help-26

[thorny flame]

Results provided by WolframAlpha

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

Requested by frosst

[jade thunder]

That’s great to know mr wolfram

[grim inlet]

I dont understand T _ T helpp

[jade thunder]

Honestly no clue

Maybe try parametrics maybe the number is nicer?

Doubt it tho

[grim inlet]

ill just ask if there's an error in the given

alright

thank you for the help guys < 3

.close

[topaz sinew]

Channel closed

Closed by @grim inlet

Use .reopen if this was a mistake.

[topaz sinew]

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 gate]

quick question, why does the degree matter in a polynomial function?

[mild hedge]

did u try to look it up or use ai

it works sometimes

just to let u know

[limpid gate]

was planning on helping you but youre an asshole

[mild hedge]

WHAT?

i was trying to help u or give u a suggestion

i am not trying to be mean

@limpid gate here
The degree of a polynomial function matters because it tells us important things about the function:

Shape: The degree determines the overall shape of the graph. Higher-degree polynomials can have more curves and bends.
Roots: The degree tells us the maximum number of roots (solutions) the polynomial can have.
End Behavior: The degree influences how the function behaves as
𝑥
x goes to very large positive or negative values.
Turning Points: The degree gives the maximum number of turning points (where the graph changes direction) the polynomial can have.
In essence, the degree provides a lot of information about the graph and behavior of the polynomial function.

[limpid gate]

yes it tells us shape and end behaviour, but unless its a quick and simple question, its not something I need to know when graphing the polynomial I assume, but for some reason my prof is pointing it out in graphs for some reason

[topaz sinew]

@limpid gate Has your question been resolved?

[limpid gate]

.close

[topaz sinew]

Channel closed

Closed by @limpid gate

Use .reopen if this was a mistake.

[topaz sinew]

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 rock]

how am i supposed to solve this?

[mortal rock]

can someone helpp

[topaz sinew]

@mortal rock Has your question been resolved?

[quiet kite]

The way Id approach this is by first solving cos(y)=-1/2

[grizzled geode]

yeah

using the unitary circle

[mortal rock]

yeaa i did that

[grizzled geode]

only two ways are there

y has to be either 120 or 240 degree

then try to do put pi/2sin(pi/2cosx)= 120 or 240 see how many satisfy

[mortal rock]

so i used the formula and i got pi/2sin(pi/2cosx)=2npi+-2pi/3

idk what to do after that

[mortal rock]

yeaa so if i divide the rhs by pi/2 then i’ll get sin(pi/2cosx)=4n+-4/3

what should i do after that i’m so blanked out rn

[grizzled geode]

n? whats n in this case?

[mortal rock]

n as natural number right, if i put n=0,1,2… then i’ll get the desired angles

[grizzled geode]

Ok so from what I am getting

there are 0 values

since by simplifiying that pi/2sin(pi/2cosx) = 120 or 240

[mortal rock]

ahh how

[grizzled geode]

I am getting values of

sin(pi/2cosx) > 1

whatever im getting on the equal sign is greater than 1

which is impossible to be true between 0 and 2pi since sine has the range of [-1,1]

[mortal rock]

yeaa okayy

[grizzled geode]

since sin(x) value is overstepping that range, there are no values to satisfy

[mortal rock]

okayy got it thankss

[grizzled geode]

np

[mortal rock]

is the answer d

[chilly walrus]

no

how did you get that?

[mortal rock]

i got theta value to be 3pi,2pi

wait no

the theta values were pi/2,2pi,5pi/2

[chilly walrus]

are you sure 2pi works?

[mortal rock]

i think soo

[chilly walrus]

what is cosec(2pi)

[mortal rock]

wait

0

[chilly walrus]

=||1/sin(2pi)=1/0, uh-oh||

[chilly walrus]

no

[mortal rock]

yeaa

sin 2pi is 0

[chilly walrus]

yea

and division by zero is no good, so it's not a solution

[mortal rock]

okay so i js have to reject 2 pi and the ans will be 3

[chilly walrus]

which leaves us with pi/2 and 5pi/2

yep

[mortal rock]

yeaaa okayy

thankss

is the answer c

[mortal rock]

can someone helpp

<@&286206848099549185>

[topaz sinew]

@mortal rock Has your question been resolved?

[topaz sinew]

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.

[trim chasm]

I'm confused that this problem even has a solution. Here, I tested some degrees of $p$: If the degree of $p$ is 1, then we have $1 \cdot 1=2$ which is not valid for all $x$. If $p$ has a degree of 2, we have $2 \cdot 2=3$ which is impossible for all $x$. From this, we can determine that the degree of "polynomial" $p$ must lie between 1 and 2, but there are no integers between 1 and 2, therefore $p$ can't be a polynomial! What do I do?

[thorny flame]

Cube

[opal vault]

how are you so sure that the degree of the right hand side is 2 and 3?

[trim chasm]

If $p(x)$ has degree one and leading coefficient negative 1, then the $ x^2 $'s cancel out, leaving a linear degree on both sides. Is that right?

[thorny flame]

Cube

[trim chasm]

I just realized this

[opal vault]

yep

[trim chasm]

Alright, that's all I need

.close

[topaz sinew]

Channel closed

Closed by @trim chasm

Use .reopen if this was a mistake.

[topaz sinew]

Available help channel!

Send your question here to claim the channel.

