger]

this one

[slim birch]

oh wait i might be blind lol... then yee ur right

[hollow dagger]

ok thanks for your help

i gtg

.close

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[stable tendon]

What approach would you take to solve this??

[cedar kiln]

@stable tendon Has your question been resolved?

[stable tendon]

@helpsr

<@&286206848099549185>

[flat prawn]

Taking a random point ( x1 , y1) on a curve
Let y be f(x)
Now we can write the equation of tangent in slope intercept form , y - y1 = dy/dx. × (x-x1)

Now using the condition in the question, and using distance formula we will get an equation
From there we'll get the value of dy/dx
Solve the differential equation
Put the value (2,1 ) to calculate the value of arbitrary constant
And then , we can write f(x) that is the equation of the curve

[flat prawn]

To get the point of intersection on x axis , on the slope intercept form , put x = 0

[flat prawn]

*u=0

*y

[stable tendon]

Thank you, I will try it out!! If i run into any problems, do you mind if I ask you for help?

[flat prawn]

It's fine

Is there any answer given?

[cedar kiln]

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[crimson sedge]

.close

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[sonic tusk]

i need to prove that if p is irrational and q is rational, then p+q is irrational

[sonic tusk]

i have p + a/b = x/y

(pb)/b + a/b = x/y

(pb+a)/b = x/y

here do i need to state an axiom?

(im using contradiction btw)

[lofty topaz]

Assume that p + q is a rational number.

[sonic tusk]

yes

[cerulean sail]

(think about what p is)

[sonic tusk]

p is uh

q - a/b

[lofty topaz]

$p = \dfrac{xb - ay}{by}$

[wraith dagger]

Roman_Garland

[sonic tusk]

ya

wait what

oh yeah

[lofty topaz]

Why didn't you used this?

[sonic tusk]

cause how does that show that p is irrational

[lofty topaz]

Contradiction?

[sonic tusk]

OH

it shows that p can be written as

a fraction between integers

tysm

wait i have a question

could i say

[lofty topaz]

Yes, therefore p is a rational number.

[sonic tusk]

let the product of p + q = r

p = r - q

where both r and q are rational numbers

and the difference of rational numbers is rational

but p is irrational

meaning its difference cannot be expressed through two rational numbers

how do i notate that mathematically

[lofty topaz]

Contradiction : Assume p + q is a rational number, that is r, such that p is an irrational and q is a rational\
\
Let $q = \dfrac{a}{b}, r = \dfrac{x}{y}$ s.t. a, b, x, y are all integers\
\
$p + q = r \implies p + \dfrac{a}{b} = \dfrac{x}{y} $\
$\therefore p = \dfrac{x}{y} - \dfrac{a}{b} = \dfrac{xb - ay}{by} \ \star$\
($\star $ is saying that the equation contradicts the given sentence (or) statement)\
\
$\therefore p + q$ is always an irrational number

[sonic tusk]

thank you sm

[wraith dagger]

Roman_Garland

[sonic tusk]

.solve

.solved

[cedar kiln]

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[fervent linden]

i neec help

[fervent linden]

can sm1 help me with these

[glacial field]

Factoring? Or solving for x

[fervent linden]

solving x

[glacial field]

Did you teacher instruct you use a certain method?

Because it’s easy to abuse the quadratic formula

[fervent linden]

i wanna use 2 brackets

why would u wanna abuse them

[glacial field]

A formula, being overused and applied everywhere and sometimes mistakenly

[fervent linden]

sorry i need help tho

[glacial field]

Do you know the quadratic formula?

[fervent linden]

i forgot

there too much

[glacial field]

But that has been introduced to you yes?

[fervent linden]

ye

[glacial field]

Alright, use that. Where a is the coefficient of the first term, b is the coefficient of the second term, and c is the final term

I’ll send it here

[fervent linden]

okay

[smoky idol]

But she said she wanted to use two brackets, which I assume meant factoring?

[glacial field]

Using this, try the first polynomial

[fervent linden]

oh no thats the hard one tho

yea idk what it was

[sonic tusk]

^

[fervent linden]

i meant factorising

[glacial field]

How much do you know about factoring

[fervent linden]

a little

[glacial field]

Work me through how you would do the first polynomial

[fervent linden]

we split 2x squared in 2 brackets

like (2x) (x)

[glacial field]

$2x^2-8x+6$

[wraith dagger]

mari

[glacial field]

Not quite, multiply the first coefficient by the last term

What do you get?

