help-13

[sly abyss]

i would just assume the peirod is 24 hours

[marble smelt]

to make a sinusoidal function I need the period or frequency

yeah kk

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[sleek birch]

If anyone could helpe with the solutions it would be appreciated

And this one

[cedar kiln]

@sleek birch Has your question been resolved?

[hazy shore]

is there a pattern to $t_{n, r}$?

[wraith dagger]

Insanity Cry

[hazy shore]

or finding it at least

it seems to follow some type of recursive rule

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[sleek birch]

No I didn't think so

[hazy shore]

is there a way the pascal triangle's made?

[sleek birch]

Not that I know of

It's literally just that

That's the question

I think its some form for terms but I'm not sure

I'm hoping someone here knows

[austere ember]

what they're trying to get at is that there is a pattern to the numbers of pascals triangle

and the pattern is so simple that you can construct the entire triangle yourself

do you see anything about how for any particular row, it relates to the row above it?

[sleek birch]

Yeah I guess

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[cedar kiln]

Please don't occupy multiple help channels.

[crimson sedge]

What

I’m not

[crimson sedge]

Liar

[crimson sedge]

Ok is the first one I did here right

[runic garnet]

Ye

[crimson sedge]

thank you gifted green name

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[leaden geode]

im so slow i dont get how these problems work

[leaden geode]

and ik this is the easiest shit i just have no idea whats going on

[sleek birch]

Nope

[slow jewel]

Try to break down each of the terms such that most of the terms have the power of a multiple of 2

For ex in the first one, x³ can be written as x² * x

[wraith dagger]

Sulphur

[slow jewel]

Similarly do the same for 112 and multiply em both

[leaden geode]

thanjk u

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[real abyss]

Hey so my physics professor showed us this example problem on half life and I’m trying to understand why in steps 2 to 3 the t 1/2 moved to the numerator

[austere ember]

step 2 is what's wrong

when they rearrange to solve for n, they should be multiplying both sides by t_(1/2) and it should end up in the numerator

so when the professor was algebraically rearranging to solve for t, he should've arrived directly at step 3

[real abyss]

Omg I see it now

Tysmmmm

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[sharp haven]

oh crud

[sharp haven]

my brain kinda dies with composite figures

i got 44 i think

[peak minnow]

u get 5 rectangles

find area and add them up

[sharp haven]

i divided it into 3

i mean 4

[peak minnow]

can u show them?

dividing into like this is easier

[sharp haven]

the numbers are the area of each rectangle is plit

i split

[peak minnow]

ok like that is fine ig

[sharp haven]

does it seem good?

[peak minnow]

no

u do not get 8 for 3rd rectangle

[sharp haven]

uh

yes

[peak minnow]

nvm nvm

yeah seems good

[sharp haven]

alr thx

[peak minnow]

yeah 44 is good

[sharp haven]

Does 50.3 sound like a good answer to this one?

this is what i did

<@&286206848099549185>

[candid marsh]

!15m

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[sharp haven]

whoops

mb

[candid marsh]

Seems right tho

[sharp haven]

alr thx

[sharp haven]

wait but dont leave yet pls i have another one soon

[candid marsh]

Sure

I'm just doing puzzles anyways

[sharp haven]

bros the thinker waht the hell

puzzles

[candid marsh]

Eh, math majors liking puzzles makes sense

[sharp haven]

alr

[candid marsh]

Oh wow, texts tiny
Can read it tho

[sharp haven]

alr u should be able to see my thought process here

[candid marsh]

Doesn't seem right

Why are there two 8^2s

[sharp haven]

oh shoot

ur ight

u right

computational error

thx

[candid marsh]

Fix that and you should be right

[sharp haven]

uhhhh i dont think i'm right

[candid marsh]

What'd you get?

[sharp haven]

i fixed it but it doesnt look right

i got 508.9

[candid marsh]

How did it get larger??

[sharp haven]

OH SHOOOT

💀

im having brain farts

i should have put 4^2 on 1 then 8^2 on another

alr mb lemme redo this

alr

i got about 131.9

or about 42pi

[candid marsh]

Yep

[sharp haven]

alr tysm

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[coral jewel]

Given the point $M(3,3,-2)$ and 2 lines [
\begin{cases}
d_1:\frac{x-1}1=\frac{y-2}3=\frac{z}1\
d_2:\frac{x+1}{-1}=\frac{y-1}2=\frac{z-2}4
\end{cases}
]
The line $d$ passes through $M$ and intersects $d_1,d_2$ at A and B respectively. Calculate the length of AB

[coral jewel]

not sure what to do here

$(x,y,z)=(3,3,-2)+\lambda(A,B,C)$

[coral jewel]

this is what i got so far

(this is d)

[wicked mantle]

Have you acknowledged the status between d1 and d2

About whether they intersect or not

[coral jewel]

they seem not to be parallel, nor perp

[wicked mantle]

How about askew or intersect?

