help-4

[tidal swift]

and we know the heights of the chord related to the radius

our goal now is to find the length of the chord made by the bottom of the boat

[stuck night]

and how do we do that ;-;

[tidal swift]

let's take this step by step

[stuck night]

okay

[tidal swift]

first, what's the radius of the waterway?

[stuck night]

5.5ft?

[tidal swift]

good

we know that the surface of the water is 4.5ft from the very bottom of the semicircle.
do we know how far from the center of the circle it is?

if unclear, we are finding this length marked by the double arrows

O is the center

[stuck night]

we can subract the radius to y axis?

[tidal swift]

mhm. what do you get?

[stuck night]

(0,-4.5)

i think

[tidal swift]

nah, just quote it in feet

and it's not 4.5

4.5ft is the distance from the bottom to the water surface

you're finding the distance in red (which is given and doesn't need to be found)
what's the distance in blue?

the answer is a very small number

ok maybe not super small but yeah

[stuck night]

1?

[tidal swift]

correct!

[stuck night]

ah! :0

[tidal swift]

so we know the water surface is 1ft under the center of the waterway

now, we are told that the boat submerges another 1ft down

so the bottom of the boat is ___ ft under the center of the circle

[stuck night]

so 3.5

ft

[tidal swift]

no, that would be from the bottom

sorry, i meant from the center

[stuck night]

does it 2.5?

[tidal swift]

why 2.5?

it's not, btw

but i want to hear why

we're finding the length in blue again btw

[stuck night]

cus as u said the water is 1 below the center and the boat is submerge 1 more

[tidal swift]

mhm

[stuck night]

or im jsut wrong]

[tidal swift]

1+1 is?

[stuck night]

btw why 4.5? the radius is 5.5

[stuck night]

2

[tidal swift]

excellent

[stuck night]

uhm ;-;

[tidal swift]

the water surface is 4.5ft from the bottom. but we know the radius of the waterway is 5.5ft. so we want to know the distance between the center of the circle and the water surface

now, the distance between the center of the circle and the bottom of the waterway is a radius, since it's a straight line from the center to the circumference

so to find the missing length we just do some good old subtraction

ok now we know that the bottom of the boat is 2ft away from the center of the circle

[stuck night]

ohh i understand the question now

yes its 2 ft

[tidal swift]

mhm

can you take it from here?

if not, i'll give you a hint: you need trigonometry

[stuck night]

ill try

[tidal swift]

also another hint - find a right angle somewhere

the initial length you get will most likely be half of what you need

i'll be here for another 10 minutes or so. you have my permission to @ me directly if you're stuck

[stuck night]

okayy tahnkss

[modest ginkgo]

u can also @ me

[stuck night]

is it like this or im completely on the wrong path ;;

[tidal swift]

wrong path

[stuck night]

hehe

[tidal swift]

if you do this you have two unknown sides

your line of thinking is right. you have to form a right triangle

but that's not the side you form it on

hint: you know one of the points must be on the circumference. you know one side must be the 2ft you found earlier
what other known length do you have that connects to a point on the circumference?

got it?

[stuck night]

no yet T^T

[tidal swift]

oh sorry to disturb then

[stuck night]

noooo its fine

[tidal swift]

i'm still here if you're stuck

[stuck night]

im kinda stuck but still thinking

[midnight pier]

Wow so much math going on here

[stuck night]

do i form the triangle from teh center?(checking if im still okay;-)

[tidal swift]

yup!

[stuck night]

OH

WAIT

[tidal swift]

let's go?

[midnight pier]

Good luck guys and girls

[stuck night]

welp i have the idea but idk where to go next ;-;

[tidal swift]

show your sketch

just to make sure you are on the right track

[tidal swift]

you identified the horizontal line as the 5.5ft radius

but what about that diagonal line?

it goes from the center to the circumference

what is it called?

[stuck night]

hypotenuse

but

[tidal swift]

in the context of the circle?

[stuck night]

uhhhhh

[tidal swift]

i've given you the biggest bombshell i could

[stuck night]

radius?

[tidal swift]

correct!

the diagonal line is another radius

and its length is?

[stuck night]

still 5.5? because the radius came from above the water

[tidal swift]

correct

now you have two sides of the triangle

i wonder what famous theorem you can use here

[stuck night]

AH

PYTHAGOREAN

[tidal swift]

something something squared = another thing squared

there we go!

[stuck night]

hehe wait

aahhh i didnt bring my sci cal with me but its root of 21

[midnight pier]

Wow u guys are deep into maths

[tidal swift]

i'll give you the answer for this then

[stuck night]

but were find the whole lenth so root of 21 times 2

[tidal swift]

it's 5.85ft (3sd)

but is this the final answer?

wait i may have mistyped

hang on

[stuck night]

🥹

9.165ft

[tidal swift]

5.12ft*

[stuck night]

ah

[tidal swift]

that's the length of the other side

but is this the final answer?

[midnight pier]

I wanna butt in but it's so long that I can't read it all😭😭

[stuck night]

wait why 5.12?

[tidal swift]

what's pythagoras' theorem?

a^2 + b^2 = c^2, right?

