help-0

[surreal meteor]

wait no

[wanton junco]

plus/minus the constant that is

[surreal meteor]

f´(g(x))*g´(x)

is the chain rule

just looked like it

[wanton junco]

yea

so when you see such integrands , you can immediatley get the integral

by just reversing the easy to see differentiation process

[surreal meteor]

oh so it was the chain rule xD

[wanton junco]

the more practice you do, the easier it becomes to identify that
which can really ease integration

However this is just a shortcut to the sub method which would always work in these cases anyway and yield nice linear integrals as you saw

[surreal meteor]

so do you mean if i see an integral with something like $\int{(2x+3)^2}$

[ocean seal]

SimonWin

[surreal meteor]

forgot dx

[wanton junco]

This is not applicable here

you'd have to open parens and integrate the polynomial

[surreal meteor]

Okay haha!

Well can you give an example

of when it's the reverse of f´(g(x))*g´(x)

[wanton junco]

sinx/cosx is one example

as the integral is -ln(cosx)

[surreal meteor]

-ln(cosx) ye this follow f(g(x))

So now I got that, but how would that make it easier knowing that?

[wanton junco]

it allows you to see things faster and preform faster and more immediate integrations

it essentially saves time

[lone heart]

@surreal meteor Has your question been resolved?

[lone heart]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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

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

[mild saffron]

hello, I'm trying to integrate it with respect to x, from 0 to 5, to find the area enclosed by those two functions on the graph on the right. I tried integrating it by subtracting the negative parabola (concave) by the positive (convex) parabola because the concave one is higher... but it gives me a wrong answer.

[mild saffron]

i apologize my oversized screenshot. i don't know how to save the cropped version of it

hopefully you can see the content clearly.

[versed crater]

Ok

I can see

Find where the 2 graphs intersect

And where the red graph has a root

That's all you need

[mild saffron]

to find where the two graphs intersect, -x^2 + 6x = x^2 -4x .... -2x^2=-10x .... 2x^2 - 10x = 0 .... 2x(x-5)=0 ... x = 0, 5

it gives me the x-values of 0 and 5

[versed crater]

Good

Now find the roots

Of the red graph

One if them looks like 0

Factorising it gives the roots as 0 and 4

[mild saffron]

you mean the x-intercepts of the red graph?

yes

0 and 4

[versed crater]

Yup

Yeh

[mild saffron]

so i have to integrate it from 0 to 4 then 4 to 5?

[versed crater]

So now you need to find area under the blue curve between 0 and 5

And subtract the area of the red graph between 4 and 5

[mild saffron]

ahh okay

[versed crater]

And then add the area of the red curve v
Between 0 and 4

Which you'll need to make positive

Because its a negative area

Got it ?

[mild saffron]

ok lemme try

[lone heart]

@mild saffron Has your question been resolved?

Channel closed

Closed by @mild saffron

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.

[copper wadi]

Just need a bit of help setting up a problem. Trying to find the slope of an equation (x, y) that is perpendicular to y=mx+b

[copper wadi]

I tried plugging in y-y1=m(x-x1)+b but didn't have any luck

An equation of a line through (-4, 6) which is perpendicular to the line y=2x+1

so it would be y=-1/mx+b?

Would you mind to work me through a problem to show me?

Doesn't have to be the one i'm trying to solve

Ohh I see. I appreciate the help!

.close

[lone heart]

Channel closed

Closed by @copper wadi

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.

[mortal mica]

For the admissible prime 3-tuple (0,4,10), it is not observed in the first 10^9 primes.
Could it mean that it is finitely many or non-existent?

[mortal trellis]

it could mean a lot of things

on the other hand 10^9 is not that much

[mortal mica]

Like what?

[mortal trellis]

who knows

the point is, 10^9 is not that much

it could mean something, it could mean nothing

could be coincidence, could be whatever

maybe smallest example is on the order 10^60284

who knows

[mortal mica]

true

. close

.close

[lone heart]

Channel closed

Closed by @mortal mica

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.

[south yoke]

Hey can someone help me with this I’m a little confused all I remember is distance = rate x time

[lone heart]

@south yoke Has your question been resolved?

[south yoke]

<@&286206848099549185>

[small fog]

you posted this yesterday

[south yoke]

Yeah I never got a response to it

It’s for a review and I still can’t figure it out

[small fog]

ok

identify the 2 variables

[south yoke]

I don’t know if it’s d=distance and t=time or if it’s one for the lawnmower and the other for the scooter

[small fog]

close

t is one of them

for distance you are very close

but it's not distance exactly

[south yoke]

Distance away from house?

Or kilometers

[small fog]

not really

[south yoke]

Kilometers traveled?

[small fog]

nope

well

kind of

but not really

[south yoke]

I don’t know what else it could be (I’m so sorry about this)

[small fog]

ok

first, try writing out what the question is asking

in a formula

[south yoke]

Distance traveled= 5(t) ?

