help-0

[royal crane]

sorry

[winter rock]

np,

[spark epoch]

go questions #serious-discussion

questions*

ill help if i can

[royal crane]

13a?

[winter rock]

@spark epoch thx

[royal crane]

and 23?

[alpine nacelle]

Just post what you need help with

[alpine nacelle]

A quadratic equation (which has roots) is a(x-r1)(x-r2) = 0 with r1 and r2 the roots

Take a = 1 or whatever a and you get one

[royal crane]

I keep getting this

how is that wrong?

[alpine nacelle]

Check the signs

It shoud be -sqrt(3)x

[royal crane]

ur right

omg im so dumb

wait

so its minus the sum of the roots?

or did i just add wrong

[alpine nacelle]

When your polynomial is ax²+bx+c, the sum of your roots is -b/a

[royal crane]

OOOO

i forgot the first negative

oops

what abt this one?

[alpine nacelle]

You need to find the coordinates of A and B

[royal crane]

how do i do that?

i forgot its been a while

[alpine nacelle]

-x²+9 = 2x²-3
4 = x²

[royal crane]

x^2=2

isnt that for straight lines not parabolas? or am i trippin?

[alpine nacelle]

x² = +-2

[royal crane]

right

[alpine nacelle]

That's the two possible abscissas

A has one, B the other

Then find their ordinates

And you'll get the length

[gray isle]

it's how you find intersections in general

the method isn't only for straight lines

[royal crane]

how do i find the absissa and ordinate again?

[alpine nacelle]

You mean, you want I rewrite what we did, or you mean the general case ?

[royal crane]

general case

[alpine nacelle]

If a point is a point of intersection between two curves, it means its coordinates satisfies both equations

So y = your first expression depending on x = your second one

[royal crane]

sorry, i completely forgot, what do i do after i get x=2,-2

[royal crane]

is this x=+_2? or x^2=+_2

[alpine nacelle]

$x = \pm 2$

[ocean seal]

Mélo

[alpine nacelle]

notation for that

let's say A has the smallest abscissa between both as it doesn't change the length, now you know that A(-2, y) and B(2, y')

[royal crane]

k...

[alpine nacelle]

and because they are on the curves, y = y' = 5 here

[royal crane]

what does y' mean? i mean like, the y with the '

[alpine nacelle]

because if the functions were different y and y' could be different

[gray isle]

don't use y' here. the notation is interpreted as something else

[royal crane]

o ok

[alpine nacelle]

oh

[gray isle]

use y_1 and y_2 to distinguish your two y values

[alpine nacelle]

ok

[royal crane]

I actually got it. ty @alpine nacelle

[charred dagger]

y=180-(4x+30)

8z-2=180-(8x-50)

[astral spoke]

thanks

[charred dagger]

All goof

*good

[stone jay]

4x+30 = 8x-50
x = 20

[astral spoke]

uh

[charred dagger]

Just form a whole bunch of equations and do simultaneous

[astral spoke]

that isnt right

and also

you did it wrong too

x would equal -20

with ur equation

and thats just gonna lead to a negative degree of an angle anywhere i would substitute that

[stone jay]

nah its right

[astral spoke]

na na

i don tthink it is

[charred dagger]

No you cant solve mine atm as i have 3 variables

[astral spoke]

hm

thats what i tried first

maby i was dumb and i just did it wrong

[charred dagger]

Emri i hate to break it to you but its wrong

[astral spoke]

hes wrong

or ur wrong?

[charred dagger]

No i've done these things a million times XD

[astral spoke]

HES RIGHT

i just did it myself

i accidentally put the equation on one side somehow

idk how i did that

somethings wrong with my brain

[charred dagger]

The first equations formed by corresponding angles then angles on a straight line

Ok all good 🙂

[stone jay]

wanna solve other part?

[astral spoke]

wait

yea

uh

[charred dagger]

Btw how do you get 4x + 30 = 8x - 50...

[astral spoke]

cus its like

alternate exterior angles i think

[astral spoke]

but when i try to solve z i cant do it

[charred dagger]

You dont know theyre parrallel...

Unless its in the question

[astral spoke]

wait

i added 2 to both sides and i got 82

instead of 72

tf is wrong with me???

[stone jay]

what grade question is this btw

[astral spoke]

well

its honors geometry in high school

it can be taken in more than one grade

freshman or sophmore year

[orchid python]

can anybody expain why in the third line its 2.d/dx(x)?

[stone jay]

i can but not in english lol

[astral spoke]

which language

[stone jay]

turkish

[astral spoke]

merhaba

[stone jay]

i dont speak english very well

[stone jay]

merhaba :D

[astral spoke]

or

do u say salam?

[stone jay]

selam actualy

[warped grotto]

They’re deriving 2x and removing the constant I think

[stone jay]

with an e

[astral spoke]

ok

[warped grotto]

And they haven’t simplified

[stone jay]

yes thats what i try to meant

[warped grotto]

👍

[wintry vortex]

for this rule, would only m be negative?

or would i distribute the negative?

[dense trail]

m=-3

so only m is negative

[wintry vortex]

ok ty!

