help-13

[crimson sedge]

4x-3x = x is indeed a result of the distributive law

So in summary it goes like
4x-4=3x
4x-3x=4
4x-3x=4
1x=4
X=4

i’m not sure why you’ve written the same line twice, but yes

do you know how to reach the answer after finding x=4?

[pulsar blade]

but do you understand why we came to 4x-4 and 3x? just making sure

[crimson sedge]

You just plug it in right.
4•4=16
And
3•4=12
Then add them

[crimson sedge]

yes

[crimson sedge]

Cool, thank you. Sorry for taking so much time. Ill watch some content on the distributive law.

[pulsar blade]

oh not micabo, @crimson sedge ^^

[crimson sedge]

Thanks for your help

[crimson sedge]

watch some on “combining like terms”

those might be more useful

[crimson sedge]

Thanks. I will

[pulsar blade]

something like this?

"2 step algebra equations worksheet pdf" type stuff like this into google or "basic algebra problems" and you can get tons of examples

[crimson sedge]

Thank you.

[pulsar blade]

don't underestimate the power of practice and perserverence

[crimson sedge]

True. Thanks for your help.

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[cursive crystal]

If i have two vector fields. Why do they commute if and only if their flow commutes?

[broken mist]

Just ask

[cedar kiln]

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[cursive crystal]

<@&286206848099549185>

[soft cargo]

Ok

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[lone lagoon]

Guys

[lone lagoon]

help me

why is the limit infinite

(I think it is infinite)

lim x->2 infinite

but why tho

[sweet knoll]

well like its more like it doesnt exist

if u plug in 2 into the first equation

you will be left with 1/0

and obviously u cant divide any # by 0

[fair geyser]

you can't get 1/0

you get 5

it says you get 5

i'm also maybe wrong but it's not infinity

depending if your x is less or more, it's inf or −inf

the lmit doesn't exist because it's two different things

but if it was inifinity from both sides that's technically also doesn't exist

idk how people work around that

[lone lagoon]

yeah

I mean

the lateral limits

they do exist, right

?

[fair geyser]

yes

except inifinite limits are considered to not exist

[lone lagoon]

okay

I get it

but why infinite tho

can you tell me that

[fair geyser]

uh

no

it's just what it is

if it was the same direction

f(2) = 5

anything close to 2 is as large as you want

[cedar kiln]

@lone lagoon Has your question been resolved?

[lone lagoon]

what

i don't get it

could you please tell me what happened there

[fair geyser]

i don't know what you're asking

i'll use desmos one minute

this is the function

i can't tell you anything else

that's exactly how much i know about this

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[dry dirge]

Two cars are coming from two places to meet each other. After 2/15 hour the distance between them is 16 km. What will be the distance between them after 1 hours. How to solve this without proportion

[worldly chasm]

There doesn't seem to be enough information to answer.

For instance, if the two cars were initially 18 km from each other, then they are moving at 15km/hr. But if it's 20 then they are moving at 30km/hr.

Unless there's been a mistranslation or something.

And they initially started at the same place and are moving apart, rather than traveling together

[dry dirge]

No translation is goof

[maiden tapir]

Use vectors

re

[dry dirge]

But they are closing at constant rate

[maiden tapir]

relative velocity

[worldly chasm]

Not enough Information then

[dry dirge]

Not allowed vectors

[maiden tapir]

use the rate of change of relative velocity

[worldly chasm]

You would need two points.

[maiden tapir]

oh

[worldly chasm]

You only have one

[hearty jetty]

yeah, i was checking it and, without the initial distance it cant be

[maiden tapir]

you mean the distance at rest ?

[hearty jetty]

yeah

distance between car1 and car2 before the 2/15 hours

[worldly chasm]

You just need the distance at any other point, doesn't matter when

[hearty jetty]

true

[worldly chasm]

(Because lines are defined by two points)

[maiden tapir]

he said they are closing in by a constant rate

[dry dirge]

Why is this not true

[hearty jetty]

hr≠km

[maiden tapir]

two different quantities

[worldly chasm]

Because that's only valid if you start from the same location.

Assuming you fix the units

(Which is pretty easy to do)

[hearty jetty]

someone wants helpme with integrals ?

