help-13

[half forge]

There's (6x+1)^2 in both the numerator and denominator so you can start simplifying from there

[vagrant elbow]

Yeah I'd split it in two fractions and go from there

[jaunty bronze]

but it's subtraction so i can't cancel

[vagrant elbow]

.

[jaunty bronze]

how would i go about splitting this

[half forge]

If you split it in to two you'll see what I mean

[vagrant elbow]

$\frac{(6x + 1)^3(27x^2 + 2)}{(6x + 1)^6} - \frac{18(9x^3 + 2x)(6x + 1)^2}{(6x + 1)^6}$

[jaunty bronze]

i see now

just to confirm, 26 is supposed to be 27?

[half forge]

Yeah

[vagrant elbow]

Yeah sorry mb

[wraith dagger]

NEONPerseus

[jaunty bronze]

okay i can figure the rest of this problem out now

i just need help with one more

[vagrant elbow]

Same principle

[jaunty bronze]

same thing with splitting it?

[vagrant elbow]

Yes

[jaunty bronze]

yeah but what's throwing me off is how to recombine them after canceling terms

wait acuatlyui

actually im stupid sorry i figured it out

thank you for the help

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[short sierra]

For c) the question asks "How long does it take before the account is worth a billion dollars

[short sierra]

I am pretty sure my calculation is right for c but I am getting a math error when i do e^(3,333,333) - 3

Am I doing something wrong?

or is my calculator just not strong enough for that calculation

The final answer is e^(10/3) - 3

I am not sure how thats the answer

[dire geode]

how many millions is one billion

[short sierra]

Oh, its in millions

Oops, okay thank you 😅

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[loud lintel]

I'm struggling to solve for x

I understand that for something like ln(x+1)=2 i can take e to both sides and get x=e^2-1 but this is hurting my brain

I'm guessing I simplify to -ln(a)+ln(b)=2t+c

Wait I figured it out I just needed to risk looking stupid for my brain to function

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[limber moon]

hi

[limber moon]

i need help with my math hw

idk what to start with

[crimson sedge]

find all the angles first

[limber moon]

okay

[limber moon]

ill skip that for now

[crimson sedge]

ok.

[limber moon]

so what should i start?

[crimson sedge]

for the second one?

[limber moon]

yes

[crimson sedge]

ok

you need to use

trignomotry

do you know cos sin and tan

[limber moon]

yes

[crimson sedge]

than try find CE first with trig

[limber moon]

okay

[crimson sedge]

and also try to find AC

[limber moon]

im having a problem witht that tho...

[crimson sedge]

use pythagoras to find AC then

[limber moon]

9 cm

[crimson sedge]

u sure?

[limber moon]

if im correct

[crimson sedge]

if you want a more accurate answer you keep 2 or more decimal places

you can maybe start with 9.43

[limber moon]

oh

ok i got it

so whats next

[crimson sedge]

find the angles inside triangle ABC

[limber moon]

PNK?

oh ok

[crimson sedge]

i was looking at reference mb

use cos inverse to solve angle C

[limber moon]

oh ok well ill do this later i got school

[crimson sedge]

sure

[limber moon]

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[forest kindle]

does anyone know how to do this?

[crimson sedge]

Good morning USA! I have a wonderfull morning ahead and a math test

[pine torrent]

You have to simplify that right?

[forest kindle]

i think so

[pine torrent]

You need any help with that? You have said that in already occupied channel

[pine torrent]

Then use the formula for sin cube a

then for sin 3a

and simplify as much as you can

[crimson sedge]

by "derive" it means differentiate right?

[foggy tendon]

Factor out the common factor first, the use the Pythagorean identity

If it’s simplify

If it’s derivative use chain rule for sine cube

[forest kindle]

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[violet flume]

integral of a matrix

so its a 3d shape?

idk you could do monte carlo i think?

im not certain, just responding since its curious

https://en.wikipedia.org/wiki/Monte_Carlo_integration

yours wont be 2d

if you already have this shape defined nicely

it shouldnt be too bad

damn interview questions

i would guess if it has to be fast, this is not the method you want

since yours has a nice structure right

like its regular

yea im really not sure

i guess id have to know more about the shape

but its a height

and then it turns into a pyramid?

but how does it turn it into a pyramid

whats the shape

and why do you care about the shape

i mean why couldnt you just treat it like a grid you know

boxes

theres probably like

some kind of whats it called

im so far out of my area of expertise lol

[cedar kiln]

@scarlet jay Has your question been resolved?

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[astral lagoon]

How do I find out if the measurements make a triangle or not?

[livid hound]

triangle inequality

[astral lagoon]

Im not sure how to know if it can make a triangle or not i know you need to add them but past that im not sure

[livid hound]

do you know the

triangle inequality

[astral lagoon]

No

[livid hound]

look that up

[astral lagoon]

ok

Oh that helps thks

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[tepid valley]

So i have been given y=kx+6 linear function and i have to find k that ONLY shares one point with a quadratic function that is y=x squared+20x+42.

