help-10

[royal basin]

i mean ok that doesnt answer my question but whatever

$F(1) = 0 + 1 + 3x \cdot 0 = 1 \ F(x) = 1 + 2 + 3x \cdot 0 = 3 \ F(x^2) = 2x + 4 + 3x \cdot 2 = 8 + 4x \ F(x^3) = 3x^2 + 8 + 3x \cdot 6x = 8 + 21x^2$

[warm shale]

Ann

[royal basin]

here are the calculations

[cedar bluff]

ya that's exactly what she did

[royal basin]

your answer is unambiguously correct

[cedar bluff]

just a second. Let me find that video and I will share a screenshot

[royal basin]

your teacher's answer is only correct if we write coordinate vectors as rows, and even then you'd have to cut off that column of zeros from her matrix.

[junior inlet]

well, she probably meant that it would have the term x^3 = 0
but it's still a bit weird, since you're asked to map it to P_{<=2}

[cedar bluff]

One second

[royal basin]

this makes no sense lmao

her notation cannot represent $(x^3, 1, 0, 0)^T$

[warm shale]

Ann

[royal basin]

like, that's not a linear combination of her e_0, e_1, e_2 and e_3

[cedar bluff]

Also, a few days back you answered my question @royal basin where you told a11=0, a21 = -1, a12 = 1 and 0 is wrong

And the answer is transpose of this matrix

But this is exactly what this teacher has done

[royal basin]

yeah again this "standard basis in matrix notation" is bullshit

she seems to think that $F\pmqty{x\y\z} = \pmqty{x'\y'\z'}$ means $F(x)=x', F(y)=y', F(z)=z'$

[warm shale]

Ann

[royal basin]

which it does not

[cedar bluff]

Also, if correct answer to the first question in this help chat is $$A = \begin{pmatrix} 1 & 3 & 4 & 8 \ 0 & 0 & 8 & 0 \ 0 & 0 & 0 & 21 \end{pmatrix}_{3\times 4}$$, then is this the correct way to write the whole equation?

$$\begin{pmatrix} 1 & 3 & 4 & 8 \ 0 & 0 & 8 & 0 \ 0 & 0 & 0 & 21 \end{pmatrix}{3\times 4} \begin{pmatrix} 1\ 1 \ 1 \ 1 \end{pmatrix}{4\times 1}=\begin{pmatrix} 16 \ 8\ 21 \end{pmatrix}_{3\times 1}$$

[royal basin]

\\

[cedar bluff]

omg!

[royal basin]

anyway, if you insist on putting dimension subscripts on every matrix, then yes

[warm shale]

Aarjav
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[cedar bluff]

Now my question is we are kind of mapping (1, 1, 1, 1)^T to (16, 8, 21)^T right?

[royal basin]

yes, (1,1,1,1)^T gets mapped to (16,8,21)^T by your transformation

your teacher seems to have gotten herself mixed up in notation and passing on the confusion to you

[cedar bluff]

Alright. Thank you so much! I was so confused because of what she was doing and what was written all over the internet was so different.

.close

[obtuse pebble]

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[median wind]

does anyone know this?

[obtuse pebble]

@median wind Has your question been resolved?

[junior inlet]

iq test questions aren't really math, but anyways....

4. rotation. look at the columns.
5. there are many patterns. look at all of them.

[median wind]

so what would 4 be?

[junior inlet]

figure it out by yourself

we can't tell you the answers

[median wind]

d?

[obtuse pebble]

@median wind Has your question been resolved?

[timid silo]

its all about iq

bro

if you want help

we need to tell answer

[obtuse pebble]

@median wind Has your question been resolved?

[median wind]

Yes please

[timid silo]

5. c

4.idk

[twilit loom]

uh. don't think that's right...

[median wind]

I also got C why is it wrong

[twilit loom]

check the direction of the curved line joining the two circles

[obtuse pebble]

@median wind Has your question been resolved?

[hot sonnet]

I don't think 5. C is correct either, it should be 5. A

[obtuse pebble]

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[rich fiber]

Been trying to solve this problem yet no luck 12th grade methods would be appreciated
$$lim ( \frac{e^{2-lnx}-e }{1-lnx})
while x \longrightarrow e$$

[warm shale]

nassim

nassim

[rich fiber]

Was able to get this far but not sure how to continue
$$lim ( \frac{e^{2}-e ^{Z+1} }{e^{Z} -Ze^{Z} })
While Z \longrightarrow 1$$

[warm shale]

nassim

[tame valley]

Use L'Hopitals rule

[rich fiber]

Not an accepted method in 12th grade unfortunately

[obtuse pebble]

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[obtuse pebble]

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[dire tartan]

do i just differentiate this then sub the numbers or should i just sub the numbers ?

[karmic cedar]

I don't see any reason for differentiating

[obtuse pebble]

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[dire tartan]

.reopen

[obtuse pebble]

✅

[obtuse pebble]

@dire tartan Has your question been resolved?

[obtuse pebble]

@dire tartan Has your question been resolved?

[obtuse pebble]

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[woeful musk]

I think i got it right but Idk

I think its right bc 7^2 so when its squared it multiplied by 2 so 7x2=14

[spiral maple]

Looks like you just added the 2 measurements.

instead of finding the area.

