help-0

[slate monolith]

kinda rusty on integrals

[echo moth]

It’s okay I’ll try it out first

Yeah idk this is all I can come up with

But I don’t see how it leads to any of the answer choices

[slate monolith]

hmm

[echo moth]

I think I might just leave this question blank and ask the teacher to explain it

Do you know how to do this one?

I have this so far

[slate monolith]

same thing as before

not quite

[echo moth]

WHAT

[slate monolith]

the integral of 1/y = ln(y)

so ln(y) = arctan

go from there

[slate monolith]

idk wtf theyre doing lol

[echo moth]

Yeah I always struggle with roots

Is there a natural log calculator

So when I plugged in the numbers, I got 0=pi/4

[slate monolith]

thats good

oh wait what

[echo moth]

Oh wait I plugged in a positive number

[slate monolith]

you get $y = e^{arctan(x) + C} = e^{arctan(x) } \ast e^C$

[ocean seal]

Kefir101Awesome

[echo moth]

The answer would be B then right?

[slate monolith]

uh

idk what you got

so you know (-1, 1)

[echo moth]

What about it

[slate monolith]

$1= e^{arctan(-1) } \ast e^C$

[ocean seal]

Kefir101Awesome

[slate monolith]

$1= e^{pi/4} \ast e^C$

[ocean seal]

Kefir101Awesome

[slate monolith]

find C

[echo moth]

How did ln(y)=tan^-1 go to this?

[slate monolith]

$y = e^{arctan(x) + C} = e^{arctan(x) } \ast e^C$

[ocean seal]

Kefir101Awesome

[echo moth]

Did u move the ln over to the other side to get the e?

[slate monolith]

yeah

[echo moth]

Ohh okay

[slate monolith]

$e^{ln(x)} = x$

[ocean seal]

Kefir101Awesome

[echo moth]

Sorry I have a hard time comprehending natural logs and e usually

[slate monolith]

no worries

do you get it now

basically ln = log base e

[echo moth]

I’m sorry I’m still confused

[slate monolith]

and we know that base^(log(base)(x)) = x

one sec

i dont know the latex for log so i just sent a photo

a here is e

N is x

[echo moth]

I think this is one of the things I just have to memorize

Cause no matter how long I look at it, my brain hurts 🫠

[slate monolith]

theres definetely an intutive explanation but idk what it is

[echo moth]

It’s okay it’s probably just me anyways

[slate monolith]

nah def not

i mean hey I dont know why either

you can think of it as an inverse of exponents I guess

like sin and arcsin

sin(arcsin(x)) = x

[echo moth]

Ohhh that actually makes a lot of sense

So would ln(e)=e

1

[slate monolith]

yes

[echo moth]

That’s actually a weight off my brain

I can remember it better now

[slate monolith]

im happy to hear that!

[echo moth]

Btw for solving for c, I’m not quite sure how it works

[slate monolith]

okay so

$1= e^{\pi/4} \ast e^C$

we know this right

[ocean seal]

Kefir101Awesome

[echo moth]

Where did the 1 come from

OH

[slate monolith]

thats the y value at (-1, 1)

[echo moth]

I’m dumb

[slate monolith]

nah

okay so

there are two ways your answer can be in

either $1= e^{\pi/4} \ast e^C OR 1= e^{\pi/4 + C}$

[ocean seal]

Kefir101Awesome

[slate monolith]

lets do the second one

$1= e^{\pi/4 + C}$

[ocean seal]

Kefir101Awesome

[slate monolith]

what value of C makes this true

[echo moth]

-pi/4?

Since e^0 is 1 right

[slate monolith]

yes

so $y = e^{x -\pi/4}$

[ocean seal]

Kefir101Awesome

[slate monolith]

do you see that as a solution

we can also write it as $y = e^{x}\ast e^{-\pi/4}$

[ocean seal]

Kefir101Awesome

[echo moth]

D is pretty close

Cause I think tan-1 is actually -pi/4

I think

[slate monolith]

yeah my bad

so D yeah

[echo moth]

No ur good

You’ve been super helpful

I only have one more question on growth decay models but I’m on the verge of passing out 😃👍

[slate monolith]

alright lol

I have to go to sleep anyways

if you get the energy later I'm sure someone else can help

[echo moth]

Sleep well

And thank you so much

[slate monolith]

no problem

[echo moth]

.close

[lone heart]

Channel closed

Closed by @echo moth

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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

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

[full fog]

can someone help me

[rich quiver]

Its correct

[full fog]

thank you 🫶

.close

[lone heart]

Channel closed

Closed by @full fog

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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

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

[unreal yew]

Hello, can anyone tell me if I set this problem right?

[lone heart]

@unreal yew Has your question been resolved?

[unreal yew]

<@&286206848099549185>

[lone heart]

@unreal yew Has your question been resolved?

[lone heart]

@unreal yew Has your question been resolved?

[lone heart]

@unreal yew Has your question been resolved?