[small fog]

what

ok

what is the question even asking

[south yoke]

Write an equation for the distance traveled by hill billie bean with the starting point at his house

[small fog]

then what does biker bean have to do with this

[south yoke]

There should be two equations and then after you plug a variable into the other

[small fog]

what

i have no clue what this question is even about

what are you calculating

[small fog]

where did you even get this worksheet

[south yoke]

That’s an example

My school

It’s summer work

We’re solving for each variable

It’s the substitution method

[small fog]

what the hell is the substitution method

anyway

try to first figure out what your mr bean question even means before getting people to solve it for you

[south yoke]

I’ve tried to

I dont get it

[small fog]

same

ask your teachers

[south yoke]

I don’t know if I can but thank you for helping me anyway I really appreciate it

[small fog]

wdym

"i don't know if I can"

[south yoke]

Right before it says this

[small fog]

it says we don't provide ANSWERS

you don't even know the question

[south yoke]

That’s why I’m asking for help because I don’t understand what it’s even asking

[small fog]

ask your teachers

[south yoke]

I will thank you have a nice day

.close

[lone heart]

Channel closed

Closed by @south yoke

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.

@low tartan Has your question been resolved?

[viscid crater]

what is f?

how is f defined?

[lone heart]

Channel closed

Closed by @low tartan

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.

[craggy idol]

Hi, I have this problem that gives me 6 men and 7 women, I need 5 to form a group

[craggy idol]

How can I get the number of possibilities if there must be max 1 man

I tried with (6C1)*(7C4) so I can firstly choose a man from the 6 I have, and then 4 women from the 7 I have

but Im not getting it right

[tribal valve]

maximum 1 man, meaning there can be no men

[craggy idol]

ohhh fk

and what about if I need "mary" and "john" not to be together

[tribal valve]

well, how much ways can only mary be in the group

[craggy idol]

sorry I got stuck with the last one

[tribal valve]

it would be number of ways you can choose the group - the number of ways you can choose the group with both mary and john

[craggy idol]

perf, just got it, ty

and in case I have to choose a president a vice president, a secretary and 2 ministers

I did 13*12*11*10*9*(1/2)

but I dont know where that 1/2 comes from

[tribal valve]

you could have john and mary as a minister

or you could have mary and john

same thing

thats why divided by 2

[craggy idol]

oh right, ty then

[lone heart]

@craggy idol Has your question been resolved?

[lone heart]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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

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

[pastel charm]

Yo how do I go about question c) - and are the above questions correct?

[slow hound]

i suggest you expand the left hand binomial

then use the binomial theorem on the right hand side and match up like powers

first problem looks a little off

[pastel charm]

Can u elaborate on ‘matching up like powers’? Does that mean to multiply like brackets

Aight

[pastel charm]

Whereabouts in the first question is it incorrect?

[slow hound]

you didnt expand right

,w (1-1/(2x))^2

[ocean seal]

Results provided by WolframAlpha

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

Requested by S̨̥̫#8871

[slow hound]

lmfao sheesh

looks like wolfram wants you to do it out

the x term shouldnt be there

[pastel charm]

Hold up

What would adding two -1/2x’s be

[slow hound]

isnt it 1/(2x)

not 1/2 x

[pastel charm]

Yea

[slow hound]

,w -1/(2x) - 1/(2x)

[ocean seal]

Results provided by WolframAlpha

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

Requested by S̨̥̫#8871

[pastel charm]

Ah

,w (-1/(2x))(-1/(2x))

[ocean seal]

Results provided by WolframAlpha

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

Requested by linlucaa#9827

[pastel charm]

I’m tripping hold on

What’s the multiply symbol for wolfram? It’s not x is it cuz that’s the coefficient

Is it .

,w -1/(2x) * -1/(2x)

[slow hound]

its just *

[pastel charm]

Ok

[ocean seal]

Results provided by WolframAlpha

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

Requested by linlucaa#9827

[pastel charm]

Did I submit that right

,w 1/(x) * 12x

[ocean seal]

Results provided by WolframAlpha

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

Requested by linlucaa#9827

[pastel charm]

,w 1/(4x^2) * 12x

[ocean seal]

Results provided by WolframAlpha

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

Requested by linlucaa#9827

[pastel charm]

.close

[lone heart]

Channel closed

Closed by @pastel charm

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.

[cold zenith]

how can i simplify the expression (sinx + tanx) / (1 + secx)

[cold zenith]

anyone who sees this please give me a hint first instead of just the answer

[languid bolt]

maybe try turning the tan x to sin/cos

and sec x to 1/cos ?

[cold zenith]

i did but i still dont know where to go from there

ive been looking at the trigonometric identities too to see what i can do with them but im stumped on this one

[languid bolt]

hmm

maybe multiply the numerator and denominator to remove the fractions?

