help-27

[devout snow]

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[restive river]

How do I solve part B?

Like I solved it correctly and it matches the answer key. But I checked the answer key after I got my equation constant things

Why am I putting c1 and c2 in terms of c3 and c4 be c5

Simplicity?

diffeq characteristic equations

[devout snow]

@restive river Has your question been resolved?

[devout snow]

@restive river Has your question been resolved?

[devout snow]

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[echo smelt]

how do you complete a square (standard form to vertex form)?

[echo smelt]

?

[flat ibex]

complteletinarawe the squrare it dumb

[echo smelt]

so how do i do it?

[dense badger]

I mean, do you understand the point of completing the square? Like, x^2 + 3x = 1 would be really easy to solve if the LHS were a square. So just make it one.

(x + 3/2)^2 gets you really close. You get x^2 + 3x + 9/4

So you just add/subtract whatever you need to make the constant term correct

[devout snow]

@echo smelt Has your question been resolved?

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[devout snow]

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[patent root]

I know how to solve without intervals, but how I do it with intervals?

[patent root]

Average rate of change

[cursive jacinth]

What happens to x in the interval [1, 3]?

[patent root]

I have no idea

[cursive jacinth]

It goes from x = 1 to x = 3 so what happens to x?

[patent root]

I see X is increasing

[cursive jacinth]

Yup

By how much?

[patent root]

from 1 to 3, 2

[cursive jacinth]

Exactly

And what happens to y during that interval?

[patent root]

The intervals for Y are also increasing

[cursive jacinth]

Are you sure?

[patent root]

My bad

No

[cursive jacinth]

What is the value of y at the start of the interval and at the end?

[patent root]

On the diagram, it went from 40 to 38

[cursive jacinth]

From 40 to 18 yeah

So did it increase or decrease?

[patent root]

decrease

[cursive jacinth]

By how much?

[patent root]

From 40 to 18, by 22

[cursive jacinth]

Okay

So we know x went +2 and y went -22 in the same interval right?

[patent root]

yeah

[cursive jacinth]

So how much did y decrease on average?

[patent root]

If I apply the formula for 40
and 18, I get ARC of -8.14

[cursive jacinth]

Well I don’t think you have to do that

You know y went -22 when x went up 2

So you need to know how much y went up/down for every x

How do you calculate that

[patent root]

I have no idea

[cursive jacinth]

If x goes up by 1 that’s only half of x going up by 2 right?

[patent root]

Yeah

[cursive jacinth]

So if y goes -22 for every 2x then for every x, y decreases by 22/2=11

[patent root]

Oh mah gad

That’s true

[cursive jacinth]

So to calculate the average increase/decrease in y you simply calculate (y2-y1)/(x2-x1)

[patent root]

slope formula?

[cursive jacinth]

In this case (18-40)/(3-1)

Yup

[patent root]

Why u chose 18 and not other any number?

Like 40 and 18

[cursive jacinth]

Because those are the numbers corresponding with x = 3 and x = 1

[patent root]

Wait

How?

Im sorry for asking many questions

Ohhh

Now I see it

tysm bro

.close

[devout snow]

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[red quartz]

I don’t even get what it’s asking

[cursive jacinth]

The formula to calculate a sphere is 4/3 * pi * r^3

[red quartz]

Yea

[cursive jacinth]

So r^3 = 4

[red quartz]

?

How

Oh

We pretend it’s 1 right?

[cursive jacinth]

Yeah sure

[red quartz]

,, 4/3pie(r)^3

,, 4/3pie(r)^3=4

[woven radish]

puckmyseen

[red quartz]

Right?

[cursive jacinth]

Well if r is normally 1 then we can say r^3 = 4 if we want the sphere to be 4x as large volume wise

So then r is 4^(1/3)

[red quartz]

Mmm ok

[supple knot]

pi, not pie

[red quartz]

Ok

[cursive jacinth]

Only thing though it says 4 times bigger rather than 4 times as big

[red quartz]

Since we’re only talking about radius

I just did

,, r^3=4

[woven radish]

puckmyseen

[red quartz]

And cubed each side

To equal 1.587

[cursive jacinth]

You’d think it would be r^3 = 5 though if it says 4x bigger rather than 4x as big but maybe that’s a mistake

[red quartz]

Yea

Well 4 x 1 Im assuming

But yea thank yoy

.close

[devout snow]

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[keen schooner]

Let f(x) = a(x-3)^2 +5, given that f(5) = -19 find the value of A. Hence, find the y-intercept of the curve of f(x)

[restive river]

what have you tried

[keen schooner]

some weird stuff

lemme send ss

[restive river]

rewrite $f(5)$

[woven radish]

kyou

[keen schooner]

like im not sure what its asking me

tbh

[supple knot]

,rccw

[supple knot]

you wrote y=-19 but put -19 for x here

[keen schooner]

how would i write it instead

[devout snow]

@keen schooner Has your question been resolved?

