#help-13

1 messages · Page 296 of 1

dreamy void
#

,w plot y = sqrt(sin(x)) between 0 and pi

dreamy void
#

ok mb

#

,,r^2(x) = \sin(x) \implies r(x) = \sqrt{\sin(x)}

wraith daggerBOT
#

𝔸dωn𝓲²s

dreamy void
#

but it would be again some kind of ball or "mountain"

#

some spherical object

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yea

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the rest should do able

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  1. notice y^4 = (y^2)^2
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and so on

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just draw the stuff

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if it's in terms of y draw a y to x coordinate system

pseudo trellis
#

this works as my answer?

dreamy void
#

else in terms of x

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as usual

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x to y coordinate

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system

pseudo trellis
#

my handwriting is incredible

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this is why i type everything

dreamy void
dreamy void
pseudo trellis
#

oop

dreamy void
#

what is it after rotation?

#

that's it

pseudo trellis
#

ah yeah

dreamy void
#

it's not half a footbal after a rotation

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or sphere

pseudo trellis
#

right yeah

#

okay so draw the next problem?

dreamy void
#

yea

#

they are easy

pseudo trellis
#

how would i draw such a thing?

dreamy void
#

you can refer to them as parabolas

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,w plot x = y^2 and x = y^100

dreamy void
#

the higher AND still even the exponent goes

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ther more it gets wider

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do you get the idea?

pseudo trellis
#

i think so

dreamy void
#

good

#

it doesnt need to be perfect

pseudo trellis
#

so we graph x=y^4?

dreamy void
#

y^4 is a little less wider than y^8 that's all

#

yea

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it's two radius

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so common region!

pseudo trellis
#

then do we do x=-y^8

dreamy void
#

no

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you fell into the trap

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(y²)²

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and

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(y^4)²

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remember the square!

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It's R²(y) - r²(y) always

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in the integrand

pseudo trellis
#

wot

dreamy void
#

😭

pseudo trellis
#

oh so we're graphing x=y^2

dreamy void
#

yes

pseudo trellis
#

and x=-y^4

wraith daggerBOT
#

𝔸dωn𝓲²s

dreamy void
#

keep this in mind!

#

so your functions are squared

dreamy void
pseudo trellis
#

ahhhh

#

like so?

dreamy void
#

Is the minus part?

pseudo trellis
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x=-y^4

dreamy void
pseudo trellis
#

i put it but icloud slow

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OH

#

wait

dreamy void
#

You are drawing

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R(x) and r(x)

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Not R(x)² and - r(x)²

pseudo trellis
#

i see

#

so y=x^4

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is what we're drawing

dreamy void
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Well other way

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But doesn matter technically

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Since it's in term of y

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Do it in terms of y

pseudo trellis
#

yeahyeah

dreamy void
#

y to x system

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Accept it

pseudo trellis
#

lol

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okay i got those drawn

dreamy void
#

It's not evil

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Show

pseudo trellis
#

i thonk

dreamy void
#

From 0 to 1

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Draw it

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Mark the region

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Between 0 and 1

pseudo trellis
#

on the x-axis?

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lmao i drew it the wrong way

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i guess not the "wrong" way, but i meant to draw it in terms of x

dreamy void
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No

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It's right

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Just this

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Now what is this solid looking like

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Around the y-axis

pseudo trellis
dreamy void
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😭

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why

pseudo trellis
#

lmao

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i see what it would look like if i rotate it around the y-axis

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it's like half a football 💀

dreamy void
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No

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It's like a funnel

pseudo trellis
#

yeah that's the right word

dreamy void
# pseudo trellis

This could be misleading thinking it's around x = 1 but it's about x = 0

dreamy void
#

It was not difficult

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I meant you to just add what I added

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Not draw it into a x to y system

pseudo trellis
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😭 my brain doesn't function when it's like that

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im bound to make mistakes when i draw it in terms of y

dreamy void
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I cant seem to find any

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You did it flawlessly

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STOP OVERTHIBKING

pseudo trellis
#

lmao

dreamy void
#

2 YEAR OLDS DONT OVERTHUNK

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😂

pseudo trellis
#

lmao okokokokokokok

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3 more problems

dreamy void
#

The rest is doable

pseudo trellis
#

that i don't think are terribly difficult maybe

#

yeah those are pretty easy

dreamy void
#

🥱

pseudo trellis
#

it's just doing the volume integral with variables, no?