[coral jewel]

seems to be askew

they dont intersect

[coral jewel]

well?

[wicked mantle]

Line d falls on the book

[coral jewel]

hm

perhaps the direction vector of the line must be the cross prod of the 2 lines?

[wicked mantle]

Give me a few minutes

I’m packing my stuff, leaving school

[coral jewel]

hm, i have a theory

2 lines intersect means they are coplanar, yes?

perhaps the line that intersect both planes is the intersection line of the 2 planes?

which should be the cross prod of the vector from A to d1 and vector from A to d2

[wicked mantle]

Find two random points O P on line d1 and get MO MP vectors

Do outer multiplication to get the plane

[coral jewel]

sure

[wicked mantle]

Find the intersect between the plane and d1; apply the same idea to d2

[coral jewel]

which yields the normal vector of the plane having line d1 and d?

[wicked mantle]

You’ll get two coordinates

[wicked mantle]

yes, it yields the normal vector of the plane

[coral jewel]

alright wait

[coral jewel]

coordinates?

you mean the vectors or the intersection of d and d1?

[wicked mantle]

No, I was referring to the coordinates of O and P

[coral jewel]

oh sure

[coral jewel]

oh what

i thought O and P both lies on d1?

[wicked mantle]

no

mb, I should have stated it clearly

[coral jewel]

oh wait

even if you didnt, i already found it

the direction vector of the line d is (2, 1, -2)

i basically find 2 points O, P on d1, find vector MO and MP and cross prod them to yield the normal vector of the plane containing d and d1

which i got (-7, 4, -5)

repeating the same process for d2, i got (-8, 6, -5)

cross prod those 2 normal vectors i got (2, 1, -2), which is the direction vector of d

seems to be correct too

found it, AB = 3

thanks!

c.lsoe

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[wicked mantle]

All roads lead to Rome, despite mine is tougher!

[coral jewel]

https://cdn.discordapp.com/emojis/1112022027847606383.gif?size=48&quality=lossless&name=catcombing

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[coral jewel]

A boat flows upstream and downstream in a 40km long river taking a total of of 4 hours 30 minutes. Given the time for the boat to flow downstream for 5km is equal to the time for the boat to flow upstream for 4km. Calculate the speed of the stream.

[coral jewel]

oh got it

let x be downstream speed, y be upstream speed

i would have a system of equations that i can solve

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[jovial panther]

HI this is an example given to me by my teacher. This is for a gantt chart creating. The red Task name are the task and the duration and underneath is the requirement to do the task. I dont quite get the part when predecessors come into play. Like for example with the detailed inspection it takes 2 days to complete it and the requirement underneath goes over 2 days. I tried to make it make sense and its just not making sense for me if someone can explain it to me in details on how they got those numbers pls im just so lost rn

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@jovial panther Has your question been resolved?

[jovial panther]

<@&286206848099549185>

[cedar kiln]

@jovial panther Has your question been resolved?

[jovial panther]

<@&286206848099549185>

<@&286206848099549185> pls anyone😭?????

[cinder storm]

sry idk what all this is

[cedar kiln]

@jovial panther Has your question been resolved?

[cedar kiln]

@jovial panther Has your question been resolved?

[granite knoll]

presumably, for "Detailed Inspections", all 3 of those can be done on the same day. or "Inspect radiation barriers" will be both days, and "Inspect equipment" the first day and "Update power" the second day? not too sure. it's a bit confusing

[odd socket]

you can run 6/7/8 all at the same time taking you maximum 2 days

the only predecessor is that you completed 3/4

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[mellow loom]

the hint are on the first and second information

what are the first and second information you can get when you read the problem?

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[late plume]

.reopen

Math Sucks

[late plume]

I hate it

it is sooooooooo bad

[idle tusk]

that's crazy bro

do you have any questions tho?

[silent fable]

yes

[late plume]

yes what is the quadratic formula times pi

[late plume]

what is the quadratic formula times pi

[idle tusk]

$\pi\frac{-b\pm\sqrt{b^2 - 4ac}}{2a}$

[wraith dagger]

artemetra

[idle tusk]

here you go

[late plume]

thank you

[idle tusk]

no problem

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[crimson sedge]

Still can't figure this out

[lyric widget]

try multiplying by (sqrt(x+64)+8)/(sqrt(x+64)+8)

[raven shard]

are you familiar with conjugate method for evaluating limits

[crimson sedge]

No

@raven shard

[raven shard]

are you familiar with l'hopital's rule?

