help-27

[devout snow]

@hollow shore Has your question been resolved?

[devout snow]

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.

[hollow shore]

Why is there no vertical asymptote?

[solar goblet]

the denominator cannot be 0

[hollow shore]

like its impossible to solve for x at the bottom

like what are the rules for it

[covert root]

There needs to be something of the form 1/0 for there to be asymptote

think of 1/x around x=0

[heavy current]

notice that x^2 >= 0 for all real x

then 3x^2 >= 0 as well, and thus 3x^2 + 2 >= 2 for all real x

so the denominator can’t be less than 2, and certainly not less than 0

[devout snow]

@hollow shore Has your question been resolved?

[devout snow]

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.

[desert estuary]

what does the whole pi [A] mean

[heavy current]

perhaps the power set of A?

I’m not entirely sure; I’ve never that notation

[desert estuary]

yeah, hmm im guess probably not poweset since im pretty sure my class uses the typical convention of that

[heavy current]

hm

then I’m not so sure, apologies

[desert estuary]

could i ask a seperate q related to the same topic

[stone stump]

it could be something like a projection

but really its something you have to look up in your notes

[desert estuary]

thanks yeah

i appreciate it

.close

[devout snow]

Channel closed

Closed by @desert estuary

Use .reopen if this was a mistake.

[devout snow]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• 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.

[fringe skiff]

Help

[elfin nexus]

with what

[fringe skiff]

can I send ss?

[rain fjord]

!da2a

[devout snow]

No need to ask “Can I ask…?” or “Does anyone know about…?”—it’s faster for everyone if you just ask your question! See https://dontasktoask.com/

[fringe skiff]

.close

[devout snow]

Channel closed

Closed by @fringe skiff

Use .reopen if this was a mistake.

[fringe skiff]

.reopen

[devout snow]

✅

[fringe skiff]

.close

[devout snow]

Channel closed

Closed by @fringe skiff

Use .reopen if this was a mistake.

[devout snow]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• 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.

[timid badger]

answer:

they took g as +9.8

but I said it's -9.8 because the ball is thrown up so I took up as positive

[acoustic leaf]

g is just the number 9.8 m/s². the sign of the acceleration due to gravity comes from the direction of the vector (it is negative if you take down to be the negative direction). the - sign was accounted for when they subtracted 0.4g, to take g as negative again is double counting it

[timid badger]

okay!

thanks !

Wait

so if down is negative g=9.8?

[acoustic leaf]

g = 9.8 regardless of whether up or down is positive or negative.
the force vector will always point down, so if down is negative then you take it as -mg, or occasionally if down is positive you take it as +mg

[timid badger]

oh okay so I alwaus put g=9.8 and just think about the signs on the forces?

-0.4g and -3

if they act up

it's +0.4g and +3 and g=9.8 still

right

[acoustic leaf]

yes

[timid badger]

yay ok

thanks

.close

[devout snow]

Channel closed

Closed by @timid badger

Use .reopen if this was a mistake.

[devout snow]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• 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.

[short iron]

How many different ways can you seat 11 men and 8 women in a row if no 2 women are to sit together?

Would this just be 11! * 12 choose 8?

[short iron]

[11! * {12 \choose 8} ]

[woven radish]

chattertonfan

[spare crypt]

yea looks good

er I guess you didn't order the women yet

[short iron]

Oh

Maybe I'm not understanding?

[spare crypt]

you have (place 11 men)*(find 8 spots between them to place women)

[short iron]

Yeah that was my thinking

Is that not right?

Oh you're saying account for the order of the women too?

[spare crypt]

yea

since people are unique

[short iron]

That'd just be an additional 8! ?

[spare crypt]

yup

[short iron]

[11! * {12 \choose 8} * 8! ]

[woven radish]

chattertonfan

[short iron]

Looks good?

thank you

.close

[devout snow]

Channel closed

Closed by @short iron

Use .reopen if this was a mistake.

[devout snow]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• 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.

[amber sluice]

any1 know why the hole is

(0, 1/3)

specifically the 0 part

i thought it was

x/x (x+3 so both x's cancel out to make 1 how come its 0

[faint zinc]

Because the denominator is 0 when x=0

if you had $\frac{(x+1)}{x(x+1)}$ then your hole would be where x+1 is 0 instead, which is at x=-1.

@amber sluice

[kindred agate]

x/x(x+3) is the function?

[faint zinc]

yes

[kindred agate]

alr

[amber sluice]

doesnt show what ur trying to type

[woven radish]

OmnipotentEntity

[faint zinc]

fixed

[kindred agate]

well theres an obvious hole at 1/3 bc the denominator becomes 1/3*0

[faint zinc]

the cancelled part is the part that makes the hole

[kindred agate]

so you are dividing (1/3)/0

[faint zinc]

you are dividing 0 by 0 you mean

[amber sluice]

yea so if ur cancelling

the

x on the numerator and x on denominator cancels

it makes a 1 no?

[kindred agate]

no in this case

at 1/3

at 0 it would be 0/0

wait

no not 1/3

wait im having a brain fart

-3

not 1/3

-3

yes

ok wait

wait are we talking about the asymptote or the hole

[amber sluice]

hole

[faint zinc]

Yes,

\begin{align*}
\frac{x}{x(x+3)} &= \frac{x}{x} \cdot \frac{1}{x+3} \
&= \frac{1}{x+3} \text{ if $x \ne 0$}
\end{align*}

[woven radish]

OmnipotentEntity

[faint zinc]

why on earth did it select that sticker?

[kindred agate]

anyways

the problem with cancelling the x's

is that you cant divide by 0

so when x is zero you cant do that

[amber sluice]

so it cant be 1 because?

[kindred agate]

1/(x+3) you mean?

