help-28

[hexed spruce]

yes

[solemn gate]

the reason changes

1/a + 1/b + 1/c + 1/d = 1 is not impossible bcs even=/= odd

[hexed spruce]

okok

[solemn gate]

its hard to explain other way

[hexed spruce]

i get it

[hexed spruce]

then the left side of the equation is imposible for it to be equal to an odd number

[solemn gate]

no

[hexed spruce]

but didn't we just prove that

[solemn gate]

im sorry i dont know how to explain it to you correctly here

[hexed spruce]

we multiplied abcd to both parts

so it's still the same equation but put differently, no?

[solemn gate]

you dont really get what equivalent equations are

its not actually the same equation

only the truth about them doesnt change

if 2nd equation is false then 1st is also

[hexed spruce]

ok

[solemn gate]

but that doesnt mean they are false for the same reason

[hexed spruce]

but what am I saying wrong here

[solemn gate]

if youre reffering to 1/a + 1/b + 1/c + 1/d = 1 equation left side is neither odd or even

beacause its not an integer (for sure)

wait, i phrased it wrong

1/a is neither odd or even

unless a=1 but it is easy to proof its not

and 1/b,1/c,1/d are not neither odd or even also

so the whole even=/=odd deal here doesnt make sense

[hexed spruce]

ok I don't really get it at all but I get why it's like that

I'd like to understand more about this, any recomendations?

like

what would I have to go over

[solemn gate]

dont really have any recomendation, i just built intuition about it after years of study

maybe after learning algebra, logic and set theory you'll understand more

[hexed spruce]

I know this is out of topic but what do you tudy

study*

[solemn gate]

physics

2nd year

[hexed spruce]

yeah this is a problem given in the first year of civil ingeneering

[solemn gate]

interesting

[hexed spruce]

I feel a bit behind ngl

I'll try to catch up

[solemn gate]

with math?

[hexed spruce]

yeah

[solemn gate]

just be open for help and you should get it

[hexed spruce]

I'll do

tsm for the help

[solemn gate]

there are channels here with specific areas of math and book recomendation channel

als i recomend to ask in college if youre studying there

[hexed spruce]

yeah

[solemn gate]

you're welcome

[full forum]

@hexed spruce Has your question been resolved?

Channel closed

Closed by @hexed spruce

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.

[solemn gate]

a and b can be negative

since a^2=b^2 cancel the negative

ok i said it wrong

if a=b then a^2=b^2 right?
if a=-b then a^2=(-b)^2=b^2

both hold

because the - is cancel out by ^2

they restricted after to N after that solution

[alpine nebula]

Take b² to other side

a²-b² =0

(a+b)(a-b)=0

now theres two cases

[solemn gate]

sqrt(a^2)=|a|

[alpine nebula]

its modulus

[solemn gate]

there is abosulte value

i can tell you where that formula comes from tho

but ok

forget the formula

start with the fact we dont restrict to N for now

[solemn gate]

read here

then

they first found sols for f: R->R

so read the 2nd and 3rd sentence

of the screenshot

they said its just a=b beacuse we restrict to N

after they found sols for a^2=b^2 for R

yes

ill rephrase what they said: a^2=b^2, thus a=b or a=-b, BUT SINCE THE DOMAIN IS N a or b cant be negative, SO a=b

it was

you can construct -b even if b is takeen from N

but since -b is not in N it was thrown out

they said b is in N

and it is

-b isnt

but -b can be constructed from b

thats why they thrown out the solution

have you learned how integer set is constructed from natural set?

the author wrote proof correct

you're the one not understading

so learn it first if you wanna ask questions like that

2nd line is not an assumption

a=-b is a sol to a^2-b^2

how 1 and 2 contradict?

beacuse they dont

1st line doesnt say -b is positive?

what contradicts

you're right i get the logic

nah ask someone else im done

[full forum]

@latent salmon Has your question been resolved?

[torn gust]

umm can you re-ask your question

[full forum]

@latent salmon Has your question been resolved?

[torn gust]

that's from how you'd regularly solve the equation without restrictions, since (-x)*(-x)=x^2 too

immediately after the problem says that a and b are positive so you'd only have a=b

[torn gust]

ah ok I think the logic works out though, doing p implies (true or false)

[pallid coral]

I think some real analysis books include 0 in N

0=-0

[torn gust]

does "Thus a∈{b,-b}" sound better?

[pallid coral]

it concludes this in the next sentence

[torn gust]

I think it would be a stylistic mistake to apply that condition to every step in your head before writing it down in a proof

[pallid coral]

I think clarity is good but you have a point

maybe that might be trivial for you but it may confuse other readers

again, if the book defines 0 to also be in N then it’s not all positive

[torn gust]

it'd be accepted, but on something like a computer theorem prover, you'd have to note that you're solving a^2=b^2 in the domain of positive numbers instead of the reals

[pallid coral]

I would personally be okay with it but that varies between people

[full forum]

@latent salmon Has your question been resolved?

[full forum]

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.

Channel closed

Channel closed due to the original message being deleted.
If you did not intend to do this, please open a new help channel,
as this action is irreversible, and this channel may abruptly lock.

[median mason]

.close

[full forum]

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.