[waxen lichen]

Hi can someone help me with these 2? I have to find the first 5 terms

[sonic wyvern]

whats going on here

ive looked this question up in multiple places and they're all solving it like me
where u = F/mg
and i use the x component of force, which is Fcos(theta)

[dense trail]

is the pulling force of 72N the horizontal component or just the entire force at the 32 degrees angle

[sonic wyvern]

it just says pulling with a force of 72N

at an angle of 32 deg

and its wrong even if i use 72 as my force

[dense trail]

well if 72 is already the horizontal force, then using F=ma, he should be walking at 72/60 m/s

otherwise, find the horizontal component using trig

72cos(32)/60

wait wat

[sonic wyvern]

?

speed doesnt matter

its only mentioned to clarify that this acceleration is 0

[dense trail]

wut this question makes no sense

[sonic wyvern]

y

[dense trail]

wait no dont worry

so yeah like you said accelration is 0

[sonic wyvern]

yes

so the force of the tension in the rope - the force of friction = 0

so F = u*mg

[dense trail]

this gets the accelration if friction does not exist

which is roughly 1.01765

[sonic wyvern]

thats F/m

not F/mg

[sonic wyvern]

based on this,

force of friction = u * n

where n is the normal force

n = mg

so force of friction = u*mg

[dense trail]

oh wait its asking for the coefficient

thought it said the force of friction

nvm

[summer dragon]

this stuff you guys are on look insane wtf

im literally trying to calculate the volume off a shape rn xd

like bro

[sonic wyvern]

just multiply..

[summer dragon]

this is the stuff im stuck on

so literally 1500 x 1000 x 200

?

[sonic wyvern]

yeah

[summer dragon]

maths is really not my strongpoint 😅

[dense trail]

wait is μ = f÷N the coefficient of friction

[sonic wyvern]

yes

and N = mg

thus u = F/mg

[dense trail]

ok

so we need to find f first then?

[sonic wyvern]

it told us he's pulling with 72N at 32 deg angle

i solve for x component of force with 72N * cos(32)

[dense trail]

mhm

[sonic wyvern]

its wrong

[dense trail]

why?

[sonic wyvern]

the website does not tell me why its wrong

[dense trail]

72N*cos(32) force of friction right

[sonic wyvern]

no

that gives you the x component of the tension in the rope

[summer dragon]

hope this kinda maths is allowed in here but could someone help me with this 😅

first one i got 300,000,000

what does the 3 mean? cubed?

[dense trail]

yeah

[summer dragon]

what does that represent?

[sonic wyvern]

cm *cm *cm

= cm^3

[dense trail]

this should also be 300,000,000cm^3

since its volume

area = cm^2
volume = cm^3

i mean it doesnt have to be cm, it could be any other unit

[summer dragon]

how do i work b out? my guess would be divide maybe?

im awful at maths but trying my best to improve a little 😅

[dense trail]

yeah divide

[summer dragon]

1000 by 300,000,000?

[dense trail]

300,000,000/1000

you are trying to find the number of 1litre cubes you can fit in the swimming pool

[dense trail]

what would be the frictional force then?

[sonic wyvern]

kinetic friction is u * n

[summer dragon]

ah i see, thanks for the help, sure that sortve stuff is super basic to you guys 🤣

[sonic wyvern]

where n = mg

[dense trail]

no im talking about F

Ff

[sonic wyvern]

the force of friction

is exactly what i just said

[wheat anchor]

@buoyant leaf

you there bro?

[dense trail]

Ff = u*mg??

[sonic wyvern]

yes

[dense trail]

then how do you find u

you need Ff to find u

[sonic wyvern]

because acceleration is zero

and the sum of forces in the x = mass * acceleration in the x

the sum of forces is tension - frictional force

so tension = frictional force

tension = u * n

tension = u * mg

u = tension/mg

[dense trail]

ok i dont get

[clever hare]

how do i do i find the x intercepts from a question like this

[dense trail]

f(x)=0

[clever hare]

so then i just solve for x?

[dense trail]

yea

[clever hare]

ah ok

wow i thought it would be harder lmao

[dense trail]

well x intercept is just when y=0

[toxic radish]

anyone got a clue how to do this?

How to do X-axis reflection?

and vertical stretch?

I have an idea of a vertical stretch by doing

g(x) = 3*(3^x) + 1

I also know the vertical translation, but which part would I have a negative sign on?

(The negative sign is for x-axis translation)

[placid zinc]

Reflecting vertically:
-3(3^x) + 1

@toxic radish

[dense trail]

so what was your answer

[sonic wyvern]

bro it shows my answer

its wrong

[dense trail]

huh

.1110483366

[toxic radish]

ty

so I would just add negative to everything right

[placid zinc]

Is that what I did?

[toxic radish]

just the -3

[orchid python]

can anybody help me with this

[toxic radish]

channel in use

[alpine sable]

Hey i have a question

[orchid python]

ok

[toxic radish]

try in like 3 mins

[alpine sable]

i dont know if its solvable

[toxic radish]

my problem should be cleared by then

[alpine sable]

Oh do i need to use a new channel?

[toxic radish]

So you only did a - sign for the vertical stretch, but why

so just the vertical stretch would be reflected?

[placid zinc]

Yes

[supple prairie]

The perimeter of a rectangular city park is 90 m, with an area of ​​450 m2. The long part of the garden will be planted with lilies every 1 m and the wide part will be planted with garden lights every 3 m. If the price of 1 lily seed is 2500, and the price of 1 garden lamp is 20,000, then the cost that needs to be spent is...
can someone help

[alpine sable]

please

[hard ether]

What does the dot thingy mean

In maths

[alpine sable]

everyone is dead

when doing calculus and encountering sinusoidal functions, when is it appropriate to use Euler's

[alpine sable]

help pls? :))

help please

[fast scaffold]

Believe it is a quadratic. This is simply a question of knowledge/terminology. Quadratics have greatest term x^2

It a=0, the x^2 term disappears, and is just a linear equation

*if

[alpine sable]

ty

[torn crescent]

help please

[quartz osprey]

why is the right side limit 5?

it ggoes from 6-3

6-1 5-2 4-3 3-4

[verbal cargo]

help, please

[shadow edge]

@quartz osprey Since the function is not continuous in x=3, you must evaluate from both sides of 3. If you approach from the left, it is 3 but if you approach from the right it is 5

[alpine sable]

who is able to help me understand hicksion and marshiallion demand? I am taking intermediate microeconomics

[quartz osprey]

ah i see

so if it were to stock at 3

it would be 3 right

[solemn phoenix]

I cant divide cause i skipped math class when i was grade 4 🤧

[shadow edge]

exactly cuz at x=3 the point is full.

