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[lone heart]

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[solemn oar]

integration of 1/(x+1)(x^2+1)^2

[median dirge]

Is it

[solemn oar]

sorry it was plus

[median dirge]

$\int{\frac{1}{(x+1)(x^{2}+1)^{2}}}$

[solemn oar]

yup

[ocean seal]

Muhammad Hussaini

[median dirge]

oh

[solemn oar]

??

<@&286206848099549185>

[alpine sable]

Partial fractions

[solemn oar]

actually i tried to solve it but there was some doubt in the steps

[alpine sable]

A/(x+1) + B/(x^2 + 1) + C/(x^2 +1)^2

This is the steps

[solemn oar]

yup did it

[alpine sable]

Show work pls

[solemn oar]

afterwards when u put the valuies of a b and c

[solemn oar]

i m on laptop i dnt own an phone 😦

[alpine sable]

Oof

[solemn oar]

can i write the steps here but it will take long

[alpine sable]

Does ur lapptop have a webcam

And the camera app

[solemn oar]

its windows 7 😭

no camera

[alpine sable]

Oof

[solemn oar]

can i write here

[alpine sable]

Wait

Lemme show u

[solemn oar]

1=A(x^2+1)^2+(Bx+C)(x^2+1)(x+)+(px+q)(x+1)

step one

[alpine sable]

Yes

Wait

Why Bx + C

[solemn oar]

A=1/4 B=-1/4 C=1/4 P=-1/2 Q=1/2

then we put the values

[alpine sable]

No

It’s not Bx + C

Afaik

It’s B and C separately

Nvm u are right

It’s Bx+ c

Sorry

Been a while since I did integrals using partial fractions

[solemn oar]

1/4∫1/(x+1)dx -1/4∫x-1/(x^2+1)dx -1/2∫x-1/(x^2+1)^2dx

[solemn oar]

its okay👍

[solemn oar]

after this step it gets a bit confusing for me

[alpine sable]

One sec

[solemn oar]

yup

[alpine sable]

One sec

[solemn oar]

i tried partial fraction again to individual part but it was not coming right for (x^2+1)^2

[alpine sable]

Hmm

Lemme solve

[solemn oar]

yup

[alpine sable]

Dayum

This shit is complex

[solemn oar]

yup😭

its been 2 days since me trying to understand myself

not completely 2 but this is needs big solution

[alpine sable]

Are u sure u found A,B,C,P,Q correctly

[solemn oar]

yep

this is the 10th time i have done this question

[alpine sable]

Oh

[solemn oar]

can i ask something

i just got an clue

[alpine sable]

I can solve the rest

[solemn oar]

after this step can we use ln (x+cpnst/x+const)

[alpine sable]

If u got the coefficient right

[solemn oar]

yes it is corrct believe me

[solemn oar]

noo i tried it not gonna work😫

[alpine sable]

I am working it out

One sec

I’m tired rn

I’m not able to work out the last one

[solemn oar]

its okay can i add u as friend i can try to send you picfrom my moms phone?

i have this question as example so i just need explanation?

[alpine sable]

Oh ok

Sure

[fathom mantle]

A/(x+1)+Bx+c/(x^2+1)+Dx+e/(x^2+1)^2

[lone heart]

@solemn oar Has your question been resolved?

[lone heart]

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[gritty jewel]

does anyone know how to do this question?

[solar merlin]

you know how to do those problems normally, right?

[gritty jewel]

with numbers yes

e.g f(4)

like that stuff

[solar merlin]

so, when we say f(f(x)), we mean "do the function twice"

[gritty jewel]

oh

[solar merlin]

so if i did f f(x), where f(x) is 2x^2, i do 2x^2 twice

it's like an onion, you do it layer by layer

[gritty jewel]

oh ok

thank you

[solar merlin]

i'll give you some examples for warm up

nah, let me help you out

[gritty jewel]

ok

[solar merlin]

if i had $f(x) = 2x$, and i did $f(f(x))$, what would that be? think about f(x) as an unknown, and then find out what it would be

[ocean seal]

alias

[gritty jewel]

erm

2x?

[alpine sable]

Nope

[solar merlin]

nope

[gritty jewel]

ah

[solar merlin]

1 sec, gtg, epsilon, can you explain?

[alpine sable]

Sure buddy

[solar merlin]

thanks, cya

[alpine sable]

So

What do u think is f(f(x))

When f(x) is 2x

@gritty jewel

[gritty jewel]

f(2x)?

oh wait

erm

is it 4?

[alpine sable]

You just need to replace x with f(x) in the function. Like say if we have f(x) = 2x, then f(f(x)) = 2(f(x)) = 2(2x) = 4x.

