help-0

[waxen turtle]

Did I do it fr

@limpid turret

<@&286206848099549185>

<@&286206848099549185>

[limpid turret]

That's a start, but you need to actually list them.

[waxen turtle]

how

[limpid turret]

you need to simplify 9/6, 9/3, 9/1, 3/6, 3/3, etc.. and remove duplicates

[lone heart]

@waxen turtle Has your question been resolved?

[lone heart]

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[alpine sable]

Indicate all the solutions for the equation

[alpine sable]

step by step please

[limpid turret]

!status

[lone heart]

What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

[alpine sable]

1

idk how to solve this at all

[limpid turret]

what do you know about modular arithmetic?

[alpine sable]

i dont know much

4 is supposed to be the rest of 34x, i think

idk the exact mathematical terms in english but yea

remainder

[limpid turret]

You can try x=0, 1, 2, ..., 9

See which have remainder of 4

I do not know a better way

But I'm sure one exists

[alpine sable]

but what the mod means

[limpid turret]

mod 10 means that 34x and 4 have the same remainder when dividing by 10

the remainder of 4/10 is just 4, so you need to find x so that 34x/10 will also have a remainder of 4

[alpine sable]

oooh

so i gotta do 34x / 10 = 4 ?

please help i got exam on friday

<@&286206848099549185>

ma god

[shut marten]

no

[slate talon]

Chad

bro just said no without giving an alternative

bro giving orders in here

[alpine sable]

what is this point of this entire thing

[shut marten]

its used alot in cryptography

sry i had to make a phone call

[alpine sable]

i meant the server

how do i solve that

[shut marten]

to help ppl with math

modulo is used to represent a remainder

when i divide 20 by 10 the remainder is 0

20=0mod10

when i divide 12 by 5 the remainder is 2

12=2mod5

[alpine sable]

right

i get it

[shut marten]

so what times 34 when divided by 10 gives you a remainder of 4

[alpine sable]

idk

[shut marten]

try when x=1

whats the remainder

[alpine sable]

4

@shut marten

[shut marten]

youre correct

theres a pattern to which numbers will satisfy it

1,6,11...

[alpine sable]

a person sent me this as the resolution but i dont understand the rationale behind it

[shut marten]

,rotate

[shut marten]

<@&286206848099549185> i need a substitute i gotta drive

[lone heart]

@alpine sable Has your question been resolved?

[storm plinth]

x = 5n + 1 where n belongs to Whole numbers

[alpine sable]

wdym

wtfdym

fuck this server

[lone heart]

@alpine sable Has your question been resolved?

[alpine sable]

nope

[lone heart]

@alpine sable Has your question been resolved?

[alpine sable]

not nice 😢

[soft kindle]

Dude

[alpine sable]

<@&286206848099549185>

[soft kindle]

Stop.

[alpine sable]

language?

<@&286206848099549185>

[shrewd prism]

Can you translate

Isn’t 4 mod 10 just 4?

34x = 4

X =17/2

@alpine sable

Do you know what mod means

[alpine sable]

modulo/modulus? I mainly use it in java,

[shrewd prism]

Mod gives the remainder when you divide

So 4mod 10 is 4 since the remainer is 4

therefore the equation is 34x=4 which you can solve @alpine sable

Mod is like elementary math yknow

<@&268886789983436800> ^

[alpine sable]

These emojis really aren't appropriate

[shrewd prism]

.close

A

[tardy stag]

good idea

.close

[lone heart]

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[flint jackal]

may i have a hint for how to solve this

[flint jackal]

without l'hopital

[foggy pecan]

change the denominator, using trigonometric identity, then you get sinus, and multply, numerator and denominator, by 1+cos(3x),m then also you will convert it into sinus

[flint jackal]

ohhh ty

[foggy pecan]

etc

[flint jackal]

got it tysm

[foggy pecan]

yvw

[flint jackal]

.close

[lone heart]

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[vagrant falcon]

So I'm confused here. EVT says that a function is continous on a closed interval has a absolute maximum and a absolute minimum. However, graph B is not continous and is not closed, yet it has a absolute maximum?

[tacit arch]

Yes. The theorem doesn't say only continuous functions have a max or min

[vagrant falcon]

so it just says a function with those conditions has to have a max and min?

but if thats the case, what about the functions y=x on the interval [1,3]?

[tacit arch]

What about it

[vagrant falcon]

does it have a absolute min and max?

cuz its continuous

and its closed

on the interval [1,3]

[tacit arch]

Yes if it satisfies the conditions for EVT then it satisfies the conclusion too

[vagrant falcon]

i meant

y=3

sorry

[tacit arch]

What about it

[vagrant falcon]

the function is y=3

[tacit arch]

Are constants continuous?