[stuck night]

yes

[tidal swift]

but we have a and c

so we wanna find b

so what do we do

[stuck night]

i got b^2= 25-4

[tidal swift]

and the square root?

eh hang on

[stuck night]

its 4.582

[tidal swift]

5.5^2 is 25?

the radius is 5.5ft, not 5ft

[stuck night]

ay

ah

xDD

[tidal swift]

oopsie

[stuck night]

my bad

[tidal swift]

anyway so we agree on 5.12ft?

[stuck night]

yess

[tidal swift]

good

but is this final?

[stuck night]

i think no

[tidal swift]

look at your diagram again

mhm

what do we need to do now

[stuck night]

multiply by 2

[tidal swift]

you have the length of part of the chord

correct!

you're essentially done

[stuck night]

10.24

ft

:0

[tidal swift]

wait

is this physics?

[stuck night]

uhm

pre calculus:>

[tidal swift]

if it's not, you can get away with putting the answer as 10.24

ok then yeah go ahead with 10.24ft

if it was physics, i'd recommend you round to 3sd
but well done!

[stuck night]

okeee thnkks

[tidal swift]

remember to .close when done so others may use the channel!

good luck with the rest of your homework!

[stuck night]

thank you🥹

.close

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[glass kelp]

let ${\sqrt{2} + 1 =a}$

[rocky lotus]

k

[glass kelp]

notice

[ (\sqrt{2} + 1)(\sqrt{2} - 1) = 1 \implies (\sqrt{2} - 1)a = 1]

[rocky lotus]

k

[glass kelp]

this thing reduces into a quadratic

[still egret]

what about the power

[glass kelp]

just let a^x = u

or some variable

[still egret]

(a)^x - (a-2)^x ?

[glass kelp]

huh

the equation becomes
[ a^x - \frac{1}{a^x} = \frac{3}{2}]

[rocky lotus]

k

[glass kelp]

let ${a^x = u}$
[ u^2 - 1 = \frac{3}{2}u]

[rocky lotus]

k

[still egret]

Ok thnaks

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[still egret]

Find natural number xy such that xy^2 + x divides x^2y+y

[stark wedge]

did you mean you want to find x and y individually or that you want to find all values of the product x*y

[still egret]

x,y

[safe tundra]

I have some questions about graphs. Is the formula y=mx+c because of change in x and change in y

[stark wedge]

!occupied

[vale dock]

Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).

[safe tundra]

I keep getting it wrong

[stark wedge]

this channel is currently taken by someone else, please move to a free one!

[safe tundra]

Y

[stark wedge]

do you have any progress on this

[safe tundra]

Yes

[normal hollow]

#❓how-to-get-help

[stark wedge]

this channel has somebody else's name on it, you have to move and claim your own

[vale dock]

@still egret Has your question been resolved?

[still egret]

x(y^2+1)|y(x^2+1)

then x|y because gcd x2+1,x=1

bounding on first step dont work

and y^2+1|x^2+1

[stark wedge]

you really shouldn't be dropping brackets like this

ok actually here is a thought

clearly any pair of the form (x, x) will work

[still egret]

Hm ok

But how to prove that

Eh wait

Nvm

x<=y implies x^2 + 1 <= y^2+1
But y^2+1 <= x^2 + 1

Therefore y^2+1 = x^2+1

y=x

So any pair of (x,x) will work

[cloud coral]

Assuming 0 is not counted as a natural number (which may depend on which teacher you are under)

[still egret]

0,0 is undefined

So clearly not

0/0 i mean

(x,x) where x in Z>0

[vale dock]

@still egret Has your question been resolved?

[vale dock]

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[mild python]

Hey

[mild python]

So I'm kind of having a problem right now solving this quadratic formula

[stark wedge]

in the future you should just send your question(s) here without a preface

[mild python]

Is it 25+24 or 24-25

[stark wedge]

neither, it's 25 - 24.

[mild python]

Oh alright, I'll keep that in mind

[stark wedge]

(-5)^2 - 4 * 2 * 3

the (-5)^2 simplifies to +25
the 4 * 2 * 3 simplifies to 24
giving

25 - 24

[mild python]

Which means the answer is going to be 5+1 / 4

Right?

I just want to make sure

[mild python]

And 5-1 /4

[stark wedge]

(5 ± 1)/4

you have to put brackets when writing fractions in plain text like this

but yes the answer will be (5 ± 1)/4

[mild python]

Oh alright thank you for your help

[mild python]

I'll take note of that

.close

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Remember:
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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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[mild python]

Can anyone check on my answers and see if its right

[mild python]

I legit don't know where I got the (5) from

[timber swan]

Its wrong

[glass kelp]

12^2 = 24 💔

[slate folio]

? Why is 5 in the square root???

[severe ledge]

wrong

[timber swan]

😔

[glass kelp]

oh ye

[glass kelp]

wtf

[mild python]

I am now just realizing all the mistakes I did

[severe ledge]

do you have to use quadratic formula or can you use factorising??

[mild python]

Quadratic formula

[timber swan]

Do u not think while writing 💔

[mild python]

Idk what I was on when i was solving this🥀

[severe ledge]

factorising it would be much easier. just sub in the a,b,c points into formula and let algebra do its job 🙂

[mild python]

I would do that but

My teacher strictly said to use the quadratic formula

[severe ledge]

always double check your answers by factorising then 🙂

[timber swan]

💔

[severe ledge]

try now

[timber swan]

Bro what

[mild python]

Thanks for your help everyone 💔

[severe ledge]

???