[crimson sedge]

Can't use it

[raven shard]

start by doing this then

[crimson sedge]

Need to find an other way

Ok

Done

[raven shard]

you are missing a 7 but yes that's right

[crimson sedge]

I see

[raven shard]

this process is called multiplying by the conjugate btw

[crimson sedge]

Ok

[raven shard]

so the important thing here is that a conjugate for cube roots also exists

the reason the square root conjugate works is because of identity like a^2 - b^2 = (a - b)(a + b)

to use conjugate for cube roots, use the identity a^3 - b^3 = (a - b)(a^2 + ab + b^2)

[crimson sedge]

I see but how

[raven shard]

consider that in your square root case, a = sqrt(x + 64) and b = 8

you multiplied by (a + b)/(a + b) to get a^2 - b^2 in the denominator, simplifying the singularity

[raven shard]

try to see how this is similar for the cube root case

(you can try to identify what a and b are, then identify what conjugate you should multiply by to simplify)

[crimson sedge]

Hmmmm

Let me think 🤔

No i can't

You need to help me

@raven shard

[raven shard]

so the expression you're dealing with is (cbrt(x + 27) - 3)

[crimson sedge]

I see

[raven shard]

say that a = cbrt(x + 27) and b = 3

[raven shard]

now using this identity, you can find the conjugate you have to multiply by

[crimson sedge]

Ok give me a minute

Ok done

Took me a while huh

@raven shard

[raven shard]

ah congrats (i'm assuming you got the correct answer)

[crimson sedge]

No

Where do i go from here

@raven shard

[raven shard]

can you show me what you have

[crimson sedge]

Ok

,rccw

[crimson sedge]

Excuse my terrible hand writing

@raven shard

[raven shard]

hm it's good progress

though it looks like you cube rooted the a and b terms

recall that when we have (a - b) where a = cbrt(x + 27) and b = 3, we aren't cube rooting a and b to find the conjugate

(we aren't cubing them either, our goal is to multiply by (a^2 + ab + b^2)/(a^2 + ab + b^2))

[crimson sedge]

..

So what is the next step

@raven shard

[raven shard]

so what you currently have on your paper is incorrect

[raven shard]

going back to the previous line, perform this operation

[crimson sedge]

...

What have i done wrong

[raven shard]

this

[crimson sedge]

No idea just tell me

Sry i am dumm

@raven shard

[raven shard]

you multiply by (cbrt(x + 27)^2 + 3cbrt(x + 27) + 9)/(cbrt(x + 27)^2 + 3cbrt(x + 27) + 9)

[crimson sedge]

Ok

What now

[cedar kiln]

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[faint dagger]

Could you determine the intersection between a line and a plane using parametric equations for both?

[hollow trail]

you'll need to use some other parameter than λ for the second one, but other than that you can set x, y, z equal and solve the system of linear equations for the 3 parameters

[faint dagger]

oh i see it now

thank you

.close

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[faint dagger]

.reopen

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✅

[faint dagger]

.close

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[green bane]

for some reason the answer key says 4n^2 over 8n^3 not 4n^7 over 8n^3.

that is the answer key

[drifting marlin]

the following lines are consistent with it being n^7

where they actually seem to goof is thinking 4/8 = 1/4 lol

[green bane]

i got 1/2n^4+n^3+1/4n^2

thats right no?

[drifting marlin]

yeah

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[green bane]

yes

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[robust skiff]

The exam consists of 4 multiple-choice questions, each with two answers. All questions must be answered. A correct answer earns 3 points, while a wrong one deducts -2 points. Total points cannot be negative. The probability of choosing the correct answer is 50%.

a) What is the probability that a student scores more than 3 points when guessing the answers?
b) 250 students take the exam. What is the distribution of the sample mean X? What is the probability P(X>=3)?
c) 28% of the students guess all the questions correctly and score a full 12 points. Among those who don't guess, 18% receive full points. What is the probability that a student who scored 12 points guessed the answers?

I got the a) which is 0.3125

Not sure about the b) tho

[robust skiff]

I'm using CLT at the moment (not sure if I should use it on this) and my result is 0.999, so about 100%

[buoyant latch]

Somehow CLT sounds wrong because if you got all 4 questions wrong you’d get 0 marks not -8

It doesn’t look very symmetrical

It doesn’t sound like to me the limiting distribution would be symmetrical

[robust skiff]

You can't get -8. if the sum of the result is negative its automatically 0

[buoyant latch]

Yeah, but there’s just as big a chance to get 4 wrong as 4 right

I’m not too sure how to do this question but I have a feeling that CLT sounds wrong

[robust skiff]

yyeeeaaah, should I do normal distribution without CLT?

Calc shows 0.5910 for the probability

I'll go with that. But how about the c)? Baye's theorem?

P(student is a guesser) x P(guesser gets all right) + P(student is not a guesser) x P(student gets all right)

I hope someone can correct me if I'm wrong

[cedar kiln]

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[wild mist]

"calculate the third row of A^-1"

[wild mist]

this is what it gives me online

but this is the professor's solution

[granite knoll]

the professor is giving the 3rd column

[wild mist]

i think i need to go to sleep

sorry i feel embarassed

thanks for the help

.close

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[final granite]

would i just find the total volume when the height is 8

then substitute the 8 for 2, to solve the volume when the water is only at 2inches

and then just do 2in volume/8in volume?