4x

[gritty jewel]

oh 4x

[gritty jewel]

thank you

i get it now

thank you so much guys

.close

[lone heart]

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[buoyant cave]

What the asnwer to this guys? and how do i find it ?

[pale kestrel]

try algebra

[buoyant cave]

i dont get how their sum is greater than the difference by 30

[pale kestrel]

You add them together

that gives you 30 more

than if you took their difference

[alpine sable]

Start the problem by assuming the two numbers to be some variable. Let say the numbers be x and y. Now the product of these is given to be 900 i.e. xy = 900. Their sum is greater than their difference by 30 i.e. (x+y) = 30 + (x-y) => y = 30 - y => y = 15 substitute it in first equation to get x = 60. So x is greater.

[pale kestrel]

For example, the sum of 2 and 3 is greater than their difference by 4 (2 + 3 = 5, 3 - 2 = 1, then 5 - 1 = 4)

[buoyant cave]

tysm

[lone heart]

@buoyant cave Has your question been resolved?

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[young thicket]

help

[young thicket]

how

the answer is 33 i looked but how do i do it

[candid torrent]

@young thicket add 8^x and 8^x

you get 2(8^x) correct?

so so far we have 2(8^x) = 2^100

divide both sides by 2

8^x = 2^99

from here can you figure it out?

[young thicket]

yeah i think

[candid torrent]

tell me then

WHO CHMONKEY'D ME

[bleak ridge]

[candid torrent]

btw if you were thinking

to convert 8^x to base 2 you'd be right

[lone heart]

@young thicket Has your question been resolved?

[lone heart]

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[sturdy storm]

!help

[sturdy storm]

Can anyone verify if these are correct

close

!close

.close

[lone heart]

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[sturdy storm]

!open

[sturdy storm]

Is this correct

anyone?

[gray isle]

last one is wrong

the work you did can also be structured better

[lone heart]

@sturdy storm Has your question been resolved?

[lone heart]

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[gritty jewel]

im not sure if i am correct and im not sure if i have done the right thing

[gritty jewel]

the answer i got is (1-x)/x+1

but

[wet trail]

So this might sound pretty stupid, but I have just a small question which I can just type through words rn so...

[glass lichen]

yes.

f is its own inverse

[gritty jewel]

i think its wrong

[glass lichen]

#❓how-to-get-help

[gritty jewel]

wait so

what i did was right?

basically

[glass lichen]

well no clue what you did

cause you opted to not post it for some reason..

[gritty jewel]

i changed f(x) to y

and

[gritty jewel]

i will send a picture

[frigid geyser]

f(x) to y, switch x and y then solve it for y?

[gritty jewel]

yes

^

[frigid geyser]

yes you did it right

and there's a general formula, $f(x) = \frac{ax+b}{cx+d}$ then $f^{-1}(x) = \frac{-dx +b}{cx - a}$

[ocean seal]

xdk1235

[gritty jewel]

ah ok

thanks guys

.close

[lone heart]

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[wet trail]

So this is what I wanted to ask. What happens if I have that x to the power of 2 and remove 5 from it. And what would happen if the x wasn't to the power of 2? Would 5 still be removeable and how? Yeah yeah I know this is stupid but I need help.

[tidal bridge]

first of all x can't be -1

[wet trail]

I always make that mistake istg

[tidal bridge]

can i see all the problem ?

[wet trail]

Yeah here one sec

I'm currently at D rn, I stopped there.

[tidal bridge]

ok

[wet trail]

I just wanna know about that x - 5 thing

[lone heart]

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[tidal bridge]

oh you don't need that x-5 you can siply do (4x^2-4x)/(x+1)

[tidal bridge]

sore there is +4x

[wet trail]

So if I substract anything from x and the problem is put like "x - 12" the answer will be +11 because the x acts like a 1?

[tidal bridge]

you can put anything in the x except -1

[wet trail]

I understand

What if the x is to the power of 2? Like "x2 - 5"

Will the answer be 4 to the power of 2.

?

[tidal bridge]

oooh you thing you need to get -1 always right if you put an x it will also put the same x under the divide like if you put up the 2 it will look like (4-5)/(2+1)

can i ask you something have you learned about hyperbola?

[wet trail]

Not yet

[tidal bridge]

ohh that makes sence why you don't understand this one

there is funcion called hyperbola and its formula is y=k/x where x can't be 0

[wet trail]

I just didn't understand that little thing I was uncertain of. That little "x -5" and what would happen if the x was to the power of 2 and I tried to substract anything from it.

[tidal bridge]

if it was like x^2-5 you can't subtract it

[wet trail]

So what's the procedure?

[tidal bridge]

you want to get x right?

