help-38

[rapid vortex]

Right, so my idea is to allow the dotted line to extend beyond the top line, and figure out how much it needs to, and allow the connection point to “move along” the dotted line

[delicate bobcat]

Okay, makes sense

Well, you see it forms a triangle, you can determine its base length at the beginning

[rapid vortex]

You know as soon as I drew that graph I should have noticed the triangle haha

[delicate bobcat]

(assuming the midpoint of the upper line can move in the range +/- 1.5 along the x-axis)

[rapid vortex]

And how would I derive the deviation of the connection point along dotted line

[delicate bobcat]

What is the base length? Can you tell me?

I mean, can you determine it looking at these constraints

[rapid vortex]

Yeah, 3”

[delicate bobcat]

Perfect, let's go ahead then

[rapid vortex]

And the altitude is 4.5”

[delicate bobcat]

Okay, so the y-coord is given, right

[rapid vortex]

Let me elaborate a bit further

[delicate bobcat]

So from here you can also determine the angle of rotation

Using trig

(if needed)

[delicate bobcat]

Just draw a circle with center at the origin and radius length 4.5

then you will be able to find where the end of the dashed line is after rotation

[rapid vortex]

oh true

[delicate bobcat]

finally, you will calculate how far the intersection point of the dashed line with the upper straight line is from the intersection point of the circle with the dashed line (after rotation)

[rapid vortex]

that makes sense, thank you

.close

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[delicate bobcat]

Something like this

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[manic jackal]

Show that if for $x \in \mathbb{R}$ the following holds
[
|a_1 \sin x + a_2 \sin(2x) + \cdots + a_n \sin(nx)| \leq |\sin x|,
]
then
[
|a_1 + 2a_2 + \cdots + n a_n| \leq 1.
]

[solid kiln]

Halex

[manic jackal]

can only use continuity and differentiation

[zinc ginkgo]

Did you try taking the derivative of the first sum in abs val on the left

[manic jackal]

$\frac{d}{dx}\Big(a_1 \sin x + a_2 \sin(2x) + \cdots + a_n \sin(nx)\Big) =
a_1 \cos x + 2a_2 \cos(2x) + \cdots + n a_n \cos(nx)$

[solid kiln]

Halex

[manic jackal]

Evaluating the derivative both sides in 0 would make it, right?

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@manic jackal Has your question been resolved?

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@manic jackal Has your question been resolved?

[zinc ginkgo]

Yes cos(0) = 1

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[tired shuttle]

ABCD is a rectangle with AB = 8 and BC = 6, E is a point on CD such that EC = 2, F is the midpoint of EB find AF

[tired shuttle]

so i got the answer using analitical geom

by defining D(0, 0) we obtain A = (0, 6) and F = (7, 3) and using the distanace formula AF is attained

How do i find AF using Eucledian Geometry?

[round imp]

Try using the Pythagorean theorem

To obtain BE

[tired shuttle]

BE is 2\sqrt(10)

[round imp]

Nice

Now can you use it again to find AF?

Note that F is the midpoint of BE

[dusky mortar]

but AFB is not right angle so we get back to same calculations as in mentioned analytical geom

[tired shuttle]

i have an idea of constructing CF then using the british flag

[round imp]

ah indeed

[tired shuttle]

since EFC is an isosceles

[round imp]

shit i got trolled by diagram

[dusky mortar]

we can extend AF to point K so AF = FK, this way K will be on line DC, and EK = AB
then you will have simple Pythagorean for AKD

[tired shuttle]

wow

magical solution xd

[round imp]

smart

[trim lichen]

ftr i think coordinate geometry is more than fine for this problem method-wise

it isn't really all that contrived especially given you are working with a rectangle

which enables a very natural coordinatization

[tired shuttle]

yea euclid geom for this types of problems is just magical

i would also resort to analytical methods like coords, complex, or trig

ty all

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[river wasp]

somebody give a simple proof of Silverman–Toeplitz theorem i get headache reading any >2page proof 😦

[river wasp]

thats the one about regular matrix summability methods incase you forgot

can use concepts in functional analysis such as weak star convergence

thanks

https://tenor.com/view/hug-gif-15819456627234943636

i am now reading the proof in my book again, let yall know when im finished!

uhhh somebody help plz <@&286206848099549185>

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[river wasp]

whatever ill just google

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as this action is irreversible, and this channel may abruptly lock.

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[pulsar jolt]

Ques 13

[cobalt drift]

Multiply the mean and extreme terms and then sub x^2 + 5x = u

[onyx snow]

hint: group the two middle terms and the two other terms

[cobalt drift]

It'll turn into a solvable equation

[nimble niche]

Biquadratic

[pulsar jolt]

Trying

[viral merlin]

i thought of doing
(x+2)(x+3)(x+4) = -1/(x+1)

graph both sides

[onyx snow]

💀

[nimble niche]

Decent but painstaking

[onyx snow]

sounds like an utter nightmare to me

[pulsar jolt]

I am only getting 2 roots but answer is 4

[viral merlin]

like i already have factors , i can see concavity , and 1/x+a is general to me-

[cobalt drift]

,w solve (x + 1)(x + 2)(x + 3)(x + 4) + 1 = 0

[solid kiln]

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[cobalt drift]

2 roots it is

[pulsar jolt]

There is a typo in this solution then, right?