[timber swan]

Just check by PUTTING THE VALUES

😭😭

[severe ledge]

?????

that’s not what I said

[timber swan]

No im telling that

[severe ledge]

can you use your eyes?

[severe ledge]

no worries, if you need more help let me know

[mild python]

Yeah

.close

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Channel closed

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[unique smelt]

Guys I am searching for someone to do group study on regular bases.
Topic - Differentiation.
Anyone down?

[unreal warren]

hm

[unreal warren]

id say go in different channel but im down to learn more info

[unique smelt]

Ok

[unreal warren]

DM me

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[mild python]

Can anyone check if my answer is right again

[mild python]

I feel like there's more to it than that

[heavy pecan]

bro

ur supposed to solvenit further

[stark wedge]

(-7)^2 = 49 not -49. you messed up under the root again

negative times negative gives positive, yeah?

[mild python]

Wait so -7² will always equal a positive number?

[stark wedge]

(-7)^2

[mild python]

Oh

That's what Google’s calculator said

[stark wedge]

there's a difference between (-7)^2 and -7^2

[mild python]

Oh

OH

That's why I always keep getting it wrong

[stark wedge]

also with all due respect you should not be relying on Google calculator for single digit multiplication imo

[mild python]

Eh fair

I know that 7×7 is 49

I just wanted to make sure

Whether it was positive or not

.close

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[mild python]

This is what I searched

Which I know is completely different

[north olive]

-(7^2)= -1×(7^2)≠(-7)^2

[mild python]

Well I got x = (7 ± √ 37) /6

37 isn't a perfect square

[mild python]

So is this the final answer?

[north olive]

,w solve 3x²-7x+1=0

[rocky lotus]

Results provided by WolframAlpha

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

Requested by ishigamisenku_

[mild python]

where did the 1/6 came from

[north olive]

It's the same as all divided by 6

[mild python]

Oh okay

Thank you

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[north scarab]

Isn’t this wrong

I was watching a video and the denominator caught my eye

[slate folio]

show the whole thing

[north scarab]

It should have been 16x^4

[noble anvil]

Bro

The whole thing

[north scarab]

why the whole thing I’m only confused with this part

[noble anvil]

:/

[wet night]

yes it should be

[north scarab]

yea

[noble anvil]

We cant say if they cut something or not without looking at the numerator

[north scarab]

ok one sec

[wet night]

yh the denominator should be 16x^4

[red tulip]

you need to square the 4 as well

[north scarab]

Not mine, I was watching a video and I was also confused why they did that

But thanks guys

.close

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[latent breach]

woudl anyone be able to explain why the lorry slows down after car is added

[latent breach]

even though it mentions nothing ab out friction and that is onyl way to interact

[brittle epoch]

does it slow down?

[latent breach]

It might actualyl speed up but why

[brittle epoch]

conservation of momentum i think

add the momentum of the car and the lorry and then divide it by the total mass

and see if the lorry would speed up

[turbid valve]

Momentum must be conserved - so if the lorry's effective mass is increased (because oh idk it's got an extra car on top of it some-the-heck-how mad props to whoever the film students are lol) then the lorry's velocity has to decrease to compensate

[brittle epoch]

would the velocity decrease?

[turbid valve]

The lorry's? Most likely

[brittle epoch]

the car is moving faster than the lorry

[turbid valve]

Oh right, if you were to also consider the car's momentum

[wise imp]

hey guys, im the friend of @latent breach

[turbid valve]

You'll have to figure out the total momentum of the system

[wise imp]

i am doing the question right now, and i have some questions about assumptions made in this case

[brittle epoch]

$\frac{momentum_{car}+momentum_{lorry}}{mass_{car}+mass_{lorry}} > 25.5 m s^{-1}$

[rocky lotus]

General_Jacob

[wise imp]

1. would it be valid to assume the lorry and the ground have no friction between them

[brittle epoch]

the friction doesnt matter

[wise imp]

2. if so, why would the car landing on the lorry accelerate the lorry?

[brittle epoch]

conservation of momentum

[wise imp]

do we assume there is friction between the car and lorry

[latent breach]

it doesn't matter it becomes one entity

[wise imp]

because if not then there is no horizontal force acting on the lorry therefore it will remain in constant motion

[latent breach]

and there has to be as it breaks

[wise imp]

they are moving at different speeds in relation to the ground therefore they cant be thought of as one body

[latent breach]

they are physically connected

[wise imp]

and if there IS friction between the car and lorry, will we not need to know the size of the car or the distance between its wheels because we cannot assume the car instantly lands on the lorry as one body

[wise imp]

bro, with what? magic?

[latent breach]

@brittle epoch @turbid valve can you help explain why he is wrong

[wise imp]

@brittle epoch please help asap

also why are you interrupting wacky

[wise imp]

or do we instead reduce the car only to its center of mass?

[turbid valve]

Wacky's the OP here

[brittle epoch]

who?

[latent breach]

both

[wise imp]

can you read my messages above please

[brittle epoch]

what is the breaking force of the car

[noble anvil]

...

[wise imp]

i think that is what we need to find out, the minimum breaking force so that the car stops motion completely

and prove it is 600N

[latent breach]

what does it have to do with anything

[wise imp]

nothing ☺️

just to brighten the mood

[brittle epoch]

you need to show that the stunt is possible

[wise imp]

with breaking force 600N yes

[brittle epoch]

where did you get this problem from?