I graphed the latter and i also looked at the answer sheet since this is not a test it's just for learning and i can't figure out how the answer is 8 and 32. I put those in a graphing calculator and somehow only k=8 and k=32 touch the parabola once and no other seems to do. I just wanna know how to get to this answer.

[tepid valley]

have to find k coefficient

have no idea

[lusty grotto]

do u know how to find the intersection of a line and a parabola?

[tepid valley]

thats exactly what i need help with

i graphed the parabola

and i wanna know how to get the correct k coefficient

[lusty grotto]

forget abt the correct coefficient for the time being

do u just know how to find the intersection of a line and parabola

[tepid valley]

No, first time doing this

first time calculating the intersection

[lusty grotto]

okay do u knw how to find the intersection of two lines then

y = 2x + 3, and y = -x + 5, can u find the intersection of these two?

[tepid valley]

put it in a system maybe?

[lusty grotto]

yeah

same with parabolas and lines

[tepid valley]

really

[lusty grotto]

put the equation of the line and the equation of the parabola in a system

[tepid valley]

and find the x from there?>

[lusty grotto]

yeah

[tepid valley]

oh wow that sounds simple

so i dont even need to graph it probably

[lusty grotto]

u dont

u know abt discriminants?

[tepid valley]

ok one minute

yeah yeah

i know how to calculate vertexes and stuff

[lusty grotto]

ull have to use this to make sure theres only one intersection

[lusty grotto]

ie one solution for x

[tepid valley]

the answer is 8 and 32 tho

so i would need two variants of k

[lusty grotto]

for x?

[tepid valley]

i have two variants of k

that both work i graphed it

[lusty grotto]

yeah that is possible there may be two possibilites for k

[tepid valley]

only crosses the parabola once

[lusty grotto]

ig

[tepid valley]

alr ill put it in a system

[lusty grotto]

yeah

[tepid valley]

so

one is quadratic

do i need to calculate discriminant

before i do the system?

[lusty grotto]

no

use ur system to find a qudratic equation in x

[tepid valley]

never done a system with a quadratic before actually

ok ill try

[lusty grotto]

eliminate y from both equations and find one equation in x only

[tepid valley]

but i have x squared

[lusty grotto]

yeah but u only have x, and no y right?

[tepid valley]

i have kx+6 and below that i have xsquared+20x+42

[lusty grotto]

yeah

[tepid valley]

how would i eliminate kx

[lusty grotto]

by "x only" i do not mean not including "x^2"

[lusty grotto]

eliminate y, let the k be

[tepid valley]

y is eliminated yeah

[lusty grotto]

okay so u r system is
y = kx + 6
y = x^2 + 20x + 42

[tepid valley]

yes

[lusty grotto]

how can u eliminate y

[tepid valley]

multiply one side by 01

-1

[lusty grotto]

and?

[tepid valley]

and then have -y=-kx-6

[lusty grotto]

can u send me the equation u get after eliminating y?

[tepid valley]

so y eliminates itself

[lusty grotto]

? just multiplying by -1 doesnt eliminate y

[tepid valley]

why

i have positive y too right

with the quadratic below

[lusty grotto]

yeah so combine the -y with +y and find one equation

[tepid valley]

i can + those two

yeah ok

[lusty grotto]

do that

[tepid valley]

so now its xsquared+20x-kx+36

should i factor out x?

[lusty grotto]

x^2 + 20x - kx + 36 = 0

[tepid valley]

yeah i got that

[lusty grotto]

this is a quadratic equation in x

[tepid valley]

so the b coefficient is 20x-kx right?

[lusty grotto]

do u know that a quadratic equation in x can have 2 solutions?

[tepid valley]

now i can find Discriminant

yeah i know those solutions

[lusty grotto]

(20-k) is the coefficient of x

[tepid valley]

discriminant would be bsquared -4ac

[lusty grotto]

to write that something is squared u wud use the symbol ^

[lusty grotto]

yeah

can u find the discriminant here

[tepid valley]

where on the keyboard lol

[lusty grotto]

are u on a computer?

[tepid valley]

yeah

[lusty grotto]

shift + 6

[tepid valley]

oh my dumbass self

so ill find the discriminant now

[lusty grotto]

😄

yah

[tepid valley]

(20-k)^2 would be 400-40k+k^2 right

and then minus 4ac

[lusty grotto]

yeah

[lusty grotto]

what is a and what is c

[tepid valley]

1 and 36

[lusty grotto]

right so what is ur disciminant

[tepid valley]

so minus 144

that gets me 256 which is a square of 16 so it looks promising

ok so

im left with a quadratic in the discriminant itself

[lusty grotto]

yeah

[tepid valley]

should i find values of k?

its k^2-40k+256

[lusty grotto]

what do u want the discriminant to be, in order that this equation have only one solution for x?