dreamy void
#

Yes

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It's a straight line

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Around x = 0

pseudo trellis
#

:P

dreamy void
#

Betwern y = 0 and y = r

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In terms of y

pseudo trellis
#

oop

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yeah you're right

dreamy void
#

Since axis of rev is vertical

pseudo trellis
#

is that really the answer? 😂

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or do we have to expand it and stuff

dreamy void
#

r < h

pseudo trellis
#

yeah

dreamy void
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Wait

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The line goes through

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(R,0) and (r,h)

pseudo trellis
#

yeah

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wait so two integrals?

dreamy void
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So

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lol

pseudo trellis
#

my brain is not braining

dreamy void
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Ohhh right i am dumb

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y = mx + b

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m = y1 - y2 / x1 - x2

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m = h-0 / r-R = h/r-R

pseudo trellis
#

right

dreamy void
#

,,y = \frac{h}{r-R}x + b

wraith daggerBOT
#

𝔸dωn𝓲²s

dreamy void
#

Now we would plug in (R,0) since it's simpler

#

,,0 = \frac{h}{r-R}R + b \iff b = -\frac{h}{r-R}R

wraith daggerBOT
#

𝔸dωn𝓲²s

dreamy void
#

So

wraith daggerBOT
#

𝔸dωn𝓲²s

dreamy void
#

Ok good

pseudo trellis
#

sure lol

dreamy void
#

Now we would do this in terms of y

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You can do that

pseudo trellis
#

what do i do?

dreamy void
dreamy void
pseudo trellis
#

$x=\frac{y(r-R)}{h}+R$

wraith daggerBOT
#

Someone

pseudo trellis
#

is that what I needed to do?

dreamy void
#

I trust it's right

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Yea

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Then integration from 0 to h

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It's around y=0 so good

dreamy void
dreamy void
#

Makes sense?

pseudo trellis
#

yeah

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i think

dreamy void
pseudo trellis
#

so that is the answer?

dreamy void
#

Square it

pseudo trellis
#

ah yes

dreamy void
#

The whole

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,, V = \pi \int_0^h \left ( \frac{y(r-R)}{h}+R \right )^2 : \dd y

pseudo trellis
dreamy void
#

Wait

wraith daggerBOT
#

𝔸dωn𝓲²s

dreamy void
#

Yeah (it's 6 am)

pseudo trellis
#

okay okay okay

dreamy void
pseudo trellis
#

2 more "similar" problems 💀

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49 & 50

dreamy void
#

I trust me

pseudo trellis
dreamy void
#

NO

pseudo trellis
#

wot

dreamy void
#

I need to sleep

pseudo trellis
#

lmao

#

okokokok

dreamy void
#

It's 6 am almost

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I helped your at least 2 hours

pseudo trellis
#

yesyesyesyes all good

dreamy void
#

Do you want to take advantage of me

#

😭

pseudo trellis
#

thank you thank you thank you thank you thank you

dreamy void
#

You can add me, I like you

#

good night

pseudo trellis
#

good night!!! ❤️

#

.solved

cedar kilnBOT
#
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cedar kilnBOT
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umbral shell
#

.close

cedar kilnBOT
#
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trim sierra
#

how can i do this?

step by step

cedar kilnBOT
harsh flare
#

Can anyone solve this elaborately ? Step by step completely

trim sierra
#

.cdot

#

.close

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#
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harsh flare
dull oxide
cedar kilnBOT
# harsh flare <@&286206848099549185>

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

cedar kilnBOT
harsh flare
trim sierra
#

.close

cedar kilnBOT
#
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blissful flare
#

How do i find d^2 * z of function z=tg(2x^2 - y)

cedar kilnBOT
#

@blissful flare Has your question been resolved?

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cedar kilnBOT
#

@twilit crag Has your question been resolved?

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frozen pier
#

For #3 the answer is C and I was wondering why

earnest geyser
#

,rotate

wraith daggerBOT
cedar kilnBOT
#

@frozen pier Has your question been resolved?

frozen pier
#

<@&286206848099549185>

fast lotus
#

what are the 11in and 8.5in?

#

l and b of page?

frozen pier
#

im assuming yeah

fast lotus
#

ok so

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do u know tht moment of inertia is maximum along perpendicular to plane of sheet?

frozen pier
#

no i didnt really know that

fast lotus
#

ever heard of perpendicular axis theorem?

frozen pier
#

yeah we did that in this test

fast lotus
#

yea wht is tht?

frozen pier
#

actually i think it was parralell axis theorem

fast lotus
#

oh not tht

#

perpendicular axis theorem

frozen pier
#

id assume its just the parallel axis theorem but for the perpendicular axis

fast lotus
#

nop

frozen pier
#

oh okay

fast lotus
#

both are different

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ok lemme explain

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assume u have a page

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along xy plane

frozen pier
#

okay

fast lotus
#

ok so assume u r rotating it along z axis

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the paper's center is at origin