[vagrant falcon]

on an interval [1,3]

[vagrant falcon]

tech yes

[tacit arch]

.

[vagrant falcon]

interesting

cuz graphically, I wouldn't know where to find the absolute min and absolute max

[tacit arch]

They're the same for constants

[vagrant falcon]

oh

gotcha

thanks

.close

[lone heart]

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[grim yew]

How to solve this question

[tardy stag]

say your fraction is a/b

[grim yew]

Ok

a

b

[tardy stag]

now turn those sentences into equations

[grim yew]

Ok wait let me process it and write it just a minute

a+6 = a+6 = 3
------ = ----- = --
b+7+6 = b+13 = 4

Done

[shrewd prism]

b=a

[grim yew]

What?

[shrewd prism]

The denominator is 7 more than the numerator so you can represent the denmenator as a+7 if a is the numerator

[grim yew]

Oh ok

Wait lemme edit

K done

[shrewd prism]

What

is a+7= b? Is that what you’re trying to do

srry I have to go

[grim yew]

What?
Imma edit back nvm

[grim yew]

No

<@&286206848099549185>

Someone pls help i got exam in 20 min

[slate talon]

what do you need help with

[grim yew]

How do i solve this

[grim yew]

I did the first step here

[slate talon]

no it doesn't mean that it is equal to 3

or 4

it only means that they have a common divider 'k'

[grim yew]

Ok

[slate talon]

so a/(a+7)

[grim yew]

Ok

[slate talon]

a+6 = k3

a+7+6 = k4

[grim yew]

Ok

[slate talon]

now solve this linear for a in N

both a and k are natural numbers

[grim yew]

a+6=k3
a+7=k4

The only. Thing i can think of here is the cross Multiplying so we gotta do cross multiplying?

[slate talon]

not that far

a = b and c = d

a - c = b-d

[slate talon]

b exceeds a by seven so instead of b just write a + 7

[grim yew]

Ok

[slate talon]

anyway after solving for k and a : k = 6 and a = 12

so the initial fraction would be

12/19

you get it ?

[grim yew]

15/22

[slate talon]

@grim yew

[grim yew]

The answer in book it says 15/22

[slate talon]

wait

[grim yew]

It says find original fraction

[slate talon]

oh yh sorry

i miscalculated it

i used my mind only

after solving you will get

[sand estuary]

I think it is 21/28.

[slate talon]

k = 7

[sand estuary]

wait nvm

[slate talon]

and a = 15

so yh

[grim yew]

Its in the book written 15/22

[slate talon]

it's 15/22

[sand estuary]

ye

[slate talon]

yh yh

[grim yew]

So what to do

[slate talon]

i did the calculus in my mind and fucked it up

[slate talon]

i showed you

you take the litteral input

and turn it into a mathmatical linear equation

[sand estuary]

so because a+6= k3 and a+13 = k4 than a = k3 - 6 and a = k4 - 13. If you look at it that means that the difference between k is 7. K is 7. This means you can multiply 3/4 by 7 on both sides to get 21/28, subtract 6 from each.

15/22

[grim yew]

Wait let me process this

Oh ok

K i understood

[slate talon]

anyway if you mess things up you can always use equations

[grim yew]

Ok

[slate talon]

are u done can i close this chat

or do you have more questions

[grim yew]

. close

.close

[lone heart]

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[polar slate]

Need help with gauss jordan elimination

[polar slate]

sending pic one sec

idk if my steps are correct for my rref

[lone heart]

@polar slate Has your question been resolved?

[lone heart]

@polar slate Has your question been resolved?

[lone heart]

@polar slate Has your question been resolved?

[lone heart]

@polar slate Has your question been resolved?

[lone heart]

@polar slate Has your question been resolved?

[alpine sable]

<@&268886789983436800> this dude straight up spammed his bot commands in OP's help channel

can you delete this

[lone heart]

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[steep axle]

Which function matches graph

[steep axle]

G?

[edgy merlin]

No, its not G

Think about it. In which points does this function reach 0?

[lone heart]

@steep axle Has your question been resolved?

[steep axle]

-c, 0 and b

Oh wait

Is it A

[edgy merlin]

yeah

[steep axle]

Oh alright

Thnx

[lone heart]

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[short basin]

Help me

[modern skiff]

send the question

[short basin]

Here's the question

[cursive lantern]

The third one (c)

[short basin]

I solved the given polynomial

Why?

