help-38

[prisma kayak]

no gamma you get from
|| alpha' + delta + gamma = 180

try again

alpha' - alpha prime

$\alpha '$

[solid kiln]

colonel blue

[scarlet totem]

Is this ok?

@prisma kayak

[prisma kayak]

Yes we going the right way

Now you build the left small triangle like i showed

We have a 50
We have epsilon as 50 again
And we have 180-alpha

[scarlet totem]

But I dont know alpha so first - alpha` right?

[prisma kayak]

we dont know alpha

but we know they all add up to 180

so we can find alpha from that itself

only one unknown right?

look at this again

[scarlet totem]

Yes

I solved it I think @prisma kayak

[prisma kayak]

Yess

Correct

Now try building the big triangle to get beta

[scarlet totem]

Can I use this on any question like this

[prisma kayak]

Remember you dont have $\delta'$ yet

[solid kiln]

colonel blue

[scarlet totem]

Isnt it the 50

[prisma kayak]

Yes so the lesson is try finding the three angles of any triangle you see
Sum them up to 180
This will give you equations to solve for your unknown

[prisma kayak]

im sorry $ \gamma' $

i cant see ffs

$\gamma$

[scarlet totem]

Got it

[solid kiln]

colonel blue

[prisma kayak]

gamma isnt 20

because gamma is the whole angle

its 20+20

[scarlet totem]

Oh so Gamma`´

[prisma kayak]

beta is correct

rest is all good

nice!

[scarlet totem]

Do you maybe have a website or so, for me to train things like this

[prisma kayak]

rightaway no
lemme see if can do a quick google search

[scarlet totem]

After I have one more question. Our teacher put it on the paper even though we didnt have it in class

[prisma kayak]

cant find but i think there should be problem sets you can try online

[prisma kayak]

go ahead

[scarlet totem]

What should I type best

[prisma kayak]

triangles solve for angles problem sheet maybe? though this can be a very random set of problems

[scarlet totem]

If you need translation just ask me

[prisma kayak]

yeah i need to know what it is asking for

[scarlet totem]

So g1 and g2 are paralell

And g3 is paralell to g4

Following angles are given: (angles)

Calculate the size of angles DAE and CBD and the rest of angles in Triangle ABD

@prisma kayak

[prisma kayak]

see, we build the triangle ABD.

<DAB = 180 - alpha
delta we know
DBA is what we dont know. So lets sum these up

(180 - alpha) + delta + <DBA = 180

now solve for what u dont know
and we have all angles of the triangle

using g1 || g2
<EAB = beta

see if you can use that to find < DAE

[scarlet totem]

How EAB?

[prisma kayak]

slide that g2 to the left until it falls over g1

you can compare both then

[scarlet totem]

What do you mean with slide?

[prisma kayak]

its just to help you imagine

parallel lines are just same line shifted right?

[scarlet totem]

Yes

But B is 100 and alpha ist 125

[prisma kayak]

ist ok
both are diff angles anyways

look carefully

they have a common area and thats <DAE

[scarlet totem]

mhm

Can u explain a bit further please @prisma kayak

[prisma kayak]

okay so where are we
did you get why beta is = <EAB

[scarlet totem]

Yes because it is on a paralell with g1 and when I slide it to g1 It ,,completes`` the angle

right?

[prisma kayak]

uh no
lemme try drawing something for you hang on

@scarlet totem can you now see why beta is <EAB

they both "lean" the same on g3

like airplane seats

xD

[scarlet totem]

A bit dumb question but why is it Eab instead of CBA for example

[prisma kayak]

CBA + beta make a straight line
so CBA + beta = 180

instead of being equal they complete each other

[scarlet totem]

Why a straight line 😢

[prisma kayak]

g3 is a straight line

[scarlet totem]

Yes

[prisma kayak]

so CBA + beta

is a straight line

180

[scarlet totem]

But why C, doesnt it make a turn

[prisma kayak]

CBA is this angle in black

[scarlet totem]

OOOHHHH

Im so stupid

[prisma kayak]

no problem xD now trace back

[scarlet totem]

angle CBA must be 80 right?

[prisma kayak]

yesss

but we dont need that

oh wait

they ask CBD

cool we have DBA and we know CBA

[scarlet totem]

So Beta in the whole is 180

minus 100 = 80

I need the 3rd angle of DBA to findCBD

So I need EAB ig

One question, how do I know if I pick DAB or BAD

@prisma kayak

[prisma kayak]

EAB is literally 180 - alpha

[prisma kayak]

for what?