[fervent linden]

i dont get it

[glacial field]

Do you know what a coefficient is

[fervent linden]

is it 6

?

[glacial field]

The first coefficient is 2

[fervent linden]

oh

[glacial field]

The last term is 6

[fervent linden]

i forgot them

6x2?

[glacial field]

That’s fine, what is the product of those two

Yes

[fervent linden]

12

[glacial field]

Okay, 12 is the number you will use to factor out the polynomial. This means you have to find two numbers that add up to -8 and multiply to 12

[fervent linden]

ohh

-6 and + 2?

[glacial field]

That would equal -4

[fervent linden]

oh im dumb

[glacial field]

The sum of the two has to be -8

[fervent linden]

-6-2

[glacial field]

Yes

Now break -8x into -6x and -2x

[fervent linden]

do i put in each bracket

[glacial field]

Sorry I don’t know what you mean

[fervent linden]

like i put uhm the numbers

[glacial field]

$2x^2-2x-6x+6$

[wraith dagger]

mari

[fervent linden]

(2x-6) (x-2)?

[glacial field]

That’s what we have so far

[fervent linden]

oh

[glacial field]

No

[fervent linden]

damn

icl i dont get ts

[glacial field]

Factor out a 2x from the first two terms

[sonic tusk]

it is close

[glacial field]

And a -6 from the other two

[fervent linden]

ohh u divide?

x=3?

[glacial field]

??

[fervent linden]

idk im just guessing

[glacial field]

Okay let’s not guess

[fervent linden]

kay

[glacial field]

These things can be done methodically

$2x(x-1)+6(x-1)$

[wraith dagger]

mari

[glacial field]

Here’s what I mean

By factoring out a 2x and a -6

[fervent linden]

i dont get it

[glacial field]

$2x^2-2x-6x+6$

From this

[wraith dagger]

mari

[glacial field]

Which part

[sonic tusk]

can i attempt to help

[glacial field]

Sure

[fervent linden]

yes

[sonic tusk]

ok

@fervent linden

when factoring

quadratic equations

the general rule of thumb is that

you look for factors that equal a*c and sum to b

what does that mean?

[sonic tusk]

well look at your first question

can you say what a, b and c are

[fervent linden]

a is 2x squared and

[sonic tusk]

no

[fervent linden]

oh

[sonic tusk]

x isn't part of it

x is what's being manipulated by your a b and c

so a is just 2

[fervent linden]

so its just 2?

[sonic tusk]

ye

[fervent linden]

okay

[sonic tusk]

whats b

[fervent linden]

its 2 -8 and 6

[sonic tusk]

right

usually, you would just look for factors that add up to c (6 in this case)

[fervent linden]

u x 2 and 6

[sonic tusk]

but in this case, a is not 1

when a isn't 1, you need to look for factors that

multiply to a*c

what is a*c?

[fervent linden]

12

[sonic tusk]

right

so what factors

multiply to

positive 12

and add up

to negative 8

[fervent linden]

2 6

[sonic tusk]

perfect

so let's start making the brackets

wait

wrong

-2 and -6

you forgot the negative sign

[fervent linden]

yea i meant that

[sonic tusk]

anyways

yeye

lets start making the bracket

so far we got

to make x^2 we just put x in each bracket

then just put the factors in

(x-2) (x-6)

but remember, we didn't just get factors of c alone

[fervent linden]

what happened to 2x

[sonic tusk]

meaning that when expanding this, you wouldn't get the exact value for c

[sonic tusk]

it will come

[fervent linden]

oh

are the answers already there

[sonic tusk]

no

[fervent linden]

oh okay

[sonic tusk]

so to get them

you divide the non x values by a

[fervent linden]

2/2?

[glacial field]

Might be overcomplicating this. I didn’t learn how to factor like this

[sonic tusk]

maybe tbh

[glacial field]

You can refer to my progress, I’ve got to go

[fervent linden]

ur going?

[glacial field]

Yes

[fervent linden]

oh

bye bye

we need to go back to the question

[sonic tusk]

ya

[fervent linden]

okay divide them by2?

[sonic tusk]

lets start from the beginning cause i overcomplifcated it

[fervent linden]

okay

[sonic tusk]

so 2x^2 - 8x + 6 yeah

you can factor a 2 out

immediately

[fervent linden]

how

[sonic tusk]

2(x^2 - 8x + 3) = 0

divide both sides by 2

[fervent linden]

8/2?

