help-39

[midnight haven]

so the answer dne?

[next dove]

can't say for sure

[midnight haven]

or 0/1

the answer does not exists, but it has nothing to do with t=0 is undefined

[midnight haven]

then

[midnight haven]

which jst leads to 0

[midnight haven]

so do i need to factorize

to find out if it dne

[next dove]

the problem here is that the expression is like infty-infty, so you can't say that it DNE {for sure}

you have to do some mathematical work to say anything here

[midnight haven]

i dont get it

so then whats the value of the limit

[cosmic garnet]

its 1

[midnight haven]

how do yk

[cosmic garnet]

the limit you have is of form infinity - infinity

nvm

i read the question wrong

[midnight haven]

oh

[cosmic garnet]

my bad

[midnight haven]

so the value of the limit dne?

[cosmic garnet]

it is infinity-infinity form but the limit isnt 1

[cosmic garnet]

idk

you will have to solve it

[midnight haven]

i got 0

[cosmic garnet]

then 0 is the limit

[midnight haven]

i dont get it

[cosmic garnet]

u dont get what

[midnight haven]

how its solved

[next dove]

how did you got 0?

[cosmic garnet]

u just said u got 0, how did u get it without solving?

[midnight haven]

factorized

[midnight haven]

but im not sure if its correct

[next dove]

can you show the work?

[cosmic garnet]

show your work

[next dove]

or explain how you've done it

[midnight haven]

i cant

ok

i think i did it wrong

the second term overtakes the first term, so it is -infty. t≤0 makes no sense, so this is limit from the right.

[next dove]

better work with t

[cosmic garnet]

thats not how a limit is solved

[midnight haven]

then how is it solved

[cosmic garnet]

also are you sure in the question its t^(2+t) and not t^2 + t

[midnight haven]

yes

[midnight haven]

i dont get it

1/t^2 goes to infty faster than 1/t

so whats the final answer

[cosmic garnet]

- infinity

limit is DNE

[midnight haven]

ok

proving this formally can be done by an estimation

[midnight haven]

how

by replacing 1/t^{2+t} with something nicer

[next dove]

It is more clear to see, if we combine both the fractions.

[next dove]

then we can directly plug in the 0, to figure out the answer

[midnight haven]

i dont get it

can someone solve it

[next dove]

only you can

we can't hand out the answers

but we can lead you to the answer

[midnight haven]

ok

technically we mentioned everything you need, you just need to put them together

so the answer dne because the limit is 0

🤦‍♂️

[torn shell]

just start by combining the fractions 1/t and -1/t^(t+2)

[midnight haven]

ok

the answer is infinity

[torn shell]

no

what you get after combining

[midnight haven]

0

[torn shell]

you can multiply $\frac{1}{t}$ with $\frac{t^{t+1}}{t^{t+1}}$

[jolly parrot]

Hugaxi

[torn shell]

to get common denominator right?

[midnight haven]

i figured it out

the question is written incorrectly

[torn shell]

how so

[midnight haven]

its supposed to be

1/t - 1/t(2+t)

[torn shell]

ok you still have to combine fractions

[midnight haven]

ok i will try now

[torn shell]

maybe factorize t in 2nd fraction

[midnight haven]

i give up

.close

[pearl pond]

Channel closed

Closed by @rustic mango

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 steeple]

Hi, can someone help me how do I ~~crossout ~~ strikethrough text in an equation? I just can't find any way to do it and no guides seems to give a comprehensible explanation on how to do it (functions and buttons are not where they say they are etc).

[pearl pond]

@peak steeple Has your question been resolved?

[pearl pond]

@peak steeple Has your question been resolved?

[nocturne plover]

not sure what you mean

[peak steeple]

You mean to crossout text? I guess it's called "Strikethrough", that word came to mind now.

How do I strikethrough text in an equation in Excel?

I want to strikethrough so that I can show which variables are cancelled out, and how, in my calculations.

[wicked oracle]

Go into format text

Try Ctrl+5

[peak steeple]

Thank you, but that doesn't work in equations unfortunately

[pearl pond]

@peak steeple Has your question been resolved?

[pearl pond]

@peak steeple Has your question been resolved?

[pearl pond]

@peak steeple Has your question been resolved?

[pearl pond]

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.

[arctic carbon]

hello im having issues with the second question of this problem

i'm not exactly sure what it really is asking for

[pearl pond]

@arctic carbon Has your question been resolved?

[plush bramble]

Yea it's a weird question

[arctic carbon]

this is what i got so far with what maybe i think

but honestly i'm not sure

😭

[plush bramble]

Arc length = r * theta where r is radius and theta is the angle in radians

[arctic carbon]

yeah i converted that at the top

[plush bramble]

From theta, find (x, y) using trig

[plush bramble]

Your r isn't correct

[arctic carbon]

alright

[plush bramble]

The question says unit circle

[arctic carbon]

where did it go wrong

oh

1?

standard

[plush bramble]

Yes

[arctic carbon]

ohhh

so i find theta

with the given s and r

theta = 3.7?

but i need to convert to degrees now

[plush bramble]

You don't if you use radians

[arctic carbon]

alright i just didnt know for the question

its very open ended

like this?

[plush bramble]

,calc sin(3.7)

[jolly parrot]

Result:

-0.52983614090849

[plush bramble]

,calc cos(3.7)

[jolly parrot]

Result:

-0.84810003171041

[arctic carbon]

just did it again in my calculator i did something wrong on the calculation

this is the right one

okay so (-0.848..., -0.529...)

will be my coordinate

.close

[pearl pond]

Channel closed

Closed by @arctic carbon

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.

[pearl pond]

@ripe panther Has your question been resolved?

Channel closed

Closed by @ripe panther

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.

