help-10

[lapis charm]

in this hypothetical world where the fly can redirect instantaneously i think it should be "actual infinity"

[leaden jetty]

Yup

[lapis charm]

a better way to say it ig is that for any natural n, the fly will hit the cars more times than that

this actual infinity is countable tho

[leaden jetty]

So totally different topic but if the cars were mirrors and fly was light beam wouldnt light beam bounce off the mirrors infinite types? (Assuming exactly 90 degeees)

So doesnt this kind of thing happen irl

[lapis charm]

i guess so

but it probably dissipates a bit every time

so its not like you get infinite energy from it

[leaden jetty]

The mirror emits thw light right?

[lapis charm]

reflects?

i dont know that much about physics but i think were saying the same thing and were right

[leaden jetty]

Okay

Ty for the help

Do i do this as resolved?

[lapis charm]

one last thing

have you ever heard of zenos paradox

[leaden jetty]

.

[lapis charm]

maybe xeno i forgot

[leaden jetty]

Nope

[lapis charm]

\

this thing

people used to be really stumped by this

how is it that to travel from one end of a room to another, you need to travel an infinite number of finite distances?

[leaden jetty]

Oh

[lapis charm]

but if you have a basic understanding of limits it makes total sense

same with fly

[leaden jetty]

Yeah ik how limit works i thoguh answe was limit

[lapis charm]

the fly hits as many times as there are digits in pi

[obtuse pebble]

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[obtuse pebble]

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[split dew]

How would I solve this?

[tame python]

are you allowed to use l'hopital?

[split dew]

Uhh I don’t believe we’ve learned that

[tame python]

are you allowed to use the limit definition of the derivative?

[split dew]

I think so

[tame python]

alr beacuse instead of either of those youre going to rationalize

do you know how to rationalize

[split dew]

Multiply top and bottom by the bottom but switch the subtract to add?

[tame python]

sure

you can go do that then see how far you get

[split dew]

Oh ok thanks I’ll try that

[tame python]

np

[split dew]

I haven’t done limits in a while and I’m doing review rn

[split dew]

Thanks I got the answer

[tame python]

nice

[split dew]

.close

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[graceful marten]

I need help changing the form of this into what they want

[tame python]

write (5x - 3)^3 as (5x - 3)(5x - 3)^2

[graceful marten]

how did you determin the side?

[graceful marten]

ill do that

Ok did it

[tame python]

dont be sloppy, write all of it

also I am realizing you calculated the derivative incorrectly

[graceful marten]

I dont think so?

[tame python]

nah I made a mistake

[tame python]

now factor a (5x - 3)^2

[graceful marten]

(5x - 3)^2 ( (30x^2 -18x) + 45x^2 )

[tame python]

then combine like terms

[graceful marten]

U can do that?

( (30x^2 -18x) + 45x^2 )

oh :/

Srsly?

damm

(75x^2 - 18x)

Or not like that

[tame python]

now factor 75x^2 - 18x

[graceful marten]

(5x - Sqrt(6) ) (5x + Sqrt(6) )

[green epoch]

[graceful marten]

(5x - 3)^2 (5x - Sqrt(6) ) (5x + Sqrt(6) )

[tame python]

first off

no

second off

reread 75x^2 - 18x

dont delete your message

I dont delete mine when I realize Ive made a brash mistake

[graceful marten]

Sry i deleted it bc i know ur usually 99% right

So thats y i deleted it

and then i read ur msg

3x(25x -6)

3x(5x - 3)^2 (25x -6)

[tame python]

yep thats all

[graceful marten]

Im a bit intrigued

5 ( (30x^2 -18x) + 45x^2 )

So you can always simplify the inner bracket

[tame python]

lets break this down first

[graceful marten]

is there a situation where you cant

[tame python]

I think its better if you stick to the rules here

first, the operations are already being done left to right

so (30x^2 - 18x) + 45x^2 is identical to
30x^2 - 18x + 45x^2

second, rewrite - 18x as + -18x
30x^2 + -18x + 45x^2

third, you use that addition is commutative
30x^2 + 45x^2 + -18x

[graceful marten]

why +- ? (is it so its easier to factor? visually)

[tame python]

because you wouldnt be asking if it said (30x^2 + 18x) + 45x^2

[graceful marten]

No i would have too

[tame python]

do you know that addition is associative?