[high bay]

Hi just wanted to check but did they just pull out the constant to get rid of 3/2?

[fathom saddle]

The constant doesn't matter here. You could have left it in, they chose to pull it out.

I personally tend to pull out constants if they're cluttering my integral. Nothing clutters my integrals.

[high bay]

ah okay cool, yeah i just wanted to make sure I was following right

trying to make a habit to pull out constants too. Thank you!

.close

[full forum]

Channel closed

Closed by @high bay

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.

[olive oracle]

I dont understand how to do this

[full forum]

@olive oracle Has your question been resolved?

[vast rover]

Do you understand question 3 part a?

[full forum]

@olive oracle Has your question been resolved?

[olive oracle]

.close

[full forum]

Channel closed

Closed by @olive oracle

Use .reopen if this was a mistake.

[full forum]

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.

[torn jolt]

im not sure how to start or what to do at all.

[full forum]

@torn jolt Has your question been resolved?

[fathom saddle]

This looks like a ransom note

[full forum]

@torn jolt Has your question been resolved?

Channel closed

Closed by @placid shard

Use .reopen if this was a mistake.

[full forum]

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.

[copper patio]

how is this 56

[quaint prawn]

how do you think

[copper patio]

i keep getting 32

idk

i put it in the calc (2) (2(2)) + 3(8)

it gives me 32

[fathom saddle]

,calc 2(2(2) + 3(8))

[glossy valve]

Result:

56

[copper patio]

so i was putting the brackets wrong

alr thanks

[fathom saddle]

Note the parentheses yeah

[full forum]

@copper patio Has your question been resolved?

Channel closed

Closed by @copper patio

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 forum]

Please don't occupy multiple help channels.

Channel closed

Channel closed due to the original message being deleted.
If you did not intend to do this, please open a new help channel,
as this action is irreversible, and this channel may abruptly lock.

[long solstice]

.close

[full forum]

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.

[dusky girder]

the first one is the correct interpretation right?

[dusky girder]

it is about multypling two vectors

[eager obsidian]

nope, the dot product will be $e_1P_1 + e_2P_2$

[glossy valve]

nebula40

[dusky girder]

the 2nd one

[eager obsidian]

think carefully about it

try to write what each option would mean in terms of e_n and P_n first

[dusky girder]

the scalar product is a multiplaction

why plus?

[eager obsidian]

i think you need to take a refresher about the dot product first then

https://www.cuemath.com/algebra/scalar-product/

heres the relevant bit

[dusky girder]

i dont get any of this

so it is multiplication between two vectors but they are in reality are calculated by adding them

with +

[eager obsidian]

you multiply the corresponding components and add the products

see some examples online, it might help

[dusky girder]

okay so let's say Vector a (2/4)

Vector b is (6/2)

dot product would be a *b

so

(2 ) * ( 6)
(4) (2)

= 2x6 + 4x2

[eager obsidian]

2x6 + 4x2, correct

[dusky girder]

yeah

[eager obsidian]

yes thats right

[dusky girder]

now the goods were multiplied

by the price

[eager obsidian]

right

so now you should be able to see which option is appropriate

[dusky girder]

at the end we would get a number

which is 12 + 8 = 20

[eager obsidian]

Yes, the scalar product gives a scalar as output

[dusky girder]

and i should be able to interpretate

this exact value

well i tells us how much money we spent all together

on each product

[eager obsidian]

this is right

[dusky girder]

it was multiplied first and then added

all together

[eager obsidian]

you mean all products here, each means something different

but i think u understood it so its all good

[dusky girder]

yeah

btw

lets say it is not about goods

or price

but something different?

then is there a general interpretation?

i cant image how this could look when it is about vectors

i am trying to understand how it would make sense if products and their value are not involved

[eager obsidian]

there is a geometric interpretation that u can read about in the link i shared before

[dusky girder]

the second one is correct right?

[dusky girder]

okay

[eager obsidian]

the second option says "number"

its not the number of copies purcharsed, that would be e1 + e2

the correct option is the last one

[dusky girder]

aaah!!

i see

i was thinking of 20 so i forgot that it means the price

thank you so much!!

.close

[full forum]

Channel closed

Closed by @dusky girder

Use .reopen if this was a mistake.

[dusky girder]

.reopen

[full forum]

✅

[dusky girder]

wait

are you good at calculating vectors?

[misty fractal]

just ask away

someone will help you

[rugged void]

^^

[full forum]

@dusky girder Has your question been resolved?

[dusky girder]

okay

[dusky girder]

yey kanna nice to c you again

.close

[full forum]

Channel closed

Closed by @dusky girder

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.

[austere oracle]

This looks false

[open igloo]

It's missing the 2xy term, yes

[austere oracle]

isn't there something missing ? like a 2*all terms

ok thanks

.close

[full forum]

Channel closed

Closed by @austere oracle

Use .reopen if this was a mistake.

[craggy tapir]

freshman dream

[full forum]

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.

[void arch]

For this question, surely any function in L^2023 has integral of 0 since X is finite so you can just write the integral as a sum of indicator’s at 2023 and 2024, measure(2023)*f(2023)+ measure(2024)*f(2024)=0

[full forum]

@void arch Has your question been resolved?