[solemn phoenix]

I cant divide cause i skipped math class when i was grade 4 🤧

[tranquil tulip]

is there a faster way to do E instead of drawing a tree

[fast scaffold]

Ahh there's a formula

I think

This is just binomial probability

[tranquil tulip]

what is the formula?

[fast scaffold]

P(X=x) = p^x * (1-p)^n-x * (xCn)

Basically, a bit of an explanation

For n trials of a Bernoulli experiment (a trial with 2 results, success or failure), p is probability of success

x is the number of "successes", in this case heads

and xCn is the binomial coefficient

That's the idea at least

R u familiar with the xCn notation?

[tranquil tulip]

No i’m in geometry rn 😭

[fast scaffold]

Oof

[past prawn]

hi, can someone point me to the derivation of an infinite sum from k to infinity for k x a^k?

[fast scaffold]

Doesn't that diverge unless |a|<1?

[glass lichen]

yes

well it isnt geometric I dont think

[fast scaffold]

Yeah

and normally u start at 1

like k-=1

[topaz canopy]

I'm using the method of elimination but I cannot find my mistake

The outcome is wrong I just can't find my mistake

[reef shoal]

my dumbass forgor what we did in class and now i wanna kms i require assistance

ok so i know you gotta do some wacky shit in the first half

find the end by them gfiving you the midpoint and one of the two end points

[past prawn]

my bad, I made a few typos in that last question: k from 1 to infinity, for |a|<1

[reef shoal]

nvm im sayin all this shit wrong

[topaz canopy]

From home base to second base is 180 feet

From home base to pitching mound is 45 feet

To get to second base you need to run 90 feet to first base from home

And 90 more feet from fist to second

Which is 180 feet

To get to the pitching mound from home you need to run 3 tiles diagonally

And since 6 tiles is 90 feet

3 tiles is 45 feet

That's about it

[pulsar cloud]

I have to explain why we are using a monte carlo approach for permutation methods
Exact permutation methods are much more computationally expensive while only giving marginially more information about the true distribution. In other words often times the total number of permutations will be massive and computating it could be potentially intractable for example if we have 1000 objects and we want all permutations of size 10 we would need to calculate over 9 e 29. However, we can randomly generate and sample from the all the permutations relying on the law of large numbers. In other words, we would expect to draw more results from the permutations that are more likely from the true distribution on average thus creating a good approximate of the true distribution.
does that seem correct?

[ivory ivy]

im so confused

[orchid python]

hey

can anybody help me

[alpine sable]

Cant do 4,6,9 question im kinda stuck and due date is in like 4 hours so any help would be very appreciated

[topaz canopy]

Im pretty sure you just need to use a ruler, but that can only be done in person

so nobody in this server could help you unfortunatly

[alpine sable]

yeah but like wtf should i do tried watching a video but kinda confusing

helloooo

cann i askk

[quaint thistle]

anyone speak indonesia?

[alpine sable]

What about these?

[quaint thistle]

A student follows the following rules. correct answer
scored 2, incorrect answers were given a score of -1, and for questions that were not answered were given a value of 0.
Of the 50 questions given, student A can answer 40 questions correctly and 3 questions not
answered. What is the value obtained?

[topaz canopy]

I believe you just need to find the distance from letter to letter using a ruler

same with the first image you sent

[alpine sable]

just use a ruler and see the length and write it down?

[quaint thistle]

help

[topaz canopy]

yea from letter from letter, and in the first image it is already sort of giving you the answer

because it is already telling you the measurements for 6

and maybe 9 but i cant see

[quaint thistle]

need help

[alpine sable]

I dont get it

Is there a ruler app i can use on my phone?

[topaz canopy]

the numbers under the line

they are measurments

[topaz canopy]

you dont have a regular ruler?

[lapis valley]

what symbol is this, sorry for disturbing, kinda need it urgently

[alpine sable]

not at the moment

[quaint thistle]

help

me

[topaz canopy]

unfortunate i cant help you at that point then, those type of questions require a ruler

[topaz canopy]

sure ill check the question for you

[quaint thistle]

ok

[topaz canopy]

i was busy

[quaint thistle]

A student follows the following rules. correct answer
scored 2, incorrect answers were given a score of -1, and for questions that were not answered were given a value of 0.
Of the 50 questions given, student A can answer 40 questions correctly and 3 questions not
answered. What is the value obtained?

here

[alpine sable]

Should i send the answer by cm or inches?

thankuu for a while ago <33

[topaz canopy]

hold on a sec

[slate heron]

2(40)+0(3)-1(50-40-3)

[wary stream]

This is just basic algebra

[slate heron]

Prealgebra

[tacit breach]

This is kindergarten shit

[quaint thistle]

me?

[slate heron]

Yes

Lol

[tacit breach]

No you Louis

[slate heron]

You have to practice and pay attention in class more..

[tacit breach]

Then y you asking questions here bro

[topaz canopy]

You get 80 points for the correct answers and -7 points from the wrong questions

[tacit breach]

[slate heron]

?