#

@frozen pier mhm?

frozen pier
#

oh yeah im following

fast lotus
#

okay

#

so the moment of inetia

#

along z axis is equal to moment of inertia along x and y axis combined

frozen pier
#

alright

#

.close

cedar kilnBOT
#
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cedar kilnBOT
#
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heavy crypt
#

Two teams A and B play games until one team has won 4 games. A tie does not exist. The probability of A winning is 0.7 if it plays on its own field and 0.3 if it plays on the opponent's field. The first two matches are played on B's field, the next three on A's field and the last two on B's field.
(a) What is the probability that A wins after 4 matches?
(b) What is the probability that A wins after 5 matches?

heavy crypt
#

,rotate

wraith daggerBOT
heavy crypt
#

so I choose one position out of the 2 where they lose on the opponents field and then if they would’ve lost on their own field

#

And I calculated it and got 0,18375 but answer says 0,17052

#

it’s for b

#

2*0.7*0.3*0.7^3 + 3*0.3*0.7^2*0.3^2

lilac rune
#

let me try

heavy crypt
#

and what did you do?

lilac rune
heavy crypt
#

what did u do?

lilac rune
#

wait a min

#

20.70.30.7^3 + 30.30.7^20.3^2

#

u did this right

#

uhh

#

did you exclude the case

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where the first 4 games are won by a

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and 5th is won by b

#

??

heavy crypt
#

ah

lilac rune
#

you shouldnt take this case

#

since the game would be stopped when a wins the first four games

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since it is given that a wins only after 5 games

heavy crypt
#

how did i take that tho if i say that out of the 3 competitions on the second field one of them is a loss?

lilac rune
#

i didnt understand you

#

the 3 competion cases are these
3rdgame 4thgame 5th game
A WON A LOST A WON
A LOST A WON A WON

heavy crypt
#

yeah but what about the first and second game because if you lose the first one and then win all the rest

#

then you won after five matches

#

same for the second game

lilac rune
#

YES

#

im saying first 2 cases of ur answer are right

#

the answer should be
2 * 0.7 * 0.3 * 0.7^3 + 2 * 0.3 * 0.7^2 * 0.3^2

heavy crypt
#

ok i get it

#

ty

lilac rune
#

ur welcome

heavy crypt
#

.close

cedar kilnBOT
#
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cedar kilnBOT
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civic whale
#

I know how to solve this equation, but, how would I come to the results of k = 5 and l = -4?

cedar kilnBOT
#

@civic whale Has your question been resolved?

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lilac flame
#

3x +(y^2)i = 1-2i^2

cedar kilnBOT
lilac flame
#

what is the value of x

#

is it 1?

modern sparrow
lilac flame
#

1-2i^2 becomes 3 right?

#

so 3 + 0i

#

and we can compare that way?

sand cradle
#

What are x, y?

#

Just real numbers?

lilac flame
#

y is complex i assume

modern sparrow
lilac flame
#

so am i right?

#

is it 1?

sand cradle
#

Why would it be?

#

Ah, you are comparing coefficients

lilac flame
#

well 3x +(y^2)i = 3 +0i

#

i had this question on the test today

sand cradle
modern sparrow
# lilac flame y is complex i assume

if y is real, then y^2 is real, so (y^2)*i is purely imaginary, and 3x is purely real, then what you've done is right. But if y is complex, then y^2 is complex (real and imaginary parts) so then no you're not

sand cradle
#

1 is correct, as you said

modern sparrow
#

write $y = a+bi$, then $y^2 = a^2 - b^2 +2abi$, so $iy^2 = -2ab + i(a^2-b^2)$

wraith daggerBOT
sand cradle
#

^ this is in case y is complex. Whether it is or not should be stated in the exercise

lilac flame
#

it wasnt

modern sparrow
lilac flame
#

i also said i assume lol

#

my mathematical knowledge is lacking

#

😭

sand cradle
modern sparrow
lilac flame
#

then y is 0 and x is 1

modern sparrow
#

yah

lilac flame
#

thank you

#

.close

cedar kilnBOT
#
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cedar kilnBOT
#
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hazy aspen
#

This question

cedar kilnBOT
hazy aspen
#

<@&286206848099549185>

lilac rune
hazy aspen
#

Yes

#

Had a milestone test today, got 228/300

hazy aspen
runic garnet
#

whatve u tried

hazy aspen
#

I have tried many things but they are not even close to reaching the solution

#

I tried taking constants out, taking uat+2 as x

#

Im not clear with u substitution

runic garnet
#

taking x = uat + 2 works

#

what will u do from there

hazy aspen
#

I have no idea

#

I watched Khan academy u substitution videos where they take certain things as x or u, but didn't really get the whole concept

runic garnet
#

wait whats the upper bound on the integral

wicked stag
#

Its option 4

hazy aspen
wicked stag
#

!nosols

cedar kilnBOT
#

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.

