help-23

[prisma wren]

The most you can do in terms of simplifying is make the exponent positive by bringing (t+3) to the denominator

[karmic zealot]

And that would become sqrt(t + 3) right

But there’s still the 1/2 that I put in front

[prisma wren]

Yeah, but the sqrt(t+3) would be in the denominator

[karmic zealot]

I’ll write it down one sec

Would this be right

[prisma wren]

no

you multiplied both sides by sqrt(t+3)

[karmic zealot]

Oh do I just separate it in another fraction?

[prisma wren]

I wouldn't do anything

you generally don't need to simplify it too much

just get the derivative right and move on

[karmic zealot]

Well my teacher wants us to simplify it

and stuff

[prisma wren]

There are a billion ways to simplify, generally combining constants/negative signs and getting rid of negative exponents is sufficient

[karmic zealot]

I would love to keep it like that but the answer in the text book looks really simplified

[prisma wren]

Does the textbook have a sqrt(t+3) on the denominator?

[karmic zealot]

2 sqrt(t + 3)^3

[prisma wren]

give me a second

[karmic zealot]

Here’s the answer

[prisma wren]

Either the derivative is wrong or the answer key is

simplifyig gives you 38t^3 and +1, not -1.

[karmic zealot]

What did you do?

[prisma wren]

multiply both sides by 2sqrt(t+3) and then combine'

[karmic zealot]

Do you still have what you’ve written down

Maybe we could see if there’s a mistake or something

[prisma wren]

found it

you made a mistake on the quotient rule

the sign seperating u'v and uv' is supposed to be a (-), not (+)

[karmic zealot]

Oh right

But I’m still confused what could I do after that

[prisma wren]

lemme write it out

[karmic zealot]

Alright thanks man

I usually understand when it’s written down

[karmic zealot]

Why did you multiply 2 sqrt(t + 3)?

Is it so you can get rid of it that fraction in the numerator?

[prisma wren]

yes

[karmic zealot]

Ohhhhh

How did you get 36?

[prisma wren]

3x6x2

When we multiplied both sides by 2sqrt(t+3), we distributed it over the - sign on the numerator

Like a(b-c) = ab-ac

[karmic zealot]

Ohhhhhh

But wouldn’t you have to multiply it with the sqrt(t+3) as well

[prisma wren]

I did

Try to figure out what that changed

[karmic zealot]

I noticed that the sqrt(t+3) isn’t there anymore

[prisma wren]

Yeah, it became a t+E

t+3

[karmic zealot]

Yup

[prisma wren]

Since sqrt(t+3) * sqrt(t+3) = t+3

[karmic zealot]

Yes

Oh so the 2 multiplied with the 6t^2 ?

[prisma wren]

Yeah I just multiplied all the constants together and moved them to the left

[karmic zealot]

Ohhhhh okay

Okay you made it look so simple 😭

thank you so much man

[safe radish]

@karmic zealot Has your question been resolved?

Channel closed

Closed by @karmic zealot

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.

[hazy valve]

I’m unsure where I’ve gone wrong. My question is what are the transformations, ie question 4

[sage tulip]

,rotate

,rotate

[safe radish]

@hazy valve Has your question been resolved?

[hazy valve]

.close

[safe radish]

Channel closed

Closed by @hazy valve

Use .reopen if this was a mistake.

[safe radish]

Available help channel!

Send your question here to claim the channel.

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

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

Channel closed

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

[safe radish]

Available help channel!

Send your question here to claim the channel.

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

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

[solemn ridge]

Hello, I need help in Linear Algebra 2.
I have a test coming up and theres some theorems I need to prove for the test.
For instance:
For all A, matrix of size nxn, and a polynomial c(x):
c(A) = 0 => m_A(x) | c(x)
Such that m_A(x) is the minimal polynomial.
I dont really know how to do that, could someone help

[lean otter]

Someone help here please: #help-29 .

[safe radish]

@solemn ridge Has your question been resolved?

[vast obsidian]

Assume the opposite. Let p(x) = q(x)*m(x) + r(x) with deg r(x) <= deg m(x). We basically do long division by the minimal polynomial with q(x) as the quotient and a non vanishing rest r(x)

Now try to get a contradiction from it

[solemn ridge]

I understand. We got r(A) = 0, in contradiction to the fact the m_A is minimal. Thank you!

[vast obsidian]

That was quick!

Well done

[solemn ridge]

Thank you!
I have another theorem that I couldnt prove.
If T is a Linear map on C, then:
forall u: <Tu, u> = 0 iff T=0
I thought about doing something like:

<T(u+v), u+v> = <Tu, v> + <Tv, u> = 0
And then maybe try for i*u and sat something like
<Tv, iu> + <Tiu, v> = 0
But I dont really know how to continue

Oh wait if I say that this implies:

<Tv, iu> = -i<Tu,v>
<Tv, u> = <Tu, v>
Then if I would say for v = Tu
0 = <TTu, Tu> = <Tu, Tu>
=> Tu = 0

I got it

Thank you!

[safe radish]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[safe radish]

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.

[lunar lagoon]

Sorry that this is messy but can someone help me out on what I did that is wrong please

[lunar lagoon]

.close

[safe radish]

Channel closed

Closed by @lunar lagoon

Use .reopen if this was a mistake.

[safe radish]

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.

[analog lake]

help

[warped tulip]

9

.close

[split ether]

,w 3+3

[flat frigate]

Results provided by WolframAlpha

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

Requested by alonelybean

[split ether]

.close

[safe radish]

Channel closed

Closed by @split ether

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.

[mental imp]

hello, let's say i have a graph of the form y = 1/x

[mental imp]

just the positive part

is there a way for me to change the axes so that it becomes a straight line y = mx + b

like a log plot but not a log plot

[dull sequoia]

you could plot it against 1/x

plotting against log x is nothing but a function of x

1/x is also a function of x

[mental imp]

oh

thanks

[dull sequoia]

but it'll break at 0

[mental imp]

wait

that's the asymptote right

[dull sequoia]

yes

[mental imp]

ok thank you

[dull sequoia]

it'll break because it wasn't in the original function

so after resizing the axis it still wont exist

[mental imp]

got it

thanks for your help

.close

[safe radish]

Channel closed

Closed by @mental imp

Use .reopen if this was a mistake.