[spiral maple]

this is also bullshit

$7^2\neq 7\cdot 2$

[warm shale]

Mosh

[woeful musk]

The area is 10 but 10 isnt answer

[spiral maple]

the area isn't 10.

cause 5.75 != 5 and 2.125 != 2

[woeful musk]

Im not dealing with decimals

They are fractions

[spiral maple]

You do realize fractions and decimals represent the same thing... numbers right?

[woeful musk]

I know that

[spiral maple]

So that's irrelevant...

anyway

What's area of a rectangle in general?

[woeful musk]

LxW

[spiral maple]

yes

so... do that with those lengths

[woeful musk]

So do i mutiply or add

bc i multiplied

[spiral maple]

You didnt multiply

you added

[spiral maple]

And.... you just wrote the formula

[woeful musk]

7x2 is 14 right

[spiral maple]

Yes... that's irrelevant though

[woeful musk]

Oh so i multiply

[spiral maple]

yes....

cause the formula... has * not +

[woeful musk]

so just 5 3/4 x 2 1/8

[spiral maple]

yes.

[woeful musk]

oh i get it

[spiral maple]

Ok

[woeful musk]

CAn i turn it into a mixed number first

[spiral maple]

They're already mixed numbers..

[woeful musk]

Nvrmind i forgot what the other thing is called

[spiral maple]

improper fractions

[woeful musk]

Yess

i was about to say that

Well can I turn it into a improper fraction

@spiral maple

[spiral maple]

yes...

[woeful musk]

Ok

[spiral maple]

Idk why you wouldn't be allowed to make them into improper fractions..

[woeful musk]

Then you take the improper fraction and multiply it by each other

[spiral maple]

yes.

[woeful musk]

ok

This is the right answer, right?

@spiral maple

[spiral maple]

yes.

[woeful musk]

oh thxs

.close

[obtuse pebble]

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[prisma shell]

how to i open a help

[prisma shell]

.close

[obtuse pebble]

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[grand rapids]

bit stuck on how to start with this one, can someone guide me in the right direction?

[grand rapids]

so obviously mu=p and var=p(1-p), but how could i turn this into the normal distribution curve that im supposed to get

[obtuse pebble]

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[sterile spire]

Hey can someone explain how to find the derivative without having to use a graph for a ration function with a quadratic in it

[sterile spire]

for example 4x over x^2+x+2

[spiral maple]

quotient rule..

[sterile spire]

ik

but our teacher only taught us for linear rational functions

[spiral maple]

Why are you using a graph to do derivatives 🤨

[sterile spire]

and the formula online is a little confusing

bruhhh

i meant a table

sorry

[spiral maple]

So approximating the slope of a tangent line?

[sterile spire]

we do these charts which are rlly annoying

ya

[spiral maple]

same thing as any other table you did then...

just... a different function

[sterile spire]

no but the reason i want to know this way

is so when im writing a test

im able to quickly double check my work

like a verification method

[spiral maple]

go through the algebra/calculator work again tbh

or just draw a rough sketch of it

[sterile spire]

its way more accurate and dependable

if it is difficult to do at this level then i understand

but looking at the formula theres just a few things i dont understand

[spiral maple]

I mean... learn the actual calculus rules and then check with a calculator what the slope is suppose to be

then see if it matches to within enough precision

[sterile spire]

.close

[obtuse pebble]

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[crisp depot]

I was watching a video about group theory and came up with a question... could every action in a group be called a generator? and is there a group that is the same as the generators?

[crisp depot]

If it helps here is the video I was watching... https://youtu.be/vzEObOzsSKY

Also can you @crisp depot me if you have the answer?... Sorry, but I am going to continue watching the videos in another tab.

.close

[obtuse pebble]

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[pine ermine]

in this expression, can i just use FOIL to simplify it or is there another way to do so?

[pine ermine]

oops nvm cause the square roots will just cancel out and result in a whole number, sorry

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[tender leaf]

Stupid question, can anyone give me a $(k-1)$-degree polynomial that bounds $f(x)=\frac{x^k}{x-n}$ above for $x>n$. And I need to be able to easily prove it bounds $f(x)$ above.

[warm shale]

Isaiah

[obtuse pebble]

@tender leaf Has your question been resolved?

[astral ivy]

What does it mean for a function to bound another function

[obtuse pebble]

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[shadow trellis]

why’s this incorrect?

[obtuse pebble]

@shadow trellis Has your question been resolved?

[noble shard]

Hi

Can anyone explain me?

This q?

[obtuse pebble]

@shadow trellis Has your question been resolved?

[slim leaf]

@shadow trellis Second line, when taking the limit, you didn't take the limit of the denominator

Taking limit on the numerator indeed gives 1 + 2 + 3 ....

but on the denominator, it's n^2

and so it goes to 0

[shadow trellis]

Makes sense, but the solution writes the general term for the numerator terms and works from there to get 1/6

[obtuse summit]

Hi

Can someone please hep

Help

Oops sorry diddnt see this occupred

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[obsidian isle]

you already asked this in the other channel

[obtuse pebble]

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[thick viper]

algebra 1: system of equations

i dont understand

[forest sinew]

a lot of info 👀

[thick viper]

yes ik

thats why im lost

im the best in my class and even i cant understand

[forest sinew]

lets try to unpack

so two classes of students

[thick viper]

mhm

[forest sinew]

were putting all these students into either vans or busses

[thick viper]

ya

[forest sinew]

one class, they used 8 vans and 8 busses, for 240 students

and the other used 4 vans and 1 bus for 54 students

[thick viper]

ye

[forest sinew]

have you done these kinds of problems before?