[mossy halo]

can someone explain to me how can that polynomial be written as that summation?

[plush bramble]

All polynomials can

[mossy halo]

how?

[plush bramble]

You mean the sum?

[mossy halo]

yea

[plush bramble]

What do you think a polynomial is

[mossy halo]

i know what a polynomial is

[plush bramble]

What is it then

[mossy halo]

an expression with variables and their coefficients

those variables can be of varying degrees

[plush bramble]

That's not very precise

[mossy halo]

i guess what i specifically don't understand is why is Z raised to k there

[plush bramble]

z is the variable

k is the power

The last term being a_n * z^n

[mossy halo]

this was a stupid question... i get it now

i was confused because since z is the root as written there, i thought why would you have z with every coefficient

i think i am lagging?

oh fine

it was my first time seeing this form i got confused

.close

[pearl pond]

Channel closed

Closed by @mossy halo

Use .reopen if this was a mistake.

[pearl pond]

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.

[karmic karma]

i understand the sin(x) and cos(x) but not the 1 and the tangent (like how does it make sense), can someone explain?

[west sapphire]

tan = sin/cos, right?

notice that you have similar triangles

the smaller one has side lengths sin(x) and cos(x)

and the larger one has side lengths ??? and 1

their ratios are the same, so:

[rugged prairie]

Two triangles are similar if the three sides of one of them are proportional to the three corresponding sides of the other.

[west sapphire]

??? / 1 = sin(x) / cos(x)

= tan(x)

hence ??? = tan(x)

[karmic karma]

ok i get that they’re proportional but i dont really understand they rest you’re saying

[west sapphire]

do you agree that the horizontal side of the small triangle is cos(x) and the vertical side is sin(x)?

[karmic karma]

yep

[west sapphire]

ok and the horizontal side of the large triangle is 1, right?

[karmic karma]

wait so how do we know that

is it just because the radius of unit circle is 1

[west sapphire]

because it goes from the origin to the circle

and the circle has radius 1

[rugged prairie]

yup

[karmic karma]

okay

[west sapphire]

ok good

now we want the vertical side of the large triangle

say we call that y

now do the side ratios and set them equal (since they are similar triangles)

for the large triangle we have y/1

for the small one we have sin(x)/cos(x)

set them equal

you get y = sin(x)/cos(x)

so your unknown side is sin(x)/cos(x), which is tan(x)

[karmic karma]

ohh

yea i get it now

[west sapphire]

cool

[karmic karma]

so it won’t matter if its cos/sin right

[west sapphire]

if you do the ratios the other way you mean?

[rugged prairie]

you have to equal to 1/y then

[karmic karma]

👍

thanks

.close

[pearl pond]

Channel closed

Closed by @karmic karma

Use .reopen if this was a mistake.

[pearl pond]

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.

[paper terrace]

Hey

[paper terrace]

Im trying to resolve this

And i get to this:

The problem is that the book, says that the unique solution is 3

But even testing the equation with the gives me a bad result:

okay nvm i did calculate bad

[cold field]

Look again at what you did from the second to last to the final line.

[paper terrace]

with 3 its okay

but with the other result is strange

[paper terrace]

mmm

what do you mean?

[cold field]

I believe that there is a mistake in that step.

[paper terrace]

In the second step?

[cold field]

Oh never mind

[paper terrace]

Applying the discriminant rule, I do get D = 0, so there only exists one solution

But why do I get 21/4??

[next dove]

The act of squaring both sides produce that extraneous root

[paper terrace]

And how do I solve it without squaring both sides?

How do I get that radical out?

[next dove]

I don't think there is any other easier method than solving by your way

[paper terrace]

So everytime I resolve a quadratic, I have to apply the discriminant rule, and based on that, always check the results?

[next dove]

erm yeah ig
or you can just plug the root in original equation to see if it satisfies it or not

[paper terrace]

wdym?

[next dove]

like substitute 21/4 in the original equation

and compare the both left and right hand sides

[paper terrace]

yeah, that's what I did, and It doesn't satisfy so that's why I came here😂

Okay, so always I do a quadratic I have to check the solutions

right?

[next dove]

whenever you square both sides in any equation, yes

[paper terrace]

Okay

Thank you very much

.close

[pearl pond]

Channel closed

Closed by @paper terrace

Use .reopen if this was a mistake.

[pearl pond]

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.

[mossy halo]

does this seem correct?

[pearl pond]

@mossy halo Has your question been resolved?

Channel closed

Closed by @mossy halo

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.

[loud juniper]

Can anyone help me from here?

G^-1 is the inverse of the function g(x)

[rough forge]

g^-1(e^x) = t
e^x = g(t)
e^x = g' dt/dx
dx = g'/e^x dt

[loud juniper]

Wait a second

So you wrote that g^-1 function as t?

[rough forge]

I subbed this yeah cause I dont see how to get g^-1 anyway

[loud juniper]

Soo

I go back to the original integral

And write g^-1(e^x) as t

And the derivative of it

[rough forge]

I do $g(g^{-1}(e^x)) = e^x = g(t)$ and take the derivative of that instead

[jolly parrot]

bacc

[rough forge]

,, \frac{\dd}{\dd x}e^x = \frac{\dd g}{\dd t} \cdot \frac{\dd t}{\dd x}

[loud juniper]

My brain is not braining

[jolly parrot]

bacc

[rough forge]

One very crucial property of inverse functions is $$f(f^{-1}(x)) = x = f^{-1}(f(x))$$

[jolly parrot]

bacc

[loud juniper]

I Didn't know that one

[rough forge]

what

[loud juniper]

That property

We are barely taught anything for the inverse function

[rough forge]

Well that's bad

[loud juniper]

So basically I can write e^x as g(g^-1(e^x))?