[tepid valley]

0

but thats not the case

[lusty grotto]

yea

[tepid valley]

the solution has 2 cases

[lusty grotto]

why not

[tepid valley]

it has 2 answers

[lusty grotto]

u r talking abt k, im talking abt x

[tepid valley]

ah ok

yeah the discriminant should equal 0

so k^2-40k+256=0

ill calculate d/4 from this ok?

which would be 400-256=144

[lusty grotto]

the solutions for x here give u the coordinates of the intersection of the parabola with the line, if the parabola shud meet the line at ONE point only, there must be only ONE solution for x

[tepid valley]

oh you're right

[lusty grotto]

and so its discriminant

[lusty grotto]

which is this

must be 0

[lusty grotto]

yeah

now solve for k

[lusty grotto]

d/4 ?

[tepid valley]

its a discriminant formula thats a bit easier to work with

when u have b coefficient that can be split by 2

forgot the word for :

english word for this

[lusty grotto]

colon?

[tepid valley]

no

\div

oh

divide

so if b can be divided

what u can do is

d/4=b/2^2-ac

so its a bit easier with smaller numbers

[lusty grotto]

oh well

[tepid valley]

and yeah

i got the correct answers

32 and 8

[lusty grotto]

there u go then

[tepid valley]

damn

i spent more than an hour doing this

thank you man

seriously you saved my nerves

legend

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[distant bridge]

How do i derivate $f (x) = (1 + tan^2x) $

[distant bridge]

i have to use the chain rule some how

so i gave g(x) = tan^2x

and f(g) = g^2

so g`(x) = 2tanx

wow

[cerulean sail]

You need the chain rule also on g(x) = (tan(x))^2

[distant bridge]

the outer function has no power here

[cerulean sail]

Putting f(g) as g^2 would return tan^4 wouldn’t it?

[distant bridge]

f(g) = g

[cerulean sail]

Returns tan^2 rather than 1 + tan^2, no?

Why not e.g. g(x)=tan(x) and f(u)= 1 + u^2, then f(g(x)) will be what you have?

[distant bridge]

okei so the deriv of f`(u) = 2u

[cedar kiln]

@distant bridge Has your question been resolved?

[distant bridge]

$f (x) = (1 + tan^2x) = 2tanx * (tan^2x + 1) = 2tan^3x * 2tanx$

[wraith dagger]

Sas

[distant bridge]

i think i got it right

@cerulean sail ?

g(x) = tanx

f(g) = (1 + g^2)

from here just g * f

[cedar kiln]

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[trim crescent]

Hello could someone please try and provide insight regarding differential equations ?

[fast hazel]

what kind of insight are you looking for

[trim crescent]

Regarding the theory

So in last years class we were taught the following :

The formula to resolve a linear differential equation of the 1st order "homogene" ( = 0 )

But last week this is what what we were taught as a recap :

2 questions : why are we now integrating from to to t and why is the formula different now ? Why isn’t it -alpha(t) ?

<@&286206848099549185>

[cedar kiln]

@trim crescent Has your question been resolved?

[cedar kiln]

@trim crescent Has your question been resolved?

[trim crescent]

.close

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[trim crescent]

.closee

.close

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[karmic knot]

which part are you stuck in?

[sharp kestrel]

4

[karmic knot]

right so

on solving you'll get argument of larger base which in this case is n since n>k, to be 7b^2, did you get that?

[sharp kestrel]

Yes

[karmic knot]

and then next step for finding Y, the difference between the base and argument would be k-7, correct?

[sharp kestrel]

Yes

[karmic knot]

they're asking for X+2Y= 7b^2+2(k-7)

that'd be 7b^2+2k-14

now you just have to substitute the values which they provided

[sharp kestrel]

So it’s 7

Can you help me on a another

[karmic knot]

yeah sure

[sharp kestrel]

@karmic knot

[karmic knot]

hol up

idk if i'm right but isn't it like directly from the question?

that'd be the quotient of natural log of 5 and natural log of 10 can be split into the so and so thing

[sharp kestrel]

I’m not sure

[karmic knot]

me neither but it's just the exact same statement as the above one so yeah

[sharp kestrel]

Ok thank you

[karmic knot]

np ^^

[cedar kiln]

@sharp kestrel Has your question been resolved?

[cedar kiln]

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[empty vapor]

A 11 N force acts due North and a 8 N force acts due East on a particle. Determine the magnitude of the resultant of the forces to one decimal place.

[empty vapor]

i got 13.4

can anyone confirm?

or 13.6

[gilded elm]

,w sqrt(11^2 + 8^2)

[wraith dagger]

Results provided by WolframAlpha

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

Requested by DerpZ#9141

[empty vapor]

thanks

.close

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[crimson sedge]

How do I find this

[hushed spoke]

!status

[cedar kiln]

What step are you on?
1. I don't know where to begin
2. I have begun but got stuck midway
3. I got an answer but I'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above

[crimson sedge]

3

And now 1

[gilded elm]

let's see your work please

[silent finch]

Find u and v in terms of x and y

[crimson sedge]

Oh I wrote it in that paper and it's wrong so I erased it

[gilded elm]

read what kappa said

[crimson sedge]

I don't understand

[silent finch]

How can you rearrange the last equation to isolate u?