[viral merlin]

i mean it just repeated the terms i think so

only 2 came up on the graph

[viral merlin]

and ^

[west saffron]

bro they are same

[cobalt drift]

yeah no idea where the other ones came up

[pulsar jolt]

But we should count repeated roots too, unless question asks 'solutions'

Or vice versa

I forgot

[cobalt drift]

these aren't duplicates

[viral merlin]

there are no repeated roots , 2 are complex

[cobalt drift]

,w plot (x + 1)(x + 2)(x + 3)(x + 4) - 1 = y

[solid kiln]

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[cobalt drift]

^

the multiplicity is 1

the key is tripping

[pulsar jolt]

Ik

Thanks guyz

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[pulsar jolt]

I solved this question by transformation of roots but ans is -5 , what did i not get right ans by that method

[lunar stirrup]

expand everything :D

[pulsar jolt]

No

I mean

[lunar stirrup]

also type .reopen

[pulsar jolt]

.reopen

[trim jolt]

✅

[pulsar jolt]

Thats lenghty

I wont have that much time in exam

[cobalt drift]

you subbed x = y + 2 and x = y - 2?

[onyx snow]

use Vieta's theorem maybe?

[pulsar jolt]

Wait

[cobalt drift]

Is this what "transformation of roots" is?

[lunar stirrup]

f(x) = (x-a)(x-b)(x-c)

put x=2

[onyx snow]

oh that's smart

[pulsar jolt]

Yh but thats not what i did

[cobalt drift]

It will help

[onyx snow]

and you just sub x=-2 for the other one

[cobalt drift]

Since you only need to extract two constant terms

[cobalt drift]

Oh much better haha

[lunar stirrup]

yeas and take care of the signs

[pulsar jolt]

I made an equation in Y whose roots are (2-alpha/alpha+2) , (2-beta/2+beta), (2-gamma/2+gamma)

So X=2(y-1)/(-y-1)

And the product of roots will be equal to whats asked

[lunar stirrup]

ok continue with ur method 🙏

[pulsar jolt]

Yh i will

But what am i doing wrong

[lunar stirrup]

dont know tbh

u wanted a fast method

and when u get one u ignore it

[pulsar jolt]

I didnt ignore it, i was busy typing my approach

[onyx snow]

sounds like an utter nightmare to do

[pulsar jolt]

Yh but i did solve it and i get 5/3 which is one of the options

[onyx snow]

the other approach takes little calculation time once you made that observation

[pulsar jolt]

Yh

I already have that solution with me

Just wanted to ask where i went wrong

Thanks

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[glad timber]

Ignore the pen markings

[tribal palm]

Try changing the x to 2x

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@glad timber Has your question been resolved?

[glad timber]

Hm k will try

[topaz fog]

This is a test question so I’d just recommend trying to find a function that works

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[jolly pebble]

hello, if X and Y are two events which are independent, are ~X and Y also always independent events?

[cobalt drift]

yep

[fleet bear]

Mhhm, you can prove this algebraically as well

[jolly pebble]

can u pls provide the proof please? if you have a link possibly

[fleet bear]

It follows from the law of total probability

If X and Y are independent events
then

P(X and Y) = P(X) P(Y)     (1)

Using law of total probability:
P(Y) = P(Y and X) + P(Y and ~X)
P(Y and ~X) = P(~X and Y)
P(~X and Y) = P(Y) - P(Y and X)

Using (1)
P(~X and Y) = P(Y) - P(X) P(Y)
P(~X and Y) = P(Y) (1 - P(X))

P(~X and Y) = P(Y) P(~X)   (2)

[lament reef]

tilde is \sim

[fleet bear]

ohhh

[lament reef]

(for some reason)

[fleet bear]

thx

[zinc ginkgo]

sim for similar triangles

[fleet bear]

is it double slash

nvm

[jolly pebble]

P(Y and ~X) = P(~X and Y)

why is this true

nvm

thanks for ur help!

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[mental isle]

hi, is anyone able to help me with this?

[spiral ocean]

does the bottom look like the top one?

can u make them the same?

[mental isle]

im sorry i dont understand what your saying

english is not my first language so im very sorry

[spiral ocean]

are these two mathematically same

[mental isle]

no

they are different

[spiral ocean]

u sure?

[mental isle]

wait 1 second

ohhh

yes they are the same

so that makes them co incident

so does that mean they are infitely many solution?

[spiral ocean]

bingo

[sudden sky]

yes

[mental isle]

but i am also confused because it says determine without solving

[spiral ocean]

ye

u havent tried to solve it

u just noticed the similarity

[mental isle]

okay, thanks for your help. Is it fine if i ask anymore questions in the future?

my final exam is tommorow, so im in desperate need of help

[spiral ocean]

ye

[mental isle]

thank you very much 🙏 god bless you

im sorry if im causing an annoyance but i also need help with this.

[spiral ocean]

"is moving faster"

[mental isle]

Ant B

[spiral ocean]

in term of speed, yup

[mental isle]

but idk the others

[spiral ocean]

ok

lets think about b)

what does t = 0 mean

[mental isle]

i think t=0 means they moved 0 cm

and the constants mean the point where the originally started

[spiral ocean]

ye

so thats b

[mental isle]

for c u just substitute and calculate

but idk about d tho

[spiral ocean]

thats one way, yup

[mental isle]

do u do t=10?

[spiral ocean]

u know taht they meet at t = 6

so whats "10 seconds after they meet"

[mental isle]

so we replace t with 10? im sorry im not the sharpest at math

40+20= 60 and 60+8=68, so after 10 seconds, the difference is 8 cm?

thats what im thinking but i am not sure

[spiral ocean]

they meet at t =6

so 10 seconds after t=6 is?