[full forum]

@void arch Has your question been resolved?

[full forum]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[full forum]

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.

[red delta]

A rental car costs 375kr per day. For this price you can drive 100km. If you drive further, there is an additional charge of 2.5kr per km. How do i write a formula for this?

[noble schooner]

I think you can write at as y = 375k + 2.5(x) where x is the additional distance travelled beyong 100km

[red delta]

thhansk

[solemn gate]

its (x-100)

[red delta]

elaborate plz

[solemn gate]

its 375+2.5(x-100)

[noble schooner]

i think it will be 375 for x less than 100 and 375 + 2.5x for x greater than 100

[solemn gate]

beacause aditional charges start after 100

you pay 2.5 per km after 100

[red delta]

ah ok

[noble schooner]

so its the same cost if the person travels 75 km or 25 km

[solemn gate]

yes

its still 375

and for example at 101km you pay 375+2.5

[noble schooner]

yep yep

but for your formula at 99 its (375 - somthing number)

[solemn gate]

if youd put x in what you write it would be 375+2.5*101

[noble schooner]

the x-100 one

(99-100)2.5

[solemn gate]

no no you start at x>100

[noble schooner]

yep thats good

then yep valib

valid

[solemn gate]

for x<=100 the formula is just 375

[noble schooner]

ye

[full forum]

@red delta Has your question been resolved?

Channel closed

Closed by @red delta

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.

[agile dirge]

If a function has two different formulas depending on the range of the input, can we prove a base case in one and then do the inductive proof on the other range? For instance, if we're proving that f(n) evaluates to n * log_2(n), and the function is 2 if n = 2 and 2f(n/2) = n if n is greater than 2, can I prove n*log_2(n) evaluates to 2 for n=2 and then do the proof on the latter portions?

[full forum]

@agile dirge Has your question been resolved?

[full forum]

@agile dirge Has your question been resolved?

[agile dirge]

.close

[full forum]

Channel closed

Closed by @agile dirge

Use .reopen if this was a mistake.

[full forum]

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.

[harsh elk]

if i need to find d(50) do i do 50=log_10 x?

[wide wind]

log10(50)

[harsh elk]

why

because d(50)

[wide wind]

f(x)=x+2
f(a)=a+2
f(2)=2+2=4

[harsh elk]

but wwhat if i wanted the population for 5 days?

in 5 days

sorry

5=log_10 x?

[wide wind]

d(5)=log_10(5)

[harsh elk]

thats wrong

it would be 5=log_10 x

[wide wind]

Yeah, guess you’re right.

[harsh elk]

r u sure?

[wide wind]

Weird that they didn’t took bacteria based on days.

[harsh elk]

yes it does

represents the number of days

@wide wind can u please help?

[wide wind]

I guess not.

[harsh elk]

why?

[wide wind]

I’m uncertain. I can’t give you a solution that I don’t know.

[harsh elk]

but u did give me the answer

[wide wind]

Compare 24h and d(x), see when they come pass each other.

[harsh elk]

what?

[wide wind]

Find another. I doing all this in a rush.

[harsh elk]

ok

thx tho

[full forum]

@harsh elk Has your question been resolved?

[full forum]

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.

[torn jolt]

Let X and Y be independent and unif[0, 1]. Find the cdf and pdf of the random
variables X/(X + Y).

[torn jolt]

I have the following

where z = \frac{x}{x+y}

but im stuck as to what

[full forum]

@torn jolt Has your question been resolved?

[full forum]

@torn jolt Has your question been resolved?

[full forum]

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.

[little owl]

https://cdn.discordapp.com/attachments/903486480075354182/1217244877981614110/image.png?ex=660352a2&is=65f0dda2&hm=603b7ae9da587ca166d80738b5fc0282fe694840954cf5f3bd302f51ec368783&

[full forum]

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

[little owl]

i dont know how to start

i belive you would times each of them by them selves but im not sure

[dull seal]

A^2 = A * A

So if you have (2x-9y)^2 that means (2x-9y)(2x-9y)

Just FOIL

[little owl]

i only learned how to use foil when they are in dif sets of brakcets how do i do it when they are in the same

wahts the steps you take

[dull seal]

I told you

[dull seal]

This

[little owl]

but do you have steps for other types of quesitons

like is there a set of rules

i dont want this makes this just becuase then i wont know how to do other questions

[dull seal]

FOIL is the explanation for the formula

You wanna FOIL here to know what does the formula means

[little owl]

no but like

(2x−9y)^3

now what do i do

(2x−9y) now what do i do

i need to know how to do all types of questions

[dull seal]

(2x−9y)(2x−9y)(2x−9y)

You first FOIL two of them and the result u FOIL with the third

[little owl]

ohhh

(2x−9y)*(2x−9y)

so how do iget the answer

[dull seal]

Distributive

(A-B)(C-D) = AC - AD - BC + BD

[little owl]

okay so

[little owl]

would i first do 4^2

is 2x*2x 4^2?

[somber hill]

4x^2

[little owl]

okay

(4x^2)+(-18y^2)+

[little owl]

how do itimes x by y

[somber hill]

you can write xy

Here it'd be (xy)^2

[little owl]

wouldnt it be -18xy^2

[full forum]

@little owl Has your question been resolved?