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

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

[alpine dirge]

This question's (Q12) in my textbook and I'm not convinced that the planes form an enclosed region

[alpine dirge]

For one it has to be a tetrahederon due to 4 intersection points but I have a very hard time convincing myself and visualising that

[icy sky]

any four planes thrown into 3d space is likely to be a tetrahedron

[alpine dirge]

Is there any visualisation/geometric explanation that makes this obvious

[icy sky]

the normal vectors have to all point in different directions

and no 3 are coplanar

you could think about some insphere and all the normal vectors pointing from the plane point of tangency to the incenter

[alpine dirge]

I'm not able to visualise that

things appear really messy adding the 4th plane

[icy sky]

try to just visualize the tetrahedron

[alpine dirge]

Would I be right to say that 3 planes divide 3D space into 8 octants, just as 2 lines in 2D divide space into 4 quadrants?

So the fourth plane has to form an enclosed region within one of the octants

[icy sky]

3 planes, not 3 lines

[icy sky]

yes to this but be careful because if planes are parallel, they wont enclose a space

[alpine dirge]

Just wondering how nightmarish would it be if I threw a 5th plane into the mix

[icy sky]

that doesnt sound fun

[alpine dirge]

[icy sky]

i also left this out because its even more confusing but if you have three which are like a triangular prism, they also wont enclose space

hence the no 3 coplanar normal vectors like i said earlier

[alpine dirge]

That's way easier to visualise actually

[icy sky]

oh

[alpine dirge]

I mean for 2D I think of the varying enclosed region as lines rotating around some pivot while doing that in 3D is pretty bollocks

[icy sky]

interesting, i find that not too bad of a jump

[alpine dirge]

.close

[topaz sinew]

Channel closed

Closed by @alpine dirge

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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

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

[south talon]

how wrong am i

[mint crescent]

$a^{b+c} \neq a^b+a^c$

[thorny flame]

Civil Service Pigeon

[south talon]

the +1 has just confued me

and i just dont know how to deal with it

[mint crescent]

$1=\log_7 7$

[thorny flame]

Civil Service Pigeon

[mint crescent]

Alternatively, just note that $a^{b+c}=a^b \cdot a^c$

[thorny flame]

Civil Service Pigeon

[south talon]

ah ok

thank you

🫡

.close

[topaz sinew]

Channel closed

Closed by @south talon

Use .reopen if this was a mistake.

[topaz sinew]

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.

[neon iron]

how is the point (-1, -pi/2) a polar coordinate too of that point

is the r and theta being converted into positive?

|r| and |Θ|

[mint crescent]

In general, $(r, \theta)=(-r, \theta+\pi)$

[thorny flame]

Civil Service Pigeon

[mint crescent]

I’ll leave it to you to justify why

[neon iron]

r is the distance so its always positive?

[glacial adder]

think about what -r does

[mint crescent]

But this gives you $\left(1, \frac{\pi}{2} \right)=\left(-1, \frac{3\pi}{2} \right)$

[thorny flame]

Civil Service Pigeon

[mint crescent]

And then you can subtract 2pi from this

Which gives you $\left(-1, -\frac{\pi}{2} \right)$

[thorny flame]

Civil Service Pigeon

[neon iron]

ahh so polar coordinates should not be linked with cartesian in any way like i was thinking u have to be give the exact point but no u can go clockwise and anticlockwise

condition is u have to keep |r|

same

[mint crescent]

If you’re asking if:

• |r| must remain the same no matter how you represent the polar coordinate
• Polar coordinates should not be confused with rectangular coordinates

Then yes, you’re right

[neon iron]

Cool!

thank you

[mint crescent]

[topaz sinew]

If you are done with this channel, please mark your problem as solved by typing .close

[neon iron]

.close

[topaz sinew]

Channel closed

Closed by @fringe hollow

Use .reopen if this was a mistake.

[topaz sinew]

Available help channel!

Send your question here to claim the channel.

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

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

[magic grail]

hello, what i can do here?

[magic grail]

i dont know how to demostrate A ⊂ A-C

[hazy pumice]

1. B and C have no elements in common (given)
2. A is a subset of B (given)
3. A and C have no elements in common (1 and 2)
4. A - C = A - null set = A

[topaz sinew]

@magic grail Has your question been resolved?

[magic grail]

and how would the demonstration be?

[hazy pumice]

That's the most rigorous proof I can give you right now. There is a more rigorous syntax, but I do not know if your class requires you use it, and I have forgotten it

[magic grail]

.close

[topaz sinew]

Channel closed

Closed by @magic grail

Use .reopen if this was a mistake.

[topaz sinew]

Available help channel!

Send your question here to claim the channel.

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

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

[haughty ember]

can somebody solve this for me?

[haughty ember]

I've tried doing it but I think I've messed up on something majorly

because theres no way it takes -0.8 something amount of seconds

[icy sky]

can you show your work please

[haughty ember]

Yes, give me a second

[haughty ember]

I probably solved the second part wrong but I can't think of other ways

[icy sky]

when you divide or take the square root, you have to divide or square root the whole of each side

[haughty ember]

oh? like the whole -30 and everything?

[icy sky]

yes

[haughty ember]

could you show me to steps or transcript it a little of how to do it?

[icy sky]

are you familiar with the quadratic formula?

[haughty ember]

yes

OHH

was I supposed to do the formula??

[icy sky]

yes

[haughty ember]

that makes a lot of sense

Thank you!

.close

[topaz sinew]

Channel closed

Closed by @haughty ember

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.

