help-42

[formal chasm]

and since a=±5, ab=15, so b=±3, so our answers are 5+3i and -5-3i, or ±(5+3i)

ask if confused plz bc I was very confusing

exact same process as last square root though

[opaque cape]

wait how do u figure out how to uhhh

write it like this

cuz i forgot

[formal chasm]

so we have a^2-b^2=-16 right?

and 2ab=30, right?

(we set the real parts of (a+bi)^2 and 30i-16 to be the same, and the complex parts to be the same)

we know ab=15, so b=15/a, which we sub into the first equation

a^2-(15/a)^2=-16, multiply by a^2, we get a^4-225=-16a^2

then I factor like a quadratic

[opaque cape]

nonono

the factoring part

i meant

how do u factor it like that cuz i knew there was a rule

but i forgot it

yk?

[formal chasm]

you can use the quadratic formula to find the roots

but I just eyeballed it

it's that if you have (x+q)(x+p), then qp=c, q+p=b for x^2+bx+c

maybe?

[opaque cape]

oh

alright

[formal chasm]

excellent!

so we know
[4z=1-i\pm(3+5i)]

[opaque cape]

yes

[formal chasm]

OOPs

istg

[opaque cape]

wait didnt we get the nuimbers already

[formal chasm]

in this step when you add 16 to both sides it means it's +16 in your equation

so your factors are (a^2-9)(a^2+25)

a=±3, a=±5i, therefore a is real so a=±3, then b=±5

so it's a+bi = 3+5i

[potent lotus]

Astral

[formal chasm]

got it backwards

[formal chasm]

wdym?

[opaque cape]

the solutions

[formal chasm]

I got this from here

[opaque cape]

o

[formal chasm]

wdym solutions? you mean when we completed the square?

that was just to isolate z

[opaque cape]

nevermind

yes

[formal chasm]

instead of having z^2+some z

we have to do quadratic stuff multiple times sadly

SO

[4z=1-i\pm(3+5i)]

[potent lotus]

Astral

[formal chasm]

4z=4+4i, 4z=-2-6i

z=1+i, z=-(1-3i)/2

[opaque cape]

ok

thats all right?

[formal chasm]

well

we did all the steps in the right order probably correctly

but idk if it's right be wolfram alpha is giving different roots

the theory is correct for sure I think

[silk heart]

When u finish can u help me?

[formal chasm]

nope! am busy with this and then with my own hw

[silk heart]

It’s way easier then this tho definitely not as hard

[formal chasm]

mmmm no thank you I don't like that kind of problem

,w x^2(1+i)=x+i-3

[potent lotus]

Results provided by WolframAlpha

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

Requested by ___astral

[formal chasm]

https://media.discordapp.net/attachments/948770026914213909/1155569043160440932/2271A45B-6A87-4B37-A32F-07F4CAF6FEB7.png?width=2268&height=434

oh I was right loll @opaque cape

sorry for any confusion I did all the steps right and arrived at the right answer

I think I typed it into wolfram alpha wrong to check 🙃

does this entire problem make sense to you?

please do not hesitate to ask

[opaque cape]

yup

all good

[formal chasm]

hooray!

[opaque cape]

im assuming the last one is just like this one but with more painful calculations right?

[opaque cape]

lol

[formal chasm]

nah c looks just like b

I'll write out the general steps but I think you can try this without my help

1. ||divide by (1-i) to isolate z^2||
2. ||multiply stuff by (1+i)/(1+i) to get rid of the /(1-i)||
3. ||complete the square to isolate z||
4. ||square root both sides, using the a^2-b^2=real part and 2ab=imaginary part method to get the root||
5. simplify (as with previous steps

[opaque cape]

got it

well i dont wanna waste any more of your time since you have homework to do

[formal chasm]

dw about it I have lots of free time while you work

I'm truly happy to help I don't get these types of problems often

I have time to finish all this, not to help more people after this

[opaque cape]

i really appreciate you helping me out

[formal chasm]

really, it's my pleasure

[silk heart]

Can u just look at it cuz no one can solve it

Some guy tried since i sent the pic and has made no progress whatsoever

#help-37

[formal chasm]

no <3

den, you good?

[opaque cape]

yeah

z is i and -2i

sthanks a lot for your help!

i hope you have a blessed day/night 🙏🙏

@formal chasm

[formal chasm]

hooray!

I hope you have an amazing day/night as well!

[formal chasm]

.close

[calm coral]

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[formal chasm]

it would've timed out anyways

[calm coral]

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[eager jackal]

how can you graph a line on the complex plane?

[rigid kettle]

someone else took the channel.

[rigid kettle]

I think you need to be more specific with your question.

[eager jackal]

for example, how can you find the line that is perpendicular to the segment 4+i and 7-2i?

[rigid kettle]

well can you show your sketch

with those 2 points marked on the complex plane

[eager jackal]

i dont have a camera mb it's broken but its just (4, 1) and (7, -2) right? on the complex plane

cuz a+bi and a is the x and b is the y

hello?