[thick viper]

in class we did one

but that was wayyy easier

[wide drift]

take students can be filled in bus as X and in vans as Y
u get 2 linear equtions and 2 variable

[forest sinew]

yea

the next step would be to decide variables

i guess define is a better word

you want to build two things that are like

(number)(variable 1) + (number)(variable 2) = number

AKA standard form of a line

[thick viper]

ohh i get it

so two equations?

[forest sinew]

yea

you find two variables that link the two problems

err, cases

or whatever you wanna think about it as

really theyre problems, right?

like say they gave you info about only one of those classes

say the one thats 8 vans, 8 busses, 240 students

if you were GIVEN the amount of students in the busses, you could determine the amount of students in a van

but you couldnt figure out both

classic function in a 2d plane behavior; one independent and one dependent variable

you get to pick x, the function tells you y

from the problem, you build two of these, and every point along each line is a solution to its own sub-problem, AKA a point where they could be true

so if they intersect thats the only place where they both can be true

[thick viper]

ya

[forest sinew]

so idk we can walk through it if you want

or if you wanna try it and see if you get stuck

[thick viper]

i think we should walk through this one

and then ill try the rest on my own

[forest sinew]

okay

so lets just assume like

well we dont have to, they tell us

every van and every bus has the same number of students

this is a huge hint that you want to use these as your variables

since it so strongly links the two classes

so well call X to be the number of students in each van

and Y to be the number of students in each bus

I can give you one equation, from class B: 4X+1Y=54

can you tell what the equation from A is?

[thick viper]

8X+8Y=240

[forest sinew]

yea

how are you with lines? you have some choices here

[thick viper]

ohhh yeah

i remember

[forest sinew]

but if youre strong with lines this problem can be boiled into intersection of two lines

[thick viper]

ok so

4X+1Y=54
8X+8Y=240

since 1Y = y

we can use that

y = -4x + 54

[forest sinew]

first one is plus, not minus, in case thats not a typo

[thick viper]

ohhhh

yeah

[forest sinew]

but on the right track in general i think

[thick viper]

so now

8x + 8(-4x + 54) = 240

8x + -32x + 432 = 240

[carmine bear]

For this problem i think it's faster if you start by eliminating one of the variables (either y or x) instead of rearranging for y and then subbing it back into the first equation (you'll get the right answer but i think it will take longer)

[thick viper]

oh

how do i do that

[carmine bear]

so you have your 2 equations:
8x + 8y = 240
4x + y = 54

[thick viper]

no

[forest sinew]

54

[thick viper]

54

[carmine bear]

sorry

i skipped ahead

anyway

you need to make one of the coefficients (the number before x or y) equal in both equations

[thick viper]

ohhhhh

yeahhh i remember that way

[carmine bear]

so you can either do
8x + 8y = 240 and 8x + 2y = 108 (multiply everything by 2 in the second equation)

[thick viper]

so its 22

y = 22

[forest sinew]

6y=240-108

[carmine bear]

yep

[thick viper]

so is the final answer

wait gimme a sec

[vale pier]

interesting

[thick viper]

(8, 22)

[forest sinew]

yea if youre comfortable with what are basically row operations

it makes your life very easy

[thick viper]

yes very

[carmine bear]

yep

[thick viper]

bro thank you all so much

[forest sinew]

there are even faster ways

[thick viper]

you've saved me so many brain cells

[forest sinew]

[thick viper]

pls tell me

pls

[carmine bear]

you'll know you're right if both the lines (8x+8y = 240 and 4x + y = 54) intersect at (8,22)

[forest sinew]

i mean its just stuff youll learn either in precalc or linear algebra

[vale pier]

so a bunch of students became co-ordinate points?

[thick viper]

pls teach me now

[thick viper]

LOL YA

fun fact shes my classmate

[vale pier]

hii

[thick viper]

yea anyways

are yall gone

well my answer was solved sooo

.close

[forest sinew]

im finding a link

[obtuse pebble]

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[vale pier]

im reading

[thick viper]

oh not

.reopen

[obtuse pebble]

✅

[forest sinew]

https://pressbooks.bccampus.ca/algebraintermediate/chapter/solve-systems-of-equations-using-determinants/

this will jump you ahead probably

[thick viper]

k

[forest sinew]

quite a bit in your material

well or maybe not

[vale pier]

tysm

[thick viper]

thank you so much dude

[forest sinew]

i didnt see this until college

i bet if you use this your teacher will be upset

but it is cool

[vale pier]

ok nvm-

[forest sinew]

[thick viper]

LOLLL

[thick viper]

LMFAO

[vale pier]

sounds horrifying

[forest sinew]

it is a bummer when the rare something makes sense and you have to pretend it doesnt just to keep pace with other people

[carmine bear]

ikr

[vale pier]

yes

[thick viper]

dude

wow

i could never put that into words

[forest sinew]

https://www.youtube.com/watch?v=JMjuaMY5BsQ&feature=emb_title&ab_channel=MichelvanBiezen

heres an example of that

if you wanna see

[thick viper]

k

well thank yall so much

[forest sinew]

ye np

[thick viper]

ima be studying that way

[forest sinew]