[cold zenith]

ill try it

i still dont know where to go from there lol

[alpine sable]

Yah tq

[languid bolt]

ok nvm i got no clue

[cold zenith]

sinxcosx + sinx can be factorized to sinx(cosx + 1) on the numerator which cancels with the cosx+1 on the denominator leaving just sinx

[languid bolt]

oh ye

[cold zenith]

.close

[lone heart]

Channel closed

Closed by @cold zenith

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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

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

[primal dew]

Can a number be?

[languid bolt]

yes

[primal dew]

Wait what?!??

They can?!?

Damn that’s cool

[primal dew]

But how?

[gray isle]

the question doesn't make sense

[pale lance]

I mean you could just use newton's 2nd law to check

[languid bolt]

or just use l hopital

[pale lance]

I thought that was last patch?

[languid bolt]

oh yeah

[pale lance]

Didn't they nerf l'hopital with the imaginary number patch

[languid bolt]

forgot about that

[swift latch]

so numbers are???

[pale lance]

Yah most of the time I'd say so

[swift latch]

:0

[pale lance]

你有问题吗?

[swift latch]

数字可以?

[lone heart]

@primal dew Has your question been resolved?

[lone heart]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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

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

[vernal lance]

I'm not sure where to start

[fathom kite]

i would factorise x

take x out of numerator and denominator

[vernal lance]

wym

take out the x next to the constants at the end>

[fathom kite]

like this

[hidden fable]

x^3-4x = x(x^2-4)

for example

[fathom kite]

yeah

do the same for denominator and cancel out x

[vernal lance]

oh alright I understand now

lemme try

okay I got this

[fathom kite]

perfect

you can cancel out x

[vernal lance]

okay nice'

[fathom kite]

good

plug in 0

[wary stream]

You can plug in zero now

[fathom kite]

the point of this was to make it so that the limit wasn't equal to 0/0 anymore

[vernal lance]

ohhhh I get it

-4/3

https://tenor.com/view/catthankyou-cat-gif-24824893

can I keep this open so I can do more limits

or is it best to close and open for every problem

[wary stream]

I think it's best to close it and come back when you are stuck

Not open a new one for every question

[vernal lance]

alright

I didn't mean every my bad

.close

[lone heart]

Channel closed

Closed by @vernal lance

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.

[vernal lance]

again, I don't know where to begin
I can't factor out x this time because of the lonely constant

[pale lance]

Ah

I think I have a solution

[vernal lance]

how did you reach it

[pale lance]

Try turning x^3 into (x+1)^3

We know (x+1)^3 = x^3 +3x^2 + 3x + 1

So we just add it and minus it

[vernal lance]

how is it okay to add that 1

seems like it's being conjured up

[pale lance]

Ok so it's like if I said x = x + 1 - 1

You can add whatever you want just as long as you subtract it afterwards

[last ether]

Long division moment

And then manipulations

[vernal lance]

long division so based
I don't get what she's saying though

[pale lance]

I'll brb and explain I'm on the phone right now sorry

[last ether]

Just do long division

[hidden fable]

hmm

you get -1/0 though

not 0/0

[vernal lance]

I only know how to do long division with numbers

[last ether]

Long division

[last ether]

https://youtu.be/_FSXJmESFmQ

[vernal lance]

is long division the only way to solve this

[last ether]

You can try doing what Phearia was doing

But like

That's pretty out there you know

And I don't think it helps all too much

[tacit arch]

No. But it is the easiest to learn

[last ether]

You'll get the limit of (x+1)^2 minus a fraction

But like

I would just do long division

[vernal lance]

it's undefined on the answer sheet

Could you just explain Phearia's reasoning?

I feel stuck on that

[last ether]

Her reasoning is pretty abstract if you don't know long division

[hidden fable]

well long division doesn't give a nice result on this one

[last ether]

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

Is what she's trying to do

Die latex

[ocean seal]

Umbraleviathan

[last ether]

Which isn't very pretty I will say

[vernal lance]

yeah I don't understand that one at all haha

I guess I'll learn long division for polynomials

[hidden fable]

I don't like whoever thought of this limit

haha

jk

[vernal lance]

I got it from google.com limit problems

[pale lance]

Alright I'm back tbh @vernal lance try theirs, mine is long

[vernal lance]

yeah I'm figuring out polynomial long division right now

[pale lance]

If you want–

[vernal lance]

[hidden fable]

my big doubt is

-1/0 is not an indeterminate form, it's undefined

so why do we continue with the limit?