😭

[worldly chasm]

! occupied

[cedar kiln]

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

[maiden tapir]

definite or indefinite?

[worldly chasm]

Omg occupied

[dry dirge]

Guys can you answer me ?

[maiden tapir]

OK

[maiden tapir]

I'll try something

[worldly chasm]

@dry dirge Your question doesn't have an answer as posed.

!original

[cedar kiln]

Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.

[dry dirge]

Tnx

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[worldly chasm]

???

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[knotty harness]

How do you remove the number of arrangements when xi is > 30 from the total

[crimson delta]

principle of inclusion exclusion

[knotty harness]

Ok so how would you do that

[fresh patio]

well the idea is that you let S_i be the number of arrangements where x_i > 30, and then you do pie on that

[knotty harness]

Pie?

[fresh patio]

principle of inclusion exclusion

[knotty harness]

Ok but I dont know how to do principle of inclusion exclusion

[knotty harness]

Is this solution valid

Some parts of it

Dont make sense to me

[fresh patio]

yeah this is essentially pie

i guess it would be better to do it on S_i the set of arrangements where there are i elements greater than 30

you are adding together the size of the individual sets, and then subtracting their intersections

[knotty harness]

Yeah thats what I thought PIE was

But I don't get how the solution is even doing that

108C8 is the total

Which I get

How is it following this formula

[crimson delta]

lets say x1>30. what can you say about the remaining elements

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[rich vault]

do you have to learn logic or math first. and can you learn logic and/or formal logic without mathematics?

[dusk goblet]

for proof writing you learn basic logic and yea you don’t need much math knowledge for it

having a familiarity with math is a benefit though of course

[rich vault]

thanks a lot for the info knief.

[dusk goblet]

philosophy majors for example take logic

[rich vault]

philosphy and logic i find interesting comparing them.

[crimson delta]

for most math you dont need more logic than basic and/or/implication/... stuff

[rich vault]

i'm interested in coding to make complex and educational games.

i wonder where's the best place to start coding if you want complete control over the code and the complexity,

i'm thinking of starting with c++

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[raw salmon]

Hello ! I need help with figuring out a formula for the surface area of a pyramid trunk based on a height. We know the small base area, the big base area, and the maximum height. At height H , be it any number from 0 to Hmax figure out the area of a cut which is parallel to both bases. I have this drawing hopefully you understand. I need it to model water flow in such shape, where water level is H.

[raw salmon]

i found this formula online, but im not sure its the right one

https://math.stackexchange.com/questions/1645234/finding-different-surface-areas-along-a-frustum-pyramid which i found here

[cedar kiln]

@raw salmon Has your question been resolved?

[raw salmon]

<@&286206848099549185>

[raw salmon]

Or the slant length at height H

[cedar kiln]

@raw salmon Has your question been resolved?

[autumn glade]

Is it a pyramid? From the drawing it looks more like a trapezoid prism

You want the area of the water surface so to speak, correct?

@raw salmon

Anyway, assuming it's a pyramid with square bases, you just need to get the side length at height h

Which is linear in h

[wraith dagger]

LooseEthics

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[worthy scaffold]

hey can someone help with 1 (a) if possible, thanks

[worthy scaffold]

<@&286206848099549185>

[minor mist]

if you don't require exact measurement then just draw a circle, then put chord AB and CD parallel to each other

[cedar kiln]

@worthy scaffold Has your question been resolved?

[azure carbon]

draw two lines, first is 12cm, second is 16 the distance between them should be 14 cm. Then you need try to draw circle around it, so both lines would be chords

but in my opinion, it easier to find radius, and then draw the circle according to exact measurements

[worthy scaffold]

this?

[azure carbon]

yeah

this should be right

[worthy scaffold]

ohh thanks then!

[azure carbon]

welcome!

[worthy scaffold]

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[orchid gazelle]

hello

[lusty grotto]

Hello what is ur question

[orchid gazelle]

Omg wait

My laptop isnt laptoping

Is this correcr?

It says quartery

Ly

nvm im a dumb dumb

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[crimson sedge]

bro this is impossible

can anybody help

[steel fractal]

what should we do?