[pallid spruce]

the problem is the top equation one, this is by far the furthest I could do it

[icy sky]

!original please

[topaz sinew]

Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.

[pallid spruce]

$\text{If } \omega \text{ is the cube root of unity, then } \tan\left(\left(\omega^{200} + \frac{1}{\omega^{200}}\right)\pi + \frac{\pi}{4}\right) \text{ equals}$

[thorny flame]

fatisco

[icy sky]

looks like you were on the right track

remember that 1/(w^2)= w^(-2)

i know its omega, but w is fine

then also note that (1+w+w^2)=0, try to work that into it

[pallid spruce]

Okay

[pallid spruce]

Now I'm stucky in $tan(-\pi + \frac{\pi}{4})$

[thorny flame]

fatisco

[icy sky]

surely you got this

its on the unit circle

[pallid spruce]

3pi/4? surely I don't assume the pi as 3 or is there any other pi tan rules I haven't learned

[icy sky]

simplify -pi+pi/4

[pallid spruce]

yeah I did

In an explanation video tan(3pi/4) is -1?

[icy sky]

ye

[pallid spruce]

is there like a way to count that without calc

Because the multiple choice was the 1, not 3pi/4

[icy sky]

tan(-3pi/4)=1

not -1

whoops

[pallid spruce]

plus lol

not minus

[icy sky]

but dont forget to plug the -3pi/4 back into tan

[pallid spruce]

the minus was put in front of the tan

i guess i'll just memorize it

thanks underful

.close

[topaz sinew]

Channel closed

Closed by @pallid spruce

Use .reopen if this was a mistake.

[icy sky]

youre welcome

[topaz sinew]

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.

[brittle void]

i have a sss triangle

this is what it should be to get angle A

but no matter what i try I can't get 31.5

[whole geode]

Check your parenthesis

Your denominator is wrongly parenthesized

You have $\frac{a+b+c}{d} \times ef$ when you wanted $\frac{a+b+c}{def}$

[brittle void]

!!!

thats it!

[thorny flame]

OmnipotentEntity

[brittle void]

ughhhh idk how i didn't notice

it comes out correctly with proper parenthesis

thanks!

.close

[topaz sinew]

Channel closed

Closed by @brittle void

Use .reopen if this was a mistake.

[topaz sinew]

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.

[fast sedge]

Can someone help me with this?
I already have the answers, I was just wondering if someone can check for me if they are correct or if i messed up somewhere.

give the exact, fully simplified values for each of the six trigonometric functions for the angle shown in the picture below (remember that the exact answers that we might get here are fractions, possibly with square roots involved, but do not use decimals).

√ = square root
sin(α) = (-5√29)/(29)
cos(α) = (-2√29)/(29)
tan(α) = 5/2
cot(α)=2/5
sec(α) = - (√29) / 2
csc(α) = - (√29) / 5

[topaz sinew]

@fast sedge Has your question been resolved?

[fast sedge]

@knotty finch

Can anyone help me with this real quick

[modern rock]

what are u after?

[fast sedge]

Its just teh messahe above

with the image

[fast sedge]

here

[fast sedge]

I just wanted to make sure I got the answers correct and didn't mess up anywhere, i have all the work

[modern rock]

can u explain where u got root 29

[fast sedge]

yes that was the radius

I plugged in the x and y into the equation to solve for radius and i got 2 root 29 from root 116

[modern rock]

yeah no it looks ifine

[fast sedge]

okay thanks

i did it correct for the angle right?

[modern rock]

yeah it looks fine, if theta is in the third quadrant that is

[fast sedge]

it is in the 3rd quadrant though right?

[modern rock]

looks like it

[fast sedge]

okay thank you really appreciate it

[topaz sinew]

@fast sedge Has your question been resolved?

Channel closed

Closed by @fast sedge

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.

[brittle void]

Help!! im actually stumped

[brittle void]

with this triangle

i need to find the remaining angles and side

is this correct?

I've gone back and forth with google and calculators for like an hour now

[tall forge]

wrong naming of sides and angles in you calculation

the one you solve using sine law is Angle C

[brittle void]

wait so did i switch them

[tall forge]

then 84.68 degrees is Angle B

be careful with the letters. Uppercase letters denote angles. Lowercase letters denote sides

[brittle void]

oh shoot

[tall forge]

2.2/sin(C) = 1.3/sin(31.9)

[brittle void]

?

[brittle void]

what does this mean

and does side c check out?

[tall forge]

ok wait. i was wrong it should be angle C not angle B

[brittle void]

oh so i was right after all?

[tall forge]

where did you get this?

it should be like this. opposite the angles are its sides

[brittle void]

hold on sorry can we backtrack

in this image

[brittle void]

are my angles labeled correctly?

then i have this thing

which was supposed to be for side c

[tall forge]

i dont trust that hehe

Angle B is unknown therefore, also, side b is unknown

[brittle void]

i think i labeled them wrong

[tall forge]

it should be

side a= 1.3
side c=2.2
Angle A = 31.9

angle B and side b are unknown

[brittle void]

i input b as c i think

so 3.19 should be

...side b

[tall forge]

not sure about that

[brittle void]

neither am i man

[tall forge]

use sine law instead of that one

[brittle void]

ok so

i need to find

side b

angle B

[tall forge]

yes

[brittle void]

and angle C

[tall forge]

yes

[brittle void]

starting with side b

law of cosines i think

[tall forge]

no!

use law of sines. Solve for Angle C

this type of triangle falls on Case 2 of obliques triangles which is solvable by using Sine Law

also, this triangle has 2 solutions. hehe

[brittle void]

ssa triangle

needs law of sines

yes

[tall forge]

and by the way you have solved Angle C already as well as Angle B

[brittle void]

how do we feel about this

good

i feel good about this one

[tall forge]

A=31.9
B=84.68
C=63.42

[brittle void]

so angle c is 63.42 i think

with

this

[tall forge]

yes. correct

[brittle void]

oh fantastic

now

i still need

side b

and

angle B

[tall forge]

just subtract A and C from 180

B= 180-A-C

[brittle void]

oh yeah!