[sonic tusk]

oh whoops

sorry

2(x^2 - 4x + 3) = 0

[fervent linden]

oh

[sonic tusk]

now divide both sides by 2

so x^2 - 4x + 3 = 0

[fervent linden]

do 2 cancel out

[sonic tusk]

yes 2 cancels out

because we divided by 2

0 divided by 2 is 0

[fervent linden]

4/2?

[sonic tusk]

what

wdym

[fervent linden]

divide by both sides?

[sonic tusk]

no look

so we started with

2x^2 - 8x - 6 = 0

yeah?

[fervent linden]

ye

[sonic tusk]

can you divide every single term here by 2

[fervent linden]

yea

[sonic tusk]

do it

[fervent linden]

0 4 3

[sonic tusk]

write it out

or type wtv

[fervent linden]

2/2=0 8/2 =4 6/2 = 3

well i got to go i think its safe to say ima fail😢

bye

.solved

[cedar kiln]

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[sonic tusk]

it might be over for you icl

best of luck, begin grinding math

i used to be worse dw

(mb if that was rude tbh)

[crimson sedge]

what is this

[cedar kiln]

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[crimson sedge]

aa ok

[cedar kiln]

@crimson sedge Has your question been resolved?

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[crimson sedge]

yes thanks

[cedar kiln]

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[bold thicket]

Are these correct notes?

[cedar kiln]

@bold thicket Has your question been resolved?

[bold thicket]

<@&286206848099549185>

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@bold thicket Has your question been resolved?

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[crimson sedge]

solve this eq

[crimson sedge]

2cosA + 3sinA = 3

[upper ruin]

Express the left hand side as R•sin(A + B)

I.e. find both R and B

[crimson sedge]

👍

.close

[cedar kiln]

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[regal yarrow]

stuck on some problems (im sending the image)

[regal yarrow]

l

the key 2|2 = 22 but

there was a first page but i completed it already snd checked over it myself so im lost on these few

[regal yarrow]

*these may or may not be right *

<@&286206848099549185>

[bleak viper]

how 35

[regal yarrow]

The reason i got 35 was because i was told to look at the graph but i thinkmits 60 because 10ou136 students is 60 somthing

[bleak viper]

count the total number of students

out of those 60 have less than 10

now find the percentage

[regal yarrow]

the total they told us is 136

60 out of 136 is 44

[bleak viper]

yeah so find the percentage now

[regal yarrow]

44%

[bleak viper]

so why did u tick 35%

[regal yarrow]

because i did 10 as from money and did it out of 136 and kept going

i made it very complicated for myself

[bleak viper]

[regal yarrow]

i changed it

[bleak viper]

its right skewed, not left skewed

[regal yarrow]

ok for the skewed thing how is it right skewed could i have a example?

to put it in my motes

[regal yarrow]

ahh thank you for that

we actually dont have one of those given to us

[regal yarrow]

now for this so uhh the key is 2|2=22 and i think somone would prefer brand x over brand y because

wait let me re open my calc

[bleak viper]

i dont understand that question so cant really answer

[regal yarrow]

Let me

send it again

oksy here

[regal yarrow]

its using the stem plot

[bleak viper]

which i dont know

[regal yarrow]

oh sorry im lost on the stem plot to lol

[mighty mural]

can someone help me 😢 sorry to interrupt I can’t figure out how to make a channel, did I do this correctly?

[regal yarrow]

.close

[cedar kiln]

Channel closed

Closed by @regal yarrow

Use .reopen if this was a mistake.

[bleak viper]

yes

[mighty mural]

ok just wanted to check

[bleak viper]

also you can open a help channel by posting your question in any of the #help- channels

read #❓how-to-get-help if you're still confused

[cedar kiln]

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[swift gorge]

I really just need the property that comes into place here to find "S". Thanks

[swift gorge]

the o on top of the 396 means multiple

S € ]0,396[

S is also natural

[dire geode]

use euclidean algorithm to find the inverse of 71 mod 396

[swift gorge]

alr

.close

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[cedar kiln]

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[lime badge]

hi

[lime badge]

im back with more coin flipping questions

frownyfrog made me a list like this last time and i basically need another one

i forgot the formula someone gave me

basically , what are the odds of me getting 2 heads in a row if i roll twice, if i roll 3 times, 4 times, all the way to 20

i know the odds are 25% if i roll twice for starters

not roll sorry i meant flip

the odds should increase with every flip righit

[brazen nimbus]

Roll twice,
once , 2 possibliities = H,T
second time , 2 possiblities = H,T
a combination of them
HH,TT,HT,TH = 4 possibilties,
3/4 possibilities could be Heads so 75% you get heads atleast one according to this

oh you mean 2 head

then yea 1/4 = 25%

[lime badge]

ok and what if i dont get heads on the second try, and keep rolling? all the way to 10

[brazen nimbus]

the probability to get a single head/

?