[full forum]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[full forum]

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.

[potent fog]

hiii are you studying algorithm ???

[agile dirge]

Yes, I’m studying algorithms.

[full forum]

@potent fog Has your question been resolved?

Channel closed

Closed by @potent fog

Use .reopen if this was a mistake.

[full forum]

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.

[spark granite]

Not sure what i did wrong here

[spark granite]

book says im incorrect

answer the book gives is (ad-bc)y / (cx+dy)^2

dx in book is dy

.close

[full forum]

Channel closed

Closed by @spark granite

Use .reopen if this was a mistake.

[full forum]

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.

[slender pond]

can someone help me with this

[slender pond]

since the first equation missing a direction vector

[shy edge]

first r minus second r u will be getting the direction vector that makes perpendicular

den juz use the formula dot product first part ans and second direction vector =0

[slender pond]

ah ok ty

[shy edge]

tbate reader

[slender pond]

yes still waiting for it to come back🙏 its oeak tho

.close

[full forum]

Channel closed

Closed by @slender pond

Use .reopen if this was a mistake.

[full forum]

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.

[sullen prawn]

Hi guys, I'm back at math after a long time and I have some issues understanding a thing with square roots:
Basically I saw that the square root of x^2 is |x| (as in the image) but i also see sometimes we write like square root of 4 = +-2, I dont get what's the difference between writing with absolute and +-
I also know that for example with ax^2+c=0 for example we do x^2=-(c/a) in this case we do x1,2= +- sqrt(-c/a), isnt this the same as x= |sqrt(-c/a)|? Im so much confused on this

[full forum]

@sullen prawn Has your question been resolved?

[sullen prawn]

<@&286206848099549185>

[solemn gate]

sqrt(4)=2

not =+-2

if someone writes sqrt(4)=+-2 its a mistake

|x| doent equal to +-x

so thats a mistake also

if |x|=2 then x=+-2 beacuse you can put 2 or -2 instead of x and equation stays true

[sullen prawn]

maybe what i mixed was the actual -c/a being 4 and so i had x1,2=+-sqrt(4) so =+-2

i think I got the answer even though im still scared of having some confusion

thanks in case I'll come back with an example if I see it not solved

.close

[full forum]

Channel closed

Closed by @sullen prawn

Use .reopen if this was a mistake.

[full forum]

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.

[sage anchor]

How can we prove the convergence of this?

I had it in my test today, spoiler alert: I didn't solve it

[opal isle]

-1 <= cosx <= 1 --> -x/2^x <= x/2^x cosx <= x/2^x

[deft tulip]

maybe try integral test on x/2^x and because of this, if that is convergent, it would prove convergence of the initial series

[opal isle]

ye

[deft tulip]

oh also ratio test on x/2^x = 1/2 is another method using again same idea with cos <= 1

[velvet sedge]

by the comparison test, if this isn't clear

[deft tulip]

@opal isle can just think of it as |cos|, then it becomes it a series of positive terms and can use the comparison test with x/2^x, since absolute convergence is a stronger condition than conditional convergence, the initial series would be convergent too

[sage anchor]

Ye, i did this step

then I couldnt prove x/2^x is convergent

[opal isle]

.

[deft tulip]

try ratio test

that's simplest way

[sage anchor]

ohhh nooooo'

i did the ratio test and i got 1

[deft tulip]

$\lim_{x\to\infty}\frac{x+1}{2^{x+1}}\frac{2^x}{x}$

[glossy valve]

Soosh

[sage anchor]

but now i get 1/2

i factored 1/2 out, 1/2 lim (...) and i found that lim (...) is 1 and i stopped

[opal isle]

it happens

[sage anchor]

Also, I had to find the area generated by rotating y = x^1/3 around the y-axis, the integral was hard/unsolvable, unless i did another mistake

[opal isle]

area?

[sage anchor]

yes, area

S = integral ( 2π f(x) * sqrt( 1 + [f'(x)] ^2)

[opal isle]

how

it would diverge doesn't it

[sage anchor]

not infinte

from 1 to 5

[opal isle]

oh

y or x bounds

[sage anchor]

x

[opal isle]

to be honest idk the formula when there's a hole

[sage anchor]

what hole

[sage anchor]

doesnt matter if theres a hole

[sage anchor]

this is the formula

[opal isle]

idk

the surface area of the circle would be gone

but now there are "inner" walls there

prob ping helpers

or if you are sure then ok

[sage anchor]

tbh, im not sure if the rotation was on the y or x axis

its okay, i did the best i could

thanks for your help

.close

[full forum]

Channel closed

Closed by @sage anchor

Use .reopen if this was a mistake.

[full forum]

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.

[hearty pasture]

can someone help me understand how 1 - 0.33 was calculated

[hearty pasture]

Pr(b) = 1 - 0.33 = 0.67*

[full forum]

@hearty pasture Has your question been resolved?

[hearty pasture]

no

.close

[full forum]

Channel closed

Closed by @hearty pasture

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.

[nova ice]

like 70 percent sure about this one

it just seems reasonable..