[rigid kettle]

yes

wait it says the line???

there are clearly multiple?

[eager jackal]

yea

just any one

[rigid kettle]

well if this were just lines in R^2 do you know the methodology

you use the same, basically

[rigid kettle]

whats the slope of this segment

then what must the perpendicular slope be

[eager jackal]

wait

its just 1 right?

so the perpendicular slope is -1?\

i am just not sure how to plug all the things in the line equation thing

it's like c|z|
2 + az − az + b = 0,

[rigid kettle]

uh

[eager jackal]

wait no that didnt copy paste right

[rigid kettle]

nah, no way its 1

should be clear from your diagram

[rigid kettle]

just find your line equation in R^2 first

before going back to complex numbers

treat it as a problem in R^2

[eager jackal]

wdym R^2?

wait whats the slope formula for lines on the complex plain?

[rigid kettle]

like a y = mx + c problem

[rigid kettle]

these are just 2 points on the (x, y) plane

can you do this problem as if it were on the x-y plane

[eager jackal]

it ownt work like that i think

like all the formulas are different

[rigid kettle]

it most certainly does, I assure you

You can convert your final answer back to the complex plane.

[eager jackal]

ok if it's just on the normal plan then it's slope would be -1

[rigid kettle]

this is yes.

so whats the perp

then using that, name one perpendicular line

[eager jackal]

ok so the perpendicular line slope would be 1

[rigid kettle]

yes, so the slopes have to multiply to -1

if they are perp

[eager jackal]

yes

[rigid kettle]

so what is one such line

[eager jackal]

give me a sec someone calling me rn

give me like 2 min

ok so y=x+5 is one of them right

cuz 5 is the y intercept of the segment

and it's slope is 1

[rigid kettle]

alright

so going back to the complex plane

you have

the complex part = y

real part = x

so

Im(z) = Re(z) + 5

right?

or if z = x + iy,

y = x + 5

[rigid kettle]

for this particular form they want, it looks like ur using conjugates or some similar transformation but its the same kinda idea

Could you show what kind of complex equation form they want

[eager jackal]

i am looking at this post rn i feel like it solves the problem

https://math.stackexchange.com/questions/1109233/how-to-write-eqn-of-line-in-complex-form

[rigid kettle]

so in terms of conjugate, sure.

I'll use * to denote the conjugate of z

[eager jackal]

k

[rigid kettle]

its better you learn how to derive the complex equation from the cartesian

so start with z = x + iy

z* = x - iy

ok?

[eager jackal]

yea

[rigid kettle]

then consider what z + z* and z - z* are

[eager jackal]

2x and 2iy?

[rigid kettle]

yes

and now you are able to write x and y

in terms of z and z*

allowing you to substitute them into y = x + 5

[eager jackal]

ohh that make sense let me try it

thats where the solution in the pose came from i got it

z(2-2i)-z*(2+2i)-20i=0 right?

[rigid kettle]

best you verify yourself by pluggin in 2 points on the line y = x+5

[eager jackal]

yea sure

[calm coral]

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[fierce cradle]

Does anyone understand mathematical induction? Can I show the reasoning for my answers and get feedback from you guys?

[still marlin]

looks good

[fierce cradle]

Can I ask on another question?

[still marlin]

ok

[fierce cradle]

The inductive step involves proving that if the statement P(m)P(m) is true for some arbitrary positive integer mm, then it follows that the statement P(m+1)P(m+1) is also true. So, the correct claim we are proving in the inductive step is B, because Z+ denotes the set of all positive integers. The option B should ideally mention positive integers right, as mathematical induction is generally applied to statements involving positive integers..?

[still marlin]

yeah

[calm coral]

@fierce cradle Has your question been resolved?

[calm coral]

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[remote mural]

can someone help me with this question

thats my process work but im getting -2.1 instead of positive 2.1 which it says in the textbook is the correct answer

id prefer not to learn any new methods but i just want to see where i went wrong

[subtle nexus]

you lost a minus sign at a green line

[remote mural]

wdym

v = u + at, rearrange to u = v - at

then its pretty easy you should get

u = 17 m/s - (2.4 m/s^2 * 6.2 s)
u = 17 m/s - 14.88 m/s
u = 2.12 m/s

[remote mural]

is v1 meant to be negative

[subtle nexus]

it had a minus in front of it

[remote mural]

ohh

so i can multiply both by -1

[subtle nexus]

you mustn't lose a random -1

[remote mural]

so like this

[subtle nexus]

yup

[remote mural]

ty

[remote mural]

idk what any of this is but ty for replying

[subtle nexus]

and yeah, you should solve in formula form

then substitute values

[remote mural]

you think i should learn this instead?