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[keen schooner]

An open-top box has a square base where the height is 4 inches longer than the length of the base and the surface area of the box is 23 in^2

A. Show that the total surface area is given by A=5x^2 +16x

[keen schooner]

B. Find dimensions of the box

Im not sure where to start

.close

[devout snow]

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[devout snow]

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[restive river]

How many 4-letter words can be created by using the letters of the word "FREEZING"?

[fierce heath]

do they have to be actual english words

or can they be jumbles of letters such ad ZGRF

[devout snow]

@restive river Has your question been resolved?

[devout snow]

@restive river Has your question been resolved?

[rigid sandal]

hey mate, don't know if you remember that you haven't closed this room. Has ur question been answered?

[devout snow]

@restive river Has your question been resolved?

[restive river]

not closing till the question is answered

How many 4-letter words can be created by using the letters of the word "FREEZING"?

[rigid sandal]

ok

is it actual words

or letter combinations

[devout snow]

@restive river Has your question been resolved?

[restive river]

How many 4-letter letter combinations can be created by using the letters of the word "FREEZING"?

[sour swallow]

repetitions allowed ?

if yes: there are 7 letters, so it's 7^4.

If no, it's 7 choose 4.

[restive river]

How many 4-letter letter combinations can be created by using the letters of the word "FREEZING" if repetitions are not allowed?

[worn adder]

anybody can help me with this

[weary hatch]

Need help with number one, I started with equation 3(1/x)+2(1/x+4)=1 and got different answer

[devout snow]

@restive river Has your question been resolved?

[twin stream]

i would like some help

[echo smelt]

try and put it in y=mx+b format m is your slope b is the y intercept

[worn adder]

thx

[echo smelt]

np

[devout snow]

@restive river Has your question been resolved?

[wooden wraith]

Holy guacamole, how many people can try to hijack the same help thread

@restive river It's not exactly clear what you're asking. You're saying combinations now, but that means something specific, and judging by your use of the word "words" at the beginning, I'm pretty sure it's not actually what you want

Also, when you said no repeats are allowed, I'm assuming you still want to allow for 2 E's since there are 2 E's in the word FREEZING

I believe you're looking for the number of unique permutations of the letters in FREEZING

That is, allowing for no more than 2 E's and no more than one of any other letter.

Is that right?

For example, REEZ and ZEER would be two of the permutations we want to count, but ZEEZ is not, correct?

[devout snow]

@restive river Has your question been resolved?

[restive river]

How many 4-letter letter combinations can be created by using the letters of the word "FREEZING" if repetitions are not allowed?

[fallen swallow]

I guess 8C4?

[wooden wraith]

You keep repeating the same ambiguous question. Read what I wrote and please clarify.

? I was responding to the person who claimed the channel

[fallen swallow]

Lol, gotta wear some sunglasses

[somber elbow]

Hey guys

[restive river]

Hello

[wanton storm]

hello, can someone help me with this?

[brazen star]

#❓how-to-get-help

[grim turret]

have you solved it yet

[fierce jewel]

I don’t understand how to solve this question

[deep cove]

Hint: $$(a - b)^2 = (a + b)^2 - 4(ab)$$

[woven radish]

jimmy1234

[worthy harbor]

@fierce jewel try using the quadratic formula and setting the difference of the positive solution and negative solution to 11

[restive river]

since x^2 has a leading number of 1 you wont need to do any crossovers

the sum of the roots gives the middle number

x's leading number is 1 so sum of the roots equal to 1

for ax^2+bx+c, if c/a(multiplication of roots)<0, one of the roots is (+), other one is (-)

6-(-5) will 11 so one of the roots is 6 and the other one is -5

so the c/a should be -30

2k/1=-30

k=-15

[mortal gazelle]

Hello

I need help

Cuz I’m a dumbass

And I can’t do math

Plz help

Anybody

[lunar harbor]

#❓how-to-get-help, don't post for help in someone else's help channel.

[brazen star]

Don't just keep the channel open without clarifying what the requirements are.

tatpoj has asked about the question but you kept repeating the same ambiguous question.

[restive river]

If you can't answer my question then just STFU.

Wise Men Speak Because They Have Something To Say; Fools Because They Have To Say Something

[wooden wraith]

My guy. I tried to answer your question, but you refused to clarify what it is you were asking.

[marsh dagger]

bro u are asking a question give some manners

and four letter words can be meaningful words or gibberish

if you cant state your requirements no one here can help you

[restive river]

hello

[lone hollow]

could I get help with this stats question?

It says to use Theorem 7 6 which is this

[brazen star]

The answer depends on the requirements bro, and don't just insult people asking you to clarify the question.