84.86

84.86+31.9+63.42

how the hell does that add up to a smidge more than 180

[tall forge]

you mean 84.68

[brittle void]

i guess i do

that is a very reasonable explanation

84.68+31.9+63.42

yes and it's fixed

sigh

anyways for side b

side a is 1.3

side c is 2.2

[tall forge]

yes

[brittle void]

angle A is 31.9

Angle B is 84.68

[tall forge]

yes

[tall forge]

yes. correct

✅

[brittle void]

oh my goodness

thank you very very much

[brittle void]

full disclosure i am incredibly sleepy

you have done the very difficult task of explaining something to me

and i am also taking micro naps between words it feels

[brittle void]

you are a very smart person

[tall forge]

thanks🤩

[brittle void]

thank you again!!

i am off to sleep, have a great rest of your day or night or whatever

[tall forge]

yeah. good night

[brittle void]

.close

[topaz sinew]

Channel closed

Closed by @brittle void

Use .reopen if this was a mistake.

[topaz sinew]

Available help channel!

Send your question here to claim the channel.

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

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

[lusty cedar]

I got B = 4 and C = 3

but I'm unsure as to how to show that A is equal to 0

[torn rover]

if you add the two terms with B and C, then that is f(x). So f(x) = A/(3x+2) + f(x), and of course A = 0

[lusty cedar]

wait so do I just substitue them into the fractions

add them, show that's f(x)

and that's it?

[torn rover]

yeah that works

try it out

[lusty cedar]

Is that what they meant by comparing coefficients?

[torn rover]

i suppose

[lusty cedar]

ok thanks

.close

[topaz sinew]

Channel closed

Closed by @lusty cedar

Use .reopen if this was a mistake.

[lusty cedar]

Also is it wrong if I put the 2

in its on bracket

and write that as to the power of -2

[torn rover]

this isnt equivalent to the original term

[lusty cedar]

oh this is a seperate question btw

[torn rover]

oh i see

[lusty cedar]

oh technically it's part b xd

its just the answer gives it in this format

[topaz sinew]

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.

[pallid harness]

Can someone explain 4?

[topaz sinew]

@pallid harness Has your question been resolved?

[modern rock]

plug z=x+iy into both equations

[modern rock]

oh yeah thats seemingly much faster

[brave coral]

mhm

[pallid harness]

thanks a lot

thanks a lot

[brave coral]

no problem

[pallid harness]

.close

[topaz sinew]

Channel closed

Closed by @pallid harness

Use .reopen if this was a mistake.

[topaz sinew]

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.

[obsidian vale]

Hey everyone, we just need our work checked for evaluating the gaussian integral via feynman's technique

[obsidian vale]

We don't use feynman's technique much at all so even though we got the right answer at the end we could've made some egregious error somewhere along the way

[topaz sinew]

@obsidian vale Has your question been resolved?

[obsidian vale]

<@&286206848099549185>

[topaz sinew]

@obsidian vale Has your question been resolved?

[obsidian vale]

No it hasn't, bot

[opal vault]

wait so you used feynman's technique to get that the gaussian integral is 2 Gamma(3/2), and then you're allowed to use the result that Gamma(3/2) = sqrt(pi)/2?

because uhm... Gaussian integral = 2 Gamma(3/2) is immediate with variable change u = x^2 at this step

@obsidian vale I suggest you look into that

[obsidian vale]

Oh we didn't notice that, but thinking back on it....ouch that's so obvious >.<

Thanks /genuine

[opal vault]

wait so you're allowed to use Gamma(3/2) = sqrt(pi)/2?

[obsidian vale]

That was a result I knew of previously because I looked it up a few months ago

[opal vault]

ah but were you allowed to?

[obsidian vale]

This was a problem we did on our own time, not for a class

[opal vault]

ah ok

maybe if you show the original question I could see what the teacher wanted you to do

[obsidian vale]

Wasn't from a teacher, just wanted to try doing $\int_{-\infty}^{\infty} e^-x^2 dx$ just for the sake of it as we'd seen the solution via polar coordinates before but wondered if there were other ways to do it

[thorny flame]

The Cat Collective

[obsidian vale]

Oops mixed up the latex

[opal vault]

well the way you did it is actually the other way around

it's because we know the gaussian integral that we know Gamma(3/2) = sqrt(pi)/2

I can give you another way to do it if you want to

[obsidian vale]

Surw

Sure**

[opal vault]

ok

study the functions:

$A(t) = (\int_{0}^te^{-u^2}du)^2$

and

[thorny flame]

rafilou2003

[opal vault]

ok there we go

and

$B(t) = \int_0^1 \frac{e^{-t^2(1+x^2)}}{1+x^2}dx$

[thorny flame]

rafilou2003

[opal vault]

So by studying I mean :

1. Find their derivatives

2. You'll find out what to do next when you've properly done 1)

[opal vault]

good luck

(you can ping for help)

[obsidian vale]

Thank you :)

.close

[topaz sinew]

Channel closed

Closed by @obsidian vale

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.