[subtle nexus]

yes

thats the proper way of doing it

[remote mural]

its the formula

you should rearrange the formula before inputting values, it makes it a lot easier

what does the u mean

initial velocity

alr thanks

havea good day

.close

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[leaden thunder]

help channels aren't really for software help

oh you have an equation

just plug in your x value there

yes

,calc 331^2

[potent lotus]

Result:

1.09561e+5

[leaden thunder]

,calc 331^3

[potent lotus]

Result:

3.6264691e+7

[leaden thunder]

,calc 331^4

[potent lotus]

Result:

1.2003612721e+10

[leaden thunder]

plug those values in for x^2, x^3, x^4

[subtle nexus]

nono, he has the values

he needs to extrapolate

[leaden thunder]

yes i know

[subtle nexus]

its some ballistic stuff, so prob not polynomial

[prisma mango]

Ew that equation is gross, yes R^2 = 1 meaning that that's the exact equation but linear equation has the R^2 = 0.9997 which a good approximation too and is 10x easier to deal with

[leaden thunder]

... i told oyu

[prisma mango]

-24.1 + 0.162x + 5.63E-04x^2 + 3.13E-06x^3 + -9.36E-09x^4 X = 331 WHAT IS Y?
If you typed in exactly that, wolfie treats X and x as two different variables because case sensitive

And there is no y in that equation so wolfie doesn't know what to do

So the better way to phrase it is

-24.1 + 0.162x + 5.63E-04x^2 + 3.13E-06x^3 + -9.36E-09x^4 for x = 331

Then you get your value

Yes

That's it

Just close the channel

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[swift marsh]

for equation of trajectory of an object in projectile motion

is there anyway to solve ofr angle theta

assuming everything else is known

or we have to use numerical methods

[hollow perch]

1/cos^2=sec^2=tan^2+1

[swift marsh]

hidden quadratic?

[hollow perch]

yes

[swift marsh]

Might as well give it a shot

cant beleive i didnt know that trig identity tbf

[swift marsh]

big thanks!

.close

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[ivory torrent]

How do we prove questions where there is an intermediary value?
For example, "m>=1, there exists a natural number p, for which for all integers n>=p, it satisfies a statement given".
Here p is the intermediary value.

I am asking how do we approach a question like this? Is there a general format?

Any help is appreciated!

[dull wagon]

induction?

[ivory torrent]

can i use that?

I dont know which technique to use for this kind of proofs

@dull wagon

[dull wagon]

yes, you can use that.

[elfin ermine]

math isn’t that simple 💀

[tacit lark]

Can you be more specific

[dull wagon]

that's why i said it

[elfin ermine]

But induction could work depending on the question

[ivory torrent]

I dont wanna indulge in academic misconduct

[dull wagon]

there may be other approaches too

[tacit lark]

You talk about some m being larger than 1 and then later you dont even mention m

[dull wagon]

but can't say that much without specific examples

[ivory torrent]

p is greater than m and less than n

[ivory torrent]

hmm

I'll try induction

I thought maybe there is a general method

[tacit lark]

Induction is a method among many

What are you trying to prove

[ivory torrent]

I cant tell cause of the question being in an assignment

I'll ask my prof then

Thanks! Sorry if I wasted your time

.close

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[wild marten]

Hi, can anyone help me go from this:

[wild marten]

to

Idk how to simplify it to that point

[hollow perch]

expand the brackets first

$\frac14x^2lnxe^{-x}-\frac12x^2e^{-x}+x^2lnxe^{-x}-x^2e^{-x}$

[potent lotus]

chlamydia

[hollow perch]

you've done something wrong in the integration

[wild marten]

I mean

@hollow perch everything else matches up

my work

profs work

everything matches up until that point

[calm coral]

@wild marten Has your question been resolved?

[calm coral]

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[hollow perch]

what, $cos2\theta=cos^2\theta-sin^2\theta$?

[potent lotus]

chlamydia

[hollow perch]

$cos2\theta=cos(\theta+\theta)$

[potent lotus]

chlamydia

[hollow perch]

and use compound angle formula

unless you want proofs of compound angle formulae

there should be plenty of proofs for that

https://www.math-only-math.com/proof-of-compound-angle-formula-cos-alpha-plus-beta.html
something like this?

what?

[hollow perch]

from here, $cos(\theta+\theta)=cos\theta cos\theta -sin\theta sin\theta$ by definition

[potent lotus]

chlamydia

[hollow perch]

you use compound angle

there's really nothing in between

cos(a+b)=cosacosb-sinasinb

you're putting both a and b as the same thing

yes

[calm coral]

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[random patrol]

no idea where to start

[hollow perch]

difference of two squares to make bottom look like top

[pure kayak]

i feel this likely follows from A

[random patrol]

part a just asked to find limits at x=25 and infinity

[pliant coral]

Yeah there’s a reason those are asked

Horizontal asymptotes are limits at infinity, while vertical asymptotes are infinite limits

[random patrol]

oh i didn't realize that

so for x -> 25 i got -1/10 and x -> infinity i got 0

.close

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[plain swift]

Okay so if 2r=16 and 5e=25 what is the value of r+s

<@&286206848099549185>

[tacit glacier]

Oh french aha, are you french?