[thick viper]

.close

[obtuse pebble]

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[thick viper]

is there a way to thank in this server

[vale pier]

pray

[thick viper]

is there any like helper leaderboard thing

[forest sinew]

some people boost but you dont have to

we already have so many

we mostly just do it for fun

[vale pier]

i like that emoji

[timid silo]

Can someone plz help me

[forest sinew]

start a new channel

this one is gonna lock

[timid silo]

k

[thick viper]

how do you do that

like how do you start a new channel

[forest sinew]

use an open channel

[thick viper]

ohh ok

got it thanks

[forest sinew]

oh, one more

https://www.youtube.com/watch?v=jBsC34PxzoM&t=218s&ab_channel=3Blue1Brown

if you never seen 3b1b

u should

👀

okay ill stop

[thick viper]

dude nah you dont have to stop its ight

thanks for the extra help dude

[carmine bear]

can't lie these are actually pretty interesting for me given that ill probably be studying these next year or the year after

[obtuse pebble]

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[ruby belfry]

anyone know how it got the thing i highlighted? I dont know where it came from

[ruby belfry]

.close

[obtuse pebble]

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[obtuse pebble]

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[mild ocean]

@leaden pulsar gotta close this channel

[ionic violet]

Pretty sure they left.

[mild ocean]

nope they got banned

[obtuse pebble]

@leaden pulsar Has your question been resolved?

[upbeat plinth]

.close

[obtuse pebble]

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[livid nova]

help I forgot how to do this

[obtuse pebble]

@livid nova Has your question been resolved?

[livid nova]

...

<@&286206848099549185>

[hidden gyro]

b is the intersection of line and y-axis, m is the slope that is (increase in y) divides (increase in x)

[livid nova]

Is that how to get the linear equation from the graph cuz I don’t remember…

[obtuse pebble]

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[glad heart]

Help please

[timid silo]

Can you state the definition of slope?

[glad heart]

slope numerical measure of a line's inclination relative to the horizontal

[spiral maple]

what's the definition that's actually useful?

[obtuse pebble]

@glad heart Has your question been resolved?

[obtuse pebble]

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[haughty stratus]

if im factorising a number sentence, can i individually factorise bits of it? (example)

ab-bc-ac

= b(a-c) - ac

[obtuse pebble]

@haughty stratus Has your question been resolved?

[wanton dagger]

Yes

[simple siren]

Nvm I thought it's yours

[haughty stratus]

so yes

[obtuse pebble]

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[dusk nexus]

can anyone help me with this?

[dusk nexus]

apparently the answer is (d), but i dont see why

wouldn't the force decrease since he's pulling less rope so t requires less force to pull it up as he pulls more and more rope?

[spiral maple]

As the rope straightens out (horizontally), more of the gravity will affect vertically

[dusk nexus]

hmm

so

[spiral maple]

wait sorry, give me a sec

[dusk nexus]

as it straightens out, he needs to put more force in to counteract the increased amount of gravity affecting the rope?

ah ok

[spiral maple]

yes

the higher the bag goes, the bag will gain more potential energy, ie the bag will "want to fall more" the higher it goes

thus you need to apply more force to counteract the increase in gravity

your force is acting more horizontally with a tiny portion acting vertically

(think of an angle of like 1 degree)

your force F requires that Fsin(1 degree)=mg (which we assume to be constant)

[dusk nexus]

mhm

[spiral maple]

one sec let me draw what I mean

[dusk nexus]

alright

[spiral maple]

as you pull the bag up, theta will decrease causing sin(theta) to decrease

however we assume mg is constant, that means F must increase to counteract the angle decreasing

[dusk nexus]

ohhh

that makes sense

and im assuming the rope must have a sag in it since sin0=0

[spiral maple]

yep

[dusk nexus]

and mg cannot be 0

[spiral maple]

if theta were 0, then the object would have no mass

which is of course false

[dusk nexus]

right

thank you so much

[spiral maple]

(or it wouldn't be accelerating, but that's also false)

[dusk nexus]

makes sense now

.close

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[spiral maple]

[mild ocean]

mosh desk reveal

[obtuse pebble]

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[devout nova]

Hey guys I'm not an accountant or anything but a really need help from some experts. I'm having some money problems with my roommate and he keeps telling me that he is wrigth and I'm wrong so I decided to look for help from a neutral third party. The story goes as follows. Me and my roommate bought a TV for a a new house we where going to move to. I now have to move out because I got a job in another state so I decide to buy his half of the tv so I could take it with me. He agreed. So I gave him the half of the money he paid the day we got it. Now he wants to keep the tv and he wants to give me my half of the money back and take the tv. I said to him that he has to give me the total of what we paid because I already bought his half. Is he right or am I right???

[junior inlet]

you're clearly wrong

well

let's say that the tv costs $2 (really cheap for a tv, but it's okay for our example)

so he will pay $1 and you will also pay $1

now when he takes the tv, he should have to pay $2

but he already paid $1

so he just needs to pay $1 more

for you, however, you shouldn't have to pay anything because you're not going to use the tv

so you should receive $1

therefore, he should just pay you $1

which is half the price

[short spruce]

what

no

you are right, your roommate is wrong

[junior inlet]

😐

[short spruce]

if you paid for half the tv originally, then paid for his half as well, he needs to give you full price

[junior inlet]

he didn't pay for his roommate's half?