[rough forge]

yes

[loud juniper]

;rotate

.rotate

,rotate

[rough forge]

,, \int_{e^0 = g(t)}^{2e = g(t)} t \cdot e^x \cdot \frac{g'(t)}{e^x} : \dd t

[jolly parrot]

bacc

[rough forge]

bounds were from 0 to ln(2e) so we need to change them in terms of t

[loud juniper]

Got it

So you wrote

G^-1(e^x) as t

[rough forge]

yes

[loud juniper]

And the derivate of g^-1(e^x) is g'(g^-1(e^x))

[rough forge]

no

or how did you get that

I know there is such rule

[loud juniper]

Yep

[rough forge]

But we dont want it cause it involves g^(-1) and we simply cannot use it because we cannot calculate it algebraically

[loud juniper]

Got it

[rough forge]

Let
\begin{align*}
g^{-1}(e^x) &= t \
\Leftrightarrow g(g^{-1}(e^x)) &= g(t) \
\Leftrightarrow e^x &= g(t) \
\end{align*}
Now you differentiate both sides and get $$ \frac{\dd}{\dd x}e^x = \frac{\dd g}{\dd t} \cdot \frac{\dd t}{\dd x}$$
which is basically $$e^x = g'(t) \cdot \frac{\dd t}{\dd x} \Leftrightarrow \dd x = \frac{g'(t)}{e^x} : \dd t$$

[jolly parrot]

bacc

[rough forge]

We can work with g'(t)

e^x gets cancelled nicely

Now we only need to also change the bounds and that's it

[loud juniper]

How did you get d/dx e^x? Sorry we aren't really taught this

[rough forge]

Differentiating both sides wrt. $x$ means we apply the differential operator $$\frac{\dd}{\dd x} ( : )$$

[jolly parrot]

bacc

[rough forge]

This is basically like implicit differentiation

[loud juniper]

Got it

[rough forge]

,, \frac{\dd}{\dd x} ( g(t) ) = \frac{\dd}{\dd t} ( g(t) ) \cdot \frac{\dd t}{\dd x}

[jolly parrot]

bacc

[rough forge]

That is just the chain rule

t = t(x) is a function of x

[loud juniper]

Alright

So you get in the end t * g(t)

Oh NVM i saw that

My bad

[rough forge]

g'(t) t'

[loud juniper]

And the bounda

Bounds*

How do we modify them? @rough forge

[rough forge]

I actually think we don't

I think we just ignore them and rather resubstitute

after we are done

[pearl pond]

@loud juniper Has your question been resolved?

[loud juniper]

Alright thx

[pearl pond]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[pearl pond]

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.

[errant depot]

to see if i understood, is this correct?

[nimble osprey]

yep

[errant depot]

fire alr thanks

.close

[pearl pond]

Channel closed

Closed by @errant depot

Use .reopen if this was a mistake.

[pearl pond]

Available help channel!

Send your question here to claim the channel.

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

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

[sharp smelt]

So I've solved this

just wanted soln verifeid

I started by dividing the numerator and denominator by (x+2)

to obtain

ykw

(x+2)(x-1)

not just x+2

[rough forge]

exactly

[sharp smelt]

so a=-3

[rough forge]

ok lol

may you explain how you got there?

[autumn fossil]

idt that works

[glacial sequoia]

Note that you need it to be 0/0

[sharp smelt]

yes

polynomial long div

oops

a=3

IHML

[glacial sequoia]

how are you getting these

[autumn fossil]

That works, and will probably give you some insight on how the function looks like, but I think neon tried to suggest a more direct approach

[rough forge]

You wanna make sure x=-2 is also a root of the numerator

[sharp smelt]

well, I get that

but I feel this is more constructive

[sharp smelt]

I know

😭

[glacial sequoia]

Well even if you do use the factor theorem you're gonna use the fact that f(-2) = 0 anyways

[sharp smelt]

well

[glacial sequoia]

Your approach is to long divide and set the remainder to 0 right?

[autumn fossil]

feel free to do the long division thing, but just a tip: if this was on a test, you should just choose the easier approach, unless you are really confident that you have enough time to do the possibly more insightful approach

[sharp smelt]

yup

so (a-3)x+(a-3) is the reminder

[autumn fossil]

I'm pretty sure it's not

you are dividing numerator by (x+2)?

[sharp smelt]

no

by x^2+x-2

[autumn fossil]

I think that it will complicate things even further

[sharp smelt]

it doesn't

,w reminder when (3x^2+tx+t+3) is divided by (x^2+x-2)

[glacial sequoia]

wolfram doesnt like it when parameters

[jolly parrot]

Wolfram Alpha doesn't understand your query!
Perhaps try rephrasing your question?
Click here to refine your query online

Requested by physicsrocks

[glacial sequoia]

,w long divide (3x^2 + ax + a + 3)/(x^2 + x - 2)

[jolly parrot]

Wolfram Alpha doesn't understand your query!
Perhaps try rephrasing your question?
Click here to refine your query online

Requested by neonperseus

[sharp smelt]

where is snow's long div tex

Should I used gpt?