wicked stag
#

Consider uat + 2 = x

#

Or (ua)dt=dx

hazy aspen
hazy aspen
lilac rune
#

@hazy aspen sorry i havent been able to reply , internet issue

lilac rune
wicked stag
crimson sedge
hazy aspen
#

How do you know what we have to take as u or x

wicked stag
#

Its actually 1/a+x form

#

So its integration will be ln(a+x)

hazy aspen
#

Hold on

#

Let's start from the start

#

So we can take u out

crimson sedge
#

dm karu?

hazy aspen
wicked stag
#

@crimson sedge yeah bro can help better i think

broken pond
#

I WNT A HELP

wicked stag
#

@broken pond can i know what help you wnt

#

@broken pond bro gave this name after watching The Devil Consipiracy, im 101% sure

#

@lilac rune hi

broken pond
#

CAN ANYONE TELL THE PYTHAGOREAN TRIPLET WHOSE ONE NUMBER IS 12

wicked stag
#

Yeah

#

Its 5 ,12,13

median lantern
#

Oops sniped

broken pond
#

NO WRONG ANSWER

#

CAN YOU TELL YOUR ANSWER WITH WHOLE PROCEES

median lantern
#

Huh it's well known

lilac rune
#

12 35 37

broken pond
#

NO STILL WRONG

wicked stag
#

Yeah another one

#

You know one thing ?

lilac rune
#

12 16 20

wicked stag
#

When the majority says the wrong answer , it becomes the correct answer.

broken pond
#

NO

wicked stag
#

No === yes

lilac rune
broken pond
#

THE CORRECT ANSWER IS 9,12,15

median lantern
wicked stag
#

@broken pond i hate lucifer

cedar kilnBOT
#

@hazy aspen Has your question been resolved?

cedar kilnBOT
#

@hazy aspen Has your question been resolved?

cedar kilnBOT
#
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#
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deep coral
#

can anyone possibly help me with biology?? idk if thats the right serv for this but i need help with punnett squares

deep coral
mighty shuttle
#

is this a test?

deep coral
#

no its homework

mighty shuttle
#

ok

#

which square do you need help with

deep coral
#

well tbh i don’t get any of it

#

but the first ones

mighty shuttle
#

do you know what a punnet square is

#

what an allele is

deep coral
#

no-

fading pewter
#

damn we got biology in a math server before GTA 6

mighty shuttle
#

better learn that first then

mighty shuttle
#

it;s kind of logical

fading pewter
#

combinatorics

mighty shuttle
#

yeah

fading pewter
mighty shuttle
#

we don't give out answers on this server

deep coral
#

oh

mighty shuttle
#

we guide you to the answer

#

so you have to know what you're dealing with, so please learn what a punnet sqaure is first

deep coral
#

i see ty for tryna help tho

mighty shuttle
#

and alleles too

deep coral
#

.close

cedar kilnBOT
#
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cedar kilnBOT
#
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dreamy junco
#

Can someone explain to me how to do a double integral with a ring behind it over the surface area of a sphere?

cedar kilnBOT
#

@dreamy junco Has your question been resolved?

cedar kilnBOT
#

@dreamy junco Has your question been resolved?

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sand valve
#

Can i do it simplier then just .(x-1)(x+1)(x-2)?

solar vector
#

Like can you do it simpler than clearing out the fractions by multiplying by (x-1)(x+1)(x-2) on both sides?

solar vector
#

There might be shortcuts here and there but none come to mind to me off the top of my head.

#

Clearing out fractions is sort of the most common trick since it works in a large variety of situations.

sand valve
#

but in this example where there are more than one of those numbers, i can just multiply it with one of them?