[graceful marten]

not sure what that means

[tame python]

of course

it means (A + B) + C = A + (B + C)

"associative" lets you show that it doesnt matter which + is done first in a chain of terms added together

[graceful marten]

But from what I understand

5 ((5x+4) -4)

Is the same as 5(5x+4) + -20
same as 5(5x)

[tame python]

and why are you doing it this way?

instead of the easier way of
5((5x+4)-4)
5(5x+4-4)
5(5x)?

if you let me finish,

similarly addition being "commutative" means addition allows A + B = B + A

[tame python]

so the real reason behind erasing the parentheses up here is that addition is associative

and also that A - B is the same as A + -B

therefore,
(A - B) + C
(A + -B) + C
associativity
A + -B + C
commutativity
A + C + -B

similarly for the other one,
(A + B) - C
(A + B) + -C
associativity
A + B + -C
commutivity
A + -C + B

[graceful marten]

Is the last associativity missing a +

Nvm

I see it

Oh ok

I think that helped me

[tame python]

its always good to be strict

youd never know when this breaks

right now, it doesnt

but you use this idea somewhere where it doesnt belong and you make a mistake

for most use cases, you can use the general idea that addition is very fluid and ignores parentheses

[graceful marten]

Im going to write down quickly what the difference with associaticity and commutatitvity is

[tame python]

and to treat - N as + -N to ensure that subtraction doesnt mess anything up

[graceful marten]

Yeah I do that always

Because it can throw you off guard when you have ()() -5()()

When you expand RHS

You either include the -5

To all

And then add it + - ?

Or you just don’t and do +5 x?

And then minus it at the end

Each of them

Either way thank you for your help

[tame python]

np

[obtuse pebble]

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[graceful marten]

.close

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[latent timber]

help

[latent timber]

12b

i did a

[timid silo]

if none of the boys walk then two girls must walk

[obtuse pebble]

@latent timber Has your question been resolved?

[latent timber]

i tried but still got it wrong

i did kike 18C8x10C6x4C4

and got it wrong

[bold abyss]

take 2 girls out of 10 girls first

[latent timber]

yeah

[bold abyss]

10C2

[latent timber]

uhuh

then

[bold abyss]

10C2x18C8x10C6x4C4

[latent timber]

ohh

i forgot that one calculation

thx

[bold abyss]

remember to close the channel

[latent timber]

okk

this my first time using

wait how do i close

[bold abyss]

. close (delete the space)

[latent timber]

okk

.close

[obtuse pebble]

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[old nymph]

I need hints

[obtuse pebble]

@old nymph Has your question been resolved?

[obtuse pebble]

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[timid silo]

this is in my syllabus..so what quwstions should i be expecting related to def of sets like do i have to define sets in the builder notation?

[dusk widget]

these are all just different examples of sets

I’m not quite sure what you’re asking?

[timid silo]

what is the syllabus telling me to do

[kind hawk]

well presumably that you can read and produce this notation

[dusk widget]

Thank you for putting my thoughts into a coherent sentence lol

[timid silo]

Basicalaly TELLING ME TO LEARN BUILDER NOTATION RIGHT

[kind hawk]

why are you always screaming

but yes it seems that way

[timid silo]

its not screaminfg (ok nvm it is)..just a lot of emotions coz exams soon and other stuff happening so confused emotions and yk wat i mean? anyway THANKS BRO..WWWWW

.close

[obtuse pebble]

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[timid silo]

what is 3x+1

[high lily]

an expression

[knotty agate]

collatz conjecture

(excuse me if i mistake the spling)

[timid silo]

yeah

[knotty agate]

https://en.wikipedia.org/wiki/Collatz_conjecture

yes

[timid silo]

yeah

[knotty agate]

so close?

[timid silo]

yeah

are u indian?

[knotty agate]

yeah why and how

[timid silo]

i am also indian

[knotty agate]

oh damn

nice

[robust bloom]

lol one more here

[timid silo]

what damn in that 😆

[timid silo]

wah badhiya

[knotty agate]

lmfao

hindi too

[timid silo]

the fact we are chatting in mathematcis channel

[knotty agate]

💀

[robust bloom]

yeah

[timid silo]

sacchi????

[robust bloom]

get back to pt

[knotty agate]

.close

[timid silo]

.close

[knotty agate]

ugh

[obtuse pebble]

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[timid silo]

i did it

[knotty agate]

oh i forgot

💀

[timid silo]

lol

[obtuse pebble]

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[fresh linden]

Can't you tahe the equations 2 at a time and get a relationship between the three sides a b and c and sub it in the formula of cosA

[wary hill]

world would have been taken over by ants till that time

got a shorter approach

[fresh linden]

I'm trying

May get the solution

[wary hill]

dont

i tried it got way too lengthy

[fresh linden]

No I'm trying to find a shorter method

[iron edge]

The actual length of a b c doesn’t matter at all

You just need to know a : b : c

[wary hill]

how didya get here?

b+c =11 stuff

[iron edge]

Trial and error

[fresh linden]

Assume

[wary hill]

ohh aight

[fresh linden]

Also I got a and c in terms of b

Can use it if you want to

[wary hill]

a is correct right?

[fresh linden]

a=154/121b

[wary hill]

option a i mean

[fresh linden]

And c=2b

[fresh linden]

Yea option a is correct

[wary hill]

we can add all these and get a,b,c equal to 7,6 and 5 right?

[iron edge]

Precisely speaking (a,b,c) equals to (7k,6k,5k)

k is a positive number

[obtuse pebble]

@wary hill Has your question been resolved?