[autumn fossil]

can it even be written nicely

if there are parameters

[sharp smelt]

Yeah

[autumn fossil]

when I think about it, it would probably look ugly

[glacial sequoia]

Just do it straightforward

There's no need to be over the top with it

[sharp smelt]

Oh well

I'll send my working

[autumn fossil]

i just did division by x+2 and it already looks ugly enough

not that much

[sharp smelt]

yeah, that'd bad

[autumn fossil]

but after dividing it by x-1 it will be

[sharp smelt]

Either that or I've forgotten polynomial dvision

[autumn fossil]

I can't even read what's going on tbh

it will have linear remainder probably

[sharp smelt]

I think I've messed up

it does, yeah

[autumn fossil]

this is extreme overcomplication

[sharp smelt]

,w 3x^2-3x-6 factors

ah shit

[jolly parrot]

Results provided by WolframAlpha

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

Requested by physicsrocks

[sharp smelt]

I was right

[sharp smelt]

Here

then I messed up somewhere

[autumn fossil]

um

are you sure

x-2

[sharp smelt]

,w factorise x^2+x-2

[jolly parrot]

Results provided by WolframAlpha

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

Requested by physicsrocks

[sharp smelt]

oh

[jolly parrot]

MæthIsAlwaysRight

[autumn fossil]

this is what I got

[sharp smelt]

oh

I'll do this tomorrow

I think I've forgotten polynomial divison

[autumn fossil]

Btw, i think this path is not a good one to take

[sharp smelt]

oh

[autumn fossil]

even if you had this, how would you continue?

[sharp smelt]

yeah, this makes more sense

subtraction mistake

[autumn fossil]

you are essentially asking for more than you need to here

[sharp smelt]

yeah

[autumn fossil]

if you ask for the remainder to be 0, you are asking for the function to be constant (f(x) = 3)

[sharp smelt]

I'll use the other methof

[autumn fossil]

and it will never be

[sharp smelt]

I'm just dumb

thans

thanks

[autumn fossil]

No, you arent

you are just overcomplicating stuff, even though you are aware of simpler solutions

you should be more lazy sometimes lol

[sharp smelt]

did that while preparing for entrance exams

not doing that again

[sharp smelt]

sort of

long story

.close

[pearl pond]

Channel closed

Closed by @sharp smelt

Use .reopen if this was a mistake.

[autumn fossil]

I meant lazy in sense of looking for simple sols

[pearl pond]

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.

[haughty cosmos]

Anyone help

[haughty cosmos]

I used Pythagoras and it still wrong

2020 squared plus 2000 squared

And square root that I get 2842.6

[pearl pond]

@haughty cosmos Has your question been resolved?

[pearl pond]

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.

[heavy token]

part b

[wet swallow]

[heavy token]

f^-1(x)=sqrt((x+3)/2)

[wet swallow]

Then set it equal to f(x)

[heavy token]

i did and got weird numbers

i havethe working but i dont understand it

want to see it?

[wet swallow]

Ok what did you get

[wet swallow]

Ok

[wet swallow]

Plug in that value into f(x) and f-¹(x)

[heavy token]

i didnt finish it cuz it looked sketchy n gave up

[wet swallow]

Why did you set f(a) =a

[heavy token]

hm?

thats not my working

thats the marking scheme

[heavy token]

tahst what i dont get too

[wet swallow]

You could just do f(x) =f-¹(x)

🤔

[heavy token]

its gives the same answer?

i mean i did that but i got inverse powers

ill try again

[wet swallow]

,w plot -sqrt((x+3)/2) , 2x²-3

[jolly parrot]

Results provided by WolframAlpha

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

Requested by ishigamisenku_

[heavy token]

sorry i attemptyed and i acvtually have no clue what i ended up with

[wet swallow]

Damn

[heavy token]

u tried to equate?

[wet swallow]

Lemme try

,calc 8-24+1+15

[jolly parrot]

Result:

0

[wet swallow]

@heavy token

[heavy token]

thats the ans for a?

@wet swallow

[wet swallow]

Now solve for x

Sub x=-1

And you have the answer

[heavy token]

sorry im confused actually

wait

[wet swallow]

Ok

[pearl pond]

@heavy token Has your question been resolved?

[heavy token]

ill close this, ill continue solving the equation u ended up with

thanks

[wet swallow]

X=-1 is a root

Then you can use polynomial division to get the other factor

And solve for other roots

[heavy token]

ahh yess

tysmm

[wet swallow]

,w plot 8x^4 - 24x^2 -x+15

[jolly parrot]

Results provided by WolframAlpha

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

Requested by ishigamisenku_

[wet swallow]

Then check which values lie in the domain of f and f-¹

[heavy token]

ohh

okay makes sense now 😭

thanks

.close

[pearl pond]

Channel closed

Closed by @heavy token

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.

[safe lance]

I have to find (D) So I found AB then used that length as CD

why am I wrong

[pearl pond]

@safe lance Has your question been resolved?

[obtuse plaza]

Show the orginal question

[pearl pond]

@safe lance Has your question been resolved?

[pearl pond]

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.

[slender lake]

Hello, I am very confident on my answer to question 1, since the third column in matrix A is the only one indicating no change in Z position (matching with rotation T), and the second column in D is the only one indicating no change in Y position (matching S). I did matrix multiplication to solve for ST and TS and assigned them to the corresponding matrices

--
I am not sure if I am missing something with question 2, though, since I originally got TS through computation, and it feels like I am supposed to have a more complex answer to the second question

I might be mistaken, though, and it may just be a straightforward question

[pearl pond]

@slender lake Has your question been resolved?

[slender lake]

<@&286206848099549185>

[pearl pond]

@slender lake Has your question been resolved?

[slender lake]

.close

[pearl pond]

Channel closed

Closed by @slender lake

Use .reopen if this was a mistake.

[pearl pond]

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.

[safe lance]

wrong

[plush bramble]

Do you know how to take screenshots

This is what your question looks like

[pearl pond]

@safe lance Has your question been resolved?

[safe lance]

A parallelogram ABCD has vertices with coordinates A, B and C at (1, 0, 3), (-2,3, 4) and (3,2, -6) respectively. Find the coordinates of the point D.

[pearl pond]

@safe lance Has your question been resolved?

[pearl pond]

@safe lance Has your question been resolved?

[terse tide]

omg, look what you drew!

you drew ABDC not ABCD :p

[pearl pond]

@safe lance Has your question been resolved?