[crimson sedge]

I need 2,3,5,6,7,9

U could help me figure them out

[steel fractal]

well… you need the number right?

[crimson sedge]

yes

[steel fractal]

6/2 = 3

[crimson sedge]

mhm?

2,3,5,7,9 left

2,3,5,7 actually

[vivid tundra]

do you have to use all the numbers?

[crimson sedge]

Yes

[vivid tundra]

ah ic, lemme try

[slate lintel]

dude I gave you a script for this yesterday

there's a link in the chat

[crimson sedge]

Yes I know that’s why I here again

It dosent work anymore

it can’t find any of the numbers

[slate lintel]

oh. right, it doesn't work with duplicates. i probably should have recognized that. i don't have the ability to fix it currently

[crimson sedge]

Oh

[vivid tundra]

I'll give answers with some steps missing
for 2, you can do 1+1

[crimson sedge]

1+1?

[vivid tundra]

for 3, you can use that

[crimson sedge]

I have to use all numbers bro

[vivid tundra]

yea, you need to figure out where to get 2 ones

[vivid tundra]

use that as a stepping point
the answer is similar

[crimson sedge]

I got 5

2,3,7 left

3,7 left

[past wave]

I wanna see that script

Can you share it again or maybe a link?

[crimson sedge]

Why

I can send u it

https://www.online-python.com/g14HJtCAN0

[vivid tundra]

can you do -(...)?
bc you can get to -7

[crimson sedge]

No

[vivid tundra]

oh wait, that's not necessary

you need to get to 4+3

[crimson sedge]

Hm

[vivid tundra]

the 3 in in the form of (...)/(...) btw

[crimson sedge]

Got it

[vivid tundra]

how'd you get 5 btw?

[crimson sedge]

5 was easiest bro

I think I know 3

Lemme try

[vivid tundra]

ah, completely missed that

[slate lintel]

It's nearly correct just needs to be a multi set instead of a set.

[crimson sedge]

Nvm

I got 1 off

[vivid tundra]

why use a set?

[crimson sedge]

The script?

[slate lintel]

Yes

[crimson sedge]

Ok ok

Thank you

[crimson sedge]

Do you think u could help me out with 3 or do u wanna wait till Hayley fixes the script and we can see if it works

[vivid tundra]

sure

(6+6)/(2+2)

[crimson sedge]

Thanks

@slate lintel tell us when ur done

[vivid tundra]

I wonder if there's only one answer to some these

[slate lintel]

I mean, I'm not working on it right now. I'm like driving to work and stuff. Maybe at some point tonight. I'll fix it. But if you want to try to fix it use chat gbt or something.

[crimson sedge]

Oh ok

[crimson sedge]

If u could add me and we could chat about it sometime and when ur done u could slide it through our dms

I gtg now tho lmk when u have time

@vivid tundra thanks again bro

[vivid tundra]

ah np

[dense kayak]

what game is this btw?

[crimson sedge]

all ten

[dense kayak]

very fun!

so the dupes are erroring?

[past wave]

Yeah

One game like this is 4=10

In that you have to sum 4 numbers to 10 using some operators

Super fun lol

[dense kayak]

i'm always playing 24 with car license plates haha

[cedar kiln]

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[inner field]

I need help with vector calculus. I am not certain whether or not I'm going in the right direction.
I only need a hint.
And yes, my calculations end with my result as the result is supposed to be a formula for r(t). It's path is something I need to describe too but I'll do that later as idk if my answer is correct even

[inner field]

I hope my handwriting is readable

Ah I do not know if it is universal but i,j,k are the unit vectors in the x,y,z direction respectively.

<@&286206848099549185>
Can you guys please help soon?
Or at least react if you're already trying to help so I know I'm being helped

[cedar kiln]

@inner field Has your question been resolved?

[inner field]

Help...

[inner field]

<@&286206848099549185> anyone interested in giving a helping hand?

[mild spear]

Magnetic field is constant throughout in the z axis.

[inner field]

Yeah that's because of vector k. I don't really get what you mean? Was I supposed to do something else with that information?