[crimson sedge]

X/y =u?

[silent finch]

Oh I thought it said u-v

[crimson sedge]

Oh it's a . For multiplication

[silent finch]

Let me read it again

Ye

[crimson sedge]

Okay 😎👍

[silent finch]

Well same stuff applies

[silent finch]

Yea now substitute in third equation

And solve for v

[crimson sedge]

But idk u value

[silent finch]

u is x/y

[crimson sedge]

But idk the values

[silent finch]

Leave that for now

Just find v in terms of x and y

[silent finch]

We can find x and y using the first 2 equations

[crimson sedge]

So its

X=y+44
Y+44+y=76
2y=32
Y=16

X=y+44
=16+44
=60
?

[slate apex]

@crimson sedge

what do you have to find?

[crimson sedge]

U^2 + v^2

[slate apex]

mhh

are you in high school?

[crimson sedge]

No

Secondary 1

[slate apex]

ok

x is 32

[crimson sedge]

How

[slate apex]

because x + y =76 and x - y =44

sorry y is 32

[crimson sedge]

So like 76-44?

[slate apex]

yea

[crimson sedge]

And you got y

[slate apex]

si

yes

si = yes in italian 😅

[crimson sedge]

Yea

[slate apex]

so x is 44

and y is 32

[crimson sedge]

No

[slate apex]

how

[crimson sedge]

. close

.close

[cedar kiln]

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[slate apex]

how ?

bro

hey

[cedar kiln]

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[slate apex]

I was helping you

[slate apex]

.close

[cedar kiln]

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[cedar kiln]

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[tribal knoll]

hi i need help with sign diagrams

[tribal knoll]

how do u make the sign diagram of a function if the function is never 0?

for example x^2 + 4, how can u make a sign diagram of that function to know when its increasing or decreasing etc

[tropic oxide]

do you want a sign diagram for the function itself or for its derivative...?

x^2 + 4 itself is always positive.

[tribal knoll]

both

[tropic oxide]

the derivative of x^2 + 4 is 2x, which does equal 0 at one point.

[tribal knoll]

ohh alright i understand now

thank uu!!!

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[graceful magnet]

Can someone help me solve this?

[carmine bronze]

#❓how-to-get-help

[graceful magnet]

You should post this in a separate channel

[fast hazel]

you can do ibp.... many times lmaoo

[carmine bronze]

Was just about to say that. That's kind of the only way, isn't it?

[graceful magnet]

I honestly tried it but found it too long so I asked here to see if there is a shorter way

[fast hazel]

its the first thing that comes to mind at least

although looking at limits, was this the full q?

[graceful magnet]

Yup that's it

[fast hazel]

rip

[graceful magnet]

I have the final answer if it helps

[fast hazel]

^ 😔

[graceful magnet]

Ah well damn

[brittle stag]

or DI method

[graceful magnet]

Thanks anyway

Hmm maybe

I'll try it

[crimson sedge]

Good Night sticky Dreams everyvone

[cedar kiln]

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[cobalt merlin]

Can someone explain why this wrong?

I looked online said point B = (3,6,-2) then line gives us v = <-1,2,3> and some poitn when u plug in t so t=0 A = (4,-1,0)

then i find another vector AB = <-1,-7,-2>

get cross product <-25,-5,-5>

then use formula

[long arrow]

you did that?

[cobalt merlin]

ye in previous attempt said was wrong

[scarlet garnet]

how confident are you about that line you found

[long arrow]

v should v = <-1,2,-3>, idk if it was a typo

[cobalt merlin]

ye typo

oh but thats what i put in calculator

[long arrow]

thing is

[cobalt merlin]

alr checked out now

[long arrow]

cross product of those two isn't what you said

[cobalt merlin]

ye i put in 3 in the calcultor instead of -3

idk why i had it written on paper

[cedar kiln]

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[edgy willow]

help me pls idk

[cedar kiln]

@edgy willow Has your question been resolved?

[edgy willow]

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[candid crane]

Need help with a probability question, using r studio rn for class

[candid crane]

pnorm(1030, mean = 1100, sd = 200) = 0.363

the question is about the SAT score

and i am supposed to find the probability that an uptake rate from the sample dataset is <15.3 umol/m^2 sec. Round your answer to 3 decimal places

[latent bloom]

Z-score?

[candid crane]

n this problem, we can calculate the cumulative probability of Edward's SAT score, which was 1030, given a mean SAT score of 1100 and a standard deviation of 200. To do this using pnorm():

pnorm(1030, mean = 1100, sd = 200) = 0.363

In other words, Edward's SAT score is around the 36th percentile, which means he scored better on the SAT than approximately 36% of the students that took the SAT.