[pale lance]

Usually it would but thankfully it's x^2 instead of just x

Since it's x^2 in the denominator the limit approach infinity or negative infinity

[hidden fable]

ohhh okay

[pale lance]

But since we know that x^3 in the negatives is a negative number, the result is negative infinity

[hidden fable]

there

[vernal lance]

okay so I was progressing on this

so I distribute x to 2x and put 2x^2 down there?

is that rightt

[vernal lance]

❓

[pale lance]

I just did it so can have a normal x+1 linear equation but then we could evaluate the -(3x^2+3x+1) part instead

[vernal lance]

I reached the answer correctly though right

.close

[lone heart]

Channel closed

Closed by @vernal lance

Use .reopen if this was a mistake.

[lone heart]

Available help channel!

Send your question here to claim the channel.

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

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

[void crypt]

(Q85) How do I handle the bias?

[trim wagon]

Well probability should always add up to 1

Meaning probability of heads + probability of tails = 1

So now can you solve it?

[lone heart]

@void crypt Has your question been resolved?

[void crypt]

i see

thank youu

[lone heart]

Channel closed

Closed by @void crypt

Use .reopen if this was a mistake.

[trim wagon]

[lone heart]

Available help channel!

Send your question here to claim the channel.

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

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

[weary void]

Hey how would you describe the shape of the curves?

I was thinking exponential but then reaches a peak

[chrome plank]

kinda looks like an erf function?

[weary void]

oh yea

i never heard that function

but it looks quite similar

[chrome plank]

what's the question you are trying to solve?

(where does this come from?)

[weary void]

not a question just a science report

and i have to interpret a graph

so i was thinking the shape could assist

alr thx

.CLOSE

.close

[lone heart]

Channel closed

Closed by @weary void

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.

[wild vault]

what is the probability that an event with .5% chance of happening, will happen 10 times in arow?

[tacit arch]

do you know the answer for two times in a row?

[wild vault]

no, but i dont deal in probabilities at all, my friend just wanted to know for conversational purposes

[ornate condor]

the probability of it happening once is 0.005 or 0.5% for it to happen n times is 0.005^n, so for it to happen 10 times is 0.005^10 = 9.765625e-24

[wild vault]

ok so my question becomes

how to put this

[vale wigeon]

that's about 1 in 10^23

or 1 in 100 billion trillion

[wild vault]

ok, so which is smaller, that or 1 in 302,575,350 happening 288 times. with about 10 billion chances

I realize this question is stupid, and i appreciate the assistance

[ornate condor]

as in the chance of an event that happens with that probability happening exactly 288 times? or more than or equal to 288 times?

[wild vault]

either is fine, whichever is easier to find

[ornate condor]

this is binomial distribution

[lone heart]

@wild vault Has your question been resolved?

Channel closed

Closed by @wild vault

Use .reopen if this was a mistake.

[lone heart]

Available help channel!

Send your question here to claim the channel.

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

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

[gritty otter]

The explanation was shown but I don't get how the answer is this

[languid bolt]

you... dont know how to add decimals?

ok let me put it this way

or should i give video

hmmm

[void solar]

Explain it to him in the forms of a musical please

[languid bolt]

♪ ok so♫

♫ you add it like... 0.04280 + 1.00492 ♪

[gritty otter]

no that's not it lol, it's the sig figs

[void solar]

You know how to add three digit numbers right?
How you add the numbers in the same place. Like the tens and tens.
Same thing with the decimals

Oh

Well

Now I’m disappointed

[frosty lark]

What sig figs

[gritty otter]

thanks for the effort tho, if u could make a video of the actual song that'd def help

[wide raven]

significant figures

[frosty lark]

Ye I know but where is that on question

[gritty otter]

basically it's a practice question, technically all of them are correct but you need to know which answer has the right amt of sig figs

lack of info on my end

[wide raven]

https://youtu.be/xHgPtFUbAeU

[gritty otter]

ty

[wide raven]

not musical, but helpful

[gritty otter]

lol

[lone heart]

@gritty otter Has your question been resolved?

Channel closed

Closed by @gritty otter

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.

[digital shard]

hey

which question

[river epoch]

All 3 pls

[digital shard]

sure

lets start with p5 number 1

[river epoch]

Ok

[digital shard]

so right off the bat, we know how many staff members there are in each department right

[river epoch]

Yes

[digital shard]

ok and how much is that

[river epoch]

Total 45 staff members

[digital shard]

yes in total

but there are 5 departments each with the same amount of people

so that means how many have to be in each department

[river epoch]

9 staff members in 1 department

[digital shard]

exactly

so let x = number of females in each department (not the company)

and let y= number of males in each department (not the company)

if we know x+y =9 like you just said

we just need one other equation relating x and y and we can solve for both right?

[river epoch]

3x+y

3 more males than females

[digital shard]

hmm

so 3x means there are 3 times as many

[river epoch]

Yes

[digital shard]

if we know that the number of males is 3 more than the number of females

^ translate that sentence to an equation

is means = sign

[river epoch]

Wait when there are 3 more A then B will it became 3A-B or 3B-A?