[frigid escarp]

Do this

Yes

How many volumes of this cone fit into this cone

[final granite]

but would that work? as the base is at the top, meaning if you pour only 2 inches, wont the base be different?

like wont the radius be different since its a cone?

if at 8 inches the radius is at 12, meaning every inch up increases the radius by 1.5, would ineed to change the equation to oatach the new radius at 2 inces? which would be 3?

im only thinking this because the base is at the top with the apex downward

if the base was actually on the bottom then the radius is the same

right?

[cedar kiln]

@final granite Has your question been resolved?

[slate lintel]

yes radius would be different at different heights

[cedar kiln]

Channel closed

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[cedar kiln]

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[ripe agate]

I don’t get what to do at all…

[hidden mural]

try to relate sin and tan

[ripe agate]

What does that mean?

[hidden mural]

find an equation with sin and tan that's always true

[ripe agate]

Like sin/cos = tan?

Or cos/sin = arctan?

[idle tusk]

cos/sin is not arctan

cos/sin is cot

[ripe agate]

Ohhh got it

[hidden mural]

yes

but you can relate cos with sin

so it's only sin and tan

[ripe agate]

Like 1-cos^2 is sin^2, so tan^2 = sin^2/(1-cos^2)?

[hidden mural]

1-sin^2 yes

[ripe agate]

Oh wait I meant sin^2

Yea

How do I apply that relation to this question?

[hidden mural]

what do u think

what angle should you evaluate both sides at?

[ripe agate]

Angle? Sorry, I still don’t get it

[hidden mural]

so we have tan^2(t) = sin^2(t)/(1 - sin^2(t)) for any angle t right?

[ripe agate]

Yea

[hidden mural]

what t should u choose here

given x

[ripe agate]

Something that isn’t 90°?

[idle tusk]

$\tan^2(t) = \frac{\sin^2(t)}{1-\sin^2(t)}$

for clarity

[wraith dagger]

artemetra

[hidden mural]

um sure

let's not worry about the denominator being zero

for now

[idle tusk]

look at you are trying to evaluate, it's sin(...)

[ripe agate]

Okay, but what am I trying to do with this question?

I’m not sure I understand the goal of it

Like what I’m trying to solve

[hidden mural]

basically write sin( arctan x ) as something involving x without trig functions

like x/(x^2 + 4) or something

[ripe agate]

Okay, so if we’re relating sin with tan, how does that eliminate trig functions?

[hidden mural]

it's easy if it was sin (arcsin x)

that's just x

[ripe agate]

Ok I kinda get that

[hidden mural]

seems natural cuz there's a sin and tan

[ripe agate]

So is there a way to apply relations between functions to eliminate each other?

[hidden mural]

yes

[ripe agate]

…can I get a hint?

[hidden mural]

t = arctan x

[ripe agate]

So… I replace the t in the relation with arctan x?

[idle tusk]

yes

[hidden mural]

sometimes you just gotta try things

[ripe agate]

So now it’s sin^2(arctanx)/1-sin^2(arctan x) = tan^2(arctan x)

[hidden mural]

yes

[ripe agate]

Isn’t that more complicated than the beginning? Or is there something that needs to be simplified?

[hidden mural]

it can be simplified

sin(arctan x) is what u want to isolate

[ripe agate]

Without bringing in any other trig functions?

[hidden mural]

yes

[ripe agate]

Sin(arctan x) = tan(arctan x)sqrt(1-sin^2(arctan x)?

I’m really confused

[hidden mural]

can you simplify tan(arctan x)

[ripe agate]

Oh that’s just x right?

[hidden mural]

yes of course

[ripe agate]

So sin(arctan x) = x*sqrt(1-sin^2(arctan x))

[hidden mural]

true

[ripe agate]

I can simplify the sqrt part right?

[hidden mural]

how

if you can, you can idk

[ripe agate]

Can I not?

[hidden mural]

no i don't see how

[ripe agate]

Ok got it

Then what do I do to eliminate the sin stuff?

[hidden mural]

wdym

what's ur goal

[ripe agate]

To make the function into terms of x

[hidden mural]

what function

i mean rn what's ur goal

[ripe agate]

Didn’t it not need trig functions?

[hidden mural]

yes that's the question

but i mean more precisely

[ripe agate]

I meant the 1-sin^2 in the square root

[hidden mural]

what ru trying to do rn

[ripe agate]

I want to turn it into smt in relation to x?

[hidden mural]

ok what about it

[ripe agate]

Doesn’t it have sin in it?