[safe radish]

Available help channel!

Send your question here to claim the channel.

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

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

[foggy cloud]

help to solve 14 please

[summer crow]

ok so given that x = 5i is a root, which other root do we instantly know

[foggy cloud]

1?

[summer crow]

no

[foggy cloud]

which method easy to solve this?

because im confused when solving with synthetic division

[mortal arrow]

Is there a proof for that thing btw

[shadow tapir]

notice how you can do factoring by grouping

[summer crow]

I can think of two possible methods, you either first state some of the roots and factorise/algebraic division to find the remaining factor of f(x) to find the root. Or you use the relationship between the sum/product of roots and coefficients of polynomial

[foggy cloud]

yes

i can do that

[shadow tapir]

what do you end up with

[summer crow]

proof of that if we know that x = 5i is a root then x = -5i is another root?

[mortal arrow]

Yes

Like idk why that should make sense

[prisma shuttle]

they come from a quadratic term

[mortal arrow]

so

[foggy cloud]

(x-1) (x^2+25)

[shadow tapir]

correct

you just gonna need to equate each factor to 0

[foggy cloud]

so what the point of zero : 5i

in this question?

[prisma shuttle]

Im guessing it lets you create the (x^2+25) root if you wanted to use long division to get (x-1)

[foggy cloud]

ok

[shadow tapir]

most likely that ye

[summer crow]

sometimes it's not so easy to spot the factorisation of f(x), and x = 5i tells you the factor (x^2+25) and makes things easier

[foggy cloud]

alright

[prisma shuttle]

yeah the imaginary roots being given helps a lot more with quartics and ones after it

since factoring those is horrid

[foggy cloud]

thanks guys

.close

[safe radish]

Channel closed

Closed by @foggy cloud

Use .reopen if this was a mistake.

[safe radish]

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.

[thorny lodge]

how are these two the same

[summer crow]

can you factor out 12 and 48 from the surd?

[thorny lodge]

dont understand

[summer crow]

ok I'll show you an example, see if you get it. sqrt(20) = sqrt(4 x 5) = sqrt(4) x sqrt(5) = 2 x sqrt(5). Does this make sense

[thorny lodge]

but how we getting 36

[summer crow]

well given the example I've shown you, can you simplify sqrt(12)?

[thorny lodge]

2* sqrt(3)?

[summer crow]

yup

do the same for sqrt(48)?

[thorny lodge]

16*sqrt (3)

[summer crow]

nope, slight mistake there

48 = 16 * 3

so sqrt(48) = sqrt(16) * sqrt(3)

which is?

[thorny lodge]

4* sqrt (3)

[summer crow]

now add sqrt(12) and sqrt(48)

[thorny lodge]

thx

[summer crow]

np

[thorny lodge]

.close

[safe radish]

Channel closed

Closed by @thorny lodge

Use .reopen if this was a mistake.

[safe radish]

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.

[fickle trail]

any issues with my description here?

co-linear has a span of R^1
co-planar has a span of R^2

the red arrow indicates "breaking out" of co-linear and co-planar with a single linearly independent vector

all it needs is one vector to give a co-linear system a full span of R^2

and all it needs is one vector to give a co-planar system a full span of R^3

[safe radish]

@fickle trail Has your question been resolved?

[peak estuary]

you are confusing "1-dimensional span" with "span of R^1"

vectors which live in R^2 or R^3 can never span R^1

vectors in R^3 can span a plane (aka a 2-dimensional space) but can never span R^2

[fickle trail]

oh good catch on the wording

that's right

[fickle trail]

do we call that a sub span instead?

"1 dimensional span" vs "span of R^1", can easily get these confused

[peak estuary]

we dont really call anything a sub span. I dont know what you want to mean with that

[fickle trail]

OK

[peak estuary]

the span will be a subspace of whatever space you are in

[fickle trail]

span just refers to linearly independence

[peak estuary]

no

[fickle trail]

wait lemme rephrase that

span just refers to vectors and if they are dependent or independent. this will indicate what areas they can reach, so we call that the span

[peak estuary]

the span of some vectors is the set of all linear combinations of those vectors

[fickle trail]

having one extra vector going rogue, as i have indicated with the red arrows, can reach anywhere in a higher dimension

when i say rogue i mean linear independence in a meaningful way where the other vectors can reproduce it somehow

wait maybe that's wrong, to say "anywhere"

it's any distance in a straight line, isn't it

we can't change the angle of that line

but we say that it fully spans because of that red arrow
whereas before it was limited to a smaller span as each vector was parallel to one another in the same direction

dang this stuff is hard to explain, words blend into one another, mumble jumble, gotta be super careful about wording

[fickle trail]

if we don't say sub span
do we say full span?
and not full span?

or the R value indicates that
spans R^3
spans R^2

[peak estuary]

what

[fickle trail]

based on the vectors provided

let's say 3 entries each vector

we know it's R^3

but span is only R^2 because of parallel lines

[peak estuary]

the span of vectors that are in R^3 is NEVER R^2

[fickle trail]

i don't understand, in my example above I stated that

[peak estuary]

the span can be a 2-dimensional plane, but it can never be R^2

[fickle trail]