[digital shard]

actually it is simpler than that

"the number of males is 3 more than the number of females"

the number of males is x

number of females is y

[river epoch]

3x=y

[digital shard]

and "is" is the english way of saying =

so the equation you just gave me

is saying there are 3 times as many females as males

[ornate condor]

so one way of thinking of it is that if there is
3 males, there is 0 females
4 males, 1 female
5 males, 2 females

[digital shard]

it's basically saying, whatever the left side of the equation is = the right side + 3

[river epoch]

Ok

X=3y

[digital shard]

almost

but we shouln't be multiplying 3 and y

it's not that there are 3 times as many guys as girls

its that there 3 MORE guys than girls

[river epoch]

3x=y

[digital shard]

ok i will tell you the equation so you can apply to the next one

so it would be x =y+ 3

number of males = number of females + 3

do you see why now

think of it as a scale

for the left side to equal the right side

we have to add 3 to the right

because there are more males

[river epoch]

Ok

[digital shard]

ok now you can solve for y and x easily

lets try number 2

[river epoch]

Ok

[digital shard]

ok so similar problem

how many partipants in each group

[river epoch]

4 people in 1 group

[digital shard]

yep

and now

let x = number of males

and y= number of females

we know x+y =4

because total = 4

what is the second equation

[river epoch]

X-2=y

[digital shard]

almost

but your equation is subracting 2 from the amount of guys

to equal the girls

however, the problem states that the number of girls is actually 2 higher than the guys

[river epoch]

X= y-2?

[digital shard]

yah

because number of girls is higher

so you have to subtract to balance it out and equal the guys

you can either add 2 to x

or subract 2 from y

[river epoch]

Ok

[digital shard]

just to see if you get it

if the problem said

"there are 10 more guys than girls in each group"

what would the equation be

[river epoch]

X=y+10

X= guys y= girls

Right?

[ornate condor]

yep

[digital shard]

niceee

ok you get it now!

[river epoch]

Ok thanks

[digital shard]

ok for the last question

[river epoch]

Ok

[digital shard]

what are your thoughts on how to solve a

[river epoch]

I don't really how to do this question

Substitution I think

[digital shard]

ok so how i would start this

you know what like terms are

right

like any 3x^3 and 5x^3 would be like terms

3x and 10x would be like terms

3x^2 and 15x^2

3 and 5

etc

terms that have the same power of x

are like terms

[river epoch]

Oh yes I know this

[digital shard]

ok so on the left

it gives you the value for each exponent of x

for example, for x^3 the value is

2

right?

for x^2 it is

-5

[river epoch]

I'm confused

[digital shard]

the number in front of x

is the value i am talking about

[river epoch]

Oh ok

[digital shard]

the numbers in front of x^3

x^2

x

and x^0 (which is 1)

[river epoch]

Ok

[digital shard]

you have all those numbers right

except the one for x

which is k

so what you need to do

is multiply out the second equation

and combine like terms

so first do that and let me know what you gety

[river epoch]

To find X right?

[digital shard]

you aren't solving for x here

ill show you what i mean

just multiply that second equation out

and combine like terms

[river epoch]

Ok

[digital shard]

and post what you get

it will make sense then

[river epoch]

Ok

[digital shard]

oh

I meant

multiply the next equation they give you

the (x-1)

times (x^2 +whatever)

[river epoch]

Ok

[digital shard]

yes

exactly

now i would go one step further

and factor the like terms out

to get something like this

ax^3 + (b-a)x^2 +(c-b)x-c

you agree?

[river epoch]

Yes

[digital shard]

ok cool

now compare this equation

ax^3 + (b-a)x^2 +(c-b)x-c

with the first equation: 2x^3-5x^2+kx-5

we know they are both equal right

[river epoch]

Yes

[digital shard]

we know they are equal because the problem statement said so

so for the first equation to = the second equation

because we are ADDING on both sides, there is no way to get x^3 from any other terms OTHER than x^3 terms

there is no way to get x^2 terms from any other terms OTHER than x^2 terms

there is no way to get x terms from any other terms OTHER than x terms

and so on

you get that?

you can think of this as 4 tiny equations for each like term

[river epoch]

A=2,B=-5+2=-3,C=-5

[digital shard]

NICE

see you get it =)

ok lets do the last part

[river epoch]

So K = -5-3=-8

[digital shard]

haha sure

but we dont need to solve for k

thats just bonus

[river epoch]

Ok

[digital shard]

ok final part

so as you know, a polynomial with a highest term of x^2

has how many roots?

it has 2

of course, it might be a double root at the same value

and the roots may be imaginary

but the number of roots will always = the exponent of the highest term

so a cubic polynomial will have 3 roots

a quartic polynimal will have 4 roots and so on

[river epoch]

Yes

[digital shard]

so this question is asking if all the roots are real

we already know one of the roots right?

it was given to us in the problem statement

in the second equation

[river epoch]