[plain swift]

No Canadian haha i go to a french school tho

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Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.

[tacit glacier]

Basically, you can just compute r and s

Since 16 and 25 are powers of 2 and 5 (respectively)

[plain swift]

Hmm i think i got it, this is for a math competition its for higher level math im in 11th grade thats why loll

[tacit glacier]

ok good luck then

[plain swift]

Thank you sir 🤗🤗

[tacit glacier]

You're welcome

Bon courage !

[plain swift]

Merci

[crude compass]

You can close this channel using ".close" if your questions is resolved.

[plain swift]

.close

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[red locust]

and this is my answer

am i right with everything here?

[manic cedar]

yes

[red locust]

thank you

[manic cedar]

np

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[calm coral]

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[crimson merlin]

Number 47

As of right now i got the common denominator as a^5 b^7

but im not understanding what to do the numerators ?

please help anyone

<@&286206848099549185>

@glacial elk

[glacial elk]

do you mean that you have arrived at the numerator "a^2 b^5 - 2a b^6 + 3"

and you aren't sure where to go from here?

[crimson merlin]

no i didn't know what to do for the numerators

is the common denominator a^5 b^7?

[glacial elk]

yes

[crimson merlin]

ok

now what do i do

[glacial elk]

you can't simplify the numerators down much further, so in order to simplify you just combine them into one big fraction, as you can do when the denominator is the same

make them the same by adjusting them to all be the common denominator

[crimson merlin]

yep yep yep

makes sense

thanks it just took me a min

one more thing

can you help me w 49

its the one thats cut off 1/x-1 - 1/x

how would i find the common den

@glacial elk

[calm coral]

@crimson merlin Has your question been resolved?

[minor vector]

multiply them by each other

multiply x by x-1

and multiply x-1 by x

(and obviously multiply the numerators as well)

[calm coral]

@crimson merlin Has your question been resolved?

[calm coral]

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[distant hinge]

How to find csc of 60°

not sure how to find the y and r given just the angle

[hushed tartan]

Why would you want to find y and r

What is cscx

[distant hinge]

sorry meant x and r

confused y and x somehow

wait

yah it is y and r

unless i can do 1/sin(60°)

well does give me the answer but dont think theyre looking for 1.154700538

[main marlin]

do you know how to express sin(60) in terms of roots?

[distant hinge]

im afraid not off the top of my head no

[hushed tartan]

There are some angles which will be good if you know there sin and cos

Which are 0,30,45,60,90,180,270,360 if you are talking in degrees

You can have them in your mind easily if you keep trig circle in your mind

[hushed tartan]

So sin(60°)=√(3)/2

[distant hinge]

ahhh

so i just gotta memorize them?

[calm coral]

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[calm coral]

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[calm coral]

@serene girder Has your question been resolved?

[serene girder]

im just unsure if my approach to this question is correct or not

[calm coral]

@serene girder Has your question been resolved?

[serene girder]

<@&286206848099549185>

[calm coral]

@serene girder Has your question been resolved?

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@serene girder Has your question been resolved?

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@serene girder Has your question been resolved?

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[fierce mulch]

I'm stuck on this proof:
let a,b be rationals and x be irrational. show that if (\frac{x+a}{x+b}) is rational, then a=b

[potent lotus]

lewis_f04

[fierce mulch]

this is my solution:
assume a $\ne$ b
$\frac{x+a}{x+b} = \frac{c}{d}$ $ c,d \in \mathbb{Q}$ since it is rational
$dx + ad = cx + cb$
$x = \frac{bc-ad}{d-c}$
but this implies that x is rational, as a,b,c,d are all integers. However x is not at rational, therefore (\frac{x+a}{x+b}) is irrational

[potent lotus]

lewis_f04

[fierce mulch]

but its strange because in the last line, even if a=b x would still be rational (it would be -1)

[vestal ivy]

do you mean the line $x=\frac{bc-ad}{d-c}$

[potent lotus]

WhereWolf(ping if needed)

[fierce mulch]

yeh

[vestal ivy]

if a=b then c=d and you get 0 in denominator

so there's no contradiction

[fierce mulch]

i see

would you have to do it the other way and assume $\frac{x+a}{x+b}$ is irrational

[potent lotus]

lewis_f04

[fierce mulch]

so it would be

[vestal ivy]

no your proof is fine

[fierce mulch]

why? because if a = b, x=0 which is rational right?

im prolly missing something really obvious

[calm coral]

@fierce mulch Has your question been resolved?

[calm coral]

@fierce mulch Has your question been resolved?

[calm coral]

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[lean cloak]

i need help with limits...

[lean cloak]

how to know its limit

[glass heart]

use log properties

[lean cloak]

ln ((n+1)/n)

you mean like that?