[echo socket]

Iirc the formula for the volume should be the integral from a to b of pif(x)^2 dx instead

[steady swallow]

is this open?

[lone heart]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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

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

[frigid zinc]

Help this question, find alpha in terms of a, b, c, d
Given this is a rectangle where the intersection between four lines is randomly picked

.close

[lone heart]

Channel closed

Closed by @frigid zinc

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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

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

[proud mortar]

Hey there does anyone can teach me 9(b) how to do ?

[lone heart]

@proud mortar Has your question been resolved?

[lone heart]

@proud mortar Has your question been resolved?

[jolly widget]

simply plug in v = 0.8c into the equation

[lone heart]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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

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

[gilded kiln]

how do i do this?

a4 = 12, a7 = 32/9

an = a*r^n-1

i cant find r without finding a and vice versa

[mellow grail]

12 = ar^3

Can u list out the factors of 12?

@gilded kiln

[gilded kiln]

1 12, 2 6, 3 4 @mellow grail

[mellow grail]

Nice

Now, list out the factors of 32/9

[gilded kiln]

uh

[mellow grail]

Actually

Dont

I should've asked u straight sorry

Find GCF of 12, and 32/9

[gilded kiln]

is it 42 and 2/3

[mellow grail]

How?

[gilded kiln]

idk

idk how to do that

without a calculator

[mellow grail]

what..the..

@gilded kiln its 4/9

[gilded kiln]

ok

[mellow grail]

GCF of two fractions a/b, c/d = GCF(a,b)/LCM(c,d)

a/b = 12/1
c/d = 32/9

Okay

Now, divide both 12 and 32/9 by 4/9

@gilded kiln

[lone heart]

@gilded kiln Has your question been resolved?

[lone heart]

@gilded kiln Has your question been resolved?

[lone heart]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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

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

[inner kayak]

small problem I truly quite forgot the basics of mathematics, how do I simplify this? $(2\sqrt 3x)^2$

[ocean seal]

Doctor beak

[craggy python]

is it root3x or root 3 and x is not under the root?

[inner kayak]

x is under the root

[plain flame]

$(2\sqrt {3x})^2$

[ocean seal]

heavy

[craggy python]

the 2^2= 4 and root3x^2 = 3x
= 4*3x
= 12x

[inner kayak]

ok thx I wasn't sure

.close

[lone heart]

Channel closed

Closed by @inner kayak

Use .reopen if this was a mistake.

[lone heart]

Available help channel!

Send your question here to claim the channel.

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

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

[worn horizon]

yall
if i multiply iota with an imaginary number z
then it rotates by pi/2 radian with changing its modulus write?

[vale wigeon]

iota?

do you mean the imaginary unit?

and do you perhaps mean 'right' and not 'write'?

but yes, $iz$ has the same modulus as $z$ and is rotated by $\pi/2$ relative to it

[ocean seal]

Ann

[worn horizon]

yep

and thank you

[lone heart]

@worn horizon Has your question been resolved?

Channel closed

Closed by @worn horizon

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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

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

[slate solar]

anyone has an idea on how to solve this problem?

[modern sedge]

Can you solve differential equations?

Using the first condition, can you find f'(x)?

[slate solar]

well it will be 2x

[modern sedge]

Almost

2x+C

[slate solar]

integrate it again then it will be x^2

+c yeah

[modern sedge]

So first let's determine this C

f'(x)=2x+C and f'(2)=5

do you know how to do it?

[slate solar]

2(2) + c = 5

c = 1

[modern sedge]

Great so f'(x)=2x+1

now integrate

[slate solar]

x^2 + x + c

[modern sedge]

Can you find c?

[slate solar]

2^2 + 2 + c = 10

c = 4

[modern sedge]

exactly

so f(x)=x^2+x+4

[slate solar]

so last answer x^2 + x + 4

damn

you are amazing

[modern sedge]

yep

[slate solar]

math is indeed always right

[modern sedge]

you find a function that satisfies all the properties

[slate solar]

thank you so much

.close

[lone heart]

Channel closed

Closed by @slate solar

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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

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

[cerulean siren]

how to do

[tacit arch]

do you have any work

[cerulean siren]

what?

[tacit arch]

.

• Show your work, and if possible, explain where you are stuck.

[cerulean siren]

oh no

i dont know what the formula/equation is to solve it

[tacit arch]

angles of a straight line sum up 180 degrees

[cerulean siren]

would it be like 21x-5/15x+5

[tacit arch]

no

[cerulean siren]

okayt

[tacit arch]

"sum up" means +

"12 and 34 sum up to 46" -> 12 + 34 = 46

[cerulean siren]

so what would i do

[tacit arch]

read this again

[cerulean siren]

so i add up both of them?

[lone heart]

@cerulean siren Has your question been resolved?

[lone heart]

@cerulean siren Has your question been resolved?