[lime badge]

2 heads in a row

[brazen nimbus]

Ohhh let me think

[lime badge]

okey

[fringe mauve]

so u keep rolling until i get a 2 heads in a row?

[lime badge]

i just did 0.5 x 0.5 for this one to get 25% but idk how to move forward

[lime badge]

yes

[fringe mauve]

what areu trynna find?

[brazen nimbus]

I think i know but i need time

[lime badge]

i want to know the % probability of getting 2 heads in a row on a coin flip on x amount of flips

so on 2 amount of flips, what are the odds i get 2 heads in a row

im also not a bad guy so apologises if bad explanation

math*

math guy*

[brazen nimbus]

what i know is 2 heads in 10 tries is 9 possibilities(2 heads first two times till end two time) which could happen and now i need to find all the possibilities possible which could happen then divide, now im thinking on the 2nd part

[fringe mauve]

if u get 2 head sin the first 2 tries

u only need to roll 2 times

[vivid tundra]

if it's just 2, then we either have to get

1. all tails
2. head, tails
3. head, tails, head
4. tails, head

so the probability of not getting it is 4/2^n?

[lime badge]

this dude basically did it for 3 heads in a row idk how he did the math

[brazen nimbus]

this is how i thought of the 9 tries

[vivid tundra]

so the probability of getting 2 heads in n flips is just 1-4/2^n

[fringe mauve]

so u have (x-1)! (1/2)^x no?

so basicaly

we choose a number of rolls

say like 10

nah

how tf do u think about this

[vivid tundra]

oh wait, what am i talking about
that's completely wrong

[fringe mauve]

really in x number of flips

all u care abotu are teh last two flips

right?

cause we nkeep rolling until we get two heas

[lime badge]

https://tenor.com/view/desmondpacito-cooking-chef-gif-12378159

im lettin yall cook

[fringe mauve]

so like say u haev 4 rolls right to get 2 heads

u can haev

u need to have H T H H

or T T H H

[brazen nimbus]

0 head possibility = all tail = 1
1 head possibility = 10
2 head possibility:-
(no gap or in a row) = 9
1 gap = 8 and so on so 9+8+7+6+5+4+3+2+1 = 45
Im starting to get it

im going from 0 head to all head and then adding all possibilities

[fringe mauve]

thats just binomial

probability

[brazen nimbus]

I dont know the word for it in maths but im inventing it

[fringe mauve]

u cant use binomial probabilty here

it tells u the P( getting 2 heads) but doesnt account for just 2 heads in a row

[brazen nimbus]

and i dont want to be told the answer what im doing im not finished yet

[fringe mauve]

it tell u 2 head anywher

[brazen nimbus]

Im just saying what im thinking i never asked for critisism

Let me continue

ill be back in like 2 mins

and finish this

@lime badge btw is it atleast 2 heads once? or like only 2 heads once or something else

[lime badge]

umm whats the difference

[brazen nimbus]

H+H+H+H is 2 heads twice so it isnt 2 heads only once

but it is atleast 2 heads once

[lime badge]

i just wanna keep flipping until i get 2 heads in a row and know the probability in % that i will get 2 heads in a row for every failed flip, so like 2 flips has a 25% chance of rolling 2 heads, if it fails then what is the % chance for 3 flips to give me 2 heads

[fringe mauve]

for 3 flips u must haev T H H

[brazen nimbus]

Ok I think thats atleast 2 head once ill explain why i think that later but let me be right bacc

[fringe mauve]

which gievs u 1/8

[lime badge]

not sure i understand sorry im a little regarded

i just know every coin has a 50/50 chance of going heads or tails, and i need 2 heads in a row

[fringe mauve]

oh i got it

its (1/2)^x * 2^(x-3)

where x is the flips

think about it

for any amount of flips

u need to have a combination of T H H as ur last three flips

[lime badge]

will you do the math for 2-10 flips and the % chance of getting 2 heads? @fringe mauve

[fringe mauve]

for each?