[scarlet totem]

Just as an example

For the future

[prisma kayak]

so if you want to to compare equal angles from parallel lines
look for PARALLEL LINES
EA is parallel to CB not DA

oh okay

you changed your question xD

DAB and BAD are same angles

[scarlet totem]

I realised I typed wrong

[prisma kayak]

no problem picking any

[scarlet totem]

ok

[prisma kayak]

i try to keep general direction same so its easier to follow with eyes

like top to bottom

[scarlet totem]

SO I need DAB to find out Beta``

[prisma kayak]

what is beta''

[scarlet totem]

So DBA

[prisma kayak]

<DBA

is

[prisma kayak]

^

[scarlet totem]

I think Im too tired for this today, can I maybe add u and we continue our lesson tomorrow?

@prisma kayak

[prisma kayak]

that works too

np

[scarlet totem]

But Thank you so much for helping me this long

[prisma kayak]

no problem!

[scarlet totem]

What Timezone are you in?

[prisma kayak]

CET

[scarlet totem]

Ah nice me too, what time works best

[prisma kayak]

i cant say now
just tag me and maybe i'll be around hopefully

prolly after lunch

[scarlet totem]

Ok Ill just Ping u and you can answer when youre on

.close

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[amber junco]

How much will (name) have to repay if he pays it back at 2.5% interest (compounding annually) over 4 years ( can you walk me through the steps if u can )

[scenic roost]

do you know the formula

and theh initial value

[amber junco]

This is the question

Wait nvm I got it

.close

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[pallid vine]

SO im doing a)
-2+1.5/2 = -0.25
f(-0.25) = 1.406
so i replace [-2,-0.25]?

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[covert wolf]

What is value of constant 'a' when there's line 4x+3y-24=0 and y=ax while area of line y=ax gets the area of triangle OAB

[covert wolf]

Also point B is x절편 of 4x+3y-24 =0 while A is y절편

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@covert wolf Has your question been resolved?

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@covert wolf Has your question been resolved?

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@covert wolf Has your question been resolved?

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@covert wolf Has your question been resolved?

[covert wolf]

Am I helpless

[neon basin]

Where is O, A, and B

[covert wolf]

O is intersection of xaxis and yaxis

A is y-jeolpyeon of 4x+3y-24=0

B is x-jeolpyeon of 4x+3y-24=0

[candid sleet]

일단 x랑 상수항 등호 반대로 옮기고 y계수로 양변 나누면 됨

아니면 x절편은 y가 0일때 좌표이니까 x절편 구하려면 y에 0대입하면 됨

y절편도 똑같이 x에 0 대입하면 됨

[covert wolf]

x,y절편은 나와있지만 삼각형의 넓이를 이등분하는 선을 만드는게 문제임

[candid sleet]

그럼 x절편이랑 y절편 값좀

[covert wolf]

문제 자체에 써있는건 아님

[candid sleet]

그럼 구하면?

4x-24=0
3y-24=0

[candid sleet]

그래프는
y=-(4/3)x+8

[covert wolf]

그거가지고 a값을 구할순 없음

[latent kite]

일단은 삼각형 OAB에서 y=ax가 O를 지나니까

y=ax가 AB와 점 T에서 만난다고 하면, OAT하고 OBT 넓이가 같으면 됨

근데 그 넓이는 각각 (AT 길이) * (밑변을 AB로 봤을 때의 높이) = (BT 길이) * (밑변을 AB롸 봤을 때의 높이)

니까

그 넓이가 같으려면 AT하고 BT가 같아야 함

그래서 T는 선분 AB의 중점

그다음에 x절편은 6, y절편은 8

이니까,

이거 갖고 계산 가능

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[gentle sleet]

the very last inequality

and the way they got this

is tripping me out

im not sure how they got (pic above) from

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[gentle sleet]

wtvr

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[past ledge]

The graph of y = f(x) has a vertical asymptote at __ a horizontal asymptote at __ and a point of discontinuity at ___ the values are. I was given the equation ((3x-b)(ax+3))/((x+1)(3x-b))

[past ledge]

This was apart of a unit we did a bit ago and I completely forgot it and I have finals soon

[trim jolt]

@past ledge Has your question been resolved?

[past ledge]

<@&286206848099549185>

[fallow goblet]

what is the question

to fill the blank?

[past ledge]

Multiple choice right now

For a practice test

I can send the whole thing

[fallow goblet]

yh sure

[fallow goblet]

,rotate

[fallow goblet]

where are you stuck

@past ledge

[past ledge]

I’m unsure how to even start my first thought was to cancel out the 3x-b since it’s on top and bottom

But than idk what information that gives me at all

[fallow goblet]

yh i also did that

what can u interpret from this cancellation

3x-b

[past ledge]

What i see now is ax+3/x+1 so I see that whatever ax cannot = -3

[fallow goblet]

Wait btw A and B are the same? And C and D are also the same?