#

for example there are 2 underlined red Xs, but i will just use one

serene umbra
#

The point of multiplying is to get the euqation in the form of a polynomial, which is easier to solve

#

The teacher who made the problem had an polynomial, done partial fractions, gave them to you

#

they want you to undo that

#

if you know what partial fractions are

serene umbra
#

but all you need to know is that there is no "tricks" other than multiplying to get rid of fractions

cedar kilnBOT
#

@sand valve Has your question been resolved?

cedar kilnBOT
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frank bronze
#

i dont understand

cedar kilnBOT
bright fiber
#

Well it wants you to say something about it's velocity

native heath
#

What is the velocity of a particle?

bright fiber
#

and how the velocity behaves

native heath
#

Given its position.

bright fiber
#

so how would you go about finding the velocity?

native heath
#

yeah maybe dont answer it straight up

serene umbra
#

alright

native heath
#

yes remove that

frank bronze
#

waht is going on

native heath
#

What is the velocity vector given a position vector

frank bronze
native heath
#

Oh you don't have vectors

#

Just ignore the word 'vector' there

frank bronze
#

velocity is undefined, position is t = 1

bright fiber
#

Do you know how to get velocity function from position function?

native heath
#

No it's not

frank bronze
#

yes

#

derive it

bright fiber
#

Good

#

then do so

frank bronze
#

why

native heath
#

...

bright fiber
#

Because you need to find out some information about the velocity

#

no?

native heath
#

You wanna find the velocity

#

that's why

frank bronze
#

hold on

#

basically

#

i need to plug in 1 into position, and plug in one into veolocty and then see if they match signs

#

yes ?

native heath
#

no.

#

You need to find the velocity function

#

then plug in 1

#

and see the sign

frank bronze
bright fiber
#

Don't plug in 1 into anything

#

until you derive

#

you'll also need acceleration

frank bronze
#

waht

#

cao

#

i quit

#

.close

cedar kilnBOT
#
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cedar kilnBOT
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vernal pebble
#

hey

cedar kilnBOT
vernal pebble
#

im confused for this question why they included the y axis of (4,2k) as it not needed

serene umbra
wraith daggerBOT
#

violet

serene umbra
#

in terms of k? (and x, of course)?

serene umbra
vernal pebble
#

but whats the use of 2k

#

theres no part b or anything

modern sparrow
serene umbra
#

so yea

#

"for completeness", i suppose

vernal pebble
#

okay thanks

#

.close

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crimson sedge
#

what is the relation between metric spaces, linear vector spaces, and normed vector spaces? are there theorems that connect them or similar versions of them in each of these spaces?

cedar kilnBOT
#

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brittle frigate
cedar kilnBOT
#

Please don't occupy multiple help channels.

subtle harbor
#

what software

brittle frigate
#

ti 84 calc

#

stuff like this i think

subtle harbor
#

if you need help doing the commands and finding them

#

but sampling distribution has a known distribution given population stdev

brittle frigate
#

so it would be 18/sqrt of 61?

brittle frigate
subtle harbor
brittle frigate
#

so what do i do for b

#

this is what i did for C

cedar kilnBOT
#

@brittle frigate Has your question been resolved?

cedar kilnBOT
#

@brittle frigate Has your question been resolved?

brittle frigate
#

<@&286206848099549185>

cedar kilnBOT
#

@brittle frigate Has your question been resolved?

hazy aspen
# deep coral

Remember doing that in my 10th grade it's pretty easy

#

The dominant trait takes over recessive trait

brittle frigate
#

.close

cedar kilnBOT
#
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cedar kilnBOT
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pseudo merlin
#

How do i draw this diagram

cedar kilnBOT
upbeat dune
#

If you take the base to be 34
What will the height be ?

pseudo merlin
#

im start the drawing like this

#

but idk which side to put the mumbers on

upbeat dune
#

Draw one of the sides flat with the ground

pseudo merlin
#

wait why

#

im just use formula 1/2ansinc

#

1/2absinC

pseudo merlin
upbeat dune
pseudo merlin
#

But the angle can also be 180-sinC

#

And that applies to all of them doesnt it

pseudo merlin
#

Wait but since that since is the longest side

#

Then the angle opposite that side

#

Is obtuse

#

Oh!!!!

#

.close

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slate garden
#

How do i do part 2

cedar kilnBOT
slate garden
#

How do i know k cuts at 0

cedar kilnBOT
#

@slate garden Has your question been resolved?

sudden anchor
#

tell ur complete idea

slate garden
#

Use the discriminate

#

But the answer says

#

K=0 is also a solution

sudden anchor
#

yup

#

when u apply the condition on discriminant

#

you will get D >= 0

#

so k = 0 will satisfy as inequality will be satisfied

slate garden
#

What’s D?

#

I thought that means it has one root

#

As well

#

If it equals o

cedar kilnBOT
#

@slate garden Has your question been resolved?