R2 span is co-planar

top left example

[peak estuary]

you mean 2-dimensional

saying R^2 is wrong

[fickle trail]

but this is correct:

the way this is worded

it's exactly word for word how the instructor said it

with the a, b example

[peak estuary]

yes thats correct. but in that example a and b live in R^2

so at least in theory they could span R^2

but if they live in R^3 they can never span R^2

no matter whether they are linearly independent or not

[fickle trail]

so what's the point of span? if it's just gonna equal the same as the dimension

even co-planar is span of R^3

[uncut skiff]

the plane is a subspace of R^3

and not the entire R^3

[fickle trail]

but i'm talking about span

not subspace

[peak estuary]

a span of things by definition is a subspace

[fickle trail]

when we say span = R^2 or span = R^3

[uncut skiff]

the span is a plane in R^3 but not R^3

[peak estuary]

a span of things is a set. a dimension is a number

they cant be the same

[fickle trail]

confused right now

so the way i worded it is technically incorrect

lemme reword to see if i get it

one sec

[uncut skiff]

well i mean

[peak estuary]

it doesnt span R^3

it spans a subspace of R^3

that subspace is 2-dimensional

[fickle trail]

oh

so i was kinda correct to begin with

spans R^3

but i forgot to say subspace of R^3

[peak estuary]

you cant say you were correct when you wrote something wrong down

[fickle trail]

tyvm
is this a better way to word everything?

no need to write "full" but just to be extra clear

not a subspace for the examples on the right

[uncut skiff]

i think thats ok

[fickle trail]

ty ty

[uncut skiff]

have you watched 3blue1brown's linear algebra series

[fickle trail]

finally i think i am starting to get it

[fickle trail]

i have but actually I am finding this course much better

[uncut skiff]

???????

most insane thing ive heard all day

[fickle trail]

why?

3B1B can be quite advanced sometimes for beginners

[uncut skiff]

not really

at least not for his linear algebra series

[fickle trail]

well, i have watched them, and i can say for myself, but i we all learn differently

not saying they are bad

but to each their own

[dull sequoia]

I told you last time that ℝ² and ℝ³ has nothing in common ie empty intersection

[fickle trail]

sorry it must have been late didn't mean to jet i think i got afk

[dull sequoia]

If you took things in ℝ³ and took its span you never get anything in ℝ²

[fickle trail]

ah OK

[uncut skiff]

do you pause the videos to think

[fickle trail]

yes

[dull sequoia]

The dimensions of the span can be 2 or 3

[fickle trail]

and I re-watch

[dull sequoia]

Or 0 or 1

[uncut skiff]

hmm ok

[dull sequoia]

But they aren’t exactly ℝ²

[fickle trail]

but sometimes it just doesn't click
i think the Krista King videos are doing that for me, could just be right place at right time though

maybe starting out it would be different

[dull sequoia]

Watch whatever helps you more

[fickle trail]

yeah, exactly. i'm 100% sure if i go back to 3B1B there is still lots to learn

even for highly skilled people in math, lots to learn from 3B1B i think

but it can be a bit over the head if you just don't follow, or not seeing it, that just comes with practice and deeper comprehension i guess

[uncut skiff]

i learnt about span through 3b1b im pretty sure

[fickle trail]

like for you it might be insane, but for me I'm just speaking the truth

[uncut skiff]

yeah ok i get that

[fickle trail]

all good, one of the great things about learning is each new student is like a fresh take on things, asking "why is that?" or "could it be this way?"
and actually teaching helps us to learn too

like a fresh slate to really not take anything for granted

the learning never ends

for me personally i find this Udemy course super helpful

and ChatGPT (lol, I know) for basic questions, not with math problem solving but for bigger picture abstract stuff I find it quite helpful indeed

and Math Discord is great when I wanna try to explain it, learning and doing can sometimes be quite different from explaining

what i think is correct, someone will always be happy to point out a flaw haha
it's the only way to get better

tyvm folks, appreciate it!

[uncut skiff]

sometimes i wish i had the humility for that

[fickle trail]

for what?

[uncut skiff]

.

[fickle trail]

oh, it can be painful sometimes yeah, you sometimes question if the person answering even knows what they are talking about lol

if you know it well enough you can explain why you think their answer is incorrect

but most of the time I'm perfectly OK with just "I don't know", and "let's learn more"

[uncut skiff]

ah sorry my english is all over the place

you know what i dont remember what i wanted to say

its 2 am

thats enough math for a day

[fickle trail]

yes, math is not a sprint, more like a daily practice

have a good one!

.close

[safe radish]

Channel closed

Closed by @fickle trail

Use .reopen if this was a mistake.

[safe radish]

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.

[lean otter]

Hello I struggle to a question: For which value of the real "a" this polynomial admit a multiple real root?

[earnest olive]

do you know descarte's rule of signs?

[lean otter]

No what is it?

I tried to set P=0 and P' =0 as a system and solve it but i did a mess

[earnest olive]

basically, the number of times the sign of the coefficient changes in P(+x) gives the maximum number of positive roots and vice versa

[earnest olive]

you can also try by P<0 and P>0 for some specific values, you'll get a range of a. (since this is a continuous function)

[lean otter]

If i understood good the Descarte's rule make you find the number of roots

But i need to find the value of a that make P admit a multiple real root

Idk how this rule will help me

[mint scarab]

have you tried vieta's formulas?

cause for sure we know that there are exactly 4 root (real or not)

we want to have a multiple real roots

so we can eliminate a case with 0 real roots and only 1 real root

so then we have 2/3 or 4 real roots and maybe we can do sth with that

with vieta formulas we get

1. r1 + r2 + r3 + r4 = -4/1 = -4
2. r1r2 + ... + r3r4 = 8/1 = 8
3. r1r2r3 + ... + r2r3r4 = -16
4. r1r2r3*r4 = a
   where r1, r2, r3, r4 are roots

[lean otter]

Its the first time i hear about it let me check this

So a is the product of all roots?