[shrewd hamlet]

these are bad questions in my humble opinion

yea i think ur right

idk what the creator of this problem was thinking

[nova ice]

!!

[shrewd hamlet]

sorry

my unhumble opinion

[nova ice]

your correct opinion

usually they are fine these are wack

i think they gve up its close to the end of the course lmao

[shrewd hamlet]

lol

[nova ice]

im gonna submit the thing and ig we will seeee

[stiff musk]

is this like math for poets or something like that?

the right first step is: start solving the problem

[slate zenith]

The first step isn't really a step 😭

Whats the first step to fix to fix the car:
a. Fix the car

[solemn gate]

tbh id start with the 2nd option

but that question is awfully stated

[shrewd hamlet]

but how would that help u to "solving" the equation

[solemn gate]

so whatever

[shrewd hamlet]

yea ikwym tho

[solemn gate]

thats the first step id do

[nova ice]

EVERY ANSWER seems to b C

[solemn gate]

but yeah maybe its isnt "solving" yet

[stiff musk]

first step: find and exploit patterns

[solemn gate]

just sue whoever made this

[nova ice]

i want my 150 dollars back.

[stiff musk]

i wouldn't take this class for minus 150 dollars

[nova ice]

accredited aschmedited

[shrewd hamlet]

as long as its accredited LOL

[nova ice]

alright

submitting time

praying to any gods listening

100 percent baybeee

somehow.

every answer was C

are they seriously asking what a denominator is.

[velvet sedge]

recall that a/b= (a)*(1/b)

[nova ice]

wat

am i the silly one

[nova ice]

how does that change the denominator here though..

[velvet sedge]

it allows for some simplification

[velvet sedge]

it may be as simple as that also

[velvet sedge]

yeah, i think you're overthinking it, it definitely is just this

[nova ice]

what a stupid ass question

ill take it guess

thanks lmao

.close

[full forum]

Channel closed

Closed by @nova ice

Use .reopen if this was a mistake.

[full forum]

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.

[frozen ore]

can someone explain how did we got that general answer? specially the part where x2=x2 and x3=x3 where we only have one equation x1+x2=x3 -> x1=-x3

[torn gust]

the "default" is x1=x1, x2=x2, x3=x3 for "anything works", and you add the restrictions from your reduced matrix to make the general solution

sothe 1 0 1 0 row gives you something for say x1, and the rest of the rows are 0 0 0 0 which tell you nothing

the rest of the general solution is just that you split it up into two vectors because you have x2 and x3 as variables

[frozen ore]

so, in order to get a value for each element in the eigenvector I have to get a unique equation for it? for example if an eigenvector has x1, x2, x3 I have to get 3 equations?

and the vectors that split is those considered eigenvectors for the lambda value 3?

[torn gust]

yea each different variable is a different dimension to the solution space

and corresponds to a different eigenvector

[frozen ore]

oh okay got it, thank you. just to make sure when do I split the eigenvector into two eigenvectors? if I dont have an equation for those dimensions?

and even so why did x1, x3 become zeros in the first vector and x2 = 1? why cant they all be 0 or 1, 1 and -1 for example

[torn gust]

there are a few ways to do it but you're always going to split it into one variable each

the coefficients in that 2nd row are just the coefficients of x2 then x3 in the above vector

[frozen ore]

ahh yes think I understood it now!

thank you sm, got some of ur time :).

[full forum]

@frozen ore Has your question been resolved?

[full forum]

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.

[nova ice]

the transformation is just 5 units left no??

[plush egret]

no

and

i think theyre asking you to write it like ...

f(x-a)+b

or so

[nova ice]

wat

oh no

idk how to do that

<@&286206848099549185>

[silk flame]

What are the types of transformations you can do?

@nova ice

[plush egret]

well try like this

can you write f(x+1), say?

[nova ice]

wait

firstly

describe

why do you think they want mathematical formatting for that

like

is just saying for ex, it moves 3 up then 5 left

not enough?

[plush egret]

i guess, idk you have more context than me

but this is not complete either

i mean, your description

your missing a component

theres a sign flip, yea?

[nova ice]

oh

wait there is??

oh

[plush egret]

it looked like it

[nova ice]

there is

im blind

f (x) = 4 f (x) = radical 3x-4 f (x) = 3/5x

wait

internet says this

is that what you were talking about

[nova ice]

Negate the function, then
Horizontal shift to the left by 5 units, then
A vertical shift downward by 8 units.
i also missed a vertical shift too

the -8 bit

<@&286206848099549185>

does this look better?

[full forum]

@nova ice Has your question been resolved?

[nova ice]

.close

[full forum]

Channel closed

Closed by @nova ice

Use .reopen if this was a mistake.

[full forum]

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 seal]

Is the answer 5 (power 2n) divided by 5 (power 3)

[full forum]

@foggy seal Has your question been resolved?

[full forum]

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.

[nova ice]

this one was a little weird but with some help here i think ive got it?

.close

[full forum]

Channel closed

Closed by @nova ice

Use .reopen if this was a mistake.

[full forum]

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.

[silver saddle]

hi

i just dont get how they got the answer

as they removed ln(5) and then made a power series

<@&286206848099549185>

or this one

i dont get how to start

[silver saddle]

hmm okay

i got that one

im stuck on 17 @buoyant pewter

[full forum]

@silver saddle Has your question been resolved?