#
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near acorn
#

in integrals with the partial fractions descompositions
is the same to say

$\frac{A}{(something)} + \frac{Bx + C}{(something}$
and \newline
$\frac{Ax+b}{(something)} + \frac{C}{(something)}$

wraith daggerBOT
near acorn
#

thtats the same thing?

cedar kilnBOT
#

@near acorn Has your question been resolved?

near acorn
#

.close

cedar kilnBOT
#
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cedar kilnBOT
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golden thicket
#

reduce fraction

cedar kilnBOT
golden thicket
#

I have no idea how to shorten this

modern sparrow
#

notice that $a = (a^{\frac{1}{2}})^2$ and similarly for $b$

wraith daggerBOT
modern sparrow
#

so a and b should be viewed as smth squared

golden thicket
#

but in the end the answer will be sqrt a + sqrt b

modern sparrow
#

yeah that's right

golden thicket
#

i have only this

#

answers

modern sparrow
modern sparrow
#

ok, so since the question has a^(1/2) and b^(1/2)

#

the best thing to do is to re-write a as (a^(1/2) )^2

#

so that we have
$\frac{(a^{\frac{1}{2}})^2 - (b^{\frac{1}{2}})^2}{a^{\frac{1}{2}} - b^{\frac{1}{2}}}$

wraith daggerBOT
golden thicket
#

but I don’t quite understand how this helps

modern sparrow
#

now to make a substitution, say x = a^(1/2) and y = b^(1/2), and see if you spot anything

golden thicket
#

x^2-y^2 / x-y = x+y

modern sparrow
#

yup

#

now substitute back x and y

golden thicket
#

a^1/2 + b^1/2 ?

modern sparrow
#

yup

#

do you know what $a^{\frac{1}{2}}$ is?

wraith daggerBOT
golden thicket
#

sqrt a?

modern sparrow
#

yeah

golden thicket
#

oh I understood everything, thanks for helping, I didn’t see it until the end

modern sparrow
#

np

golden thicket
#

.close

cedar kilnBOT
#
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cedar kilnBOT
#
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hoary parrot
#

Is this possible to factor without a calculator? I'm not concerned about the inequality rn, just want to factor that quartic

fallen moat
#

you can first use factor theorem to check for zeros of the polynomial, and then use long division to factorize it

hoary parrot
#

I've tried that

#

but no values I put in f(x) would give remainder 0

fallen moat
#

interesting, lemme try

hoary parrot
#

Is there any other way?

#

I'm trying comparing coefficients, with multiplying 2 quadratics with unknown variables, but that seems ways too lengthy

fallen moat
#

i tried x=-1

hoary parrot
#

did you get 2 as a remainder?

fallen moat
#

4(-1)⁴+4(-1)³-3(-1)²-4(-1)+1
=4-4-3+4+1
=2

hoary parrot
#

its -3

fallen moat
#

nope

hoary parrot
#

not +3

fallen moat
#

oh

hoary parrot
#

-3(-1)² = -3

fallen moat
#

mybad

hoary parrot
#

yeah np

fallen moat
#

haha

#

yea, it's 2

#

time to try some more interesting

#

4(1/2)⁴+4(1/2)³-3(1/2)²-4(1/2)+1
=1/4+1/2-3/4-1/2+1
=1/2

#

hmmm

hoary parrot
#

for 1/2 I got -1

fallen moat
#

ohhh

hoary parrot
#

4/8 is 1/2

#

for the x^3

fallen moat
#

my bad

hoary parrot
#

np np

#

happens to the best of us 😂

fallen moat
#

rip

#

i have one more method

#

i usually do this when i cant factor

hoary parrot
#

what's the method,

fallen moat
#

i will look for similarities for the ⁴,³,² terms and ²,¹,⁰ terms

#

4x⁴+4x³ and -3x²-4x are a little bit similar, so I'll try to construct 2 terms and try to make them similae

#

but it doesn't seem to work...

hoary parrot
#

This is kind of annoying me, let me put it into desmos and see the x-intercepts

fallen moat
#

sure

hoary parrot
#

oh yeah

#

ok

#

there's 2 real roots

#

and they are decimals

fallen moat
#

interesting

hoary parrot
#

but like, not like 1/2, 1/3 or 1/4

opaque root
#

Are you trying to factor over what

hoary parrot
#

don't think they can be represented as fractions

fallen moat
#

time to do the xy

hoary parrot
fallen moat
#

!xy

cedar kilnBOT
#

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

hoary parrot
#

this is the question

fallen moat
#

interesting

hoary parrot
#

doesn't really give much more information

opaque root
#

You do not factor the second one

hoary parrot
#

Then how do you solve it?

#

do you need a calculator?

opaque root
#

Doesn’t look like you can do manually, unless i am missing something, let me check the solutions quickly

#

Doesn’t look like

#

Give me more time

dusk finch
#

it seems like applied quartic formula

opaque root
#

It is the solution

#

I was thinking about trig sub but i cant find which one

#

Or maybe a subtitution that eliminates the cubic term

dusk finch
#

trig sub?