[cursive lantern]

wellp

(x-1)^2(x+2)=y

[short basin]

ok

[cursive lantern]

(x^2-2x+1)(x+2)=y

[short basin]

i got a cubic polynomial

[cursive lantern]

yes

you need to find the highest point on x

and nulls by x

(x^2-2x+1)=0

and x+2=0

[short basin]

ok

x=-2

[cursive lantern]

x=-2 and x=1

[short basin]

yeah

[cursive lantern]

as we can see graphic can cross those points

at the picture c

[short basin]

it also crosses in (a) and (b)

[cursive lantern]

no

when you find nulls of function

it must be points, that at y gives you 0

(-2;0) ; (1;0)

understood?

[short basin]

what is nulls of function?

[cursive lantern]

the values of x

at which y equals 0

[short basin]

okay understood

[cursive lantern]

In Russia, we call it that way

[short basin]

nicee

thank you

.close

[lone heart]

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[formal void]

i need help with trigonometry word problems! question 2 in the image

[modern skiff]

apply the Pythagoras theorem

[coral flower]

use law of cosine

[formal void]

i did use law of cosine but i got 15 as an answer

[coral flower]

it doesnt state that <A is right angle

[formal void]

which is too small

[coral flower]

show working

[formal void]

Sry i erased it 😭

[coral flower]

np ill solve it and check the answer i get

[formal void]

Okok thank u

[modern skiff]

oh that's right..but it's a trigonometry question so we usually assume an angle to be 90

[formal void]

That’s what i thought too! i also tried using pythagorean theorem

Maybe i just didn’t do it correctly

[coral flower]

try solving again

i got AB = 476.25

[formal void]

damn okay

one sexond

i got 26 this time lord

[coral flower]

which formula are u using?

[formal void]

i feel like i’m plugging in the information incorrectly

cosine law

[coral flower]

show ur formula with the values

[formal void]

the top formula

[coral flower]

yeah

[formal void]

ok this is what i put down

Ii think i’m just putting things in the wrong place but um idk

[formal void]

OHHH

my gosh

silly@goose

ok i got the same answer as u

i didn’t even notice that 😭😭

[coral flower]

subtract BW to get AW length

[formal void]

ok awesome 😭

can u help me with another one

[coral flower]

ok

[formal void]

this is the only word problem i have left to solve

[coral flower]

u should draw a diagram for this question

[formal void]

will do

how do u draw this

[coral flower]

wait ill draw it and send it and if any questions then ask

[formal void]

Okok

[coral flower]

smthing like this

[formal void]

Wait i think i got it

ok i did the same thing too

[coral flower]

so the first ship (the top one) left at 12:00 with a speed of 20km/hr , the second ship (bottom one) left at 12:30 with speed of 15km/hr

first find where both ships are at 14:30

u are given time and speed and u have to find distance

[formal void]

Okok

ok so the side length for the first boat is 50km

and the bottom boat is 30km

and the inside angle is 130

i can use cosine law now, yeah?

to find the distance from the 1st boat to the 2nd boat

[coral flower]

yeah

[formal void]

okok

[coral flower]

i dont understand the term radar bearing so i cant help with that :(

[formal void]

It’s ok we will get thru this

i can probably ask a teacher cuz i’ mat school rn

LMFAO

ok i got 72.99 as an answer

so like 73km

[coral flower]

same

[formal void]

ok awesome!!! i think i’m good here :3

thnx for helping me man

[coral flower]

np

[formal void]

byeyeyey u’re very helpful

how do u close the channel again

[coral flower]

bye , good luck on next questions

".close"

[formal void]

okok thnx

.close

[lone heart]

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[lone heart]

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[tardy elm]

<@&286206848099549185>

[tardy elm]

can someone tell me the answer for b and c

[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.

[lone heart]

The purpose of this server is to help you learn, not to hand out answers. Do not ask someone to give you the answer directly.

[tardy elm]

yeah i would love to

<@&286206848099549185>

[burnt bolt]

I don't think helpers are supposed to hand out answers...

Either way, let me see what I can do

[tardy elm]

sorry i wanst aware about that

my apologies

[burnt bolt]

It's ok!

If you need help with solving a problem but don't have anyone to help you with that I'd recommend you ask Bard to do it for you, Google's Ai

The reason I recommend Bard is because Bard explains mathematical problems very well

It's not perfect but it's already something

[mortal trellis]

dont use ai if you cant verify what it says

which you cant if you are learning stuff

[thorn tapir]

wtf

[tardy elm]

ty i'll give it a try

.close

[lone heart]

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[lapis goblet]

can someone please check these and let me know if any are incorrect, ty

<@&286206848099549185>

[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.

@lapis goblet Has your question been resolved?