Use the mean and SD you calculated from question (1) and the pnorm() function in R to answer questions 6-9

no i wish

[dire geode]

tf is pnorm

[candid crane]

its this code in r studio that we use

[latent bloom]

What does it do or what does it stand for?

[candid crane]

it just provides the distribution

pnorm(datum, mean, sd)

[latent bloom]

Hmm

[candid crane]

the mean and sd are given

[latent bloom]

normal distribution curve

[candid crane]

and the datum 1030 is form the example

[dire geode]

do you know formulas

e.g. the CDF of the normal distribution

[candid crane]

I just know I am supposed to pnorm

[dire geode]

well you should state what that formula refers to

[candid crane]

I just looked up the CDF and it looks way advanced than anything i have ever done

it just Cumulative Distribution Function (CDF) of the Normal distribution in R

[dire geode]

wat does this have to do with sat scores

[candid crane]

gives the CDF of the normal distribution in r so i dont have to manuyally enter it in the CDF formula

oh the sat scores are the question problem

I think I will jsut see if i can contact my assistant teacher

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[teal grotto]

how would i do part a

[honest imp]

@teal grotto you don't need to take into account wind resistance, right?

[teal grotto]

nah

ignore air resistance and take g to be 9.8m/s

[spice pier]

We know from Newton's first law that a particle keeps moving with the same velocity as long as they are not acted on by any force right? Can you think of any force in the horizontal direction?

[honest imp]

I'm pretty sure gravity would only effect the vertical velocity so the answer to a(i) and a(ii) would be the same: 200m/s

nvm. listen to Bono, his explanation is better

[teal grotto]

i thought it was 200 as well but isnt that for the plane

[spice pier]

We know there is not wind resistance and gravity is always in -y direction.

[spice pier]

If you drop something from a moving body the body acquires the same velocity as the body it was dropped from.

[teal grotto]

ah ok so it would be 200 then

[spice pier]

Yup.

[teal grotto]

for b

would i use suvat?

[spice pier]

Yes.

[teal grotto]

i will need to find final velocity

[spice pier]

The acceleration in this case will be g. Remember that the velocity initially in the vertical direction is zero.

[teal grotto]

yes cause gravity

it would be -9.8 for acceleration as im taking downwards to be negative

[spice pier]

Yup.

[teal grotto]

cool ill try that

thanks

[spice pier]

Btw, for more physics related stuff there is a physics server in #old-network .

[teal grotto]

oh i should join that then for sure

thanks for letting me know

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[vital mulch]

Need a bit help understanding this

[vital mulch]

Using standard normal table,

P(Z > z) = 0.33

= 1 - P(Z < z) = 0.33

= P(Z < z) = 1 - 0.33

= P(Z < 0.44 ) = 0.67

z = 0.44

where is the .44 coming from??

[dire geode]

show the original question

[vital mulch]

ok

Social Security Payments Consider the distribution of monthly Social Security (OASDI) payments. Assume a normal distribution with a standard deviation of $113. If one-third of payments are above $1222.79, what is the mean monthly payment? The mean monthly payment is $?

[cedar kiln]

@vital mulch Has your question been resolved?

[dire geode]

looks like they got 0.44 from the z-table. do you have a picture of one

bottom right entry

[vital mulch]

howd they figure that out from the z table?

[dire geode]

P(Z < z) = all the area under curve from –infinity to z

find the z value that corresponds to area = 0.67

each entry in the table is area

[vital mulch]

so theyre usig .67 on the z table?

but .67 on the z table is .7486

[dire geode]

you got it backwards

[vital mulch]

i seen that .44 on the z table is is .67

im still confused on how they knew to use .44 on the z table

[dire geode]

The entry is 0.67. that's not the z value

[vital mulch]

ok

[dire geode]

Area under curve is your probability

[vital mulch]

= P(Z < z) = 1 - 0.33

= P(Z < 0.44 ) = 0.67

OOOH

they use the zscore that equal to .67 which is .44

what z that has a score of .67

[dire geode]

It'd be good for you to conceptually assign meaning to the numbers

z can take any real number value

But probability is between 0 and 1 inclusive

[vital mulch]

dang turns out the answer i put there was wrong

what i gave they didnt calculate it correctly

thank you

!close

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[long arrow]

,rccw

[jaunty shoal]

its rotated sorry bout that

[long arrow]

find perimeter of ABC then take 150%

[jaunty shoal]

can you give me a hint

[muted bear]

That was a big hint

[jaunty shoal]

u sure

[muted bear]

Yes

[jaunty shoal]

I’m kinda confused I’m sorry

[scarlet garnet]

do you want to find the new perimeter in terms of 'old perimeters'?

[jaunty shoal]

original to new

[scarlet garnet]

so perimeter is all sides added together, just do that and then multiply by 150% right?