[clear wolf]

AB=(1,0,3)-(-2,3,4)=(-3,3,1)

BC=(-2,3,4)-(3,2,-6)=(-5,1,10)

D=(x,y,z)!

(x,y,z)+AB=C

(x,y,z)-BC=A

[pearl pond]

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.

[hybrid basin]

Hello

[hybrid basin]

I need help finding the domain

.close

[pearl pond]

Channel closed

Closed by @hybrid basin

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.

[lethal vigil]

A clothesline is tied between two poles, 8 m apart. The line
is quite taut and has negligible sag. When a wet shirt with a
mass of 0.8 kg is hung at the middle of the line, the mid -
point is pulled down 8 cm. Find the tension in each half of
the clothesline.

[lethal vigil]

I drew an x-y plane where the clothesline is the x-axis and the y-axis as the middle of the clothesline

<@&286206848099549185>

.close

[pearl pond]

Channel closed

Closed by @lethal vigil

Use .reopen if this was a mistake.

[pearl pond]

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.

[rotund osprey]

can someone get an answer pls

i just dont know if mine is corect

since i dont have answers

[summer gorge]

is the z here a complex number

[rotund osprey]

no

this is only y11 math

[summer gorge]

ok so what do you need to find exactly?

[rotund osprey]

uhm

solve for z

wait i think

perhaps my teacher

wrote it wrong

cos it seems there are no solutions

[west haven]

yea there are none

[rotund osprey]

okok

yeah i think

he made a mistake

oopsie

.close

[pearl pond]

Channel closed

Closed by @rotund osprey

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.

[dark sparrow]

Just looking for a explanation really, this is about probability. Without translating the whole question im just gonna give the numbers and the question itself.

[dark sparrow]

$P(A)=0.1$, $P(B)=0.2$, $P(A\cap B)=0.05$.
What is the probability that the item has exactly one of each error A and B?

[jolly parrot]

Totalani

[dark sparrow]

nevermind I got it, add prob of having A and not B, and prob of having B and not A, togheter

.close

[pearl pond]

Channel closed

Closed by @dark sparrow

Use .reopen if this was a mistake.

[lusty magnet]

Question one. I plugged in the formula and got 10x but did I do that correctly??

[pearl pond]

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.

[lusty magnet]

bruh!

[lusty magnet]

^this btw

[pseudo oxide]

no, try again

technically, slope, yes

but you differentiated incorrectly

[lusty magnet]

ok so what am i supposed to do then

did i use the formula correctly

Idk this is what I did

[pseudo oxide]

last step

how does -4 change to zero

[lusty magnet]

ohh

so the slope would be 10? but the equation is 10x-4?

im still stuck

[pearl pond]

@lusty magnet Has your question been resolved?

Channel closed

Closed by @lusty magnet

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.

[midnight haven]

how do i write this as piecewise function? i'm confused

A school's fair committee wants to sell t-shirts for their school fair. They found a supplier that sells t-shirts for ₱165.00 apiece but can charge ₱15,000 for a bulk order of 100 shirts and ₱120.00 for each excess t-shirts after that. Use a piecewise function to represent the cost in terms of the number of t-shirts purchased.

[tulip kiln]

||/|| 165x, for x < 100
f(x) = { 15000, for x = 100
120x + 15000, for x ≥ 100

do u understand my function 😭

x = no. of t-shirts

[pearl pond]

@midnight haven Has your question been resolved?

Channel closed

Closed by @opaque elk

Use .reopen if this was a mistake.

[pearl pond]

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.

[livid bolt]

How do i do question c

Did i start it right

.close

[pearl pond]

Channel closed

Closed by @livid bolt

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.

[cunning compass]

I need help in findign

[cunning compass]

how do i find a-sub1

in an arithmethic/harmonic sequence

i already have the D ( common difference)

and a4 and a6

what formula should i use in fidning a1? without substracting a4 to a1 to find it

ik an = a1 (n-1)d and all that but what woudl i replace (an) to find (a1)?

[pearl pond]

@cunning compass Has your question been resolved?

[verbal whale]

Substitute n=4 and n=6

This way you have a system of 2 equations in 2 unknown (i.e. d and a1)

[cunning compass]

oh

will it be the same outcome if i use either equation?

[verbal whale]

You only need the formula $a_n = a_1 + (n - 1)d$

[jolly parrot]

Alberto Z.

[verbal whale]

Forst you sub n=4, and this is an equation

The other equation is the one you get subbing n=6

[cunning compass]

oh

so like

a_4 = a_1 + ( 6-1) d

or

a_4 = a_1 + (4-1)d

a_6=a_1 (6-1)d

.close

[pearl pond]

Channel closed

Closed by @cunning compass

Use .reopen if this was a mistake.

[pearl pond]

Available help channel!

Send your question here to claim the channel.

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

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

[cerulean quail]

Hello, I need some help with interpreting a multivariable integral

Consider an arbitrary function, F(x)=y. A way of interpreting the average of this function F, is to multiply F by x and find the integral of that.

But then, consider the arbitrary multivariable function, F(x-y)=z. If I were to use the same method, (mutliply F by x, and find the integral) would that be interpreted correctly as the average of F? If not, then what can it be interpreted as?

Does a method where I multiply F by both x and y and find the double integral of that, give the average of F?

[pearl pond]

@cerulean quail Has your question been resolved?

[cerulean quail]

No

<@&286206848099549185>

[zenith pond]

Mhm! a double integral with F(x-y) and its bounds would give u the average of F
also a triple integral with F(x,y,z) bounds would give u the average of it
it’s basically the same principle
but to get the average of F, u will have to take every x, y, z variable from its lower bound to its upper bound and put them into the function F to get the final result
it’s basically taking the sum of everything you get from integrating the F(x,y,z) under every condition

[cerulean quail]

I suspected that, thank you. However, in real life, my function really is the integral of F(x-y)x. Is there any interpretation of that? Actually, maybe I could use integration by parts, or something.