Channel closed

Closed by @cerulean siren

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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

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

[sharp moth]

I seem to be having an issue with my graphs. It looks like my y position on the first row was way off. I’m using this formula and wanted to see if anyone could help?

[sharp moth]

Here’s my initial velocity and other variables

[lone heart]

@sharp moth Has your question been resolved?

[lone heart]

@sharp moth Has your question been resolved?

[lone heart]

@sharp moth Has your question been resolved?

[ancient saddle]

What do you mean? How's it supposed to look like

[lone heart]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[sharp moth]

.reopen

[lone heart]

✅

[sharp moth]

Yes the graph, the position should go up and down, it should be like a bell curve I would think.

[ancient saddle]

Well it depends on your values for y0 and v0

Mmm ok I see

Did you use +(1/2)gt²?

You should use -(1/2)gt² if you are considering up direction to be positive

[alpine sable]

Can anyone here help me?

anyone down?

[tacit arch]

!help

[lone heart]

Please read #❓how-to-get-help

[lone heart]

@sharp moth Has your question been resolved?

[lone heart]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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

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

[regal wadi]

hi

[raven haven]

ask your question or nobody can help

[regal wadi]

ok

here it is

wait

no

not tht one

here

this one

im currently studying for a math olimpiad

so pls help

[jagged cobalt]

thats way too blurry to read easily

[regal wadi]

bruh

ok

lemme try to read it

ill post it back

bruh

[slate monolith]

@regal wadialso its way too many questions

post a specific question

[regal wadi]

ok

thx

for the thing

heres the question

hold up

6 people participated in a checker tournament. Each participant played exactly 3 games with each of the other participants. How many games were played in all?

pls show me a quick way to do ths

*this

bruh]

oh wait

thats too ez

bruh

ill show next one

ok

this ones bit hard

question = Which one is true

a: 15 ---> XV

oh wait

nvm

T37V represents a 4 digit number with different digits. T37V is divisible by 88. What is T?

pls help

T37V represents a 4 digit number with different digits. T37V is divisible by 88. What is T?

[lone heart]

@regal wadi Has your question been resolved?

[lone heart]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[lone heart]

Available help channel!

Send your question here to claim the channel.

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

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

[proven tendon]

i have a question about continuity

[proven tendon]

if im given a equation and asked to show that its continuous at a point

im thinking of using squeeze theorem

but usually we're given something in the form of H(x) <= F(x) <= G(x)

in this question im given only F(x)

but F(x) involves cos

so i was thinking of

-1 <= cos(x) <= 1

then adding on the complications of the equations until i arrive at F(x) in the middle

[lone heart]

@proven tendon Has your question been resolved?

[jagged jewel]

left lim = right lim = fuction value

[proven tendon]

right, isnt that what my approach is saying?

[jagged jewel]

basically yes

[proven tendon]

thanks!

.close

[lone heart]

Channel closed

Closed by @proven tendon

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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

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

[rare heart]

does this also mean lim t->0 g(t) is not indeterminate?
also since this is probably not true for all functions, i'll just say that f(x) is sin(x)/x and g(x) is x/sin(x)

[merry depot]

that's red box is not true

[rare heart]

why not

[weak field]

$g(t)=g(\frac{1}{x})=\frac{1}{f(\frac{1}{x})}$

[merry depot]

$f(x) = \frac{e^x-1}{x}$ then as $x\to 0, f(x)$ is indeterminant. \
$g(x) = \frac{x}{e^x-1}$. Plug in $1/x$ and it's not the same

[ocean seal]

Zybikron

Ｓａｓｕｋｅ

[rare heart]

okay

[lone heart]

@rare heart Has your question been resolved?

[lone heart]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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

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

[ocean seal]

Someone_21

[wet nest]

n belongs to to natural numbers and [x] represents greatest integer function or floor function

[lone heart]

Channel closed

Closed due to the original message being deleted

Available help channel!

Send your question here to claim the channel.

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

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

[olive citrus]

is a span in linear algebra a subset?

[merry depot]

a span is a set, yeah

[olive citrus]

ok

ok thats it for now

.close

[lone heart]

Channel closed

Closed by @olive citrus

Use .reopen if this was a mistake.

[olive citrus]

thank you

[lone heart]

Available help channel!

Send your question here to claim the channel.

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

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

[modern wyvern]

anyone down to help me with this

Lily is holding a 55 ft
rope attached to a hot‑air balloon. The hot‑air balloon is moving downward towards the ground at a rate of 17 ft/s.
As the balloon moves towards the ground, Lily keeps the rope taut and walks away from the balloon.

Calculate the rate at which Lily is moving away from the hot‑air balloon when the balloon is 36 ft
above the ground. Round your answer to three decimal places.