[wet trail]

Nah I just wanna know what the result would be for x^2 - 5, I'm just uncertain of that small thing.

[tidal bridge]

it will be nothing you can't do nothing here

if it was x^2-5x like in the problem then you can do x(x-5)

[lone heart]

@tidal bridge Has your question been resolved?

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[rugged turtle]

why is this 5i

not 5

[pale kestrel]

what is 5 squared?

[rugged turtle]

25

and -25

[tidal bridge]

it is +- 5 because -5^2 also is 25 and both are correct

[rugged turtle]

but why i

[rugged turtle]

this is wrong

i realised

you cant get minus numbers

:/

[rugged turtle]

but why this

[tidal bridge]

because if you do -5^2 you get possitive number

because (-5)*(-5)

[pale kestrel]

Have you heard of complex numbers?

If not, I don't advise attempting these questions until you learn about them

$$i := \sqrt{-1}$$

[ocean seal]

Shuri2060

[pale kestrel]

That is how it is defined.

[tidal bridge]

is this the academic mathematics?

[lone heart]

@rugged turtle Has your question been resolved?

[rugged turtle]

Yeah i’ve started just yesterday with them

[lone heart]

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[fair osprey]

How do I solve this?

[fair osprey]

it'd be 3/2 added with the recipricol of smth is 1, so wouldnt it be -1/2? then wouldnt that be -2? but it says its wrong

[bleak ridge]

Weird

Ohh

Pay close attention to the wording

It's three times the reciprocal

Not "add on 1/2 three times"

That's what I read it as at first also

[fair osprey]

wdym?

[bleak ridge]

3/x+1/2=1

Like that

Rather than 1/x+3/2=1

[fair osprey]

if its added 3 time isnt it the same as 3 times 1/2?

[bleak ridge]

It's added once

[fair osprey]

OH

wait so the fraction in questoin's recipricol is multiplied by 3?

[bleak ridge]

Yeah

Or the number I assume you mean

I guess it prob is a fraction

[fair osprey]

so 6?

[fair osprey]

I'm kinda confused on hwo you got that but it's correct

[bleak ridge]

It's just 3*1/x+1/2=1

Simplified

Also yeah 6 it looks like

[fair osprey]

but how do you know it's a 1?

[bleak ridge]

Since that's what the problem said

Since it said that the result is 1

[fair osprey]

I mean like how do you know its 3*1 not 3 * smth else?

[bleak ridge]

Oh

Maybe my notation is confusing

$3 * \frac{1}{x} + \frac{1}{2}=1$

[ocean seal]

PapaBread

[bleak ridge]

I'm just saying the reciprocal

[fair osprey]

yeah but how do you know its a 1/x not lkie a 2/x where HTE original wuld have been x/2?

I'm probably askig obvious things lmao but minf blanking a bit

[bleak ridge]

The reciprocal of a number will always be 1/

I mean it can be multiplied by other things and simplified

But just a reciprocal alone will always be 1/x

[fair osprey]

what of the number was a fraction?

[bleak ridge]

In that case it simplifies to something else

Like the reciprocal of 3/2 for example

Starts as 1/(3/2)

But simplified nicely into 2/3 by just flipping the fraction

But yeah you're completely right in that you don't normally show a 1 over the reciprocal of a fraction

I probably should've been clearer

[fair osprey]

this is porbaly smth that I was supsoed ot learn but iddnt bc I start russian msth late

[bleak ridge]

Oh

[fair osprey]

Welp, thanks for he help /gen

.close

[lone heart]

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[bleak ridge]

Np

[lone heart]

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[hallow hinge]

uh is it just me or does this make no sense

[hallow hinge]

I just stop at theta = ~28 degrees

[lone heart]

@hallow hinge Has your question been resolved?

[lone heart]

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[real tree]

is the equation log 7 and log x^2 equivalent to the equation 7=x^2? how can u be sure?

[real tree]

how do i write the first part out?

[alpine sable]

Yes it is

x^2 = 7

So u just take log both side

I can explain how that work in detail if u want

[real tree]

gimem a sec

also can u help me with my other work too

OHH I GET IT NOW

okay

[alpine sable]

Yeh

[real tree]

log10=log(2x+3)

can u help me solve

do i divide both sides by log?

[alpine sable]

Are they on the same base

[real tree]

yes

[alpine sable]

U can't divide byy log

[real tree]

oh

[alpine sable]

Log is not a number

[real tree]

i can if they share the same bases though right?

is log an exponent

[alpine sable]

Log is inverse of exponent

U just equate 2x +3 to 10

Since they are one the same base

[real tree]

so

2x+3=10 because they’re the same base?

and then solve for x?

[alpine sable]

Yes

[real tree]

perfect

3.5?