[topaz canopy]

so 73 points

[wary stream]

Don't give out answers

[quaint thistle]

ok thanks

[topaz canopy]

my bad

[slate heron]

I gave you the equation, use that instead

[tacit breach]

Expression

[topaz canopy]

bad habit

[fair osprey]

You still won’t know what to do if you get this on a test though

[tacit breach]

So basically you do

[topaz canopy]

by the image it looks like its in cm or mm

[minor junco]

hello

[topaz canopy]

you would know if you had a ruler

[alpine sable]

ill look for a ruler

[topaz canopy]

ight

[alpine sable]

and then use it between the two words they gave me?

[topaz canopy]

you mean letters?

[alpine sable]

wait

ill send the example they gave me

[topaz canopy]

ok

[alpine sable]

it doesnt make sense for me

sending

[wary stream]

What was the question?

[topaz canopy]

It is higher up in the chat

the images

[wary stream]

That's buried

[wary stream]

What was the question?

[alpine sable]

Question

[alpine sable]

Example

I didn’t get the example

[wary stream]

Can you repost it?

[alpine sable]

Just click on the reply

[wary stream]

,rotate

[topaz canopy]

there they are

[wary stream]

There

[alpine sable]

Yeah

[wary stream]

That's the orientation I wanted

You don't need a ruler

[alpine sable]

What do I need to do?

The example doesn’t make sense to me

[quaint thistle]

Mother is a towel trader in a traditional market near her house.
Currently, the supply of towels is low. Mrs. Wati will buy towels at the market
big. He visited three shops that offered towels at the following prices.
Blessing Shop = IDR 300,000 per 10 towels
Gemilang Store = IDR 210,000,- per 6 towels
Toko Maju = IDR 96,000 per 3 towels
Mrs. Wati ensured that the towels offered by the three shops had brands,
same size and material. In which shop should Mrs. Wati buy towels so that
make the biggest profit?

[wary stream]

You know the length of XZ, and because it states that WX = XY = YZ that means point Y is the midpoint of XZ, meaning that it splits that segment equally into two part

[quaint thistle]

this is indonesia but i translate to english

[quaint thistle]

this

[wary stream]

Can you not tell this channel is busy?

Like stop interrupting

[quaint thistle]

i want to ask

[alpine sable]

fuck i dont really understand so like what should i do

[wary stream]

Don't care

[alpine sable]

this hw is like due in 2 hours

[quaint thistle]

ok

[wary stream]

XZ is comprised of XY and YZ. If XY = YZ that means that are two equal parts, right?

[alpine sable]

im not that good at math i dont understand very sorry man

[wary stream]

Do you understand that XY = YZ?

And that you are given the value of XZ?

[alpine sable]

no sadly

[wary stream]

That's the given info

XY = YZ

And XZ = 20

[alpine sable]

ohh

That

okayyy

i just saw it

[wary stream]

Now as I was saying, because they give the length of XZ and point Y is in that segment, and knowing that XY = XZ, that means they are equal parts

And there are 2 segments that make up XZ, XY and XZ

[alpine sable]

yeah

kind of understanding

[wary stream]

So if they are equal that means if you do XZ/2, that gives the value of each segment

Since they are the same length

[alpine sable]

yeah

[wary stream]

So then was does XY and XZ equal to?

[alpine sable]

yo

someone pls

real quick

1 more ixl question

[alpine sable]

im confused im sorry

[wary stream]

No

[alpine sable]

The number w is rational and negative. Which statement about
7
w
is true?

is it rational . irrational, or depending on the value of w

its 1 quick answer

real quick

@alpine sable there is #help-1 you can send ur question too

[wary stream]

XZ/2 is the length of XY and XZ individually

[alpine sable]

https://tenor.com/view/omni-man-punch-gif-22647069

[wary stream]

No

[alpine sable]

is that even allowed in the server?

gore

its a cartoon calm down buddy

it aint real

that doesnt really matter

[lime mulch]

would the gcf of 36b^2 and 30b just be 6 or 6b

[alpine sable]

oh you have a sans profile your asking 7th grade math questions my bad

but that was so unnecessary to send

your a little kids its ok sorry buddy

[alpine sable]

9th*

https://tenor.com/view/cap-doktor-cap-gif-22715858

[alpine sable]

ignore him

[eternal arrow]

Yo can one of y’all help me with a couple hw questions?

[wary stream]

So do XZ/2

[eternal arrow]

il send in a sec. lol im playing smash

[alpine sable]

help

I don’t understand

[eternal arrow]

C

@alpine sable

[alpine sable]

How

Nvm I get it

https://tenor.com/view/omni-man-invincible-gif-21644488

[alpine sable]

10?

[wary stream]

Don't give answers

[alpine sable]

does this make your stomach sick @alpine sable

:(

[eternal arrow]

Ok lol

[alpine sable]

i literally watched invisible

not the right place to send it

are you like 10?

[alpine sable]

invisible?

are u retarded?

[hard ether]

Toxicity

[alpine sable]

invincible typo

[hard ether]

What does the dot mean

[eternal arrow]

What unit is this?

[alpine sable]

joe biden nuke coordination

[eternal arrow]

@hard ether

[hard ether]

For real what does it mean

[wary stream]

Stop trolling

[hard ether]

What unit?

[eternal arrow]

ye like in marh

[wary stream]

Math topic

[hard ether]

I’m not sure, I was just reading some science papers when I came across this formula

[eternal arrow]

Like is this physics,

oh ok lol

[hard ether]

Astrophysics

[eternal arrow]

I was gonna say

To be honest with you I Havnt studied astro physucs

[hard ether]

Well I don’t know the dot sign

[eternal arrow]

You should search it up

[alpine sable]

hes like 12 and started to be edgy and shit just ignore him

[alpine sable]

ur asking 7th grade math questions tho

[eternal arrow]

Me?