[mental isle]

i am not very sure

i dont understand, isnt t= to the amount of seconds

[spiral ocean]

if two people meet at 6 o'clock and will meet again 10 hours after that, what time will they meet

[mental isle]

4 am

[spiral ocean]

6'oclock in the morn

[mental isle]

*pm

[spiral ocean]

yup

whats that in 24-hour system

[mental isle]

16:00

[spiral ocean]

yup

similar analogy

t = 6 is when they meet

[mental isle]

and then we add 10? just like we did in the example?

alright thanks

[spiral ocean]

so t= 16

[mental isle]

ill calculate it and could you please tell me if its correct?

[spiral ocean]

aight

[mental isle]

the difference is 20cm?

[spiral ocean]

,calc 4(16) + 20 - 6(16) - 8

hmm

[mental isle]

i think ik the mistake

[solid kiln]

Result:

-20

[spiral ocean]

its 20

i made the mistake

[mental isle]

oh

so i was correct?

[spiral ocean]

yup

[mental isle]

thank you very much, from now if i feel stuck on anything, ill send it to this channel. thank you so much.

sorry for the annoyance, but would you be able to help with question 41? I feel enough information is not provided.

[spiral ocean]

u just solve the simultaneous eq

no?

[mental isle]

how do you do that? neither x or y is given a value.

[spiral ocean]

https://www.youtube.com/watch?v=68hMhae269k

[mental isle]

i figured it out, using the elimination method. im sorry lol i learnt this like 3 months ago, this is for my final exam so i just forgot.

i got x=4.5 and y=8

im pretty sire thats correct bc chatgpt agrees with me

[spiral ocean]

,w 3x+4y = 45.50 and 5x+4y = 54.50

[solid kiln]

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[spiral ocean]

wonderful

[mental isle]

👍

just so you know i might have other questions as well.

[spiral ocean]

k

[mental isle]

can you help with this? ik c but idk a and b.

[spiral ocean]

just draw

a line through the cluster

[mental isle]

i did, my line doesnt seem to match the answer

my line vs the questions line

[spiral ocean]

It’s close

[mental isle]

ik, but i need 2 points on the line, i only had 1.

[spiral ocean]

Make it straight that’s all

[mental isle]

oh

so i qould be correct

would

[spiral ocean]

Still acceptable

[mental isle]

ok thanks!!

[spiral ocean]

U don’t the points so there ain’t a perfectly u find a linear regression using that

In addition, the formula for it is hideous

[mental isle]

how would i find b? i tried but its different for every point

also the slope aswell

[spiral ocean]

Looks linear

Can u make it straight 😭

[spiral ocean]

Then just find the slope of ur line

[spiral ocean]

Do u know how to find linear regression using a calc

[mental isle]

there is no calc allowed in the exam. and im sorry but i dont understand whats linear regression

[spiral ocean]

Method of finding Line of best fit

Essentially

[mental isle]

i got y=9/2x-1.5

[spiral ocean]

Yup

Good enough

[spiral ocean]

It’s in the acceptable range

[mental isle]

also what does it mean by interpret the slope? do i just write the slope down?

[spiral ocean]

Maybe explain what it means in this context?

[mental isle]

wait so as long as i use points on the line to find slope and y intercept its correct?

[spiral ocean]

As long as

U draw the line through the cluster

Ye

[mental isle]

thanks 🙏

[spiral ocean]

But ask ur teacher to confirm

Some teachers can be ridiculously strict

[mental isle]

in my school, student do not know who grades their exams. its randomized everytime, our exams are not held inside class, its held in an exam hall. so im just hoping the teachee who grades it doesnt hate me

[spiral ocean]

💀

[bright oracle]

@mental isle

The idea is that you plot the points

Then you find the line of best fit

(either by linear regression or eyeballing it, depending on your level)

And then you use the line of best fit to find the slope

Any 2 points on the line of best fit will work

[mental isle]

i remember my teacher saying take the highest point and lowest point on the line to find slope

[bright oracle]

Yeah that's a good idea

Because it will make your measurement error smaller

[mental isle]

alright thank you

[bright oracle]

The data points may or may not lie on the line of best fit

Most of the time, most of them won't

[mental isle]

im confused very much because even the books answers are different from mine, so idk whether im correct or not

[bright oracle]

Does the book give an acceptable range?

Also, use a ruler to draw the line of best fit. Your line is very wavy in the picture

[mental isle]

this is what the answers in the book are usually

[bright oracle]

"any value close to -0.5 is acceptable"

[mental isle]

im scared ill just screw over the exam and fail bc most times my answer doesnt match it

[bright oracle]

Is it close usually?

[mental isle]

most times

[bright oracle]

So it should be fine then

[mental isle]

but idk what they mean by “close”

like within a range of 5? 1?

[bright oracle]

Yeah a range would be better

[mental isle]

they do not specify

thanks for your help

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@mental isle Has your question been resolved?

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[livid kiln]

tanθ+sinθ=m tanθ-sinθ=n
Then prove secθ=√mn cosec^2 θ

[main sigil]

you could express tan and sin pretty easily

[wet quarry]

this is one of those substitute into the expression and simplify

[main sigil]

and with tan and sin, you can express sec and cosec very easily

[livid kiln]

Let me try

Can you give me solution steps

[wet quarry]

!nosols

[trim jolt]

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

[main sigil]

though there will be some extra steps needed

perhaps it might be better substituting for m and n instead

[livid kiln]

Bro I'm stuck for like 40 minutes

[wet quarry]

the first step was given lol

substitute the expressions for m and n into √mn cosec^2 θ

[livid kiln]

Thanks

Finally,it solved

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[sharp stream]

he;[

[sharp stream]

so

is my wording wrong or the ai

its saying im loosing out on 2 marks

[fierce lake]

What exactly is it showing to be wrong

[sharp stream]

thats the thing

i dont know

[fierce lake]

Also there can be multiple congruence criteria here

[sharp stream]

maybe my wording is wrong?