[shrewd cave]

would the formula to calculate how much left of a loan you need to pay off be

[shrewd cave]

p(1+i)^n - (r/i)((1+i)^n - 1)

[topaz sinew]

@shrewd cave Has your question been resolved?

[shrewd cave]

aint nobody helping me bruh

shit server

shit people

fuck you all

can never get help in this shitty fucking server

[topaz sinew]

@shrewd cave Has your question been resolved?

[waxen dome]

You need to learn patience

[waxen dome]

This makes 0 sense, I don't understand what you're asking for

[waxen dome]

You sent this with no context

[shrewd cave]

id!ot

[waxen dome]

🪞

mb

Please rephrase with clarity

[vast temple]

whats p? whats i? whats r?

[topaz sinew]

@shrewd cave Has your question been resolved?

[cinder sequoia]

not with that attitude you're not

[topaz sinew]

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.

[tepid glacier]

I can do most prisms

but

idk how to do trapezoidal

do I just find the sa of the trapezoid

then * it by the height

of prism

like

I make it stand up

so that the height is 10

oh

woops

I dumb

[modern rock]

i'd recommend just breaking this up into basic shapes

[tepid glacier]

hm

google telling me to use this formula

length of base 1 + length of base 2

multiplied by height of trapezoid

• perimeter

and height

of prism

sa of the trapezoids is 22?

ok

top base is 40

bottom base is 70

back side is 40

idk front side

cause idk slant height

how do I find slant height in this situation

yeah

ik this

but idk how to get the bottom

3

ohh I see

the bottom 7 - top 4

forgot about the top 4

ok

so 5

because triples

ok

50

?

so 40 + 40 + 22 + 22 + 70 + 50

244

cool

thanks alot

👍

.close

[topaz sinew]

Channel closed

Closed by @tepid glacier

Use .reopen if this was a mistake.

[topaz sinew]

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.

[sly pasture]

!status

[topaz sinew]

What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

[sly pasture]

what is your current process

[autumn junco]

I found all the angle measures but I’m not sure where to go after that

I do know it’s a 30-60-90 and stuff

[sly pasture]

did you find length of AD?

[autumn junco]

no i didnt know how to do that

im pretty sure it is 2 times the length of AC

[sly pasture]

did you find DAB angle?

[autumn junco]

yeah

30

[sly pasture]

what is it

so you have a isosceles triangle right?

[autumn junco]

ohh yeah i see that

[sly pasture]

I guess now you can find legnth of AD and then AC

[autumn junco]

so AD is 100

[sly pasture]

yes

[autumn junco]

so AC is 50 times square root of 3 right

[sly pasture]

yep

[autumn junco]

thanks man

[sly pasture]

no problem

[autumn junco]

.close

[topaz sinew]

Channel closed

Closed by @autumn junco

Use .reopen if this was a mistake.

[shrewd cave]

p is poop i is igloopoop and r is roopoop 🤣

[topaz sinew]

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.

[fiery grove]

Triangle ABC is a 30-60-90 degree triangle with BC as the shortest leg, and Angle C as the right angle. Find the coordinates of A in Quadrant I if B(-4, -2) and C(2, -2)

[fiery grove]

help plx

[austere remnant]

Can you first try to draw the diagram yourself and show it to me?

[topaz sinew]

@fiery grove Has your question been resolved?

[topaz sinew]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[topaz sinew]

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.

[bitter swan]

Why is the graph stopping here?

[fiery grove]

what do you need from it

you can just enter a new line and put an x value you want

like

"x="

or "y="

[bitter swan]

limit, I mean i get the idea that its e but why is it stopping there

[fiery grove]

yeah idk its desmos

[bitter swan]

might be a bug then

[fiery grove]

most likeley

[bitter swan]

cool thanks

.close

[topaz sinew]

Channel closed

Closed by @bitter swan

Use .reopen if this was a mistake.

[topaz sinew]

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.

[neon iron]

Small question how do I write this in repeated multiplication

[restive inlet]

do you know what it means to cube something

[neon iron]

power of power second one

yes

by 3 right

[restive inlet]

multiply three of the same thing together
do it like they dyd for squaring

[neon iron]

they jus do it for squareing

cubed

[restive inlet]

same idea

[neon iron]

measn to the poeer oif 3

like squared is ? to the power of 2

[restive inlet]

squaring is multiplying two of the same thing together
and they've explicitly written that

4^2 multiplied with 4^2
same idea applies for the rest

[neon iron]

How u do that

Tho

Oh it just tells u how many times it’s being multiplyed

?

[restive inlet]

try writing it

[neon iron]

Multiplied*

4^2 that 3 times

4^2 x 4^2 x 4^2

[restive inlet]

yes

[lone hill]

you would do 4^2 first, then you would do the answer but with an exponent of 3 instead of 2

wait nvm am stupid

[neon iron]

What

I’m so lost sorry mb bro

[neon iron]

What I said was right or wrong ?

[restive inlet]

yes, seems fine

[neon iron]

Okay appreciate it

Thank you bro

.close

[topaz sinew]

Channel closed

Closed by @red minnow

Use .reopen if this was a mistake.