[lime badge]

yeah wait

i asked chatgpt 💀 usually it just breaks down but it spat this answer

maybe u can save the trouble and confirm if the math checks out

[vivid tundra]

2: 0.25
3: 0.375
4: 0.5
5: 0.59375
6: 0.671875
7: 0.734375
8: 0.78515625
9: 0.8261719
10: 0.859375
I did this computationally

[lime badge]

ok i think it checks out

the ai spat the same answer

i trust the human more tho

[vivid tundra]

yea, I'm pretty impressed with chatgpt on that one

is that the new one?

[lime badge]

bro same because in the past it would just confidently lie to me

[vivid tundra]

the one that can do math

yea

[lime badge]

i have no idea man im on the free version but you get x amount of premium questions

[vivid tundra]

yea there's no way that's not the new one
the new one can use python to evaluate expressions

[lime badge]

wow

i have no idea what that menas

means

does it mean it wont give me a bullshit answer anymore?

[vivid tundra]

it can use a calculator basically

[vivid tundra]

well, it might forget to use the "calculator"

[lime badge]

💀 wait what was it using before

[vivid tundra]

and give you bs answers

[vivid tundra]

just pure guessing

[lime badge]

wtf

yeah i got to a period where i was heavily relying on chatgpt cuz its so convienient but man i just have trust issues now

this shit is not replacing our jobs anytime soon

[vivid tundra]

how gpt works is just predicting what token/word will probably come next
in very simple terms, bc idk the non simple terms are

[vivid tundra]

well, it can use python and search the internet now, so idk

maybe this'll help, it's the ratio of 2 in a row combinations / total
||2: 1 / 4
3: 3 / 8
4: 8 / 16
5: 19 / 32
6: 43 / 64
7: 94 / 128
8: 201 / 256
9: 423 / 512
10: 880 / 1024
||

[lime badge]

% is way easier

anyway my question is solved, thank you guys

[vivid tundra]

it's for imnewtodisco

[lime badge]

ah ok

[cedar kiln]

@lime badge Has your question been resolved?

[cedar kiln]

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[upbeat pike]

Can someone explain this

[upbeat pike]

Isn't the relative velocity supposed to be Vab = Vb - Va

So velocity of aeroplane with respect to wind = 300 -100

Why was taking the velocity with respect to earth necessary

The earths rotation or stuff is not mentioned so we can just ignore that like we do to air resistance right?

[cedar kiln]

@upbeat pike Has your question been resolved?

[upbeat pike]

<@&286206848099549185>

[topaz prism]

Do it 3 more times

Cuz it's been one hour

[upbeat pike]

Won't I get banned or smth

[topaz prism]

It's the rules

You have to ping the helpers every 15 min

[upbeat pike]

And if I dont

[onyx cave]

They have done that but with two perpendicular directions North and East-West

[onyx cave]

Relative velocity is when there is a frame of reference generally it’s the earth
So when the questions says 100 or 300kmph it automatically means wrt earth

Please lemme know if this is making sense

[upbeat pike]

Yes I didn't pay attention to the direction

But why did the 100 turn to -100?

Because both are in different directions?

So north would be +y axis that's makes east -y axis that's why 100 is -100?

[onyx cave]

Wind is blowing east to west so I guess that is the -ve x-axis

[upbeat pike]

Yessss

But how did they get Vaw

They put i = -100 and j =300?

[onyx cave]

The velocity is 100 only but the direction is -I

[upbeat pike]

That's basic magnitude right I forgot

Root of a² + b² here being -100 and 300

Makes so much sense now

[upbeat pike]

Is it possible to find the direction without logbook or any calculator stuff

[zealous fable]

North is +y and East is +x so West is -x

[onyx cave]

Not that I know of

[upbeat pike]

Damn I didn't join the classes when they taught about logbook I'll just have to youtube it

[upbeat pike]

What

[zealous fable]

The wind is blowing from east to west so its direction is -x

[upbeat pike]

9hohh

Yeses

[onyx cave]

Good luck ✌️

[upbeat pike]

Thanks

.close

[cedar kiln]

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[jaunty flare]

I News help with question d please

[jaunty flare]

A isnt a variable listed in any of these so how do I approach solving this?