[glass heart]

yes

[lean cloak]

idk what to do next

[glass heart]

you know that ln is continuous

which means that lim ln(stuff) is equal to ln(lim stuff)

[lean cloak]

oh

is the limit 0?

[glass heart]

why

[lean cloak]

(n+1)/n
we put infinity on n's place then it will look like
(Inf + 1)/Inf
and we know that 1/Inf is 0 sooo... idk

i think it's wrong isn't it?

[glass heart]

well what about the other Inf tho

[lean cloak]

idk how to deal with that

[glass heart]

plugging in Inf like that is not exactly the best idea

[lean cloak]

i know... but that's the only thing i know

[glass heart]

can you factor out the n in the numerator

[lean cloak]

(n/n + 1/n)/(n/n)
1+1/n

devide everything by n

and then we left with 1+1/n

[glass heart]

yes

[lean cloak]

1+1/inf
1+0=1

is it right?

the lim is 1?

[glass heart]

the inner limit, yes

don't forget that there is an ln around it

[lean cloak]

ln 1 is 0

so the answer is 0

[glass heart]

yes

[lean cloak]

thank you

youmade me understand little bit

.close

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[hidden tinsel]

mathematica induction

[hidden tinsel]

i write so shit in my paper let me write clearly and send my work

i just dont know how to make lhs = rhs

[short seal]

you can always expand and collect terms of both the rhs and the lhs

[glass heart]

factor out (k+1) on the left. and then I am not sure if there is something smarter to do other than multiplying out the rest and see what you get

[hidden tinsel]

ok

I'll expand everything than and compare

torture

😭

i made a mistake

i give up

.close

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[calm coral]

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[floral fulcrum]

I'm doing implicit derivatives and the initial equation was find dy/dx by implicit differentiation for tan(x-y) = y/(7+x^2). I feel pretty good about implicit derivates as a whole, but this example problem while doing the product rule at some point multiplies the gf' by (1-y'). I've understood how y' comes in so far, but if possible I'd like a little bit of explaination for why the 1-y' enters the equation.

[calm coral]

@floral fulcrum Has your question been resolved?

[calm coral]

@floral fulcrum Has your question been resolved?

[calm coral]

@floral fulcrum Has your question been resolved?

[midnight knoll]

the derivative with respect to x, of (x - y) is (1 - y')

[calm coral]

@floral fulcrum Has your question been resolved?

[floral fulcrum]

Oh wait

Yea I just didn't recognize that lmao

Thanks

[calm coral]

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[floral fulcrum]

.close

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[sterile vault]

How would I go about finding all 2x2 matrices A such that ColA = NulA. The second picture is the conclusions ive drawn so far that could be helpful but I really cant figure out what to do next

[calm coral]

@sterile vault Has your question been resolved?

[sterile vault]

<@&286206848099549185>

it's over

.close

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[mighty tapir]

can i get some tips on how to approach this problem?

[pallid halo]

do you have any thoughts about where things could go wrong?

[mighty tapir]

im just wondering what a is

specifically what values for approaching it

[foggy nest]

Expanding, why the function does not exist @mighty tapir

[mighty tapir]

so what would be in the list?

.close

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[foggy nest]

@mighty tapir

What type of discontinuity? Make a checklist of what is going on --

f(a) = limit x approaches a, f(x) approaches - must equal

f(a) - must exists

limit x approaches a, f(x) - must exists

[calm coral]

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[terse badge]

how did i do this wrong

,rotate 270

[pure kayak]

whats wrong?

[terse badge]

my graph

[pure kayak]

oh

[terse badge]

it looks so diff

from the answers

😭

[pure kayak]

yeah the points to the left of -1 are wrong

[terse badge]

how did they get that

[pure kayak]

oh wait its a piecewise

[terse badge]

ouh acc

[pure kayak]

just noticed

[terse badge]

yea

[elfin ermine]

Lol it’s you again 💀

[terse badge]

LMAOO

STOP

IM SUFFERING

how r my answers

wrong

i put x

in abs

and added 2

,rotate 279

whops

the nine

,rotate 270

[pure kayak]

the +2 is inside the ||

[elfin ermine]

Oh it’s |x+2|

[pure kayak]

not outside

[terse badge]

Oh

[elfin ermine]

Rip

[terse badge]

HELP

LMAFHCWCHWJE

ouh

omg

im acc

such

a clown

😭😭

thank u very much

i can do the rest😭

.close

[calm coral]

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[remote mural]

no idea what to do on these last 3 questions any help would be appreciated

[remote mural]

nvm i can do the first one

now just the last two

[wintry grove]

hat does mean, mean?

[remote mural]

i think that mean is the average

[amber bolt]

it is

[remote mural]

oh should have put algebra tag

whoops

my bad

absolutely stumped

[wintry grove]

? you just answered your own question, no?

[remote mural]

?

i dont think i did

[wintry grove]

16 people travelled between 0-20km, 9 travelled between 40-60, multiply that, you have the mean?