[obtuse pebble]

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[obtuse pebble]

@wary hill Has your question been resolved?

[severe reef]

I believe the data is insufficient

Are ABC given to be angles of a triangle or something?

[wary hill]

triangle ofc

[severe reef]

It's not an 'ofc' thing, there could be any arbitrary relation between 3 angles.

It should be mentioned

Anyway

You can assume sinA=3/5 and sinB=4/5 and sinC=1 for a quick solution

A triangle right angled at C

Or if you want to solve it properly , use sine law to see how the ratio of sides is the same as that of the sine of the angles

Then apply cosine rule

By letting sides =3k,4k and 5k respectively

[wary hill]

ig the first one would work better

[severe reef]

Yeah it's quicker

Essentially I'm just letting the 'k' =1

Since the options are implying that the answer is independent of the actual value of k

If you work it out without assuming k, you shall arrive at the same result

[wary hill]

4:3 right?

[severe reef]

Yes

[wary hill]

yeah but it would take time

thnx!

[severe reef]

You're welcome

[wary hill]

.close

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[timid silo]

Are these two the same thing

[tardy epoch]

no because

,tex .freshman

[warm shale]

riemann

[timid silo]

Oh

[timid silo]

What about this

Or is it not valid for the same reason

[obtuse pebble]

@timid silo Has your question been resolved?

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[timid silo]

standard deviation

[timid silo]

how did he get that s.d.?

i got 15.81

[rapid tusk]

how did u get 15.81

[timid silo]

for the first one

where it just gives you all of the x values

mean is 30, right? so

[rapid tusk]

u might have set up ur numbers wrong

mean is 30 ye

[timid silo]

nope

[rapid tusk]

can u show me ur work

if possible

[timid silo]

(10-30)^2 + (20-30)^2 + (40-30)^2 + (50-30)^2

gives u 1000

[rapid tusk]

yes

then divide by 5

[timid silo]

i divide by 4

no 5

4*

[rapid tusk]

5 numbers in the set

[timid silo]

ur meant to divide by n-1?

[timid silo]

why did this guy say n-1

[rapid tusk]

u only use the (n-1) formula if u know ur numbers are from a sample

he is using the formula for when u know there are more values that u dont have

but for ur case u have all ur numbers

so u use the population version

https://www.google.com/url?sa=i&url=https%3A%2F%2Fm.youtube.com%2Fwatch%3Fv%3DUk98hiMQgN0&psig=AOvVaw3CyvMS2Y4gsaUR2e_SilxY&ust=1709923183412000&source=images&cd=vfe&opi=89978449&ved=0CBUQjhxqFwoTCLDn9LDm4oQDFQAAAAAdAAAAABAS

[timid silo]

sk];

fair man fair

thank u

[rapid tusk]

np

[timid silo]

.close

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[elfin cedar]

i need help for 1+1

[elfin cedar]

i need help for 1+1

[gilded needle]

don't troll in the help channels

[elfin cedar]

what

[whole dock]

.close

[obtuse pebble]

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[elfin cedar]

i need help

for 1+1

[boreal belfry]

its 2

you can stop now

[elfin cedar]

how did u get it

[boreal belfry]

getting ban for saying the nword what a beatiful life

[obtuse pebble]

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[junior kiln]

What went wrong, where did i make a mistake?

[junior kiln]

sorry if the handwriting is bad, i was just writing for myself

[junior kiln]

dont mind the range i have on te top, should be -137 not 137

[obtuse pebble]

@junior kiln Has your question been resolved?

[surreal solar]

in your 7th line you should have -2, as you're substituting in sin^2-1 so you need to multiply the -1 by 2 also

[junior kiln]

ah, youre right

!close

?close

/close

.close

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[cosmic veldt]

2 distinct subgroups of Z36 with order 9 are?

[obtuse pebble]

Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.

@cosmic veldt Has your question been resolved?

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[midnight moat]

Valid?

[vague spindle]

You made an error on the second operation; the -sin^4(x) doesn’t just vanish when divided by itself, it should become 1

[midnight moat]

u right

im doing it rq again

[vague spindle]

Additionally, your last step would be fallacious as proving the identity for x=2pi does not prove it in general

You’ll want to use double angle identity for cos2x

[midnight moat]

when i use my sci calcu tho, theres an option for var x

both still still equates 1

[vague spindle]

Because x is probably set to a specific value?

Also the identity is true that’s just not a valid proof of it

[midnight moat]

nah i didnt let it be anything

i mean

i didnt let it be specific

[vague spindle]

Enter just x into your calculator and hit enter

[midnight moat]

yah is what i did

[vague spindle]

Did it return a value?