[hard ether]

Oh ok

[alpine sable]

okay? doesn't fucking matter. you probably cant go outside or have any irl friends so don't take to me.

[hard ether]

I see

[eternal arrow]

Can y’all help me with this question?

lol its from my one note questions

[slate heron]

i think its a vector facing out of the page

[hard ether]

Expand and find terms right

[wary stream]

Everyone has different learning speeds. Geometry is a high school topic

[eternal arrow]

but what formula do I use?

[hard ether]

I’m not sure

Do you know how to expand

[eternal arrow]

i do but theres a formula for this

[hard ether]

Oh

[eternal arrow]

il ask in the other questions tab

[slate heron]

@eternal arrow

[eternal arrow]

Your funny

[alpine sable]

@alpine sable

[slate heron]

?

[hard ether]

If the dot represents the solar system, why is it used next to ‘L’?

[alpine sable]

ok but your in 7th grade your a child, you dont understand this world

[slate heron]

it doesnt represent the solar system

[hard ether]

What

[hard ether]

What

[eternal arrow]

no your right

[alpine sable]

you are pathetic

[alpine sable]

okay then mic up rn

[alpine sable]

call

do it

[eternal arrow]

Bro this is a math discord

Chill

[hard ether]

But someone showed a screenshot and I searched it up

And the paper I got the formula from is astrophysics

[slate heron]

i think it was an irrelevant screenshot

https://www.quora.com/What-does-cross-x-or-a-dot-Mean-interms-of-current-direction

[alpine sable]

get the mods on him not me

ur the one talking sh*t

hes calling me retarded and stuff

[eternal steppe]

its a circumpunct

[wary stream]

That's circuits related

[hard ether]

I’m just confused

[alpine sable]

and ur sending cartoon gore wtf

:(

[slate heron]

can you send the context

[wary stream]

The paper was astronomy related

[slate heron]

it could also mean vector direction

[hard ether]

So the formula I got this was from an astrophysics research paper and I found this weird circled dot symbol

And I don’t know what that means

And why it’s used

[alpine sable]

are you going to call?

take it on vc not on a god damn math server

[alpine sable]

join off topic voice

dm call

[hard ether]

Seriously

Someone

Help me

[alpine sable]

bro

search it up

[slate heron]

can you send the context

[hard ether]

I did but now I’m confused

[slate heron]

like a screenshot of more things

[wary stream]

This is an advanced answer but it should help

[charred flint]

@hard ether it means of the sun

Mdot is mass of the sun

[slate heron]

ohhh

makes sense now

nvm everything i said

[hard ether]

OH

[hard ether]

Ok thanks

[wary stream]

L is luminosity and M is mass

And the circle with dot is the sun

[hard ether]

So m with the dot is the mass of the sun?

[wary stream]

Yes

[hard ether]

Ok thanks

[alpine sable]

I have a question: For what a/b would f(x) = x^a/b have where f'(-1)<0 and f'(0) does not exist where 0<a,b< 10, a and b are integers, and a ≠ b.

I did this and got an answer not even there

[hoary copper]

It should be D,

d/dx(x^2 - x) = 2x - 1
Sub 4, and you get 7

[alpine sable]

I got 8

I did it a diff way

You did it wrong then

Really? Never knew that

Show how you did it

So we can tell you what you did wrong

[charred flint]

@alpine sable just when a/b is an integer right?

[alpine sable]

Yes

[charred flint]

I mean the answer

like a/b=n

[alpine sable]

It doesn't matter if a/b = n. Just a and b have to be integers themselves

[charred flint]

otherwise the (-1)^a/b is weird

yea I'm claiming an answer

[alpine sable]

I meant to send this

What did I do wrong

[hoary copper]

Do not do average rate of change, its asking for the instantaneous rate of change

[alpine sable]

That’s not the average rate of change

it’s the average rate of change for the tangent line which is the instantaneous

[hoary copper]

are u trying first principles then?

[alpine sable]

Yes

Use difference quotient: f(x+h)-f(x)/h

I did that too

[alpine sable]

Here

and got 8 again

[alpine sable]

?

[charred flint]

like the question just leads to whether (-1)^(a/b) is a real number

[hoary copper]

do not substitute any numerical values, get an equation first when h --> 0

[alpine sable]

I did that

Wait

let me try again

[alpine sable]

I don't know what that means but I'll restate the problem. Create a function so that f'(-1)<0 and f'(0) does not exist. f(x) = x^a/b. a and b have to be 1-9 where a and b are integers and a can't equal b.

[alpine sable]

You messed up on difference quotient. You should get something like 2x + h -1

[charred flint]

a=b and only a=b

oops I mean a, a multiple of b

a/b integer

[alpine sable]

which part did I mess up

a/b doesn't have to be an integer. they only have to be integers on their own, but a/b could be an integer if that's a solution

This is like the 50th time

[hoary copper]

@alpine sable

use variable raws values first

the sub in the gradient point

[alpine sable]

You can't cancel out the hs. You have to factor them out first

Oh

2xh + h^2 -h = h (2x + h -1)

thanks

[hoary copper]

yeah what they said...