Channel closed

Closed by @silver saddle

Use .reopen if this was a mistake.

[full forum]

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.

[visual token]

how do i solve the pie thing + second questions i just need to know how to found asymptote

[visual token]

can you write how to solve the question on the question?

live write it on the question

yes

like not write the explaination

just write how to solve it step by step

i just understand it better

1st thing its not a homework its me studying for my final

here on the top u can see it says EOT which stands End of term

i can but tbh i dont understand anything u wrote

i am a visual learner not a reader tbh

okay they can also screen shot it and just write how to solve step by step

in general

what

bruv

i literally just said I don't understand text I understand step by step

look everything ur saying I have it already on some pdfs

and i didnt understand thats why i came here hoping someone will visually teach me

step by step thats how i learn

yes i dont understand any of it

i dont understand how the graph has to do with the question

okayy

how did u find that

how do we know where cosine is

yes

i dont know anything tbh

i just know the top is 0, 1

bottom 0,-1

left -1,0

right is 1,0

okay

okay now how do we solve the question

hey bro I appreciate what you are doing for me but you are complicating it ngl my teacher just sent me a 3 mins video explaining the whole thing

[wide star]

Okay, I'm tired of the critiques. Good luck.

[visual token]

ty

.close

[full forum]

Channel closed

Closed by @visual token

Use .reopen if this was a mistake.

[full forum]

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.

[hollow grove]

What's the doubt?

[peak bone]

Hello, I would like to ask for advice on this problem of finding limits with polynomials

Is it possible to bring up just the seventh power of X without the factor of 18 when splitting?

[rapid rain]

You could do that, but it's easier to bring it out as well so the big fraction on the left has limit 1

If you don’t bring it out then what's left will have limit 18

[hollow grove]

It's quite the same thing

[full forum]

@peak bone Has your question been resolved?

[full forum]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[full forum]

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.

[pure plume]

.reopen

$$2^{x}+x^{2}+4+\frac{1}{x^{3}}=(2^{x})^{2}$$

[glossy valve]

died_of_cringe

[near mirage]

Where did you get this from?

And do you know the lambert W function

[pure plume]

I like writing down random equations and solving them, and yes, I do know the Lambert W function but i have not used it often

[near mirage]

Well if this is a random question the solution might be unnecessarily long

[pure plume]

i just want a solution, or else i might go crazy

[near mirage]

The question requires the use of lambert W function so if you haven't tried solving this with it, give it a shot

[pure plume]

ok

.close

[full forum]

Channel closed

Closed by @pure plume

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.

[odd wolf]

how do you solve this question?

[open igloo]

$(1+n^{1} + n^{2}...)^{-1}\neq 1+n^{-1}+n^{-2}+...$

[glossy valve]

Sulphur

[odd wolf]

fair enough

i still don’t know what to do here

oh let me try it in proper way this time

[twilit leaf]

honestly just try plugging in values of n

also alpha is infinity btw\

[odd wolf]

makes sense but i also have x doimg it this way

is it?

[twilit leaf]

yeah, thats what the ... is doing

[thick hedge]

this is a GP

notice that

[odd wolf]

then i’m even more confused

[odd wolf]

what is GP

[thick hedge]

Geometric progression

[odd wolf]

alright thanks for letting me know

i’ll try again

ok still no idea what to do

[thick hedge]

is that a summation to infinity

then use the formula 1/1-r

[odd wolf]

that’s the logic right?

makes sense

thanks a lot!

.close

[full forum]

Channel closed

Closed by @odd wolf

Use .reopen if this was a mistake.

[full forum]

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.

[fathom marsh]

If I have a mean = 22 and st dev = 3 and then i code data using h = 3/4(x-9) how would i find new data?

[full forum]

@fathom marsh Has your question been resolved?

[full forum]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[full forum]

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.

[fluid prawn]

??

[fathom saddle]

Note the double prime

They're looking for the second derivative

[fluid prawn]

Where double prime

[fathom saddle]

Whoops I thought I saw a double prime. Mb I'm seeing things

They don't want x as the variable, they want a

[fluid prawn]

Oh

.close

[full forum]

Channel closed

Closed by @fluid prawn

Use .reopen if this was a mistake.

[full forum]

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 tapir]

Cubes edge is 1 need the cordinets of every corner

[hard veldt]

Where is A at?

[fathom saddle]

Are you struggling with any that aren't C1?

[full forum]

@gilded tapir Has your question been resolved?

[gilded tapir]

A is 0 right

C(1,1,0) right?

@fathom saddle

[fathom saddle]

Yeah that's true

[gilded tapir]

And is D1(1,0,1)

??

@fathom saddle

<@&286206848099549185>

[full forum]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[full forum]

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.

[native lodge]

Hi, can anyone help me this problem? I think it a logic one

[native lodge]

They are both male and female employees in the company. Each male employees has as many female coleagues as he has male colleagues. And each female employees has twice as many male coleagues as she has female colleagues. How many male and female employees are there in the company?

[rare dock]

let m be the number of male employees and f the number of female employees

[native lodge]

ok

[rare dock]

pick some man

he has as many female coleagues as he has male colleagues

so that means other than him, there are as many female employees as male employees

can you write a relationship between m and f now?