[sharp stream]

oh?

[kindred pier]

your answer to a) makes no sense

[sharp stream]

huh

explain pls

[kindred pier]

where are you getting "size of angles" from?

[sharp stream]

i meant length

[dusty sleet]

Length of angle?

[sharp stream]

of side

wait wat

?

[dusty sleet]

I think you should read once more the question of the exercise

(suggestion: angles don't have anything to do with this)

[sharp stream]

wait

i know that you use pythagoras to find out the shorter side of triangle A

which is 5

and the length of sides 5 and 12 match

which makes it a sas

@dusty sleet

[kindred pier]

It could also be SSS

[sharp stream]

oh yeah true

wait leme calculate rq

[kindred pier]

Overall, the question is worded oddly, and if you are being graded by AI, then I pray for your soul

[sharp stream]

i am bro 😭

all of my homework is graded by ai 🙏

[dusty sleet]

Oh
My
God

What are teachers paid for then? 😅

[kindred pier]

your education is doomed

GG

[sharp stream]

sit around all day and make us watch other people's videos

nah my history teacher was making us watch thoes brainrot science videos with subway surfer clips 😭

[kindred pier]

where do you go to school, if you don't mind answering such a personal question

[sharp stream]

nah its alr i go to Brompton Academy

[kindred pier]

Oh in UK

This sounded like a USA school I'm actually surprised

[sharp stream]

lmfao 🙏

shouldve went to a grammar school man

@kindred pier can u give me a model perfect answer for the question?

[kindred pier]

should've went to gamer school

[sharp stream]

🙏 if only

[kindred pier]

Not really. 😦 The question is kinda worded badly. I feel like even the question was generated by AI. But for part A, use pythag to find the length of the missing side of triangle A. Then, it is clear that the two shorter sides match

[empty orchid]

I’ve seen this software, it is quite stupid with the wording of some answers

[sharp stream]

alright bet ill try make something up

[sharp stream]

MathsWatch 🔥 🔥

@dusty sleet bro i got mocks next week am i cooked?

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[empty orchid]

I’m sorry for the unreadability but I’m trying to evaluate $\int_0^{\infty}\frac1{x^{2n}+1}dx$ for $n>\frac12$

[solid kiln]

;(

;(

[empty orchid]

Bump

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@empty orchid Has your question been resolved?

[empty orchid]

Bump

[spare yarrow]

<@&286206848099549185>

[vagrant prism]

having a hard time deciphering what's happening here

[empty orchid]

I’m just summing the residues based on the p/q theorem

dyxn mentioned it earlier in #「helpers-lounge」

Since they’re all simple poles the residues will be $\frac1{\dv{z}(z^{2n}+1)}\bigg\vert_{z=c_k}$

[solid kiln]

;(

[empty orchid]

Then I just continue with a geometric sum approach

[eternal ginkgo]

tbh it seems fine as long as you havent messed up some calculations or simplifications

the logic is rigght

as for the summing i cant read that im sorry 💀

[empty orchid]

Yeah sorry

I was on the road

I can take a better picture

I also have a shit phone

[eternal ginkgo]

that part is correct

but i think a professor wouldnt be so forgiving for that transition i pointed at

oh nvm i didnt see the i

DUDE THATS PI????

OMG

[empty orchid]

Yes

I am sorry

[eternal ginkgo]

naaah

[empty orchid]

My handwriting is shit

[eternal ginkgo]

you deserve reductions for that

[empty orchid]

I cannot be bothered to TeX right now, I hiked 5 miles today

[eternal ginkgo]

jk lol your proof is fine

[empty orchid]

Ok thanks

[eternal ginkgo]

im stuck with isomorphism's and im not reading letters like im used to

[empty orchid]

I’m gonna end up getting glasses at this rate

Alright I’m gonna go watch some good fútbol

Cya. And thanks!

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[tired badger]

what does this even mean

[tired badger]

what is "no 2 parallel" and "no 3 concurrent"?

[burnt mulch]

• "no two parallel": No two of the lines go in the same "direction". Aka every pair of lines intersects exactly once.
• "no three concurrent":No three of the lines meet at the same point. So this is essentially saying that no two pairs of lines both meet at the same point.

[tired badger]

does this mean that line x iwll intersect x-1 lines?

[tired badger]

?

[trim lichen]

this is correct if you imagine placing the lines one at a time

but in your case it is better to say that every line intersects every other line

[tired badger]

can we show that n lines make n regions

[trim lichen]

....

what?

[tired badger]

nvm

can u just explain the solution

after drawing i can see that the second line after intersecting the first creates 2 new regions and the third creates 3 more after intersecting the 2 lines but can this be made intuitive

[trim lichen]

ok so it looks like they do think of the lines as being placed one at a time

here are two lines. they make four regions.

[tired badger]

what does it mean by no two pairs of lines can meet at a point

can 4 lines meet at a point?

[tired badger]

yes

[tired badger]

so <3 lines can meet at a point

basically 2

[trim lichen]

here are 3 lines now with the freshly-drawn one in red.

the red line intersects the previous two and so passes through 3 regions slicing each one in two

[tired badger]

ohhh

got it

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[wise sentinel]

what did i do wrong?