[past ledge]

The difference is in ii

And I

[fallow goblet]

oh so u have the choice between two answers

alright

anyway

[past ledge]

I’m assuming the horizontal is b/3

[fallow goblet]

the factor (3x−b) appears in both the numerator and the denominator. You have to find for what value does the factor (3x−b) becomes zero

[past ledge]

Or wait no the discontinuity

[fallow goblet]

well

[fallow goblet]

i gave u a hint there

for the first one

[past ledge]

My best guess would be C because b/3 would = 0

Than I am unsure if we can calculate a

Would x also = -3?

As well as -1?

[fallow goblet]

tbh i think it's C as well

but

yh

its C

bro u made me hesitating for a sec lol

[past ledge]

I got the x = -1 from the bottom being (x+1) since it’s plus

[fallow goblet]

because the function's denominator becomes zero while the numerator remains non-zero

[past ledge]

I wouldn’t guess my answers lol math is my worst

[past ledge]

Ooh okay so that means x cannot become -3 per say if a is 1

Because anything 0/x is error

[fallow goblet]

its more x/0 is error

0/x is 0

[past ledge]

Ooh

Okay

[fallow goblet]

for x different of 0

[past ledge]

I got it mixed up again

[fallow goblet]

0/9=0

while 9/0 is undefined

[past ledge]

Ooh that’s why it’s the asymptote

Because it’s undefined

[fallow goblet]

x cannot be b/3 because it would make the original function undefined due to a 0/0 form which is impossible

its an undefined form

same thing

[past ledge]

Ooh okay I understand now

Thank you

[fallow goblet]

yw

[fallow goblet]

what do u think about the second one

[past ledge]

What second one?

[fallow goblet]

ii

or u only needed help for the first one?

[past ledge]

I think it would be a

The options are a or 3

But I don’t see a way to get a 3 out of it

[fallow goblet]

yh

its y=a

[past ledge]

Because ax whatever is in front of the x would be the answer

Right?

Say if the a was 3 instead of a than the answer would be 3

[fallow goblet]

it's more because the limit when x tends to +infinity of f(x) equals to a

[past ledge]

I checked my profs answer sheet and the answer was C for the exact same reasons lol

[past ledge]

Oooh okay

[fallow goblet]

haha nice

[fallow goblet]

do u understand the concept of asymptote

[past ledge]

When there is an error in the line?

So when 0 is onto bottom of the equation?

[fallow goblet]

not really

have you studied limits

[past ledge]

Like 0 <= x <= 99

And stuff like that?

[fallow goblet]

nah

wait lemme show u

$\lim_{x \to +\infty} f(x)$

that

oopsie

that

[solid kiln]

caffu

[fallow goblet]

better now

[past ledge]

Ooh okay

[fallow goblet]

u studied this?

[past ledge]

We haven’t done any of that

Since I’m in pre calc

Not calc yet

And mainly despite being pre calc we mainly do algebra

[fallow goblet]

oh

wait

so

you're not supposed to use limits to solve your problem?

[past ledge]

No we use the equation we have and get information from it

[fallow goblet]

oh

well

idk how to help you then

since i used limits to evaluate the asymptote

[past ledge]

Ooh

How did the limits work?

[fallow goblet]

idk how to explain

i'd advise you to watch a youtube video on it

[past ledge]

Hmm any advice on who?

[fallow goblet]

nah sorry

it's very easy tho

[past ledge]

Hmm okay

Well that answers all my questions I understand how I got to C anyways lol

Thank you very much!

And have a great day!

[fallow goblet]

oh that's very cool

[fallow goblet]

You're welcome

[fallow goblet]

thank you, you too

[past ledge]

Thank you

Idk how to close this lol

[fallow goblet]

.close

@past ledge

[past ledge]

.close

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[rain shell]

$x = 2017 - \sqrt{2017 - \sqrt{x}}$

[solid kiln]

cffex

[rain shell]

How would I approach this problem

[hallow kite]

oh you're trying to solve for x

[rain shell]

yes

[hallow kite]

try to isolate the radical term and then square both sides

so sqrt(2017 - sqrtx) = 2017 - x

[rain shell]

Yes

[hallow kite]

square both sides

so 2017 - sqrtx = (2017 - x)^2

[rain shell]

Ok let me try

[rain shell]

$x^2 - 4034x + \sqrt{x} + 4066272 = 0$

[solid kiln]

cffex

[rain shell]

this is a cubic which I haven't learned yet

[nova spire]

worse, a quartic

[nova spire]

there's something you can do from here that might help

[rain shell]

oh yeah

[nova spire]

when letting y = sqrt(x)

you have (y^2 - 2017)^2 = 2017 - y

you can factor the left hand side better

so it can be written as:

[hallow kite]

problem is you won't get a y - 2017 term that will cancel with the right

once you get to this point i don't really see an easy simplification

wolfram thinks the answers are really messy

there's no nice factor you can easily find by hand to try to reduce this to a cubic either

only thing i'm seeing is quartic formula

[nova spire]

not sure

I think we can dumb down to a quadratic

also

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[nova spire]

ok so the only thing I found for myself is that for solving for $x$ in $x =k - \sqrt{k - \sqrt{x}}$ with $k >0$, $x = \frac{2k+1 + \sqrt{4k+1}}{2}$ is miraculously the only solution

[solid kiln]

rafilou2003

[rain shell]

and why is that though

.close

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[twilit dome]

Am I correct in thinking that there must exist some real numbers that can't be specified in any system of mathematics using a finite number of symbols?

[twilit dome]

Since the set of all series of symbols of finite length would be countable

And the reals are uncountable

And by specified I mean uniquely specified

[river willow]

yes? look at pi

[twilit dome]

Pretty sure pi can be uniquely specified in our system of mathematics

Using infinite series notation and other ways

Like this I think

[nova spire]

yes, this was already subject of a thought based on a Turing machine

https://en.wikipedia.org/wiki/Computable_number

[twilit dome]

Oh that's kinda cool

[unique minnow]

In fact most real numbers aren't definable in that sense, since the formal systems only make up countable formulas. See this.

[twilit dome]

Thank you! That's exactly what I was looking for

.close

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[round galleon]

Any reccomendations for learning Trigonometric Identities?

[round galleon]

I think its called Trigonometric Identities

anyways something that goes like
sina•sinb= 2cos((a+b)/2)•sin((a-b)/2)

[split chasm]

learn how they're derived

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[trim jolt]

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

[tacit sun]

1. I dont know where to begin

I don't even know what to do!

uh if i knew what to do I would've

i know

OH

a^m / a^n = a ^m-n

is this correct??

still doing

(a^m)^n = a^mn

yes

i got it

tysm

wait am doing my best

[trim jolt]

@tacit sun Has your question been resolved?

[tacit sun]

leave it man 😭

im gonna ask my teacher

i need help with this one now

q.1

[neon basin]

Do you know how to denest radicals?

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[solid kiln]

faiyrose

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[random niche]

How could I evaluate this without using the u-substitution?

[shy nacelle]

Its just easy

You can visualise x+3 as z

[trail ingot]

[shy nacelle]

so it was basicall 1/(x+3)³ before becoming this

-3 will come on diff. So

Just multiply by -1/3

[random niche]

not sure what you mean you might just use latex to show it to me or smt

[split chasm]

its recommended that you first do this with the substitution

you'd still be applying the same chain rule

being able to visualise that bypasses the introduction of another variable

[random niche]

I just don't know how to take the antiderivative of the term above. My textbook hasn't taught me substitution about integrals just yet.

[split chasm]

look up integration by substitution first i suppose

[livid thunder]

looks like a reverse chainrule

take the denominator to the numerator and you'll be left with 3(x+3)^-4

now if u think about how to derive a chain rule then you can just apply the steps in reverse to find the antiderivative

to derive [f(x)]^n , you multiply by the power and take one off the power, then multiply by the derivative of the function inside the brackets{n*f'(x)[f(x)]^(n-1)}, so in order to do this in reverse we divide by the the derivative of the function inside the brackets, add one to the power, then divide by the new power.

[trim jolt]

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[plain wolf]

find the equation of the line that is parallel to the y axis and passes the point (-1,4)

[tidal forge]

do you know the equation of s.t. which is parallel to the y axis?

[plain wolf]

no

[tidal forge]

ok, so let me explain

[plain wolf]

yes

[tidal forge]

line is made by infinite amount of points

[plain wolf]

yes

[tidal forge]

a s.t. that parallel to the y-axis, which is a vertical line

you got that?

[plain wolf]

yes

[tidal forge]

les make some points

[plain wolf]

if we draw it out is it easier

[tidal forge]

oh ye

you can draw it

[plain wolf]

okay

[tidal forge]

and now, there's a vertical which passes through the point of (-1, 4)

[plain wolf]

if its vertical its straight right

[tidal forge]

ye

[plain wolf]

so if its sraight

how does it pass through

[tidal forge]

You may want to mark the point (-1, 4) in the graph

[plain wolf]

i did

[tidal forge]

where?

can you show me?