[midnight moat]

yah is 1

i tested

[vague spindle]

Then x is set to 1 by default…

[midnight moat]

oh

but when i let x be 2pi

in my pic

[vague spindle]

Well yes the identity is true

[midnight moat]

its still 1

[vague spindle]

You just can’t prove it like that

[midnight moat]

yeah i get u

im fine if its valid enough tho, dk how much this assignment is asking tho

this the instructions

[vague spindle]

Then you have to prove it

Do you have the double angle identities for cos2x on hand

[midnight moat]

the formulas right

i wrote it but it looks dreadful os imma use the pics from google

[vague spindle]

Using that and the Pythagorean identity it seems you can prove this

I recommend eliminating either sin or cos in the RHS using Pythagorean identity

[midnight moat]

alr i will try now

[obtuse pebble]

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[earnest field]

Helllo

[earnest field]

Not working lmao.

How would that be?

I would like to know to actually solve it

[pastel wren]

a^-1 is not -a its 1/a

so (9x^2y^6)^-1/2=1/(9x^2y^6)^1/2

[earnest field]

Correct

So now I have 1/3x3y?

Or is it 1/3xy^3?

[pastel wren]

latter

[earnest field]

Whet

[pastel wren]

this one

[earnest field]

Ohh

So the answer is 1??

[pastel wren]

yes

[earnest field]

Thank you!

[pastel wren]

you're welcome

[earnest field]

i only have 3 more problems I need help with

[pastel wren]

im going to sleep now sorry

[earnest field]

Lol it’s okay

Any other helpers available??

I completed the one below it correctly I believe

<@&286206848099549185> anyone able to help with the top problem please?

Or is this it?

[surreal solar]

I believe it is asking you to take the first one away from the second
So (x^3+3x^2-2x) - (x^2+3x-4) which would be (1)

[earnest field]

OHHH

wtf I got every answer except the right one lmao.

Thank you!

And for number 2

I have no idea where to start

[surreal solar]

When working out the domain you can't square root a negative number so 9-x^2 >=0. Rearrange this to find your possible values of x

[earnest field]

How?

(9+x)(9-x)^ 1/2

[surreal solar]

$9-x^2 \geq 0$

So how would you get the x^2 to the RHS?

[warm shale]

Savinia

[surreal solar]

Can you rearrange this for x? ^

[obtuse pebble]

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[obtuse pebble]

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[signal fox]

What would the factors of x^2-2x-12 be i had to use the quadratic formula and got 3+/- i (something like that it was a test question)

[signal fox]

Please ping me when you get around to answering it

[marsh geyser]

Show your work

[marsh geyser]

That has real roots

[obtuse pebble]

@signal fox Has your question been resolved?

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[static relic]

I am confused on how to do question d and also the only reason I got the -oo and oo for the domain was i notice that was the answer for the first 3 but I dont know why can someone explain why?

[drifting badger]

First find the expression for f/g

[static relic]

(x^2 -4x) divided by x+2

[drifting badger]

Yes

For which value of x is this not defined?

You're dividing by x + 2 - when can't you divide by this?

[static relic]

when the denominator is 0?

[drifting badger]

Yes

[static relic]

so x=-2?

[drifting badger]

So f/g is not defined for g(x) = 0

Exactly

[static relic]

so i just replace x with -2

[drifting badger]

If x = -2 then f/g is not defined

It will be defined for any other value

So -2 is not in the domain of f/g

But hey, that's just a theory

A Math Theory

[static relic]

why is the domain for the others -infinity,infinity

is it cuz there is x?

and not a number?

[drifting badger]

Because there are not values within (-∞, ∞) that x cannot have

That is, f + g, f - g and fg are all defined for any value of x

[static relic]

so is the only reason d has something that can make it untrue is since its a fraction?

and 0 cant be a denominator

[fathom flicker]

@drifting badger is a troll ignore him 👁️

0 cant be a denominator

[zenith raft]

[drifting badger]

Yeah

[static relic]

ok thanks

[drifting badger]

https://tenor.com/view/dhmis-dont-hug-me-im-scared-duncan-duck-gif-27455353

[static relic]

.close

[obtuse pebble]

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[narrow hemlock]

What is this? I don’t know where to start

[tender rune]

-9 x -9 x -9 = -729

[narrow hemlock]

where the -9 come from?

Or is that just an estimation

Or guess

To get the right answer

[high lily]

identify factors of 729

[narrow hemlock]

9^-3?

[tender rune]

that = -729 yes

[narrow hemlock]

Ah I see

So for my assignment for the work I just put that then?

[tender rune]

yeah

unless u need to show some working

u can just make one of these branches that have common factors

[celest dune]

729 = 9x9x9 = 9³

Multiple by (-)

-729 = -9x9x9 = -9³

Now the thing about the number in your image call cubic root will will reduce all the ³ from your number

So the cubic root of -729 = -9

Which is the answer of your questions

[obtuse pebble]

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[narrow hemlock]

Yes thanks

[obtuse pebble]

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[visual helm]

so sigma (infinity), n=1, 1/ln(n+1), is it convergent or divrgent? use DCT or LCT

[visual helm]

I learned p series, geometric, dct, lct, alt, ratio, root, integral, telescoping, limit of n th

[gilded needle]

i think a simple comparison will work here

[visual helm]

but my teacher want this question to be solved in dct/ lct and Iam not rlly good at both ngl

[visual helm]

so just dct?