Insults are the arguments employed by those who are in the wrong.
• Jean-Jacques Rousseau

[lone hollow]

<@&286206848099549185>

[brazen star]

this channel is taken bro

#❓how-to-get-help

[lone hollow]

Mb thought wad empty

[marsh dagger]

im closing this channel

no ones asking question and its dead

.close

.close

,close

great i cant close this

.close

[grim agate]

u need to be helper/helpful

[brazen star]

yeah

like me 😄

[grim agate]

or help

[brazen star]

:/

[marsh dagger]

smh

[marsh dagger]

i was helper

i couldnt stand 90 pings pr day so

[grim agate]

[marsh dagger]

lmao

i dont have that much spare time

so helper pls close <3

[grim agate]

my alt gets around 4k pings per month

@lean matrix

[marsh dagger]

how do you get very active

smg

[brazen star]

You need to be active in the advanced math section if I'm not wrong

[marsh dagger]

sad

i suck ass in mathematics

[brazen star]

same

[marsh dagger]

i mean i self learn all my mathematics soo

[prime egret]

Sorry bro it was a misinput

[brazen star]

wdym

[marsh dagger]

learning abs alg and mv calc rn

[brazen star]

oh the ping earlier?

all good

[marsh dagger]

which is burning my brain btw

welp mathematics thats actually hard takes time to swallow

[grim agate]

self learning math

[prime egret]

Yes it was a misinput I did it for my family

[grim agate]

based

uh

what was that

[brazen star]

wait what

oh this year

good

you are underaged

[grim agate]

[brazen star]

yes

[grim agate]

i c

[brazen star]

no

i mean yes not for discord tos

[grim agate]

ur account is from 2019

[brazen star]

im 15 and still procrastinating calc 😄

[grim agate]

okay maybe not hav this discussion

[marsh dagger]

yes

[brazen star]

yeah

[marsh dagger]

close pls

[prime egret]

Why

[grim agate]

no

[marsh dagger]

welp

[marsh dagger]

^

for anyone that wants to answer the question

(warning: op extremely unfriendly)

[meager wigeon]

helping my cus out with homework and idk myself can someone help

help her and me guys it's due in 7 minutes

[prime egret]

2 mins too late …

[mint sequoia]

do you still need help?

[upbeat dock]

Hello I want to do this step by step

I’ll start with number 1

A)20 m/s

Can someone check that one

[junior cloak]

@restive river words or strings of 4 letters

isnt it just like 8 choose 4 divided by 2 to account for the repeated e

[grim agate]

@ yes ig

[arctic field]

@

[grim agate]

i mean they requested ¯_(ツ)_/¯

[wooden wraith]

So, this channel has been open for four days. The OP is clearly not interested in getting their question answered, as they have repeatedly refused to clarify their question when asked, and been hostile toward people who have tried to help. Is there a mod who could comment on whether or not it's appropriate to close this channel?

[hazy yarrow]

.close

[devout snow]

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[devout snow]

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[steel oxide]

Can someone explain the red part?

[steel oxide]

Context is attitude determination and normalizing a quternion estimate from the algorithm causes a ill-condtioning of the Pqq matrix but I have no clue about the biased covariance part nor why the hell they do:

$q^T P_{qq} q$

[woven radish]

Hamza

[steel oxide]

to the found pqq matrix.

This might be niche so any help is welcome.

[devout snow]

@steel oxide Has your question been resolved?

[devout snow]

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[elfin orchid]

that's very hard to read. cannot you write it clearer ?

not to mention i don't speak spanish

[crystal dew]

.close

[devout snow]

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[vernal anvil]

how do i solve

[neon folio]

Do you know the formula for the volume and surface area?

[vernal anvil]

yes i ended up figuring it out

had to draw a relation for LW from volume and surface area

ty though

.close

[devout snow]

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[grand cosmos]

I have so far
Let s = num single tickets sold
Let c = couple tickets sold
s + c = 144

[grand cosmos]

not sure where to go now

[unreal thunder]

@grand cosmos

[grand cosmos]

Yes

[unreal thunder]

Let's think it as an actual problem

alright. You are the cashier and you have 1098 dollars in hand

so finding how many couple tickets were sold is a natural question

as you know one couple ticket is 15 dollars, your instinct will make you take each 15 dollars out from 1098 and place it each.

and surely counting each of those 15 is same as finding how people brought couples tickets from 1098

@grand cosmos are you following ?

[grand cosmos]

Yea

[unreal thunder]

so taking each 15 dollars out from 1098 and place it each then counting the number of 15s is same as 1098/15

[grand cosmos]

Okay

[unreal thunder]

because 1098/15 technically asks what multiple of 15 is 1098

or how many ways can you place 15 in groups so that you get 1098

so 1098/15 =73.5

since we don't care about the remainder we can take the integer part 73

[grand cosmos]

Ok

[unreal thunder]

1098/15 = 73.5, which means there are 73 groups of 15 presents and some remainder left ungrouped

so which means 73 coupled tickets sold.

so naturally if 144 people attended. 144-73=71 tickets are single

[grand cosmos]

Ok

How do we get the system from that?

[unreal thunder]

system ?

single you mean?

There are only two possibility to get the money, from singles and couples

we counted all the possibilities of couple tickets

so the rest of the total must be the difference

[grand cosmos]

Oh

Wait so now I’m confused

What’s the next step

[devout snow]

@grand cosmos Has your question been resolved?

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[restive river]

Hi guys why to do the Row reductiom, they do A1<->A4?

[restive river]

I mean, my opinion was that the correct transformation T1 was a2<->a1

Like here

[raw granite]

I think it's just a style difference. You want the first column to end up with a 1 in the top left with 0s elsewhere. However you get there is fine.