That problem, is that I cant introduce y through the integral. I can introduce dy though.

[zenith pond]

If the function is already the integral of F(x-y)x, then its not the average of F, the average of F is just the regular F with no x variable in it

yeah, then that doesn’t measure the average of F because you’re gonna integrate F under condition of x-y
the same way if you said F(y-x) the average would change)
i am a bit confused, what do u want to know about this F? are u looking for the area under its curve?
because F is undefined and the way its gonna be used depends on what u want to know: the average of F or the area or smth else

[cerulean quail]

Yeah, I just realized I have no definable bound for y anyway.

[zenith pond]

if u are looking for the average of F, then u need a function F without any variables, just a simple plain normal F
because when u integrate F, whether F is F(x-y) or F(y-x), it’s gonna be the same result
but the average is going to be different

[cerulean quail]

I was trying to simplify some stuff, and that integral came up. Its the only thing that I didn’t know how to further simplify, but it looked like taking an average.

I thought that the average of a function, F(x)=y, is the integral of F(x)•x.

[lilac jackal]

in the single variable case, theres another way to interpret integral xf. its one of the factors used to find the “center of mass” if f represents density. more specifically x_c = integral xf/integral f

the center of mass formula extends to multivariable

[cerulean quail]

So another way of understanding an average is interpreting it as density? The thing I was doing irl more resembles density than averaging, so, hmmm.

[pearl pond]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[lilac jackal]

.reopen

[pearl pond]

✅

[lilac jackal]

here M=integral f

[lilac jackal]

not density directly but smth proportional to center of mass

[cerulean quail]

Wow, that’s very interesting. My thing is a coordinate. Yeah, its part of the equation to a center of mass.

Not actually irl, i meant that I see it that way now

Thank you a lot

[lilac jackal]

no prob!

[cerulean quail]

I remember learning this in calculus years ago, and never really paid much attention to centers of mass. I’m glad it finally was relevant to something!

My question is resolved.

.close

.close

[pearl pond]

Channel closed

Closed by @cerulean quail

Use .reopen if this was a mistake.

[pearl pond]

Available help channel!

Send your question here to claim the channel.

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

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

[sharp smelt]

So as $v_1,v_2,v_3,v_4$ form a basis of $V$ . They are all linearly independent. Thus ,in $U$, $v_1,v_2$, are LI too.

[jolly parrot]

Veni, vidi, perii

[sharp smelt]

Now every element in $V$ is spanned by $v_1,v_2,v_3,v_4$. If there exists a subspace of V that doesn't have $v_3,v_4$ . It won't contain any scalar multiple of $v_3,v_4 $ either, and thus none of the vectors spanned by them. . Thus, it will contain all vectors of the form $av_1+bv_2$.Thus $U$ must be spanned by $v_1, v_2$.

[jolly parrot]

Veni, vidi, perii

[cursive wraith]

and thus none of the vectors spanned by them
why?

[sharp smelt]

if it doesn't contain v_3,v_4. It can't contain any of the vectors spanned by them

[cursive wraith]

uh

[sharp smelt]

I have to prove that now

don't I

[cursive wraith]

that's not how it works

"if v and w in U, then av+bw in U"

that's U being a subspace of V

[sharp smelt]

yes

[cursive wraith]

A => B

[sharp smelt]

I know

[cursive wraith]

and you're telling me

not(A) => not(B)

[sharp smelt]

it should be not B \implies not (A)

[cursive wraith]

well yeah

but that's not what we're interested in either

[cursive wraith]

does this have a lot of chance of being true everytime?

[sharp smelt]

I mean it's the contrapostive

no?

if that's false

[cursive wraith]

the contrapositive is this

[sharp smelt]

no

[cursive wraith]

the reasoning you used is this

[sharp smelt]

oops

[cursive wraith]

alright so

if your reasoning doesn't work everytime

maybe it's worth looking for an example of

where it doesn't work

[sharp smelt]

I mean I can just identity what not B and Not A are

[cursive wraith]

you've asserted

"v3 and v4 are not in U, thus no linear combination of v3 and v4 is in U"

first of all that's false with vector 0

but it's not a counterexample we're looking for

can you find an example for U

such that

you do have a linear combination of v3 and v4 in U

but neither are in U

(hint : think U = span(v1,v2,...))

[sharp smelt]

Other than the 0 vector, no

[sharp smelt]

OK. I'll prove the contrapositive

If $v_1,v_2$ aren't the basis of U. Then $u_1 \notin U \vee u_2 \notin U \vee u_3\in U \vee u_4 \in U$

Is this right?

[cursive wraith]

wait what

the contrapositive is if (v1,v2) not a basis then v1 not in U or v2 not in U or v3 in U or v4 in U

[sharp smelt]

ah

[jolly parrot]

Veni, vidi, perii

[cursive wraith]

it's still gonna be hard to prove something false

go back to the original statement

[sharp smelt]

okat

[cursive wraith]

and try to find a counterexample

[sharp smelt]

okat

[cursive wraith]

so U such that

[sharp smelt]

so there is a counter example

[cursive wraith]

v1,v2 in U

v3,v4 not in U

and (v1,v2) not a basis

bruh you spoiling

[sharp smelt]

I mean every spanning list can be reduced to a bases

[cursive wraith]

yeah but we don't know a spanning list of U yet

we do know a LI family of U tho

first of all

what's the dimension of the U we're looking for

[sharp smelt]

My point though is that u_1,u_2,u_3,u_4 are LI

[cursive wraith]

LI in V

but in U?

