help-39

[opal cape]

7x = 54

[little sundial]

both sides

[light helm]

no

you obliviated that x again

[little sundial]

if you have 6=6 and subtracted 1 from only one side, you'd have 6=5 which obviously isn't right! if you do something on one side, you have to do it on both sides

[opal cape]

Ok so i subtract the x from 7x

[little sundial]

if you subtract 1 from both sides of 6=6 then you'd have 5=5, but you can't just do it on one side because that wouldn't be equal

[light helm]

you subtract x from BOTH sides

[little sundial]

you subtract the x from the 7x AND from the x+54, yeah

[light helm]

the xs on the right would cancel
you'd have 7x - x on the left (which can also be simplified)

subtracting both sides by $x$
$$7x \ \red{- x} = x + 54 \ \red{- x}$$

[jolly parrot]

ℝamonov

[little sundial]

@opal cape can you simplify the above

[opal cape]

7x = x54

[little sundial]

where did the x go

[opal cape]

That?

[little sundial]

7x is multiplication, so it means Seven X'es.
if you have Seven X's and take away one X, how many X's do you have?

[light helm]

are you implying that if you had
7 apples and I took an apple away
that you'd have 7? (just the number 7)?

[little sundial]

x is like a "thing" and 7 is saying you have 7 of those things.

so if you had 7 "cars" and took away one "car" how many cars would you have

[light helm]

or taking this to an even more ridiculous level
if you had 10 billion dollars and I took away a dollar,
would you now just have the number 10 billion (not money)

[opal cape]

6

[little sundial]

you'd have 6 x's

so 6x right?

[opal cape]

Can you tell me the answer so i can anlyze it

[light helm]

well now you understand that
7x - x = 6x right?

[little sundial]

7x-x=6x, not 7 👍

if you have 7 groups and take away one group you have 6 group

[opal cape]

Yes

[little sundial]

so now you have 6x=54 as your equation

[light helm]

and you should also know that
x + 54 - x simplifies to 54 right?
(that's the whole reason you're choosing to subtract x from both sides in the first place)

and then just like the burger example or the equation representing that situtation
apply the same idea to solve

6x=54

[opal cape]

Now i divide?

[little sundial]

yessss

but by what

[opal cape]

The biggest number that can divide it?

[little sundial]

so what

you have 6x=54 and you wanna get it to be x=something

so what should you divide 6x by to get x=something

[opal cape]

27

[little sundial]

no

[little sundial]

read this

@opal cape

[opal cape]

Ok so im gonna divide 54

[little sundial]

no.

how does that help you get x=something?

[opal cape]

Oh so i divide 6x

By 2

[little sundial]

why by 2

why not by 6

[opal cape]

Ok so 6

[little sundial]

yeah

what is 6x divided by 6

and what is 54 divided by 6

@opal cape

[opal cape]

1 and 9

[little sundial]

nope.

6x/6 is not 1

where did the x go?

@opal cape

do you keep falling asleep or something

[opal cape]

Sorry

6x/6 is 1x?

[little sundial]

yeah

alright to summarize, you have 7x + 2 = x + 56

you can subtract 2 from both sides, which gives 7x = x+56

then you can subtract x from both sides, which gives 6x=56 (7x-x does NOT equal 7)

then divide both sides by 6, which gives x=9

you divide by 6 so that you get x=something

if you did 6x/54 that wouldn't help you at all

[opal cape]

I gtg

Im gonna be back

[little sundial]

your answer is right here @opal cape

gl

[opal cape]

Yep

[pearl pond]

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[hollow marten]

are -5.7/10, 5.1 x 10^-6 and -2.33 rational numbers or are they irrational?

[honest bison]

for the first one, it's -57/100 right ?

[hollow marten]

if u remove the decimal yeah but the question is same as in the message

[honest bison]

what is a rational number ?

[feral sedge]

What's a rational number?

[honest bison]

bruh

[feral sedge]

[honest bison]

it's a number that can be written as p/q where p and q are integers

possibly negative

[feral sedge]

There ya go

[hollow marten]

ratios n stuff

[honest bison]

yeah so what about -57/100 ?

[hollow marten]

damn i feel dumb now

what about 5.1 x 10^-6?

i feel like its an irrational number

[feral sedge]

can you write 10^-6 as a fraction?

[hollow marten]

no

[honest bison]

you can !

10^-6 is just 1/1000000

[hollow marten]

damn

soooo same can be done with -2.33 if i turn it into -233/100?

[honest bison]

yes !