Yes

[digital shard]

what is it

[river epoch]

All roots of the equation f(X)=0

[digital shard]

right

but we know one of the roots already

because they told us

f(x)=(x-1)*(ax^2+bx+c)

that means 1 HAS to be a root

because when you plug in 1, f(x)=0

[river epoch]

Ok

[digital shard]

so to find the other 2 roots

we can use the quadratic formula

however, we don't really need to know the actual roots, we only care about whether the roots are real or not

the quadratic formula is (-b +/- sqrt(b^2-4ac))/2a

whether the roots are real or not depends on the what is in the square root

if b^2-4ac is negative, we have imaginary roots

if it is positive, we have real roots

if it is 0, we have 1 real root but its a double root

here is what all 3 situations would look like visually

does that make sense

[river epoch]

No 😭

[digital shard]

hmm ok which part didnt make sense

u know the quadratic formula right?

[river epoch]

Yes

[river epoch]

The drawings

For the ans disagree there are no real numbers, right?

[digital shard]

how did you get that

ok forget the drawings for now its not super important

[river epoch]

Correct?

[digital shard]

your math is right

but the final conclusion i disagree iwth

you got 2 real roots

and 1 is also a root

which means it has 3 real roots

[river epoch]

Yes

[digital shard]

ok good

so answer should be agree then

[river epoch]

I thought the number need to be =0😅

[digital shard]

oh no

as long as the roots you find were real

a root means

the x value where y is = to 0

in plain english

wherever the graph touches the x axis is a root

that explains the pictures I sent

if you have one root only

i.e. the last picture

that means the graph only touches the x axis once

if you have 2 real roots i.e the 2nd picture

that means the graph touches the x axis twice

if you have 2 imaginary roots, i.e the first picture

that means the graph touches the x axis 0 times

and to determine which of the 3 situations we are dealing with

all we need to do is find b^2 -4ac

because the formula for roots is (-b +/- sqrt(b^2-4ac))/2a

[river epoch]

Yes =49

[digital shard]

if the sqrt comes out to be 0, then +/- 0 is the same

if inside the sqrt comes out to be positive

then it will be 2 real roots

if inside the sqrt comes out to be negative

then we have to take the sqrt of a negative number to find the roots

which means the roots will be imaginary

[river epoch]

=0 real roots

[digital shard]

what = 0

whatever is inside the sqrt?

[river epoch]

0

[digital shard]

im not sure i understand

what do you mean by 0

so to figure out what roots we are dealing with, need to find b^2-4ac because that is the value inside the sqrt

if b^2-4ac >= 0

then we have only real roots

if b^2-4ac <0 then we have 2 imaginary roots

b^2-4ac can be equal to 0 or > 0

but if is equal to 0, that means there is only one root (still real but only 1)

if it is > 0, there are 2 roots (both real like i said)

since you found that b^2-4ac is 49

this a positive number

so that means there are 2 real roots

if it was 0, that would mean there is only 1 real root

if it was like -49 for example, that would mean 2 imgariny roots and then your answer would be no

[river epoch]

Oh ok I understand now thanks

Thanks so much for ur time and helping me

[digital shard]

np bro

gl with future questions!

[mellow reef]

yo

u mind helping me

its simple

[lone heart]

Channel closed

Closed due to the original message being deleted

[river epoch]

Thanks

[lone heart]

Available help channel!

Send your question here to claim the channel.

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

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

[alpine sable]

Am I doing this right

💀💀

[ornate condor]

hey i love hutao

[lone heart]

@alpine sable Has your question been resolved?

[lone heart]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[ornate condor]

lol

[lone heart]

Available help channel!

Send your question here to claim the channel.

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

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

[weary void]

how do i find the dy/dx of b

the derivative of part b please

[vale wigeon]

(4x+1)/(x-2)?

have you made any progress or are you stuck not knowing how to begin?

or do you perhaps want someone to just give you the answer?

[weary void]

I’ve tried using first principles

I want someone to give the answe plz

[lone heart]

@weary void Has your question been resolved?

[weary void]

.close

[lone heart]

Channel closed

Closed by @weary void

Use .reopen if this was a mistake.

[lone heart]

Available help channel!

Send your question here to claim the channel.

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

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

[hard ether]

?

[hard ether]

@tribal valve

[echo haven]

I’m on #4 and I don’t understand what the question is asking

I thought I was supposed to just plug in -1 into each one and so I got 4 is less than f(x) less than 2

[void solar]

bruh thats like 2 days ago

[hard ether]

Whoops sorry

What do I do

[void solar]

pm him if you really need

[hard ether]

Yeah I pinged him

[echo haven]

But there’s no # less than 4 and less than 2 💀

[hard ether]

I’ll dm him

[ionic trail]

So there is a number less than 4 and less than 2, but I doubt that's what you meant😅

[echo haven]

on the the answer choices lmao sorry

[bleak pine]

If lim x->-1 g(x) = lim x-> -1 h(x), then lim x-> -1 f(x) = lim x->-1 g(x) = lim x-> -1 h(x), because g(x) <= f(x) <= h(x)

[ionic trail]

Oh ok but I think you meant less than 4 and bigger than 2?