[topaz sinew]

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.

[ivory musk]

<@&286206848099549185>

Can someone explain what they mean by this writing in green

[urban grove]

Please wait 15 minutes before pinging Helpers

[ivory musk]

Okay

[urban grove]

It's because x is an odd function though

And if you integrate an odd function over a domain symmetrical about the origin, you get zero

[ivory musk]

So integration any function of the kind x^(2n+1) will give 0? If it’s symmetrical about the origin

can someone explain where i went wrong

answer supposed to be 19 pi

[urban grove]

yup

[urban grove]

I guess I should say, if it's symmetrical about the reflection x -> -x

so, reflection about the yz-plane you could say

[topaz sinew]

@ivory musk Has your question been resolved?

[topaz sinew]

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.

[plush oar]

duds

[plush oar]

,wolfram t\frac{dt}{dy}+19y=\frac{1}{t},:t>:0

[thorny flame]

Results provided by WolframAlpha

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

Requested by bigyannis

[raven sparrow]

$t\frac{dy}{dt}+19y=\frac{1}{t}$?

[thorny flame]

Azyrashacorki

[topaz sinew]

@plush oar Has your question been resolved?

[topaz sinew]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[topaz sinew]

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.

[ripe heron]

The lines with equations y = 7x − 4, y =x/13 + 3, and y = −9x/10 + 15 divide the (x, y)-plane
into seven regions, one of which is a triangle. Determine the number of lattice points in this
triangular region. A lattice point is a point (a, b) where a and b are both integers. Each point on at least one of
the three lines is not considered to be in the triangular region.

[topaz sinew]

@ripe heron Has your question been resolved?

[rustic totem]

you can just graph all of lines and count

[ripe heron]

the teacher said this about that

Graphing would be a good place to start, but you will want to include an algebraic argument that shows why lattice points are indeed inside (or outside) of the region.

<@&286206848099549185>

[topaz sinew]

@ripe heron Has your question been resolved?

[topaz sinew]

@ripe heron Has your question been resolved?

[topaz sinew]

Channel closed

Closed by @ripe heron

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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

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

[limpid wave]

can anyone help me how to approach this problem?

[leaden hatch]

first plot the three points they give and then f' and f'' to figure out concavity

[topaz sinew]

@limpid wave Has your question been resolved?

[topaz sinew]

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.

[brittle void]

so i tried using my wonderful inverse sine calculator

womp womp

[cinder sequoia]

i would like to add that this is a stupid question because arcsin outputs only one angle ._.

[brittle void]

most of my questions are stupid

[cinder sequoia]

the answer you've selected is correct

simplest way is to just take sine of your multiple choice options to see which ones give -1/2

[brittle void]

basically what i did

but im curious as to why my calculator spat out something i didn't expect

[cinder sequoia]

well 210 degrees is 7pi/6 so that accounts for that

[brittle void]

clarification, is my asking the question i asked stupid or is the actual question in the image stupid

[cinder sequoia]

and -30 degrees is -pi/6 which is the same as 11pi/6

[cinder sequoia]

oh sorry, the original question in the image is stupid

[sinful pumice]

is using the angle between the x axis and terminal side that i cant think of the name of right now

[cinder sequoia]

reference angle?

[sinful pumice]

yes

[brittle void]

no need to apologize! I take criticism for asking dumb things

[sinful pumice]

youre supposed to able to use the reference angle or something with arcsin

[brittle void]

the reference angle is like

[cinder sequoia]

yeah i mean the reference angle for 1/2 is pi/6, you want -1/2 as your y value so you'd go pi/6 below the x axis

[brittle void]

this

[cinder sequoia]

pi/6 below the x axis on the left side of the origin is 7pi/6, pi/6 below the x axis on the right side of the origin is the same as 2pi - pi/6 which is 11pi/6

[brittle void]

did I input something incorrect here?

the first option was one of those trick you questions where the answer is similar to something you'd get if you did it wrong

[cinder sequoia]

no you didn't input anything incorrect

i mean probably don't use that calculator

if you know your unit circle this isn't necessary

the two angles it gives you are -30 degrees and 210 degrees

which are -pi/6 and 7pi/6

which are 11pi/6 and 7pi/6

[brittle void]

yeah i guess my calculators days are numbered

not as reliable as just doing the thing by hand

thanks!

.close

[topaz sinew]

Channel closed

Closed by @brittle void

Use .reopen if this was a mistake.

[topaz sinew]

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.

[outer socket]

I've attempted to plug in numbers but I feel like I'm going in the complete wrong direction, am I thinking abt it wrong?

[sinful pumice]

you cant have each side be 20

triangles have to have the sum of 2 sides be greater than the third side for every combination of sides

[outer socket]

oh

so i should make ba bigger than ac and bc

[sinful pumice]

it feels like theres information missing

[outer socket]

should i js skip it?

.close

[topaz sinew]

Channel closed

Closed by @outer socket

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.

[timber schooner]

are these the correct formulas for truncated cone

[outer portal]

they should be
what makes you think theyre not

[timber schooner]

oh no i just have no idea

never played around with a truncated cone before

thats all

🙏 wanted to make sure

[outer portal]

its best if you figure out a (calculus, similar triangles, or otherwise) way to find those formulas by yourself

then its more of "do what I found match these images?"

[timber schooner]

yeah yeah i need it for a homework task

[outer portal]

I imagine they look weird at first?