[hollow marten]

damn tysm for the help

almost got the answers wrong 😅

[honest bison]

np

[pearl pond]

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[junior pawn]

,w series expansion 1/(1+x) at x = 0

[jolly parrot]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by Max.cc#5208

[junior pawn]

,w series expansion 1/(1-x^2) at x = 0

[jolly parrot]

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Upgrade to WolframAlpha Pro!

Requested by Max.cc#5208

[junior pawn]

i don't get the result

for me i would be -1 + x^2 - x^4 etc...

why are they all positive

[timid spindle]

Replace x with -x² in this

[junior pawn]

ok i got my mistake

thx

.close

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[lost sigil]

hey

[lost sigil]

i need help with the last two points here

@mystic spoke

[mystic spoke]

1min

here @lost sigil

[lost sigil]

thank you so much

but what does the middle say? "since a is the" whats the rest

[mystic spoke]

positive

+ve

[lost sigil]

okay thank you so much

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[cunning remnant]

Not sure what to do with 18 either

[pearl pond]

@cunning remnant Has your question been resolved?

[cunning remnant]

<@&286206848099549185>

[patent anvil]

@cunning remnant Hi there

[cunning remnant]

Hi

[patent anvil]

Do you want a hint or a full demonstration?

[cunning remnant]

Hint would be great

I don't rlly get what to do with the abs(z)^2

[patent anvil]

Yeah that will come in handy actually

OK now given a complex number, do you know a trick that lets you extract its real part?

Using its conjugate for example?

[cunning remnant]

No

[patent anvil]

If z= a+ib

[cunning remnant]

Like z*?

[patent anvil]

Then z*=a-ib right?

[cunning remnant]

Yeh

[patent anvil]

What if you add them?

[cunning remnant]

Oh right

I don't think we've gone through that yet

But I see how that works

[patent anvil]

Oh OK so you're just starting out

Cool

[cunning remnant]

Yeh

We only started complex numbers like last week

[patent anvil]

Now try taking the conjugate of ω and adding it to itself, thay should give you 2Re(ω)

And I reckon you will find |z| somewhere there

Oh and don't forget edge cases

[cunning remnant]

Isn't |z| refering to rcis form

[cunning remnant]

Yeh never heard of that 💀

[patent anvil]

I meant the really specific cases that break things hhh for example if z=1,ω doesn't exist

[cunning remnant]

Ah ok

[patent anvil]

What do you mean by rcis?

[cunning remnant]

Rcistheta

Like r(cosx+isinx)

[patent anvil]

Oh OK we call that form trig form here in my town hhhh

OK so have you done the calculations

[cunning remnant]

1/1-x-iy +1/1-x-iy?

Idrk

+iy on the second one*

Nah that's wrong

[patent anvil]

I'll try to write down something detailed gimme 10min

[cunning remnant]

Thanks ,Ill try to figure it out

[patent anvil]

OK then

[cunning remnant]

Ok I get everything except how u got z*z = 1

[pearl pond]

@cunning remnant Has your question been resolved?

[pearl pond]

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[midnight haven]

when can you switch sum and sum or sum and integral or sum and derivative?

[hazy solar]

I suggest you paraphrase your question

[timid spindle]

there are conditions on when you are allowed to

in general, no

in practice, most of the time its fine

you usually need conditions like uniform convergence etc

[midnight haven]

hmm which ones?

[timid spindle]

just google the one you're interested in and find out

i.e. "when can i switch sum and derivative"

[tropic saddle]

switching sum and stuff is always fine

switching series and stuff can be wrong

[midnight haven]

wheres the difference?

oh googled it

thanks

.close

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[plush nexus]

How do I fix no14?

[wary bane]

Error 1:
-6x = -2
x = 1/6?

[old geyser]

What's with the 1/2^2 (2^(-4))^2x

[plush nexus]

is 1/4 equal to 2^-2?

Ah nvm I think I’ve got this

Thanks anyways God bless y’all! Jesus love you!

.close

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[stuck wedge]

An ornament of mass 26.6 g is attached to a vertical ideal spring with a force constant (spring constant) of 48.7 N/m. The ornament is then lowered very slowly until the spring stops stretching.

How much does the spring stretch?

[stuck wedge]

I need a walk through on how to solve this

[topaz terrace]

0.0266x9.81=48.7xs

[stuck wedge]

so i turn 26.6g to kg right?