[mint scarab]

yeah

[lean otter]

No way

[mint scarab]

i know

[lean otter]

It is this easy

[earnest olive]

i'll be trivial here (no rules, just basic math)
we need multiple roots, we can clearly see that if a=0, x=0 will be a root. lets say a<0 or P(0) < 0
P(-1) = -11 + a
P(-2) = -16 + a
P (0) = a
P (1) = 29 + a
P( -4) = 64 + a
lets say a>-64
then P(-4) > 0
P(-3) = -3 + a < 0
so it has multiple roots in this case because P will be positive for sure after some after x>3

[mint scarab]

cool right

[earnest olive]

ah should have just done that lol, much easy

completely out of my mind even though i have done many questions like that

[lean otter]

Lmao how in the world never have i heard abt this cheat

[mint scarab]

https://en.wikipedia.org/wiki/Vieta's_formulas

[lean otter]

Thanks a lot it sures help me

[lean otter]

Ill try it too so ill train lmao thanks all of u

[earnest olive]

it wont be helpful here but in questions where you have to find out the number of roots when you know nothing about the function, you can remember this trivial method

[lean otter]

How do i close this chan man

Or it is automatic

.close

[safe radish]

Channel closed

Closed by @gentle valley

Use .reopen if this was a mistake.

[safe radish]

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.

[left gyro]

n is an odd natural
u = e^(1/(2n) * 2πi)
can someone verify this identity real quick (i.e. both are equal for all complex x)

work shown in https://www.desmos.com/calculator/omvx6dqycn, but refrain from revealing spoilers until I verify that this "approach" is valid

[safe radish]

@left gyro Has your question been resolved?

[safe radish]

@left gyro Has your question been resolved?

[safe radish]

@left gyro Has your question been resolved?

[safe radish]

@left gyro Has your question been resolved?

[safe radish]

@left gyro Has your question been resolved?

[safe radish]

@left gyro Has your question been resolved?

[safe radish]

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.

[mossy hill]

Guys, isn’t cos(2x) = sin^2(x) - cos^2(x)?

[mossy hill]

And if so, can’t I use the golden rule to make different rules out of that?

[cold aurora]

It's not.

[mossy hill]

what is it then?

[cold aurora]

Your RHS needs to be negative of what you have written.

[mossy hill]

So cos^2(x)-sin^2(x)

[cold aurora]

Yes

[mossy hill]

Thanks

[safe radish]

@mossy hill Has your question been resolved?

Channel closed

Closed by @mossy hill

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.

[modest rain]

Vectors x and y are each have a length of 3 units. If |x+y| = square root 17, find |x-y|

[modest rain]

How do I ger started

[hushed tendon]

use the identity for square of a modulus

[modest rain]

I'm afraid that doesn't help me

I wasn't taught to find it like that

[hushed tendon]

so

what is $|x+y|^2$

[flat frigate]

axxy

[hushed tendon]

@modest rain

[modest rain]

I was doing some cleaning

Ok so it's cos law, how do I find angle?

Wait hold on

[hushed tendon]

use this information

[modest rain]

62 degrees

[hushed tendon]

hm let me verify

also u dont need the degree

just find cos(x)

the ratio

whats ur ratio?

[modest rain]

17/36

[hushed tendon]

are u sure

rearrange for cosx

[modest rain]

Let me think

[solar hazel]

[modest rain]

It's 36(cosx)

If I want to isolate cosx I just need to bring 36 to the other side

[hushed tendon]

$17-18 = 18cos(x)$

[flat frigate]

axxy

[hushed tendon]

$-1 = 18cosx$

[flat frigate]

axxy

[hushed tendon]

$-1/18 = cosx$

[flat frigate]

axxy

[modest rain]

Oh got it I got my algerbra wrong

[hushed tendon]

okay so we found the ratio right?

now we want

|x-y|

can u deduce an expression for $|x-y|^2$

[flat frigate]

axxy

[hushed tendon]

similar to $|x+y|^2$

[flat frigate]

axxy

[modest rain]

Does one length become -3?

[hushed tendon]

no

the new expression just negates the cosine term

now input the values and square root both sides to find |a-b|

[modest rain]

square root 19

[hushed tendon]

yes

good job

[modest rain]

Helpful, thank you

.close

[safe radish]

Channel closed

Closed by @modest rain

Use .reopen if this was a mistake.

[hushed tendon]

also nice pfp

[safe radish]

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.

[meager bane]

Idk if i set it up right either

[steel stag]

hmmm, what is page 42 about? the usual way is called Heron's Formula and is really complicated

[meager bane]

It’s the same set up but just different numbers

[steel stag]

do they use the heron formula or some weird trig thing

[meager bane]

Some weird trig thing which I don’t get 😭

[steel stag]

I think you just have to follow what the book does but with different numbers, there are a lot of ways of doing it

[meager bane]

Alrighttt

Thanks

[steel stag]

👍

[meager bane]

.close

[safe radish]

Channel closed

Closed by @meager bane

Use .reopen if this was a mistake.

[safe radish]

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.

[valid mauve]

if m and n are positive integers with m>1,then n<m^n

[valid mauve]

I think Induction does it but I get that m^n≥n+1 and would have to show m^n ≠ n+1

.close

[safe radish]

Channel closed

Closed by @valid mauve

Use .reopen if this was a mistake.

[safe radish]

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.

[rose ether]

I now know how to solve to get angle B, but how do you solve for angle A and C?

[safe radish]

@rose ether Has your question been resolved?

[safe radish]

@rose ether Has your question been resolved?

[safe radish]

@rose ether Has your question been resolved?

[safe radish]

@rose ether Has your question been resolved?

[vocal nymph]

Cosine rule

And sine rule

[safe radish]

@rose ether Has your question been resolved?

[safe radish]

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.

[torpid nova]

how do you calculate x?

[eager plover]

Ok

So

There is a rule you need to know

[torpid nova]

yes?

[eager plover]

(Sin of angle A)/side a = (sin of angle B)/b

[torpid nova]

got it!

which one is angle a?

27?

[eager plover]

Label angle A the 35 because it has a corresponding side

that is already defined for you

so side a = 12
Angle A= 35°

[torpid nova]

12xsin(35)/sin(25)?

is that correct

[eager plover]

Ultimately the side that corresponds to 27 doesn’t matter

The reason 27 is there is so you can calculate the last angle

The sum of a Triangle’s interior angles = 180°

Knowing that two of the interior angles are 35° and 27° you can figure out the last angle

[eager plover]

No

So with the information that is given to you and knowing that the sum of the interior angles =180° find the 3rd angle

[torpid nova]

is the third angle 118?