[restive river]

Ok thank you, but the result Is different

Let see picture

This online solver gives my solution

[raw granite]

The matrices will be different along the way, yes. But the value of row reduction is that everything is reversable and doesn't change the matrix rank.

Both ways are valid, and give rank = 4. (Assuming rango means rank.) There can be different reduced triangular forms. There isnt a canonical anwer for the triangular answer.

[restive river]

Oh ok Joe thank you very much.
I didn't know about this.

[restive river]

Yes rango Is the italian Word for rank

.close

[devout snow]

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[devout snow]

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Remember:
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• Show your work, and if possible, explain where you are stuck.
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Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[restive river]

help

[midnight dirge]

i think these 2 are equal

[restive river]

yes

[midnight dirge]

so u can form an equ with 2 vars

[restive river]

lets name those double tagged a and tagged with one b

so 2 a + 2 b = 180

[midnight dirge]

using the angles on the blue line

and green triangle

form equations and u shld b able to solve the angles

[restive river]

3 a + 1 b = 150

[midnight dirge]

yes

[restive river]

then

[midnight dirge]

yes

[restive river]

a + b = 90

so

[midnight dirge]

mhm

[restive river]

2a = 60

[midnight dirge]

yes

[restive river]

a = 30 ?

[midnight dirge]

yep

[restive river]

then x is 60 ?

[midnight dirge]

i think u can do it from here

yep

[restive river]

;-;

ok

ty

[midnight dirge]

nice

fast

haha

[restive river]

yup

[midnight dirge]

np

💕

[restive river]

.close

[devout snow]

Channel closed

Closed by @undone perch

Use .reopen if this was a mistake.

[restive river]

❤️

[devout snow]

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

[devout snow]

@distant herald Has your question been resolved?

[distant herald]

no

[devout snow]

@distant herald Has your question been resolved?

[devout snow]

@distant herald Has your question been resolved?

[devout snow]

@distant herald Has your question been resolved?

[mild zenith]

.close

[devout snow]

Channel closed

Closed by @mild zenith

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[mild zenith]

Due to inactiveness.

[devout snow]

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[nocturne horizon]

So I am trying to solve this integration by partial fractions and I am not sure if I have set up the system of equations right

[patent tartan]

All except purple seem right

there should be a 9A term

[nocturne horizon]

oh i left out the 9A

[nocturne horizon]

alright i see it now thank you

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[restive river]

Hi there, so at question 3.1 should I use the conjugate of the root?

[round abyss]

Hello!

@everyone

[patent tartan]

@restive river In exponential form, if you take the conjugate, the exponent picks up a minus sign

[round abyss]

i dont get how to do this question

[random temple]

use negative arg

[patent tartan]

$z = re^{i \theta} \implies z^* = re^{-i \theta}$

[woven radish]

nvx

[restive river]

I was actually referring to question 3.2

[patent tartan]

lol

[restive river]

Bu thanks nvx, that was going to be my next question

Any luck?

[patent tartan]

Yes the conjugate would be the third root

assuming that a, b, c, d are all real

[restive river]

So how would you go about solving this nvx?

[patent tartan]

You can write it as a product of linear factors (corresponding to the roots)
\begin{align*}
f(x) &= ax^3 + bx^2 + cx + d \
&= (x+3)(x + 1 - \sqrt{6} i)(x + 1 + \sqrt{6} i)
\end{align*}

[woven radish]

nvx

[patent tartan]

If you multiply this out you can compare the coefficients to find a, b, c, d

[restive river]

So a=1

B=5

C=13

D=21

Or what do you think?

[patent tartan]

👍

[restive river]

Thanks so much

So then for 3.3.1 it just becomes -3pi/4 ?

[patent tartan]

yes

[restive river]

Cool , then 3.3.2 I’m a bit lost, what do you think is the best way to approach the sum

[patent tartan]

"Write down z in polar form"?

[restive river]

Jip

[patent tartan]

Polar form you mean z = a(cos(...) + isin(...)?

or as a tuple (r, theta)

[restive river]

A(cos( etc.

[patent tartan]

know about eulers formula?

[restive river]

E^ix=

[patent tartan]

apply that to $e^{\frac{3 \pi}{4} i}$

[woven radish]

nvx

[restive river]

So then the 3pi/4 replaces the x

In the formula

[patent tartan]

yes

[restive river]

So then -sqrt(2)/2+isqrt(2)/2

[patent tartan]

in polar form you usually keep the sin & cos

[restive river]

So then cos(3pi/4) and so forth?

[patent tartan]

ye

[restive river]

Cool thanks for your help so far nvx, you’re a lifesaver

[patent tartan]

np, you manage 3.3.3?

[restive river]

No I don’t really understand the Moivre theorem very well

[patent tartan]

do you know the formula?

[restive river]

Not even

Is it that r(cos) thing

[patent tartan]

well you should know it if they ask you that in the problem set

[restive river]

Probably why I should focus more in class😅

Btw if you plug in 1 in that answer of 3.2 does it give -80?