[faint zinc]

when x is 1, there is no hole, because x/x = 1/1 = 1

[kindred agate]

x cant be one?

it can

why wouldnt it be able to

[amber sluice]

for the hole

i answered

(1, 1/4)

instead of (0,1/3)

[kindred agate]

it can be 1

why would 1 not be valid

you have 1/(1+3)

which is perfectly well define

[amber sluice]

because the paper said so that the hole is

(0,1/3)

[kindred agate]

d

yeah

whats the question

0,1/3 is the hole

[knotty mantle]

what kind of math is that?

[amber sluice]

why is it 0,1/3

[knotty mantle]

what grade

[kindred agate]

bc you cant plug 0 into the formula

it returns 0/0

[faint zinc]

I think Railey is hung up on the fact that x/x cancels to 1, which he seems to interpret as there being a problem at x = 1. But that is not the case.

[amber sluice]

exactly

[kindred agate]

OH

[amber sluice]

lot of people confusing me here

[faint zinc]

the problem is when the denominator is 0

which occurs when the thing you canceled (in this case "x") is equal to zero

[kindred agate]

x/x being equal to 1 has nothing to do with x=1 causing issues

try plugging 1 into the formula

for the function

it returns 1/(1+3)=1/4

perfect

normal

so do you get why "holes" happen

[amber sluice]

i get why holes happen, i dont get why this one in particular is not 1 but 0

if i plug in 1
it becomes

1/4

[kindred agate]

yep

[amber sluice]

no problem right but my teachers solution shows

0,1/3 instead

[kindred agate]

so thats a number so we're good

[kindred agate]

yes

bc if you put in 1

it becomes 1/4

thats a number

so theres no hole

try plugging in 0

for the formula

see what happens

[amber sluice]

is 1/3 not a number too

[kindred agate]

you didnt plug it into the formula

plug it into the original formula

x/x(x+3)

plug in 0

and see what you get

[faint zinc]

(you only get 1/3 if you plug it into the cancelled form of the formula, you get 0/0 if you plug it into the original.)

[amber sluice]

0

[kindred agate]

0/0

right

0/(0*(3))=0/0

[amber sluice]

ill figure it out, rn i still dont get it thanks though.

.close

[devout snow]

Channel closed

Closed by @amber sluice

Use .reopen if this was a mistake.

[kindred agate]

wait

why did you come here then, im here to help you understand

[devout snow]

Available help channel!

Send your question here to claim the channel.

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

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

[void mica]

Can someone tell me if this is wrongly multiplied?

[void mica]

This is the matrix we are working with

This is quantum computing-related, but what it says is basically multiplying vector |0> with aforementioned matrix

Therefore, we get:

(cos(theta) sin(theta); -sin(theta) cos(theta)) * (1; 0)

Written as this, to be more clear

Then, the result is:

Therefore, it is: cos(theta) * |0> - sin(theta) * |1>

[void mica]

Where did the minus disappear in this image?

[devout snow]

@void mica Has your question been resolved?

[devout snow]

@void mica Has your question been resolved?

[devout snow]

@void mica Has your question been resolved?

Channel closed

Closed by @void mica

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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

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

[restive river]

can someone explain how they changed the bounds of y to 0 <=y<=t?

[graceful cosmos]

Note they changed the order of integration

[restive river]

right

[graceful cosmos]

I personally draw a region wherever I change the order of integration, it can be pretty involved

They skip all that here though

[restive river]

ahhhhh

I forgot yeah if we're chaning variables i can just use a graph to visualize

whoops sorry yeah now I can see how they changed the bounds to that

ty

.close

[devout snow]

Channel closed

Closed by @deep silo

Use .reopen if this was a mistake.

[restive river]

.reopen

[devout snow]

✅

[restive river]

oh yeah wait one more thing

when Im drawing out the graphs for stuff how do I determine when to say like 0≤y≤x or x≤y≤1

like say for uh

[graceful cosmos]

Integrating x first, or y first?

[restive river]

dx

like between uh

y≤x≤1 or 0≤x≤y

[graceful cosmos]

If we're integrating x first, then the x bounds have to depend on y

Since we're integrating y last, y has no variables left to depend on. y bounds will be constants

[restive river]

I understand that part, but I just cant figure out when to make like

[restive river]

between this

[graceful cosmos]

0 ≤ x ≤ y

[restive river]

because to me if we want the shaded region to be the same I thought that y≤x≤1 makes sense

i should probbably put it in a graphing calc and actually see it

[graceful cosmos]

x can always reach 0

[heady plinth]

You can visualize

[graceful cosmos]

And doesn't usually get as large as 1

[heady plinth]

Imagine y going from 0 to 1 and visualize x being between y and 1

It would be a different triangle, right below the one you actually want

[restive river]

ah wait yeah now i see it

sorry guys ;;

.close

[devout snow]

Channel closed

Closed by @deep silo

Use .reopen if this was a mistake.

[devout snow]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• 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 wharf]

i got 11 but i'm not sure that I did it correctly

A=80
B=55
C=45
a=14
b=12
c=10

how would I find D, E, and DE

[unkempt warren]

you can use similar triangles

[lunar wharf]

wdym

[unkempt warren]

angle D is the same as angle C

angle E is the same as angle B

[lunar wharf]

mm

how?

nvm, I see your point

[unkempt warren]

👍

[lunar wharf]

is that relative to the law of sines though?

it probably is

[devout snow]

@lunar wharf Has your question been resolved?

Channel closed

Closed by @lunar wharf

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.

[smoky sentinel]

.close

[devout snow]

Channel closed

Closed by @smoky sentinel

Use .reopen if this was a mistake.

[devout snow]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• 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.

[worldly latch]

A basketball court measures 25m by 15m. The court is surrounded by a row of benches that is the same width on all sides. If the row of benches has a total area of 325m^2, find the dimensions of the space needed for the court and benches. Round answers to one decimal place if necessary. Include a diagram in your solution. (6 marks)

[solar goblet]

is this a test?