[topaz terrace]

yeah

because net force = 0, gravitational force = spring force

[stuck wedge]

then i did 0.0266 x 9.8/48.7

[topaz terrace]

yeah

[stuck wedge]

i got 0.00535277

[topaz terrace]

seems right

[stuck wedge]

would i have to round my answer?

[topaz terrace]

3 sig figs ig

so 0.535 cm

[stuck wedge]

😦 it said it was wrong

bruh idk this thing weird

[topaz terrace]

weird

is it in meters?

[stuck wedge]

i did the same steps for a similar question

[topaz terrace]

or centimeters

[stuck wedge]

maybe meter

all i see really is

N/m

does that mean Newtons per Meter?

[topaz terrace]

ye

[stuck wedge]

well

[topaz terrace]

try 0.00535823409 meters

[stuck wedge]

my thing changes the questions if i get the prev one wrong

so heres the new question

[topaz terrace]

aight

[stuck wedge]

An ornament of mass 27.3 g is attached to a vertical ideal spring with a force constant (spring constant) of 40.8 N/m. The ornament is then lowered very slowly until the spring stops stretching.

How much does the spring stretch?

[topaz terrace]

so 0.0273*9.81/40.8

it gives me 0.00656404412 meters

[stuck wedge]

so 0.0065m

[topaz terrace]

yeah

[stuck wedge]

bruh

this thing saying wrong

its making me frustrated

[topaz terrace]

tf

[stuck wedge]

An ornament of mass 10.6 g is attached to a vertical ideal spring with a force constant (spring constant) of 42.3 N/m. The ornament is then lowered very slowly until the spring stops stretching.

How much does the spring stretch?

0.00245579

i got this

[topaz terrace]

ok but before you submit make sure the question asks for units or something

[stuck wedge]

the question i sent you is all that is says

0.0024 m

that should be my answer right?

[topaz terrace]

maybe put more sig figs

[stuck wedge]

like the whole thing

im gonna try maybe space me units

from the answer

i get unlimited tries

[topaz terrace]

ok

[stuck wedge]

but it gives me a new question everytime i get it wrong

idk its kinda making me mad

[topaz terrace]

is that moodle? lol

[stuck wedge]

yee

[topaz terrace]

i mean when i used moodle it didnt care about how many numbers you put so you can try putting more numbers after 0.0024

[stuck wedge]

alr

An ornament of mass 34.3 g is attached to a vertical ideal spring with a force constant (spring constant) of 11.7 N/m. The ornament is then lowered very slowly until the spring stops stretching.

How much does the spring stretch?

this the new question

im not even gonna round it

[topaz terrace]

kk

0.287592308 m

maybe dont put the m?

just 0.287592308

[stuck wedge]

ok

so i def need units

[topaz terrace]

rip

[stuck wedge]

An ornament of mass 20.6 g is attached to a vertical ideal spring with a force constant (spring constant) of 37.8 N/m. The ornament is then lowered very slowly until the spring stops stretching.

How much does the spring stretch?

0.0053407

is what i got

[topaz terrace]

0.00534619048

ye

[stuck wedge]

do i use yours

or mines

[topaz terrace]

what do you use for g

i used 9.81 for my class

[stuck wedge]

9.8

[topaz terrace]

ok then use yours

[stuck wedge]

omg

yay

[topaz terrace]

ez

nice

[stuck wedge]

new question

[topaz terrace]

well

26=0.67*k

so 26/0.67

[stuck wedge]

wait do i divide 26 by 0.67

[topaz terrace]

ye

[stuck wedge]

38.80597014

[topaz terrace]

seems right

[stuck wedge]

das my answer

or should i round

[topaz terrace]

no

[stuck wedge]

no on which one?

[topaz terrace]

dont round

because moodle

[stuck wedge]

me got it correct

[topaz terrace]

gg

[stuck wedge]

An object attached to a spring is pulled across a horizontal frictionless surface. If the force constant (spring constant) of the spring is 56 N/m and the spring is stretched by 0.46 m when the object is accelerating at 1.6 m/s^2.

What is the mass of the object?

[topaz terrace]

1.6*m=56*0.46

[stuck wedge]

25.76

dis my answer?

@topaz terrace

[topaz terrace]

sounds right

[stuck wedge]

25.76 N

?

[topaz terrace]

kg

[stuck wedge]

it was wrong

[topaz terrace]

did you put kg?

[stuck wedge]

yea

[topaz terrace]

and did you do 56*0.46/1.6?

[stuck wedge]

oh

no

[topaz terrace]

oh

[stuck wedge]

An object attached to a spring is pulled across a horizontal frictionless surface. If the force constant (spring constant) of the spring is 34 N/m and the spring is stretched by 0.47 m when the object is accelerating at 1.5 m/s^2.