[cerulean sail]

,rccw

[cerulean sail]

Just as you replaced, e.g. in part a), all x's with 2/3, replace all x's in the definition of h with a

[jaunty flare]

So would that just become 3/a+4?

[cerulean sail]

Yep

[jaunty flare]

Oh I didn’t realize it was that simple

Thanks

[cedar kiln]

@jaunty flare Has your question been resolved?

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[wary fjord]

Currently at the last picture but idk how to continue

[cedar kiln]

@wary fjord Has your question been resolved?

[wary fjord]

<@&286206848099549185>

[glacial field]

Unfortunate end

[sonic tusk]

ong 😔

[cedar kiln]

@wary fjord Has your question been resolved?

[cedar kiln]

@wary fjord Has your question been resolved?

[wary fjord]

<@&286206848099549185>

[cedar kiln]

@wary fjord Has your question been resolved?

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[lofty rivet]

im stuck and i don't know where to start

[cedar kiln]

@lofty rivet Has your question been resolved?

[cedar kiln]

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[paper surge]

how come this is false?

[paper surge]

isn't the set restricted to [2,6]?

hence being finite

[stoic gale]

there are infinitely many real numbers between 2 and 6

[paper surge]

how come?

[worthy ridge]

Density of reals

[paper surge]

wdym

[stoic gale]

see Cantor diagonalisation argument

[worthy ridge]

the Archimedean principle

[paper surge]

this is discrete math btw

idk what that is

[worthy ridge]

Search it

Well you’re dealing with properties of R

Which basically states that there are always an infinite number of numbers between any 2 real numbers

[stoic gale]

think about it intuitively - we can always create another real number between any two real numbers

for example between x and y, there lies a number (x+y)/2

[worthy ridge]

If the set were for $x \in \mathbb Z$, then yes

[wraith dagger]

normalAtmosphericPa=101,325

[paper surge]

I see then, thanks

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[dapper quarry]

I want to know why (b) and (c) are incorrect

[humble karma]

It's not 2

Check the tickmarks

[dreamy void]

Yes Sasuke

check the tickmarks

[dapper quarry]

what tickmarks?

[dreamy void]

on your x-axis

[humble karma]

The axis

[dapper quarry]

i see that f is not continuous on x = 1 and 3

[dreamy void]

ahh

and what did you type

[dapper quarry]

2

what about (c)?

[dreamy void]

same

it's not 2

[dapper quarry]

same as (b)?

[dreamy void]

no

you just need to change the 2 into 3

that's all

else it remains as it is

[dapper quarry]

okay

Thank you

.close

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[cedar kiln]

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[crimson sedge]

How to do #43 of this? Which tells to solve difference quotient.

[crimson sedge]

I don’t know how to simplify numerator that invokes both fractions and radicals

Here are some stuff I tried but I have no idea

[worldly chasm]

@crimson sedge have you tried multiplying the top and bottom by (√(x) + √(x+h)) ?

[crimson sedge]

How

[worldly chasm]

From the point in your derivation

Actually

One second

I think you have made a mistake to get to this point

Because both your numerator and denominator have a factor of (√(x+h) - √(x))

And so you're left with 4/h

Ah I see

You added your fractions incorrectly

[crimson sedge]

How am I supposed to add

[worldly chasm]

4/√(x+h) - 4/√(x)

4√(x)/√(x(x+h)) - 4√(x+h)/√(x(x+h))

You find the common denominator like normal

[crimson sedge]

What do I do after

[worldly chasm]

Try to combine everything down to a regular fraction

And then show your work when you get to that point

[crimson sedge]

What do you mean by combine

Where else can combine

[cedar kiln]

@crimson sedge Has your question been resolved?

[crimson sedge]

Do I do like this?

[worldly chasm]

This is where I was doing my work

You made an error adding these two fractions

@crimson sedge

[cedar kiln]

@crimson sedge Has your question been resolved?

[cedar kiln]

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[devout urchin]

how to solve this?

[fair geyser]

wow what

[raven shard]

suppose x is a power of 2

[devout urchin]

okay

wait

[fair geyser]

you have to guess i'm pretty sure

sqrt x = t

[devout urchin]

can i simplify the left by doing x^1/2^1/2^1/2

[fair geyser]

then 2 is not enough

[devout urchin]

or should i keep it the same

[fair geyser]

and 4 is right

[devout urchin]

yeah i guess i could just try plugging in perfect squares

it's 16

but theres no other way to solve for it?