[grave cedar]

is she holding it above her head initially?

ig so

so balloon travelled 55-36 ft

right?

at 17 ft /s

[modern wyvern]

i just got it

lol it was 14.718

[modern wyvern]

do u think u could guide me on a different question though

[grave cedar]

ig

not sure

i can try

send q

[modern wyvern]

would u understadn this

I had an idea

18 = 2/3 pi r dr/dt h + 1/3 pi r^2 dh/dt

[grave cedar]

hmm

we need to find speed

[modern wyvern]

dr/dt is 13

dv/dt is 18

i dont know what this is

well ik but like how to apply it when i already to deriverative

[grave cedar]

oh its similar triangles thats why

idk how to proceed with differentiation so

[modern wyvern]

can u understand this one then

[grave cedar]

lets see

nope

ig first we will tan theta

[modern wyvern]

okay

[grave cedar]

check dm

[limpid turret]

This was an oddly worded problem.. She's technically always 55 ft from the balloon with this setup

It should've asked, "At what rate is lily walking away from the balloon's eventual landing spot" or something like that

@modern wyvern do you still need help?

[lone heart]

@modern wyvern Has your question been resolved?

[lone heart]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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

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

[ember dagger]

SOMEBODY HELP ITS THE LAST DAY FOR ME TO MAKE THESE UP

[ember dagger]

THERES NO HELP VIDEOS NO NOTHING AND I HAVE TO MAKEUP SOME OTHER WORK TOO

😭

<@&286206848099549185>

[surreal meadow]

!15m

[lone heart]

Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.

[jagged cobalt]

bruh, calm down

[merry depot]

First. Caps lock doesn't make anyone work faster.
Second, maximo beat me to it

[ember dagger]

Sorry I’m super desperate

[lone heart]

@ember dagger Has your question been resolved?

[lone heart]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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

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

[primal warren]

this maybe a dumb question but say i have an expression that contains only one variable, say x, and we want to take the limit as t approaches infinity, is this possible?

[echo socket]

$\lim_{t\to\infty}f(x)$?

[ocean seal]

A Lonely Bean

[primal warren]

yes

[echo socket]

If x and t are unrelated and indepedant from each other

Then it's simply f(x)

[primal warren]

and how could you check if they are related?

[echo socket]

Check their definitions

[primal warren]

alright, thanks!

[lone heart]

@primal warren Has your question been resolved?

[lone heart]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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

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

[foggy sage]

what is the analytical solution for an equation like this?
2x³ + x - 6 = 0

[foggy sage]

i know i can just try with diff values of x to see what satisfies the equation (in this case its x = 1)

[vale wigeon]

wdym by "the analytical"?

[alpine sable]

p(1)=3...

[foggy sage]

yeah i know
but like if say the correct solution was x = 10

i would have to go evaluating x = 1, 2, 3... and so on

[alpine sable]

welp if you would know that p(10)=0, you could use division to reduce it into a quadratic (or in another problem with higher degrees, you can use the rational roots theorem again)

[vale wigeon]

you could throw the rational root theorem at this to somewhat cut down on guesswork

[foggy sage]

so there's no "direct" way to just solve something like this right

.close

[lone heart]

Channel closed

Closed by @foggy sage

Use .reopen if this was a mistake.

[limpid turret]

cubic formula

but it's better to guess

[lone heart]

Available help channel!

Send your question here to claim the channel.

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

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

[normal bridge]

Students in a science lab are working in groups to build both a small and a large electrical circuit. A large circuit uses 4 resistors and 2 capacitors, and a small circuit uses 3 resistors and 1 capacitor. There are 100 resistors and 70 capacitors available, and each group must have enough resistors and capacitors to make one large and one small circuit. What is the maximum number of groups that could work on this lab project?

[foggy sage]

find out how many resistors and capacitors one group would need (the total for a large and small circuit)
then you can find out the maximum number of possible groups by just dividing the components into the groups

[normal bridge]

ty, I got it :)

.close

[lone heart]

Channel closed

Closed by @normal bridge

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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

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

[proven tendon]

im having a bit of trouble solving this

im thinking of using the conjugate some how but im lost

on desmos i see that i can use b = 1 c = 1

[median oar]

What’s your Choices

[proven tendon]

but i dont know how to algebrically get to that

[median oar]

Look at the function, when is that function = 0

When is a/b = 0

[proven tendon]

at x = 1

[median oar]

No no no

That’s not what I’m asking

[median oar]

Look at the limit you’re given

When is that equal to 0

When you have a fraction a/b

What values of a and b make it = 0

[proven tendon]

when a is aproaching 1 and b = 1

[median oar]

????

1/1 is equal to 1 man

[proven tendon]

i dont know :/

ah yeah

[median oar]

If I give you a fraction a/b

I want you to make this fraction equal 0

What values would you put for a and b

[proven tendon]

well if i have a = 0

then for any value of b it will always be 0

but thatll just make a horizontal line

and cant rlly take a limit for that

[median oar]

Any value of b?

[proven tendon]

0/anything = 0 no?