[eager plover]

hold on gimme one second

Yes

It is

now you know the 3rd angle

Now you know all the information needed to plug into the formula

[eager plover]

^

[torpid nova]

sin(35)/12 = sin(118)/b?

[eager plover]

YES! Great job

Now isolate b

[torpid nova]

how do i do that? sorry 😭

[eager plover]

Ok

Let me draw it out for you

[torpid nova]

thank you! :)

[eager plover]

so you multiply both sides by b

Then divide both sides by sin 35°/12

When dividing by a fraction skip flip multiply

[eager plover]

(flip the fraction upside down and multiply)

Now you have b alone

Just solve and you find the final side

[torpid nova]

i understand it now

thank you for all your help :)

.close

[safe radish]

Channel closed

Closed by @torpid nova

Use .reopen if this was a mistake.

[safe radish]

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.

[random topaz]

helo

[safe radish]

Please don't occupy multiple help channels.

@random topaz Has your question been resolved?

[safe radish]

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.

[summer crow]

Can someone help me/give me a clue on why f(γ_1(t)) and f(γ_2(t)) meet at f(z_0) with angle pi? Thanks in advance!

[safe radish]

@summer crow Has your question been resolved?

[safe radish]

@summer crow Has your question been resolved?

[summer crow]

<@&286206848099549185>

[vagrant ice]

$z_0 + t = z_0 + it \implies 0 = t(i - 1) \implies t = 0$

[flat frigate]

south

[vagrant ice]

And also look at the direction vectors: t makes an angle of pi/2 with it

From the definition of i

[summer crow]

ty for responding, and yh I'm convinced about that part

[vagrant ice]

No worries

[summer crow]

but

my question was why f(gamma_1(t)) meets f(gamma_2(t)) with angle pi

[vagrant ice]

Ah shit

Okay it's cause cosh(it) = cos(t)

$\cosh t = \frac{e^t + e^{-t}}{2}, \cos t = \frac{e^{it} + e^{-it}}{2}$

[flat frigate]

south

[summer crow]

right so cos(t) = cosh(it) / cosh(t) = cos(it) [both are true], taking cosh(t) = cos(it), we're trying the find the angle where cos(it) meet cos(t) essentially. I feel like I'm missing smth obvs that tells me the angle for that is pi

[vagrant ice]

True I can't figure it out either

[summer crow]

haha thx for helping though, I thought I was missing smth really simple (maybe it is who knows XD)

[summer crow]

still need help with this

[safe radish]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[summer crow]

.reopen

[safe radish]

✅

[safe radish]

@summer crow Has your question been resolved?

[safe radish]

@summer crow Has your question been resolved?

[summer crow]

<@&286206848099549185>

[safe radish]

@summer crow Has your question been resolved?

[safe radish]

@summer crow Has your question been resolved?

[safe radish]

@summer crow Has your question been resolved?

[summer crow]

.close

[safe radish]

Channel closed

Closed by @summer crow

Use .reopen if this was a mistake.

[safe radish]

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.

[edgy sedge]

Can someone please go over how to set up the equation for this problem, I'm not sure where to start

[median vigil]

you have the choice of either disk method or shell method

[edgy sedge]

I'm not sure which is which 😓

I think in class we called it the washing machine method

[warm stirrup]

washer method?

[edgy sedge]

Yeah

[warm stirrup]

that's same as disk I think

[edgy sedge]

ok

[median vigil]

disk method is a special case of the washer method (the hardware, not the machine)

[edgy sedge]

Ohh I see

Then yeah could you pls explain it using the disk method 🙏

[safe radish]

@edgy sedge Has your question been resolved?

[median vigil]

https://www.khanacademy.org/math/ap-calculus-ab/ab-applications-of-integration-new/ab-8-9/v/disc-method-around-y-axis

[edgy sedge]

thank you!!

.close

[safe radish]

Channel closed

Closed by @edgy sedge

Use .reopen if this was a mistake.

[safe radish]

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.

[west hedge]

Given two objects, one possess a mass of m_1 and kinetic energy of k_1 while the other possess a mass of m_2 and is stationary, have a head-on elastic collision. Then in what configuration will the transformed kinetic energy from the m_1 object to the M_2 object to be the greatest?

[west hedge]

there's five options

I would like someone to check my approach which contributes to a wrong answer

After some analyses, I realized that v_2 and k_2 are in direct proportion as well as k_2 and m_2.

Despite both v_2 and m_2 are in direct proportion with k_2, the ascending trend of k_2 = v_2 is more significant to its counterpart k_2 = m_2. It is due to the difference between linear relations and quadratic relations between them.

[safe radish]

@west hedge Has your question been resolved?

[west hedge]

<@&286206848099549185>

stop.

are you high

[terse lichen]

<@&268886789983436800> drunk man spotted

[west hedge]

ain't the result indicates k_2 has its maximum when the value of m_2 can no more be greater than m_1.

[safe radish]

@west hedge Has your question been resolved?

[safe radish]

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.

[iron basin]

Does anyone know what f(u) should be if its not ln(u)/5u ?

[iron basin]

Would you not let u = t^5 + 26 and then have du/5 = t^4 dt

Which would end up with that

Because its wrong on my hw

[sharp tiger]

yeah that looks correct lol

[safe radish]

@iron basin Has your question been resolved?

[iron basin]

Thats so stupid i had a perfect hw grade in this class so far and if i check the solution or regenerate a problem it takes partial credit

I feel like i have to be missing something but i have no idea

The final answer at the end of the problem was correct so i dont know

[sharp tiger]

Maybe the way we write it, can you separate the factor of (1/5) in another bracket

[iron basin]

I tried that too it still counted it as wrong

[sharp tiger]

Yeah then it's the website

[safe radish]

@iron basin Has your question been resolved?