[gilded needle]

what's a simple thing you can compare 1/ln(n+1) with?

[gilded needle]

what is that, direct comparison test? yea

[visual helm]

yes

1/ln(n)?

[gilded needle]

try something without a log

use the fact that log grows very slowly, so 1/log(n+1) decreases very slowly

[visual helm]

1/n?

or 1/n^2?

[gilded needle]

1/n should work

[visual helm]

ok

so comparing with 1/n, then since 1/n= then since 1=1(p series), then it is divergent so

1/n>1/ln(n+1) which is ln(n+1)>n

it is diverent

@gilded needle like that?

I am not rlly sure am I doing it right

[swift sky]

I believe you can use 1/n LCT

Try

[visual helm]

nvm I solved it

yes it is lct

cuz dct failed cuz I plugged 1 in which is ln2> 1(false)

[swift sky]

LCT is so good for most problems

I just had tedt on series today

[visual helm]

then I switched to lct which is 1/n/1/ln(n=1)

plus lhospital = infinity aka divergent

[visual helm]

I learned power yesterday

still a bit confused ngl but gonna study it later

and how to cancel this channel

since I got my question solved

.close

[obtuse pebble]

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[foggy prism]

Is this how you do sin(a+b)?

[fierce elbow]

right

[foggy prism]

so 56/65?

[fierce elbow]

oh mb i was afk

yeah correct

[crude coral]

sin(a+b) = sina cosb + sinb cosa

[foggy prism]

i think i mistyped that the numbers are still right tho correct?

[crude coral]

the values u used were of
sina sinb + cosa cosb which is equal to cos(a-b)

[foggy prism]

oh

[crude coral]

here

[foggy prism]

So it would be the highlighted?

[crude coral]

why highlighted?

[foggy prism]

for sin(a+b)

would thaat be the equation

[crude coral]

yes

[foggy prism]

and cos(a+b) would be -12/13 x -3/5 - 5/13 x 4/5?

[crude coral]

yeah

[foggy prism]

what i got for both is sin(a+b)=-93/65 and cos (a+b)=16/65

[crude coral]

how do u get -93?

$$5 \times -3 + (-12 \times 4) = -15 - 48 = -63$$

[warm shale]

JustToPro

[foggy prism]

i used my calculator but it may be wrong

i will do it by hand right now

[crude coral]

use brackets , calculator doesnt read minds

if u typed some thing like this
$$5 \times -3 -12 \times 4$$
the calculator goes
$$- 15 - 12 \times 4 = -27 \times 4 = -108 $$
which still isnt 93 so idk how u got that

[warm shale]

JustToPro

[foggy prism]

i got -63/65 by hand

[crude coral]

thats the correct answer

[foggy prism]

wait wtf

how did i get -93/65

is cos(a+b) 16/65 still?

[crude coral]

yes

[obtuse pebble]

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[sinful seal]

Can someone help me with these questions, what do all the symbols mean and how do I solve the questions?

[latent walrus]

you dont know any of the symbols?

8|9^n-1 for example means 8 divides 9^n-1
ie 9^n-1 is divisible by 8 (is a multiple of 8)

[sinful seal]

I think I know some of them but not 100% sure, n = integer, z = complex number and the plus means positive, the funny e means element

Don’t know about the triangle one

[latent walrus]

the big Z's represent integers

[sinful seal]

Oh

[latent walrus]

Z^+ means positive integers

[sinful seal]

Ok

[safe haven]

if you meant like the upside down A, it means for all

[sinful seal]

Yes thanks

[latent walrus]

$n\in\mathbb{Z}^{+}$

[warm shale]

AℤØ

[latent walrus]

means n is a positive integer

[sinful seal]

Oh so n has to be a positive int

So how do I start the question off and correctly write it out?

[latent walrus]

do you know what induction is

[sinful seal]

Yeah sort of, it’s the k + 1 stuff

I just suck at writing it out and haven’t done it with divisiblity

[latent walrus]

whats our base case

[sinful seal]

N = 1

[latent walrus]

does that hold

[sinful seal]

Yeah because 8/8, but how would I write it for a exam?

[latent walrus]

$n=1$
$$9^1-1=8=8(1)$$ True for n=1

thats that

[warm shale]

AℤØ

[sinful seal]

Alright

Then assume true for n = k?

[latent walrus]

indeed, what would that look like

[latent walrus]

you should state A belongs to the integers

[latent walrus]

good, ish

[warm shale]

AℤØ

AℤØ

[sinful seal]

Is that a the same one that the 8 was in front of?