[raven shard]

no matter what approach you take you will use some kind of guessing

[fair geyser]

i don't see any approach

like in the sense that there are steps before you start guessing

[cedar kiln]

@devout urchin Has your question been resolved?

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[nimble mountain]

Find all of the abelian groups of order less than or equal to 40 up to isomorphism.

[nimble mountain]

for some int k we write it in terms of its prime factors, k=p1^a1 p2^a2 p3^a3..pn^an

[cloud pulsar]

I think bro is cooked, what even is that 😭

[cloud pulsar]

na bro needs an angle to save him, too bad I don' know what abelian groups are

[nimble mountain]

lets just consider k=p^n first

please leave as u are not helping

if we have a group of order k=p^n we can write it as a direct product of cyclic groups of order,

p,p,...p
p^2,p,p,..p
p^3,p,p,..p

as long as powers are different they are distinct i believe?

so trivially for order 1 = {e}

order prime p will be a cyclic group of order p

we are left with, 4 = 2^2
6 = 2 * 3
8 = 2^3
9 = 3^2
10 = 2 * 5
12 = 2^2 * 3
14 = 2 * 7
15 = 3 * 5
16 = 2^4
18 = 2 * 3^2
20 = 2^2 * 5
21 = 3 * 7
22 = 2 * 11
24 = 2^3 * 3
25 = 5^2
26 = 2 * 13
27 = 3^3
28 = 2^2 * 7
30 = 2 * 3 * 5
32 = 2^5
33 = 3 * 11
34 = 2 * 17
35 = 5 * 7
36 = 2^2 * 3^2
38 = 2 * 19
39 = 3 * 13
40 = 2^3 * 5

i got llm to do this so hopefully its right anyway

[woven crescent]

honestly i wouldnt even trust llms with doing addition

[nimble mountain]

ok well

i looked through it and they are all correct

[woven crescent]

i know theyve gotten better but the fact that ive seen them mess up 2+2 before scares me

[nimble mountain]

any that can be written in the form of k=p1p2 are direct products of cyclic groups of order

p1p2 or
p1, p2

[nimble mountain]

@woven crescent is this correct btw?

[woven crescent]

yep

[nimble mountain]

8 = 2^3
12 = 2^2 * 3
16 = 2^4
18 = 2 * 3^2
20 = 2^2 * 5
24 = 2^3 * 3
27 = 3^3
28 = 2^2 * 7
30 = 2 * 3 * 5
32 = 2^5
36 = 2^2 * 3^2
40 = 2^3 * 5

these are left

any p^3 are dir prod of order,
p^3
p p^2
p p p

p^4 as
p^4
p^3 p
p^2 p^2
p^2 p p
p p p p

p^5 as
p^5
p^4 p
p^3 p^2
p^3 p p
p^2 p^2 p
p^2 p p p
p p p p p

left with
12 = 2^2 * 3
18 = 2 * 3^2
20 = 2^2 * 5
24 = 2^3 * 3
28 = 2^2 * 7
30 = 2 * 3 * 5
36 = 2^2 * 3^2
40 = 2^3 * 5

p1^2 p2 as
(p1^2 p2)
(p1^2) p2
p1 p1 p2
(p1 p2) p1

just

every regrouping as long as their cyclic order number is different in some way its different right?

@woven crescent

i think i kinda got the idea i believe

[woven crescent]

ye

for abelian groups of a given order, different groupings (direct products) of cyclic groups with distinct orders will result in different groups up to isomorphism.

[nimble mountain]

i think ill not continue with the rest haha

[woven crescent]

will save a lot of eye pain

and carpel tunnel

[nimble mountain]

to be fair im nearly done

[woven crescent]

could just finish it for the satisfaction if you want

[nimble mountain]

yea

left with
24 = 2^3 * 3
40 = 2^3 * 5

p^3 q

pppq
ppp q
ppq p
pp p q
pp pq
pq p p
p p p q

curious, how would i write this in combinotorics? any idea?