[wise sentinel]

I was asked to differentiate

[hidden vortex]

How do you know your answer is wrong?

And do you know the correct answer?

[vagrant marsh]

looks right to me

[hidden vortex]

That's why

[vagrant marsh]

if it looks different from your answer key, youre probably missing algebra

[hidden vortex]

I've read through this 3 times

[wise sentinel]

Oh nvm I looked at the wrong solution

[zinc ginkgo]

!done

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[wise sentinel]

.,•+{

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[lament rose]

how am i supposed to do this

[lament rose]

the f(x) part

[odd ocean]

Bro u literally know g(x) , then whats the problem with f(x)?

[lament rose]

I can't get it

[odd ocean]

Ahh

U messed up

The trash in g(x) should be in f(x)

And then

g(x) = √(x+5) -(1-x)

Just verify by limits

[lament rose]

It said g(x) was right

Everything is right except f(x

[odd ocean]

Nah g(x) is wrong

[wicked badge]

if the computer says its right im sure its probably right my man

[lament rose]

I believe it was made by my teacher

I've had to email him a few times already

I've got no clue what it could be

Put it in desmos

-5 to -1 the parabola hits itself instead of the other function

[wicked badge]

yo rq

can you see if $1 - x - \sqrt{x + 5}$ is right

[solid kiln]

thecrumbeler2

[lament rose]

Any other suggestions

[wicked badge]

im guessing thats a no

alright hold on let me actually go through and try to do it

[lament rose]

I was gonna head to bed gotta start my computer

To check

[wicked badge]

oh alr

[nimble niche]

,w plot the curves y=1-x, y^2=x+5

Um

[wicked badge]

say wut now

[solid kiln]

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[wicked badge]

lel

[nimble niche]

F

[wicked badge]

alright desmos maybe

[full dock]

,w graph y^2 = x+5

,w graph y=1-x

[solid kiln]

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Requested by waterrbeam

[nimble niche]

You should be able to put a comma as well i did it before

[full dock]

nah no comma

[solid kiln]

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Requested by waterrbeam

[nimble niche]

Ok anyways

[odd ocean]

As u can see for x belonging [-5,-1] there's only -ve branch

[lament rose]

Ye

[wicked badge]

,w integrate (1 - x - sqrt(x+5)) from -5 to -1 + integrate (1 - x + sqrt(x+5)) from -1 to 4

,w plot y=1-x, y=sqrt(x+5), y=-sqrt(x+5) from x=-5 to 4

[nimble niche]

!nosols

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[solid kiln]

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[wicked badge]

mah bad

[odd ocean]

So f(x) = 1-x - (-√(x+5))

Understood?

[wicked badge]

wait wut, he already got it tho

[wicked badge]

huh

[nimble niche]

Oh, so you're checking?

[wicked badge]

yeah

and somehow it gave 20.833 but its wrong?

whjat

hold on

,w integrate (1 - x - sqrt(x+5)) from -5 to -1 + integrate (1 - x + sqrt(x+5)) from -1 to 4

[solid kiln]

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[wicked badge]

bro what

am i being dumb rn

[lament rose]

(1 - x - sqrt(x+5)) thats not right

[nimble niche]

It's right

It's the decimal form

of 125/6

[wicked badge]

yeah

which according to the computer is right

but the function i used to get it for f(x) is somehow wrong?

and why is the minus sign highlighed?

[lament rose]

no reason

[wicked badge]

mmmm

im gonna go insane

[lament rose]

ive gone insane already

[nimble niche]

Why are you guys taking the line

It doesn't even cut the graph at -5

It's just the parabola that covers the area until the POI

[lament rose]

how would i find that area

[nimble niche]

By integrating just the parabola

[lament rose]

sqrt(x+5)?

[lament rose]

not it

[odd ocean]

Nvm

[wicked badge]

,w integrate (1 - x + sqrt(x+5)) from -5 to -1 + integrate (-1 + x + sqrt(x+5)) from -1 to 4

[solid kiln]

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[lament rose]

could i set a line to x=-1

then do that

[nimble niche]

Yall still using the line....

[wicked badge]

harion i dont think ur right ngl

73/2

[lament rose]

is everyoen stumped?

im lost

and tireed

[wicked badge]

im stumped because my answer is correct

yet it marks it wrong

executor is talking about something idk

and its 2am

so

rahhhhh

maybe ur teacher just like swapped aroung the terms a bit

[lament rose]

i think this is what he means

this is -1 to 4

this is what ur trying to do with -5 to -1

what its supposed to be

bc this is what were finding

[wicked badge]

hm

oh dude its just whichever one is greater minus whichever one is lesser

[wicked badge]

thats 1 to 4 you drew but ok

im sticking with 1 - x - sqrt(x+5) cause it got the right answer

[nimble niche]

It's solved

.close

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[nimble niche]

in dm

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[wraith hinge]

heulp... what did i do wrong here? I'm supposed to get ( 0,5 | -4,5 ) according to my work sheet

[wraith hinge]

I wrote " • (-4,5)" but the answer 7,5 came from typing - ( -4,5) in my calculator, i just didn't erase that yet

Idk if - or • is right, both do not lead to x = 0,5

with multiplying it, the answer would be -13,5x = 3 | : (-13,5) which would lead to x = -0,2

[brazen current]

So this system of two equations with two unknowns right?
I. 3x - y = 3
II. -3 - y = 6
Is this correct?

[wraith hinge]

Yes, i think this is called Addition method, sorry didn't mention this

I'm learning math in German so it's kinda hard for me to translate the titles

[brazen current]

Ok
Can you explain how did you get to -2y = 9?