Because I got the cross product of k and v.
Then I saw the equation as a first order ODE and solved it by y'/y = c
Integrating over t
gives ln|y|=c*t + C

Which is in this scenario a/v = qB/m
Integrating over t
gives ln|v| = qB/m *t + C

Afterwards I treated V(v2,-v1,0) as the point through which the individual vectors go through:
x=x0+at
V={y=y0+bt
z=z0+c*t

Where V(v2,-v1,0) gives
x=v2+at
V={y=-v1+bt
z=0+c*t

[mild spear]

How could you divide two vectors?

[inner field]

They are functions right?

It looked similar as a first order ODE so I instantly took it as one

[mild spear]

You got something like..
q(B0v2,-B0v1,0) = m(a1,a2,a3)
Maybe you should use matrix algebra.
like Ax=B.
I'm not sure though.

[inner field]

We haven't had linear algebra yet, that's like in the last semester.
I think what I am supposed to do is to take the integral of each component but I'm not sure how to define that as I can't instantly take an integral within an equation as I like as that will give a different outcome

[mild spear]

Can you wait till tomorrow. I'll try doing it in the morning.

[inner field]

Wait, maybe

qB0(v2,-v1,0)=m(a1,a2,a3)
And integrate like that

[inner field]

Sure, I'll try this out though and see if I get an answer

[mild spear]

Okay

[inner field]

Then I'll close this help channel now

.close

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[north whale]

what does the mode of a geometric distribution even mean?

[dire geode]

do you know what mode means?

[north whale]

yes

[dire geode]

do you know what a geometric distribution is?

[north whale]

yes

[dire geode]

combine those two definitions

[north whale]

i tried

i dont get it

cuz here its different

[dire geode]

what did you try

[north whale]

1 2 2 2 3

mode is 2

simple

but how does that tie into geometric distribution?

cuz we dont have a fixed set of data now

[north whale]

thinking how it ties in together

its something to do with highest probability ik

x=1

but whats highest probability gotta do with mode?

[dire geode]

this is a dataset, not the distribution

the distribution would be a histogram with P(X=1) = 1/5, P(X=2) = 3/5, P(X=3) = 1/5

Notice how P(X=2) has the highest probability?

[north whale]

well yeah

[dire geode]

great do the same for geometric distribution now

[north whale]

so mode of a distribution is simply the PROBABILITY of obtaining the mode?

[dire geode]

no

[north whale]

no wait

[dire geode]

.

[dire geode]

.

[north whale]

yea

but i still dont get how it works with geo

lets take example

flipping a coin

lets say success is getting head

how does getting head on 1st try become a mode?

[dire geode]

P(X=H) = P(X=T) = 1/2

i don't know how you break ties, but some places call both the mode

[north whale]

but the mode is 1 right?

[dire geode]

yes

[north whale]

oh so here 1/2 is the highest probability

that makes sense ig

[north whale]

ty so much

.close

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[craggy sphinx]

How to do these

[smoky cliff]

Id try using the quotient rule

You literally just substitute to it

[craggy sphinx]

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[tall granite]

how do you do these? we have revision. I have to find x

[tall granite]

best i can do is find angle OAB = angle OBA = 50 degrees

possible answers for x:
110
120
130
140

im stuck

[rain walrus]

so, we know arc AB is 80 degrees, and thus angle AOB is 80 degrees

[tall granite]

yes

i got that

[rain walrus]

so then O, A, and B create an isoceles triangle with 80, 50, 50 angles

[tall granite]

yes i got this too

and i have no idea how to go from here

[rain walrus]

what do we know about angles on a straight line?

[tall granite]

OAB is 50

whole angle of straight line is 180

so basically 180 - (x + n + 50) = 0

[rain walrus]

where does n come from here?

[tall granite]

unknown value

[rain walrus]

what unknown? you have x and angle OAB on a straight line

[tall granite]

oh x is the whole thing?

isnt x only the

intersection

[rain walrus]

yeah, x is the whole thing

[tall granite]

then it makes sense

[rain walrus]

if x was that intersection then it would be 90 by virtue of line OC being from the radius

[tall granite]

i have another geometry question but i have no idea of it

[rain walrus]

go ahead :)

[tall granite]

oh its in lithuanian

ignoro the question itself, if something is unclear let me know

[rain walrus]

ok, so we know b is at (-1/2, root3/2)

[tall granite]

yeah

[rain walrus]

we can create a triangle with O, B, and (0, root3/2)

that contains a small portion of angle a

so the opposite is 1/2, adjacent is root3/2, and tan(a) = opposite/adjacent

[tall granite]

what

im so lost sorry

[rain walrus]

sorry that's my fault

you see the horizontal line from b to the y axis?