[plain wolf]

ill do it on my laptop as well wait

[tidal forge]

k

[plain wolf]

here

[tidal forge]

No

[plain wolf]

what

[tidal forge]

Do you know what is a point

[plain wolf]

oh wait

im dumb

[tidal forge]

bruh

[plain wolf]

sorry

here

[tidal forge]

ys

draw a straight line that pass through that point

[plain wolf]

okay

here

[tidal forge]

great

[plain wolf]

now what

[tidal forge]

Note that it should be expand to the whole graph lol, not just from 5 to -1

[plain wolf]

oh okayy

so what do i do

[tidal forge]

Tell me, what you observe about this line using the definition of a line that I have mentioned

[plain wolf]

itoasses through

-1

[tidal forge]

Yes

every x coordinate or y coordinate is -1?

[plain wolf]

there is no y

just x

[tidal forge]

yup

[plain wolf]

so what wld i write as the equasion

[tidal forge]

ys

can you write that equation?

[shy nacelle]

Um what?

[plain wolf]

x= -1

[tidal forge]

correct

there you go

[plain wolf]

oh was that it

[tidal forge]

?

ye

[shy nacelle]

-1,4 passes ?

[tidal forge]

?

[plain wolf]

i over anazlysed tht sm thankyou

[tidal forge]

np apramms

[plain wolf]

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[thick badge]

how do i do this

[thick badge]

length is 40

side is 20

angle is 40

tsa

i need

[dire vortex]

Area of the base • height

[solemn thorn]

they need surface area i think

[thick badge]

yea.

i do

and i dont know the radius

[dire vortex]

You can find it

[thick badge]

bro

im asking how

if i knew i wouldnt be here

tf

[thick badge]

oh so thats the radius?

[solemn thorn]

no

[thick badge]

.

[dire vortex]

Diameter

[thick badge]

oh

so 10

[dire vortex]

10 what

[thick badge]

so i find

tsa

radius is 10 right?

so i find tsa and then times by 40/360?

[dire vortex]

No

[lapis star]

((Perimeter of base ) x height ) + (area of base )x 2 = TSA

[thick badge]

Then what bro

How is diameter 20

Explain

[lapis star]

They are messing with ya

radius is 20

[thick badge]

Bro why the fuck

I’m trying to get help and they are being twats

[thick badge]

Alright

Ty

So it would equal

2x pix20^2 +2 times pi times 40 times 20

Right @lapis star ? For confirmation

Sorry for the ping

[lapis star]

oh no problem idm

I was playing valo lol

[lapis star]

yep

its right

[thick badge]

Ty sm

[lapis star]

dont type 'times" instead try placing a period

or x

[thick badge]

Alright sorry I’m on phone in bed haha

[lapis star]

nice repo bro just went through

[thick badge]

Haha on my github? Ty

Which one 👀

[lapis star]

The anticheat is great

[thick badge]

Ah yea helped work on it. Contributed. It has like 197k downloads 🙏

Ty for the help brotha as well

[lapis star]

👍, got any doubt, dont seem to get any real help you can always dm me

[thick badge]

Will do ty

[lapis star]

thats so cool man

[lapis star]

do they pay u?

[thick badge]

🙂

[thick badge]

Nah I volunteered.

It’s fun experience

[lapis star]

oh cool

[thick badge]

Yuh Java is fun

Ty will dm ya if I need help 🙂

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[lilac ridge]

Hi. I wonder how to continue the exercise. The question is solve sin(π/4+a) and cos(π/4+a) if tga=-3/4, a€(π/2,π)

[lilac ridge]

so i can use alpha in sina huh

[burnt mulch]

Yeah you can let A = alpha

[lilac ridge]

just second

[lilac ridge]

I can use that value?

[burnt mulch]

3/5 is sin(alpha), not (alpha).

[lilac ridge]

how do i get alpha

[burnt mulch]

You don’t

Just expand out $\sin \left(\frac{\pi}{4}+\alpha \right)$ fidst

[solid kiln]

Civil Service Pigeon

[burnt mulch]

Leave alpha as is

What do you get

[lilac ridge]

just second

[lilac ridge]

And i guess i just change the values right?

[burnt mulch]

[lilac ridge]

thank you

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[blissful vigil]

The 2X2 matrix question

[blissful vigil]

Upon solving it I'm getting an eigen value of 1+i

What to do in this case

[wooden plover]

and also 1-i

well it's fine

you can still find eigenvectors

even if they're complex

@blissful vigil

[blissful vigil]

I'm getting zero.

[wooden plover]

well ok det of A-lambda I is zero sure, that's a good sign we have an eigenvalue

that still doesn't tell you the eignvectors

@blissful vigil

[blissful vigil]

ohh

after solving the second eq I got -5i-7

so should I consider the first part as [0 ,0]

[wooden plover]

what second eq

what are you talking about ? what does that -5i-7 mean ?

do you know how to find eigenvectors yes/no ?

@blissful vigil

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@blissful vigil Has your question been resolved?