[hidden mural]

true

[ripe agate]

Or do I not need to get rid of it?

[hidden mural]

no you can't

[ripe agate]

Ok, so then am I done?

[hidden mural]

if you want

you wouldn't get full marks tho

[ripe agate]

So then I’m not done……

[hidden mural]

alright u want full marks

[ripe agate]

Yea I’d also like to understand the question tbh

So I want to do it all

[hidden mural]

go ahead

[ripe agate]

Uh so I know that sin(arctan x) = x*sqrt(1-sin^2(arctan x)), and i need to eliminate the sin stuff on the right. Do I need to keep on isolating the sin(arctan x) side or is it possible to move things around?

I think I messed up somewhere

Um are you online?

[hidden mural]

should be = x^2

[ripe agate]

Oh yeah

So x = tan?

[hidden mural]

tan what

[ripe agate]

Tan(arctan x)

Wait

What

[hidden mural]

um yeah

[ripe agate]

Woah

That’s actually really cool

This would be the end right?

[hidden mural]

ummmm 😂

[ripe agate]

….is it not?

[hidden mural]

no it just means we've reached a tautology and there's no contradiction

so everything is consistent

[ripe agate]

What’s a tautology?

[hidden mural]

something trivially true

like x = x

[ripe agate]

Oh… trivial sounds nice :)))

[hidden mural]

okay but we haven't progressed

[ripe agate]

So what does that mean for my original problem?

[hidden mural]

cuz you need to have a goal in mind

ok think of it this way

let u = sin (arctan x)

we have u^2/(1-u^2) = x

we just want u in terms of x

[ripe agate]

Ok, so I multiply both sides by the denominator and then move stuff around?

[hidden mural]

yea sure

[ripe agate]

Like this?

@hidden mural?

[hidden mural]

yassss

[ripe agate]

Ty wait so is this the answer?

[hidden mural]

what do you think is the FINAL answer

sin(artan x) = .... ?

[ripe agate]

… sqrt(x/(x+1))?

[hidden mural]

yes

[ripe agate]

Rlly? This is actually the end? Omg tysm

[hidden mural]

np lol

[ripe agate]

😁

Now I’m going to rest for some time

[hidden mural]

good idea

[ripe agate]

How can I mark my question as solved?

[hidden mural]

!solved

i think u need to type that

[ripe agate]

!solved

[hidden mural]

sorry

maybe it's .close

[ripe agate]

.close

[cedar kiln]

Channel closed

Closed by @ripe agate

Use .reopen if this was a mistake.

[hidden mural]

wait i just realized you might need to rationalize the denominator

[ripe agate]

What does that mean?

.reopen

[cedar kiln]

✅

[hidden mural]

so we have a sqrt(1+x) in the denominator

[ripe agate]

Yea

Does that mean smt?

[hidden mural]

basically u just want to get rid of the sqrt

[ripe agate]

How do I do that?

[hidden mural]

you could multiply top and bottom by sqrt(1+x)

[ripe agate]

Ohhhh ok got it

[hidden mural]

cool

[ripe agate]

Like this?

[hidden mural]

erm almost

[ripe agate]

What else do I have to do?

[hidden mural]

should be sqrt(x)

[ripe agate]

Ooh yea

[hidden mural]

cool

you're welcome

[ripe agate]

?

[hidden mural]

yes

second one

i mean the last line is true

[ripe agate]

Got it!

Ty!

.close

[hidden mural]

np

[cedar kiln]

Channel closed

Closed by @ripe agate

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[cedar kiln]

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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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[wide badger]

Is it possible to graph a simplified revolution of a planet around the sun as a sinusoidal function? the diagram below shows what we have to work with, and I am unsure of what the x and y would have to represent as variables in order to make a proper sinusoidal function

[wide badger]

we also have the fact that the period of revolution for the planets are (rounded) 225 and 88 days

[boreal hazel]

you can use that fact that period = 360/k
and solve for ‘k’

and make a sinusoidal function with that

[wide badger]

ohh makes sense

the instructions for this task want us to define what the x and y axis would be representing before we actually create the function

i tried doing x=days passed and y=position from starting point in degrees but that doesn't work for sinusoidal

as well as x=degrees and y=days of cycle but it makes the same mistake

[boreal hazel]

X should be days passed and y should be position as u said

[wide badger]

cool cool

the issue comes when we get to a full cycle completed, as the position just either rises continually not creating the wave for a sinusoidal function or if you reset to 0 instead of 360, it suddenly drops at 225 days for venus and 88 for mercury

[boreal hazel]

are u given any other info other then the period of revolution of the planets?

[wide badger]

that's all the info we have

sorry, we are allowed to use the internet to find other information if we need it, but I wasnt sure what other info I would be missing

that I need to make it work as a sinusoidal function

here is the small table of values I have currently made

i am so sorry, I just realized that i misheard the instructions as they were told to us verbally. the start point is not a line, but a dot on each circle representing the revolution meaning that I can use height compared to that start point instead of degrees

i appreciate your help so much, but now that I know that information I am able to complete the problem myself! thank you!