[tall granite]

yes

[rain walrus]

that line, the y axis, and the line to b make a triangle

you see it?

[tall granite]

yes

and we have part of B angle which is root3/2

wait no we dont

we just have the triangle

[rain walrus]

yh

[tall granite]

god last time ive even seen sinus was an year ago

[rain walrus]

lol it happens

[tall granite]

yeah what about the triangle?

[rain walrus]

ok, so the bottom angle is a portion of the angle we need

[tall granite]

yes

wait no

we need whole alpha angle

[rain walrus]

yes but the other part of that angle is 90 degrees, that's easy

[tall granite]

oh yeah

[rain walrus]

we know that the opposing line to that angle is of length 1/2

we know that the adjacent line is of length root3/2

[tall granite]

wait which angle

[rain walrus]

the small part of angle a

[tall granite]

why is opposing angle 1/2

[rain walrus]

no, the length of the line is 1/2

[tall granite]

sorry which line again?

[rain walrus]

top blue one

[tall granite]

blue?

[rain walrus]

yeah

[tall granite]

oh yeah i got that

[rain walrus]

the blue is 1/2

the yellow is root3/2

[tall granite]

right

pythagorean?

[rain walrus]

trigonometry

[tall granite]

OB^2 = ... yes?

wait i dont need OB

[rain walrus]

it's just 1

[tall granite]

yeah

[rain walrus]

unit circle and that

[tall granite]

do i do the reverse sinus formula thing and get the little angle we need and then add to 90 degrees and

wait no i dont know

[rain walrus]

yeah this is a bit more strange, and requires knowledge of how the functions work

hold on

we know that sin(90) is 1 and cos(90) is 0

[tall granite]

right

i have to use calculator for those since i forgot the values

[rain walrus]

wait are you allowed a calculator?

[tall granite]

yes

[rain walrus]

oh sweet this is a lot easier then

yeah do the reverse sine

reverse cosine of -1/2

[tall granite]

we cant

wait no we can

idk

i get 60

[rain walrus]

is that -1/2 or 1/2?

[tall granite]

root3/2

reverse sine

1/2 would be cosine no?

[rain walrus]

yeah you can do reverse cosine of -1/2

[tall granite]

120

great. 2 different answers

[rain walrus]

okokok hold on, 120 is correct

[tall granite]

why isnt 60

[rain walrus]

the reason you get 60 is because inverse sine gives you the first answer for sin(60)

but we know the angle is above 90

[tall granite]

hm?

do we?

[rain walrus]

well the full angle a

[tall granite]

its 90 degrees + x

so perhaps + 60?

[rain walrus]

ok, so to find x

im sorry it's been a long time since i did this lol

[tall granite]

can you guess which grade im in?

[rain walrus]

it's been so long i can't anymore

10th?

[tall granite]

yeahg

[rain walrus]

oh wow

anyway, yeah to find the small x you do inverse sine of 1/2

[rain walrus]

i'm in my third year of a degree if you were curious

[tall granite]

why not cosine

[rain walrus]

because sin(x) = opposite/hypotenuse, which we know is (1/2)/1

which is 1/2

[tall granite]

nooo

answer is bad

very bad

[rain walrus]

what happened?