[latent breach]

its an a level practice question

we are both 15 though so thats why he still doesn't know much

[wise imp]

disrespectful

[brittle epoch]

is it on the internet?

[latent breach]

i assume

[brittle epoch]

can you send me a link to it

[wise imp]

since he already forgot newtons first law and said that 2 bodies moving at different speeds can be classed as one body with one unchanging centre of mass

[latent breach]

IK just have the question

[wise imp]

if someone can read my messages before and disprove/clear up assumptions then that would be greatly appreciated

[brittle epoch]

do you know how to solve this?

[latent breach]

I think

I calcaulte thgge new momentum as it has to be conserved

I can calcualte the new speed of the lorry

then w = f x d

I know distancce

[brittle epoch]

and does the car have enough room to brake?

[latent breach]

it says it does we have to prove it

the entire arguemnt is weather the loprry changes speed

[brittle epoch]

it speeds up

[latent breach]

can u disprove my friend please

[cloud coral]

there must be otherwise the car cannot slow down

[wise imp]

if so do we assume the car is a point in its center of mass or a long body that gradually moves onto the lorry

like the question specifies

[cloud coral]

I think assume landing time << time spent slowing down on lorry

[wise imp]

so we reduce the car to its center of mass?

[vale dock]

@latent breach Has your question been resolved?

[wise imp]

i said dis

[latent breach]

how do I say question uayd been resolved

[spring jackal]

type .close

[latent breach]

.close

[vale dock]

Channel closed

Closed by @latent breach

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[vale dock]

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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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[vague monolith]

When i cancel out |x| will it become 1 or 2

[vague monolith]

Or i cant cancel it out

[glass kelp]

depending on ur x

wait

(2)

[vague monolith]

Oh alr

Its bc x^2 is always positive so when it is canceled by a positive value it needs to return a positive value too right?

[stiff lily]

x^2 = |x| |x|

[vague monolith]

Oh alr

Thx yall

.close

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[river shale]

Def 2 without 0

[vague monolith]

u mean when x isnt 0 right?

alr thx @glass kelp

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[fathom oasis]

clknrvejknevf

[west cloud]

Hey, do you have a question?

[fathom oasis]

@oak crane

[fathom oasis]

oh hey, i do actually

[west cloud]

!noping

[vale dock]

Please do not ping individual helpers unprompted.

[oak crane]

hai

[fathom oasis]

its this

my homework

[oak crane]

I told them

[west cloud]

ah, ic

[stiff lily]

did you find your notes / make an attempt

[fathom oasis]

i did

but i got stuck on 9/4

[oak crane]

you can show work

[fathom oasis]

i already crumpled the paper hold on let me rewrite 😭😭

here

dm my handwriting i always had bad handwriting lmao

i can send my notes if needed so u guys can explain to me it

[tidal terrace]

that's nice

[stiff lily]

are those -9 or do you write your 9s weird

[fathom oasis]

but after that i really just got lost

[fathom oasis]

yeah those are -9

[tidal terrace]

you know the square formula ?

[stiff lily]

you shouldn't be doing that then

- * - → +

[fathom oasis]

maybe ive seen it, can u type it out for me?

[tidal terrace]

$(a\pm b)^2=a^2 \pm 2ab + b^2$

[rocky lotus]

qimmah

[fathom oasis]

oh yeah

right right

[fathom oasis]

yeah i do

[tidal terrace]

then you could try and write the left side as some form similar to this\

[fathom oasis]

so x^2 - 3x + 9/4?

oh wait

i mean

[cloud epoch]

yes that's it

[fathom oasis]

x^2 - 2 * x * 3x + 7?

[tidal terrace]

this is already in the form I stated earlier

[tidal terrace]

you just need to turn it to the left side

[cloud epoch]

you have this form, so now what is a=? and b=?

then you can turn it into the left side

[oak crane]

,tex .cts

[rocky lotus]

アキラ (>⩊<)

[oak crane]

you can use this

and tell us what you have for left side

[fathom oasis]

im a bit confused

[fathom oasis]

Isnt it already on the left side?

[cloud epoch]

this left side i mean

[stiff lily]

you've completed the square
the next step is to explicitly express it as such

x^2 - 3x + 9/4 = what^2

[cloud epoch]

You have x^2 -3x + 9/4 now
You know that a^2 + 2ab + b^2 = (a+b)^2
So what must a=? and b=? such that:
a^2 + 2ab + b^2 = x^2 -3x + 9/4?

[tidal terrace]

lemme do something rq

$x^2 -2(x)(\frac{3}{2}) + (\frac{3}{2})^2$

[fathom oasis]

ohh i didnt notice the left side, i thought the left side was just an indicator or label or smth

[tidal terrace]

$(a\pm b)^2=a^2 \pm 2ab + b^2$

[rocky lotus]

qimmah

[tidal terrace]

looks similar doesn't it

[rocky lotus]

qimmah

[cloud epoch]

So now you need to find a and b, then you can write it as (a+b)^2 with the a and b you found

[fathom oasis]

a is x^2 and b is -3x

[cloud epoch]

not quite

[tidal terrace]

check your b again

[cloud epoch]

and a

both are wrong

[fathom oasis]

What

[tidal terrace]

compare the forms .

[tidal terrace]

.