.close

[cedar kiln]

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[boreal hazel]

👍

[cedar kiln]

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[ebon aurora]

I forgot this completely, i thought i had to add 7 and 2, 9 and then divided 45 by 9

but after that i forgot

[wicked stag]

You will have to consider the parts 7k and 2k where k is a non zero constant

Then 7k+2k = 9k = 45

@ebon aurora Do you remember ?

[ebon aurora]

i havent been taught that way

so not really

[wicked stag]

Ok so see

since its a ratio

we can consider the two parts to be 7k and 2k

@ebon aurora Ok?

[ebon aurora]

yep

[wicked stag]

Now total length is 45

So 9k = 45

Or we get k = 5

Now the length of two parts were 7k and 2k so we can found them

[ebon aurora]

so 7x5=7 part

and 2x5=2 part

[wicked stag]

Yeahhh

🙂

[ebon aurora]

35:10

?

[wicked stag]

Undeestood ?

[wicked stag]

Yeahh

[ebon aurora]

alr thanks

.close

[cedar kiln]

Channel closed

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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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[blazing wraith]

How do i go about solving this

[crimson sedge]

so

have you tried factoring

[blazing wraith]

Yeah

but i think im doing it wrong

since im not getting the answer

[cedar kiln]

Show your work, and if possible, explain where you are stuck.

[crimson sedge]

and

what does not make sense

[boreal hazel]

you’ve got the answer

u set each of the factors equal to 0 and solve for x

[blazing wraith]

yeah ig so

but

why is it b and not e

[crimson sedge]

because

[blazing wraith]

and where does that extra x^2 go

[crimson sedge]

0

the 0

[boreal hazel]

x^2 = 0, swuarerrooot both sides x = 0

[crimson sedge]

the x^2 is 0 at 0

[blazing wraith]

ohhhhhh

Thank you

.close

[cedar kiln]

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[hot sigil]

Is there any “easy” proof for a specific case of the Euler’s theorem? I just want to prove that $a^{16}\equiv1\pmod{17}$ for all $a$ coprime to $17$ without going through the main proof, since there are some concepts I can’t use yet.

[wraith dagger]

BeeReallyYum

[crimson delta]

you can factor a^16-1 quite a bit

and then you "only" need to show that for every number 1 to 16 one of the factors is a multiple of 17

which is still quite a bit of work tho

!xy

[cedar kiln]

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.

[crimson delta]

probably better to consider -8 to 8 actually

then you only need to check 8 numbers

[hot sigil]

I just want to show that if $2023\mid a^{2023}-a,$ then $a$ is not $4,5,$ or $31.$ (quite an odd problem I know)

[wraith dagger]

BeeReallyYum

[hot sigil]

So I’m considering the problem mod 17

[crimson delta]

and thats the actual original problem? or is that also already another formulation

[hot sigil]

That’s pretty much it

.close

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[frigid sinew]

did my teacher make a mistake here

[frigid sinew]

or am i very high

on something

[harsh ginkgo]

Yeah thats a mistake.

[frigid sinew]

oh okay i can keep taking my drugs in peace then

.close

[cedar kiln]

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[hollow wagon]

Hello everyone, I'm currently taking a college math course.
This question is currently stumping me as I can understand how to work out the math but the actual logic of how dividing 117 by 4 1/3 gave the missing answer is confusing me.

[polar sigil]

117 milligrams of cholesterol -> 4 and 1/3 of milk

x cholesterol in 1 cup of milk

then you multiply

[hollow wagon]

So if i'm understanding,
117 = 4 and 1/3
x = 1
but what am i multiplying?

[polar sigil]

you multiply the numbers across

$117*1 = x(13/3)$

[wraith dagger]

Miliski

[hollow wagon]

I appreciate your effort but the logic of it still just doesn't make sense to me, guess this is just another "it is what it is" math thing for me that causes headaches lol

.close

[cedar kiln]

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[mortal sigil]

who can pass tha chat of algebra

[cedar kiln]

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[shell gust]

WHAT IS THIS QUESTIONN

[lone plaza]

what about it

[shell gust]

its hard

lol

i dont know where to even start to be honest i tried deriving the original function and substituting X for 0

but didnt end up anywhere

[median lantern]

draw y=3x+1

label the points there

[shell gust]

what do u mean

by that

what do i do

with those calcuations

p(0)=1

y=1

1=1

[lone plaza]

well you know that if the curve intersects the tangent line at (0,1)

the point (0,1) exists on the curve

[shell gust]

yeah

[lone plaza]

so p(0) = 1

hence* you know d = 1

[shell gust]

no i didnt know that

wait how come

[lone plaza]

because p(0) = a(0)^3 + b(0)^2 + c(0) + d

so p(0) = d

so d = 1

[shell gust]

oh

and what about for a,b and c?