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[odd sierra]

what is going on here 😦

Like how many hours in 2 days i get it

just do 2 days Times 24 hours divided by 1 day

but what this whole thing here 😭

just keep breaking them down????

idk

[soft idol]

so

this is basically

just desired units/initial units

so yea you just multipy 30x24x60x60x10^9

*10e^10

or whatever scientific notation

[odd sierra]

ok i have practice problems

I will show work in a bit

And see if i get it surely

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[celest flame]

okay so basically i'm going through my practice booklet of previous exams before my exam, and i have 0 clue how to solve this, I'm supposed to solve for the area of it and don't really know what to do

[normal cipher]

Can you use calculator

If yes can consider cos rule

[celest flame]

Yes I can use calculator I just don't really know what to do or where to start

[west path]

is this a trapezoid chat

[normal cipher]

Yes

So we can find BE by Pythagoras

Sorry idk latex

[celest flame]

Yeah I got 18.73 on BE but like now I don't know what to do

[normal cipher]

Basically area = base sum * height / 2

So we just need to find ED

Then note that BE is 18.73 and then using sine rule, BE/sin 55=ED/sin 35

Yeah then find ED and then we can get the area

[celest flame]

Oh that makes a lotta sense

Thanks

[normal cipher]

Np

[celest flame]

That's a lot simpler than I thought it was gonna be haha

[normal cipher]

🙂

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[random urchin]

Hi

[random urchin]

I’m very confused on what’s going wrong here

I do the y^2-y^1 / x^2-x^1

10.814-58.551/35-7

And I get

-1.70489

Rounded to three decimals I sssumed it was -1.70, that answer was wrong

But it seems -1.71 isn’t it?

I’m not sure

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[fluid quarry]

Is this true?

If so then how

Point to remember is that z is a complex number

[wicked mantle]

Which statement?

[wicked mantle]

This one?

[bleak viper]

yes

if $z + \frac{1}{z} \in \mathbb{R}$ then $z+\frac{1}{z} = \overline{z}+\frac{1}{\overline{z}}$

[wraith dagger]

Astar777

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[hoary parrot]

what am I doing wrong

shouldn't it be 6 and not 4?

ah fuck gtg eat lunch, I'll read replies later thx in advance

[brazen dagger]

Surface area of sphere= 4 * pi * r²
2 hemisphere= 1 sphere

So 4 * pi * x²

[idle crystal]

the surface area should not include the circles on top of the cylinder

since its covered by the sphere

[brazen dagger]

Total SA = (Surface area of cylinder(without top and bottom hemisphere)+ 2 * surface area of hemisphere

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[dreamy summit]

Hey there

[dreamy summit]

can someone give me a hand?

nevermind

i just got it

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[crude atlas]

Why do we take positive 1.37 not the negative answer, I understand there is only 1 intersection

[crude atlas]

Nevermind just realised

But I got a new question how would u find where it intersects at 2 points

Would it just be where r is greater than 1.37?

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[naive iron]

can someone help me understand my math homework im in grade 8

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[stray otter]

How do I use induction to prove the AMGM inequality

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[stray otter]

<@&286206848099549185>

[mental trail]

you mean the general AM GM?

ok

what I would do

you want to prove that for any n, for any a_1,...,a_n positive real numbers, AM(a_1,...,a_n) >= GM(a_1,...,a_n)

[stray otter]

Yeah

[mental trail]

ok

[stray otter]

I did the base case

[mental trail]

what I recommend:

[stray otter]

Of a1 and a2

[mental trail]

suppose n = 2^k

prove it by induction on k first

to show that it's true for any n = 2^k

do you understand what I mean?

[stray otter]

Wait

Hol up

We assume n=2^k works and we need to prove n=2^(k+1) works?

[obtuse mango]

yeah so if u try a normal induction on AM-GM it's actually really hard

[stray otter]

Uh huh

[obtuse mango]

if u try the problem u'll realise it's fairly easy to do for powers of 2

[mental trail]

so this is the first step yeah

do an induction to show that it works for

n = 2,4,8,16,32,etc...

and then, if you pick any other n

you'll be able to find k such that n <= 2^k

and use the fact that AM-GM inequality is true for 2^k

to show it works for n

try it out and if you're stuck at some point we're here to add more info

[obtuse mango]

once u've done this think about how you can use the fact that it's true for powers of true to prove it true for a general n

[stray otter]

Ok

I’ll try

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[hexed vortex]

Suppose that dy/dt = f(y) has a finite number of equilibrium points, the number of sources must equal the number of sinks

[hexed vortex]

is this true or false?

I put false

because

if you have like an odd degree that has 3 equilibrium points for f(y)

then

2 can be a sink

and 1 can be a source

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[dapper mulch]

probably a dumb question but why is
+-a>x equal to [-a,a]

[crimson sedge]

because