[lone heart]

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[lean forge]

I have the DE $y'=y^2$. If we suppose $y(0)=0$, I have to show that $y=0$

[ocean seal]

Azenx

[limpid turret]

!status

[lone heart]

What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

[lean forge]

Cant you see me typing -_-

If we take $A = {t \in [0; +\infty[ \ | \ y(t)=0}$ then by proving that A doesnt have an upper bound i think thatll do

[ocean seal]

Azenx

[lean forge]

To do so if we take $f = \frac 1 y$ and suppose that A has a lower bound

[ocean seal]

Azenx

[lean forge]

we can say that $f$ is decreasing and that $f' = -1$

[ocean seal]

Azenx

[lean forge]

idk where to go from here

[limpid turret]

I'm not familiar with the approach you are doing. And it sounds overly complicated

Can you not just solve the DE?

[lean forge]

no

I can't use separable equations

as y(0)=0

so cant divide

[limpid turret]

Oh because it won't allow 0, right.

[limpid turret]

I could not

[lean forge]

sorry np

[worn fox]

Then I would also be concerned about setting f = 1/y

[lean forge]

If A has a lower bound "m" we could just take f from $]- \infty;m[$ and perhaps find a countradiction

[ocean seal]

Azenx

[limpid turret]

Perhaps you can assume that y is not zero at some x, then you can prove that y would not be zero anywhere.

[lone heart]

@lean forge Has your question been resolved?

[lean forge]

I can't seem to find any answer that treats the case of the zeros of y, they just all assume y != 0 as a whole 😭

[lone heart]

@lean forge Has your question been resolved?

[limpid turret]

Here's a hint: If you assume $y\ne 0$ for some $x$, then you can solve the D.E. at that $x$. But it will lead to problems.

[ocean seal]

SWR

[lean forge]

I guess so

Dont you think there is a way to do it as I described ?

[lean forge]

Using this set is the hint they gave

[limpid turret]

Ah their hint was to show that that set doesn't have an upper bound?

Ah you know what, @lean forge? Their hint and my approach are practically the same.

Assume the set does have an upper bound. Then use my suggestion on the least upper bound to find a contradiction.

[lean forge]

ok ok

thx

.close

[lone heart]

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[signal marten]

am I doing it correctly?

I don't know how would I draw the graph, to see the signs of the function

[lone heart]

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[opal sphinx]

Why is this one wrong?

Did I miss something?

[lone heart]

@opal sphinx Has your question been resolved?

[opal sphinx]

.close

[lone heart]

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[void ledge]

I NEED HELP PLEASSEE I SAT HALF MY MOCK YTDAY HALF TODay someone pls go over it w me im in set 1 it was non calc i remember most questions

[proven leaf]

do you have a specific question?

[buoyant saddle]

ask

[void ledge]

Yes

They gave us volume

It was 125

And said find aurface area

[buoyant saddle]

of what

[proven leaf]

did it give you the shape?

that's not sufficient information to determine the SA

[void ledge]

Nah they didnt give us no shape

It said volume of a cubd

Or cuboid

Was 125cm cubed

[west ginkgo]

Then a=5

[proven leaf]

is 125 the volume of a cube?

[void ledge]

Yes

[west ginkgo]

SA=150

[lone heart]

As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.

[void ledge]

Ohh

I get it

[proven leaf]

but yes a volume of 125 implies that a side length is 5

[void ledge]

Cube root

[west ginkgo]

Yes

[void ledge]

5x5 and then x6

[proven leaf]

a side length of 5 implies that SA is 5^2*6

[west ginkgo]

Yes

[void ledge]

There was some wwird one

[proven leaf]

[void ledge]

Weird

They gave us a shape

Half of it was shaded

The outer part

A circle

2 circles

[proven leaf]

find the area?

[void ledge]

And the inside was 4cm outside was 2cm

Nah agree with someone that 2cm was half of 4

I kust skipped it

[proven leaf]

simply just take the area of the larger circle and subtract the area of the smaller circle

[void ledge]

There was one on surds

Surds

Surd with bracket

And a power

It was non calcukator asw

[proven leaf]

can you send an image of the question?

[void ledge]

Which

[west ginkgo]

The surd one and the circle one

[void ledge]

Ill try

Surd one was like

A surd

With a bracket

And a power at top right

Circle one i cant just forget that one

How do i solve

X squared + 12x +25 =0

[proven leaf]

[ax^2+bx+c=0\implies x_{1,2}=\frac{-b\pm\sqrt{b^2-4ac}}{2a}]

[ocean seal]

PajamaMamaLlama

[void ledge]

.

Bx?

Wtff is that

[proven leaf]

you have x^2+12x+25=0, correct?

[void ledge]

Yes

[proven leaf]

what's the number in front of the x?