[native lodge]

so it mean m-1 = f?

[rare dock]

yep exactly

so now think about the condition

And each female employees has twice as many male coleagues as she has female colleagues

and get another relation between m and f

[native lodge]

f-1=2m+f

isnt it?

[rare dock]

pick some woman

[native lodge]

ok

[rare dock]

she has f-1 female colleagues

and twice that male colleagues

[native lodge]

Yeah

I;m still stuck in that sentence

[rare dock]

twice as many male coleagues as she has female colleagues translates to m = 2(f-1)

because she has f-1 female colleagues

[native lodge]

Ahh

[rare dock]

and twice as many male colleagues

[native lodge]

Ok 👌

[rare dock]

👌🏻

got it from here?

[native lodge]

Yeah i got it

Thank you so much

[rare dock]

[native lodge]

So it 3F and 4M

IS it right

[full forum]

@native lodge Has your question been resolved?

[full forum]

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.

[ashen silo]

$\int e^x(cot(x) + log(sin(x)) )dx$

[glossy valve]

Barbie

[ashen silo]

.close

[full forum]

Channel closed

Closed by @ashen silo

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.

[peak bone]

Thank you my friend !

[full forum]

@peak bone Has your question been resolved?

[full forum]

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.

[hard veldt]

Given that a number q can be expressed as the sum of two integer squares, prove that 5q can also be expressed as the sum of two integer squares.

[hard veldt]

I have no idea where to start with this question

[white smelt]

5q = q + 4q

and 4 = 2^2

[hard veldt]

oh damn

im dumb

.close

[full forum]

Channel closed

Closed by @hard veldt

Use .reopen if this was a mistake.

[full forum]

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.

[frail elbow]

I didn't understood in 2√x²

How the x² came

[glad hound]

sqrt(x) * sqrt(x) = sqrt(x^2)

You multiply them just like anything else

[frail elbow]

That I got but how x² came?

[glad hound]

Only in this case, the radical and the ^2 cancel each other out and you're left with x (or the absolute value of x)

[stiff musk]

it's strange because they seem to be assuming that x > 0, but then they dogmatically put a |x| at the end

[frail elbow]

And why doesn't 2 multiply and become 4

[glad hound]

I thought it was unnecessary, too, but..

[frail elbow]

What do u mean

[stiff musk]

i mean it's not wrong, but i don't get the point

[glad hound]

Don't worry about it at the moment, Zuhayr... let's deal with x^2

[frail elbow]

Okay

[glad hound]

So... what is y/y?

[frail elbow]

Y²

Like that I got but shouldn't it be 4√x²

Why didn't the 2 got multipled

[glad hound]

No

y/y is not y^2

y * y is y^2

[frail elbow]

Ohh y+y u mean?

[glad hound]

That's what's happening to sqrt(x)

No.. y divided by y

[frail elbow]

Y/Y is

Nothing

[frail elbow]

Both

Cancel

[glad hound]

Anything over itself is 1

[frail elbow]

Out

[glad hound]

They cancel out and leave 1/1

That's 1

[frail elbow]

Ohh

[glad hound]

So that's what they're doing with sqrt(x) here

They're just multiplying by 1 to get the sqrt(x) out of the denominator

[frail elbow]

It's kind of getting confusing

[glad hound]

Ok.. so do you understand why they're doing this in your problem?

What's the purpose?

[frail elbow]

The purpose is to rationalize and remove the surd from denominator

[glad hound]

Yep

So.. let's step back one pace

Does this make sense?

[frail elbow]

It's still what it's is

[glad hound]

Yes, but does the fact that we're multiplying the values in the denominator to get a single denominator make sense?

[frail elbow]

No wait 2 gets multiplied with 2 and become 2√x

[glad hound]

We no longer have two different denominators

Ok.. next step - let's multiply by 1

[frail elbow]

Wait the denominator always needs to be single

[glad hound]

What do you mean?

[frail elbow]

Just like variables

[frail elbow]

I mean no partner with them

[hot herald]

sqrt(x) * sqrt(x) = x
by definition
not sure why they did what they did, and weird stuff can happen depending on domain / whether you work with complex numbers

[glad hound]

No, it can have a partner

[frail elbow]

Ohh

[glad hound]

variables have partners all the time... they're called "coefficients"

In "2x", 2 is the coefficient

[frail elbow]

Answer is 1y/2√x√y

[hot herald]

and rationalisation of variable components in single term denominators usually gets thrown out the window

[frail elbow]

Ohh

[glad hound]

... where did y come from?

[frail elbow]

I multiplied

[glad hound]

or is that just commentary on my bad handwriting

[frail elbow]

Noo it isn't

[glad hound]

Yeah, but you have no "y" in your problem

You only have the single variable, "x"

[frail elbow]

Ohh yea purpose is to remove surd from x

So we ignore other

Variables

Always

[glad hound]

o.O

[frail elbow]

Ain't It right?

[glad hound]

So.. we're just multiplying and reducing... I think you get the idea

[frail elbow]

Ye

[full forum]

@frail elbow Has your question been resolved?