[patent tartan]

3.3.2?

ah

,w x^3 + 5x^2 + 13x + 21 where x=1

[woven radish]

Results provided by WolframAlpha

Click here to refine your query online
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Requested by Navix#0001

[patent tartan]

My bad. This should actually be
\begin{align*}
f(x) &= ax^3 + bx^2 + cx + d \
&= a(x+3)(x + 1 - \sqrt{6} i)(x + 1 + \sqrt{6} i)
\end{align*}

[woven radish]

nvx

[patent tartan]

note the factor "a" in front of everything

[restive river]

A okay thanks

So back to3.3.3😅

Just ignore the calculation error at the end, would this also work

<@&286206848099549185>

Everything fine nvx

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[velvet olive]

The radius r of a sphere is increasing at a rate of 3 inches per minute. Keep "pi" in your answer.
(a) Find the rate of change of the volume when r = 12 inches.
in.3/min

(b) Find the rate of change of the volume when r = 34 inches.
in.3/min

[velvet olive]

i missed this lesson in class i was wondering if anyone could help explain this to me

[supple knot]

The lesson is related rates

[velvet olive]

ok yeah i jsut found a couple vids with the dx/dt

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[wooden wraith]

If f(x) is a cubic function and m is some slope, then you're looking for where f'(x) = m

Although there will be more than one solution

[clever wadi]

ah ok

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[white nest]

can someone explain how i go from the first step to the soln.s

[white nest]

how is u/v = to those specific numbers

[craggy anchor]

the scalar projection of u on v is zero, therefore they are perpendicular

one of them is arbitrary, but the other is based on that

[white nest]

i dont understand

why is u = (0-1--2)

[craggy anchor]

Is vector n defined?

[white nest]

yes

[craggy anchor]

what is it defined as?

[white nest]

3,-2,-1

i understand until the last part

i dont know how they get the answers in the example

[craggy anchor]

They're trying to find alternate planes that fit n dot x = 0, but instead of x, they're using the planes u and v

The goal is to find parallel planes, so they've defined 'some plane' u and v, which must be normal to n in order to be parallel to x

From there, they've found two vectors which fit that condition, using the general form logic from the previous part

[white nest]

the goal is to find the vector form equation

my qestion shouldve been worded better

i was wondering are u and v given

or do we have to solve for them

somehow

because it says for example then lists values for u and v

[craggy anchor]

It found two examples that they solved for u and v

[craggy anchor]

You wouldn't be given u and v, you would have to solve for them

[white nest]

can you explain one last time how i solve for u and v

[craggy anchor]

So we know that whatever values of u (lets say ai+bj+ck) dot n has to equal zero

[white nest]

yes

[craggy anchor]

So 3a-2b-c=0

[white nest]

ye

[craggy anchor]

Since you're only trying to find a parallel plane and not a specific parallel plane, you can choose any values for a and b (in this case, they chose 0 and 1) and then solve for the final value c

It would be a slightly different process if they, for instance, gave you a specific co-ordinate the plane had to go through

But since it just asks you to give a parallel plane, you can choose any two values for a and b

(as long as they're not the same as x)

[white nest]

why am i allowed to choose any two points for a and b

and not c

[craggy anchor]

Well, you could choose two numbers of a and c or b and c

[white nest]

oh

[craggy anchor]

The point is, there is a relationship between a, b and c

[white nest]

were not given x in this example, how am i supposed to know its not the same as x

[craggy anchor]

Just guess

If you're not given it

Just assume they're not the same

[white nest]

i would prolly choose small number like 1,1 since theyre small

[craggy anchor]

That's the smart thing to do

Never make more work for yourself

[white nest]

alright well thank you for you help!

[craggy anchor]

You're welcome!

[white nest]

.close

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[molten trellis]

Hi

[molten trellis]

Can you express theta

I need representation of theta by the other variables l, g, x, y

This is what i tried to do

And in the end i got this 4rth order polynomial

Which i can not solve

I used the universal substitusion for sin and cos

Where i express sin(theta) and cos(theta) by tan(theta/2)

Sorry for my bad english

Also

Ignore the dots on top of x and y

Thats because they mean velocity

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@molten trellis Has your question been resolved?

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[amber mural]

why this wrong

[long kettle]

Show your work

[amber mural]

how i find pattern 4x - 16x^2/2! + 128x^3/3!

4, -16, 128

f^0(x) = ln(1+4x) 0

f^1(x) = 4/(1+4x) = 4

f^2(x) = -16/(1+4x)^2 = -16

i got sequence but i dont know pattern

[supple knot]

look up the taylor series for log(1+x)

[amber mural]

alr

i guess its something i got to memorize

i got it

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[cursive jacinth]

Why does lim(h->0): (sqrt(h+3) - (sqrt3))/h result in sqrt(3)/6?

[supple knot]

multiply the top and bottom by the radical conjugate

[cursive jacinth]

What does that get you?

[devout snow]

@cursive jacinth Has your question been resolved?

[supple knot]

do the algebra and lets you take the limit

[devout snow]

@cursive jacinth Has your question been resolved?