[worldly latch]

practice test for tomorrow

i just searched up a bunch of practice tests

[stiff gorge]

(25+2x) * (15 + 2x) = 325+25*15

[worldly latch]

then expand and quadratic formula?

[stiff gorge]

if needed

Oh wait that needs some fixing

[worldly latch]

wdym

[stiff gorge]

fixed the equation, think it meant 325 was only the area of the benches

[worldly latch]

yeah

ok so then you move the 325+25*15 to the other side of the equation and then expand

and then how do i find x

quadratic formula?

[stiff gorge]

Think so

If nothing seems to work

[worldly latch]

ok thank you

.close

[devout snow]

Channel closed

Closed by @worldly latch

Use .reopen if this was a mistake.

[devout snow]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• 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.

[lone gate]

can someone help? at the moment i got to this point

[lone gate]

found y not sure where to go next

[stiff gorge]

Just plug in sin^(-1)(3/4) for alpha and cos^(-1)(-5/13) for beta, make sure they're in the second quadrant, then add them up and take the cosine

[lone gate]

i thought i need to find sinB and cosine alpha first

[ocean silo]

you can just do this right away without having to find the angles

you have two sides of two triangles, use pythagorean theorem, find the unknown trig functions, use cosine angle sum identity, finished

[devout snow]

@lone gate Has your question been resolved?

[devout snow]

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.

[restive river]

I need to find the integral of this function

[restive river]

I know the integral is arcsin but I don't know what the numbers/variables with arcsin are

[mighty knoll]

So, you know that $\int \frac{1}{\sqrt{1-x^2}} = \sin^{-1} (x)$

[uncut crow]

@royal laurel

[woven radish]

ℑμΤ𝛄𝛗θ

[mighty knoll]

What you can do with your problem is factor constants out of the integral, and use a substitution to get to this form

[restive river]

Oh I see

Wait so its just 2 arcsin x?

[mighty knoll]

there would be some constant with the x if you perform the sub correctly

if you want a hint: ||first step is to factor 25 out of the denominator||

[restive river]

(5-x)(5-x)

@mighty knoll Is this right

[mighty knoll]

No, but it's not the factoring I meant. Let me show you :)

[restive river]

Ok

[mighty knoll]

$\int \frac{2}{\sqrt{25 -x^2}}\dd{x} = 2 \int \frac{1}{\sqrt{25(1-\frac{x^2}{25})}}\dd{x}$

[woven radish]

ℑμΤ𝛄𝛗θ

[mighty knoll]

Now, see how this 25 can be taken outside the integral, getting us one step closer to the base form we know

[restive river]

Oh ok

[mighty knoll]

After that, do you see the substitution we should make?

[restive river]

It's 2/5 instead of just 2

2/5 arcsinx

[mighty knoll]

Not quite. You have the 2/5 part right, but now we have this integral: $\ \frac25 \int \frac{1}{\sqrt{1-\frac{x^2}{25}}}\dd{x}$

[woven radish]

ℑμΤ𝛄𝛗θ

[mighty knoll]

And we should get that x^2/25 term to be just u^2, for the integral to truly be arcsin

[restive river]

Oh so square root of it

[mighty knoll]

not sure what you mean, but as long as you find the substitution you'll get there :)

if you're stuck: ||let x/5 = u||

[restive river]

Yeah so square rooting it

Then multiplying by du

1/5

[mighty knoll]

it might have been 2arcsinx honestly I didn't check and now I'm scared I made you do work for nothing

,w integral 2/sqrt(25-x^2)

[woven radish]

Results provided by WolframAlpha

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

Requested by imtyp0

[mighty knoll]

oh okay yeah no there was a constant inside

[restive river]

That's the answer?

[mighty knoll]

That would be the answer yeah. Did you arrive at that with your sub?

[devout snow]

@restive river Has your question been resolved?

[devout snow]

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.

[short iron]

The book says 13 choose 10 is the answer and I don't understand why?

[short iron]

What does the 13 represent?

[graceful cosmos]

Know stars and bars?

[short iron]

I do not

[graceful cosmos]

Give the intro to this a quick read:
https://brilliant.org/wiki/integer-equations-star-and-bars/#:~:text=We discuss a combinatorial counting,which is easier to count.

[short iron]

yeah reading up on it now

alright

[graceful cosmos]

Basically we have 10 stars and 3 bars. Any arrangement of them gives a solution to this equation

There's 13C3 ways to choose the slots which should be bars

[short iron]

I see

[graceful cosmos]

The 13 being the total number of empty slots before stars and bars are placed

[short iron]

Ah wait maybe i don't get it

I thought 13 was the total of both bars and stars

And then you take total choose stars

I'll have to review, thank you for help

.close

[devout snow]

Channel closed

Closed by @short iron

Use .reopen if this was a mistake.

[graceful cosmos]

That can work too

13C10 is exactly the same as 13C3

[short iron]

.reopen

[devout snow]

✅

[short iron]

That I do not get

[graceful cosmos]

"Choose which slots should be stars" vs "choose which slots should be bars" either strategy works

[short iron]

If I were to apply the same idea here

Would I have 7 stars and 2 bars?

Or 9 choose 7?

[graceful cosmos]

Yes exactly

@short iron

Oh wait, but note the condition that x1 ≥ 3

[devout snow]

@short iron Has your question been resolved?

[devout snow]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[devout snow]

Available help channel!

Send your question here to claim the channel.