[blissful vigil]

oh I'm sorry for the late reply,
I substituted lambda as 1-i

[blissful vigil]

somewhat🥲

no.

[wooden plover]

substituted in what ?

idk what you're doing rn

you have to be a bit clearer

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[wooden plover]

.reopne

.ropen

.reopen

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✅

[blissful vigil]

bro I'm fed up, I'm not continuing it anymore

ty for your timee!!

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[mighty bramble]

T(f(x)) = f(x+1) we are in T:Q_3[X] -> Q_3[X]

[mighty bramble]

can we diagonalize T ? if yes diagonalize it

hellloo

fk

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[mighty bramble]

help me do this

[quaint garnet]

i need help in de point 3

[gritty notch]

on the right u can use sin(2x)=sin(x)cos(x)
or take out cos(a\2) as a common factor and then use it

[mighty bramble]

this is my help

channel

[gritty notch]

@mighty bramble

[mighty bramble]

didn't get it

where is sin(2x)

[gritty notch]

sin(2x)=sin(x)cos(x)
sin(a)=2sin(a\2)cos(a\2)

sin of double angle

[mighty bramble]

i have this sin(a)=2sin(a\2)cos(a\2)

so i can make it 2sin(2x) ? this is what u mean ?

[gritty notch]

oh i forgotten c

[mighty bramble]

why the c ?

in the last line you are dividing ?

[gritty notch]

not its expalation

[mighty bramble]

oh so the final answer is the one on the left

[gritty notch]

ya

whats that?

[mighty bramble]

that's an i

we need to use de moivre

ig

[gritty notch]

so u need to add that as well

[mighty bramble]

so we don't need to use de moivre ?

and where to add it

[gritty notch]

idk, didnt learn about i yet

[mighty bramble]

complex numbers

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[zinc raft]

If 2 angles are supplementary/complimentary then will one angle be called a supplement/compliment?

[nova spire]

an angle can only be the supplement of another angle

"a and b are supplementary" is the same as saying "a is supplementary to b"

[zinc raft]

Uh so what does supplement mean

They can’t both be a supplement?

[austere cedar]

"Supplementary" is a relationship between two angles. It is not a property that one angle can have.

a and b are supplementary if a + b = 180

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[old falcon]

The last four people on a sold-out flight enter the airplane one-by-one. All four people have reserved seats. The first of the four people (A) just chooses a random seat to sit in. Each subsequent person (B, C) sits in the correct seat if available, or a random seat if not. Determine the probability that the last person (D) to sit down sits in the correct seat.

[old falcon]

This is supposedly a grade 7 question??

[raven flare]

this aint

[old falcon]

it was on my test 💀

[raven flare]

tell your teacher to remove it

or explain it

atleast

[old falcon]

I'll try

she didn't bother after she handed it back though, this is an old test

[raven flare]

pester her

its ok

I think she also messed up the q

[old falcon]

ok

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[gleaming ermine]

can anyone explain how they integrated that

[orchid orbit]

What have you tried?

[gleaming ermine]

i dont even know how to start

substituting?

[last nebula]

Did you read Appendix I?

[gleaming ermine]

it is just the formula

that this form is equal to that

but i wanna know how it happened

[orchid orbit]

Which book is this?

[gleaming ermine]

resnick halliday

[orchid orbit]

name of the book? (+ edition maybe)

[gleaming ermine]

resnick halliday krane
physics
wiley student edition
fifth edition
volume 2

[scenic fractal]

physics people just use the formula for that integral,
here's what you can do:
z = ytanx
dz = ysec^2x
substitute it and integrate

[gleaming ermine]

right one secon

okay

thank you

gotchu

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[neat crystal]

when exactly do i utilize the tangent half-angle substitution?

[neat crystal]

like which form of integral do i use it on

[last nebula]

When you have a quotient of polynomials whose variables are sin and cos

Note however that some other substitutions like u = sin x, cos x or tan x sometimes work in those cases too, and when they do, the new integral is a lot simpler

[orchid orbit]

and as a last resort

[last nebula]

^

[orchid orbit]

because the Weierstrass sub gives you a rational function

[last nebula]

Tangent half-angle substitution has the advantage that it always works

[orchid orbit]

(and then you're in the unholy land of partial fraction decomposition etc.)

[neat crystal]

you mean it always works but it isnt always the fastest and most beautiful?

[last nebula]

Yes

[neat crystal]

got it

[last nebula]

If you use it you might have to factor polynomials of degree 4 or 6 or something

[orchid orbit]

long division

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[ornate cedar]

I have a question about mathematic models of cancer, I have this model by Kuznetsov and Knott, that describes the growth of cancer, and then I have som graphs showing cancer cells in mice out the y-axis, and time out the x-axis. The dotted lines are the actual data points, while the black curve is made up by the variables in the model, where we change them so they can fit the datapoints. My topic is meant to be about differential equations, as seen by the K&K model, but does the graph actually have anything to do with differential equations? My guess is, that the black curve is the solution to the model given by K&K. Am I correct?