[remote mural]

i dont think you are supposed to multiply with the mean

im not very good with mean

[wintry grove]

(1610)+(950) should get you close

[remote mural]

close?

160 + 450?

but the mean has to be somewhere between 0 and 60

[wintry grove]

how do you calculate an average?

say i walk 10 and you walk 20. hat's the average?

ffs, *what's

[remote mural]

idk

i managed to oget them in the end tho

[wintry grove]

mean is $total/ ~ of participants$

[potent lotus]

WayneTundra

[calm coral]

@little heron Has your question been resolved?

[calm coral]

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[polar harbor]

I'm having trouble figuring out the cotangent

[polar harbor]

Ah shoot gotta blast I'll be back later

.close

[calm coral]

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[polar harbor]

.reopen

[calm coral]

✅

[calm coral]

@polar harbor Has your question been resolved?

[halcyon haven]

$$cot(\theta)=\frac{1}{tan(\theta)}$$

[potent lotus]

Luna

[polar harbor]

Ah so, it'd be 2/Sqroot of 5>

Negative?

[halcyon haven]

it's a well known relation!

[polar harbor]

yeah I know, the sin and cosine stuff rly mess me up tho

[halcyon haven]

yes, negative as well

$$-\frac{2}{\sqrt{5}}$$

[potent lotus]

Luna

[polar harbor]

Heck yeah, okay another question if you're up for it, I have to add sin 1 + sin 2 + sin 3 up to sin 359 and I'm not really sure where to start

[halcyon haven]

One thing, let me guess

you found the tangent using opposite/adjacent thingy?

[polar harbor]

I did yes, I think I understand now, I was getting confused cause I was correlating x and y values with sine and cosine instead of the original x and y values

that I had to find to get sine if that makes sense

[halcyon haven]

Okay okay, nice!

[polar harbor]

haha agreed it was driving me bonkers

Do you know where I might start with adding the sin 1 sin 2 etc?

[halcyon haven]

Oh yes, a french mathematician named Lagrange has derived closed-form identities that you can use here

[polar harbor]

Oh my

[halcyon haven]

😃

[polar harbor]

do I just plug in my final number sin 359 into N and execute?

[halcyon haven]

i mean, you want sin(1) + sin(2) + ... + sin(359)

automatically theta must be set to 1

and N to 359 yes

[polar harbor]

I see and that'll give me the answer or do I have to do each 1 sin 1, sin 2 etc

[halcyon haven]

No

When you set theta = 1 and N = 359

The left hand side will be your sum

Try it

[polar harbor]

Okay

[halcyon haven]

you will get sin(1) + ... + sin(359)

[polar harbor]

I do top one since I'm finding sin yes?

[halcyon haven]

Whiiiiich is equal directly to the right side

[halcyon haven]

yess

[polar harbor]

okay

I don't really know how to do this to be honest, I plugged in the values so 1/2 cot 1-cos(359+1/2)(1) over 2 sin 1/2

[halcyon haven]

Yes, that's it

Calculator time

[polar harbor]

I dunno why I never think to use a calculator it's a real issue

[halcyon haven]

Hahaha

😛

But one thing

Are the angles inside of the sines in degrees or in radians?

[polar harbor]

degrees so I should set my answer to degrees correct?

[halcyon haven]

yes, set your calculator to degrees before computing

sin(1) is not sin(1°)

[polar harbor]

err I got 22.4956

[halcyon haven]

i got -28.65

Try again!

[polar harbor]

okay

Ah sweeet! Got it, thanks so much ur a lifesaver

[halcyon haven]

You are welcome!

[polar harbor]

That's all for me, have a great rest of your day

[halcyon haven]

Thank you, you as well

[polar harbor]

.close

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[digital pivot]

just a simple complex number question

[digital pivot]

when multiplying (1+i)(-3+2i)

the answer is -5-i

i thought it’s -1-i

cause for the real number isn’t it (ac-bd)

so wouldn’t it be -3-(2i^2)

which is -3-(-2)

which is -1?

[marsh valley]

The real number is ac-bd for a,b,c,d real

The - takes into account the i^2

Because you have (a+bi)(c+di), so if you develop for just the real part, you get ac+bidi = ac + bdi^2 = ac - bd

[strange lichen]

Freshman

$(a+b)(c+d) \neq ac + bd$

[digital pivot]

shutup stephen

[potent lotus]

Stephen

[digital pivot]

thanks @marsh valley

[strange lichen]

? U good ?

[digital pivot]

.close

[calm coral]

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[strange lichen]

.reopen

[calm coral]

✅

[strange lichen]

Nah what was that for

@digital pivot

[digital pivot]

shutup stephen

pls i’m tryna read

.close

[calm coral]

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[strange lichen]

oddity.

[prisma mango]

You don't need to be rude to helpers

[digital pivot]

he called me freshman

[strange lichen]

No I meant freshman’s dream

[digital pivot]

oh my bad

😭😭

[strange lichen]

But it actually isn’t freshman’s dream it’s just one of those common mistakes ig

[strange lichen]

U good

[digital pivot]

alr alr

[calm coral]

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[remote mural]

need help with this hw,, its discrete math

[remote mural]

@rigid mortar u free?