where do i start

[lone plaza]

well okay

since there is a turning point at (-1,-3)

you know that p'(-1) = 0

since the derivative equals 0 at a turning point

so from that we get p'(x) = 3ax^2+ 2bx + c

then p'(-1) = 3a - 2b + c

3a - 2b + c = 0

you also know that p(-1) = -3 since that point exists on the graph

so p(-1) = -a + b - c + 1

-a + b - c + 1 = -3

• a + b - c = -4

that first thing is meant to be a negative sign idk what happened

[shell gust]

sorry give me a second to process that

ok

i understand how you got there

but for the question the answer sheet says to find the individual values of a,b and c

[granite knoll]

yes

[shell gust]

how do you get from -a+b-c=-4

to finding the indiivdual values

[granite knoll]

for the third equation, use the info of the tangent line at (0, 1)

you need to solve a system of 3 equations

[shell gust]

so -a+b-c

is 3x+1

or

am i confusing myself

[granite knoll]

no. you are given the equation of the tangent line at x=0. so you know the slope tangent to p(x) at x=0. i.e., you know p'(0)

[shell gust]

so p'(0)=3x+1

[granite knoll]

no

p'(0) equals the slope

[shell gust]

oh the slope as in

the original function

p'(0)= 3a+2b+c

right?

[granite knoll]

no

what is the slope at x=0

[shell gust]

3x+1

[granite knoll]

no. that is the equation of the tangent line

what is the slope

[shell gust]

a+b+c+d

[granite knoll]

have you learned how to find the slope of a line?

[shell gust]

what is a slope

oh

gradient

sorry

-3

the slope of the tangent

[granite knoll]

no

[shell gust]

3ax^2+2bx+c

=0

is equal to the slope

[granite knoll]

yes, p'(x) = 3ax^2 + 2bx + c.

you do not set it equal to 0

[shell gust]

oh

[granite knoll]

the slope at x=0 equals the slope of the line

[shell gust]

so

3a+2b+c

[granite knoll]

you're saying p'(0) is 3a + 2b + c?

[shell gust]

oh

wait

3+2+c

[granite knoll]

...no

[shell gust]

no

c

[granite knoll]

yes, p'(0) = c

[shell gust]

3a*0=0

and so on

[shell gust]

so the slope of the line =c

[granite knoll]

yes

[shell gust]

so c is 1

[granite knoll]

no

what is the equation of the tangent line

[shell gust]

C is 3x+1?

[granite knoll]

the equation of the line is 3x + 1. what is its slope?

[shell gust]

-3

[granite knoll]

no

[shell gust]

C is -3

[granite knoll]

no

where are you getting -3 from?

[shell gust]

I looked on my calculator and counted

[granite knoll]

I think you should review slopes: https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:linear-equations-graphs/x2f8bb11595b61c86:slope/v/introduction-to-slope

[shell gust]

Ok

[cedar kiln]

@shell gust Has your question been resolved?

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[quartz crypt]

log2((0)+4)+1
would give 1+4 =5
+1
=6
(0,6) for yn intercept
or am I missunderstanding htat

[carmine bronze]

log_2(0+4) = 2

[quartz crypt]

wait how

[carmine bronze]

log_2(x) is basically asking what power of 2 equals x.

[quartz crypt]

Okay I see

so 0,2

but then what do I do with +1

0,3?

[carmine bronze]

Yes.

[quartz crypt]

Okay I see

Just double checking if I am doing that right

yeah then +1 on the outside right

[carmine bronze]

Yes.

[quartz crypt]

Okay perfect

[quartz crypt]

thx

.close

[cedar kiln]

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[half quest]

Basic mathematical proof question I think but proof isn't my strong suit

[latent current]

How can you express the area of the bigger square in two ways?

[half quest]

2(a+b) ?

[latent current]

(a+b)^2

And also as the sum of 4 blue triangles and the small white square

[half quest]

Oh yeah that makes sense

[cedar kiln]

@half quest Has your question been resolved?

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

[fickle sorrel]

need help to learn these two problems before my exam

[fickle sorrel]

the first one is prime factorization the second is GCMF i believe the third one is graphing rational functions

[hexed cloak]

ok

[fickle sorrel]

you can help?

[hexed cloak]

what do you mean first one is prime factorization

like you can't factor primes?

bruh

[fickle sorrel]

i think im going to use prime factorization on it cause this the reference sheet the teacher gave me

[hexed cloak]

I mean like are you having problems with prime factoring?