[jaunty shoal]

50 x 150%

[scarlet garnet]

yes

[jaunty shoal]

75

[scarlet garnet]

h

[muted bear]

h!

in other words, yes, thats correct

[jaunty shoal]

75cm^2

[scarlet garnet]

no

cm+cm+cm=cm

[jaunty shoal]

?

15 + 15 + 15 + 15?

[cedar kiln]

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[covert ferry]

just need to check if my answer is right

can someone say the answer

[harsh basalt]

Should be 0

[solid juniper]

what is the question?

[covert ferry]

okay

ummm can you tell me what you did

[harsh basalt]

Expand

[covert ferry]

i wanna see where i messed up

[muted bear]

🙅

[harsh basalt]

oh damn

[violet night]

is there actually a question or have you just posted an equality

[harsh basalt]

Where did I screw up?

[muted bear]

expand

[solid juniper]

probably in the algebra, and in not asking what the question is

[covert ferry]

it is algebra

[harsh basalt]

ohh hold up

[solid juniper]

what is the question??????

[covert ferry]

its a linear equation

click on the picture i think

[violet night]

a false one?

[covert ferry]

i see it

idk

[covert ferry]

wdym?

[violet night]

is the goal to say if its true or false?

[harsh basalt]

Would it be just 2?

[covert ferry]

no you have to actually get the answer

[solid juniper]

what is the question??????

[harsh basalt]

Isolate n ig?

[covert ferry]

yes

it is

[violet night]

but there is no answer, this relationship doesnt hold

and there is no clear question

[muted bear]

is that what the teacher told you to do or are there words above the problems describing the equation?

[harsh basalt]

0=2 doesn't work

[solid juniper]

the equality evaluates to false for any n

[solid juniper]

send the entire page this image is from

[covert ferry]

its a lecture

thats just a question from a video

[muted bear]

do you have a video link?

[covert ferry]

idk how i can send it

its all g guys its not a question i actually like need the answer to

[muted bear]

does the teacher/prof continue and solve it?

[covert ferry]

no lmao

thats exactly why i was asking to check

[cedar kiln]

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[short sierra]

I got the right answer, however I am not sure if this is by luck or I did everything correctly. can someone please make sure I did it the right way?

[gilded elm]

actually you did it correctly

good job

but did you understand what you were doing?

[short sierra]

My issue was after deriving (1-3e^x) I thought that there might be more work to it since i was left with -3e^x. I was thinking maybe I was supposed to do something more but it ends up getting canceled in the end

Thats what I thought happened but I just didn't do that part

[gilded elm]

chain rule.

[short sierra]

Only the chain rule right

Nothing else

[gilded elm]

oh you tried differentiating e^x?

that thing when differentiated becomes itself

which you should know

[short sierra]

Yeah so I don't write it again

Yeah

[gilded elm]

the reason it got cancelled is probably because of that

[short sierra]

Oh okay

I only used the chain rule

[gilded elm]

why be rude?

[short sierra]

I was just making sure

Thank you for your help

[gilded elm]

some people don't learn calculus until university moondom

no worries

wow that was a quick ban

[short sierra]

Lol

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[cosmic steppe]

Idiot alert

[cedar kiln]

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[gilded elm]

kill me I can't find delta such that 1/x is uniformly continuous on (0, 1)

[gilded elm]

i can't believe this

help

,w 1/x

[wraith dagger]

Results provided by WolframAlpha

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

Requested by DerpZ#9141

[gilded elm]

,w graph 1/x

[wraith dagger]

Results provided by WolframAlpha

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

Requested by DerpZ#9141

[gilded elm]

I always get stuck on things dealing with 1/[blah blah]

[flint plinth]

why do you think it is uniformly continuous?

[gilded elm]

it looks like it is on (0, 1) tho

[flint plinth]

it blows up as x->0+

[gilded elm]

oh

[flint plinth]

tiny changes in x will result in huge changes in y

[gilded elm]

I think i did not sleep enough

well

[flint plinth]

a more suitable question would be: prove that it's not uniformly continuous on (0,1)

[gilded elm]

the question does ask me to prove or disprove

[flint plinth]

oh

[gilded elm]

I can handle that myself awesome

[flint plinth]

what's the question?

[gilded elm]

it just asks if 1/x is U.c. on (0, 1)

[flint plinth]

ah got it

[gilded elm]

but what that means is that I'll have to show it is NOT

if I say it isn't

which I can handle myself

awesome ty

love how fast the response was

.close

[cedar kiln]

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[gilded elm]

yup found the sequences thanks

[cedar kiln]

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[crimson sedge]

Why does the work turn negative ?

[latent bloom]

"Stop"

"How much work must be done to stop a 1000kg car traveling 30m/s?"

In other words, you are running at 5 m/s. Someone wants to stop you completely. What would the direction of the force be if he were to stop you?

[crimson sedge]

the force of the other person?

the direction of the force would be the opposite direction

[latent bloom]

Exactly

So stopping the car would need a force opposite to the direction of traveling or with the direction of traveling?