[alpine sable]

Yes

I prefer leaving it in fractiond

[real tree]

ok

[alpine sable]

That way u can do log7 - log2

Hehe

[real tree]

tysm

LOL I NEED UR HELP AGAIN

(5.825)^(x-3) = 120

i do not remmeber learning this in class

do i set each equation to a log

[alpine sable]

Can u use a calculator

[real tree]

yes

[alpine sable]

Is it allowed

[real tree]

oh yeah oops sorry it says round to the nearest 0.001

[alpine sable]

Ok then log both sides

[real tree]

kk

[alpine sable]

Calculate log120

[real tree]

ok

[alpine sable]

Do u know property of log

[real tree]

yes

which one

[alpine sable]

So whats loga^b

[real tree]

the power one?

[alpine sable]

Yes

[real tree]

bloga

[alpine sable]

Yes

Use that here

[real tree]

OOHH

[alpine sable]

Take out x-3 from da powah

[real tree]

i think i get it

can i solve and u check my answer

[alpine sable]

I don't have a calculator with me

Wait ...

I'm using a phone

[real tree]

LOL U DONT NEEDA ITS OK

i think i’ll be fine

i can have my math mentor check tmrw

[alpine sable]

🤦‍♂️

I'm using a phone

And I'm like

Where da calculator

[frigid geyser]

,wa log_5.825 (120) + 3

[real tree]

🤧

[frigid geyser]

hewwo mr bot..

.wa log_5.825 (120) + 3

5.716833

[buoyant kayak]

,w log_5.825(120)+3

[ocean seal]

Results provided by WolframAlpha

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

Requested by a disappointing son#0540

[frigid geyser]

omg im so dumb

thanks lol

[real tree]

ok perfect that’s what i got but 5.717 bc rounded to the thousandth

omf bye it has a word problem

shood i just do it tomorrow

oh actually ik how to do this

i should be fine

THANK U SO MUCH!!!

.close

[lone heart]

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[placid rapids]

10sin(6(9.5-15))+12

[placid rapids]

well it's actually f(9.5) = 10sin(6(9.5-15))+12

[buoyant kayak]

what is your question

[placid rapids]

f(9.5) = 10sin(6(9.5-15))+12

[buoyant kayak]

that's not a question

[placid rapids]

how do i solve that?

[buoyant kayak]

put it into a calculator

[placid rapids]

How do i know if its right?

diffrent calc say diffrent things

[buoyant kayak]

by using a calculator correctly

[placid rapids]

how do i know if i use RADs or DEGs?

[buoyant kayak]

by seeing if your angle needs to be in radians or degrees

i don't know the context of the question so i have no idea what your question wants

[placid rapids]

trying to find the height of a ferris wheel when rotated at a 90 degree angle

the time it takes to make a full rotation is 38 mins

[buoyant kayak]

90 degree angle

[placid rapids]

.close

[lone heart]

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[dusty loom]

hey so i was doing some stuff like this and it said it was incorrect and i didnt know why, could someone explain if im doing something wrong?

[frigid geyser]

it's $30 off vs 40% off

not 30% vs 40%

[dusty loom]

oh

i feel dumb now lol

thanks

.close

[lone heart]

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[frigid geyser]

np!

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[fleet phoenix]

Is this channel available?

[fleet phoenix]

Okay cool here's my question. How do I prove the angle between two lattice vectors is never π/6?

[lone heart]

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[copper wedge]

I understand how to get the quadratic function using the sum and the product and how to find vertex and the value

i don't know understand where the contains the point comes in

[bright hedge]

x = -b/2a is gonna be the x coordinate of the quadratic

And then if the leading coefficient of the x^2 term is negative then it’s a max, and vice versa

(Try to think about why that is geometrically)

,w graph -x^2 and x^2

[ocean seal]

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[copper wedge]

so just to confirm i have x^2 + 2x + 9/4=0

i need to turn into vertex form

[bright hedge]

yes so complete the square

[copper wedge]

i need to do -b/2a to find x and find y

and then plug in the two points

[bright hedge]

Okay I didn’t know that you only knew vertex form

So for this u should complete the square

Instead of using -b/2a

[copper wedge]

yes its basic honors alg 2 and i dont have to graph

for this question *

[bright hedge]

So do you know how to complete the square?