[fathom oasis]

oh i need to find mb i didnt see that

gimme a sec

[cloud epoch]

You can write them like that one under the other, then you can easily see what a and b are

[fathom oasis]

i dont get this, are the 3/2 the simplified of 9/4?

[tidal terrace]

ok the brackets would really show the help

[tidal terrace]

(3/2)^2=9/4

[cloud epoch]

(3/2)^2 = 9/4

ye

[tidal terrace]

https://tenor.com/view/kasane-teto-gif-7491957198027907152

[fathom oasis]

what do i do woth this again?

[tidal terrace]

convert it to the form (a-b)^2

[cloud epoch]

What you need to do right now is find a and b then you can move forward

[cloud epoch]

Look here, what do you sub out a and b for so that the bottom equals the top?

[fathom oasis]

uh

x and 3/2?

[cloud epoch]

yess

so a=x and b=3/2

[fathom oasis]

okay

[cloud epoch]

now you know that a^2 -2ab + b^2 = (a-b)^2

so x^2 -3x + 9/4=??

[fathom oasis]

(x-3/2)^2

[cloud epoch]

exactly

[fathom oasis]

UAY

[tidal terrace]

https://tenor.com/view/jerma-luddy-no-chat-im-not-gonna-hit-the-luddy-yoinky-sploinky-no-chat-im-not-gonna-hit-that-yoinky-sploinky-gif-27239856

[fathom oasis]

whats next

[tidal terrace]

hell yeah

[fathom oasis]

i feel like i was taught differently

[tidal terrace]

. back here continue solving

[cloud epoch]

now by looking at your original equation, you have:
(x-3/2)^2 = 7 + 9/4

[tidal terrace]

maybe but who knows

[fathom oasis]

ill send it later

[fathom oasis]

yes

my paper is so dirty alr

oml

so this is correct?

[tidal terrace]

yep now continue solving
for me I would first add 7+9/4 then continue on

[fathom oasis]

thats rhe thing

i dont know how to add or subtract fractions

thats where i got stuck on earlier lol

[cloud epoch]

Im sorry, i wrote 7 on the right, but it is -7

[tidal terrace]

ok lemme try to find it cuz I hate typing it out

[cloud epoch]

so your last equation should be -7 on the right

[fathom oasis]

OH RIHT

right right

[fathom oasis]

sure

[tidal terrace]

$\frac{a}{b}+\frac{c}{d}=\frac{d}{d}\cdot\frac{a}{b}+\frac{c}{d}\cdot\frac{b}{b}$

[rocky lotus]

qimmah

[tidal terrace]

that's the general idea having common denom. then you can add them

[cloud epoch]

You just want to write it so that all the things you add have the same number on the bottom

then you can add all the top numbers normally, and the bottom number stays the same

[fathom oasis]

-7/1 + 9/4 right, automatically has 1 as its denominator?

[tidal terrace]

continuing from here $\frac{da+cb}{db}$

[rocky lotus]

qimmah

[fathom oasis]

db are denominators?

[tidal terrace]

like I know that's extra explanation but it's good down the road

[cloud epoch]

Yes

because 7/1 = 7

then you can multiply the top and bottom by the same number, and it wont change the fraction

for example 7/1 = 14/2 = 21/3 = ...

[tidal terrace]

that's one way but given it would happen that he would come across a lot of fractions making it general is better imo

[oak crane]

there’s another method i have and it’s easier

[tidal terrace]

the cross multiply ?

[fathom oasis]

(4)(-7)+(9)

(4)

?

[cloud epoch]

exactly

[oak crane]

yes

[cloud epoch]

Yes, but giving the general form directly is sometimes hard for people that havent seen a lot of formal mathematics in their life, like we just experienced with the whole a and b situation

[tidal terrace]

i see your point

[fathom oasis]

= 37/4

?

[tidal terrace]

-28+9 ...

[cloud epoch]

You forgot the -

[fathom oasis]

HUH

[cloud epoch]

lol

[fathom oasis]

wait

[cloud epoch]

(4)(-7) = -(4x7)

[fathom oasis]

why 28?

[fathom oasis]

ohh yeah

[cloud epoch]

4x7 = 28

so -28 here

[fathom oasis]

what about + 9?

because i added 9

[cloud epoch]

you add it

yes

so -28+9

and then divide it all by 4

[fathom oasis]

so its -37/4.?

ohh divide

mbmb

[cloud epoch]

noo

[tidal terrace]

or also 9-28 maybe this is better

[cloud epoch]

-28 + 9 = ?

or ye 9 - 28= ?

[fathom oasis]

ohh

19

-19

[cloud epoch]

so you have -19/4

[fathom oasis]

yes

now divide by 4?

[cloud epoch]

it is divided by 4

you can leave it as -19/4

you can also write with a decimal, like -4.75, but you'll find that leaving it as a fraction is what is usually best

We usually prefer integers divided by integers over writing it with decimals

[fathom oasis]

-7/1 + 9/4 = 19/4

[cloud epoch]

-19/4

[fathom oasis]

i js noticed apple has auto calcu

oh yea right

-7/1 + 9/4 =-4.75

6/4 + 2/5 =1.9

[cloud epoch]

but leave it as -19/4

[fathom oasis]

it calculates automatically thats so cool

okay

so do i write that down as my next uhh

like thing in the solution

[cloud epoch]

step

yes

now you have (x-3/2) ^2 = -19/4

[fathom oasis]

dang its already 1:30am

Whats next?