[void ledge]

Which one

[proven leaf]

hang on

[\underbrace{1}{a}x^2+\underbrace{12}{b}x+\underbrace{25}_{c}=0]

[ocean seal]

PajamaMamaLlama

[proven leaf]

in your case, a=1 b=12 and c=25 for your quadratic

[void ledge]

Yh

[proven leaf]

to solve any quadratic simply plug the values of a,b,c into the formula

[void ledge]

It was non calc

[proven leaf]

you can do this without a calculator

what's 12^2?

[void ledge]

I24

24

[proven leaf]

12^2=12*12

[void ledge]

Why is it x2

[proven leaf]

12^2 is not 12*2

12^2 is saying multiply 12 by itself 2 times :)

[void ledge]

Oh

So 12x12

Is it xuz of the x2

When u add x squared by another x its squared?

So 12x + x squared is 12x12

[proven leaf]

not quite

[void ledge]

How

Then

[lone heart]

@void ledge Has your question been resolved?

[lone heart]

@void ledge Has your question been resolved?

[lone heart]

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[shut saddle]

From what I can remember you do the right hand side of the equation using the power of a power rule right

[shut saddle]

.close

[lone heart]

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[full nimbus]

Is it not -10+10i sqrt(3)?

[winter light]

,w calc 20 * exp(i6π/9)

[random scarab]

yes that's correct

[winter light]

,w calc -10 + 10i* sqrt(3)

[full nimbus]

what the flip

[ocean seal]

Results provided by WolframAlpha

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

Requested by zuanon.alberto

[full nimbus]

I needa go eat

[random scarab]

ur answer is right mate

[ocean seal]

Results provided by WolframAlpha

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

Requested by zuanon.alberto

[winter light]

Yep it's correct, I just messed up with Wolframalpha lol

[random scarab]

welp thats one way to prove it

honestly genius

[lone heart]

@full nimbus Has your question been resolved?

[lone heart]

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[full nimbus]

Alright lets think about this

[alpine geyser]

help me think..

[full nimbus]

they gave a function and you need to plug in the 2400 into either P(t) or t, which one would you choose based on context?

[alpine geyser]

t

[full nimbus]

are you sure?

[alpine geyser]

dude idk i thought p(t) was like p=600e^0.2 and t is t

[full nimbus]

p(t)=600e^0.2t

[alpine geyser]

how does plugging in 2400 in p(t) change the equation

[full nimbus]

well then you can solve for t and in the function, t is the amount of time and P(t) is the population size

you did read the question you posted right?

[alpine geyser]

okay so p isnt its own variable?

its not p for population n t for time?

is that not what the question is saying

NVM I UNDERSTAND

[full nimbus]

ok, what P(t) means is that if you plug in t into the function 600e^0.2t, then you will get P(t)

idk

just think of P(t) as the variable of the population

[alpine geyser]

is this just

multiplication

[full nimbus]

ummm, what are you multiplying?

[alpine geyser]

im j doing 600e^.2 x 2400?

[full nimbus]

you plug in 2400 for P(t), not t

[alpine geyser]

2400=600e^.2t?

[full nimbus]

yes

cus P(t) is the poplation size

and t is for the amount of time in years

[alpine geyser]

ohh

and its asking what the population will be in 2400yrs

waiy

when the population reaches 2400

im solving the yrs

[full nimbus]

The last sentence says, "After how many years will the population reach 2400?"

[full nimbus]

yes

[alpine geyser]

D

4=e^.2t

[full nimbus]

idk

[alpine geyser]

r u saying that bc u dont know or ur not telling me

[full nimbus]

yea, thats right

I didn't do it

but I just did it

[alpine geyser]

so i just divide both side by .2

[full nimbus]

yes

[alpine geyser]

awesome

thanks tony love you lots

[full nimbus]

make sure to close the channel when you finish

[alpine geyser]

how

[full nimbus]

just type ".close"

[alpine geyser]

is this j same thing going backwards

[full nimbus]

ummmmmmmmmm

ummmmm, so you want to find at the start, how much did you invest sooo

the time would be what?

[alpine geyser]

2000

[full nimbus]

this means that you started at year 2000, so that means you count 2000 as 0

and a year after like 2001 would count as 1

so you would plug in 0 for t and solve for A

[full nimbus]

hello?

[alpine geyser]

hi im doing the equatio n

isnt the 4600 the initial amount

n the ^.054t the exponential growth

[full nimbus]

yea

[alpine geyser]

i dont like my math teacher very much.

[full nimbus]

is it cus their black?