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

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

[frozen shore]

$$
\begin{aligned}
&\int\sqrt\frac{4+x}{4-x}:dx \
&\int\frac{\sqrt{4+x}}{\sqrt{4-x}}\cdot\frac{\sqrt{4+x}}{\sqrt{4+x}}:dx \
&\int\frac{4+x}{\sqrt{16-x^2}}:dx \
&\int\frac1{{\sqrt{16-x^2}}:dx}+\int\frac{x}{\sqrt{16-x^2}}:dx \
\end{aligned}
$$
$$
\begin{aligned}
\arcsin(4/x)+&\int\frac{x}{\sqrt{16-x^2}}:dx \
&u=16-x^2\qquad du=-2x:dx \
-\frac1{2}&du=x:dx \
-\frac1{2}&\int\frac{du}{\sqrt{u}} \
&\int u^{-1/2}:du \
\arcsin(4/x)-\frac1{2}&\biggr[\frac2{1}u^{1/2}\biggr] \
\arcsin(4/x)-&\sqrt{16-x^2}+C
\end{aligned}
$$

[woven radish]

AWACS Sky Eye

[frozen shore]

oh wait, i flipped it. it's supposed to be arcsinx/4

[fossil locust]

Should be 4 integral of 1/sqrt(16 - x^2) dx, by the way

[frozen shore]

....OH.

because you can pull out the 4 as a constant and make it... ugh.

thanks

(is that logic right?)

i guess it is. thanks!

.close

[devout snow]

Channel closed

Closed by @frozen shore

Use .reopen if this was a mistake.

[fossil locust]

Yeah you just had a little slip: the other integral is independent so just replace what you have with 4 arcsin(4/x) - sqrt(16 - x^2) + C

Npnp

[frozen shore]

.reopen

[devout snow]

✅

[frozen shore]

.close

[devout snow]

Channel closed

Closed by @frozen shore

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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

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

[mortal tinsel]

Hi, the dimension of a mxn matrix is exactly mxn, but matrices encode linear maps, so can we say that the dimension of a map phi is equal to the dimension of its input space times the dimension of its output space?

[graceful cosmos]

"dimension" is something that belongs to a vector space, not a matrix

Now, all mxn matrices do form a vector space, and that vector space has dimension mxn

But when you're using a matrix as a linear map, the dimension of all such linear maps is usually not relevant

[mortal tinsel]

Alright thank you. My question came from reading

“Dim(Hom_F(V, F) = DimV * DimF” Which I can see is a vector space and since F is a field, it is also a vector space so there’s no problems

.close

[devout snow]

Channel closed

Closed by @mortal tinsel

Use .reopen if this was a mistake.

[mortal tinsel]

.reopen

[devout snow]

✅

[mortal tinsel]

wait i’m back

What about for a field like Q which isn’t finitely generated? What would we say the dimQ is?

[devout snow]

@mortal tinsel Has your question been resolved?

Channel closed

Closed by @mortal tinsel

Use .reopen if this was a mistake.

[devout snow]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• 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.

[restive river]

Cube

[restive river]

any idea how to find N to H

[spare crypt]

is this all in 2d and H is midpoint?

[restive river]

3d

[restive river]

Wdym H is midpoint?

[spare crypt]

uh how where the two lines there drawn

oh sorry I meant M midpoint

and it looks like the two lines are all on the AEFB face

[restive river]

point n is the intersection of EB and AM

[spare crypt]

how was M chosen

[restive river]

M is the middle ofFB

[spare crypt]

ah okay

simplest way is just graphing it like y=9-x and y=x/2 and just finding the intersection

[restive river]

and then how to find the distance between N to H?

[spare crypt]

M would be the point (9,9/2) and you just do the distance formula sqrt(y^2+x^2)

[restive river]

its (x,y) = (6,3)

[spare crypt]

ok so sqrt(3^2+1.5^2)

for the answer

[restive river]

11,25

[spare crypt]

square root of that yea

[restive river]

3/2 and root 5

hmm

is it like this?

[spare crypt]

that formula was for this

[restive river]

oh NM

then we should find for MH?

[spare crypt]

if you want to find MH you do the distnace formula between (9,9/2,0) and (0,9,9) with sqrt(x^2+y^2+z^2)

[restive river]

hmm how about find NH?

[spare crypt]

(6,3,0) and (0,9,9)

[restive river]

wait i am little bit confuse of xy "z" pythagoras

[spare crypt]

proving the extra z^2 part is a really weird double pythagoras thing

like you do sqrt(x^2+y^2) for the green diagonal, then you use that side and do pythag with z

[restive river]

hmm

i see

ABC, got AC

ACD, got AD

[spare crypt]

right

[restive river]

what if we do it one by one? Don't go straight to Z Pythagoras

[spare crypt]

uh like this?

[restive river]

yeah

it can be

[spare crypt]

that works too

[restive river]

if the blue one is O

Then N to O is square root of 6^2+9^2 ?

3 root 13

[spare crypt]

right

[restive river]

then we can find the NH

=

square root of (3 root 13)^2 + (6)^2

[spare crypt]

just (6)^2 at the end

[restive river]

eh

sry

its 3 root 17

ty

.close

[devout snow]

Channel closed

Closed by @pallid jacinth

Use .reopen if this was a mistake.

[devout snow]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• 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.

[buoyant cipher]

how do i get there?

[twilit comet]

rational root theorem i think

then factorize

[buoyant cipher]

the p/q?

[twilit comet]

yes

[faint hearth]

You use rational roots theorem to get the root 2, and then factorise it and solve the quadratic you get after factorising

[buoyant cipher]

so i get x=2 or (x-2) and then i factor it out?

[twilit comet]

yes

via long division

[buoyant cipher]

does synthetic work cause i suck at normal

ok finished it, thank you

.close

[devout snow]

Channel closed

Closed by @buoyant cipher

Use .reopen if this was a mistake.

[devout snow]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• 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.

[chrome nymph]

Why does such a solution not work?