[sharp smelt]

yes

and thus u_1,u_2 must be LI in U too

[cursive wraith]

yes

[cursive wraith]

.

[sharp smelt]

2?

[cursive wraith]

if it were 2

then (v1,v2) is LI in U

and has two vectors

so it would be...

[sharp smelt]

LI?

[cursive wraith]

already said

you have a LI family with exactly dim(U) number of vectors

[sharp smelt]

I don't know any properties of dim

[cursive wraith]

you have 2 vectors in U that make a linearly independent family

[sharp smelt]

so v_1,v_2 is a basis

[cursive wraith]

it would make a basis

so not what we're looking for

[sharp smelt]

I don't follow

doesn't this prove that v_1,v_2 form a basis

[cursive wraith]

when dim(U) = 2

[sharp smelt]

yes

[cursive wraith]

did we say dim(U) needed to be 2?

[sharp smelt]

no

[cursive wraith]

alright

so we have to check if it's possible for other dimension values

what are the other possible values for dim(U)

[sharp smelt]

3 and 4

[cursive wraith]

alright

but what does dim(U) = 4 imply

[sharp smelt]

These don't form a basis

[cursive wraith]

again you didn't get the point

we're trying to find a counterexample

so for instances where (v1,v2) is not a basis

given v1 and v2 in U

and neither v3 nor v4 in U

if dim(U) = 4, is that possible

[sharp smelt]

I mean it would prob be (v_1,v_2,v_1,v_2) for instance

[cursive wraith]

(v_1,v_2,v_1,v_2) is a basis now?

[sharp smelt]

no

[cursive wraith]

ok

[terse tide]

ooo, me likes this exo, me joins

[cursive wraith]

what dim is V

[sharp smelt]

4

[cursive wraith]

so U and V are the same dim (same size)

[sharp smelt]

yes

[cursive wraith]

and yet U is a subspace of V

so do we have a lot of choices for U?

[sharp smelt]

How isn't dim(U) 2 though

I'm lost

[cursive wraith]

?

again

we're trying to establish that it's possible

[terse tide]

if dim(U)=4 then U=V but V contains v3 and v4, so U contains v3 and v4

cant be

[sharp smelt]

Yeah, so dim(U)=2

[terse tide]

3

[cursive wraith]

nuh uh

we've shown dim 4 is impossible

but that doesn't mean dim 2 is the only possibility

[merry carbon]

Why do the two vectors that are linearly independent in U span U, then?

[sharp smelt]

dim(3) would mean that the basis are either (v_1,v_2,v_3) or (v_1,v_2,v_4)

[cursive wraith]

why?

[sharp smelt]

but that's not possible

again

so dim(U)=2

[cursive wraith]

can't I complete (v1,v2) into a basis that doesn't contain v3 or v4?

for example

if you combined v3 and v4

and only put their combination as third vector of a basis...

[autumn fossil]

Btw, try not using "the basis", unless you are talking about one specific established basis

[sharp smelt]

then v_4+v_3 would lie in U

but v_4, v_3 don't

[cursive wraith]

?

we're combining v3 and v4

not v1 and v3

make U have a basis (v1,v2, combination of v3 and v4)

for example... v3 + v4

[sharp smelt]

yeah got it

Thanks

[merry carbon]

Remember that in itself doesn’t really mean much, considering…

[merry carbon]

…here

[sharp smelt]

I see

okay

thanks

.close

[pearl pond]

Channel closed

Closed by @sharp smelt

Use .reopen if this was a mistake.

[pearl pond]

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.

[iron shore]

for part C) would the answer be China or India? China increases a lot (about from 1 to 11) but India goes from like (0 to 2.5)

[iron shore]

and for part D) do I add together (all others, China, and the US)?? or do I not include "all others"

[pearl pond]

@iron shore Has your question been resolved?

[pearl pond]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[iron shore]

.reopen

[pearl pond]

✅

@iron shore Has your question been resolved?

[iron shore]

.close

[pearl pond]

Channel closed

Closed by @iron shore

Use .reopen if this was a mistake.

[pearl pond]

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.

[lethal vigil]

How do I decide which expression is meaningful?

[west sapphire]

i assume these are vectors and that . means dot product?

[lethal vigil]

yes

[west sapphire]

any thoughts about any of them?

[lethal vigil]

I think all of them are meaningful

what's the criteria for being meaningful?

[west sapphire]

sadly there are several that are not

remember that you can only take a dot product of two vectors

you can't take a dot product of a scalar and a vector

[autumn fossil]

for example:
scalar product must be applied on a real number and a vector
dot product must be applied only on 2 vectors
vector addition must be applied only on 2 vectors

[lethal vigil]

ah ...ok

so only a and f are meaningless?

[west sapphire]

there's another one that is invalid for a different reason

can you add a scalar and a vector?

[lethal vigil]

no

ah so it's a, e, and f?

[west sapphire]

yea

[lethal vigil]

thanks for your help

.close

[pearl pond]

Channel closed

Closed by @lethal vigil

Use .reopen if this was a mistake.

[pearl pond]

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.

[exotic violet]

a = v* dv/ds
so does that mean a = 5 sin 3x * 15cos 3x
and idk what to do next with that

<@&286206848099549185>

[cedar bough]

shouldn't that be dv/dx, since i see no s

[exotic violet]

yeah i thought so too-

but idk im confused with this one

[cedar bough]

use double angle identity of sine

and since there is no 2 in the coefficient, jus diovide by 2

[exotic violet]

oh so a=(5sin(3x)).(15cos(3x))=75sin(3x). cos(3x)

[cedar bough]

now just convert to only sine

using double angles

[exotic violet]

a= 75/2 sin(6x)

and since x=2

so do i do

a =75/2 sin(6*2)

[cedar bough]

ueah

[exotic violet]

alright thank u so much

fr

[cedar bough]

now if you want then you can use calculator to find sin(12)

yw

[exotic violet]

yess

[cedar bough]

and that's about it

[exotic violet]

thanks a lot

[cedar bough]

sis jus close this

[exotic violet]

.close

[pearl pond]

Channel closed

Closed by @exotic violet

Use .reopen if this was a mistake.