[ornate cedar]

<@&286206848099549185>

aren't there anyone thats smart enough for this? <@&286206848099549185>

pls its important, its for an exam tomorrow, and I need this to reach the needed score for my university <@&286206848099549185>

[whole granite]

Gimme the question

Me gonna try..

Wait

[ornate cedar]

its this "does the graph actually have anything to do with differential equations?"

[whole granite]

What you are telling is correct

[ornate cedar]

so its just the solution to the differential equation?

[whole granite]

Yeah

[whole granite]

yeah obvio

[ornate cedar]

okay thank u very much

[whole granite]

Welcome

[ornate cedar]

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[whole granite]

All the best

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[wraith hinge]

If a matrix X = A•B•A-transpose
Can i say X=B because multiplication of a matrix with it's transpose gives identity matrix

And if A•B•C same as A•C•B( for matrices I am talking)

[orchid orbit]

Matrices do not commute in general like real numbers

[wraith hinge]

Opps yeah
Thanks!

[orchid orbit]

because multiplication of a matrix with it's transpose gives identity matrix
this is also false

simple examples of 2x2 matrices are very helpful for this stuff :)

[wraith hinge]

Shit!!!!!
Ii actually wanted to write A inverse

[wraith hinge]

So... The question is same
Just replace A transpose with A inverse

[orchid orbit]

that's if the matrix inverse of A exists

(which it might not, because matrices can have determinant = 0)

but also no that's false

you can't conclude that X=B

🤣

[wraith hinge]

Sure but let's say it exists

[wraith hinge]

Ohh.. Thanks!

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[dapper blaze]

Hi

[dapper blaze]

I learned for addition with integrals i can scrap out the number above and below integral like the below equation

[nimble stone]

if the upper and lower limits match, then sure

[dapper blaze]

But for the upper equation what do i do ? Do i remove the numbers above and below integral?

[warm trellis]

simplify it

you get zero

[dapper blaze]

So i get no numbers on that integral?

[nimble stone]

you can flip the limits by factoring out -1

$\int^{a}{b}=-\int^{b}{a}$

[solid kiln]

AℤØ

[warm trellis]

you can do taht?

[dapper blaze]

No but i need to add those into 1 integral

[nimble stone]

they negate eachother

[nimble stone]

its like x-x=0

[dapper blaze]

U can see for this one it has one integral as anwser need to do same for upper but what does it become?

[nimble stone]

this is fine, im not sure what you mean

[dapper blaze]

Is this the answer for upper?

[nimble stone]

the top line?

[dapper blaze]

Ye

[nimble stone]

your integral doesnt even have any limits at the end

[dapper blaze]

Whats the anwser the bottom was example

[nimble stone]

its 0

[dapper blaze]

Ye cuz its probably wrong i wanna know whta it would be

So i write 0?

[nimble stone]

if youre bent on keeping it as is it becomes the integral between 5 and 5

which is 0 anyway

sorry

4 and 4

well, either actually

[swift thistle]

well a and a

[nimble stone]

but i like this

[dapper blaze]

So i wirte 0 and 0 on the integral?

[nimble stone]

no, its just 0

[swift thistle]

you do not get an integral

[nimble stone]

its =0

[dapper blaze]

Oh the whole answer is 0?

[swift thistle]

yes

[dapper blaze]

Thnx

Alright

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[nimble stone]

that is one mighty 0

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[heavy elbow]

how would one do a problem such as writing ln3 = x in exponential form

[wraith hinge]

e^x = 3

[stable ore]

By definition, ln(a)=b is the same as e^b=a

[heavy elbow]

oh so e

that was what i was missing

on the topic of logs

how would i do a problem like condensing 4 - 2log6(a)

6 being the little down thingy im forgetting the name of

[main sigil]

base

[main sigil]

I think this is nicely simplfied

if you wanna simplify it into a single logarithm, you will need to apply few properties

[solid kiln]

MethIsAlwaysRight

[main sigil]

power rule tells us that 2log6(a) = log6(a^2)

so it simplifies to 4 - log6(a^2)

now quotient rule tells us that 4 - log6(a^2) = log6(4 / a^2)

and that's it

[heavy elbow]

ok

but how would you get the four in there? its not being logged

[main sigil]

wait you're right

im stupid

you need to do 4 = log6(6^4) first

this works by definition of log

log6(6^4) = 4

[heavy elbow]

ok

[main sigil]

so then it simplfiies to log6(6^4) - log6(a^2)

which is log6(6^4 / a^2)

[heavy elbow]

okay yeah i got that!

thanks man 👍

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[zealous canopy]

When finding the derivative of the position function you get the velocity function

but if you try to do it the other way around you end up with + c

how do you find the value of c?