[timber schooner]

the shapes for homework?

not really

our task wass more like a word problem

[outer portal]

no the formulas

[timber schooner]

oh

yeah for sure

looked weird

but it makes sense

[outer portal]

its still weird how cones can be made from a flat piece of paper

[timber schooner]

fr

anyway my task for homework was select a complex household item

then

calculate its current volume and surface area

right?

then using calculus, tweak the measurements of the item using calculus

to get the SAME volume

but less of a surface area

which in turn pretty much improves production costs

makes sense?

[outer portal]

yea

[timber schooner]

ill do it later cause i gotta prob do my own measurements of a sauce bottle

dont think ill find that online

gonna be weird measuring them with a ruler but ill try my best to be as accurate as possible

anyway thank you

.close

[topaz sinew]

Channel closed

Closed by @timber schooner

Use .reopen if this was a mistake.

[outer portal]

np

@timber schooner (btw I checked, the formulas are correct)

[topaz sinew]

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.

[barren radish]

Help please I think I have the answer I’m just not sure I’m right

[meager dawn]

there are solutions on kedlaya’s website

if you know the year this was released

[marsh wagon]

So what do you think the answer is?

[barren radish]

Oh really?

[meager dawn]

if you look up the putnam archive it should be the first result

[barren radish]

Uh bob wins only if it’s even

Bob has a winning strategy if and if n is even

[marsh wagon]

I think thats right but its a pretty confusing question so wouldn't know for sure

[meager dawn]

bob has a winning strategy when n=1

so it can’t just be when n is even

[barren radish]

Lemme try it again

gimme like another hour

[keen night]

hello!!

[topaz sinew]

@barren radish Has your question been resolved?

Channel closed

Closed by @barren radish

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.

[shy lance]

how did they arrive to a<-1 or a>4 from the discriminant

[coarse herald]

write the discriminant and make it negative

[arctic briar]

Just try and expand the whole eq out first

[shy lance]

i got -4a^2 +4a +40<0

makes a^2-a-10>0

am i doing something wrong

[coarse herald]

yeah its correct

[shy lance]

it doesnt factor tho?

should i use completing the sq or something

[coarse herald]

no, you will have to find the roots and factor it out that way

but the roots wont be integers

[shy lance]

like quad formula?

[coarse herald]

the roots are sqrt 41+- 1/2 right so im saying the range will be-inf to sqrt 41-1/2 U sqrt41+1/2, inf

i dont know how to use texit im sorry

[coarse herald]

yes

[shy lance]

how did they conclude to be a <-1 and a>4

since the ans is not integer

[coarse herald]

yeah thats what im confused about too

there arent any more conditions given as well

btw you can prove their ans is wrong

plug in -1.5 = a

you get x^2-8x-9

and thats clearly not always positive

you can look at this: https://www.desmos.com/calculator/wsxrnanukg only for the range sqrt((41)+1/2 , ∞)approximately 3.7 the graph is always positive denoted by the red area

[shy lance]

haha i will ask the prof thanks a lot! @coarse herald

.close

[topaz sinew]

Channel closed

Closed by @shy lance

Use .reopen if this was a mistake.

[topaz sinew]

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.

[woeful stone]

It is best write using exponents

For example cube root of x can be written as x^(1/3)

[acoustic pecan]

its incorrect

[woeful stone]

The point I am getting at your expression is hard to read because does not follow convention. I am more than happy verify if it is correct or not but you need to rewrite it

[acoustic pecan]

if what were a 4

uh, sure

im with team though, just write things as exponents its much easier

[topaz sinew]

Channel closed

Closed by @pure juniper

Use .reopen if this was a mistake.

[topaz sinew]

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.

[worn gorge]

i dont get how to do it

i know i could guess and check but how do i do it mathemtically

[thorny remnant]

Do you know half and double angle formula?

[worn gorge]

um

yes

[thorny remnant]

Then consider x=2(x/2)

[worn gorge]

uhm

[thorny remnant]

Then do for sin(2(x/2))

[worn gorge]

ohhh

okok

lemme give a go thanks

okok

what do i do

about the 1-cosx

[thorny remnant]

Do the same thing for cos

[worn gorge]

uh

double angle it?

[thorny remnant]

And write 1=cos²(x/2)+sin²(x/2)

Then do for cos(2(x/2))

[worn gorge]

wait what

dont i just choose

like

1-2sin^(x/2)

as cos (2(x/2))

[thorny remnant]

That works also

[worn gorge]

ohhh

yeah i got it

thanks a lot

[thorny remnant]

:)

[worn gorge]

can i just ask

for these types of questions

how did u recognise like

what to doo

[thorny remnant]

It's due to practice

[worn gorge]

mhm alright

fair enough then

[sly pasture]

also everything in the options have x/2 so you can guess you havee to do something like that

[worn gorge]

ohhh yeah good point

okok thats a good tip

thanks 🙏🙏🙏

[thorny remnant]

Sure it works only when there's options

[sly pasture]

yes

[thorny remnant]

When there's no options you have to do many methods

Well for pre uni it's not many

[worn gorge]

bruh i am so lost

im guessing its smth similar

but i cannot figure this out

[thorny remnant]

convert cot into 1/ tan

[worn gorge]

for top and bottom?

[thorny remnant]

Yes

[worn gorge]

wait

okok so

i reached

1-tan^2 x / 1+tan^2 x

idk what to do next

[thorny remnant]

That's equivalent to cosx

[worn gorge]

huh

wait why

how did u get that

[grand bluff]

You could also use t-formulae?