[red turret]

it does work, but you're taking away another solution which is when cosx - sinx = 0

[devout snow]

@chrome nymph Has your question been resolved?

[chrome nymph]

As I thought, thanks

.close

[devout snow]

Channel closed

Closed by @chrome nymph

Use .reopen if this was a mistake.

[devout snow]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• 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.

[wooden tiger]

hi

[wooden tiger]

how can i find the sum of this sequence

[devout snow]

@wooden tiger Has your question been resolved?

[wooden tiger]

do i ping helper now

[manic condor]

Not needed.

[wooden tiger]

hi hi hi help pls

[manic condor]

If you consider the sum to be let's say S, then it's possible to generate another sum by multiplying each term of S with a number. Then, you can take their difference or summation to obtain some form which you know how to sum.

I'm being a bit vague because I want you to find it on your own. Lol

Let me know if(and when) you need more explicit hint.

[wooden tiger]

😭

i tried multiplying it by 3/9

to create a GP

[manic condor]

9? or 19?

[wooden tiger]

9

[manic condor]

Huh. How would that make it a GP?

[wooden tiger]

so that i can do 10-1, 100-1, .... in the numerator

should i send an img of what i did

[manic condor]

Yeah. That seems to work. So where did you get?

[manic condor]

Yes.

[wooden tiger]

oki wait

[manic condor]

You have done it correctly. Just compute the values. Why did you stop there? Lol

[wooden tiger]

bcuz i dont know how to use the sum of infinite gp formula here

the common ratio isnt -1 or 1

[manic condor]

Well, Formula says that Sum of infinite GP with first term a and common ratio r is,
$S = \frac{a}{1-r}$

[woven radish]

Enemagneto

[wooden tiger]

isnt r supposed to be either -1 or 1?

[manic condor]

Common Ratio*. Also, have never solved questions where common ratio isn't 1 or -1? I'm surprised because in those cases, sum of infinite GP would be infinite. Lol

[wooden tiger]

YO

YOU'RE RIGHT

I actually

[manic condor]

No. r is just the common ratio. It's like the value with which each term is being multiplied to get next term.

[wooden tiger]

misunderstood

r isnt supposed to be -1 or 1

LMAO

THANKS

.close

[devout snow]

Channel closed

Closed by @wooden tiger

Use .reopen if this was a mistake.

[devout snow]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• 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.

[uneven hazel]

hello guys i need help, im currently struggling with multiplication, can someone help me?

[red turret]

what grade are you in?

[uneven hazel]

grade 4

[red turret]

how old are you?

[mystic scarab]

You can't use Discord, I believe

[uneven hazel]

no ium 13

i just got held back

[red turret]

huh

[uneven hazel]

cause im struggling with math

[stuck field]

You started using discord in kindergarten?

[uneven hazel]

most of my subjects are line of 7 and my highest in 82

[red turret]

nice question

[winter torrent]

tbh this is the sort of thing that you should just memorize

up to 12x12

[uneven hazel]

what is 12 x 12

[winter torrent]

write out a times table

[uneven hazel]

please help guys

this is due tomorrow

[mystic scarab]

This is so basic maths that you need to do it on your own

[uneven hazel]

i thought this discord server is to help people struggling with math

[mystic scarab]

Otherwise you won't understand anything later

[mystic scarab]

Of course, but for people who make an effort

[uneven hazel]

whats that

effort?

can anyone here actually help?

[mystic scarab]

You can do them with a calculator

[uneven hazel]

we are not allowed to use that

its banned

only highschoolers get to use it

[mystic scarab]

Then you simply need to memorize them

But I don't understand where your difficulty is

[uneven hazel]

well what does it mean

and what do we memorize?

[red turret]

the multiplication table.

[eager nova]

The problem here is that, you dont understand what a multiplication is

[uneven hazel]

yes

thank you for stating my problem

[eager nova]

Read the definition for multiplication of natural numbers

[uneven hazel]

where

[eager nova]

And you will be able to solve it

In you text book

[uneven hazel]

my classmates are using their hands and fingers

how do i do that

[eager nova]

Do you have fingers in your hands?

[uneven hazel]

yes

[eager nova]

Then do the same. When you have for example 3 * 3 what do you do to solve it

[uneven hazel]

but thats what im asking you

what do i do to solve it?

[eager nova]

You add the numbers the number of times you multiply for example

3 * 3 = 3+3+3

[uneven hazel]

oh ok i get it now

thank you

i can finally solve this

[eager nova]

2 * 4 = 4+4

[uneven hazel]

no its 2+2+2+2

[eager nova]

It is commutative

You can write in both ways

[uneven hazel]

oh ok

[feral agate]

How come you’re 13 yet your account is 6 years old?

[mystic scarab]

I'm sorry, I didn't understand that this was your problem, I thought you didn't learn the table sorry

Yeah at the age of 13 this should be soo obvious but seems not, that's why I took for granted he knew it

[uncut crow]

no let’s ask if he’s trolling and interrogate him on his age and academic history some more

who cares

don’t ask don’t tell

[vernal grail]

But what is pre-university?

[uncut crow]

if someone wants math help and this is all you can think about then move on

[feral agate]

Anything before university

[vernal grail]

ah okok

[devout snow]

@uneven hazel Has your question been resolved?

[devout snow]

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.

[restive river]

im trying to solve part d

but my calculator returns with error

.close

[devout snow]

Channel closed

Closed by @chilly tundra

Use .reopen if this was a mistake.

[devout snow]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• 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.

Available help channel!

Send your question here to claim the channel.