[cloud epoch]

oof

[fathom oasis]

also, can i send my notes so u can like see how they taught us?

[cloud epoch]

If you want sure

[fathom oasis]

look at uh

example 7

closest comparison to our original equation

[cloud epoch]

yes

[fathom oasis]

x^2 - 3x + 7

[cloud epoch]

Problem is on the right you have a negative number

and you can't just root a negative number

[fathom oasis]

uh huh

[cloud epoch]

unless you have seen imaginary numbers?

[fathom oasis]

yes

[cloud epoch]

You know what that is?

[fathom oasis]

sqrt i

[cloud epoch]

i^2 = -1

[fathom oasis]

yeah but i didnt understand it that much

i just know that if its not a perfect square, imaginary roots are applied

[cloud epoch]

the only thing you need to know is that i^2 = -1

[fathom oasis]

okay

[cloud epoch]

incorrect

2 isnt a perfect square, but sqrt(2) has no imaginary

it's just to find the root of a negative number

[tidal terrace]

if b^2-4ac (in a quadratic ax^2+bx+c) is less than 0 then the roots are imaginary but that's not the topic for now

[cloud epoch]

all positive numbers have a square root

the only time where we need imaginary numbers is for the root of a negative number

[fathom oasis]

ahhh

[fathom oasis]

ooay

so the next step is?

[cloud epoch]

or the root of an imaginary number itself, but not useful here

soo

you have -19/4 on the right

-19/4 = -1 x 19/4
and i^2 = -1
so
-19/4 = (i x sqrt(19/4))^2

do you follow?

[fathom oasis]

oh and should i also write it like this already like on my lecture?

-19/4*

[cloud epoch]

i dont know how your teacher wants it

but in France where im from we Never ever write sqrt of something negative

[fathom oasis]

oh

[cloud epoch]

I think its a pretty common take

in math

[tidal terrace]

in my country you only start doing roots of negatives in 2nd highschool year

[cloud epoch]

same for me

[fathom oasis]

oh yeah i see

[cloud epoch]

but you never write the root of a negative with the symbol

[fathom oasis]

there are no sqrts of negative number

its all positive which are in radical

[tidal terrace]

at least not in the Real numbers

[fathom oasis]

yes yes

[cloud epoch]

ye so basically, because your equation is (something)^2 = something negative you have no real solution

but you can find the complex solutions with imaginary numbers

[fathom oasis]

(x-3/2)^2 = -19/4

[tidal terrace]

the word imaginary itself is misleading to the complex unit

[cloud epoch]

so as i said
-19/4 = (i x sqrt(19/4))^2

but also
-19/4 = (-i x sqrt(19/4))^2

[fathom oasis]

uhh

[cloud epoch]

you follow?

[fathom oasis]

so something like this?

[cloud epoch]

you can write +- in front of i

its + or - i

i^2 = -1
(-i)^2 = (-1)^2 x (i)^2 = 1 x (-1) = -1

[fathom oasis]

FIUGRHJEGJHSBDKJGVDKHGVES

[fathom oasis]

uh

oiay

[cloud epoch]

you need to thoroughly understand it so you're able to do it urself

the point of math isnt to get done with the homework and just have the solution, you need to understand so you can do it again

[fathom oasis]

yeah

but you kinda have to draw it out for me 😭

[cloud epoch]

Thats not a problem

[tidal terrace]

Something like this would show btw and it may help

[fathom oasis]

i almost couldn't visualize this

[cloud epoch]

just if anything is confusing tell me so i can elaborate

yeah its complicated by just typing

[fathom oasis]

and its also nearing 2am so my brain is fried

[cloud epoch]

ofc

[cloud epoch]

You can do it like this too yeah

i just dont like it because you write sqrt(-1) but that may be just me

maybe your teacher doesnt care

[tidal terrace]

i just write it to show that "i" will show up
i just simply skip those 2 steps directly when i'm solving

[cloud epoch]

I understand it, I just dont like it lol

[tidal terrace]

i feel you

[cloud epoch]

anyways, did you understand this rco?

[fathom oasis]

not really

[cloud epoch]

hm

did you understand what i was saying?

[fathom oasis]

like why did we only distribute x to -3?

why not the whole fraction (-3/2)

or did they just write it wrong

[cloud epoch]

he did root

so he didnt multiply

he rooted both sides

so the square on the left goes away

no distributing

[fathom oasis]

i maybe should get some sleep

[cloud epoch]

yeye

sleep is goated

[fathom oasis]

i do not remember the last like 3 steps

ill ask my friends for help tomorrow too

[cloud epoch]

sounds good

[fathom oasis]

but i understood what u guys were teaching me

WAIT

BEFORE I SLEEP

[tidal terrace]

calm down lol

[fathom oasis]

can u teach me the fraction part again

[cloud epoch]

ok

I can if you want

[fathom oasis]

cuz i feel like thats one of the biggest obstacles ill face in completing swuars

yes pls

[cloud epoch]

lets say you wanna add these

[fathom oasis]

yes

[cloud epoch]

what you do multiply the left by the bottom of the right side and vice versa

so on the left you multiply by d/d and on the right by b/b

[fathom oasis]

so b x d
a x c?

a

[cloud epoch]

i didnt understand what you said

[tidal terrace]