[thorny remnant]

it's a well known result

[worn gorge]

wait rly

[thorny remnant]

Yes

[worn gorge]

is it

an idenitty

or smth

[worn gorge]

oh yeah

bruh

so should i just memorise that one

1-tan^2x/1+tan^2x

[chilly walrus]

if you want to see how that is cosine, go off of tan(x) = sin(x)/cos(x) and simplify

[thorny remnant]

Well you should but you gotta know how that result arrived

[worn gorge]

oh okok

[worn gorge]

uhm

[chilly walrus]

i honestly did not know that myself lol

but it's derive-able

[worn gorge]

rly

i just tried but i wsear

i didnt even get it

unless i made a mistake somewhere

[chilly walrus]

show your work

[worn gorge]

wait is

[chilly walrus]

you might've missed that you started with a half angle or double angle

[worn gorge]

hm

wait lemme try again

[thorny remnant]

Ok I'll tell you how directly
$$\cos(2x)=\frac{\cos(x)^2-\sin(x)^2}{1}$$
$$ \cos(2x)=\frac{\cos(x)^2-\sin(x)^2} {\cos(x)^2+\sin(x)^2}$$ then divide $\cos(x)^2 $ on numerator and denominator

[thorny flame]

convergence

[worn gorge]

wait

how did u go from

first line to 2nd line

wait nvcm

i got u

[thorny remnant]

:)

[worn gorge]

ohhh

wait i tihnk i got it now

alr alr thank u

.close

[topaz sinew]

Channel closed

Closed by @worn gorge

Use .reopen if this was a mistake.

[topaz sinew]

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.

[keen linden]

can someone look at this and tell me if i did anything wrong, H is the orthocenter

[ruby tree]

Presumably you meant FDH = HDE

(4th sentence)

Other that that, looks good

Though tbh you only need two angle bisectors

[topaz sinew]

@keen linden Has your question been resolved?

[topaz sinew]

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.

[keen linden]

ye tnx

[keen linden]

why?

[ruby tree]

Two angle bisectors are sufficient to find the incenter of any triangle

The third will always go through the incenter as well

[keen linden]

okay thanks

[topaz sinew]

@keen linden Has your question been resolved?

[topaz sinew]

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.

[final fossil]

this is the rotation matrix

of 45 degrees counter clockwise

the 1/root(2)

is the cos45 and sin 45 from the rotation

so the matrix essentially is
sin 45 -sin45
cos45 cos45

multiplied by matrix
1
0

im struggling to understand why the second column of the rotation matrix is needed

[odd pagoda]

well you use the matrix to multiply it with vectors (x,y). the way matrix multiplication works you need a second column

[final fossil]

so those could just be any numbers

?

[odd pagoda]

x and y? sure

[final fossil]

no, why is -1 and 1 in the second column of the rotation

[odd pagoda]

they need to be whereever (0,1) ends up at

when you rotate it by 45 degrees

[odd pagoda]

btw this is false, it always needs to be both sin and cos in each row

[final fossil]

why

[odd pagoda]

well ok here by coincidence it works but for other angles it would be wrong

[final fossil]

.close

[topaz sinew]

Channel closed

Closed by @final fossil

Use .reopen if this was a mistake.

[topaz sinew]

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.

[indigo ice]

tried rational roots theorem and factoring. can't seem to work it out

[torn rover]

since the question asks for all "possible" zeros

youre likely meant to state all zeros that r possible w the rational root theorem

i.e. ±1, ±3, etc.

bc i also tried w rrt, and there dont seem to be nice rational solutions

[indigo ice]

but its 3 marks so i don't know if they want the specific zeroes in which i can't even find any

[opal vault]

well it looks like no rational roots, but 3 real roots

I don't see any real way but to apply the Cardan formula

Also it's just a possibility but maybe they made a mistake by writing +3 instead of +2

[torn rover]

i would just write out all rrt zeros

because if ur meant to find the zeros, itd say "state all the zeros", not the "possible" zeros

[indigo ice]

okay i'll do that

.close

[topaz sinew]

Channel closed

Closed by @indigo ice

Use .reopen if this was a mistake.

[topaz sinew]

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.

[toxic aspen]

In how many ways can the word MATEMATIK be arranged?

[toxic aspen]

I'm having a really hard time distinguishing between when to use permutations vs combinatorics

Considering they use two different formulas

$P(n,r) = \frac{n!}{(n-r)!}, C(n,r) = \frac{n!}{r!(p-r)!}$

[thorny flame]

Merineth

[toxic aspen]

Where n is the total amount? What does r represent?

[coarse tusk]

You use combinations, not combinatorics, when you need to select/choose objects from some set of objects. In this case, the order of the choice doesn’t matter

You use permutations when you need to arrange/permute objects. In this case, the order does matter

If you can figure out where order matters and where it doesn’t you’re good

[coarse tusk]

r is the number of objects you choose/arrange

From a total of n objects

[toxic aspen]

oooh i see very nicely explained, i'll make sure to write that down

And since it's asking me for how many ways we can arrange we use permutations?

Since MATEMATIK has two M and two T and two A

[regal harbor]

yeah, in that case order matters

https://www.youtube.com/watch?v=XJnIdRXUi7A&t=839s&ab_channel=TheOrganicChemistryTutor skip to 14:08 if you want a practical example