[copper wedge]

yes

thanks for your help

ill @ u if i run into a proble,

[bright hedge]

Alright

[copper wedge]

@bright hedge i feel like i did something wrong

vertex form is y-5/4=a(x+1)^2

[bright hedge]

Let’s check

,w vertex of (x-(2+5i)/2)(x-(2-5i)/2)

[copper wedge]

ngl i don't know what this is doing

[ocean seal]

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[bright hedge]

Okay it says the vertex is 1, 25/4

[copper wedge]

i am using the a{x^2-sumx+product}=0

[bright hedge]

That’s fine

[copper wedge]

and then i move the 9/4 over

[bright hedge]

It should be the same thing

[copper wedge]

Getting x^2+2x=-9/4

then adding one to both sides s

so it is (x+1)^2=-5/4

or in other ways 9 -5/4=(x+1)^2

vertex would then be -1 and 5/4

yea idk what im doing wrong

[bright hedge]

I can help when I get home

[lone heart]

@copper wedge Has your question been resolved?

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[lone heart]

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[copper wedge]

.close

[somber bronze]

Hello

[somber bronze]

Anyone here?

[wanton junco]

perhaps

[somber bronze]

Anyone know the answer?

Gonna do other problems first

[wanton junco]

the degree bounded by 2 lines in a circle is half the degree of the arc

from there it's just simply adding subtracting

[lone heart]

@somber bronze Has your question been resolved?

[somber bronze]

What?

I don’t think that is it

[wanton junco]

consider this

[somber bronze]

Tho I solved other problems first and then came back and solved it

[wanton junco]

what does c+120 equal to

[somber bronze]

So never mind

I used the

CQ conjecture to solve it

Cyclic quadrilateral

And also the property

That all radii

In a circle are congruent

So Never mind

Thx for ur help

[lone heart]

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[gloomy pumice]

is the answer to this problem -2x+2?

[gloomy pumice]

what I did was to solve for t in terms of p

obtaining t = p + 8x

and then I substituted in the average of t and u

(t+u)/2 = 2x+2

[covert agate]

y???

[gloomy pumice]

thanks, was a typo

[covert agate]

yea continue

[gloomy pumice]

and then I did (p + 8x + u) / 2 = 2x + 2

(p + u) / 2 + 8x / 2 = 2x + 2

[covert agate]

yea should be correct

[gloomy pumice]

(p + u) / 2 = 2x + 2 - 4x = -2x +2

[gloomy pumice]

so the answer is -2x + 2 right?

ok thank you very much!

.close

[lone heart]

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[wild pendant]

just wanted to see if my proof for the convergence is valid. Exemplars use epsilon definitions for convergence but I just used a known fact.

[remote pollen]

hello, any germans?

[frigid geyser]

$\lim_{n \to \infty} a_n = a$, $\lim_{n \to \infty} b_n = b$ then $\lim_{n \to \infty} a_n b_n = ab$ is true

[ocean seal]

xdk1235

[frigid geyser]

but the converse doesnt necessarily hold

[wild pendant]

ok, thanks

[lone heart]

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[lone heart]

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[wild pendant]

Just wanting to know if this reads truthfully

[covert agate]

huh

[wild pendant]

I was investigating some inequality stuff that I needed for my own squeeze theorem proof.

[covert agate]

1 ≤ 2 ≤ 4 and 1 ≤ 3 ≤ 4

2 ≠ 3

[wild pendant]

Ty

So my stuff doesn't even make sense in the first place?

[covert agate]

you’re doing squeeze theorem right

that’s in calculus

[covert agate]

i didnt read your proof

[wild pendant]

No just epsilon proof for that stuff

Not using it

Real analysis

[covert agate]

this is hardly epsilon delta

lol

[wild pendant]

Wanna see my proof

[covert agate]

on squeeze thm?

sure

[wild pendant]

The boxes result is my issue

Proof starts below drawn line

[covert agate]

i dont understand your proof lol

but squeeze thm can be proven easily through inequality thms

channel occupeid

[wild pendant]

Ok

Calm down

[sly mantle]

ty

[wild pendant]

Are you doing a test?

[sly mantle]

theyre b&

[covert agate]

they literally said theyre in an exam

lol

[wild pendant]

Damn

Well we can't help them haha

Have to let them be at their fate

[sly mantle]

@covert agate pls dont delete modpings, other mods who come later may be confused

[covert agate]

alright

[wild pendant]

Didn't believe he was oiterally saying that

I thought he was just packing an all nighter, not trying to cheat

Bruh

Ty chrome I'll be on my way.

. close

.close

[lone heart]

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[alpine sable]

I need help understanding Pythagorean Theorem Applications

[vague coral]

channel occupied

yea what dont you understand in it ?

do what ?

[leaden barn]

it

[vague coral]

which one

[tacit arch]

Lol this exchange

[glass lichen]

1. no
2. that's a domain

[vague coral]

no

[glass lichen]

what is the range by definition?

be as clear as you can.

better, the range is the set of y values a function puts out

so where is the smallest value of that range going to be?

at x=-1, yes.

but more generally it'd be the lowest place on the y axis.

and where is the largest value in the range?