[wraith hinge]

Yes, 3x -3x is 0, -y -y is -2y and 3+6 is 9

Did i do it right? I mean i hope so

[brazen current]

Oh sorry I misread that part

[wraith hinge]

and then i did it : (-2) to get one x which also makes the 9 to -4,5

[wraith hinge]

It's oki!

[brazen current]

The error comes from
I. 3x * (-4.5) = 3
it should be
I. 3x * (-(-4.5)) = 3
you are replacing y with -4.5 not 4.5

Also why are you multiplying it?

[wraith hinge]

Ohhh, so when the equation says "-y or -x" it should be -(-4,5) when the number is negative! i get it

and the additional brackets are because of the *

The answer is now 13,5x But when i do 13,5x = 3 | : 13,5
I get this: x = 0,2 again

But like the 2 has a line above, does that mean it's 0,22222... ?

[brazen current]

You should rewrite the I. equation and only change y to its value
You have rewritten I. 3x - y = 3 to I. 3x * y = 3 which you can't do
Maybe I misunderstood the problem, if yes, let me know

[wraith hinge]

One sec

i didn't really rewrite the first equation, i just copied it from the work sheet yk

[brazen current]

one sec

[wraith hinge]

i think i gotta do - y * (-4,5)?

not 3 * (-4,5)

i just watched a short video

so basically -1 * (-4,5)

[brazen current]

So you have two equations. You have calculated y, so now you can get x by subtituting y to any of those equations. You have done that, but the equation you've written in the bottom part of the paper is not the same as the original one. Does this make sense?

Bassically you're calculating different equation

[wraith hinge]

Ohh

Hold up

Lemme send a pic i erased smth

I've put -4,5 in the place of y, so (-(-4,5)

[brazen current]

what's the I equation?

[brazen current]

that part is correct

[wraith hinge]

It's 3x -y = 3

[brazen current]

So why is there  3x * (-(-4.5)) = 3 and not 3x - (-4.5) = 3?

[wraith hinge]

Idk in every tutorial video i saw they said you gotta multiply it 🥲

Maybe i understood it wrong?

So the right one would be 3x - not *?

[brazen current]

You need to keep equations the same in the exercise

[brazen current]

yes

[wraith hinge]

maybe the videos i saw meant -y * (-4,5)

?

[brazen current]

can you send me the video you're watching?

[wraith hinge]

Some exercises I've done were successful with the multiplying, I'll show you a picture

[wraith hinge]

They're in German...

😅

[brazen current]

fine, I'll understand the numbers 😄

[wraith hinge]

oh right, I'll show you one sec

[brazen current]

Oh I understand now

no need for that

[wraith hinge]

https://youtu.be/TPOc0kgfkCU?si=cVpvEEe1BGnFYu4E At 10:20 she does a similar way of my problem rn

[wraith hinge]

Oh alright

[brazen current]

So you need to know how you substitute (replace the letters with their values) the unknowns.
If you have 3x + y and x = 2 how would it look after substituting?

[wraith hinge]

Uhhh

Wdym 🥲

[brazen current]

replace x with its value

the thing you've done when you wanted to get x before

[wraith hinge]

Oh wait

So you mean i should change the 3x? like 3x - (-4,5) = 3 | : (-3)?

[brazen current]

no, no

[wraith hinge]

I mean -

[brazen current]

I'll explain

[wraith hinge]

I don't get it I'm sorry I'm lost 🥲

Okay thx!

[brazen current]

Firstly, do you understand what are those letters in math like x and y?

[wraith hinge]

Yes i do, x is the horizontal line and y is the vertical line in an coordinate system

And those two are the P (x | y) that i have to calculate

and as of now i only got y right

[brazen current]

Yes, that's true, x and y represent axis in coordinate system.
But here the letters have different meaning. It's just coinsidence that they're called x and y. They could be called anything, a, b or 🍕.
They're variables which means, that they're representing certain value(like 1, 9, or 1657.1354). So your goal is to find values of these variables.

hold up

fixed

[wraith hinge]

Hmm okay

So like x and y if you just write x and y

it's 1x and 1y?

they will always have a value?

[brazen current]

I'll try to explain. I'm not a teacher so it may not be accurate, please let me know if you understand.
Sometimes you know the value and sometimes the value is defined trough equation for example x = 5 + 2 or 4 * x = 8. In some cases it's impossible to find a value, for example x + 1 = x, sometimes there are infinite correct solutions, for example x * 0 = 0.

[wraith hinge]

Sorry for interrupting your explaining rn, But i tried doing it again, is this right maybe?

[wraith hinge]

Ah, i understand

But i mean when u have 2 equations that "match" like 3x and -3x you can do that Addition method

And then u add both equations together and then u try to get y out of it or x for example

but now i inserted my y in the 1st equation and now I'm just stuck there yk

[stone tusk]

You could use lcm to use the addition method for any equations

[wraith hinge]

cuz I can't get 0,5 out of it

[wraith hinge]

what's lcm?

[brazen current]

Nice, you corrected the 3x - (-4.5) = 3, but now you need to do -4.5 not +4.5

[stone tusk]

least common multiple

[wraith hinge]

Oh i see, why?

[wraith hinge]

Idk what that is sorry 🥲

[brazen current]

why?