[short spruce]

"...so I decide to buy his half of the tv so I could take it with me. He agreed. So I gave him the half of the money he paid the day we got it"

[devout nova]

Thank youuuuu!!!

[junior inlet]

So I **gave him the half of the money he paid **the day we got it

[short spruce]

yes.... he paid for half originally, then gave his roommate the other half of the payment...

so he essentially paid for the entire tv

[devout nova]

I paid 1$ to the store and later on I paid 1$ to him (the half he paid in the store with me)

[junior inlet]

oh, if that's the case, you're right

he should give you the entire price of the tv then

[devout nova]

Thank youuuuuuuuu for understanding me

It feels soo good for someone to finally understand

I dont even want the money anymore all I want is to be understanded

@short spruce @junior inlet THANK YOUU GUYS. I know we are never going to meet again but be assured you just gave me peace...

.close

[obtuse pebble]

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[inland matrix]

Should i use arrow instead of an equal sign

because something cant equal an indeterminant form?

[scenic sundial]

is this from a problem?

[inland matrix]

yea

just want to make sure on the notation

[obtuse pebble]

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[timid silo]

Does an increase in acidity from pH 4.7 to
pH 2.3 result in the same change in hydrogen
ion concentration as a decrease in alkalinity
from 12.5 to 10.1? Explain.

[timid silo]

how can i set up the equation for just the comparison of one of those sets?

im mainly confused on setting the ratio and if the exponent is positive or negative

with logs

[astral ivy]

@timid silo what’s the relationship between pH and H+ concentration

[timid silo]

ph=-log[H+]

[astral ivy]

Does the “decrease in alkalinity” part matter

[timid silo]

idek

this what the textbook soln did

[astral ivy]

Here look

[timid silo]

but i dont c y its positive

shouldnt is be a negative exponent

[astral ivy]

Hm

[astral ivy]

Yeah but I think they removed it

Lile

Look

10^-a / 10^-b = 10^b / 10^a

[timid silo]

how do i know which goes above?

[astral ivy]

Oh I see why this is confusing

The bigger number goes on top

[timid silo]

ohhh

yeah

i get it now

[astral ivy]

Hold up

Nvm nvm

Realize that 10^-2.3 is in fact larger than 10^-4.7

[timid silo]

yeah

ik

yeah so bigger number starts at the top

[astral ivy]

Yeah that’s confusing haha

[timid silo]

💀

[astral ivy]

Yeah because like

[timid silo]

lol tysm bro

i got it frm here

thx

.close

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[astral ivy]

Nice

I almost feel like I’m more confused than you

[obtuse pebble]

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[mint patio]

im so confuse on how to solve

[mint patio]

lemme find hte name of the unit

[astral ivy]

Ok

[mint patio]

creating systems with linear equations

does anybody know how to do that

[astral ivy]

I mean

[uncut robin]

ask your question

[astral ivy]

Kind of vague

Do you have an example

[mint patio]

yes

[astral ivy]

Send

[mint patio]

i know how to solve it regular just not with a system of equations

i dont even know where to start tbh

or how to start

[unborn valley]

you have to devlop 2 equation

and equate them

Let "x" be amount of months since you have to find it

[sonic bough]

then 150+35x=60x

[mint patio]

oh

then do i just solve

after i create that first equation how do i create the second

[warm shale]

Thunder7

Thunder7

[uncut robin]

your two equations

[mint patio]

oh

[empty sleet]

i miss the rage

[obtuse pebble]

@mint patio Has your question been resolved?

[deft hazel]

If you're done close the channel

[obtuse pebble]

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[errant sinew]

hello, few days ago i got interested in a topic called vector valued functions and though it is not in the scope of my curriculum yet (i still havent finished my precalc course) i was wondering if it is possible to differentiate such functions?

[errant sinew]

i took an initiative and defined the gradient of some point A on a function f(x) as this:

i tried differentiating ->F(x) and heres how i did it:

i arrived at <1, 3x^2> but i am not sure what this is implying? i dont even know if my method of differentiating it is correct

i recognize the 3x^2 as the derivative of x^3 but as a column vector its hard for me to think what it might be

[obtuse pebble]

@errant sinew Has your question been resolved?

[obtuse pebble]

@errant sinew Has your question been resolved?

[obtuse pebble]

@errant sinew Has your question been resolved?

[obtuse pebble]

@errant sinew Has your question been resolved?

[fresh peak]

your vector function

$\vec{F}(x)$

[warm shale]

Fede Bosio

[fresh peak]

is a parametric curve

and what you call "gradient"

is the velocity that a particle on that curve has

it's a vector that is always tangent to the trajectory the curve describes

You can think of x as time

(I suggest you to call it t like everyone else does)

so

in your case

$\vec{F}(x) = x m + x^3 n$

[warm shale]

Fede Bosio

[fresh peak]

is the position of a point on a cubic curve with respect to time

in physics, that's written like this

$ \vec{r}(t) = x \hat{\imath} + x^3 \hat{\jmath} $

Is it me, or @warm shale has just broken?

Whatever

r(t) = t i + _t_³ j

and the velocity is

v(t) = r'(t) = i + 3 t² j

@errant sinew Is it clear for you? If it is, close this question so others can use it to ask.