**x=**4

you need to say x= else it's wrong.

but then find the y values corresponding to those x values, then your range is that interval

f(-1) is neither of those.

yes

cant answer that, going to bed

[vague coral]

inverse of f ?

the classic way is to solve f(x) = y

thats what im doing

[vague coral]

...

you solve it

what do you get ?

what was the equation you solved ?

f(x) = 3x-2 = y
3x = y-2
x = (y-2)/3
f^{-1}(x) = (x-2)/3

its not an equation, its an expression

now, if you know how to find f^-1, you should know the domain of f^-1

the domain of f is the range of f^-1, the range of f is the domain of f^-1

try it first yourself

and what have you got ?

its (fof)(x) if im not wrong

o is the law of composition for the function

think of it as + or x, but they dont respect the same property

(f o f)(x) = f(f(x))

yes

x=5

2(2x-3)-3 = 4x - 9 = 11
4x = 20
x=5

[pliant mortar]

hi

can u help me

[alpine sable]

@pliant mortar #❓how-to-get-help

Make a new channel

[pliant mortar]

how

[vague coral]

#❓how-to-get-help

[alpine sable]

Go the channel

Read

[vague coral]

why tho

[lone heart]

@alpine sable Has your question been resolved?

[lone heart]

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[lone heart]

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[fathom mantle]

Help with what

[proven rune]

@alpine sable they have ABC~DEF
therefore A=D
B=E
C=F
equate the respective angles and ur done

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[granite sedge]

Is it me or does this Q not make any sense? if the set was {1,2,3,4,5,6} then i know the answer would be 7/2 but with just {1,2,3} the probabilities don't add up to 1 right? and i just get an expectation of 1

[pale kestrel]

?

Question is fine

'{1,2,3,4,5,6} then i know the answer would be 7/2'

no.

[granite sedge]

isn't the expectation just 1*1/6 + 2*1/6 + 3*1/6?

or am i tripping

[pale kestrel]

maybe i am.

how did i get 1/2 earlier

yh ur right mb

wait no

URGH

[stark lantern]

1/6, 2/6 and 3/6 are the probabilities right?
if we multiply with their respective values and add we should get 14/6

[pale kestrel]

Doesn't this give 1?

How on earth could E(X) be 1

That is just the total prob

[granite sedge]

ah ok

i got it

[pale kestrel]

yh yh ok

expectation you need to multiply probability by each x and sum

[granite sedge]

thank you

[lone heart]

@granite sedge Has your question been resolved?

[empty ivy]

Can anyone help me solve this question, like help kinda tutor me through this

I’m so confused

Would be appreciated

[alpine sable]

Are you aware that tan theta = Perpendicular/Base?

[lone heart]

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[empty ivy]

No

[empty ivy]

I need help if possible

Can you explain it

I’d be ok with a VC if you want

[alpine sable]

Where's your question?

[empty ivy]

I’m not sure ho i solve it

How*

[alpine sable]

@empty ivy post your question

[empty ivy]

How do I determine the Tangent of the angle at the centre of the spiral for each of the first five triangles.

[alpine sable]

Oh

[severe sluice]

two words

pythagorean

theorem

[alpine sable]

Do u know how to find the bases

yeh

[empty ivy]

No

[alpine sable]

Oof

[empty ivy]

Can someone go through it with me

[alpine sable]

Pythagoras theorem ?

[empty ivy]

If not it’s fine

[alpine sable]

Ok what’s the hypotenuse of the 1st triangle

[empty ivy]

Ye ik Pythagorean Theoram but it’s been a while

[alpine sable]

It’s sqrt(2)

[empty ivy]

The hypotenuse would be 1

Wouldn’t it?

[alpine sable]

No

1^2 + 1^2 = (hypotenuse)^2

[frosty violet]

Take the squares of both sides and add them

[wary stream]

a^2 + b^2 = c^2

[empty ivy]

Ohhhh right

So hypotenuse would be 2?