[crimson sedge]

opposite the direction of travel

[latent bloom]

So the force will be opposite to the distance traveled

And so you will get negative work

[crimson sedge]

but the answer is postivie

[latent bloom]

Answer key?

[crimson sedge]

sorry, it is

[latent bloom]

Hmm

[cedar kiln]

@crimson sedge Has your question been resolved?

[cedar kiln]

@crimson sedge Has your question been resolved?

[lethal jackal]

work is done by something on something

in this case, the car is doing work 450,000 J of work onto something else

or something else is doing -450 kJ of work on the car

[cedar kiln]

@crimson sedge Has your question been resolved?

[jaunty pumice]

@crimson sedge answer key is wrong

It will be (-45 ×10⁴)J

[cedar kiln]

@crimson sedge Has your question been resolved?

[cedar kiln]

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[brave frost]

If x^4 = 3
find the value of x^8

[brave frost]

(Index laws btw not logs)

would x^8 = 9

since (x^4)^2 = x^8

and to balance we do the same to the other side

3^2

= 9

correct or am I tripping

[gilded elm]

✅

[brave frost]

ok

.close

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[verbal forge]

hey

[lusty grotto]

hi what is ur question

[verbal forge]

so I dont know how to do the differentiation for this equation

[lusty grotto]

send the eqation

[verbal forge]

with respect to x, I know that I should use the quotient rule

but how do I differentiate it with respect to y?

[lusty grotto]

when u r differentiating wrt y, x is a constant

how wud u differentiate something like 1/(1+x) wrt x

u do it the same way

[verbal forge]

is it bad that I forgot how to do 1/(1+x)

😬

[tepid valley]

wouldn't this be f(xy)=xy/xy+y ?

[lusty grotto]

u can use the quotient rule for this

it is also a quotient

[verbal forge]

ohhhh

makes sense

ima give it a try

[lusty grotto]

?

[verbal forge]

is the answer -x / ( x+ y )^2 ?

[lusty grotto]

Yeah

[verbal forge]

thanks

so much

is this the same thing

both Gy and Gx are solved using product rule?

[cedar kiln]

@verbal forge Has your question been resolved?

[cedar kiln]

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[fast hazel]

im having a little bit of trouble understanding degrees of field extensions
so we have that [L:K] is defined to be the dimension of the vector space of L over K
which is... fine, but then why, for example, [C:R] = 2 with the basis {1,i}? what can actually go into the basis, since i isn't in R, for example

[crimson sedge]

elements of L can go into the basis

[fast hazel]

oh does it take like

K[a] where a is from L

as an element of the basis

[crimson sedge]

yeah it can take a into the basis

[fast hazel]

oki oki

thx

.close

[cedar kiln]

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[rough yoke]

Consider a function f(x) with f(1)=0, f(2)=2 and f(x)=f(x−2)+x for x>2. Use induction to prove that
f(n)≤ (n^2/2) for all integers n≥1.

Could anyone help me with this?

[rough yoke]

Base cases:
n = 1, f(1) <= 1^2/2
0 <= 1/2 , true

n = 2, f(2) <= 2^2/2
2 <= 2 , true

IH:
for 1 < k' < k, if it is true for k', it is true for (k + 1). (k>2)
Is this part correct?

(I typed too fast, sorry for edits)

[cedar kiln]

@rough yoke Has your question been resolved?

[cedar kiln]

@rough yoke Has your question been resolved?

[worn prism]

Let it be true that $f(n)\le\frac{n^{2}}{2}$

Then, $f(n+2)=f(n)+n+2\le\frac{n^{2}}{2}+n+2\le\frac{(n+2)^{2}}{2}=\frac{n^{2}}{2}+2n+2$

[wraith dagger]

natsumi3hara

[worn prism]

honestly, idk what induction is so just googled and tried

[cedar kiln]

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[merry nacelle]

I tried the substitution method on this

[cedar kiln]

Please don't occupy multiple help channels.

[merry nacelle]

And got this, is this correct?

[lusty grotto]

what is this?

[merry nacelle]

Integration by substitution

I get somethinig crazy when I check wolfram

hahaha

[lusty grotto]

u r integrating (x^2 + 3x)^3 * (2x + 3) ?

[merry nacelle]

Yes, correct! 😄

[lusty grotto]

and u make the substitution t = x^2 + 3x ?

[merry nacelle]

I say dt/dx = 2x + 3

and then find dt/2x+3=dx

Like this^

[lusty grotto]

oh right

right

[merry nacelle]

Then I put t back

and the new dx we just isolated

and then the rest is history

[lusty grotto]

yeah this is correct

[merry nacelle]

cect?

Oh!

Awesome!

Why does wolfram give me something insane?