[brazen current]

please correct rest of the calculation

[wraith hinge]

Okay ima do it

[stone tusk]

Even if the coefficients are different, you can multiply each equation by the lcm divided by the other equation's corresponding coefficient to make the coefficients cancelable

[brazen current]

I think the problem isn't there, he's using additon method

[stone tusk]

Ik

Sorry if i'm adding too much info

[wraith hinge]

now i got 0,5 Thank you!! but I'm still confused why i have to do -4,5 instead of +4,5

[brazen current]

Thanks for trying to help, I apprecheate it 😄

[wraith hinge]

i mean -(-4,5) -4,5 makes 0? I'm kinda confused with that

[brazen current]

ok

[wraith hinge]

It's okay tysm!

[stone tusk]

Yw guys!

[brazen current]

So you have
3x - (-4.5) = 3 ->3x + 4.5 = 3
do you understand this part?

[wraith hinge]

Ohhh

• and - make +

bruh

i mean

[brazen current]

xd

[wraith hinge]

Negative and negative make positive

[brazen current]

yes

[wraith hinge]

🤣

I get it nowww

And then it's +4,5 and then -4,5 makes 0

[brazen current]

I'm glad you understood it, have a nice day

[wraith hinge]

Alright all cleared up now, Tysm!!

[wraith hinge]

Thx you too :D

You've put a smile on my face

[brazen current]

You're welcome

If you have any other questions, ask 😄

[wraith hinge]

Will do! Byebye :D

.close

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[brazen current]

bye

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[empty tulip]

how do i know this has a oblique and horizontal asymptote

[empty tulip]

and ik the eqaution for the oblique asymptote by using polynominal long division but how do i find it for the horizontal asymptote

[kindred pier]

Are you allowed to plot the graph? What information are you able to gather?

[empty tulip]

im not allowed to plot a graph

[magic badger]

Well consider what happens as $x \to \pm\infty$. We see that $\sqrt{x^2 + 1} \to x$ so what does this tell you about $y$ as $x \to \infty$ and $x \to -\infty$?

[solid kiln]

Awesam

[empty tulip]

so as apporaches infinity we can look at the dominant term x^2

[magic badger]

yes

[empty tulip]

so could we replace that with infinity

and see what happens?

sqrt a very lardge number?

[magic badger]

we look at the behavior as x approaches infinity

what happens to y as x becomes very negative or very positive?

and this will tell you what the asymptotes are

[empty tulip]

so sqrt x becomes very large and positive

[magic badger]

well yes but specifically it becomes the function x

well, actually |x|

so if x is large and negative, we have y = x - x = 0 and as x is large and positive we have y = x + x = 2x

[empty tulip]

how do we know it becomes x

becuase that bit confuses me

we focus on the sqrtx^2+1

[magic badger]

correct. as x becomes very large, we focus on the dominant term $x^2$. so we have $\sqrt{x^2}$ which is just equal to $|x|$

[solid kiln]

Awesam

[empty tulip]

so we ignore the +1

and only focus on the dominant term

[magic badger]

correct

when numbers get really large we can just focus on the dominant term

[empty tulip]

also what does it mean by change in concavity

is this where the second derivative is 0 and the third is a different number?

[trim jolt]

@empty tulip Has your question been resolved?

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@empty tulip Has your question been resolved?

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[thorny tendon]

Prove if B is a subset of A intersection B, then B is a subset of A. Do I have the proof correct? I just don't know how else to word this otherwise. Thank you.

[quick tusk]

thats an immensely disgusting and hard to read proof but it looks fine

[thorny tendon]

Hhahahhahah. Understandable. 🤣 I really do not know how else to write it.

[quick tusk]

less words more symbols

[thorny tendon]

I tried copying the exists symbol in my program, it broke what it looked like.

I could open it in doc and copy it into there though, if that's the issue.

[quick tusk]

I don't think it's a big deal, it's just a bit wordy but the logic is sound

you basically start with an element of B, given that B is a subset of A cap B, x must be in A cap B, hence x must be in A

[thorny tendon]

Ok, that makes sense then. To be frank I've had trouble writing proofs a lot.

Thank you for checking over my work. Have a good day/night.

.close

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[wraith hinge]

Can someone help me with these?

[gray nebula]

draw on the diagram the vector vz knowing that vz = vw + xy

[wraith hinge]

?

[gray nebula]

its in french i translated it

[wraith hinge]

wdym

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[wraith hinge]

<@&286206848099549185>

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[flat spruce]

a pair (n,m) is shortened if

[flat spruce]

Can someone explain the "|" to me?

[digital bolt]

in this context it means 'divides'

k divides n iff n divides by k

so 2 | 6

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[flat spruce]

as in 2|6 and 2|8?

[digital bolt]

yes

[flat spruce]

so it's common divident?

[digital bolt]

think so

[flat spruce]

gotcha

.close

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[zinc timber]

Hey can someone tell me for 20 C how are C and D graphed?

[zinc timber]

Like I see how are A and B graphed

But not C and D

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[viscid flower]

have you tried other uhh

1s

so heres the one for A

ignore the extra bit, it's just numerical so its getting confused

and you may wanna try this site

https://homepages.bluffton.edu/~nesterd/apps/slopefields.html

saved my butt in diff eq

anyways

heres for the first one

which hopefully makes sense, your y is increasing up to a point

x is decreasing up to a point

then theyre both at the origin so no more changes

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[trim jolt]

@wraith hinge Has your question been resolved?

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@wraith hinge Has your question been resolved?

[wraith hinge]

<@&286206848099549185>

[wraith hinge]

<@&286206848099549185>

[wraith hinge]

I have an exam in exactly 23 Minutes , let's see if I get my answer by then :
<@&286206848099549185>

[wraith hinge]

?