[bleak pine]

You just need to check if x->-1 g(x) = lim x-> -1 h(x) is true

And if both functions approach the same value, then f(x) also approaches that value

[echo haven]

so x -> -1 g(x) = 4 and x->-1 h(x)=-1 and it would be D?

Since they aren’t equal

[bleak pine]

lim x->-1 h(x) = 6 but yeah, thats the point

[echo haven]

alright thanks

.close

oh lmao it’s not on my username

@hard ether need any help? If not close this channel cause it’s on your name

[bleak pine]

Maybe a bot will close it for inactivity if we just leave it be?

[hard ether]

Wait no is it 1/2?

[bleak pine]

the probability of chosing a white jelly from jar A is 3/10, and probability of chosing a white jelly from jar B is 6/8.

And the probability of chosing each jar is 1/2

So there are two paths to get a white jelly

jar A -> white jelly

jar B -> white jelly

Probability of first path is 1/2 * 3/10

And of second path is 1/2 * 6/8

And as these two paths are independent you add the probabilities

(1/2 * 3/10) + (1/2 * 6/8) = 21/40

[lone heart]

@hard ether Has your question been resolved?

[lone heart]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[lone heart]

Available help channel!

Send your question here to claim the channel.

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

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

[magic falcon]

f(x) = 2^(x+3)
g(x) = 2^x

(f+g)(x) = (2^(x+3))+(2^x)

(2^(x+3))+(2^x) = 2^3 * 2^x + 2^x = 4^x * 8

[magic falcon]

so that means

(f+g)(x) = 4^x * 8

is that correct

[mortal trellis]

no

[magic falcon]

oh

whered i go wrong

[mortal trellis]

maybe to avoid some confusion, set z=2^x

then we have 2^3*z + z = 8z+z = 9z = 9*2^x

[magic falcon]

thank you that made me finally understand it

.close

[lone heart]

Channel closed

Closed by @magic falcon

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.

[limpid spade]

Say u and v are two non zero vectors in R3. Then is the lineair transformation .. surjective

I know how to show that lin trans are injective, but dont know how to do with surjectivity how do i show that phi(v)=w with v element of R3 and w element of R

this is a true or false question btw

[keen plinth]

i assume its taking the dot product?

[limpid spade]

yeah if it was multi it would be just . i think

[keen plinth]

so do you think its true or false

[limpid spade]

so to verify it i just apply some values to u v and w?

and see if phi(v)=w?

[keen plinth]

to show surjectivity

you need to show that for every x in R

there is a w in R^3 such that φ(w) = x

that is if the statement is true

if the statement is false you only need to provide a counterexample

[weary wyvern]

It may be easier to view this as w.(u×v)

[keen plinth]

yes

so do you think w.(u×v) can take on every value in R

[limpid spade]

w.(u×v) needs to have grade 1 right

[keen plinth]

what does grade 1 mean here

[limpid spade]

like x^1

[keen plinth]

dimension 1?

[limpid spade]

yes

[keen plinth]

yes

its a real number

[limpid spade]

so lets say w in R3 is x^3

what if we take u=x^-1 and v=x^-2

wait

zeroeth grades are allowed right in R?

[keen plinth]

what does x^3 mean in this case

R^3 is a 3 dimensional vector

with 3 real components (w1, w2, w3)

[limpid spade]

its surjectiv

becase 3>1

[keen plinth]

not necessarily

[limpid spade]

are there lineair transformations that go from lower to higher dimension that are surjective?

[keen plinth]

in finite dimensional i dont believe there are

[limpid spade]

so higher to lower doesnt always implyy surjectivity

[keen plinth]

it does not

say you have the 0-map

f : R^3 -> R where w -> 0.w

then every vector w is sent to 0

[limpid spade]

oh yes

[keen plinth]

the question is can uxv be 0

[limpid spade]

so u here can be zero

yes

[keen plinth]

u and v are nonzero vectors

can uxv be 0

[limpid spade]

ohhh read it as w is non zero LOL

no

only if w is zero

[keen plinth]

why not

|uxv| = |u||v|sinθ is it not

what happens when sinθ=0

[limpid spade]

0

[keen plinth]

so when u and v are parallel

uxv is 0

[limpid spade]

so its only surjective if sin(theta)!=0

[keen plinth]

i believe so

[limpid spade]

nice if it was dot product then theta !=90°

[keen plinth]

im not sure what you mean there

but if you choose u and v such that uxv = 0

[limpid spade]

cos(90°)=0

[keen plinth]

then φ is the 0 map

and its not surjective

[limpid spade]

nice nice will remeber thx

[keen plinth]

|u . v| = |u||v|cosθ would be 0 if θ=90° yes

[limpid spade]

nicee

t!rep @keen plinth

[quasi bramble]

User not found!