[alpine sable]

np

[peak summit]

yo i need some help

[hoary copper]

wait cobb_2's question first

[alpine sable]

it's alr

[vocal dirge]

A)

[alpine sable]

Help them. don't just give the answer

[vocal dirge]

Ok

[hollow hawk]

a because 8^x is 2^3x (remember the exponent rules?) then you would want to divide them, which would give you 2^(3x-y), another exponent rule which we know 3x-y=12

try simplifying terms to match them

[vocal dirge]

Here, @peak summit (sorry english isn't my mother language)

[hollow hawk]

yup you got it, good job 👍

[hoary copper]

@alpine sable i am not able to solve your question, but I got till a < b.

@alpine sable see if you can continue further

[peak summit]

Alr appreciate it!

[odd vale]

Four satellites revolve around the earth once every 6, 8, 10, and 15
hr, respectively. If the satellites are initially lined up, how many
hours must pass before they will again be lined up?

cansomeone help me?

i cant understand this at all

[hollow hawk]

so one satellite revolves every 6 hours

one every 8 hours

one every 10 hours

and one every 15

[odd vale]

yee

[hollow hawk]

why don't we explore a simplified version of this problem:

2 satellites

one 5 hours

one 3 hours

they can revolve as many times as possible

(they don't have to revolve the exact same times)

[odd vale]

when will they line up

[hollow hawk]

you know what lcm is right

[odd vale]

ye ofc

its either 90/200/120 or 180

i am just too confused

ohh wait maybe the answer is 120

nvm i figured it out xD thanks for the help

[hollow hawk]

nice

glad you figured it out on your own

[small helm]

When we're talking about sets, is the intersection of sets associative? So can I do A ∩ (B - C) = (A ∩ B) - (A ∩ C)?

[vale wigeon]

that's not what the word "associative" means

intersection \textit{is} associative but that means $(A \cap B) \cap C = A \cap (B \cap C)$

[small helm]

oh

I meant distributive

[ocean seal]

Ann

[small helm]

mb got mixed up

[vale wigeon]

anyway, as for your question of whether intersection distributes over set difference

yes, that is also true

appears so, anyway

[shut knoll]

is this channel free

[vale wigeon]

unless naru has some follow-up questions, yes, this channel is free

[shut knoll]

stuck on this

i started with multiplying sqrt(ax+b) + 2 / sqrt(ax+b) + 2

[vale wigeon]

parentheses

[alpine sable]

2yq5...

[vale wigeon]

but yes that's the right move

[shut knoll]

eventually i got a = 2

(ax + b - 4) / (2[sqrt(ax + b)] + 2x) = 1

i set the numerator and denominator equal to each other\

[vale wigeon]

i think you may have messed up already

yeah, you have messed up

what you will have is $\lim_{x \to 0} \frac{ax+b - 4}{x(\sqrt{ax+b} + 2)} \overset?= 1$

[ocean seal]

Ann

[shut knoll]

yeah i got that

i have no idea how i turned that into what i had

pretty sure i distributed

[vale wigeon]

no need

the first thing you should note is since the denominator approaches zero, so must the numerator (otherwise your limit won't exist) thus b = 4

and then you can replace b with 4 and cancel out the x's in the num and denom

[shut knoll]

wouldnt 1/0 be approaching infinity?

or anything over 0

couldn't that also be a solution

[vale wigeon]

you want the limit to exist and be finite

(or more specifically, equal to 1)

[shut knoll]

oh i see

[vale wigeon]

besides the limit wouldn't exist anyway since you'd have +∞ from one side and -∞ from the other

[shut knoll]

ah yea

[dreamy ridge]

guys i have uestion

[shut knoll]

where did u get that the denominator approaches 0

[dreamy ridge]

its based on limits as well

[vale wigeon]

wyldfyre and i weren't done @dreamy ridge please move to another channel

@shut knoll look at the denominator

[shut knoll]

oh if i plug in x = 0?

i see

[shut knoll]

ok i have done this

but now we have a limit question with no x

do i just ignore the limit then and just treat it like a normal equation and solve for a?

[quaint rock]

Help me plz!

[somber osprey]

ahahhaha

[shut knoll]

im using this channel .-.

@vale wigeon

[somber anvil]

this channel free? i asked in 5&1 but no one responded

[alpine sable]

How do you know when to use the quotient rule, could I say that if what is on the top if the derivative of that isn't zero you would use the quotient rule?

[alpine sable]

thx

[vale wigeon]

@shut knoll yes just solve for a now

[shut knoll]

mhm i got a = 5

ax / x(sqrt[a+4]) + 2

cancelled out x

a / sqrt[a+4] + 2

multiplied by sqrt[a+4] - 2

a(sqrt[a+4] - 2) / a = 1

cancelled out a

and i got sqrt(a+4) = 3, a = 5

[shut knoll]

i'm just not sure if this step is ok

[restive hill]

Can anyone help me?

[placid zinc]

@alpine sable
Quotient rule will still work here, as it always does. Why is applying the quotient rule not the best way to solve this problem?

[alpine sable]

ah ok. so like even if there were no functions i could still use the quotient rule? like because there's no function on the top does that mean i dont use it? i saw a video that told me this, i think

[shut knoll]

@vale wigeon can u verify?

[alpine sable]

i was more thinking like when do you have to if you get my drift

I still don't get this... I've been trying to do these steps on other equations but it doesnt work out, the only difference is usually only the sign at the end result... what are constant terms and based on what do they change signs??

[vale wigeon]

@shut knoll when you plug x=0 into ax, you do not get a.

apologies for my delayed replies

[glad mango]

Anyone tryna help me in #help-1

[shut knoll]

im not sure what to do then

[vale wigeon]

you are overcomplicating it and also misplacing parentheses again

you have $\lim_{x \to 0} \frac{a}{\sqrt{ax+4} + 2} = 1$

[ocean seal]

Ann

[vale wigeon]

plugging in $x = 0$ you get $\frac{a}{\sqrt{4} + 2}$

[ocean seal]

Ann

[shut knoll]

i see, how come what i did didn;t work?