I honestly thought it was wrong 😂

[lusty grotto]

what did u put into wolfram

[merry nacelle]

But couldn't see where it felt really simple

[lusty grotto]

and theres a +C

[merry nacelle]

Oh yes the constant

😂

This is wolfram

[lusty grotto]

if u expand this u shud get that

they are the same thing

[merry nacelle]

yes

just checked

[lusty grotto]

its like how (a+b)^2 and a^2 + 2ab + b^2 are the same thing

[merry nacelle]

Yes, makes sense!

I just thought wolfram would like automatically pack it down

but i guess not 😂

[lusty grotto]

lol

[cedar kiln]

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[trim crescent]

Hello is anyone familiar with the parameter variation method for differential equations of the second order ?

[lyric jungle]

[trim crescent]

I don’t understand how it works haha

I’m stuck at the start lol

How does algebra fit in here ?

Hello is anyone familiar with the parameter variation method for differential equations of the second order ?

[cedar kiln]

@trim crescent Has your question been resolved?

[trim crescent]

.close

[cedar kiln]

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[cedar kiln]

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[gilded elm]

who knows

this is insufficient context

[crystal raptor]

Represents v/ρ

[crimson sedge]

its a physics equation

what is it exactly

[foggy merlin]

can you give us the context tho

[gilded elm]

you're going to need to give us more context

[crimson sedge]

@gilded elm @foggy merlin @crystal raptor

[gilded elm]

beta appears to be an angle

read it carefully yourself

[crimson sedge]

it just says where B appears to be in rad

[cedar kiln]

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[cedar kiln]

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[halcyon island]

Hello! I'm working on programming a vision cone for an intelligent agent to detect other agents in a simulation.
The agent has an x, y coordinate as well as a direction it's facing between -2PI to 2PI.
I want to figure out if it's able to see other intelligent agents based on the direction it's facing.

Current formula (not sure if it's accurate):

• Use Euclidean distance to check if any agents are in range, if they are further than the vision distance than it's not possible for them to be in view.
• Normalize the other agent's x, y coordinate by taking x / distance and y / distance.
• Calculate dot product between other agent's normalized x, y coordinates and the original agent's x, y rotations
• Calculate angle between them using acos(dot)
• If angle < agent orientation / 2, it is in view?

Thank you in advance.

[halcyon island]

Here is the Java code I've currently attempted :

The predator agent is the agent who is seeking the prey agents.

Rotation of predator agent is calculated as follows:

    float predXRotation = (float) Math.cos(predOrientation);
    float predYRotation = (float) Math.sin(predOrientation);

[cedar kiln]

@halcyon island Has your question been resolved?

[cedar kiln]

@halcyon island Has your question been resolved?

[cedar kiln]

@halcyon island Has your question been resolved?

[cedar kiln]

@halcyon island Has your question been resolved?

[cedar kiln]

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[rigid helm]

help

[cedar kiln]

What step are you on?
1. I don't know where to begin
2. I have begun but got stuck midway
3. I got an answer but I'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above

[rigid helm]

1

[ancient lodge]

🤔

[scarlet garnet]

nah uh

[long arrow]

Try to answer to this question:
What does that mean they are perpendicular to each other? (Hint: slope)

[rigid helm]

they intersect at a 90 degree angle

[long arrow]

thanks for defining perpendicularity

[rigid helm]

yw

[ancient lodge]

...

[long arrow]

ah that's same person hehe

so yes, we know this but what about slope?

[rigid helm]

negative reciprocal?

[long arrow]

yeah, knowing this you should be able to find P

[rigid helm]

oh ok thank you!

.close

[cedar kiln]

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[fallow plaza]

hi

[cedar kiln]

Please don't occupy multiple help channels.

[fallow plaza]

can someone help me

[tropic oxide]

.close

[cedar kiln]

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[cedar kiln]

What step are you on?
1. I don't know where to begin
2. I have begun but got stuck midway
3. I got an answer but I'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above

[jaunty shoal]

1

I dont know where to begin

[grand forge]

split into smaller parts

smaller shapes as one must

https://gyazo.com/2c48431459c5e25de33203c833a23779

see how it makes it easier

[jaunty shoal]

wait

thats the wrong image sorry bout that

[grand forge]

do the same thing with that one

need me to do it or u got this?

[jaunty shoal]

i got it

[grand forge]

Ok

[jaunty shoal]

nvm the shapes arent the same

[grand forge]

Yea

[jaunty shoal]

when i try to cut in to rectangle theres something off

[grand forge]

mhm

try cutting it horizontaly

Instead of vertically

[jaunty shoal]

yup i need help with this one

[grand forge]

https://gyazo.com/9eb61a6da432e7e4c02f0e8fe6c7e1ba

all g

see that

[jaunty shoal]

4 now

[grand forge]

Yep

Split into as many as u need too

not limited to 3 or 4

[jaunty shoal]

ok

for the traingle 16

*15

15 x 8

/2

60

[grand forge]

Yep

[jaunty shoal]

1st rectangle

16

2nd