$\frac{a}{b}+\frac{c}{d}=\frac{d}{d}\cdot\frac{a}{b}+\frac{c}{d}\cdot\frac{b}{b}$

[rocky lotus]

qimmah

[cloud epoch]

you do this

yeah

that way you have the same bottom on both sides

[tidal terrace]

but just a note for the future if it happens

[cloud epoch]

example if you wanna visualize better

[tidal terrace]

$\frac{a}{b+e}+\frac{c}{d+f}=\frac{d+f}{d+f}\cdot\frac{a}{b+e}+\frac{c}{d+f}\cdot\frac{b+e}{b+e}$

[fathom oasis]

hm

wait

[rocky lotus]

qimmah

[tidal terrace]

that's an extra

[fathom oasis]

is that the same for

this?

cuz i find this the easiest

[tidal terrace]

yes

[cloud epoch]

when you have the same bottom, you can write the whole under one unique bottom

[fathom oasis]

sorry?

[cloud epoch]

if you understand this forget what i said

lmfao

[tidal terrace]

the word you are looking for is denominator

[fathom oasis]

i know common fractioons

[cloud epoch]

I know but idk if he knows it

[fathom oasis]

lmfao alr

my bed feels so heavenly

[cloud epoch]

idk what you already know, so i try to do as simple as possible

[tidal terrace]

good I wish my AC would be that cold lol

[cloud epoch]

man just go to sleep

[fathom oasis]

LMFAO

alr

thank u guys

big life savers

[tidal terrace]

https://tenor.com/view/mana-sama-malice-mizer-egl-jfashion-harajuku-gif-19234526

[cloud epoch]

glad we could help

sleep tight

[fathom oasis]

^^

thanks thanks

[tidal terrace]

https://tenor.com/view/mana-sama-malice-mizer-goodnight-sleepy-vkei-gif-7450623220532652531

[fathom oasis]

BYEBYEE

.CLOSE

.close

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[fathom oasis]

😭😭

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[ivory valley]

hey, did you open by accident?

[river shale]

Hii, question?

[vale dock]

@left glacier Has your question been resolved?

[brittle epoch]

https://tenor.com/view/bh187-spongebob-patrick-star-derp-duh-gif-21500098

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[hidden sinew]

used symbolab?

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[twin garden]

I dont think my picture is correct, I also have no idea how to continue from where I am at

[vale dock]

@twin garden Has your question been resolved?

[shut cobalt]

@twin garden Think of a property of a 45 45 90 triangle

more generally of triangles with angles $\alpha, \alpha, \beta$

[rocky lotus]

Katharine

[twin garden]

so my drawing isn’t wrong?

[cloud epoch]

your drawing isnt wrong

@twin garden what can you say about the lengths of the different sides of the triangles ABM and CDM?

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@twin garden Has your question been resolved?

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[timid briar]

i need help

ive tried over

a million times to get this right

someoneee

anyonee

[tidal terrace]

just to make sure the formula is Pe^rt ?

[fleet dune]

i think it's compounded yearly, not continuously

[fickle rose]

so (P\qty(1+\frac{r}{n})^{nt})?

[rocky lotus]

PajamaMamaLlama

[fleet dune]

yes

I would find the factor the loan grows by from 2003 to 2008

[vale dock]

@timid briar Has your question been resolved?

[final adder]

!nosols

[vale dock]

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.

[desert stone]

Then

The identity here because bank takes interest each year so the rate is one time per yes

The formula thus $P(1+r)^n=P’$

[rocky lotus]

Emmaaaaa

[desert stone]

n is year and solve this $1+r=(\frac{P’}{P})^{1/n}$

[rocky lotus]

Emmaaaaa

[desert stone]

And then just plug in will be fine

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@timid briar Has your question been resolved?

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[delicate lotus]

hello i would like someone to help me calculator weighted grade in my biology class because i don't know how they got this number lol

[delicate lotus]

my final grade is the "final adjusted grade:

"

[oak crane]

ur 75% is 110, right?

[delicate lotus]

i dont know, it went from 99.96/110 to 61.83/75, and i dont know where they got the 61.83 and the 75 from

it went from 90% to 82%...

[wintry oxide]

Do they grade on a curve ?

[oak crane]

30% here is missing

have you did the exam?

for 75% i got 68

,calc (99.96/110)*75

[rocky lotus]

Result:

68.154545454545

[oak crane]

whatever the 30% is its probably affected

[delicate lotus]

i did everything but this is another thing

[oak crane]

ah d2l

maybe try contacting them it must be a typo

[spring jackal]

i see an exam 4 in the announcement but not in the d2l, i wonder if that's why

i.e. grades arent released yet and the teacher didn't drop it either so it shows up as a 0

[spring jackal]

the hardest part of any course is using D2L

[delicate lotus]

i also did that bonus thing but they didnt count it i think

[delicate lotus]

does this help?

[oak crane]

so true

[oak crane]

honestly the "dropped" stuff must affected ur final grade

[delicate lotus]

does the final adjusted grade seem correct>

[spring jackal]

iirc it did something funky for me too, they kept saying "your D2L grade is not indicative of your final grade, check [other software]"

[oak crane]

ur best just contact ur teacher and then they can fix ur issue

[spring jackal]

no, the subtotals are all correct but i think the final adjusted grade is counting some dropped ones as zeroes

[oak crane]

for me it looks they made a mistake cause of d2l stuff

so ask them

[delicate lotus]

omg my course closes after tomorrow ;-; I NEED TO CONTACT THEM ASAP AND TYSMMM

[oak crane]

yw

[spring jackal]

aaa good luck!