[wary stream]

No

2 = c^2

[frosty violet]

You have a and b there. You solved for c^2

[empty ivy]

Ye and then I square that

[alpine sable]

No

[frosty violet]

Almost

[alpine sable]

U sqrt(c^2)

[empty ivy]

Ye

And that’s one

[alpine sable]

Noooo

[frosty violet]

nope

[alpine sable]

It’s. 2

1 + 1 is 2

[frosty violet]

when you take the square root of a squared number, they cancel out

[empty ivy]

Oh

Is it possible if you can go on VC with me

To help

To make your job easier

[alpine sable]

Ok

I’m coming

[empty ivy]

Ok which chat

[frosty violet]

I'd say a good way to think about it is to say

1^2 + 1^2 = c^2
2 = c^2
sqrt(2) = sqrt(c^2) = c

[alpine sable]

Nvm I can’t VC

Not this time

We can talk to u

[empty ivy]

Ok

[alpine sable]

But u gotta figure it out

[empty ivy]

Ok

[frosty violet]

I think knowing the steps to the theorem and knowing why they are such are the big ideas here

[empty ivy]

Ik the theorem just been a while

So it’s 1^2 + 2^2 = c^2

Which means it’s 1 + 1

= 2

Then I sqrt 2

Which is 1.41

[frosty violet]

If both sides are 1, it'd be 1^2 + 1^2 = c^2 because you know both sides are 1 and 1

[empty ivy]

And that’s the hypotenuse?

[frosty violet]

You can keep sqrt(2) as is

[empty ivy]

Ok

So hypotenuse would be sqrt 2

[frosty violet]

Yes

[empty ivy]

So I never use decimals in this right

Just leave it as sqrt

[frosty violet]

Don't use decimals if it's irrational

[empty ivy]

Ok

So that’s the hypotenuse of the first triangle

?

[frosty violet]

Yes

Just know that your known sides are a and b

and that a^2 + b^2 should give you c^2

but you want c

[empty ivy]

Ok

Then what do I do for second triangle?

[frosty violet]

Consider the sides you know

[frosty violet]

then find c^2

[empty ivy]

So the second triangle only has one measurement

Wait no it has 2 now

Cause I have hypotenuse for 2nd triangle

Is that how I do it?

[frosty violet]

You have the hypotenuse for the first triangle

[empty ivy]

Ye

It’s sqrt 2

[frosty violet]

So you have two measurements

Now you repeat the steps for the first one

on the second one

Except now you have different numbers

[empty ivy]

Wait so I do

1^2 + sqrt 2^2 = c%2

[frosty violet]

Identify a and b then square them

[empty ivy]

A is

Sqrt 2^2

[frosty violet]

When you have any a or b, you square the whole thing

[empty ivy]

B is 1^2

[frosty violet]

So what do you say sqrt 2^2 is?

[empty ivy]

Just 2

So A is 2

B is 1

Square them both and that = c2

?

[frosty violet]

For future reference, it'd probably be best to maybe write it out as sqrt(2)^2 so it doesn't look like sqrt(2^2)

[empty ivy]

Oh ok

Thx

[frosty violet]

So you have sqrt(2)^2 + 1^2

and you squared them and found the result

[empty ivy]

4+1= 5

Which means

[frosty violet]

uhh

[empty ivy]

C2 = sqrt5

[frosty violet]

4 came out of nowhere lol

[empty ivy]

(2)^2=4 right

[frosty violet]

Not if you're taking the sqrt(2) and squaring that

[empty ivy]

Ohhhh

So it would equal 2

Right?

[frosty violet]

Because you'd cancel out the sqrt() and the square

yes

[empty ivy]

Ok

Thx so much for that

How do I find the tangent tho

Or is that what I’ve been doing

[frosty violet]

I'd probably find that after solving for the sides of the triangle

[empty ivy]

So for the first tangent I would write sqrt 2

Ok

[frosty violet]

The tangent has to do with angles

[empty ivy]

Oh wait isn’t that opposite/Adjacent

For that

[frosty violet]

It is

But the opposite and adjacent parts are sides

[empty ivy]

Yup

And then I use the angle as theta

Right?

Then use inverse tan?

[frosty violet]

The angle could be represented however you want

[empty ivy]

Ok

So I don’t have to fight theta right?

[frosty violet]

but I might need to refresh myself on tangent and inverse tangent

[empty ivy]

I can write it as X

Ok

[frosty violet]

You could

[empty ivy]

Ima draw first 12 triangles

I’ll be back

[frosty violet]

But theta is the universal symbol of angles

go for it :)

[empty ivy]

Should take me like 5 minutes

Thx

[frosty violet]

Take your time

[empty ivy]

Ok

This looks wrong to me

[frosty violet]

I've never done a Pythagorean Spiral, but I'd say it looks kinda close

[empty ivy]

Ok

Ok so I’m start labeling sides

Ima try to solve it

And can you check if there’s mistakes after?

[frosty violet]

Sure

[empty ivy]

Ok

Done i think

So how do I solve tangent?

[frosty violet]

So tangent is opposite/adjacent and you want the tangent of the angle at the center of the spiral

[empty ivy]

Is the spiral measurements good?

For sides?

And when solving tangent

Can I choose any angle other than the 90 degree one?

[frosty violet]

You have to use the one at the center

[empty ivy]

Oh wait u said centre angle right?