[vale wigeon]

you plugged in x=0 into ax and somehow got a and not 0

[shut knoll]

oh i also somehow lost the x in ax

yeah

[restive hill]

Can anyone help me?

[shut knoll]

@vale wigeon so a and b are both 4? is there anyway to check

[vale wigeon]

yes a and b are both 4

,w lim[x -> 0] (sqrt(4x+4) - 2)/x

[ocean seal]

Results provided by WolframAlpha

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

Requested by Ann#0413

[eternal arrow]

Im so lost :/

[shut knoll]

how would i check this though

[vale wigeon]

idk

[shut knoll]

is there a way graphically

[vale wigeon]

no there's no obvious way to check your solution without just calculating the limit with your values of a and b and seeing whether you get 1 or not

[shut knoll]

the denominator is 0 though

plugging in those values i get approaching infinity no?

[vale wigeon]

no

"calculate the limit" does not mean "just plug in x=0 and do nothing else"

so what if the denom approaches 0

so does the num

[shut knoll]

oh yeah it does

this one id assume is similar, i multiply by (sqrt(x) + 1) / (sqrt(x) + 1)?

[eternal arrow]

When will you finish your question

[vale wigeon]

@eternal arrow you have posted in multiple channels already

@shut knoll you could do that but it's going to be a pain because the cube root will still need dealing with

[shut knoll]

could i multiply by the cube root instead of square root?

then i have a 4th root on the denom

[vale wigeon]

you would not.

[shut knoll]

oh

id have x^2

[vale wigeon]

$\sqrt{x} \cdot \sqrt[3]{x} \neq \sqrt[4]{x}$

[shut knoll]

i think

[ocean seal]

Ann

[vale wigeon]

you wouldn't have x^2 either

[shut knoll]

6th root

[vale wigeon]

you would have something with x^(5/6)

[shut knoll]

x^1/2 * x^1/3

[vale wigeon]

i would suggest substituting u := x^(1/6) here to make this into the limit of a rational function

[shut knoll]

what about substituting u as sqrt(x) ?

[vale wigeon]

you can do that but then you will have to deal with u^(2/3)

[shut knoll]

oh no cuz 1/6 is the common factor

[vale wigeon]

so it doesn't really reduce the amount of work to be done

[shut knoll]

thats why right

so (u^2 - 1) / (u^3 - 1)

im guessing i factor these now?

and i get 1/u

nvm i dont

i forget how to do difference of the cubes

[vale wigeon]

yes, factor these

u^3 - 1 factors as (u-1)(u^2+u+1)

[shut knoll]

o

which factors into (u-1)(u+1)(u+1) ?

actually is that necessary

i dont think it is

i dont think it factors like that anyways

u+1 / u^2 + u + 1 = 2/3

i dont remember what to do with u though

[surreal kindle]

can someone help me factorize this?

to this

i want to learn the process cuz the internet isnt helping alot atm

[vale wigeon]

no it doesn't

[vale wigeon]

parentheses!!!

when writing fractions in plaintext you should surround the numerator and denominator in parentheses so as to respect the order of operations

[shut knoll]

aa ik

i just keep forgetting

but ye wats next

[vale wigeon]

after you simplify your function to (u+1)/(u^2+u+1) you can and should plug in u=1 as that no longer results in division by zero

[shut knoll]

yeah i found 2/3

by plugging in u = 1

but thats not the answer is it

bc i substituted u for x^1/6

[vale wigeon]

x approaches 1

therefore u will approach 1^(1/6), which is also 1

[shut knoll]

ohh

if x approached 2 instead

would the u approach 2^(1/6)

[vale wigeon]

yes

[shut knoll]

and then would i plug 2^(1/6) when solving

[vale wigeon]

it's the same as any other limit substitution

[shut knoll]

i just didnt know how substituting u affected the limit

ty for the help!

[alpine sable]

Have I done something wrong here?

[jagged imp]

yes. for instance, in the first step you tried to use power rule where it doesnt apply

[stable pecan]

Remember that you are integrating here

[alpine sable]

Sorry but I'm a beginner

[stable pecan]

not differentiating

[alpine sable]

What should I do?

[alpine sable]

..

[stable pecan]

are you aware of the derivative of arctanx?

[alpine sable]

No :/

[jagged imp]

you either need to do a u sub or rewrite x/(x+1)

such that it looks like integrals you know how to do

really not sure what arctan has to do with this, so i tentatively want to tell you to ignore alacris

[alpine sable]

Ok.

[jagged imp]

you can't use power rule as you did since x/(x+1) isn't in the form x^n

and power rule is used for evaluating integrals of that form

[alpine sable]

Got ya

But I have x1 in my denominator

Then why?

@jagged imp

[stable pecan]

I was trying to get them to do add and subtract 1 from the numerator so they can eventually integrate 1/1+x, which is the derivative of arctan

[jagged imp]

alacris

the derivative of arctanx is 1/(1+x^2)

[stable pecan]

oh yeah

my bad

[alpine sable]

Whatever

[jagged imp]

yeah but you also have x+1 in the denominator

[alpine sable]

Tell me what should I do ;_;

[alpine sable]

Then it doesn't apply?

Ok

[jagged imp]

yes

you can either long divide or add and subtract 1 in the denominator to rewrite it as $1-\frac{1}{x+1}$

[ocean seal]

Sneaky

[jagged imp]

at which point, the integral of 1 is x and the integral of 1/(x+1) is ln(x+1)

[alpine sable]

Oh ok thanks bud, got it! @jagged imp

[pliant barn]

I think substitution would be easier. x+1=u
then you have $\int \frac{u-1}{u} du$ which is solvable.