[median oar]

Not if b = 0

[proven tendon]

ah right

[median oar]

Why not

[proven tendon]

can u take the limit of a horizontal line?

like it dosent make sense to i think

well

im not sure

[median oar]

$\lim_{x\to 5} 3 = 3$

[ocean seal]

Frosst

[proven tendon]

hmm right

cause i was thinking i can set b to b=x

then the numerator is always going to be 0

[median oar]

Ok but the thing you have to realise is

[median oar]

This is not true

Because x is not really a variable

x tends towards a

When you evaluate the limit you sub x = a

a is a constant

#❓how-to-get-help

Then you wouldn’t be here

Read it again

That’s their wrong

[proven tendon]

right

so

hmm

then for the sake of simplicity

i can think of x = a

[median oar]

No you can’t

You need to define an a

That’s part of the question

[proven tendon]

yeah thats what i mean

like

x is a place holder almost for a

[median oar]

You can’t change x

x is not a variable you can change

[proven tendon]

ah yeah ok

my bad i see my mistake

[median oar]

The things you can change are a, b, and c

[proven tendon]

so like whats the approach with this q? like do i need to factor it somehow or something?

im confused on what the method or the intuition is here

[median oar]

We want this limit to equal 0 right?

[proven tendon]

yes

[median oar]

Hint 1

This a and the a in your question are different a’s btw

This a is the a in a/b = 0

[proven tendon]

ah ok

[proven tendon]

so we want to make the numerator = 0 ?

since that a is from a/b

[median oar]

That’s 1 way of answering the question

[proven tendon]

yeah thats what i thought of earlier

and it makes a horizontal line which is a bit of a cheeky way to solve it

so ive been trying to think of other ways

[median oar]

So we want to make sqrtx - sqrtb = 0

How can we do that

[proven tendon]

sqrtx = sqrtb

x = b

[median oar]

You can’t change x

There’s a limit in the question though

You can change what x tends towards

[proven tendon]

so just sqrtx = sqrtb?

[median oar]

No!!!

You cannot change the value of x

You can only change a b c

[proven tendon]

we can only do this if b = x tho?

[median oar]

dude

x cannot be in your equations

It CANNOT be changed

How many times do I have to say that

x is like 5

You can’t change 5 = b

5 is 5

[proven tendon]

so then how do we get this?

[median oar]

Look at your question

[proven tendon]

how can we make this happen if we cant touch it at all

[median oar]

You can’t change what x is because x tends towards a

[proven tendon]

ok so if a = b

[median oar]

You can change what a is

But you cannot change x

[median oar]

Yea

[proven tendon]

so a = 1 b = 1

[median oar]

No!!!

[proven tendon]

why not 1?

[median oar]

Well actually

[proven tendon]

like any values >= 0 would work

[median oar]

Yeah that’s fine

They can be 1

Yeah that’s fine

[proven tendon]

so then c can be anything >= 0 cause by this method the denominator dosent really matter

[median oar]

Yup

[proven tendon]

ah cool

thanks for the help!

[median oar]

The other way thing you can do is

[proven tendon]

yeah

[median oar]

How else can you make a/b = 0

[proven tendon]

well if b = 0 then its undefined

uhh

not sure tbh

[median oar]

Hint: ||1/2, 1/3, 1/4, … 1/100000||

[proven tendon]

oh just make b a rlly large number?

[median oar]

Yes

[proven tendon]

yeah i guess but it says "equal to 0"

[median oar]

If you make the bottom grow faster than the top it’ll tend to 0

Yes but you have a limit

[proven tendon]

so i think the first method is better

cause its more direct

[median oar]

Not necessarily

[median oar]

This is still correct

[proven tendon]

which one do you think is better?

[median oar]

I think the teacher has set this problem with an easy and hard way

Depending on the circumstances

[proven tendon]

i think the first one is more accurate to how he wants it

cause yeah in the second one it tends towards 0

[median oar]

On a homework I’d find try the hard way to help my understanding

On an exam I’d go with simple and easy

[median oar]

It’s not “more accurate”

[proven tendon]

i can honestly put both and see what they think

[median oar]

He also clearly knows there’s a hard way

Because he says to justify at the end

[proven tendon]

but what can b be in the second method

like can we say b -> inf

[median oar]

b is the bottom right?

[proven tendon]

yeah

[median oar]

We want the bottom to grow faster than the top

[proven tendon]

we can do like

b^2

[median oar]

Hmm it looks like we might need some tricks to get the bottom grow faster

[proven tendon]

yeah cause if i graph it

its the same thing

[median oar]

Hmm I doubt they want it that way then I think

[proven tendon]

like if we put our variable to ^2

yeah thats what i think to

like maybe i can add a explanation "b can also be growing faster...."