[tall granite]

a lot of decimal numbers

oh wait

its 30

[rain walrus]

there we go lol

[tall granite]

now what

[rain walrus]

we know that a = 120

try plugging 120 into the three trig functions

[tall granite]

what?

what functins

oh

yeah i got

sorry

[rain walrus]

sin, cos, tan

don't be sorry lol

[tall granite]

yeah no way im doing this on my own

thanks

.close

[cedar kiln]

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[tall granite]

idk

[rain walrus]

hey, if you want a shortcut for this

[tall granite]

im here

[rain walrus]

on the unit circle, the sine of an angle is the height of the point made by the angle

the cosine is the height of the point if you turn it 90 degrees counterclockwise,

sorry i didn't mention this before but it's better to at least see the maths first

i'm not too good at explaining things yet =w=

[tall granite]

well i dont got much time to rewrite all of it

its half past 10PM im not even quarter way there 😉

[rain walrus]

ouch, good luck lol

[tall granite]

i dont even understand half the stuff

but ill figure it out

[cedar kiln]

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[modest mason]

confused how they got to that final answer

[idle tusk]

they divided top and bottom by sin(a)sin(b)

[modest mason]

wow i didnt know you could do that

[cedar kiln]

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[cedar kiln]

@floral condor Has your question been resolved?

[floral condor]

<@&286206848099549185>

[merry solstice]

what have you tried

[floral condor]

uhhh counting the triangles

[merry solstice]

ok

anything else?

[floral condor]

nope

i dont know where to go

[merry solstice]

one way of making the pattern is making it symmetric

so how do you think we can go from there

[floral condor]

split the pattern into 3 equal parts?

[merry solstice]

explain

more

[floral condor]

uhhhhhh vertically?? but thats not equal tho

nor horizontally

14/3 gives remainder

[merry solstice]

we can make the line of symmetry the line like a diameter going through the hexagon

so we could make the figure with 6 triangles

[floral condor]

ohh

[floral condor]

but then there will be 5 triangles 5 traingles and then 4

[merry solstice]

sorry had to eat

[merry solstice]

ok neverm ind

look at the shapes made

the middle is a hexagon(6 triangles)

then after one deviation outward is a trapezoid(3 triangles)

then one triangle

[floral condor]

its okay

[merry solstice]

so it's 6-3-1

so the patter repeats

with another hexagon

and that's the reasoning

[floral condor]

ummmm what does deviation mean

[merry solstice]

it just means one more step

[floral condor]

oh okok

[floral condor]

okayy

i understand now

[merry solstice]

hope that helps

[floral condor]

thank you very much

[merry solstice]

ye

yw

[floral condor]

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[cedar kiln]

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[frank shale]

slope to find functions y=2x+2, y=-2x+2

i need explaination on how i should start and do this problem

<@&286206848099549185>

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[frank shale]

<@&286206848099549185>

[cedar kiln]

@frank shale Has your question been resolved?

[cedar kiln]

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[humble lintel]

yoink

[humble lintel]

What does finiteness have to do with this?

I guess to guarantee the finiteness of n then

[cedar kiln]

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[feral basalt]

Could someone please help me out with this problem?

Could someone please me with this problem?

I have to solve the given symbolic initial value problem

nvm im ok now

[cedar kiln]

@feral basalt Has your question been resolved?

[feral basalt]

No nvm

I still need help

[cedar kiln]

@feral basalt Has your question been resolved?

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[rose stump]

guys i have a problem goes like:
pick a suit, draw 5 card, possibility of getting 0, 1,2,3,4,5 of that suit card.

[cedar kiln]

@rose stump Has your question been resolved?

[fast verge]

anyone able to help me on this?

[rose stump]

Stop stealing peoples spot

Very disappointed

[fast verge]

I thought this chat was open

my bad.

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[ebon nebula]

can someone help on 19 please

[spare kettle]

whats the problem?

[ebon nebula]

how do i find the surface area and volume of figure 2

[spare kettle]

yk how to find surface area and volume of a cone right?

and cylinder too

[ebon nebula]

yes

[spare kettle]

so to find surface area of figure

you need to add the surface area of the top of cone

the long part of the cylinder

and the base of the cylinder

[ebon nebula]

so do u just add the surface area of cone+cylinder

[spare kettle]

no no the thing is

the surface area of the cylinder includes both the top and base disc too

[ebon nebula]

oh

[spare kettle]

but there the top disc is not included in surface area

so you have to deduct its area

and instead put a cones top surface area

[ebon nebula]

oh i see so if i were just to do the regular formulas for each shape it would be incorrect

[spare kettle]

yes for this case

thats why split it into some pieces and add

so like top of cone + body of cylinder+ base of cylinder

[ebon nebula]

is the formula still 2(pi)(r)(height) for this

[spare kettle]

yess 2πrh

for the body of cylinde

[ebon nebula]

ok ill try it ty!