[safe radish]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[safe radish]

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.

[unique quiver]

Anyone able to help with part b?

I do not know how to begin

[tidal bramble]

95% confidence

[unique quiver]

I believe this should be 2 standard deviations from mu right?

[tidal bramble]

yes

your sigma or std dev is 3.2

so to get the 95% confidence is mu+-2*3.2

[unique quiver]

right

[tidal bramble]

your variance is 3.2^2

[twilit spindle]

wouldn't it be z=1.96, because you have to consider both sides of the distribution?

[tidal bramble]

yes

[unique quiver]

oh so we we then using the coding for Z?

to find mu?

[twilit spindle]

confidence interval is $\mu\pm Z^{}\frac{\sigma}{\sqrt{n}}$ and you want to differ from the mean by 1, so the $Z^{}\frac{\sigma}{\sqrt{n}}$ term should be 1, you know $\sigma$ and $Z^*_{95}$ so solving for $n$ is trivial

[flat frigate]

PajamaMamaLlama

[unique quiver]

ohhhhhh

I get it now ty

.close

[safe radish]

Channel closed

Closed by @unique quiver

Use .reopen if this was a mistake.

[safe radish]

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.

[raven atlas]

Hello

[raven atlas]

so I've been messing around with some models and ideas, and I've come up with a function v that "should satisfy these criteria"

let F be the set of all functions from the natural numbers to the 3d euclidean space

then v is a strictly concave function from F to the reals

is there any sense in which such a function, possibly with other constraints, could be "optimised"?

(I wanna find a global maximum)

<@&286206848099549185> ?

also, I should say that I have absolutely no idea about the specific form of the function beyond concavity for now

[safe radish]

@raven atlas Has your question been resolved?

[safe radish]

@raven atlas Has your question been resolved?

[safe radish]

@raven atlas Has your question been resolved?

[safe radish]

@raven atlas Has your question been resolved?

[steel stag]

uh natural numbers to 3d real space sounds unworkable, but in general yea you just need convex functions to optimize stuff https://en.wikipedia.org/wiki/Convex_optimization

[raven atlas]

thanks

I'll look into it

.close

[safe radish]

Channel closed

Closed by @raven atlas

Use .reopen if this was a mistake.

[covert yoke]

Minor thing that might help you find literature on this topic. A function that maps another function to a number is a generally called a "functional." @raven atlas

[safe radish]

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.

[lean otter]

How do I do this sort of thing? This is homework and if I get it wrong I can try again.

[steel stag]

that's correct just put the -6 in front since you divided by it

[lean otter]

How do I tell where to multiply the 6? Do I do the smallest one?

[wheat lagoon]

help me

Given an infinite set of X1+X2.... Xn. How much is Xn!

<@&286206848099549185>

[lean otter]

This is occupied

[wheat lagoon]

uh

sorry

[safe radish]

@lean otter Has your question been resolved?

[safe radish]

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.

[dull sequoia]

so im trying to show that this is true

[dull sequoia]

there's 2 statements here (iff), if Y and h are measurable functions then clearly the composition of them h after Y is also measurable and we can call this Z and it's measruable

now if Y and Z are measurable functions, how do i show that Z after Y^-1 is measurable

in particular, $\forall \delta \in \sigma(Z), \text{preim}_{Y^{-1}}(\delta)\in \mathcal G$

[flat frigate]

Frosst

[dull sequoia]

okay hold up we have that $\sigma(Z) \subseteq \sigma(Y)$

[flat frigate]

Frosst

[dull sequoia]

so how do i use this with the Y^-1...

hmm

[safe radish]

@dull sequoia Has your question been resolved?

[safe radish]

@dull sequoia Has your question been resolved?

[safe radish]

@dull sequoia Has your question been resolved?

[tiny hill]

I am a tad bit confused: The diagram on the bottom has the the arrow for h going the wrong direction

[dull sequoia]

Fuck

I wrote it wrong

[tiny hill]

Which one, the diagram or the domain/codomain of h?

[dull sequoia]

The diagram is correct

[tiny hill]

ah i see

Alright, the forward direction is clear; composition of measurable functions is measurable

[dull sequoia]

Yes

Very clear

But backwards

[tiny hill]

Do we require commutativity of that diagram? Otherwise the statement as written is trivially true.

[dull sequoia]

The diagram is just for me to see what is being written

I’m trying to show the 2 statements above

The one connecting the iff

[dull sequoia]

This is the original statement if you want to see if I’ve mistranslated it

[tiny hill]

Ok yeah we require commutativity of the diagram. As written on the board, you only require the existence of measurable functions, which are trivially satisfied by constants.

It's not an existence statement for Z, just for h

[dull sequoia]

But it says iff

[tiny hill]

right, but you are given Z already
The iff only concerns the measurability of Z

[dull sequoia]

Oh I’m misinterpreting

I see

So it’s more like this

And the existence of h forces the diagram to commute?

Right

Because then Z is just the composition of h after Y

[tiny hill]

the top condition is missing a piece, it's required that Z = h o Y

[dull sequoia]

Hmm

Ah because h after Y is indeed a measurable function from σ(Y)

But my Z could be some other thing completely unrelated

So we need to force the Z to be actually that composition

Then if a measurable h can be found then Z is composed of measurable functions

[tiny hill]

No, the statement is saying that Z is measurable iff there is a measurable h such that the diagram commutes.

The commutativity is required for h here.

[dull sequoia]

If I can’t find a measurable h then it’s not measurable? How do I show then that Z is also not measurable for sure

[dull sequoia]

Yeah I’m saying this is why me missing the restriction for Z is wrong

[tiny hill]

Ah I see

I think you should be able to do it via characteristic functions

Suppose that $Z = \chi_{Y^{-1}(E)}$ for some $E \in \mathcal{G}$; then $h = \chi_E : (\Lambda, \mathcal{G}) \to (\mathbb{R}^k, \mathcal{B}^k)$ is measurable and $\chi_{Y^{-1}(E)} = Z = h \circ Y = \chi_E \circ Y$

[flat frigate]

LJ NG+

[tiny hill]

So for any measurable Z, write Z as a limit of simple functions and show that the resulting sequence of measurable h you get converges.