[alpine geyser]

so the answers just 4600??? what is the point of this question

hes fat n white

i dotn have a single black teacher this yr

[full nimbus]

ummm, cus the dude who was investing forgot how much he invested at the start

[alpine geyser]

a real businessman

okay thanks tony!

.close

[lone heart]

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[next osprey]

no idea

on how to go about it

[pallid scarab]

Express the left and right limits of f at -2 and at 6

[next osprey]

N=0?

Bc 6N=-2N

6N+2N=0

Then N=0?

Can I apply that logic to the first one?

Oh I can’t

[pallid scarab]

No

The right limit at -2 and the right limit at 6 have no reason to be correlated

However, the left and right limits at 6 for example...

[next osprey]

mm

so N= 7/6

no

6/7

[pallid scarab]

Yes N = 6/7

[next osprey]

ok i solved all the way

[pallid scarab]

Because the limit at 6 exists, the left and right limits have to be equal

[next osprey]

i got it right

yea

and -2 doesn't correlate since its a different x

[pallid scarab]

Exactly

[next osprey]

.close

[lone heart]

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[lone heart]

Please don't occupy multiple help channels.

[fleet kayak]

I have this now,
when Im multiplying the first set of numberx
(x)
Would i multiply with the negative number
-2(3x?
or just 2(3x

system of elimination

ag 1

[shrewd prism]

Not understanding the 2(3x

[shrewd prism]

You would multiply a full equation by -1

that would cancel out the y term yes

Nvm it depends on how you want to do it

[shrewd prism]

Both ways are fine as long as you add/subtract the equations correctly

[fleet kayak]

so like

-1 times 3x + 4y =6

or -1(3x+4y)=-1(6)

[shrewd prism]

Yes that keeps the equation equal

there are a lot of ways to eliminate variables in this equation but remember that you can add or subtract systems of equations to eliminate variables

You don’t need to do any manipulation in this problem to eliminate the y variable do you see how

[fleet kayak]

and i do the same for the bottom one?

[shrewd prism]

why do you want to do the same for the botto,?

[fleet kayak]

Not saying i wanted

I was just trynna know if I had too

[shrewd prism]

no

when you manipulate one equation you don't have to for the other

[lone heart]

@fleet kayak Has your question been resolved?

[shrewd prism]

@fleet kayak what do you need?

[fleet kayak]

so i did the equation and i got a deciam

decimal

[shrewd prism]

can i see how you did it

[fleet kayak]

-1(3x+4y) = -1(6)

-3x -4y =-6
than cross out the 4

and do -3x=-6

or do i not need to cross out the 4

[shrewd prism]

what do you mean by cross out the 4?

[fleet kayak]

i did something in a few lessons ago

where i just elimited that 4

[shrewd prism]

the 4y?

[fleet kayak]

in the same senario

[shrewd prism]

or the 4

[fleet kayak]

ues

4y

-4y

[shrewd prism]

ok that's called elimination which is one of the ways to solve systems of equations

[fleet kayak]

ye

[shrewd prism]

but you can't just "cross it out"

[fleet kayak]

What am i supposed to do with the equation

[shrewd prism]

-3x-4y = 6
-2x + 4y = 1

[fleet kayak]

the 4y and -4y cancel eachother out

so im left with 0

[shrewd prism]

YES but you need to add the equations together

[fleet kayak]

am i supposed to add the -3x and -2x

[fossil reef]

They dont cancel out, they are both seperate equations

[shrewd prism]

you need to add the equations together to cancel them out

so your result should be -5x=7

[fleet kayak]

so -5x =7

alr

thx

[shrewd prism]

and x = 7/-5

@fleet kayak I also want to show you

[fleet kayak]

alr

[shrewd prism]

instead of multiplying by -1

you can just subtract both equations

because you have 4y in both equations

subtract 1 from the other and you get 0 y

then you get the same result 5x = 7

just another way to look at it

[fleet kayak]

ok

thanks

wait

[fleet kayak]

this negative -6

so would it be -5x=-5

[shrewd prism]

uhhh

[fleet kayak]

@shrewd prism

[shrewd prism]

ur right i think

wait

but that shouldn't be right im slightly confused now

[fleet kayak]

i think u didnt see the negative'

-6+1 is -5

[shrewd prism]

yes ok I made a mistake in my calculation too lol

make sure you distribute the negative when you subtract equations 😅

[fleet kayak]

-3x -4y =-6
-2x +4y =1
gives -5x=5

[shrewd prism]

yes

x = -1

[fleet kayak]

i get a decimal

[shrewd prism]

???