What is the mass of the object?

(34*0.47)/(1.5)

=10.653

@topaz terrace

[topaz terrace]

sure

[stuck wedge]

so 10.653 kg

is my answer

[topaz terrace]

yeah

[stuck wedge]

alr i have 2 more assignments

but these other questions ik how to do

should i close

or no

[topaz terrace]

i mean sure

if you know what to do

[stuck wedge]

yea but i dont know about the 2 other assignemnet

[topaz terrace]

you can keep it open ig

[stuck wedge]

ok

[pearl pond]

@stuck wedge Has your question been resolved?

[stuck wedge]

@topaz terrace

[topaz terrace]

theres no other information?

ig its 39.4 then

energy conservation

[stuck wedge]

nope it only has this

so is it 39.4 J

or just 39.4

[topaz terrace]

-39.4 J

[stuck wedge]

ok

@topaz terrace

[topaz terrace]

yes

[topaz terrace]

ek=1/2mv^2

convert into m/s first

[stuck wedge]

@topaz terrace

thanks for the help

cheers!

.close

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[midnight haven]

Can someone go over these for me

[pearl pond]

Channel closed

Closed due to the original message being deleted

[midnight haven]

hello

[distant skiff]

type .reopen

[midnight haven]

.reopen

[coarse dawn]

Can't

[midnight haven]

Holdup

[coarse dawn]

Need to open a new chanel

[midnight haven]

Ok

channel 27

.close

channel still has my name

[coarse dawn]

Just wait

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[vernal grove]

how exactly am I suppose to do part a?

[vernal grove]

can I get a hint

[signal cargo]

find area

under the graph

at each point

[vernal grove]

oh so for g(1) it should be 1 right

(2(1))/2

since it forms a triangle

[signal cargo]

yeah

[old marsh]

Isn’t it from -1

[vernal grove]

but

oh

g(-1) is just 0?

[signal cargo]

but it starts from -1

you have to consider another triangle yoo

[vernal grove]

another?

for -1?

oh yeah

im stupid

I confused -1 for 0

since I couldnt see the point on the graph

g(-1) = 1/2

so I just keep adding for all the points?

[signal cargo]

noo g(-1) shoud be zero

[vernal grove]

why

isnt this the -1 part

oh

coz the integration

from -1 to -1

is 0

[signal cargo]

integration is from -1 to -1

[vernal grove]

ah yeah

[signal cargo]

means just a ponit

[vernal grove]

and -1 to 0 would be

1/2

[signal cargo]

yeah

[vernal grove]

alright but

u see how the graph isnt

cont

what would I do for x = 3

[signal cargo]

umm....i am not sure

[vernal grove]

doesnt matter if the graph isnt cont?

oh

oh watched this vid apparently doesnt matter https://www.youtube.com/watch?v=rexiwhcXJhw

also wont I be subtracting

[signal cargo]

okie

[vernal grove]

instead of adding

[midnight haven]

i agree

[vernal grove]

alr

for 4 doe

I add right?

since its increasing?

[pearl pond]

@vernal grove Has your question been resolved?

[pearl pond]

@vernal grove Has your question been resolved?

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[weak surge]

How often do you use these formulas?

[coarse dawn]

Tbh not often

[grizzled shadow]

Well, depends, but Id say, not very often

[weak surge]

And is there a way to memorize them easily?

[chilly sigil]

Doing problems

[grizzled shadow]

Except for if you're in India and are doing trigonometry

in High School

[weak surge]

Not really needed for Calculus?

[chilly sigil]

If you’re doing trigonometry anywhere

[grizzled shadow]

Some times

[grizzled shadow]

No, we tend to over do this stuff

[coarse sage]

I'm from India, can confirm we all didn't memorize.

[chilly sigil]

Everywhere

[grizzled shadow]

Did you go for JEE?

[coarse sage]

we as in from my high school.

Yes.

[midnight haven]

it's not needed for calculus, but there could be calculus problems that involve things like this

[coarse dawn]

Very little

[weak surge]

OK

Thank you, maybe I will skip over this for now

Come back to it later

[coarse sage]

It's better to have an idea about derivations, so you can come up these formulae whenever you want.

[weak surge]

Hmmm OK

I think we are learning about derivatives in Calculus 1 this semester

[chilly sigil]

Memorize how to derive it

[chilly sigil]

That’s not what they meant

[weak surge]

Derivation does not mean derivatives?