[cursive jacinth]

If someone could show the step by step math that’d be great

[supple knot]

it's against the rules to give answers. try it yourself first then show your work here if you get stuck

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[cursive jacinth]

Who cares lol I already know the answers since I literally gave them…

[supple knot]

answers include full work

[opal scroll]

reopens thread 2 hours later to say you never needed help in the first place

Bro can someone help me prove sqrt(2) is irrational???

[cursive jacinth]

No that’s not what I said 😅

[opal scroll]

Just give me the steps. I don't need to be walked through the proof since I already know all the steps

Assume sqrt(2)=m/n where gcd(m,n)=1. Then rearrange to get 2n^2 = m^2 but this contradicts unique factorization

So yeah anyways please help????

[opal scroll]

Look

There are two possible things you could have been saying there

And both are stupid

[cursive jacinth]

Well I need answers so if you don’t wanna give them you don’t have to respond 😁

[opal scroll]

I'm choosing to interpret you as having meant the funnier one

[supple knot]

if you don't want to be told to not break rules, don't break rules

it's that simple

[cursive jacinth]

Rules 😂 There’s no need for rules lol it’s literally a one on one conversation lmao

[opal scroll]

😂

[cursive jacinth]

Anyway I’ve been noticing before that you’re an insufferable person to other people too so I’m gonna block you now have a nice day

[supple knot]

you must be new to the internet if you think this is a 1 on 1 conversation

[opal scroll]

joins math server and clicks through server rules
asks question in help channel
server member volunteers their time to help you out for free
instead of accepting their help, break server rules by asking for the answer without putting in any work yourself
get told you're breaking the rules and leave the convo
come back 2 hours later to state that you don't understand how math problems work and then accuse the person or bring insufferable

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[exotic violet]

help

[exotic violet]

sorry grace

[faint valve]

ur good haha

[exotic violet]

.close

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[tough cedar]

How do I find the Oblique Asymptotes for number 4?

[topaz beacon]

Look at this highest degree of each

Since x^2 is one more degree than 2x, you then look at the coefficients

1/2 is the slope

[tough cedar]

so 1/2

[topaz beacon]

Yeah

[tough cedar]

and rise is 1 and the run is 2?

but when i graph is on desmos it doesnt look accurate

[topaz beacon]

Hmm can you show me?

[topaz beacon]

Zoom out

[topaz beacon]

It checks out

[tough cedar]

the answer should be

y=1/2x + 1/2

it doesnt overlap the slope

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[supple knot]

https://www.cuemath.com/measurement/surface-area-of-cylinder/

[cedar kite]

areas of two circles plus the rectangle that wraps around the side

[cedar kite]

you got it, good luck!

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[carmine hemlock]

How can there be 14 people in the team if the total of this adds up to 16? The question wants me to put this data into a Venn diagram

[carmine hemlock]

I remember that part just forgot how to work it out, would this be correct? Maybe I need to rewatch the lecture

Thats what I had initially but then I'm not too sure how I'd get how many did both

I'll try just rewatch the lecture, they're all prerecorded

Only issue is that it's filled with alot of stuff I already know, just this that I cant wrap my head around

Just remembering the formula to get how many did both

yeah

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[hybrid snow]

You didn't even answer the question

You just gave out slopes or b values

You didn't do what was asked

"Write an equation for each line in Slope-Intercept form"

Check some of your slopes

Do they make sense

Like 17

Is the slope positive or negative

Or rather, should the slope be positive or negative?

So in your equation, why is the slope negative

Check your answers

Which is correct for number 17

Fix 18, 20, 21 and 22

Make sure that your answers make sense

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[dense crane]

https://media.discordapp.net/attachments/903430333888884736/1037203118674419772/701043425029652550.png

[dense crane]

https://media.discordapp.net/attachments/903430333888884736/1037202914931912704/rn_image_picker_lib_temp_944b843c-0605-4228-90ee-68b8ded49f7c.jpg

guys any idea how to solve the first question?

i have some idea on how to solve this, just one question that do i need to use subgroup test of group theory on it or this is not a question based specifically on fields and groups ?

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[pallid silo]

1. a line tangent to the graph at x=2 means it has the same gradient

so find the gradient of the linear line by finding the gradient of the function at that point

Now to get the full line equation you need to find c (y=mx+c)

your missing one variable, c.
So you only need to sub in one point. Can you find one coordinate the line passes through?

[flat ibex]

what is a gradient

dont listen to him

[pallid silo]

what do you want?

[flat ibex]

he trippin

[pallid silo]

Did i do something wrong?

[flat ibex]

slope of -5 at 2,3

answer is b

[flat ibex]

maybe? you might be right but idk anything ur saying and it seems more complicated than it should be

[flat ibex]

its literally just this theres absolutely nothing else to it

[pallid silo]

i was finding the full equation. But you can get the answer from just the gradient cause its multi choice. So your way is quicker i guess

[flat ibex]

whats a gradient

[pallid silo]

yeah why not

[flat ibex]

my way has nothing to do with multiple choice

[pallid silo]

maybe you guys call it something different. Gradient is the slope.