[median oar]

,w lim x to a (sqrt(x)-sqrt(b))/(sqrt(x+1)-sqrt(c)), a = infinity, b= 0, c=ix

[ocean seal]

Results provided by WolframAlpha

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

Requested by Frosst#1111

[proven tendon]

hmm i think ill ask in office hours for other strats

[median oar]

,w lim x to infinity (sqrt(x)-sqrt(0))/(sqrt(x+1)-sqrt((-ix)^2)

[proven tendon]

but i think the horizontal line is a safe one

[ocean seal]

Results provided by WolframAlpha

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

Requested by Frosst#1111

[median oar]

There we go

That’s really wack though

[proven tendon]

oh u just multiplied it but inf 😂

i mean yeah that works

[median oar]

Not quite

I had to use complex numbers umbers as well

[proven tendon]

hmm sounds good thanks for the help!

.close

[lone heart]

Channel closed

Closed by @proven tendon

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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

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

[bronze bone]

Hello, can someone help me?

[bronze bone]

the answer key is 158, but i don't know how to get it, pls help me

[lone heart]

@bronze bone Has your question been resolved?

[bronze bone]

<@&286206848099549185> I need your help so much

[lone heart]

@bronze bone Has your question been resolved?

[bronze bone]

<@&286206848099549185>

[bronze bone]

<@&286206848099549185>

[south ermine]

hey!

[bronze bone]

Hi, can you help me solve this question ?

[south ermine]

ill try,what lesson is that?

[bronze bone]

Nonlinear System of Equations

thank u bro, i am so frustated

hope this can help u

[south ermine]

remarkable identities,classic one

@bold dawn need anything?

@bronze bone QUESTION

[bold dawn]

no, nothing really, i was trying to see the question

the guy pinged helpers 3 times

lol

[south ermine]

my brain is getting fried istg

[bronze bone]

yes, cuz no one help lol

[south ermine]

i cant remember this even if my life depended on it

[bold dawn]

how about you subtract the equations in pairs of 2? from first two you get, y^3-x^3=4; then z^3-y^3=14; and z^3-x^3=18

[alpine sable]

honestly it looks really familar to identity 4 (from your list) but probably is much deeper

like whenever I look at a question like that my maths senses trigger and beg me to apply that identity because it is really used less

[bold dawn]

@bronze bone i've solved it, first do the substitution as told, then from those equations you find out x^3+y^3+z^3 in terms of a single variable and put it in one of the remaining equations given in the problem

the values of x are (-2)^1/3 and -1/(7)^1/3

[lone heart]

@bronze bone Has your question been resolved?

[bronze bone]

OMG, did you write the solution? can i see it ? because i am still confused

[alpine sable]

honestly at this point I am also curious to know the answer after 3 helper pings 😅

[bronze bone]

yes, i have been trying to solve it for 3 days lol

[bold dawn]

i'll much rather give you hints

subtract eq (3) - eq(1) and eq(2)- eq(1), and then obtain y^3 and z^3 separately in terms of x^3

[bronze bone]

ok, i'll try

[bold dawn]

thereafter, put the values of y and z in the first equation, and you'll be able to come to this equation after simplification: 7x^6+15x^3=-2

From that, you solve for x^3 = -1/7 and x^3=-2

Then use the already derived equations to solve for y^3 and z^3, and you get their values. The sum of the cubes of first solution pair is 151/7 and that of the second pair is 16. The greater one is the first, and on comparison with m/n, we find m+n = 158

[lone heart]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[bronze bone]

THANK YOU SO MUCH BRO @bold dawn

[lone heart]

Available help channel!

Send your question here to claim the channel.

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

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

[bronze bone]

.close

[ember dagger]

I don’t know how to start these

[loud orchid]

Forget about the sigma for the moment. What can you say about the numbers 3, 7, 11, 15?

[vale wigeon]

@ember dagger #❓how-to-get-help

oh

wait

im a fool

this is your channel

don't mind me

[ember dagger]

There’s 4 of them

D=4?

Also

Yea

The pattern is +4

@loud orchid

Hello

[bold dawn]

can you say that each number is one less than the multiples of 4?

[ember dagger]

Idk I think so

[unkempt sundial]

then you can deduce that 3, 7, 11, 15 is an arthemetic sequence

[ember dagger]

How

[unkempt sundial]

and how do you write an arthemetic sequence?

you have the sequence growing with a distance of 4

[ember dagger]

3,9,12 etc

Yea

[unkempt sundial]

?

[ember dagger]

Oops

[unkempt sundial]

the form of an arthemetic sequence is dn+a_0, d is the distance, n is the term, a_0 is the first term

can you write the sigma notation now?

[ember dagger]

What’s the “_”

What’s n?

And what’s a??

I’m so lost

[unkempt sundial]

$a_0$ just a symbol im using to represent first term

[ocean seal]

alihsaas

[ember dagger]

I’ll try

Wait but what’s n????

[unkempt sundial]

the terk you are currently at

3 is the 0th term

n=0

[ember dagger]

Oh

[unkempt sundial]

11 is 2nd term, n=2

[ember dagger]

4(0)+9

?