[midnight haven]

as in it's good to know where these formulas are derived from

(where these formulas come from)

[weak surge]

Alright

Thanks

.close

[pearl pond]

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[pearl pond]

@soft otter Has your question been resolved?

[soft otter]

huh?

yeah

what instrument do you play?

[coarse dawn]

Mayonnaise

[soft otter]

oh cool

i was curious

i just performed yesterday

i play double bass

i performed a solo with pianist accompany

[coarse dawn]

This was a spongebob reference if you couldn't tell

[soft otter]

lmao i never watched spongebob

rip

it's always great to meet pianists

anyway im pretty sure the answer was the first choice

[pearl pond]

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[prisma sedge]

I need help solving question a and b. I'm not sure how to find the value of n, assuming the correct formula to use is PV = R(1-(1+i)^-n/i

[prisma sedge]

ah it's fine

.close

[pearl pond]

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[pearl pond]

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[midnight haven]

I have no idea what to do next

ik it can be simplifed more, but idkd how

[pearl pond]

Commands:
clopen: .close, .reopen, .solved, .unsolved
consensus: .poll
factoids: .tag
help: .help

Type .help <command name> for more info on a command.

[finite crown]

Is that -y -4 or -9

[midnight haven]

-4

bad handwriting

[finite crown]

2/-4 = -1/2

[finite crown]

So just put a -2 on the bottom

[midnight haven]

but why?

whered you get -2 from

[finite crown]

What’s 2/-4

[midnight haven]

-0.5

[finite crown]

Mhm

Or

-1/2

It’s like

[midnight haven]

this is what mathway says but its just confusing

[finite crown]

$0.5x = \frac{x}{2}$

[jolly parrot]

Mortta

[finite crown]

Yea

Which is what we got

[midnight haven]

-1/2

but the asnwer mathway gave doesnt have a negative 2 on the bottom

it has a positive 2

[finite crown]

It took the negative out

And put it beside it

$\frac{-x}{y} = \frac{x}{-y} = -\frac{x}{y}$

[jolly parrot]

Mortta

[midnight haven]

Oh cool good to know lol

so thats the final answer

[finite crown]

Yep

Works just as well

[midnight haven]

alright thank you for the help!

desperately studying last minute so i appreciate the fast response

.close

[pearl pond]

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[wispy heart]

please help me out haha

[finite crown]

This is more physics but fair enough

[wispy heart]

this is in my calc 2 class

[finite crown]

???

Tf

Fair enough

[wispy heart]

lmaoo

[finite crown]

Work done = force x distance yes?

[wispy heart]

college calc 2 go crazy

yes i agree

[finite crown]

The distance from 23 cm to 33 cm is 10 cm

[wispy heart]

how do i get that distance of the line though it aint straight and all

[finite crown]

Or 0.01 meters

[wispy heart]

nah i dont think thats the approach...

[finite crown]

Why not?

[wispy heart]

is it?? that doesnt make sense to me

cause like

[finite crown]

Well

We could integrate the graph

That’ll get us the energy

[wispy heart]

yes

[finite crown]

So count the squares I guess

[wispy heart]

i think thats what i need to do all the qwuestions i have

aint no way actuallyyyy

[finite crown]

?? Do u know the formula

Of the curve

Coz I don’t

[wispy heart]

no sir i dont

[finite crown]

So yes I don’t see any way around this lol

[wispy heart]

so i gotta count squares

so work is force* distance

[finite crown]

Yes

[wispy heart]

this is so sad

[finite crown]

Remember we work in SI units

Yea I know

[wispy heart]

cause i cant show work like that

this help at all

[finite crown]

I’d say

From 26 to 31

Each is about 1.5 squares

[wispy heart]

yooo

found this

[finite crown]

Oh shit yea

[wispy heart]

mgiiht help

sir cmon nowwww

[finite crown]

F= Ke

Find k

[wispy heart]

ok ok hold!

[finite crown]

Rememver

Si units

[wispy heart]

wait

[finite crown]

Cm change to meters

[wispy heart]

my question says ignore hoooks law

[finite crown]

Bro

[wispy heart]

says it disobeys

[finite crown]

Naw

[wispy heart]

wdym

[finite crown]

Yea well

[wispy heart]

question says that

[finite crown]

Good luck countin!