[rigid mortar]

no but someone can help easily i think

[remote mural]

ohh gigrise is typin

[echo cairn]

1. is equivalent to "For all y = y" which is true. its negation is "it exists an y not equal y"

[remote mural]

i dont understand what you mean

what do you mean is equivalent to "For all y = y"

[echo cairn]

basicaly P is a statement parametrised by x,y. P(0,y) means u plugin x=0 for the statement. if u do it P simplifies to y=y

[remote mural]

ahh got it

[echo cairn]

and so on, different x and y give different statements which can be true or not

[remote mural]

does this look right?

the 2nd line

[echo cairn]

looks okay

[remote mural]

Wym okay

wait hold on

i see

[echo cairn]

The answer could be written better, but im just pedantic..
but negation is right 👍

[remote mural]

how should it be written

[echo cairn]

Let y in Z. Then P(0,y) is equivalent to" y = y". which is true, hence i. is true.

[remote mural]

i dont even understand number 3 ques

[echo cairn]

number 3 means. I give you x, you have to find y such that P(x,y). And i will be very mean. if its possible u win and statement is true

[remote mural]

whaaa

can you explain it to me like im 5

[echo cairn]

x can be anything. You have freedom to choose y such that equation P(x,y) holds

basically can you isolate x to one side of =

[remote mural]

thats obiously false

[echo cairn]

yep

[remote mural]

so then 4 is also false

[echo cairn]

btw P(x,y) is same as "0=x^2 +x" if that makes it easier for u

[echo cairn]

right

[remote mural]

wait

how is the reading difference between 3 and 4

[echo cairn]

3. says there is one special y that makes P(x,y) true for all x

4. says For any y there is x depending on y, which makes P(x,y) true

[remote mural]

wym by depending

[echo cairn]

Means changing y you most likely will be forced to change x for P(x,y) to remain true.
Different ys result in different x values in general.

Like I give y, you have to find x such that P(x,y) is true. that means ur x depends on mine y that i provide u

if u cant find such x then 3. is false

[remote mural]

how would you solve it?

[echo cairn]

i mixed 3 and 4 with 4 and 5. i apologise.

Lets do 3. its false because negation is true. Let x=1 then for any y its true that "y-1 not equal y+1" because "0 not equal 2" is true

[remote mural]

okay

wbhat abvout 4

[echo cairn]

false, because negation is true. let y be any integer. then for x=2 it is true "y-2 not equal y+4"

[remote mural]

ohh i see what u r doing

ig its easier to do the negation

[echo cairn]

🙂

[remote mural]

than solving for a case where a num makes the statement false

got it

[echo cairn]

ye u provide an counterexample to the statements

if u feel like their wrong

[remote mural]

i dont understand how to read the shit tho

like the difference between 4 and 5

[echo cairn]

comes with practice when u read alot of proofs

[echo cairn]

the difference is 4. provides magical y that makes everything true.
and 5. for every y that i give u its possible to find x to make P(x,y) true

[remote mural]

i still dont get it ngl

[echo cairn]

okay here is how to read it

[remote mural]

its the form thats confusing it

the s.t that comes before and after

how do i differentiate it

[echo cairn]

after such that follows a statement

[remote mural]

okay lemme explain how i read it

4. there exist a y such that for eveery x, p(x,y) is true

5. for every y there exist x such that p(x,y,) is true

oh wait

i got it

masybe i dont

[echo cairn]

4. u can also state as "there is y auch that p(x,y) is true for every x"

but ye ur right on both

U can practice reading quantors with P(x,y)="y is cooler than x" where x and y come from the set of people.

[remote mural]

okay i did hw

now im doing chap 2 and 3 for exam friday

can i add you?

[echo cairn]

[remote mural]

arigato sempaii

!dismiss

!close

[calm coral]

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[burnt cobalt]

ignore that first question about the diagnals

these pics are just for context:

i don't really understand teh last question

like first, am i taking the dot product of AC and DB?

secondly, i do not understand that notation at all.

.close

[calm coral]

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[terse plinth]

how do i find these

[calm coral]

@terse plinth Has your question been resolved?

[merry carbon]

alright

so

basically

look at the bottom

and them as (x- or x+ a number)

so

at a

we have x^2-1

another way i see x^2-1 is as (x-1)(x+1)

and then make both equal to 0

and we ahve where it is (at 1 and -1)

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[desert anvil]

brain isnt braining how do I explain my reasoing

.close

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[compact root]

Can someone check this for me? I wanna know if it is correct. This is for Signal Analysis

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[grizzled bay]

bro aint answer smh

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[fallen meteor]

Can someone explain the yellow part to me?
I get that the complex conjugate is also a valid solution, but idk about the rest

[fallen meteor]

Especially this part

Where does that even come from?