[ocean seal]

Mattan Hoory

[jagged imp]

i just did this since it requires less knowledge

[pliant barn]

But obv both ways are good

[jagged imp]

i can assume they know how to add and subtract 1 or long divide

but i cant assume they know u sub]

[pliant barn]

yea nice

[jagged imp]

i would also argue u sub is longer in this case for the fact its a definite integral

but maybe not

there are other steps my method introduces too

really doesnt matter much lol

[alpine sable]

Again... What should I do?

[jagged imp]

do you know u sub?

[alpine sable]

No

[jagged imp]

Uh have you been given some special rule that the integral of f'(x)/f(x) is ln(f(x))?

[alpine sable]

Nope

[jagged imp]

yeah idk what you're supposed to do with this then

sorry

[alpine sable]

:/

Tell me how to u sub @jagged imp

[pliant barn]

Did you learn that the integral of 1/x is ln(x) ?

[alpine sable]

Like this? @jagged imp

[pliant barn]

yes

this is exactly how u do subtition

[jagged imp]

yeah that is u sub lol

[alpine sable]

Alright

This is multiplication

But what should I do when it's division? @jagged imp

[pliant barn]

try subbing this way, and see if you get something you can rewrite as something solveable

[jagged imp]

are you suggesting x+1=u? That's not gonna do anything ,,,

try u=x^2+1

the motivation being that you have a function involving x^2+1 multiplied by the derivative of x^2+1

[alpine sable]

Well nvm

[alpine sable]

I think I can do with this

Lemme try

[pliant barn]

I think it gives $\frac{u-1}{u} = 1-\frac{1}{u}$ whic is very easy

[ocean seal]

Mattan Hoory

[jagged imp]

we aren't talking about the first question they posted

[alpine sable]

Umm

[jagged imp]

this is about 2x/(x^2+1)

[jagged imp]

close but the c is misplaced

[pliant barn]

oh ok my bad ^

[jagged imp]

its just added onto the end of the function

so log(1+x^2)+c

[alpine sable]

Oh thanks

[pliant barn]

Hey, I'm a bit confused about uniform convergences of function series (Into to Calc II)
let
$$ f_{n}(x)=\begin{cases}
n & 0\leq x\leq \frac{1}{n}\
0 & else
\end{cases} $$

Then fn converges uniformly on the closed interval $[0,1]$ to $f(x)=0$ because $\sup|f_{n}-f|=\frac{1}{n}\to 0$

But the integral of fn does not converge to the integral of f.
$$\int_{0}^{1}f_{n}(x)=1\neq0=\int_{0}^{1}0=\int_{0}^{1}f(x)$$
Which contradicts a theorem which states Riemann integrability transfers to the limit f.

[ocean seal]

Mattan Hoory

[pliant barn]

Anyone knows about Riemann integrability and can shed light on this one ?

[eternal arrow]

Can somebody help me answer this question?

its 3x^2 btw

[jagged imp]

Uh the existence of the riemann integral transfers to f, not the value of the integral itself.

it is also not true that the integral from 0 to 1 of all f_n is 1 if that's what you're implying

What we can say is that $\lim_{n \to \infty} \int_0^1 f_n(x) dx=\int_0^1 f(x) dx=0$

[eternal arrow]

Can one of y’all still help me on my question? Will probs be my last or second last question of the night before I go to bed

[ocean seal]

Sneaky

[jagged imp]

which is true in general for uniformly converging functions (save the =0 part)

@pliant barn

to be more general on that last bit, if $f_n$ converges uniformly to $f$, we would have $\lim_{n \to \infty} \int_C f_n(x) dx=\int_C f(x) dx$ for any compact interval C

[ocean seal]

Sneaky

[pliant barn]

hmm

[pliant barn]

the area of the rectangle is always 1

so $\int_0^1 f_n = 1$ ?

[jagged imp]

,w integral from 0 to 1 1/n dx

[ocean seal]

Mattan Hoory

Results provided by WolframAlpha

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

Requested by Sneaky#0928

[jagged imp]

is only 1 when n=1

The integral from 0 to n would surely be 1

but we aren't dealing with that

[pliant barn]

I think this is incorrect, becasue its 1/n only if 0<x<1/n

[jagged imp]

uh

you wrote if 0<x<n

in your original message

[pliant barn]

ok right

myb ad

my bad

I meant 1/n

$$ f_{n}(x)=\begin{cases}
n & 0\leq x\leq \frac{1}{n}\
0 & else
\end{cases} $$

[ocean seal]

Mattan Hoory

[pliant barn]

yea ok this it

sorry I've made a mess

[pliant barn]

like so

So now
$$\int_{0}^{1}f_{n}(x)=1\neq0=\int_{0}^{1}0=\int_{0}^{1}f(x)$$
which means

$$\lim{n \to \infty} \int_C f_n(x) dx=1 \neq\int_C f(x) dx=0 $$

[ocean seal]

Mattan Hoory

[pliant barn]

kind of in the middle right here :

[jagged imp]

isn't sup|f_n-f|=n now? Therefore no longer uniformly convergent

i'm not too experienced here so I could be wrong but that seems to be the issue to me

[pliant barn]

You are correcty

I was looking at 2 different examples

and I was confused

[jagged imp]

lol nw

[pliant barn]

This is not uniformly convergent, and the integral indeed does not converge

This IS uniformly convergent , but the integral is non convergant on non compact interval

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