@unkempt sundial

[unkempt sundial]

why 9?

what are you showing me exactly

[ember dagger]

Because a0= 9

It’s the first one

Right?

[unkempt sundial]

that's the other question

im answering the first image you sent

[ember dagger]

Oh oops

4(0)+3

[unkempt sundial]

okay closw but why did you take n=0

[ember dagger]

I’m not sure anymore

Anymore*

[unkempt sundial]

okay let's say im trying to get what's the nth term in this sequence

can you tell me it?

[ember dagger]

It’s the number below a

It’s what it is

Like a1 is the first one?

And a2 is the second sequences

[unkempt sundial]

hmmm?

look

ill use $a_n$ to symbolise the nth term in our list of numbers

olay?

[ocean seal]

alihsaas

[unkempt sundial]

okay*

?

[ember dagger]

Ok

[unkempt sundial]

then according to the formula we have of the arthemetic sequence

$a_n = 4n+3$

[ocean seal]

alihsaas

[thorn tapir]

[unkempt sundial]

@ember dagger ? 🥹

[ember dagger]

Sorry

I’m back

@unkempt sundial

My phone died

Now I’m back

[unkempt sundial]

👍just check on last thing i sent

[ember dagger]

What’s n= to then

We need to find n?

[unkempt sundial]

in sigma notation it will vary depending on what you put in the bounds

you know how sigma notation works?

[ember dagger]

Kind of

And I thought that was arthmetic sequences the entire time 💀

I’m still new to this

[unkempt sundial]

say we have $\sum_{n=1}^{3}{n}$

can you tell me how this will evolve

[ember dagger]

Yes?

[unkempt sundial]

wrong one 💀

[ember dagger]

Oh

I was confused for a sec 💀

Alr

So

You mean what it = to?

[ocean seal]

alihsaas

[unkempt sundial]

yah

and how did you reach it

[ember dagger]

I’m trying to rn

[unkempt sundial]

take your time 👍

[ember dagger]

It’s 6?

@unkempt sundial

[unkempt sundial]

yah correct cause we have n inside the sigma and n will go from 1 to 2 and then 3, while summing the terms

back to original question, i already told you 3 is the 0th term

so we know n will start from 0

right?

[ember dagger]

Yea

Ok

[ember dagger]

Nah I plugged it into a graphing calculator

That’s how my teacher taught us to do it

💀.

[unkempt sundial]

ah, and didn't teach how sigma works?

[ember dagger]

Kind of

They taught us how to plug it into the calculator

@unkempt sundial

So what will the sigma thing be

[unkempt sundial]

$\sum_{n=p}^{q}{a_n} = a_p + a_{p+1} + a_{p+2} + ... + a_q$

[ember dagger]

Tf

What do I even do to that

[unkempt sundial]

try to understand what's going on

[ocean seal]

alihsaas

[ember dagger]

There’s a sequence

I think

[lone heart]

@ember dagger Has your question been resolved?

[lone heart]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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

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

[steady basin]

could i get some help with b iii plz

<@&286206848099549185>

[thorn tapir]

Kernel of a Matrix is the set of all such column vectors which if, right multiplicated, gives 0 column vector.

Basically all Xs such that BX = 0

[steady basin]

at this stage so far

bit stuck now what to do

so i guess i can deduce that x3 = 3x4

[thorn tapir]

And so, in this case, the Kernel is actually the solution of the system you're given.

[steady basin]

yh bit stuck on finding the solution here

[thorn tapir]

You seem to have $x_3 = 3x_4$

Oh wait sorry

[steady basin]

x3 = 3x4

[ocean seal]

rikusp2002

[steady basin]

ye

[thorn tapir]

Hmm, so basically this has infinite number of solutions

[steady basin]

i see

[thorn tapir]

The vectors are of the form

[steady basin]

do i need to write this in parametric from?

the solution

[thorn tapir]

$\left[a;b;c; \frac{c}{3}\right]^{T}$

[ocean seal]

rikusp2002

[thorn tapir]

T means transpose basically

[thorn tapir]

Where a + 2b + c = 0

you can replace b by -(a + c)/2

So only a and b is required from real numbers

And it also shows for any a and b there will be a valid solution, so the kernel is infinite.

[thorn tapir]

Yes

[steady basin]

gimme a moment

@thorn tapir agree with this?

[thorn tapir]

Ahhh absolutely

You did it better than me

Very nice

[steady basin]

kl kl thx

[steady basin]

what about the basis for the kernel of the matrix then

[thorn tapir]

You have the two vectors.

Your s and t are scalars

So the kernel is the span - set of all linear combinations of the two vectors you've yourself written

(-1 1/2 0 0) and (-1 0 1 1/3)

Take the transpose of these row vectors and those would be your required basis vectors

@steady basin

[steady basin]

^^

agree?