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

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

[odd ore]

hi

[odd ore]

someone helo me

i need to make the red curve and the blue curve how do i do that

[muted garnet]

uhhh maybe you can use y= a^x+b

for red

[odd ore]

yeah but that wont make the curve proper

[muted garnet]

idk but i can make this

[odd ore]

wait a sec let me try something

[muted garnet]

you can make it a bit lighter (im using 2.5^x-1.2)

[odd ore]

ok i tried but the curve isnt exact like how do i make it more exact

[muted garnet]

hmmmm

maybe you can make it 2.25 or sth lower?

[odd ore]

let me try

[muted garnet]

*1.9

[odd ore]

wont ork

work

[muted garnet]

can i see it?

[muted garnet]

not "light" enough

try lower

[restive river]

recreation of pepsi logo?

[odd ore]

if u keep it lower then the line is going to not touch red in the first quadrant

so hard

[odd ore]

let me try that

[muted garnet]

maybe you can offset the exponential?

[muted garnet]

this have so much potential

[odd ore]

isnt too bad

[muted garnet]

try 1.43 or sth

u can also increase the expoential too

[odd ore]

ok leave it like this for the red

what about blue

in the assigment there is a short reflection where we have to write the limitations so that could be one of the limitation

[muted garnet]

too strange for me fr

my only idea for this is make it 2 graphs

ax+b for the straight
x^2+y^2 for the rest

[odd ore]

i already used the circle formula

[muted garnet]

or u can again use a^(x+b)+c if u see that "straight line" is a curve lol

[odd ore]

the blue one is like

[muted garnet]

u can try this

[muted garnet]

btw, it never can make a curve like that

[odd ore]

there is an exam which is worth 90% and a test which is worth 10%

sorry i mean assignment

so dont really care about the assignment

u know how to do this just asking

i know how to do it but

[muted garnet]

uhhh just make it (x^2+1)/x=k

then make it x^2-kx+1=0

then use that i guess

[odd ore]

this is a year 10 paper where they put hard questions

[muted garnet]

uhhh lol that's like grade 8 in my country

asian thing

[devout snow]

@odd ore Has your question been resolved?

[devout snow]

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 tusk]

the first picture is the question itself and the second picture is the answer my practice test got. I understand the first parts but im confused on how im getting -8 / 3x^3

[viscid tusk]

here is my work

https://cdn.discordapp.com/attachments/930733590709411910/1222544588598939788/IMG_0427.jpg?ex=66169a5f&is=6604255f&hm=cd10e99f29c9250156c83eb06cacd431a57548167115fdb56f29bc4335e60dd8&

i divided all components by 3x^2 then got the derivative of it but im just extremely confused why my came out to be -8/3x^3 and theres is -4 / 3x^2

[safe knoll]

what do u need to do ?

[viscid tusk]

i need to find the derivative of the original problem

and i was told not to use the quotient rule due to it being tedious

[safe knoll]

ok

[leaden venture]

Use this

I also have other methods

[viscid tusk]

i don't understand im sorry

[safe knoll]

thats quotient rule

[viscid tusk]

im just confused in my own work how i got -8

[safe knoll]

confused of this?

this is wrong , should be -4/3

[viscid tusk]

yes that's where im confused idk how i got that

[safe knoll]

$$\frac{4}{3x} = \frac{4}{3}x^{-1}$$

[viscid tusk]

and the 3 should be x^2

[woven radish]

JustToPro

[safe knoll]

differentiating we get

[leaden venture]

Second method

[safe knoll]

$$\frac{d}{dx}\frac{4}{3}x^{-1} = \frac{4}{3} \frac{d}{dx}x^{-1} = \frac{4}{3} \cdot -1x^{-1-1} = -\frac{4}{3}x^{-2} = \frac{4}{3x^2}$$

[woven radish]

JustToPro

[leaden venture]

Divide each term by 3x2

[leaden venture]

-4/3 *

[devout snow]

As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.

[viscid tusk]

thank you avarice i think i see where i went wrong i think in my original dividing i didn't get 4x^-1 i think i ended up accidentally putting a negative 2 getting me negative 8

it makes sense now thank you to both of you

.close

[devout snow]

Channel closed

Closed by @viscid tusk

Use .reopen if this was a mistake.

[devout snow]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• 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.

[sinful wave]

Hi I kinda need help on the 1st question

[sinful wave]

1. Give the coordonnate of the point I and J

I is the middle of the segment EF and
J is the middle of AE

The issue is with i,j and k I don't know if I need to keep the fraction or not

I tried both and I can't justify at question 2.a that vec(n) is normal to the place IGJ

Bcs when I do vec(n).vec(IG) i found 1 when i use fraction and I found -1/4 if I use natural numbers

[devout snow]

@sinful wave Has your question been resolved?

[devout snow]

@sinful wave Has your question been resolved?

[devout snow]

@sinful wave Has your question been resolved?

Channel closed

Closed by @sinful wave

Use .reopen if this was a mistake.

[sinful wave]

Yeah forget it

[devout snow]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• 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.

[cobalt mauve]

Hi, can somebody please tell me if this is correct?

$$
\int_{-\frac{T_1}{4}}^{\frac{T_1}{4}}\left|A\cos\left(\frac{2\pi}{T_1}t\right)\right|^2dt = \frac{|A|^2T_1}{4}
$$

[woven radish]

konxmok

[spare crypt]

yea that's right

idk why |A|^2 is in absolute value unless it's complex or something?

[cobalt mauve]

yeah lmao me neither, i am doing hw for signals and systems and i am not really used to notation, once they use complex paramters, once they use real... I see why it would be without abs, thank you

[spare crypt]

ah makes sense

[cobalt mauve]

thank you for checking it, bye

.close

[devout snow]

Channel closed

Closed by @cobalt mauve

Use .reopen if this was a mistake.

[devout snow]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• 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.