[latent walrus]

im just using a to denote terms

like a_1 was your base case n=1

a_k is n=k
a_(k+1) is n=k+1

[sinful seal]

Yep

Like that

[latent walrus]

yeah

try see if you can simplify that into a multiple of 8

[sinful seal]

Does 9^k+1 - 9^k =9^1?

[latent walrus]

no

[sinful seal]

my brain just can not figure it out for some reason

[latent walrus]

try factoring out 9^k

[sinful seal]

i just cant do it for some reason, should be easay'

[latent walrus]

may help if i say 9^{k+1}=9*9^k

[sinful seal]

?

[latent walrus]

oh dear

theres technically only one thing wrong

but youve made it messy

[sinful seal]

1/9k

[latent walrus]

just simplify to 9^{k+1}-9^k first

then factor out

[sinful seal]

yeah ok like that?

then i have 9^k(8) which is divisible by 8?

[timid silo]

💀 is this sixth form stuff

[latent walrus]

yeah, now just add a_k back

which is 8A

[sinful seal]

No im just stupid lol

[sinful seal]

wdym, factor it back in?

[latent walrus]

no, literally add it

$a_{k+1}-a_k=9^k (8)$ So add $a_k$ back so you just have $a_{k+1}=...$

[warm shale]

AℤØ

[latent walrus]

you dont want to add it in that form

what does 9^k -1=

[sinful seal]

8A

[latent walrus]

thats what you want to add

so you can just factor out 8

[latent walrus]

si

[sinful seal]

Which is what we want

?

[latent walrus]

indeed

that shows a^{k+1} is divisible by 8

[sinful seal]

Ok sorry that took so long

[latent walrus]

no worries

[sinful seal]

Do I have to write that in math language?

[latent walrus]

you do need to write a statement yeah

like hence true for n=k+1

then your inductive statement

like true for n=1, if true for n=k then true for n=k+1 hence true for all positive integer n blah blah by induction

[sinful seal]

alright cool, imma leave this chat open and try b reeal quick, thanks

[latent walrus]

np

[sinful seal]

Think I might have butchered the last step

Oh I stuffed something up 1 sec

what next i cant really factor 3 out without fractions

[latent walrus]

one momento

[sinful seal]

oh i stuffed up gotta redo it dont worry

Yeah I don’t know I get to there and don’t know what to do

[latent walrus]

4*5^k+20*11^k
4[5^k+5*11^k]=4[ (5^k+2*11^k) +3*11^k]
=4( 3A + 3*11^k )=3[4(A+11^k)]

a bit of algebraic trickery

can add a_k back

[sinful seal]

thats disgusting, so you times every thing by 4 so you could bring 5 out the front?

[latent walrus]

i didnt times everything by 4

i just factored 4 out that was already there

my first line follows directly from your last one

[sinful seal]

from that line yeah? Because the other scrren shots i sent were wrong?

there*

[latent walrus]

yup from there

[sinful seal]

what happened to the 5^k+1?

[latent walrus]

became 5*5^k

subtracted the other 5^k

became 4*5^k

[sinful seal]

oh is that a exponent law?

[latent walrus]

hm?

sure

[warm shale]

AℤØ

[sinful seal]

where did 20 come from?

oh i think i see

Got that I just don’t understand how 55^k-5^k = 45^k

[latent walrus]

same as how 5x-x=4x

no difference

[sinful seal]

yeah ok make sense

*close

.close

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[deep ferry]

finished part A but now I struggling on part b

[deep ferry]

got an integral in terms of dr but i only have x+y+z

[worn yoke]

https://tutorial.math.lamar.edu/Classes/CalcIII/FundThmLineIntegrals.aspx

use the gradient you found earlier

[deep ferry]

oh so its just the original function composition?

with r

is it this instead?

[worn yoke]

yes

[deep ferry]

ok thank you

.close

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[gleaming rose]

create a tool using either excel or python that will translate
two axis of rotation and their length of arms (input) to a location in X and Y
space ((x,y) output) and vice versa. The tool will generate both kinematics
and inverse kinematics for a parallel SCARA robot. We are then going to
test the tool by building an example according to the tool data for
validation.
I know how to do the python writing i just need to understand the trig involved. The L1,L2 can be filled with any values along with the rotation i just need to understand how this works.

[obtuse pebble]

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[gleaming rose]

.reoopen

[onyx fossil]

Is there a way to prove that this solution for extended proportionality works?

[onyx fossil]

If 120 workers finish a job in 12 days working 8 hours a day, how many workers are needed to
finish the job in 10 days working 6 hours a day?
Solution :
x*10*6=120*12*8

I saw this method and it works everywhere but I cant seem to find any proof

[fresh linden]

i don't think there's a proof

[onyx fossil]

But there must be right?

[fresh linden]

there is the case of simple proportionality as well

i didn't find a proof for that either

but the theorem is usel in a lotta ways

[onyx fossil]

Anyone else may know an answer to prove this?

[obtuse pebble]

@onyx fossil Has your question been resolved?