[fleet kayak]

0.25 when i completey finish equation

[shrewd prism]

x = 5/-5

[fleet kayak]

I have to find what Y is

so i go

-2(-1) +4y-1

gives me 2+4y=-1

-2 both sides

4y=-1

[shrewd prism]

y = -0.25

nice

seems right

[fleet kayak]

Im just confusde cuz i dont get decimals in this typa stuff

and my teacher always says ur not supposed to get one

but thx

[shrewd prism]

@fleet kayak I would be worried if it was like .17539

[fleet kayak]

k

[shrewd prism]

but 1/4 is fine and it looks fine, if you want to double check, just plug the values in both equations

[fleet kayak]

alrighty

thanks

[lone heart]

@fleet kayak Has your question been resolved?

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[lone heart]

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[gritty marten]

I don't understand what the question wants me to solve for, and how to do it

[bitter viper]

hi

im not a helper but

i think u plug it in

like on the graph what is x=5

where is the apex of the line thing

[shrewd prism]

this is an aside but it's just asking which x value produces the biggest area right @bitter viper

[gritty marten]

ohhhhhh

[bitter viper]

idk

is this alg 2?

[shrewd prism]

no it's calculus

[gritty marten]

okay so then it'd just be x= 5

[bitter viper]

oh then idk what im doing

[shrewd prism]

wait isn't it 1

[gritty marten]

because total area (not displacement) would be largest from 0-5?

[shrewd prism]

below x=0 is negative area I believe

[gritty marten]

yeah, but I don't think it's referring to displacement though

[shrewd prism]

yeah i don't know too much so you are right

wait so x is on the bottom and it's bigger than 2

it is the same thing as 2 on bottom and x on top?

[gritty marten]

• integral bounding from 2 to x

negative*

[shrewd prism]

ok I am learning integrals next semster so I will understand soon 🤩

[gritty marten]

oh okay

I got a quiz tmrw and this is the only thing I don't know :(((

[shrewd prism]

i only know basics from what I have learned from watching instagram reels 🤩

sorry i'm kinda clogging this channel I will leave now for someone more experienced to do this

[gritty marten]

No its alr

<@&286206848099549185> Would x= 5 since its a negative integral, and the area bounded by the region is also negative so negative multiplied by negative would result in a positive answer?

or is my logic bs

[lone heart]

@gritty marten Has your question been resolved?

[open compass]

i think that works yes

you could also use ftc and find max value of -h(x) out of the options

[gritty marten]

thats what I'm supposed to do

and how would I do that?

[open compass]

you seem to have written down the part of the ftc that u need

[gritty marten]

yeah, but how do i numerically evaluate it?

[open compass]

so the derivative is just -h(x)

[open compass]

the actual value?

[gritty marten]

yeah

[open compass]

it doesnt ask for that

[gritty marten]

okay, so how would I get x= 5 from -h(x)?

[open compass]

i suppose you could approximate it with riemann sums

but you dont need that

[gritty marten]

We're only supposed to use the ftc

[open compass]

with derivatives, you would look for local maxima and compare the value with endpoints

[gritty marten]

mhm

[open compass]

what would that be in this case

if local maxima is when derivative changes sign from positive to negative

[gritty marten]

yes

[gritty marten]

but since I'm given h(x) directly, would I still use this? I don't think so

[open compass]

the derivative is just h(x) in this case

[gritty marten]

ohhk

[open compass]

so you can look for where h(x) changes from positive to negative

[gritty marten]

well technically at x= 2

[open compass]

yes

but by extreme value theorem global maxima can occur at endpoints

[gritty marten]

yes

[open compass]

x = 5 is one of such endpoints

[gritty marten]

ohhk so I'd just use that

ohk ohk that makes sense

[open compass]

by how the integral is defined, any x less than 2 will produce a negative value

[gritty marten]

so if I were to justify my answer, Id do it with the extreme value theorem, and not by saying "negative integral * negative sign = positive area"

[open compass]

and at x = 2 will be 0

[gritty marten]

mhm

[open compass]

and negative times negative will be positive, netting a positive area

and h is strictly nonpositive from 2 to 5

[gritty marten]

so, theoretically I can use both the EVT and the area explanation to justify my answer?

but the evt would be better to use

[open compass]

yes
it could also just be inspected graphically but

doing this is usually the case for these types of problems

with evt and finding local extrema

[gritty marten]

okay

thank you

.close

[lone heart]

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[atomic valley]

what is the least possible degree

[atomic valley]

will it be quadratic?

online it says quartic and idk y

[serene junco]

The minimum possible degree is the number of turning points, plus 1

A quadratic only turns around once

[atomic valley]

ohhh ok makes sense

thank you

[serene junco]

no problem 👍

[atomic valley]

.close

[lone heart]

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[frigid rapids]

I've made a matrix out of this and reduced it to

1 0 5 2
0 1 4 3
0 0 0 0

I think that means that B is a linear combination because the system is consistent and infinitely many solutions exists?