[wispy heart]

oh lordddd

gottaaaa be a better way

[finite crown]

But than again

Maybe that’s why U have a grid

[wispy heart]

i mean i suppose but that isnt accurate

[finite crown]

Yea I know

But I remember I had to d o this once

We had a speed velocity graph, and we had to get distance traveled

Counted so many squares that day that I keep seeing squares till this day

[wispy heart]

awh man

r u sure thoughhh

i geel like gotta be better way

we are given points 23,0 24,10 33,30

32 ,20

[finite crown]

When were u plannin on tellin me this

[wispy heart]

aint no way

so we given points what now

also i just looked at group

[finite crown]

Use fken

Trapezium rule

[wispy heart]

graph

ok

[finite crown]

Or like rienman sums

[wispy heart]

ok ok

lemme seee

[finite crown]

WAIT

NO

[wispy heart]

wha

[finite crown]

I think it’s tellin us

That we have 4 area of the graph

[finite crown]

Draw verticale lines at these points

[wispy heart]

so trapezoidal rule ?

[finite crown]

No no

We split it up into 2 trapezium 1 rectangle

And a triangle

I think

[wispy heart]

sec ok tyyy

gimme 5

[finite crown]

If u draw vertical lines I think it should help see it

[wispy heart]

end of textbook has answers ill show hold

[finite crown]

Mhm

[wispy heart]

fucking stupid

imma kms

[finite crown]

bro why

What

Wtf is average force

[wispy heart]

idk :(

[finite crown]

Did they literally

Just use 1.5

As the average boxes

So said it was the average force

Wow

[finite crown]

So basically since most of this is 1.5 boxes or 15 dyn it just used this as an average per

So times 15 by 10

Stupid question

[wispy heart]

dude

i wanna kms

its such an ass question

literally counting blocks is the answer then

holy shit

thanks for your help i suppse

i hate doing online class

your help was mid at least your cool

[finite crown]

I hate when books are special

[wispy heart]

helped me work through it

mentally im gone

[finite crown]

Violated me

[wispy heart]

i worked a 12 hour day today

[finite crown]

For what

[wispy heart]

sowwy

helped me stay alive

i work as a cyber seurity architect

my brain

is burnt out

you helped ty

[finite crown]

U studying maths at uni?

[wispy heart]

12 hours day kill me

yas working full time and college full time

[finite crown]

??? Tf Are u suicidal

Too much cor me

[finite crown]

Sounds cool

[wispy heart]

nah i just am in my bag fr

its alr im way underpayed

[finite crown]

That’s not good

[wispy heart]

training someone rn who earns 2.5x my salary

and is really stupid

[finite crown]

What

[wispy heart]

i want degree so more moneys

[finite crown]

How is that fair

[wispy heart]

IM ASAYINgf

[finite crown]

Idk how it works over there but in uk u don’t even have to work to go to uni

Coz goverment fund u

[wispy heart]

my job pays for mine

but yeah

[finite crown]

Ohhhhhh

[wispy heart]

im debt free heheeh

[finite crown]

That’s good at least

[wispy heart]

its expensive here

it shoudl be free fr

[finite crown]

BRO

IM SO JEALOUS OF EUROPE

most unis are free there

Then u got England who’s is like 9k a year

Not as bad as US Tho

[wispy heart]

dude one of my 3 semsters is 5k

its nasty

alr ill close this now sorry dont wanna waste your time

[finite crown]

Bro it’s 3 am I’m the one wasting my own time

[wispy heart]

thanks for the help nice meeting you!

hahah

.close

[pearl pond]

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[pearl pond]

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[woeful vessel]

Question 10… I don’t understand how to find the solution to the linear equality, I need help 😅
(The “not” under the circle answer means I didn’t find the answer, that’s the just the answer on the answer sheet so I circled it)

[toxic lichen]

you are not expected to "find" the whole solution set

only to test these particular points as to whether they satisfy the inequality

[woeful vessel]

What does “satisfy the inequality” mean?

[little merlin]

If you plug a number in and the inequality stand true then that point satisfies that inequality.

So, say I have an inequality
x^2-1>0 and I plug in 3 then I get 8>0. This means that x=3 satisfies the inequality.

[woeful vessel]

Could you give me an example of an answer that wouldn’t satisfy that inequality? /genq

[little merlin]

x=0
Plugging in x=0 gives us -1>0 which is obviously false, -1<0. So x=0 does not satisfy this inequality.

[woeful vessel]

Oh! Okay! That makes a lot more sense

Thank you!