[obtuse pebble]

@onyx fossil Has your question been resolved?

[obtuse pebble]

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[hard crystal]

i think i have gotten the 4 equations but q2 and q3 do not make sense to me at all

[hard crystal]

the equations i have are:
x4-x1=10
x2-x3=5
x3+x2=5
x3+x4-x5=40

<@&286206848099549185>

<@&286206848099549185>

😭 😭

pls help

<@&286206848099549185>

[dark hedge]

Hi

[hard crystal]

YES

hello i require assistance with q2 and q3 please

[dark hedge]

I have the same situation as u.No one is coming in my server

[hard crystal]

bruh

[dark hedge]

I don't know these 😅

[obtuse pebble]

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[sour lantern]

how do I find the formula of this function?

[timid silo]

lagrange interpolation?

[sour lantern]

I don't know what that is. I just have to find the formulas for each range

so for example
$f(nTs)=0$ for $n < 2$

[warm shale]

Erzis

[sour lantern]

I guess something like that

and then come up with a single formula to describe it

so generally just find f(nTs)=...

[obtuse pebble]

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[dusk solstice]

how to solve this

[mental hatch]

Hi

[dusk solstice]

$(1+2)(3+4)$

[warm shale]

Katanapultti

[dusk solstice]

i get this wrong

[deft vine]

okat let me solve

[mental hatch]

[(1+2)(3+4)\
= 13 + 14 + 23 + 24\
= 3 + 4 + 6 + 8\

[deft vine]

this?

[dusk solstice]

ok ty

[mental hatch]

If u still don't get it tell me

[dusk solstice]

.close

[obtuse pebble]

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[mental hatch]

Yw

Did u find the answer

[dusk solstice]

yes

[mental hatch]

Ok

[deft vine]

its 21

[mental hatch]

.21

[deft vine]

yea

[dusk solstice]

why point?

[deft vine]

it can be 3.

3.7

[dusk solstice]

???????????

.reopen

WHAT

[obtuse pebble]

✅

[deft vine]

the answer is 21

.close

[dusk solstice]

or 3???

3.8

[deft vine]

21

21

[dusk solstice]

6*3=21

-3

[deft vine]

what are u asking

tell me

[dusk solstice]

how can i be 3.7

[deft vine]

the answer is 21

[dusk solstice]

u say 3.7

[deft vine]

3.7 is wrong

[dusk solstice]

so you got it wrong?

[deft vine]

missanswer

ye

[dusk solstice]

okay nt. it was complicated so no wonder

.close

[obtuse pebble]

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[graceful marten]

Ok uhh....

Sin ^-1 1/2 and -1

gives you

1/2Pi and -1/6Pi

where did they get thoes values from????

[fallow reef]

@graceful marten

If you're getting -pi/6, then there's a negative associated with your arcsin somewhere

So while the Unit Circle normally traverses counterclockwise from 0, negatives traverse clockwise instead

[obtuse pebble]

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[sturdy bridge]

I need to learn stochastic for my exam this Monday and its going pretty well but I don’t get the difference between these two experiments:
There are two red balls and one blue ball in a pot. You don‘t put them back in both cases.

1. You grab a random ball and then a second one, what are the chances of getting 2 reds?
2. You grab two at once. Whats the probability for 2 reds?

[sturdy bridge]

So essentially i just don‘t know how to calculate probabilities for multiple simultaneous events

Wouldn‘t it just stay the same?

[drifting wraith]

there's no difference

[sturdy bridge]

My teacher gave us this example: 4 red balls, 5 green balls, 3 blue balls. You don‘t put them back once again. The solutions are 1 over 11 for the successive pulls and 1 over 22 for the simultaneous pulls

[sturdy bridge]

[sturdy bridge]

How in gods name did she come up with those numbers then

[drifting wraith]

i don't know what she meant

i think she was trying to explain something real but it came out making zero sense

[sturdy bridge]

The chance of getting two red balls in a row is roughly 9% and the chance of getting 2 simultaneously seems to be half of that

So somewhere near 4.5%

[sturdy bridge]

She didn‘t literally say it tho

It’s in the exercises she gave us

And those are her solutions

[drifting wraith]

there are 66 different pulls you can make

6 of them are 2 red

[sturdy bridge]

So one in 11

I got that one

[drifting wraith]

yeah

there's no difference, it's the same procedure and the same answer

i can't tell what mistake she's making

[sturdy bridge]

She also said P(D) = P(E) tho

I think she‘s just tripping💀

[drifting wraith]

you need 2 pots to do this

[sturdy bridge]

Huh

Should i just correct her then?

[drifting wraith]

it's like she's saying we don't put the ball back, but if I pull them at the same time, it doesn't matter haha now i get the answer like i did put it back

[sturdy bridge]

As I’ve said I’m confused too lmao

I‘ll just say it‘s 1 over 11 again

Thanks tho @drifting wraith

.close

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[oak plover]

$a, b, c, d \in \mathbb{Z}^+$\\
$a^b = cd$\\
$b^a = c + d$\\
Find all quadruplets $(a, b, c, d)$.