[lone gate]

im stuck i goth here so far

[misty crest]

what’s cos(2t) expanded

[lone gate]

cos(2t) = 1/sec(t)

[misty crest]

no

1/sec(t)=cos(t)

cos(2t)=cos^2(t)-sin^2(t)

=2cos^2(t)-1

[lone gate]

i thought its cos^2(2t)

[misty crest]

yes but that’s just (cos(2t))^2

you can expand the inside

and square it

you have 2cos^2(2t)-1

just expand cos^2(2t)

[misty crest]

using cos(2t)=2cos^2(t)-1

[lone gate]

its from that

[errant ravine]

Thank you

[lone gate]

do u mean where it says cos4t?

[misty crest]

no

in your last line

you do the same thing twice

double angle identity twice

[lone gate]

like that?

[misty crest]

why did you write the last line

there’s 2 negative ones

and an extra cos^2

[misty crest]

it’s cos^2(2t)-sin^2(2t)= cos^2(2t)-(1-cos^2(2t)=2cos^2(2t)-1

[lone gate]

ohh

lemme check my formulas

do i need to do the right side now? @misty crest

[misty crest]

you can just work the left side

and end up with that

@lone gate

you’re using the same formula

you used to break down the 4t into 2t

now you’re going from 2t to t

[lone gate]

i dont know what the formula i was using

i think it was cos0+sin0=1

[misty crest]

no

you used cos(2u)=cos^2(u)-sin^2(u)

=2cos^2(u)-1

[lone gate]

wont that just take me backwards to where i was

[misty crest]

no

it’ll take you forwards

you have

2cos^2(2t)-1

this is the same as 2(2cos^2(t)-1)^2-1

[devout snow]

@lone gate Has your question been resolved?

[devout snow]

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.

[zenith elk]

dont know where to start for this

[misty crest]

it’s the same thing as before

the factors will be (x+4)(x-3)

notice that when you put -4 and 3 you get zero

now for a quadratic to go to negative infinity

it needs to be concave up or concave down

[zenith elk]

so is the anwser y= -(x+4)(x-3)

@misty crest

.CLOSE

.close

[devout snow]

Channel closed

Closed by @zenith elk

Use .reopen if this was a mistake.

[devout snow]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• 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.

[gentle wagon]

how do i do this 30 times

this is my first time doing sequences and series btw so idk what to do

is there like a formula for this

[spare crypt]

yea this is the main formula

[onyx rune]

do you understand what sigma summation sign is and do you know how to read it?

[gentle wagon]

oh so my answer is 2385

[gentle wagon]

a little

[dense lynx]

ye

[gentle wagon]

how do i find the recursive and explicit sequence for something

[devout snow]

@gentle wagon Has your question been resolved?

Channel closed

Closed by @gentle wagon

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.

[glossy pine]

I'm trying to calculate the area under a semicircle when the circle is tilted at angle A.

[glossy pine]

The area with no tilt is R*R * pi / 2 where R is the radius.

I think with a tilt, the area would be...
cos(A) * R* R *pi/2 . So, scaling by a constant factor of the cos of the angle

Is that right?

[spare crypt]

yea sin or cos whatever makes it work at 0 and 90 degrees

from the projection vector formula

[glossy pine]

Ok, and follow up: What if the origin of the circle is above the X axis? How can I generalize the area under the curve to account for that?

[spare crypt]

is that like a height? you get a simple volume of height * [cos(A) * R* R *pi/2] added to the complicated part

[glossy pine]

Yeah I want the volume under the permimeter of the circle (not the volumn of the cylinder). I guess it's maybe equivalent to the surface area of the cylinder

[glossy pine]

I think this makes sense

[glossy pine]

wait but, doesn't that just scale the complicated part? That formulat doesn't seem right

[spare crypt]

if it's this direction, not sure if that's what you meant

[glossy pine]

yeah that's what I'm going for

[spare crypt]

so just base*height for the green extra bit

for the red you need some integral of the plane with that angle

[glossy pine]

Just calculating the surface area of the exterior side, not the cylinder volumn

I think the perimeter of the shadow would be (2*R*pi)*cos(A) so the surface area would be (2*R*pi)*height*cos(A)

[spare crypt]

oh gotcha

perimeter of curves doesn't scale nicely though

like a circle has circumference 2pi*r but for an ellipse it's an impossible integral

[glossy pine]

is the perimeter of the tilted circle not just scaled by a factor of cos(a)?

err... I guess maybe not, if it's exactly flat, it would be a 0

err... maybe I use opposite sin/cos for the complicated part and the simple part?

so like cos(A) * complicated + sin(A) * simple

[spare crypt]

uh it should be the same thing

just depends on where you write the angle, and you can just use what makes sense at like 0 degrees to check

but yea there's no formula to get from left perimeter to right

[glossy pine]

yeah so I want it to be between a simple rectangle (2*radius*height) and a semi-cylinnder

for the simple part

so neither can have a 0 term

[spare crypt]

you just have to do the arc length integral

[glossy pine]

Man this is hard 🙂

I think maybe I'm doing it wrong

Maybe I'm formulating the question wrong. I need to rethink

Imagine I have a sphere that has a circle defined with a radius a in this picture determined by the cos(theta).

Given an arbitrary circle of such description, I want the average y coordinate.

(Ignore the "solve for" test, used for image only)

When the tilt is either 0 or 90, it's easy. It's either a constant y, or the y is the integral of the circle

[spare crypt]

average over the angle?

[glossy pine]

average of the y coordinate, which effectively is the cosine of some angle, I think

[spare crypt]

and y is the height?

[glossy pine]

yeah

[spare crypt]

you'd do like 1/(angle range) * integral of rcos(theta)

er I guess sin since it's height

[glossy pine]

and what's integral of rcos(theta)? I think it would be r*sin(theta)+C right?

[spare crypt]

right

[glossy pine]

Ok interesting. I'll try it

thanks

[spare crypt]

👍

[glossy pine]

.close

[devout snow]

Channel closed

Closed by @glossy pine

Use .reopen if this was a mistake.