Ok

[frosty violet]

Yeah lol

[empty ivy]

Wait ima solve first one

And I’ll say what I got

[frosty violet]

Sure

[empty ivy]

Can you tell me if it’s right

[frosty violet]

I'll probably clarify what your opposite and adjacent are

[empty ivy]

Opposite is outside side

And adjacent is the inner one next to the centre angle

[frosty violet]

Yeah

[empty ivy]

Ok

Well here I go lol

[frosty violet]

Good luck :)

[empty ivy]

Thx

First angle is

45?

2nd angle is 35.26

Right?

2nd triangle*

[frosty violet]

I know tan(theta) = 1/1 = 1

for the first triangle

[empty ivy]

Wait first triangle is 1?

For angle

[frosty violet]

no

[empty ivy]

I’m pretty sure it’s 45 degrees right

Cause you inverse tangent it

[frosty violet]

Yeah it is lol

[empty ivy]

Oh ok

[frosty violet]

I was trying to catch up

[empty ivy]

And is 2nd angle correct lol

I said it’s 35.26

If that’s right I think I’m good

[frosty violet]

Yeah

[empty ivy]

Thank you

Omg that was actually so helpful

[frosty violet]

I think it just relies on remembering the steps

[empty ivy]

Ye

I like people that actually explain it

Rather than do all the steps

Thx for that

[frosty violet]

You seem to understand it just fine lmao

[empty ivy]

If I have any other questions I need help on can you help explain too

But so far I know how to do this cause of you

Thx 🙏

[frosty violet]

I don't normally help on the channels since I'm not an active member and only stumbled upon this help channel but sure, I can help

[empty ivy]

Ok

Can o add you?

I*

If it’s fine with you

[frosty violet]

Sure

[empty ivy]

Thx

[frosty violet]

Np lmao

[empty ivy]

I’ll be back if I have questions but I’ll try to figure it on my own

Peace for now lmao

✌️

[frosty violet]

Later!

[lone heart]

@empty ivy Has your question been resolved?

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[gusty walrus]

not sure why this isnt correct

[tacit arch]

which one?

[gusty walrus]

it doesnt tell me

so im not sure

i think B is on the xz plane

[tacit arch]

ok so that part's right

do you know how to find the distance from a point to a plane?

[gusty walrus]

is it not pythagoras?

[tacit arch]

what is it for A to yz plane and C to yz plane?

your formula should look something like this
https://d138zd1ktt9iqe.cloudfront.net/media/seo_landing_files/distance-between-point-and-plane-1636487624.png

[gusty walrus]

ok

ill try

[gusty walrus]

wait are those points the closest/furthest to each plane though?

was i correct on that part

[tacit arch]

idk

[lone heart]

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[alpine sable]

Hello

[alpine sable]

How to solve the question number 2?

Will the answer be negative infinity to positive infinity?

No

Note that the first function is not defined for all values of x.

When denominator is 0, function is undefined.

I apologize.

The question number is 3.

[severe sluice]

how can a function like that be discontinuous?

[alpine sable]

Yes, I just wanted to confirm.

[severe sluice]

(proving that all polynomials are continuous is a good exercise)

[alpine sable]

Indeed. Thank you for guiding me.

🙂

.close

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[warm anvil]

Not sure on how to prove if this is true or false

[severe sluice]

my intuition says "how on earth did beta end up in that relation"

[warm anvil]

oh right yea, beta is 4, im going through past exam papers

they did it to stop people from cheating online i think

[severe sluice]

okay

so can you send the question please?

this looks like an infoslide

[warm anvil]

cant send the actual PDF in

if thats what youre asking

[noble sinew]

they haven't even specified the measures used for H, E and W

and this has nothing to do with math

[warm anvil]

i cant just guess true or false

this module is maths based

[noble sinew]

they haven't said that exercise has the same weight as weight, they haven't specified how much more it benefits doing exercise for a heavier person

so not enough to say anything

[noble sinew]

and

[warm anvil]

what is it then

[cerulean vine]

halp please

[tacit arch]

#❓how-to-get-help

[cerulean vine]

ok

[lone heart]

@warm anvil Has your question been resolved?

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@warm anvil Has your question been resolved?

[alpine sable]

calculate the volume of pyramid

calculate the volume sphere balls take

[lone heart]

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[copper tangle]

Can someone help me with this integral?

[copper tangle]

<@&286206848099549185>

[wild pendant]

I am not helping (sry) but that integral looks like a fat L

[copper tangle]

-_-

[wild pendant]

the bounds are negative

check symmetry first before you ask further

if the function is odd, then there is no work and hooray

otherwise... well, we will get there somehow

ok, I think the function is even