[warm shale]

Oğuzhan

[oak plover]

(2, 3, 1, 8), (2, 3, 8, 1), (2, 2, 2, 2), (1, 2, 1, 1)
I think these are all but I can't prove it. Any ideas?

[graceful marten]

Sorry for the late reply,
Thanks for your message!!! I’ll have a look at it again :>

[timid silo]

maybe x² - b^a * x + a^b = 0

i might have to think

[oak plover]

What's x?

[timid silo]

uhh use quadratic formula and use the fact that b²-4ac must be a square

i just set it up

[oak plover]

Oh also I should have said that too

Things found:\
$b^{2a} - 4a^b$ is a perfect square\
$3 \le a < b$

[warm shale]

Oğuzhan

[oak plover]

Second condition doesn't apply to the small solutions I sent earlier

[brazen viper]

[ b^{2a} = 4a^b ]

Which seems to imply that $b$ is divisible by 2. But you have solutions where this is not the case.

[warm shale]

OmnipotentEntity

[oak plover]

?

Why is b^2a = 4a^b

[brazen viper]

Oh my bad

It just needs to be positive, not a perfect square

It needs to factor.

Sorry

I was thinking b^2 - 4ac should be zero

[timid silo]

it has to be a perfect square

[oak plover]

Oh no

[brazen viper]

Making the quadratic a perfect square

[timid silo]

or c,d arent integers

[oak plover]

Yeah

[brazen viper]

Not b^2 - 4ac specifically

Yes b^2 - 4ac should be a perfect square

Ignore me

[timid silo]

idk maybe put in x = 1,2,3... since the roots are all natural numbers

[oak plover]

A revised version of the message I sent:\\
$a, b, c, d \in \mathbb{Z}^+$\\
$a^b = cd$\\
$b^a = c + d$\\
Find all quadruplets $(a, b, c, d)$.\\
So far only solutions are:\\
$S = \{ (2, 3, 1, 8), (2, 3, 8, 1), (2, 2, 2, 2), (1, 2, 1, 1) \}$\\
Things found:\\
$b^{2a} - 4a^b$ is a perfect square\\
$3 \le a < b$

[warm shale]

Oğuzhan

[oak plover]

What did you define x as?

[timid silo]

its just a quadratic that has c,d as roots

[oak plover]

Oh okay

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[iron beacon]

Hello! I need help!

[iron beacon]

this is graph theory

im having trouble understanding a lemma in the text

it says given a graph G, the dual graph of the dual graph of G (G**) is isomorphic to G

im not sure if I have the defintion of duals down because I came up with a counter example

so my udnerstanding must be wrong but I dont know why

google is not helpful

pls ping me if respond

I will continue googling

[royal onyx]

omg hi twin

[iron beacon]

OMG

@analog vault asssssissstance plz!!

[royal onyx]

fr i think they are absoltuely ignoring mine cuz its too hard

but idk urs either im bad at math

😞

[iron beacon]

these guys never help!!!

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[iron beacon]

whatever

[obtuse pebble]

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[random olive]

2. Derive the matrix for the linear deflection that rotates the plane 75◦ counterclockwise around the origin by considering
   it as a composition of two appropriate twists.

[random olive]

someone please help me solve this

[obtuse pebble]

@random olive Has your question been resolved?

[random olive]

<@&286206848099549185>

[minor delta]

What’s up?

[random olive]

I need help solving this

Do I just put in 75 degrees into the formula cos -sin, cos sin

Or do I have to do 45 counter wise and the the rest clockwise?

@minor delta

Answer these questions for each of the three images in opg. 6, 7 and 8 below:
a) Take the mapping matrix A and determine whether it is diagonalizable. If so, please specify
(without counting!) the matrix P for which the matrix D = P^−1AP is diagonal;
b) Determine (again, without calculating!) whether the mapping is reversible;
c) Enter (without counting!) the matrix A^2
(Lead: What does the mapping with matrix A^2?)

8. Reflection plane 5x + 7y + 5z = 0.

can someone help me with this?

i get the matrix A

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[random olive]

.close

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[timid silo]

Hey my answer is different from the key did i do something wrong?

[knotty crow]

x^2 - 2x - 1 cannot be factored

that's wrong

Proof:
D = (-2)^2 - 4(1)(-1) = 4 + 4 = 8

D > 0

-> 2 real roots

Ah

[timid silo]

Whaaa

[knotty crow]

then your roots for the thing in the bracket

are calculated incorrectly

how did you get x = 4

[timid silo]

How

Used quadratic formula

[knotty crow]

Mhmm

Look at your quadratic formula once again

[timid silo]

I don’t see the error

[knotty crow]

That's the proper form

[timid silo]

Oh bro

I haven’t used quadratic formula in a long time

So I forgot