[swift thistle]

c doesnt have a specific value - its just a constant

[zealous canopy]

it's suposed to be 5 though

in the example where I found the derivative of the position function

5 is the constant

[wraith arch]

if you use the original equation, you’ll get that s(0)=5

you would use that initial condition to solve for C

[zealous canopy]

but if I didn't have that initial function

[wraith arch]

then you would just leave it as +C

[zealous canopy]

but then it is wrong

[wraith arch]

if it wants you to find C it’ll give you an initial condition

yeah obviously for this case

because it has an initial condition

[zealous canopy]

what?

[wraith arch]

if it only gives you the velocity function

and no other information

there are an infinite number of functions that could give you the same velocity function

[zealous canopy]

ah

[wraith arch]

they would need to give you an initial condition if they want the exact constant

[zealous canopy]

so like

if it says s(1) = 5,7

then I know that the constant is 5

[wraith arch]

well you would plug in 1 for t

and then 5.7 for s(1)

that’ll be enough information to solve for C

[zealous canopy]

because if I sett the constant to 0 then s(1) = 0,7

[wraith arch]

wait what

yeah

you just have to make sure it matches up

[zealous canopy]

okay I see

thank you^^

[wraith arch]

yw!

[zealous canopy]

.close

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[full dock]

For two AP's

1. 2,5,8,....,(3n-1)

2. 47,45,43,....,(49-2n)

If their sum to the first n terms are equal, find the value of n

[full dock]

how do i start

[wraith hinge]

Do you know the formula for sum of AP?

[full dock]

yrs

[wraith hinge]

Right

What's a in both sequence?

[full dock]

seq 1 is 2
seq 2 is 47

[wraith hinge]

Yeah

And d?

[full dock]

seq 1 has d=3

seq 2 has d=-2

[wraith hinge]

Yeah

Then keep n as it is and put values of a and d in the formula for sum of both seq. And compare them.

Understand?

[full dock]

hold on lemme do it rq

so i got this

$S_{n_{1}}=\frac{n}{2}\left(3n+3\right)$

[solid kiln]

water beam

[full dock]

$S_{n_{2}}=\frac{n}{2}\left(-2n+95\right)$

[solid kiln]

water beam

[full dock]

do i set Sn1 and Sn2 equal to eachother?

[wraith hinge]

Yeah

[full dock]

i get n = 92/5

[wraith hinge]

Wait

Some mistake In calculations

Make sure you have used the right formula aswell

[full dock]

yes

[wraith hinge]

You've got both of your sums wrong

[full dock]

well thats embarassing

[wraith hinge]

No not really

Happens

[full dock]

okay

i got n = 19

5n =95

[wraith hinge]

Good

[full dock]

thanks for the help

[wraith hinge]

Np

[full dock]

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[next raven]

Completely stuck I’m not very good with this stuff.

[dull temple]

first find the hypotenuse using the Pythagorean theorem

then refer to this chart

,tex .sohcahtoa

[solid kiln]

open up my e-girl eyes

[next raven]

So tan is 7/24

Cos is 24/25

And sin is 7/25

Is that right?

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[warm trellis]

with respect to which angle

cos of waht

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[still bough]

I don’t get how this determinant is wrong

[fast fractal]

where'd the x come from?

[still bough]

I found the error a -4 became a 4 at one point

[still bough]

That’s the multiplication symbol

[fast fractal]

ah

[still bough]

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[leaden walrus]

Suppose I have a set of 2d functions drawn on parallel planes. How do I create a 3d function out of this ? Do I just use classic interpolations methods or are there more specific applications ?

[acoustic flint]

Is the data discrete?

[leaden walrus]

Yes it's all discrete data, I've taken measurements at different values(Let's assume the axis varying between -2 to 2 in this picture), which allowed me to trace the 2d functions.

[acoustic flint]

What I meant was if the data itself is discrete (not the samples you have taken) then there is no point in visualising it with a surface

[leaden walrus]

No the data itself is analog, In this case I am measuring the speed of a car

[acoustic flint]

But, if you do form a surface, i’d probably go with lagrange interpolation

[gilded plover]

what is the x-axis(-2.0,-1.5...2.0)

[leaden walrus]

Well, that image was taken from the net to illustrate what problem was, but the data actually looks more like this:

[gilded plover]

pretty chaotic

[leaden walrus]

This would be a braking test performed using 100% brake pressure

Then I have similar tests with 90%, 80%,70% and so on

[leaden walrus]

At 30% brake pressure

[gilded plover]

quite interesting