[full forum]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[full forum]

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.

[misty topaz]

Lovetofishya Lake has a serious problem with algae because of the influx of phosphorus
carried by the local river. The lake contains a water volume V and an algae concentration A (mg
L-1 ). The river flowing in the lake, at a rate Q r, carries a concentration of algae of A0 (mg L-1 )
into the lake. Water leaves the lake via a river that also flows at rate Q r (evaporation is
negligible). Algae grow in the lake due to photosynthesis according to the following rate
equation: rg = k gA. Algae decay in the lake according to the following rate expression: rd = -kd A

(a) Assuming that the lake is completely mixed and that the lake volume and reaction rates are
constant over time, derive an equation to describe the accumulation of algae in the lake over
time.

so for this problem I honestly think I might be undercomplicating it

[misty topaz]

what I have right now is

$\frac{dA}{dt}= (A_{0}Q_{r})+(k_{g}A-k_{d}A)-Q_{r}\frac{A}{V}$

[glossy valve]

InfinityMango

[misty topaz]

but Im also thinking that I have to use the integrated rate law to include time in the equation,

$[A]= [A]_{0}*e^{-kt}$

[glossy valve]

InfinityMango

[misty topaz]

mostly because of the second part

Calculate the steady-state concentration of algae in the lake, given the following data: Qr =
100 m 3 d-1 , A0 = 10 mg L-1 , V = 1000 m 3 , kg = 0.95 d-1 , kd = 0.90 d-1

but if I all I have is a rate of change, and I dont have time, im not completely sure how I would go about finding the concentration

[full forum]

@misty topaz Has your question been resolved?

[full forum]

@misty topaz Has your question been resolved?

[full forum]

@misty topaz Has your question been resolved?

[full forum]

@misty topaz Has your question been resolved?

[full forum]

@misty topaz Has your question been resolved?

[misty topaz]

.close

[full forum]

Channel closed

Closed by @misty topaz

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.

[fluid jackal]

Anyone knows any short trich to solve these types of lengthy calculation

[hot herald]

,rotate

[hot herald]

no calc allowed?

[torn jolt]

24800/9.1e-31? is that the problem?

note that this is 2.48e5/9.1e-31

= 2.48/9.1 * 1e5/1e-31

[full forum]

@fluid jackal Has your question been resolved?

[fluid jackal]

naa manually

[fluid jackal]

didnt got u

[torn jolt]

?

as for summing reciprocals

idrk

[full forum]

@fluid jackal Has your question been resolved?

[torn gust]

trust me there's no way to do it by hand unless you wanna do 2 pages of long division

[full forum]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[full forum]

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.

[wild sleet]

yes

that's 12×30

[still moat]

hi

so do I do .99 x 360?

[wild sleet]

yes

[still moat]

so right now I'm thinking it's 1052.33/355.4

[wild sleet]

there's a huge difference though if you don't round to 0.99

,calc 0.99^360

[glossy valve]

Result:

0.026833050939886

[wild sleet]

,calc 0.993213^360

[glossy valve]

Result:

0.086151395790358

[still moat]

I'm not very good at math so I'm not sure why you choose to stop at .993213

[wild sleet]

my calculator app shows 7 by default

[still moat]

I feel so lost on how to do this

I'm not sure I follow on what you meant by 7 there

apparently the answer was 1151.54

I'm not sure how it got to that at all

since I had 1052.33/355.4 I got 2.96 which is completely wrong compared to 1151.54

[full forum]

@still moat Has your question been resolved?

Channel closed

Closed by @still moat

Use .reopen if this was a mistake.

[full forum]

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.

[half remnant]

Can someone please help me with question 3

[full forum]

@half remnant Has your question been resolved?

[onyx glen]

you should do a sketch

it will help u

heres a rough sketch of what i got

now for the equation they give you, i moved the right side integral over to the other side

so now u can see what they are trying to say is that

the area of these two integrals added together is the area of basically a rectangle with side lengths a and b

the left integral should be easy to understand. lets draw it on the graph

sorry i shouldve drew the the functions linear it would be easier to understand

just pretend those are linear functions

this is definitely a tricky problem but here is what i think the answer is

pretending those are linear functions, if you want to get the integral of the f(x) from 0 to a. well thats basically an area of a triangle.

so we get (1/2)ab

now i know its hard to see in the picture but i also drew horizontal lines below the inverse function because we needed to get the integral of f^-1(x) from 0 to b

now from a quick understanding of a inverse function, they told u that f(a) = b

which means that f^-1(b) = a

so to get the integral of the inverse function, it is also a triangle: (1/2)ab

and then u add those two areas up to get: ab

@half remnant thats basically how i understood the problem

honestly im not 100% sure if thats a correct explanation but thats how i saw it

easier to see on desmos

as u can see they are two triangles with the same area

i used a random number for a, b

[full forum]

@half remnant Has your question been resolved?

[half remnant]

oh damn lemme read through this

[half remnant]

That makes sense

but what if the function's not linear?

[onyx glen]

you wont be able to explain by using area of triangles if its not linear

but the answer is still going to be the same

the two areas will be the same

its just easier to explain if the functions were linear

[half remnant]

ah ok

[half remnant]

Like this?