.close

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[pearl pond]

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[viral inlet]

The depth of water in a harbour as a function of time can be described by a cosine function. The maximum depth is 12 m, the minimum is 1.5 m, and at
t=0, the depth is at its minimum. In 65 hours the minimum depth is reached 6 times (including the times at t=0 hours and t=65 hours). What is the equation of the cosine function that describes the depth of water in the harbour?

[viral inlet]

Anyone can help with this?

I know it’s a bit tough

[pearl pond]

@viral inlet Has your question been resolved?

[viral inlet]

Please can anyone help?

[serene wave]

This question is about transforming a cosine graph to fit the shape of waves.

First, since the depth is minimum at t=0, the first change that needs to be made is flipping the graph about the x-axis.

Second, the amplitude of the graph is half the distance between the maximum and minimum depth.

Third, the graph must be shifted upwards to match the minimum of 1.5.

Lastly, the wave reaches a minimum 6 times, so 65/5 = 13 units of time coincides with 2 pi.

[pearl pond]

@viral inlet Has your question been resolved?

[serene wave]

I think it should be this

[pearl pond]

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[tall tangle]

I don't quite understand the solution, from the word either

Idk this was my own work before checking solution. I thought the function must be a constant function

But pretty lost

[pearl pond]

@tall tangle Has your question been resolved?

[pearl pond]

@tall tangle Has your question been resolved?

[feral sedge]

I don't think h can be anything other than linear or constant

otherwise f(2^n) would grow too fast

[tall tangle]

can u help to understand the solution?

tbh i really just don't get why it has to be ut+v

the expansion and equating step is calm

[feral sedge]

deg(f(2t)) = deg(f)

deg(h(f(t)) = deg(h)deg(f)

so deg(f) = deg(h)deg(f)

so deg(h)=1 or deg(f)=0

[tall tangle]

if a polynomial times a degree 1 polynomial, doesnt that make the degree plus 1?

[feral sedge]

its not multiplication

its composition

[tall tangle]

oh

composite

[tall tangle]

this is multiplication tho?

[feral sedge]

the degrees are multiplied

[tall tangle]

right??? so if deg(h) is 1, how does it still hold

[feral sedge]

?

[tall tangle]

?u said the degrees are multiplied?

[feral sedge]

yes

[tall tangle]

like degrees 4 times

degree 1

[feral sedge]

it just does

[tall tangle]

is degree 4?

[feral sedge]

no

composed

not times

[tall tangle]

wuttt, this is times

[feral sedge]

those are the degrees

[tall tangle]

ok right take, x+4. f(2x) would be 2x+4, and if composite function is degree 1

the result from the composite function is still degree one

ie. x+1 as composite function. It becomes 2x+5

still degree 1

can u explain the thing after thus?

[feral sedge]

Do you know how indicative it is that you're attempting problems outside the level you should be that you need help understanding proofs on a daily basis?

unless you're putting in almost no effort to understand the proof yourself before asking for help

[tall tangle]

if ur not gonna explain, stop flooding the channel

this book is specifically designed for high schoolers and ive completed sections before this question

the last few questions are designed to be challenging

jesus

ive thought about that section for 20 min +

[tall tangle]

stop generalizing others experience without any proof

[tall tangle]

which are specifically for the basics of the concepts explained previously

anyway, if anyone is willing to help, I'm stuck on the step after thus

[midnight haven]

what's 'this'

[tall tangle]

wdym?

im in a debate tournament fuck, will respond in an hour

[midnight haven]

where are you stuck

[tall tangle]

after thus

[tall tangle]

if u can just write explanation, i can read latertoo

[midnight haven]

gl

yes

[midnight haven]

a constant u cannot be equal to 2^k for all k

so a_k must be 0 for most of them

we know a_0 and a_n nonzero

so the rest are 0

@tall tangle

[feral sedge]

i posted 2 messages

[feral sedge]

the proof is how often this happens

[midnight haven]

I agree with moni

should I delete all my messages

[tall tangle]

it must be a constant?

[midnight haven]

yeah

[tall tangle]

im thinking to create a new account to ask questions

[midnight haven]

we would immediately know its you

[tall tangle]

why

[midnight haven]

because you talk in a very distinctive manner

you are unique ✨

[tall tangle]

oh misread

i thought u=you

[midnight haven]

cri, I think about questions for 20+ hours

[tall tangle]

instead of u the variable

[midnight haven]

yes you are a constant

[visual light]

lint

[midnight haven]

u is also a constant

[visual light]

why are you trolling

[tall tangle]

why is v=

[midnight haven]

think lint think

[late moon]

Who's lint?