#

hm?

#

this feels like it doesnt have nice solution

opaque root
dusk finch
#

approximate solution is x in (-inf, 0.226) union (0.852, inf)

#

@hoary parrot this doesnt have a nice factorization unfortunately

opaque root
raven shard
dusk finch
#

hmm i havent seen trig subs in polynomial inequalities yet

opaque root
#

Maybe separating x^3 +3x^3 and -x -3x

raven shard
#

it makes no sense for trig sub to be the intended approach here when the previous sub-problem is directly factorable

#

(and judging by the answer wolfram gave it also most certainly doesn't work)

opaque root
#

Yes i assumed it was probably a typo before but i am now in mode einstein lol

cedar kilnBOT
#

@hoary parrot Has your question been resolved?

cedar kilnBOT
#
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coral jewel
#

Let there be 2 positive real numbers $x, y$ such that [
2(x^2+y^2+4)+\log_{2022}\left(\frac2x+\frac2y\right)=\frac12(xy-4)^2
]
Calculate $\frac{y}x$ as $x+4y$ reaches its minimum

wraith daggerBOT
coral jewel
#

not sure what to do tbh

cedar kilnBOT
#

@coral jewel Has your question been resolved?

vagrant elbow
#

since you can AMGM between those

#

and get a relation for x + 4y

coral jewel
vagrant elbow
#

[ \f{a + b}{2} \geq \s{ab} ]

wraith daggerBOT
#

Sadie Carnot (η > 1)

coral jewel
#

oh cauchy inequality

#

seems good, ill try that out

vagrant elbow
#

arithmetic on the left

#

geometric mean on the right

#

AMGM

sacred grail
#

,w expand 2(x^2 + y^2 + 4) - 1/2(xy - 4)^2

sacred grail
#

this is straight up just 2(x + y)^2 - 1/2 (xy)^2

#

naively if you just want to satisfy the condition
[ 4(x + y)^2 = x^2 y^2 ]
and minimise $x + 4y$, you're just looking for
[ 6(x + y) = 2xy^2 - \f12 x^2 y ]

wraith daggerBOT
sacred grail
#

completely ignoring the log term

#

rearranging gives something like
[ 12(x + y) = xy(4y - x), \quad 2(x + y) = xy \Implies 6 = 4y - x ]

wraith daggerBOT
sacred grail
#

,w 2(x + y) = xy, 6 = 4y - x

sacred grail
#

,w 2(x^2 + y^2 + 4) + log_2022(2/x + 2/y) - 1/2(xy - 4)^2 where x = 6, y = 3

sacred grail
#

its actually on the curve

cedar kilnBOT
#

@coral jewel Has your question been resolved?

cedar kilnBOT
#
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pseudo merlin
cedar kilnBOT
pseudo merlin
#

for the last question how come its 1-300/630

fathom night
#

$P(X \ge 1) = 1 - P(X=0)$

wraith daggerBOT
nimble veldt
#

630 is explained in (I), 300 is explained in the last question.

pseudo merlin
nimble veldt
pseudo merlin
#

why do we do 1 - subtract dat

nimble veldt
#

the probabiltiy having at least one anniversary card = 1 - probability having no anniversary card.

pseudo merlin
#

ya

#

i got dat but

pseudo merlin
#

ohhh

#

u are right!!

#

thank u

#

.close

cedar kilnBOT
#
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craggy stratus
#

Hi everyone

cedar kilnBOT
craggy stratus
#

Currently reading about matrixes and well, I am struggling a bit about when they're not quadratic and what their properties become then

#

The questions we get is in the form of if you have a matrix A where m < n, which of the following statements are guaranteed to be true

#

and then for example the rows in A are linearly independent so that the equation Ax = y for each y that is a real number there's always at least one solution

#

Are there any good resources online to get familiar with this? I feel like our textbook just isn't.. comprehensible enough

#

If it's about quadratic matrixes then I feel a lot more comfortable, but I think I struggle with knowing what it means to have for example 3 rows and 2 columns

#

is it that you have 2 vectors in R^3? In which case they can never be a base, so then you wouldn't be able to get all y in R^3

#

and then in this case, if it's that m < n, that means we have 2 rows and 3 columns, in which case we'd have a linearly dependent vector in r^2 from the columns

#

would just like to ask for some guidance on where to find resources that explains (preferably visually) in great detail how to treat such a matrix xd

#

i think what makes me confused is that im not sure if I can treat the rows AND columns as vectors / planes or what is going on :/

craggy stratus
#

thank you a ton

#

you're an angel

#

wish you an amazing week <33

#

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#
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stuck solstice
#

Is this correct?

cedar kilnBOT
#

@stuck solstice Has your question been resolved?

cedar kilnBOT
#

@stuck solstice Has your question been resolved?

cedar kilnBOT
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@stuck solstice Has your question been resolved?

cedar kilnBOT
#

@stuck solstice Has your question been resolved?

gritty viper
cedar kilnBOT
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autumn nebula
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hola

cedar kilnBOT
autumn nebula
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i’m not quite sure how we could sketch the points MN and NX seen in question 20. could someone please help with this?