[obtuse pebble]

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[timid silo]

I have to make a general formula for this problem, and I am really stuck with it.

Please help!

[obtuse pebble]

@timid silo Has your question been resolved?

[royal basin]

@timid silo general formula? as in, you are tasked with solving this same problem for a revolver with n chambers?

[timid silo]

yes

I think

[royal basin]

you think?

[timid silo]

Well I know

[royal basin]

so there is uncertainty in what it is you're actually instructed to do?

[timid silo]

No there is none, I was just trying to be polite.

I'm sorry

[royal basin]

you tried to be polite but all you achieved is that now i am suspicious of your words

[timid silo]

what words

[royal basin]

"make a general formula"

i don't know for sure what your teacher wants from you

[timid silo]

it is

Actually I will ask them rn

Hold on

[timid silo]

This is a possibility

And I confirmed it with them just now

So you don't need to doubt my words anymore 🙂

[royal basin]

okay

fine

so have you solved the particular case with n=6?

[timid silo]

no

Tbh I am quite lost with this question

I just know

there is a probability of 1/5 if he rotates the gun

and a probability of 1/6 if he spins it

[royal basin]

and how do you know that?

[timid silo]

so Bond should ask him to rotate the gun one chamber

[royal basin]

...

"rotate the gun one chamber"?

[timid silo]

Well

[royal basin]

do you mean fire immediately

bond's options are fire immediately or spin

[timid silo]

yes

if he fires immediately

the chance is 1/5

[royal basin]

so you have calculated the probabilities for n=6

[timid silo]

if he spins again the chance is 1/6

[royal basin]

which means you have contradicted yourself when you said that no you had not solved the case n=6

[timid silo]

apparently I have

[royal basin]

so why did you say no

[timid silo]

you seem to question my decisions instead of the problem

[royal basin]

im just confused lol

[timid silo]

sure

I guess for n chambers

You would have

if it fires immediately

1/n

and to spin 1/n+1

[royal basin]

missing parentheses

also aren't there still two bullets in the gun

why is the probability of death 1/6 if we spin

there are 2 bullets out of 6

so should it not be 2/6

or 2/n generally

if we spin

[timid silo]

yes it should

so 2/5 if it fires immediately

and 1/3 if it spins

[royal basin]

now hold on

'fire immediately' sounds like a different story

[timid silo]

you know what I mean

by fire immediately tho

I think

[royal basin]

no, i'm now questioning whether you have the right answer for that.

here are the possible configurations of the gun before the first shot:

X X _ _ _ _
X _ _ _ _ X
_ _ _ _ X X 
_ _ _ X X _
_ _ X X _ _
_ X X _ _ _

here the chambers' contents are listed in order (X = bullet) and the first chamber is the one whose contents are shot

the first shot was empty, so we know the configuration would have to have been one of these:

_ _ _ _ X X 
_ _ _ X X _
_ _ X X _ _
_ X X _ _ _

as the other two have a bullet fired. notice that the first shot would advance the contents of all chambers forward by 1, like this:

_ _ _ X X _
_ _ X X _ _
_ X X _ _ _
X X _ _ _ _

so we have 4 possible configurations and only one lethal

thus in the case n=6 we have that the probability of bond dying on the second shot is 1/4

[obtuse pebble]

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[obtuse pebble]

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[autumn lintel]

how do i get a function notation out of this?

[calm quail]

So you need functions that goes like this:
y=mx+n

m is slope here

[junior portal]

hey i wanna ask smthing

[autumn lintel]

oh okay so ill just find the slope and sub in the values to obtain a equation

right gotcha

[autumn lintel]

whats up

[autumn lintel]

wait but like ill get different slopes

so like which one do i take?

[calm quail]

yes, there are 3 different slopes and functions

This is why question has "a, b, c" in answer section

(-2,4) and (1,1) are together
(5,25) and (2,4) are together and so on

[autumn lintel]

wait when u said about having abc in the answer section its bcause theres 3 diff sub questions ... the question im asking is b so techincally i should only have one answer right?

sorry im just like wondering

[obtuse pebble]

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[obtuse pebble]

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[novel mica]

A person throws an object downwards from the top of a building. The building is 26.8 m high. The object hits the ground at the base of the building with a velocity of 28.2 m/s. Calculate how long it takes between the object being thrown and hitting the ground. Give your answer in SI units.

[novel mica]

I tried to use x = ((v0 + v)/2)t

With v = 28.2, v0 = 0, x = 26.8

Got 1.9 but it appears to be incorrect

[spiral maple]

v_0 isnt 0

you know displacement, final velocity, and acceleration.

[novel mica]

ohhhh so I need to use x = v0t + 1/2at^2?

because I don't know the final velocity?

[spiral maple]

you do know the final, I corrected myself.

[novel mica]

and I don't know initial?

[spiral maple]

nope.

[novel mica]

Which equation can I use? Since I'm trying to find time, now none of them seem to work

Ohhhh

Can I just use the velocity formula?

[spiral maple]

you can find initial velocity

[novel mica]

using this?

[spiral maple]

no clue what "the velocity formula" is

[novel mica]

velocity = distance/time

[spiral maple]

you dont know time.

nor the other velocity

$v_f^2=v_i^2+2a\Delta x$

[warm shale]

Mosh

[novel mica]

oohhhhhh i get it now
v^2 = v0t,.... yes

thank you!!