[midnight haven]

what is u

[midnight haven]

boki

[late moon]

[tall tangle]

oh yeh

i got it

[late moon]

And why do you call boki "lint"?

[midnight haven]

idk

everyone does

https://tenor.com/view/lint-fucking-lint-thick-lint-gif-15471655

[late moon]

Ah yes, the 🚎

[tall tangle]

good question

.close

[pearl pond]

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[midnight haven]

.reopen

[pearl pond]

✅

[midnight haven]

huh?

.close

[pearl pond]

Channel closed

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[late moon]

Lmfao

[visual light]

bruh lintahlo

[pearl pond]

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[frozen forge]

x+2 / x+3 = 4/5

[frozen forge]

how u do this

is it 5(x+2)=4(x+3) then u solve?

[timid spindle]

yes

[frozen forge]

alr

.close

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[quaint otter]

Can anyone help me understand these. I do not understand what “having an rquivalence relation with <something> elements.” even means

[plush bramble]

<@&268886789983436800> spam

[quaint otter]

<@&286206848099549185>

[wary bane]

@stiff summiter

<@&268886789983436800>

[pearl pond]

@quaint otter Has your question been resolved?

[quaint otter]

.close

[pearl pond]

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[pearl pond]

Please don't occupy multiple help channels.

[barren bolt]

You already have a channel open

[wary bane]

.close

[pearl pond]

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[chrome marsh]

Am I solving for t wrong

actually nevermind

i see what i did wrong

you gotta divide by /2 then square root it

since its =0

then your left with 0 = (t -1.5)

you just flip t's sign

so basically just take t off the bat and flip the sign

[muted fossil]

Yes

[chrome marsh]

.close

[pearl pond]

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[chrome marsh]

i see you typing

i fear im wrong

[muted fossil]

-2(t-1.5)²=0 <=> (t-1.5)²=0
<=>t-1.5=0
<=>t=1.5

[chrome marsh]

ty

[muted fossil]

Anytime

a*b=0 means that a=0 or b=0

[chrome marsh]

.close

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[faint onyx]

hi, can someone help me with this qn?

@rustic gate

[rustic gate]

use expectation of linearity?

[faint onyx]

hmmmmm

wut

[rustic gate]

linearity of expectation lol

[faint onyx]

E[X + Y] = E[X] + E[Y]

[rustic gate]

yes

[faint onyx]

hmmm

how do i sue that hmm

[rustic gate]

hire a lawyer

[faint onyx]

LMAOOOO

XD

ok but hmm

@rustic gate is this ok

[rustic gate]

that notation doesn't really make sense

[faint onyx]

hmm

[faint onyx]

can me get sum help pls

like what would my random variable look like

[rustic gate]

so you want to count how many pairs are the same right?

[faint onyx]

uh

[rustic gate]

and X_ij is like

[faint onyx]

ye

[rustic gate]

the indicator for pair i,j being the same

[faint onyx]

ye

[rustic gate]

so like

if you add up all the X_ijs

you get the total count

[faint onyx]

wait

X_ij

is 1/2 right

[rustic gate]

[faint onyx]

P(X_ij = 1) = 1/2

[rustic gate]

yes

[faint onyx]

so

uh

why do i need to add all of them up

me no get the intuitive idea

[rustic gate]

because like

each X_ij is a potential tally in the total count

like

[faint onyx]

hm

[rustic gate]

X_ij = 1 if i,j same

and 0 otherwise

so like

[faint onyx]

oh wait i did it like

x_ij = 1 is i,j different

[rustic gate]

oh

[faint onyx]

ye['

[rustic gate]

hm

well this is kinda trippy

[faint onyx]

design and analysis of algorithms is too hard for me

this is like

randomized algos part of it

[rustic gate]

this is mostly probability

[faint onyx]

im dying at probability

[rustic gate]

[faint onyx]

aaa

[rustic gate]

okay so like

if we define X_ij to be 1 when they're the same

[faint onyx]

yes

[rustic gate]

then like

for example

X_12 + X_13 + X_23

that counts the total number of pairs which are the same

out of {1, 2, 3}

[faint onyx]

wait i dont get why we need to add them up tho

[rustic gate]

because it's like a tally

[faint onyx]

,w define tally

[jolly parrot]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by HellO#6239

[rustic gate]

X_ij will be 1 when you get a match

and you want the total number of matches

[faint onyx]

yes

[rustic gate]

so you add it all up

[faint onyx]

hm..

[rustic gate]

like

[faint onyx]

oh wait

OHHHH

OKAY

I GET IT

so like

[rustic gate]