[thorn tapir]

💯💯💯

[steady basin]

perfect

thanks so much for ur help

[thorn tapir]

So you can now find the dimension.of the kernel

Which is 2

[steady basin]

so is dimension

just the number of vectors

[thorn tapir]

You're welcome

[steady basin]

there are

in the set

[thorn tapir]

Absolutely true. Such vector spaces with finite basis sets are called finite dimensional vector spaces.

Also, the dimension of Kernel is called the Nullity of The Matrix

So, you also found something else - that is the rank of the Matrix.

Nullity + Rank = Number of Columns.

Rank-Nullity Theorem.

Rank is defined as the maximum number of independent columns or independent rows in the matrix.

In this case rank is 1, so it's only 1.

[steady basin]

ye kl

perfect

thanks a lot

[thorn tapir]

,

Lol i was blabbering my bad

Linear Algebra was traumatic for me

[steady basin]

nah nah i understand

[thorn tapir]

One more thing I might add -

[steady basin]

ok

[thorn tapir]

Determinant of a matrix is 0 if the rank of a matrix is less than the number of columns

Or basically if, the kernel of the matrix doesn't only have 0 column vector as the only element

[thorn tapir]

And that's also why you couldn't find the inverse of the matrix

The reduced row echelon form stopped before reaching identity

[steady basin]

i see i see

interesting

[thorn tapir]

That's all

[steady basin]

just lastly

[thorn tapir]

Yes

[steady basin]

the rank here is 2

right?

[steady basin]

ranks 2?

[thorn tapir]

.....wait. if rank is 2....

Oh lmao my bad number of total columns.was 4 😂😂😂

Yeah 2

2 + 2 = 4

[steady basin]

yh kl

lmao

[thorn tapir]

Both Nullity and Rank are 2

This is not even a square matrix we won't even be able to find determinants lol my bad

[steady basin]

lmao

[thorn tapir]

......wait wait wait.

[steady basin]

isnt the nullity

3

[thorn tapir]

Count the columns.

Isn't it 5

💀

Wtf happened to me am I seeing hallucinations

[steady basin]

the nullity is the number of columns without a pivot

[steady basin]

ye

so surely nullity is 5

and that makes sense

[thorn tapir]

Bruh then rank is 3

[steady basin]

3 + 2 = 5

[thorn tapir]

I can see 3 independent columns

[steady basin]

the rank is number of non zero rows buddy

thats 2

[thorn tapir]

Nullity is 2 because dimension of kernel is 2

[steady basin]

rank is 2

number of non zero rows

thats 2

[thorn tapir]

It can also be columns

[steady basin]

in my notes its defined by rows

[thorn tapir]

It doesn't have to be

[steady basin]

ik but its what my notes say

so imma just go by that

[steady basin]

ive learnt it as rows so imma just stick with that tbh

[thorn tapir]

What do you mean by pivot

Nullity can't be 3 as then your kernel needs to have 3 basis vectors

[steady basin]

ye this makes sense by these definitions, rank is 2, nullity is 3, number of columns (n) is 5

2+3=5

[thorn tapir]

no wait.

[steady basin]

@pseudo ice sry for the ping

may need ur intervention

cuz im getting confused

from my defintions this makes sense to me

[thorn tapir]

Is your row echelon form completely reduced..?

[steady basin]

yes

[thorn tapir]

If your rank is 2, then your kernel is wrong.

[steady basin]

this is a different question

btw

[thorn tapir]

If your kernel is correct, your method of determining rank is wrong

[steady basin]

like a different part

idek anymore

im so confused now

[thorn tapir]

Dimension of Kernel is nullity

Dimension of Row Space is Rank

Add them -> you get number of total columns

[pseudo ice]

[steady basin]

chartbit plz

save me

[thorn tapir]

Uhhhh help us please

[steady basin]

im so confused

[pseudo ice]

Catch me up please?

[thorn tapir]

I don't know wtf happened

[steady basin]

im pretty adamant what ive done is correct

chartbit can i just resend the questions and my solution

and just lmk if its correct

[pseudo ice]

me every day I exist

Cool cool!

[steady basin]

ill dm

[thorn tapir]

OH WAIT LOL

AHAHAHAHAHHAHAHHAHA

I'm so sorry

The matrix given is different right?

[steady basin]

this is part bi

this is biii

[thorn tapir]

Yeah rank is 2 lol

First column x 3 + 3rd column x (-3) = 4th column

2nd column = 2 x first column

5th column = (-1) x first column + (3) x 3rd column

Only 1st and 3rd are independent

Nullity is 3

Fr, my bad I was stupid

[steady basin]

u said tho dimension of kernel is nullity

and isnt the dimension 2

[thorn tapir]

Yes, I thought the kernel was of the same matrix as the previous one

We didn't solve for kernel of this one

[steady basin]

for biii tho

lets just do it

whats the rank and nullity

for our own sake

[thorn tapir]

Nullity is 2

Rank is 2

[steady basin]

rank is 2 as well ?

[thorn tapir]

No of columns 4