[obtuse pebble]

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[nova bane]

i have a question

[nova bane]

i want to participate in imo(international mathematics olympiad) but idk where to start what to read and aslo iam in 8th grade if i want to participate now does imo(international mathematics olympiad)take seperate contest for junior?

[unborn valley]

well you should ask in math discussion

not here

[nova bane]

oh ok

[unborn valley]

but which country are you from?

[nova bane]

thx tho

[nova bane]

bangladesh

[unborn valley]

close this one ask in math discussion

[nova bane]

ok

[obtuse pebble]

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[obtuse pebble]

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[obtuse pebble]

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[obtuse remnant]

would i need 2 equations for +6 and -6?

[alpine raven]

nah not really

if a quadratic function has two zero, you can write it as (x-x1)(x-x2)

x1 and x2 are obviously the zeros

[obtuse remnant]

would i leave it as + and - until i solve for a?

[obtuse pebble]

@obtuse remnant Has your question been resolved?

[alpine raven]

wdym ?

[obtuse pebble]

@obtuse remnant Has your question been resolved?

[obtuse remnant]

like what would i do here?

[upbeat island]

i would start with simplifying y = a (x - x1) (x - x2)
then plug in the point (-1, 20) later for finding a

btw x1 = -5 + √6 and x2 = -5 - √6
it seems like you split it up weird

[obtuse remnant]

they have 2 integers in them because of the +-sqrt6 right? if it was just a normal 6 would x1=-5 and x2=-6?

[upbeat island]

nope

the plus minus is a shortcut

if there were no root you would have x1 = -5 + 6 = 1 and x2 = -5 - 6 = -11

[obtuse remnant]

then where would i plug in the -1?

[upbeat island]

for x

you can do it whenever i guess, but you substitute (x, y) = (-1, 20)

[obtuse remnant]

so -1-5+6 and -1-5-6?

[upbeat island]

you have to distribute that negative in x - x1 and x - x2

so your first step would be

y = a (x - (-5 + √6)) (x - (-5 - √6))

[obtuse remnant]

this right?

[obtuse pebble]

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[haughty stratus]

if |x+1| + |x-3| = 8 what is x

[haughty stratus]

help please

[spiral maple]

do it by cases on when each abs value is +(stuff) or -(stuff)

[haughty stratus]

yeah i know its when x<-1, -1<_x<_3, x>3

but idk what else to do

[spiral maple]

well if x<-1, |x+1|=-(x+1) and |x-3|=-(x-3)

thus you get a linear equation in x.

[haughty stratus]

huh

[spiral maple]

huh

[dusk nexus]

okay so you know how |x| = x when x>=0 and -x when x<0

[haughty stratus]

oh then u just open it?

[haughty stratus]

yeah

[spiral maple]

expand the -'s, yes

then check if you get a solution that makes sense given the restriction

repeat for the other 2 cases.

[haughty stratus]

but if x = -1<_x<_3, then what would the linear equation be?

[spiral maple]

do what I did..

what sign will |x+1| have when getting rid of the abs value, likewise for |x-3|

[haughty stratus]

ohh

so itll be

(x+1)-(x-3)

right

[haughty stratus]

i dont think thats right^

[spiral maple]

that's right.

|x+1|=x+1 and |x-3|=-(x-3) on that interval

[haughty stratus]

but if you calc it

it equals

0=4

[spiral maple]

yes

hence no solution exists on [-1,3]

[haughty stratus]

ahh

makes sense

thanks for the help

[obtuse pebble]

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[fast light]

Can someone help me out with this

[fast light]

Differentiate u*dv/dx ?

[cedar lichen]

He's saying to find d(uv)/dx, which will equal some expression, then integrate both sides

[fast light]

oh, the uv on the right side

[cedar lichen]

No, just d(uv)/dx in a vacuum. We don't care about the formula in the question right now. We are going to come to it.

[fast light]

I get v(dv/dx) + (dv/dx)(u)

[cedar lichen]

It's v(du/dx) + (dv/dx)u, but I'll assume that's a typo

[fast light]

yeah it is

[cedar lichen]

Anyway, since we have d(uv)/dx = v(du/dx) + (dv/dx)u, try integrating both sides of this with respect to x

[fast light]

what does the right side become by intergrating?

[cedar lichen]

It doesn't become anything. There's no way to simplify it, so we just leave it as ∫ vu' dx + ∫ v'u dx (I've replaced du/dx with u' and the same for v)

[fast light]

And if I rearrange it, it becomes like the question after intergrating it

[cedar lichen]

Exactly

Bada bing bada boom

[fast light]

yay

[cedar lichen]

Don't forget the QED or the box thing for style points

[fast light]

QED?

[cedar lichen]

Mathematicians will often mark the end of proofs by either writing QED or by drawing a box. You dont have to do that, I was joking. QED stands for Quod erat demonstratum, which is latin for something like "haha epic proof complete"

[fast light]

Nice

thanks for the help

.close

[obtuse pebble]

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[serene dawn]

what's the fastest method to find the prime factors of REALLY big numbers? i've tried modulo and the 6+-1 rule

[cedar lichen]

An online calculator like wolframalpha or sumn will probably be the fastest way

[serene dawn]

i meant, what type of algorithm to do it myself

[obtuse pebble]

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[frank swallow]

for a limit problem where x -> 0 for the function sin(3x)/(2x) is it possible to just rewrite the function as 3/2(sin(x)/x)) and simplify to 3/2

[unborn valley]

the format is lim x->0 sinx/x=1

try converting it to sinx/x

[unborn valley]

you cannot write sin3x as 3sinx

[frank swallow]

yes I've done that but I was wondering if its legal to factor the 3/2 out and using sin(x)/x to get 1 and then 3/2 as an answer

[frank swallow]

ah so i cant take stuff out the numerator?