[flat ibex]

it tells you the gradient tho

[flat ibex]

its given

f'(2) = -5

[pallid silo]

Dw about it Vc05, im pretty sure we're on the same side lol

yeah

1. a line tangent to the graph at x=2 means it has the same gradient

lol

[flat ibex]

ok but this is unecessary

[pallid silo]

yeah i realised

[flat ibex]

y-y1 = m(x-x1)

[flat ibex]

no i didnt use process of elimination

[flat ibex]

i used this

do you know how to derive this

[pallid silo]

same method

[flat ibex]

or this

[flat ibex]

same question actually is it not

[pallid silo]

yeah dw about it. I never said you used process of elimination. Its all good.

[flat ibex]

no it has nothing to do with multiple choice

[pallid silo]

yeah i know

[flat ibex]

in any context this way is fastest

[pallid silo]

yeah i said it was faster

dont worry about it

find gradient (or slope) at x=1 for the curve. That'll give you m. Then find c (vertical translation) by subbing in the points (1,f(1)) and solving.
You should get the full equation y=mx+c

[flat ibex]

what country are you from

[pallid silo]

Australia

why?

[flat ibex]

because you use mx + c instead of mx + b lol

[pallid silo]

ohh

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[white nest]

can someone help me where vector n [0,6,0] comes from

i guess i will just assume the guy who made the soln. made a mistake

...

oh ok

.close

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[uncut crow]

can anyone explain what the hint for b is getting at?

[uncut crow]

the thing in [ ]

I might be able to do what it says but how is it going to help 🥺

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.close

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[finite palm]

can anyone help with my brothers question?

[rotund heron]

Has he tried anything?

[finite palm]

nope

i got my answers though i just want to make sure cries

[rotund heron]

Okay, what are your answers?

[rotund heron]

I read “I got my answers though I just want to make sure he cries”

[finite palm]

1.) x + 2y = 3

kind of system - consistent dependent
type of graph form - intersecting
number of solutions - 1

2.) x - y = -3

kind of system - consistent dependent
type of graph form - intersecting (not sure)
number of solutions - 1 (not sure)

3.) 4x-y = -1

kind of system - consistent dependent
type of graph form - coincide (not sure)
number of solutions - infinite

[finite palm]

srry english isnt my first lang so my grammar is a bit yk

[finite palm]

here is my answer btw

[rotund heron]

that’s not correct

[finite palm]

op that sucks

is it the solution and type of graph?

[rotund heron]

And the consistency too

Wait

I’ll refer you to some resource

Let me find

Given equations $a_{1}x+b_{1}y+ c_{1}0$ and a_{2}x+b_2{y}+c_2=0$

[woven radish]

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

[rotund heron]

If there solution exists, it is a consistent system

If not then it is inconsistent

[finite palm]

When lines intersect, there is one solution and the system is consistent independent. When the lines coincide, there are infinite solutions and the system is consistent dependent. When the lines are parallel, there is no solution and the system is inconsistent.

this is the only thing i remember in grade 4 💀

[rotund heron]

Yes

[finite palm]

so i was basically right on my first answers

why did i change it

[rotund heron]

Third one is inconsistent

[finite palm]

yupp

[rotund heron]

…

[rotund heron]

You wrote consistent

[finite palm]

yes since i changed my answers

bc they were intersecting when i graphed them

basically all typed was wrong, right?

1.) x + 2y = 3

kind of system - consistent dependent
type of graph form - coincide
number of solutions - infinite

2.) x - y = -3

kind of system - consistent independent
type of graph form - intersect
number of solutions - 1

3.) 4x-y = -1

kind of system - inconsistent
type of graph form - parallel
number of solutions - none

this was my first answers

[finite palm]

I assume this is right?

[finite palm]

i meant this

[finite palm]

<@&286206848099549185>

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[ebon nova]

hi

[ebon nova]

28 -> 9 52 -> 15 84 -> 23 20 -> 7 100 -> ?

What number should replace the question mark

ive tried to find patterns so far

Bengo this channel is occupied

Please don't post here

Use a free channel

28 -> 9 52 -> 15 84 -> 23 20 -> 7 100 -> ?

[craggy vessel]

Oh sry

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[stable lantern]

In this problem I'm asked to find the angle theta so that the swimmer doesn't collide with the rock. The height h is 20 meters and |v_0| is 4m/s

[stable lantern]

what I thought of was that theta has to be in [0, pi/2]

so then I can use the formula to find out the distance on the x axis, x=-2|v_0|cos(theta)sin(theta)/g

and check when it's 0<=x<2 or x>8

I can't solve this system of inequalities though

[devout snow]

@stable lantern Has your question been resolved?

[stable lantern]

The one answer I get is theta = 2πn

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[thorny pawn]

How to do this?

[pseudo basin]

this is the integral of x^p dx, where p = 1 - 1/2 + 1/3 - 1/4 + 1/5 - 1/6 + ...

do you understand this?

[thorny pawn]

Yes

[pseudo basin]

is this enough info for you to solve the problem?