[sour verge]

So long as at least one solution exists, then it is a linear combination.

[frigid rapids]

okay thanks!

.close

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[empty mason]

Hi, I was wondering is there a way of finding all the factors to any polynomial over the set of complex numbers?

[empty mason]

Like for example, z^6+z^3+z^2+z+1

[alpine sable]

its irreducibile

the example

but sometimes it can be reducible

[empty mason]

Oh, may I ask how it is irreducible over complex numbers?

[alpine sable]

wait

hm

you are right mb

i just woke up

[empty mason]

oh no worries

[alpine sable]

you can use roots of unity for this

it is reducible

[empty mason]

yes, thats what i was thinking

but how would u apply it in the example

[alpine sable]

it can be grouped into two parts

z³ and z⁶ + z² + 1

[empty mason]

sorry, could u elaborate

[alpine sable]

you group the terms so you can factor out

[empty mason]

how would you group the example?

[alpine sable]

.

[empty mason]

how about the z

wait, im sorry, i dont get it

my example was z^6+z^3+z^2+z+1

[proud creek]

What is the full question?

@empty mason

[empty mason]

The question was is there a way of finding all complex roots of any polynomial

[proud creek]

Hmm

Does it lead to the above eq?

[empty mason]

i just gave the above equation as an example as to if u can find all the complex roots of it

[proud creek]

We have to use trail and error method to find a root for eq. more than power 2

and use that to simplify - This is the general one

If the poly. can be splitted into quadratic or cubic we can calulate its complex roots

using quadratic / cubic formula

what abt substitution a = z²?

@empty mason

[empty mason]

let me see

[proud creek]

NO it isnt

z^3 cant

brb

[empty mason]

oh ok

[empty mason]

hmmm

[empty mason]

i get that

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.close

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[clear ridge]

[phone] if any help needed call this number this my sir sandeeps he is good maths lecturer

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@grizzled garden Has your question been resolved?

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[solar mica]

Hey I just checked your derivatives
Check f_yy again

[solar mica]

Hmmm, I had a quick look
If D (=rt-s^2) = 0, then the test fails

So cannot say it's a saddle point either

Not necessarily
Remember it is local minimum as one of the answers, not global minimum
So it is perfectly fine for the function to reach a local minimum and then (at f(0,-1)) to drop even further

Not sure if this is correct procedure: "when it equals zero, we check by putting points from the neighbourhood"
But I havent done this stuff in years

The first derivatives at the origin are 0

The second derivative of x is 2

Second derivative of y is 0

Looks like a local minimum

Cos the slope is increasing yeah

But there is probably a more robust way to confirm it

You're welcome!

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[shy solar]

helpp

<@&286206848099549185>

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[lavish sedge]

what

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[strange bramble]

I just need help to make sure I'm on the right path. Find the area of the shaded region in the figure. Large outer rectangle is 2x + 5 by 8x. Smaller rectangle is x - 1 by 2x. If we let X be 3 what is the total area of the shaded region. I have 252

[shrewd prism]

What is the shaded region

[tough pilot]

I'd assume Big - Small

[shrewd prism]

Answer checks out

[tough pilot]

looks correct

[strange bramble]

Thank you!

.close

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[smoky berry]

Can somebody help me find the radius of the semicircle (midpoint M)
A=90⁰

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<@&286206848099549185>

[dense stratus]

<@&268886789983436800> I have seen this account troll on two help channels now. worth keeping an eye out for them

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[thick shard]

Hi, could someone help me with this question?

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Please don't occupy multiple help channels.

[thick shard]

I'm not really sure where to start with converting the z coordinate

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[thick shard]

<@&286206848099549185>

[foggy pecan]

look at this:

but my graph on my paper is not nice, so you must make it by yourself

[thick shard]

how did you come up with the limits of integration?

[foggy pecan]

certainly, evaluating the volume of cylinder is useless, usign sphericla, becasue we use cylyindrical ones

i draw it

look, forgve my eng, is not my native one, but

you need to draw a rectangle and see how the psi angle changes

the change line is diagonal

that is very artificial approach, suing spherical, i said, but i verified it , calculating the volume

and all is ok

[thick shard]

ok cool thanks

[foggy pecan]

yvw)

[thick shard]

.close

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[spiral haven]

hi i need help with this question, basically i tried using the order of operations and solver the () first and the result it gave me was -4 but it says its incorrect, the hint says i solved the () wrong, why is it?

[sour dove]

can you show your work and each step?

[spiral haven]

i dont know exactly if this is what you mean, but here is basically how i tried solving it