[unborn valley]

no,

but there is formula in some cases

[frank swallow]

can i factor stuff out the denominator? like the 2 in 2x

and write it as 1/2(lim x->0 sin(3x)/x)

cause i think i may know how to solve from there

[unborn valley]

yes you can

you have to basically follow rules of alegrba

[high lily]

you can't say that sin(3x)/(2x) = 3/2 * sin(x)/x
but you can say that
lim as x→inf sin(3x)/(2x) = lim as x→inf 3/2 * sin(x)/x

[frank swallow]

ah ok

[mild ocean]

you can just rewrite it as 1.5sin(3x)/(3x)

[frank swallow]

how so?

[unborn valley]

yes this is better, you directly get the needed format

[frank swallow]

i dont know if i have been taught that tbh

[mild ocean]

it’s just multiplying it by 1.5/1.5

[high lily]

its more or less the same application of the limit property for sin(x)/x

[frank swallow]

oh ok wait so i think i get it

so you can multiply the function to by 1.5/1.5 which is equal to one which will make the function 1.5(sin3x/3x) which is equal to 1.5*1

[mild ocean]

as a limit of x approaching 1 yes

[mild ocean]

but this makes no sense

[frank swallow]

dang i thought i got it

nvm then

[high lily]

you can't just not include limit in your explanation

[frank swallow]

alright im going to restart on my thought process using a way i learned in class

so the og problem is lim x -> 0 sin3x/2x so what i would do it take the 2 out and get 1/2 lim x -> 0 sin3x/x

yet now looking at it i dont know how to conitnue

[unborn valley]

i
mean you kind of got it

[frank swallow]

yeah cause at this point i believe you would do something where you sub in 3x with another varriable or something

i didnt understand that part of the lesson

[unborn valley]

yes make it equal to sin(3x)/3x

[frank swallow]

but how thats the part im confused on

how do i got from sin3x/x to sin3x/3x

[unborn valley]

multiply num and dim by 3?

[frank swallow]

but wouldnt multiplying 3 to the numerator give me sin9x?

[unborn valley]

no

[mild ocean]

no

3x is inside the sin

[frank swallow]

or is that what i multiply 1/2 by

[mild ocean]

why are you doing limits if you think this

[unborn valley]

do you know how trig functions work?

like the algebra

[frank swallow]

its very vauge since i took pre calc 1.5 years ago

[unborn valley]

n * sinx = nsinx

[mild ocean]

that’s not true either

[unborn valley]

gasp

basically 3* sin3x is 3sin3x

[frank swallow]

ok let me try again so once at 1/2 lim x -> sin3x/x i would multiply by 3/3 and get 3/2 lim x -> sin3x/3x and that would be 3/2? if this isnt it i dont know where my thinking is going

[unborn valley]

yes

[frank swallow]

alright thanks

[high lily]

missing a 0 after the arrow

[obtuse pebble]

@frank swallow Has your question been resolved?

[obtuse pebble]

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[autumn lintel]

how do i solve the following question

im lost

[obtuse pebble]

@autumn lintel Has your question been resolved?

[autumn lintel]

<@&286206848099549185>

[forest sinew]

did u find out when they start saving

that seems like a good first step

[autumn lintel]

@forest sinew how do i do that

[forest sinew]

well one is compounding

the other is linear

[autumn lintel]

does the above i write make sense or nah

compounding and linear ?

idk what that means

i mean i kinda know what compounding is but what do u mean by linear

[forest sinew]

the first scheme

its a linear increase

always by the same amount

the other one is 6%, so it depends on how much youre already making

[autumn lintel]

oh okay , so how do i transalate the linear one into a equation?

[forest sinew]

starting salary plus some number of years times the yearly increase, yea?

[autumn lintel]

idk im kinda confused rn

[forest sinew]

get rid of the 0.1

youre on the first part of the question, im guessing?

"find out who starts to save first"

[autumn lintel]

yeah

[forest sinew]

0.1 is part of the amount saved

you dont need that yet

[autumn lintel]

oh right right

sorry

[forest sinew]

youre good

they start saving when their salary reaches a certain amount

when it reaches that amount depends on the scheme

so you need to set the formula for their salary after n years equal to the amount where they start saving

and solve for the number of years

this will give you the answer to first part of the question

[autumn lintel]

so at this point scheme a takes faster

so now

[forest sinew]

this doesnt make sense

[autumn lintel]

oh

hmm

[forest sinew]

your second column

im thinking more like

[autumn lintel]

oh right

its suppose to be 1600 + 1600(0.06)

[forest sinew]

no

[autumn lintel]

oh

um

[forest sinew]

it compounds

so think like a compound interest formula

[autumn lintel]

oh ok

so this right ?

[forest sinew]

yea but we dont need something that complicated

try to suss it out like

here ill tell you

the salary after the first year

it goes up by 6%

so we take the base salary

1600