[thorny pawn]

Yes I think so it’s a telescoping sum right?

[pseudo basin]

no

[pastel pasture]

Do you know how to sum an infinite harmonic progression

[thorny pawn]

But doesn’t it diverge

[long kettle]

The harmonic series does, but the alternating harmonic series doesn't

[thorny pawn]

Idk how to sum it

Oh is it just ln(2)?

Taylor series

Kk cool Ty everyone

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[tight estuary]

I need help visualizing, this

[tight estuary]

what happened to the cos and sin in the numerator?

did the sin turn into a cos?
or did something else happen?

[random temple]

where is sin

in numerators

[celest tide]

express cot^2 = cos^2/sin^2 and open the bracket

[tight estuary]

my bad , i mean csc

[tight estuary]

i get what you mean but where would i place that in the equation?

[celest tide]

exactly where it already is

[tight estuary]

So like this,

[celest tide]

you missed a (-); but yea

[tight estuary]

k thank you for the lead

when we multiply do we turn the sin^2 back into 1-cos^2?

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[lucid oracle]

This is more of a simple algebra question than a physics one so thats why im posting this here. idk how they got from one step to the other, marked in yellow. Could someone clarify pls

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[lucid oracle]

<@&286206848099549185>

[supple knot]

taylor series expansion of $\frac{1}{1-x}$

[woven radish]

riemann

[lucid oracle]

Ahh thanks!

[lucid oracle]

My teacher told me to use newtons binomial, is that the same as the taylor expansion in this case?

[supple knot]

in this case yes

[lucid oracle]

how would i go about that

[supple knot]

binomial expansion of $(1-x)^{-1}$ is the same as the taylor expansions around 0

[woven radish]

riemann

[supple knot]

use the binomial formula?

[lucid oracle]

ohh but its an expansion of (1-x)^-2

Didnt know the formula worked ith negative

stime to refresh my calculus

thanks!

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[supple knot]

that's this step

[supple knot]

.close

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[lucid oracle]

.reopen

Oops

[lucid oracle]

i did my expansion for (1+h/R)^-2 instead of (1+h/R)^2 and ive almost got the right answer. I get g (1-2h/R-3h^2/R^2) = h-2gh/R - 3h^2/R^2. Did i go wrong somewhere? If not how do i get rid of 3h^2/R^2?

[supple knot]

.reopen

[devout snow]

✅

[supple knot]

yea (1+h/R)^2 is just 1 + 2 * h/R + h^2 / R^2 and that's wrong

[lucid oracle]

but then the h^2/R^2 would have to reduce to 0 for the formula to be correct tho right

[supple knot]

yes that term's correct. but the 2h/R is wrong

just because you "almost got the right answer" doesn't make your mistake correct

[lucid oracle]

hmmm

confusion

Im not quite sure i follow, you're giving me (1+h/R)^2 but im trying to calculate (1+h/R)^-2

[lucid oracle]

1+h/R)^-2 = 1-2h/R-3h^2/R^2 no?

[supple knot]

oh yes. i mis-read what you said earlier

[supple knot]

I get g (1-2h/R-3h^2/R^2) = h-2gh/R - 3h^2/R^2. Did i go wrong somewhere? If not how do i get rid of 3h^2/R^2?
3h^2 / R^2 is encapsulated in o(h/R)

[lucid oracle]

whats the o? 😅

[lucid oracle]

Does that mean it reduces to zero? (if so, why?)

[supple knot]

https://www.tau.ac.il/~tsirel/dump/Static/knowino.org/wiki/Little_o_notation.html

[lucid oracle]

😖 i thought newtons binomial was easy for n = -2 💔

Thanks for the help but i'm not sure i get it yet

[supple knot]

you only keep the first 2 terms, constant and linear. the rest are consumed by the o(h/R)

but understanding little o notation is a completely different problem

some practice problems
http://wtworden.org/teaching/calc_2_s20/assets/littleo.pdf

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[upper coral]

? Not sure how to even start

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[median moat]

Can someone help me with the process of solving these

it's not something we went over in class unfortunately

[wild creek]

do you know what is series of a^n equal to? for n going from 1 to infinity?

assuming |a|<1

[median moat]

do you mean a/1-x?

[wild creek]

why x?

[median moat]

oh ig it's not gemotric

the x is the common ratio

[wild creek]

yeah but i used a here as the ratio

w/e

[median moat]

oh wait

hmm

it would work wouldn't it?

5 = a

actually idk

[median moat]

what formula does this derive from

ah

[wild creek]

your answer was close

but my formula doesnt involve x

so your answer shouldnt

[median moat]

ok

right cuz we are solving for x

I'm not sure how though

[wild creek]

so this is a geometric series

so its (1st term in the sum - 1st term not in the sum)/(1-ratio)

here since we go up to infinity

the "1st term not in the sum" goes to 0

so we have

a/(1-a)

now lets transform our original series into something of this form

[median moat]

5/1-3?

[wild creek]

no i meant

transform it into series of a^n

with some a

and then we use the formula

[median moat]

5x^3n

[wild creek]

currently thats not it

[median moat]

I'm confused