[pearl pond]

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.

[tiny wadi]

Help with part a plzzz

[pearl pond]

@tiny wadi Has your question been resolved?

[pearl pond]

@tiny wadi Has your question been resolved?

[tiny wadi]

nvm I've done part a

could anyone help me with part c

<@&286206848099549185>

.close

[pearl pond]

Channel closed

Closed by @tiny wadi

Use .reopen if this was a mistake.

[tiny wadi]

.reopen

[pearl pond]

✅

[tiny wadi]

<@&286206848099549185>

. close

.close

[pearl pond]

Channel closed

Closed by @tiny wadi

Use .reopen if this was a mistake.

[pearl pond]

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.

[strange grail]

May I acquire some assistance on my physics homework I just started speed and velocity but we had substitute and he barely went into detail and just gave us worksheet

[strange grail]

The question is

It's the third question

[pearl pond]

@strange grail Has your question been resolved?

Channel closed

Closed by @strange grail

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.

[elder plaza]

I was wondering if I did this problem correctly.

A steel rod of length L cm has variable cross-section area A(x) cm^2, where a is measured in centimeters from one end of the rod. The rod has uniform mass density p g/cm^3. (a) Using Riemann sums, derive an integral for the total mass of the rod M. (hint: divide the rod into n slices, find the mass of each slice, ...) (b) Compute the total mass for the case L = 25 cm, A(x) = (1+sqrt(x)) cm^2, p = 8 g /cm^3. Express M in Kilograms

[pearl pond]

@elder plaza Has your question been resolved?

[pearl pond]

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.

[fossil drum]

can someone break down this question for me

[fossil drum]

I'm not sure what its asking

I looked up what cummaltive sum is

and it seems to be an array where each element is the sum of the previous elements

but is says a die is being tossed repeatedly

does that mean its being tossed an infinite amount of times?

oh

hmm

I see what its getting at now

[west sapphire]

i guess it is tossed until you either reach or exceed 20

in any case, a finite number of times

[fossil drum]

yeah thats what I was thinking also

[pearl pond]

@fossil drum Has your question been resolved?

[fossil drum]

I was able to write the code thanks'

.close

[pearl pond]

Channel closed

Closed by @fossil drum

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.

[real gyro]

how to do this?

[real gyro]

A/(x-2) + B/(x-2)^2 + C/(x+3) + D/(x+3)^2
what to do after this

[lost sigil]

this equation that you wrote equals the Numerator

and try to get how much does A,B,C,D equals

[pearl pond]

@real gyro Has your question been resolved?

Channel closed

Closed by @real gyro

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.

[lethal vigil]

How would I tell if two vectors are parallel?

[lethal vigil]

Is there any way that's related to the dot product?
Because cross product is in the next chapter

And if the dot product is not equal to the product of their magnitudes, would this mean that the vectors are not parallel aka either orthogonal or neither?

.close

[pearl pond]

Channel closed

Closed by @lethal vigil

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.

[candid bone]

How is this wrong

[simple vapor]

So the >=3 is inclusive, which means that exactly at 3 or more you'd use the bottom formula

4x - 12

4(3) - 12 = 0

[tardy oak]

uh no it's asking for g'(3) not g(3)

[dreamy wind]

The derivatives at both ends don’t match

U have to evaluate the derivative of both functions

[simple vapor]

oh I see, my bad

[dreamy wind]

From the left the derivative is 1

From the right it’s 4

Therefore dne

[candid bone]

Oh

U mean the limits from both sides when x =3?

[pearl pond]

@candid bone Has your question been resolved?

[pearl pond]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[pearl pond]

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.

[tranquil badger]

Please format your response and provide clear thought-out explanations.


Q: When graphing a quadratic, what numbers would be assigned to the X and Y values? Or do both values receive all given ammounts (x being both x and y)?

1. I am confused regarding how this is equivalent. If quadratics are functions that apply various operations such as addition to an input value of X and the goal is to find the zeroes to describe/graph their behavior on a 2d plane via x and y coordinates then how is it that you can remove some of the operations (subtracting c/a) if they were apart of the behavior they were trying to graph?

Additional Prompt: Please describe how one would come to the conclusions given and what the context or preliminary concepts are to understanding the explanation.```

[tranquil badger]

▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬

[slender viper]

(Strictly speaking, quadratics are not functions. Quadratic functions are obtained when one applies the evaluation map to the quadratic. This side note is emphasized when working with polynomial rings.)

I'm not sure what you mean by "removing" an operation. It seems that it could be that you are plotting it incrementally from an easier case to transform it to the general case.

[tranquil badger]

thinking:```

[slender viper]

I'm also not sure why you need to talk in terms of code blocks.

The extra syntax highlighting may be distracting.

[tranquil badger]

I don't talk that way all the time, and it's because it looks more professional.

Alright, I may remove the "Lua" modifier as to remove the syntax.

[tranquil badger]

1. Would you be willing to further explain what an evaluation map is along with what polynomial rings are?

2. By function I just meant that the behavior of quadratics appears to work in that you give inputs and receive outputs and the goal is to achieve a result of zero to graph the behavior of it (parabola).```

[sudden badger]

lol

[slender viper]

<@&268886789983436800> spam

[tranquil badger]

https://tenor.com/view/the-pharaohs-curse-gif-14161134732063804368