[trim lichen]

.close

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[wraith hinge]

.reopen

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✅

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[void kindle]

Does anyone know how ud get rid of the 9 im blanking out 😵‍💫

[flint tinsel]

bring it to natural number form
u get something like
3^(x+5) + 81 = 3^(4x) (10)
since it is a multiple of 10 on the rhs
so 3^(x+5) should end with 9
so I checked for the nearest value so I got 1

@void kindle sorry for the ping got what I told ?

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@void kindle Has your question been resolved?

[void kindle]

Il check it out later

but it looks pretty straight forward thx!

[flint tinsel]

ok

[void kindle]

il let u know in ab it

[flint tinsel]

np
k sure

u can dm also

[void kindle]

Gotchu thanks! but hol uppp im really lost rip

from which point do u bring it to natural number form??

[flint tinsel]

no u've 1/9 right take lcm and bring that 9 to the other side

[void kindle]

oooof i dont get it

which 9 are we taking where lol

and how do u use lcm

[flint tinsel]

not 9
1/9

[void kindle]

so u take the 1/9

and bring it to the other side??

[flint tinsel]

ya 1+1/9 = 10/9

ya and bring 9 to other side

got it ig

[void kindle]

so it would be 3^x * 27 = 9^2x * (1/9 + 1) - 9?

[flint tinsel]

ok wait let me write it

[void kindle]

tyty

[flint tinsel]

@void kindle

[void kindle]

AIGHT got it thanks! W8 but what do we do after this just to double check?? sry it took so long too i got stumped way too many times somehow lol

@flint tinsel

[flint tinsel]

this is how I did

[void kindle]

but wb da last line???

Would it be

3^(x+5) / 3^(4x) = -71??

[flint tinsel]

how ?
bcos if we take 3^4x won't it go below 81 also ?

[flint tinsel]

this is how I solved from here

[void kindle]

OH alr i think i got it

like i get how u got to where u got

but when it came to x u just checked for the neareast value right??

based off of the right side

like 3^4x and 3^x+5

YE tyty

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[void kindle]

unlessss

[flint tinsel]

np if u still didn't get it u can dm too

[void kindle]

alrighty thanks :)

it makes sense

its just the way u got about it

i have to learn more and more ways so i can be more versatile

and not rely one 1 strat

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[marsh basalt]

Suppose the lung cancer rate is 30 per 100,000 people. Among all people, 20% are smokers. Smokers are 10 times more likely to develop lung cancer than nonsmokers. What is the probability that a smoker develops lung cancer? Steps to doing this problem?

[austere cedar]

Almost always, the hard part of these problems is to determine what these numbers are, in terms of common probability notation

P(what) = 20%?

[marsh basalt]

Smoker

Do we use Bayes here ?

[austere cedar]

You know, I started saying that, but now I'm realizing you're not given a lot of numbers hehe

Let me reset here

[marsh basalt]

Thanks haha

Uh lemme find the thread

Where someone else tried to help

#help-9 message

[austere cedar]

The big deal here is this equation:
P(L|S) = 10P(L|~S)

"Smokers are 10 times more likely to develop lung cancer than nonsmokers"

And we also have
P(S) = 0.2
P(L) = 30/10000

[marsh basalt]

Yeah

[austere cedar]

Anyways, let's write that first equation using the conditional probability equation.
P(L ∩ S) / P(S) = 10P(L ∩ ~S) / P(~S)

[marsh basalt]

Wait why is that the way to write it

[austere cedar]

P(LS) / P(S) = 10[P(L) - P(LS)] / [1 - P(S)]

That's the definition of P(A|B)

[marsh basalt]

Wait it’s not P(B|A)P(A)/ P(B)

[austere cedar]

That's Bayes'

[marsh basalt]

Yeah

You don’t use Bayés here ?

[austere cedar]

I can't see a pretty way to apply it, no

Bayes' is great when the condition swaps, but it isn't really happening here

Unless I've misinterpreted the question?

Does this look right?
P(L|S) = 10P(L|~S)

And we want P(L|S)?

[marsh basalt]

I think so ?

Yeah

(0.0003 + 0.2) - (0.0003 * 0.2)

Oh wait

[austere cedar]

That leads to
P(LS) / P(S) = 10[P(L) - P(LS)] / [1 - P(S)]

With P(LS) being the only unknown, so we solve for it

And then we're handed P(L|S)

[marsh basalt]

Wait LS is (0.0003 * 0.2) ?

[austere cedar]

Nu. P(LS) (which is P(L and S)) is unknown

[marsh basalt]

Oh

I thought that was just multiplication oops

P(LS) / 0.2 = 10[0.0003 - P(LS)] / [1 - 0.2 ]

P(LS) / 0.2 = [0.03 - 10P(LS)] / 0.8

P(LS) / 0.2 = 0.0375 - 12.5P(LS)

P(LS) = 0.0075 - 2.5P(LS)

3.5P(LS) = 0.0075

P(LS) = 0.0021

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[marsh basalt]

Why Is P(LS) not just multiplication

[austere cedar]

P(AB) is usually not P(A)P(B)

If P(AB) = P(A)P(B)
Then we say that A and B are independent events

In a sense, one occurs without influencing the other

Clearly, S influences L, so they are not independent.

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[marsh basalt]

Can you do it like ```P(L) = (P(S) * P(L | S)) + (P(~S) * P(L | ~S))

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@marsh basalt Has your question been resolved?

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@marsh basalt Has your question been resolved?

[austere cedar]

You have the answer now, right?

P(L|S) = P(LS)/P(S)

Yeah, you should be able to do it that way too. Nice catch

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