[fickle sorrel]

yeah i’d like a refresher havent done it inna bit

[hexed cloak]

@fickle sorrel the little tricks like Magic cross all of them are weird, just use middle split or quadratic formula

[fickle sorrel]

magic cross? wdym

[hexed cloak]

that cross thing drawn on the page

nvm

Imma go

[fickle sorrel]

oh

can someone else help me?

[candid mason]

So how do you expand (x-a)(x-b)

[fickle sorrel]

i dont know what that is

[candid mason]

You have studied algebra correct

[fickle sorrel]

this problem?

a little

[candid mason]

x is a variable and a, b are some unknown constants we are trying to determine

So how do you expand (x-a)(x-b)

[fickle sorrel]

which problem is this for

[candid mason]

The problem you are working on

[fickle sorrel]

number 8?

[candid mason]

You don't actually need the prime factorisation but it always good to know

Q10

I don't know what you want to do in Q8

[fickle sorrel]

hmm

[candid mason]

Do you want the prime factorisation of 22?

[fickle sorrel]

is this right?

[candid mason]

Yes you can write it like that. I would keep it has it is as the notation is more compact

There should be negative sign

[fickle sorrel]

oh yeah

ok done

can i do one more thing

[candid mason]

yep

[fickle sorrel]

number 10. the other one ignore it my teacher will help ke

[candid mason]

So how do you expand (x-a)(x-b)

Oh wait maybe that is not what your teacher wants

[opaque root]

No

[fickle sorrel]

(4x-40)(4x+100)

idk

[candid mason]

Just do it the same way as Q8

[fickle sorrel]

no dude

[opaque root]

You have 4x^2-40x+100

Rigjt?

[fickle sorrel]

factoring polynomails

[opaque root]

Factor out 4 first

Do you know how to do that?

[fickle sorrel]

no i do not

subtract it?

[opaque root]

4(x^2-10x+25)

Like this

Do you see why?

[fickle sorrel]

i dont see why i do that

[opaque root]

4 multiplies everything inside parentheses

Exactly

Now factor the inside parenthesis

[fickle sorrel]

but how do i know when i need to do that

what is this gcmf or difference of two squares

[opaque root]

Because you see the common factor

Of 4x^2-40x+100 is 4

Now

With the inside

U factor it easily

[fickle sorrel]

how do i know when i need to do that

[opaque root]

As (x-5)^2

[candid mason]

Experience and practice

[opaque root]

You look for the hcf

And factor out whenevr u can

Also have in mind that

You don’t “have” to do this

It depends on what you wanna achieve

[fickle sorrel]

whats the difference between gcf and hcf

[candid mason]

same thing

[fickle sorrel]

wait guys sorry

[opaque root]

Is the same

[fickle sorrel]

i gotta go

how do i close the chatroom

[candid mason]

type .close

[fickle sorrel]

.close

[cedar kiln]

Channel closed

Closed by @fickle sorrel

Use .reopen if this was a mistake.

[cedar kiln]

Available help channel!

Send your question here to claim the channel.

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

[river topaz]

how do we solve this?

[half bloom]

This is part of circle theorems

I think you have to combine a load of these rules

[tepid blade]

First of all, find aed, we have acd

[river topaz]

aed is 115

i mean 105

[tepid blade]

Yeah so z plus aeb is 105

Now if we see, Chord ab subtends angle AEB

And it also subtends angle y

[river topaz]

so y = x = w?

[tepid blade]

How did you get y = x?

[river topaz]

you said itsubtends angle y

[tepid blade]

Yeah so y = aeb

[river topaz]

ah

yea

[tepid blade]

So from here we got y + z = 105

[river topaz]

alright

[tepid blade]

Now angle bed and edc, are supplementary

So z + y + eda + bdc = 180

But z + y = 105, so eda + bdc ?

[river topaz]

i do not know

35?

no

idk

[tepid blade]

Put the value of z + y in this

[river topaz]

105 + eda + bdc

two variables

are they equal??

[tepid blade]

No, find their sum

[river topaz]

dude

hold on

what do you mean supplementary

im so confused

[tepid blade]

=180

[river topaz]

how is bed

bed and eda?

[tepid blade]

Yeah I mean same side of transversal

Look at the parallel lines

[river topaz]

Ah.

sothey add up to 180

eda + bdc = 180

[tepid blade]

Yeah

No, eda + bdc + 105 = 180

[river topaz]

how

OHHH

I GOT IT

alright i got that part

i still dont know how to solve eda + bdc + 105 = 180

i feel like it sreally obvious and im stpid

[tepid blade]

Ok

eda + bdc = 75

We don’t need their separate values

[river topaz]

alright

yea

[river topaz]

eda + bdc = 75

OH WAIT

• 45

[tepid blade]

So now see that 20 + eda + y + bdc + 25 = 180

[river topaz]

115

Y = 180-115

Y IS 67

65

[tepid blade]

120

[river topaz]

75 + 65 + z = 180

wha

45 + 75

oh yea