You may need to first write Z = Z^+ - Z^- for this, taking the positive and negative parts of Z.

[dull sequoia]

let me think about this

[toxic stratus]

this is a good one

you have to construct the function

its a fun construction

[safe radish]

@dull sequoia Has your question been resolved?

[dull sequoia]

I’ve cheated

My second book has a proof

It does not look as though I would’ve been able to come up with this

[lean otter]

<@&268886789983436800> 1122830721195716639

[dull sequoia]

.close

[safe radish]

Channel closed

Closed by @dull sequoia

Use .reopen if this was a mistake.

[safe radish]

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.

[west hedge]

Given A,B,C, and X are all 2 by 2 matrix

[uncut skiff]

!occupied

[safe radish]

Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).

[west hedge]

Given A,B,C, and X are all 2 by 2 matrix

And

answer the questions below:

If XC=CX, then what possible matrices could X be?

[uncut skiff]

wow chinese

I would write X as a b c d then just do the matrix multiplication

the 4th one is the identity so its one of the solutions

[west hedge]

That's quite a straightforward and efficient solution

[uncut skiff]

its tedious if youre doing it a lot but yeah

[west hedge]

what do you mean by "identity"?　I cannot seems to understand it.

[uncut skiff]

identity matrix, any matrix multiplied to it is itself

[safe radish]

@west hedge Has your question been resolved?

[safe radish]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[safe radish]

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.

[feral kernel]

Hi

[dense wadi]

hi

so whats your quesiton 😭

[feral kernel]

Sorry lol

The last one

Is it correct?

Or is it i*cosO + sinO

[icy lance]

the right side is equal to this

[feral kernel]

Oh okay

Thankss

.close

[safe radish]

Channel closed

Closed by @feral kernel

Use .reopen if this was a mistake.

[safe radish]

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.

[normal rose]

What are the rules for multiplying Matrixes?
Something simple like this?

[meager merlin]

Use Dot product rule

[rustic goblet]

in the most general form, take the ith row of the first matrix (starting from the top) and dot product it with the jth column of the second matrix (starting from the left)

this gives you the entry for the ith row, jth column of the product AB

now... what does that mean?

@normal rose take the first row of A and dot product it with the first column of B

[normal rose]

hmm

[rustic goblet]

that gives you the first row first column entry of AB

[normal rose]

so 8* -5 and 1*7?

[rustic goblet]

yes

well

add the two

dot product is defined to be the sum of the products

[normal rose]

-40 + 7 = -33
and that's the first term? or do i keep it as -40 + 7?

[rustic goblet]

-33 is the first entry, yes

it goes in the 1st row, 1st column of the matrix AB

[normal rose]

so first row by first column
second row by first column next?

[rustic goblet]

other way around

first row by second column next

[normal rose]

first row by first column
first row by second column
second row by first column
second row by second column?

[rustic goblet]

yes!

that gives you the entries for the
first row, first column
first row, second column
second row, first column
second row, second column
of the matrix AB, respectively

[normal rose]

perfect, Thank you!

/close

[rustic goblet]

[rustic goblet]

it's .close

[normal rose]

.close

[safe radish]

Channel closed

Closed by @normal rose

Use .reopen if this was a mistake.

[safe radish]

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.

[ancient snow]

what's the question

[crimson ridge]

find square

[ancient snow]

square?

[crimson ridge]

yea?

[ancient snow]

ohhh

the area under the line

[crimson ridge]

yea

[ancient snow]

you don't really need integration here

you can find the area of the trapezium formed between the line and the axis

[crimson ridge]

but when i use integrate i get different response

integration

[ancient snow]

ill do it both ways

if you find the trapezium area

the height is 7 and the sum of parallel sides is 11

so the area is 1/2(7)(11) which is 77/2

[crimson ridge]

38.5

[ancient snow]

now using integration

the equation is y = 5/7 x + 3

integrate that you get 5/14 x^2 + 3x

plug in 7 you get 35/2 + 21

which is 17.5 + 21 which is 38.5

same answer

[crimson ridge]

why 5/7?

i don`t get it

[ancient snow]

the gradient is change in y/change in x

[crimson ridge]

okay

thank you man

.close

[safe radish]

Channel closed

Closed by @crimson ridge

Use .reopen if this was a mistake.

[safe radish]

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.

[desert pasture]

so this is equivalent to integrating between -pi/2 and 3pi/2 right?

if not I fear this will be rather nasty

will require IBP multiple tomes

*times

[obtuse plover]

cant u just do a triangle diagram or smth

the integrand becomes pi/2 - x or smth right

[desert pasture]

yeah

pi-arcsin(x)

[obtuse plover]

just pi/2 - x no?

[desert pasture]

ah

yes

oh

right

[eternal carbon]

domain restrictions are still in effect

[obtuse plover]

idk, check if im right

[obtuse plover]

ye

[desert pasture]

didn't notice the arccos 💀

[desert pasture]

hmm, so this would be π-x in (pi/2,pi), right?

[eternal carbon]

but yeah all there is to this question is to think of what arccos(sinx) is geometrically

[eternal carbon]

how did you get this? also no

[desert pasture]

then what would it be

sin(π-x)=sin(x)

is what I used

I'll do this later

.close

[safe radish]

Channel closed

Closed by @desert pasture

Use .reopen if this was a mistake.

[safe radish]

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.

[viscid grail]

quick question for vector product

[viscid grail]

if a(a1, a2), and b(b1, b2)

then axb=a1b2-a2b1

is this true?