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<@&286206848099549185>

cedar kilnBOT
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@autumn nebula Has your question been resolved?

autumn nebula
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<@&286206848099549185>

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pls ong

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ong

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omg

crimson sedge
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hey

autumn nebula
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yo

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Yo

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YO

crimson sedge
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wyd

autumn nebula
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WHATS GOOD

crimson sedge
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nun

crimson sedge
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let me check

autumn nebula
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aight bet

crimson sedge
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how u do 19

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is 20 both rays

autumn nebula
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what

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idk we just have to do 20

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i’m not even sure

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what to do

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idk how to really sketch points

cedar kilnBOT
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Channel closed

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Use .reopen if this was a mistake.

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

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

autumn nebula
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idiot

cedar kilnBOT
autumn nebula
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.reopen

cerulean sail
autumn nebula
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HELO ME

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HELP ME

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ILL DO ANYTHING

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I Locs you

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CHARTBIT PLS HELP

cerulean sail
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Honestly I don't know sadcat

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Do you have any more context to that question at all?

autumn nebula
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sketch the figure

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described

cerulean sail
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What's the examples 3 and 4?

autumn nebula
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it’s not related to it

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like at all

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how do we usually

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sketch these type of ooints

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@cerulean sail

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sorry for the ping

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u said to ping tho in ur bio

cerulean sail
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I did catThumbsUp

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And I really don't know what they're looking for tbh - that said, why to they say you should see those examples if it isn't related(?)

autumn nebula
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Idk

autumn nebula
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please…

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i can’t

gleaming imp
autumn nebula
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I OVENYOY

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I LOVE YOU

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YES SIR

gleaming imp
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Alright lol

autumn nebula
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i’m so grateful

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i’ve been waiting

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for 3 hours

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for a helper

eager wraith
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@gleaming imp have you seen the examples

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?

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this is my other acc btw

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honestly i think im just gonna quit

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i cant keep waiting

gleaming imp
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Ok so

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for exercise 17, you can simply draw a plane (denoted as P) and a line (denoted as l) intersecting at any point on the line.

eager wraith
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I just need it for

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20

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and 22

gleaming imp
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Bruv

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hold on

eager wraith
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sorry i forgot to say that

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mb

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oh wait

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i did

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this was my attempt for 20

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idk if that’s right

gleaming imp
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nah i dont think so

eager wraith
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oh

gleaming imp
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I believe you have to draw two vectors, MN and NX

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with thir tails at the same initial point

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wwhich is M

eager wraith
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how do we do that

gleaming imp
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just draw one vector on top of other

eager wraith
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yeah uh

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whats a vector

gleaming imp
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:))

eager wraith
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i mean

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sorry

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i know what it is

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but like

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how to draw it

gleaming imp
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---------->

eager wraith
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wait

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oh

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so two lines on top of each other

gleaming imp
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Exactly

eager wraith
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like this

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like this

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u may need to flip

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it

gleaming imp
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no...

eager wraith
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so wait

gleaming imp
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MN> and NX>

eager wraith
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u want me to just draw

gleaming imp
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right?

eager wraith
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a parallel line

eager wraith
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yes

gleaming imp
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wat

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Okay

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so whats in commin in that 2 vectors?

eager wraith
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they share

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N

gleaming imp
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"n"

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Exactly

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so Starting from N point

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draw 2 lines

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and yk what to label them

eager wraith
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omg my storageh

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ok

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lemme send

gleaming imp
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Okay

eager wraith
gleaming imp
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vectors

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what indicates a vector that it's a vector?

eager wraith
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a point

gleaming imp
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DIRECTION

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so u need arrow head

eager wraith
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ok

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Wdym

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arrow hwad

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head

gleaming imp
eager wraith
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oh

gleaming imp
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Yeah

eager wraith
gleaming imp
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And u don't plot the point labels on the line btw, On either the arrow or starting point

gleaming imp
eager wraith
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ok wait

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could u sketch it and show me