Please re-enter a user in this server

Gruba#2374

[limpid spade]

t!rep @keen plinth

[quasi bramble]

Gruba has given @keen plinth a reputation point!

[limpid spade]

.close

[lone heart]

Channel closed

Closed by @limpid spade

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.

[twilit breach]

What continuous function, f(x), satisfies the conditions f(x) + f(1/x) = 4π, and goes through the points (0,0), (1/5.002,π), (1,2π), (5.002,3π), and f(x) -> 4π as x -> Infinity?

I’ve tried a few trial and error things but to no use, and I’m not exactly sure how to even approach this problem.

[lone heart]

@twilit breach Has your question been resolved?

[lone heart]

@twilit breach Has your question been resolved?

[tawny schooner]

https://math.stackexchange.com/questions/2098990/functions-f-that-satisfy-fx-f1-x-rm-constant-for-each-x

[twilit breach]

Thanks

I’ll try to use that

.close

[lone heart]

Channel closed

Closed by @twilit breach

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.

[split glade]

Help Mia

Mua

Plz

lmfao my infinity sign

oh wait

wrong question

[lone heart]

Channel closed

Closed due to the original message being deleted

[split glade]

wait hold up

yeah this one

[lean depot]

And you want to check the answers?

[split glade]

yes please

cuz I just want to make sure im doing it right

I think i am

[lean depot]

Yes the domain, range, and y-intercept are all correct

[split glade]

how about the x?

[lean depot]

But there is a little bit of confusion with the x-intercept, because in fact the line touches the x-axist twice

[split glade]

intercept

[lean depot]

Firstly at (-2, 0) which you noticed

but also at (1, 0)

[split glade]

oh so should I add 2 points?

[lean depot]

I'm not sure what the question was expecting you to do, but perhaps you should mention that (1, 0) is also a point where the curve touches the x-axis.

[split glade]

yeah, so I'll add both

thank you so much for the help

byeeee

.close

oh breh

is it already closed??

.close

@lean depot

its not closing

[lean depot]

No idea mate, I'm not a mod

Glad I could help

[lone heart]

Available help channel!

Send your question here to claim the channel.

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

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

[smoky tangle]

How do you do this

[smoky tangle]

using quadratic equations

ping me when answering

[alpine sable]

do you know how to use the quadratic equation?

[smoky tangle]

?

wdy

wdy

wdym*

@alpine sable

like do you mean irl?

[alpine sable]

huh?

of course in real life

[smoky tangle]

uh

no

like in math yes

how do you solve it

[alpine sable]

what?

dude there is one quadratic equation, do you know how to use it or not?

[smoky tangle]

yes

i know how to solve it

in this case

[alpine sable]

can you write it out here

[smoky tangle]

you need to complete the square

[alpine sable]

so you cant use the formula?

[smoky tangle]

ax + bx + c = 0

wait what is the formula for completing the square again

i forgot that

[alpine sable]

that is not the quadratic formula, this is the standard form of quadratic equation

[smoky tangle]

yes

i know

[alpine sable]

the quadratic formula is a formula that lets you find x

using ax^2+bx+c=0

[smoky tangle]

what

one second

ok yes got it

we do this

1/2 * b

right

[alpine sable]

it says x= -b +/- sqrt(b^2 -4ac) all divided by 2a

[smoky tangle]

then (x + or - half of b)^2 - half of b^2 + c = 0

thats what we di

do

[alpine sable]

im not sure whats that

just plug in a, b and c in this formula

[smoky tangle]

uh ok

wait

bqwegwi this is confusing

[alpine sable]

$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

[smoky tangle]

wait

huh?

thats now how we do it

we do like

[ocean seal]

Jin឵

[smoky tangle]

yeah

pretty much that

one sec

[alpine sable]

plug in the numbers

[smoky tangle]

wait

[alpine sable]

but just a tip, dont plug in the numbers yet

[smoky tangle]

wait

thats now what we do

im confused

[alpine sable]

im not sure what you guys do

[smoky tangle]

for eg

if the equation is

[alpine sable]

but this rule works everytime

you should start using this rule

[smoky tangle]

x^2 + (1/2)x + 1

we write it as

(x + (1/4))^2 - (1/4)^2 + 1

like that

yeah

@alpine sable

[alpine sable]

completing the square?

[smoky tangle]

yes

that

[alpine sable]

sure you can try that

[smoky tangle]

yes

thats what we're supposed to do

[alpine sable]

so you cant use the formula?

[smoky tangle]

the thing im doing

im using that formula

im using it but im not getting the answer in the book