[glass heart]

multiply out the lhs

they made a typo

should be 1 instead of the second z in each factor

[calm coral]

@fallen meteor Has your question been resolved?

[fallen meteor]

Wow okay. Thanks.

Now I have this

[fallen meteor]

How do I get to 2/3 then?

"After dividing ...", after dividing what?

oh just by the original poly

[hushed tartan]

divide the original polynomial by the one resulting from this multiplication

[fallen meteor]

Yep

And for that i suppose I need Long Division?

Thx.

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[eager acorn]

Is this statement true?

[glass heart]

what is Q? rationals?

[eager acorn]

Yes rational

[glass heart]

well what do you think

[eager acorn]

I am confused with the 0 element

Because inverse is not available

[glass heart]

yes

so it's not a group

[eager acorn]

Thanks

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[rough ferry]

quick question, is the displacement of the interval I highlighted E or W? Assuming the positive direction is E

[pure kayak]

E, the velocity is always positive so always moving east

[rough ferry]

thank you!

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[remote mural]

Just a small quick question on notation

[remote mural]

How would I Solve this inequality

[mellow crater]

you can multiply by x^2(x-6)^2

both sides

then it won't be rational anymore

[remote mural]

0<x<3, x>6

would that work

sorry Im not saying like

solve

ty for the help, the question says we can use desmos, so i put it in to get the shaded area...would my notation be correct?

[mellow crater]

,w (x-2)/x < (x-4)/(x-6)

[potent lotus]

Results provided by WolframAlpha

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

Requested by modus7591

[mellow crater]

ye

[remote mural]

ok tyvm!

.close

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[gilded surge]

Am I doing this right? Or is this terribly wrong

[gilded surge]

Given: r(t)=<1/t, -1lnt> u(t)=<t^2, -2t, 1>
Find d/dt [r(t)•u(t)]

My answer: 4-2lnt-t^-4

[subtle nexus]

,rccw

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[remote mural]

I need help you have numbers and - and all that u place the numbers on the lines and u put the pluses and all that in the circle. The clear box means deviding

[remote mural]

Ik it looks like fuckin grade b

But idk..

If u need more explanation just lmk ping me

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<@&286206848099549185>

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<@&286206848099549185>

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[remote mural]

<@&286206848099549185>

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[remote cedar]

I wanna ask about the question 6(b), howto prove that the sequence a_(2m) is always smaller than a_(2n-1)?
Also I want to know that how can I prove both of them are bounded and their limits are both equal to k in question 6(c)?

[remote cedar]

And currently I can only process to this step without any furtherer

<@&286206848099549185>

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[remote cedar]

<@&286206848099549185>

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[remote cedar]

<@&286206848099549185>

[astral sandal]

We can use the results from a on b
What numbers are of form 2m and 2n-1?
Let's suppose m >= n.
For a pair a_2m and a_2n-1, what can you say about which is bigger?
Consider the strict monotonicity of the subsequence you got from part a, what does this say about the previous terms relating to these two terms (with our assumption, n is one of those terms!)?
And for m<n the proof can be done symmetrically.

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[remote cedar]

I see, thanks

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[fading blaze]

hello, i need help with this question pleasee. Basically, i have to the calculate the probability of drawing exactly 3 aces by drawing 5 hands in a 52 card deck and it's also saying to use pascal's triangle. How do i calculate the probability and how should i use pascal's triangle to help me in calculating the probability?

[fading blaze]

so far I only have the amount of different hands i can get by drawing 5 cards randomly in the deck, which is 52!/5!(52-5)! = 2598960

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[fading blaze]

<@&286206848099549185>

[rugged cloud]

$\binom{5}{3}\frac{4}{52}\frac{3}{51}\frac{2}{50}\frac{48}{49}\frac{47}{48}$

[potent lotus]

Scerball

[fading blaze]

what is that

[rugged cloud]

the brackets mean 5 choose 3

[amber bolt]

they want you to use pascal's triangle instead of the formula

it's kinda sad

just pointless wrk

i literally don't know how to use it

[fading blaze]

ah i see then the part on the left are the factorials to use

yeahhh im assuming it has something to do with the 5th row in the triangle since its 5 cards

1 4 6 4 1 but like wtf do i do with that

[amber bolt]

to count the hands you multiply 4!/3!(4-3)! by 48!/2!(48-2)!

[fading blaze]

the hands where there are 3 aces exactly?

[amber bolt]

hold up

so you would need to make 52 rows of the triangle

wut

[fading blaze]

💀

[amber bolt]

the hands with 3 aces have 3 aces and 2 not aces

multiplying 3 out of 4 by 2 out of 48 counts the hands

it really just makes no sense, how do you use pascal's triangle, you can't

you wouldn't

[fading blaze]

i just need to divide the amount of hands with 3 aces with this to get the probability right?

still no idea what im supposed to do pascals triangle

[amber bolt]

ok ok