[devout snow]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• 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.

[flat stratus]

I have a question with some statements:
statement:
angles subtended by a chord at the circle in the same segment are equal in magnitude
converse also holds:
if the line joining 2 points a and b subtend equal in magnitude angles at 2 other points on the same side of it, then the 4 points lie on a circle
how can I use the converse to provethis:

if theata = pi/2, use the scalar product of two suitable vectors to find the cartesian equation in terms of x and y of locus of points which satisfy the relation Arg(z-a) - arg(z) = pi/2 where a = 2+0i.

[flat stratus]

also another qu: how do i write a rotation matrix of z when applied by a multiplication of w (z and w are both complex numbers), in terms of w, using polar form. do i write like [w-rsintheta] for rcostheta cuz w = rcistheta which is rcostheta rsic theta and etc for sintheta, -sintheta

[devout snow]

@flat stratus Has your question been resolved?

[flat stratus]

<@&286206848099549185>

[flat stratus]

:0

[flat stratus]

<@&286206848099549185> i only really need help on confirmation on this now as the 1st question i kind of get

[devout snow]

@flat stratus Has your question been resolved?

[devout snow]

@flat stratus Has your question been resolved?

[devout snow]

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.

[patent lodge]

I split the triangle but how do I find the value of the line

[meager yarrow]

find the angle opposite to the side to use the law of sine

[patent lodge]

Which side

[meager yarrow]

The side you’re looking for
Find the angle that opposites it

[patent lodge]

X?

[meager yarrow]

Yeah

[patent lodge]

Do I ignore the line I put

[patent lodge]

How do I do that

[meager yarrow]

Recall the sum of interior angle of a triangle

[patent lodge]

You’re not helpful at all

.close

[devout snow]

Channel closed

Closed by @patent lodge

Use .reopen if this was a mistake.

[devout snow]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• 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 marsh]

What is your answer for 6.a and b? I got a correct according to answer scheme but for b i got -9<f(x)<5

[winter torrent]

reminder that it's sin^2 in your function

not just sin

[devout snow]

@viscid marsh Has your question been resolved?

[livid hamlet]

xd

[viscid marsh]

How does this make a difference though

[solar goblet]

the domain of sinx is [-1, 1], while sin^2x is [0, 1]

[viscid marsh]

Oh right

[devout snow]

@viscid marsh Has your question been resolved?

Channel closed

Closed by @viscid marsh

Use .reopen if this was a mistake.

[devout snow]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• 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.

[fresh harness]

can i get help with this question

[fresh harness]

wait

yea im confused

[heavy current]

this looks good so far

[floral ridge]

multiply numerator and denominator by cost

[fresh harness]

OHHHHH

ahahah im so dumb ty

[restive river]

you could have split the fraction

[floral ridge]

no identities are just annoying

[restive river]

it looks easier

[floral ridge]

yep that too

[fresh harness]

yeah i was like cross multiplying it but i got it now thnx

[restive river]

splitting is way faster than this

[fresh harness]

oh how does that work

[floral ridge]

imma explain with an example

(1+1)/2

can you rewrite it as 1/2+1/2

yes or no

[fresh harness]

yeah i think

[floral ridge]

so now

[restive river]

similarly sec x - cos x/ sec x = sec x/ sec x - cos x/sec x

[floral ridge]

can you rewrite your expression as sect/sect-cost/sect

[fresh harness]

no.. i dont think so

[floral ridge]

is that a mushroom cloud i see

[floral ridge]

why

[restive river]

prolly

[floral ridge]

wdym prolly

[fresh harness]

im confused actually

i know sec is like opposite of cos

[floral ridge]

get ridda that for a sec

pun not intended

[restive river]

$$ \frac{sec x - cos x}{sec x} $$

[fresh harness]

yeah

similar to what im doing

[woven radish]

Tuf Dawg

[restive river]

yup

[floral ridge]

can you rewrite $\frac{x-y}{x}$ as $\frac{x}{x}-\frac{y}{x}$?

[fresh harness]

oh shoot yeah

[woven radish]

The Prophet Of The Damned

[floral ridge]

boom

[fresh harness]

wait this makes so much sense now

[floral ridge]

\sec(x) and \cos(x)

[restive river]

so can you rewrite $\frac{sec x- cos x}{sec x}$ as $\frac{sec x}{sec x}-\frac{cos x}{sec x}$ ?

[woven radish]

Tuf Dawg

[fresh harness]

yeah u can

[floral ridge]

\sec(x) bro

[restive river]

oh i am new to the commands actually

[floral ridge]

1/sec is?

[restive river]

so basically $\frac{sec (x)}{sec (x)}$ = 1 ?

[woven radish]

Tuf Dawg

[fresh harness]

yea

[restive river]

cool

now

wat is the equation?

[fresh harness]

cos/sec - 1

[restive river]

nice

now what is sec(x) =

(hint: turn it to the form of cos(x))

[fresh harness]

oh 1/cos(x) right

[restive river]

yeah

now what happens in $\frac{cos (x)}{\frac{1}{cos(x)}}$

[woven radish]

Tuf Dawg

[fresh harness]

multiply by reciprocal?

[restive river]

gud what do you get?

[fresh harness]

cos^2

[restive river]

exactly

now what is the full equation?

[fresh harness]

1- cos^2

[restive river]

what do you get by using identity?

[fresh harness]

o sin^2

[restive river]

and that is the answer

[fresh harness]

wow thats simpler actually

i appreciate the help mane

[restive river]

exactly

just a tip

while doing these stuff

don't directly go at identitities

first try to split

then try to reciprocal into the rhs

and then if needed identities

[fresh harness]

gotcha

[devout snow]

@fresh harness Has your question been resolved?