[faint seal]

$\vec{a}=a_1 \hat{i}+a_2\hat{j},\vec{b}=b_1\hat{i}+b_2\hat{j}$

oh god

[viscid grail]

lol

[peak estuary]

$\hat i$ iirc

[flat frigate]

Denascite

[viscid grail]

it's just about this

[flat frigate]

kheerii

[faint seal]

then $|a\times b|=a_1 b_2 - a_2 b_1$ yes

[flat frigate]

kheerii

[viscid grail]

ok ty

.close

[safe radish]

Channel closed

Closed by @viscid grail

Use .reopen if this was a mistake.

[safe radish]

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.

[last geyser]

can you guys help me with this?

what will be the annswer

?

when i say it is decaying 0.45% every month it says its wrong . idk why?

[drowsy moss]

because it's not every month

t is in months, but the exponent is t/30
so you won't have a decay of .45% until the exponent 1

[last geyser]

so what would it be?

[drowsy moss]

when is t/30 = 1?

[last geyser]

when t is 30

[drowsy moss]

so it decays .45% every 30 months, or 2.5 years

[last geyser]

got it.

thanks!

[safe radish]

@last geyser Has your question been resolved?

[safe radish]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[safe radish]

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.

[cyan sorrel]

On the slopes AB and CD of the trapezoid ABCD, the points M and N are chosen such that MN||BC and AM:MB=3:4. Find the length of segment MN if the lengths of the bases are 8cm and 22cm (AD is the larger base)

[cyan sorrel]

this is what i got in school 😭

answer is 16cm

pls help i have exam

[safe radish]

@cyan sorrel Has your question been resolved?

[steel stag]

a parallel line along a trapezoid, when you move it around, gets bigger and smaller at a constant rate

so if you go from the top to the bottom you're just stretching from 22 to 8

and 3:4 means you want a number which is slightly closer to 22, 3/7 of the way to 22=AD

like red is where the answer is on a number line

so try to find out how much 1/7 of the distance is and move 3 of those from 22 for the answer

[cyan sorrel]

ty, i think i may get answer from proportion

isn't it ?

[steel stag]

yea the proportion is 3:4 between 22 and 8

[safe radish]

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.

[viscid grail]

If a(a1, a2) and b(b1, b2), axb=a1b2-a2b1 then what is a(a1, a2, a3), b(b1, b2, b3) axb?

[viscid grail]

as product

[hoary wind]

$\begin{vmatrix} i & j & k \ a_1 & a_2 & a_3 \ b_1 & b_2 & b_3 \end{vmatrix}$

[flat frigate]

TayBee

[hoary wind]

Assuming you're comfy with determinants

Or

You can memorise that

[viscid grail]

ahhh I see

thank you

.close

[safe radish]

Channel closed

Closed by @viscid grail

Use .reopen if this was a mistake.

[safe radish]

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 cosmos]

Can someone please help me simplify this

[ancient snow]

uh that's not exactly correct cuz

the hypotenuse squared = a^2 + b^2

in this case the hypotenuse is x+10

not x

[limpid cosmos]

Wait

OHHHH

hold up

So it would be

(X+10)^2 = 14^2 + x^2 ?

I somehow forgot how to do x+10^2

Could you help me out please 😭😭

[flat frigate]

faiyrose

[limpid cosmos]

Oh ok

So would it be

x^2+100=196+x^2

[flat frigate]

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

[limpid cosmos]

So it’s x^2 + 20x + 100 ?

[fathom jewel]

⚔️

[limpid cosmos]

Awesome thank you so much so I think the answer is x = 4.8 ?

Epiccc thank you so very much!!

.close

[safe radish]

Channel closed

Closed by @limpid cosmos

Use .reopen if this was a mistake.

[safe radish]

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.

[ancient snow]

always try and simplify

[pliant egret]

it doesnt have real solutions you know it?

[mellow mountain]

yes

[mellow mountain]

😲 i wonder why im here then

i tried i failed why else am i here

[safe radish]

@mellow mountain Has your question been resolved?

[safe radish]

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.

[upbeat basin]

does this diverge or converge?

[obtuse jackal]

Do the terms go to 0 ?
If so, how?
Monotonically?
Fast enough for convergence to be absolute?

[upbeat basin]

i don't think it is monotonic

when I did the ratio test I got that it diverges but on my answer key itdiverges

[obtuse jackal]

"I got diverges but I should have gotten diverges"
Except it converges

[upbeat basin]

ssorry it is a typo

yes on the answer key it converges but I don't understand why

the series doesn't go to 0, it isn't monotonic, and it is fast enough to be absolute

[obtuse jackal]

ratio test harder

[obtuse jackal]

are you ratio testing by looking at the quotient of consecutive partial sums?

[upbeat basin]

no

i don't think so

oh thank you

u split it into two fractions bc same denominator

i mean one fraction

[obtuse jackal]

the ratio of two consecutive terms goes to -1/2 by a simple computation?

[upbeat basin]

what do you mean by that?

[obtuse jackal]

*better

[upbeat basin]

does 2n+3 cancel out 2n+1 because they are basically the same except 2n+3 is just one terms ahead of 2n+1

kinda like a factorial?

[obtuse jackal]

they ratio goes to 1
You're just doing a computation
Don't overthink this

[upbeat basin]

im sorry but I stil dont get it

how does the ratio go to one

[obtuse jackal]

(2n+1) / (2n+3) = ((2n+3) - 2) / (2n+3) = 1 - 2/(2n+3) -> 1 - 0

[upbeat basin]

oKay I understand that, but how would that fully simplify the limit when doing the ratio test?

[obtuse jackal]

have you tried just writing it out and simplifying just about everything ?

[upbeat basin]

let me try again

causd ehen I do it seems to get more complex

oKay I got it

lomit goes to 1/2

thank you

.closs

.close

[safe radish]

Channel closed

Closed by @upbeat basin

Use .reopen if this was a mistake.

[safe radish]

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.

[dense wadi]

hwo do we determine volume of 0 to 2

if it passed section of intersection