[oak crane]

dont forgot to close the channel!

!done

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If you are done with this channel, please mark your problem as solved by typing .close

[delicate lotus]

.close

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[azure sun]

can someone tell me how to do this i let the sin cos expression as alpha and wrote numerator as
8+alpha-1/8+alpha
and now just did range but i think i am missing like denominator cant be zero stuff so can someone help me here but yea use the method i used

[wraith heart]

Where's the question

[azure sun]

this is the question

u gotta find range of it

[wraith heart]

Find the domain of the inverse

[azure sun]

8 + alpha>=0?

so yea now what to do i am having a lil problem in applying this domain to my range that came

like removing the values cuz 6/5 is coming in the actual answer too and i have no idea how

<@&286206848099549185>

[fleet dune]

I would probably first find the range of 12sin(x)-5cos(x) but that may be difficult

[slate folio]

find the range of 12 sin x - 5 cos x

[fleet dune]

(there is a clever way to do it though)

[slate folio]

it's not that difficult

therr's a quick formula for that

[azure sun]

that will be [-13,13]

[azure sun]

yea

[fleet dune]

yep

[slate folio]

now what you need to do is suppose 12sin x - 5cos x = t

[ashen prawn]

u know hindi?

[azure sun]

yea

[ashen prawn]

shall i tell/try to tell?

[azure sun]

yea sure

[slate folio]

wait a second

[fleet dune]

so we have (\frac{7+t}{8+t}) with (t\in[-13,13])

[rocky lotus]

Sapien

[slate folio]

actually it's easy to see that the range also covers t = -8

[azure sun]

yea and then i wrote numerator as 8-1+t

[ashen prawn]

ok. isme aisa hua hoga ki you know acosx+-bsinx ki range nikali hogi, jo aai hogi [-13,13] and uske saath some 't' wla term too

[slate folio]

and since the numerator and denominator are both linear functions

[azure sun]

and then split the denominator

[ashen prawn]

acc to that result aaya hoga

[slate folio]

it has to cover all real values

[azure sun]

ha

[azure sun]

so i did this and then applied elementary method

the problem is that denominator cant be zero so i have to makae a seperate condition of that and i am having a problem in applying that condition

[ashen prawn]

hey fella help my mate, ok?

i tried ma best

[slate folio]

nvm I was wrong

doesnt cover all real values

[azure sun]

yea

[ashen prawn]

dms

[slate folio]

oh I figured it out

I made a dumb mistake

[slate folio]

so this function always increases

and it has an asymtope at t = -8

so you can draw a rough graph of it

[vale dock]

@azure sun Has your question been resolved?

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[vale dock]

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[night patio]

If I roll a fair 6 sided die, what would be the expected number of rolls before 5 comes? Would it be 6 rolls?

[merry crystal]

yes

[west cloud]

seems so to me; do you have any other questions?

[night patio]

You roll a standard 6-sided die repeatedly until you get a 5. What is the expected value of the minimum value rolled before (and including) the 5?

this was the main question

[west cloud]

ah

[night patio]

I mean ig i get what they want

btw i already know the answer is 2.45

How do i go on approaching this problem

[fleet junco]

notice

how

theres only 2 cases for the minimum

eitehr 5 or 6

so just calculate the probablity u roll a 6 bfeore a 5 and the probably u dont

and just calc expected val based on that

wait nvm

i miseread

[night patio]

hmmm i got confused haha

[west cloud]

ig u can do casework

[mild marsh]

Does conditioning on the min not work?

[night patio]

I was thinking of making cases for when 1 is the min, or 2 or 3 or 4

But then I got confused about how many rolls should i consider

ig it should be 6 rolls then, since ill get a 5 before 6 rolls?

thats expected right

[mild marsh]

For the min=4 case, suppose we finish in k rolls, then we need m 4’s to appear, k-m-1 6’s to appear and one last 5 to appear which has sum(m=1 to k-1 of (k-1)Cm) ways of occurring and probability 1/6^k for each case

[fleet junco]

ok

i think

i got it

the expected value

is

P(min >=5) + P(min >= 4) + P(min >= 3) + P(min >= 2) + P(min >= 1)

and

which is just a geometric series which is ez to calculuate

[mild marsh]

Yep

But keep in mind that to calculate expected value, you need P(min=5), P(min=4), etc

[fleet junco]

@night patio

[fleet junco]

no beucase

the >=

like

[night patio]

i need a bit of time to process all of this sorry

[fleet junco]

yeah lol

[night patio]

im dumb 🙏

[fleet junco]

but P(min >= 2) = P(min = 2 or 3 or 4 or 5)

so when u expand the sums

u get

sum(x P(min = x) )

which is the foormula for EV

[night patio]

can you explain that sum?

isn't k always bigger than m

so woudn't the mC(k-1) term be 0 for all values of m < k-1

[mild marsh]

Sorry abt notation, meant for other way around

[night patio]

(k-1)Cm?

this right?

[mild marsh]

Yep!

Fixed it

[night patio]

okay easy

got it

thank you

let me read the other messages too