[cedar kiln]

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[sick herald]

how do i find the time taken to cross the river?

[sick herald]

this is what ive done but its not right

[cedar kiln]

@sick herald Has your question been resolved?

[slender ginkgo]

,rotate

[sick herald]

<@&286206848099549185>

<@&286206848099549185>

[cedar kiln]

@sick herald Has your question been resolved?

[sick herald]

<@&286206848099549185>

<@&286206848099549185> how do i find the time taken to cross the river? vector help pls

[dull oxide]

The theta you calculated measured angle BCA, not BAC

[sick herald]

oh what do you mean?

[dull oxide]

I mean x is wrong because your theta is not measuring the angle that you (probably wanted)

In short, look again at how you calculated theta and how you are using it.

[sick herald]

Ohh really

I just assumed my method was right because i got the answer haha 😓

ill look again

[dull oxide]

Also, you mixed up your units with km and m. Make them consistent

Btw you really don’t need any trig at all to solve this

Regardless of the speed of the current, she is rowing north at 4 km/h, right? Or is she moving along the path AC at 4 km/h? i assume the former but that also trivializes the problem

[sick herald]

ohh right youre right i see now

thanks

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[steady plover]

why is this the hint to the problem, "is 9409 a prime?"

[steady plover]

is it to identify if 9409 is a perfect square?

[idle tusk]

yes

[steady plover]

but the solution got really messy

9409=10000-200x+x^2

then 591-200x+x^2

then quadatric formula?

[idle tusk]

yes

oh hm

[idle tusk]

no need

factor 591

[steady plover]

i see... i wasn't just sure bc problems in aops books usually doesnt lead to messy sols

[steady plover]

factor?

[idle tusk]

yes

factorize

[steady plover]

oh

197 and 3

i see

then should i plug thesw values to (100-x)^2?

100-197 is negative so extraneous root ig

97 is the sqrt

thus not prime

i see

thank u

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[karmic jungle]

Hello!
I have this table and want to calculate di/dE.
This would be the right solution but i have no idea how to get there

[cedar kiln]

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[buoyant latch]

https://en.wikipedia.org/wiki/One-way_analysis_of_variance

[buoyant latch]

am i going crazy

why is there that multiplication by the number of things in the sum

oh i am going crazy

it's to cancel out that factor in the other parts of the sum

.close

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[bronze kelp]

does anybody know where i go from here to find if this series diverges or converges X_X

[half salmon]

What's the rule for geometric series, the rule to determine if they're convergent or divergent

[flint plinth]

what kind of series is that?

[bronze kelp]

converges if |r| < 1

geometric

[half salmon]

so is |r|<1?

[bronze kelp]

yea

[flint plinth]

your k should be n btw

[bronze kelp]

how do i fnd the limit value

[bronze kelp]

ye oops

[half salmon]

Do you know the formula for the sum to n terms?

for a geometric

[bronze kelp]

S = a/1-r

i forgot what a is

[half salmon]

first term

[bronze kelp]

ohh

so itd be 4

[half salmon]

btw just so you know

thats the sum to infinity not sum to n terms

[half salmon]

yes

[bronze kelp]

when should i worry about this

[half salmon]

Do you know the sum to n terms?

[bronze kelp]

no

[past wave]

When this isn't inf

[bronze kelp]

o

[half salmon]

Can you see how the a/1-r is derived from this?

Another fyi the top and bottom equations are the same, its just easier to work with the top when r<1 and the bottom when r>1

[bronze kelp]

https://tenor.com/view/oh-no-cute-cat-gif-15060173

[half salmon]

Okay so think of it like this

for a sum to infinity, n approaches infinity

correct?

[bronze kelp]

yea

[half salmon]

if |r|<1 then what does r^n approach as n gets larger and larger

[bronze kelp]

0

[half salmon]

so what does 1-r^n approach?

[bronze kelp]

so thats just 1

[half salmon]

Yep

Thats it

[bronze kelp]

i see

[half salmon]

Everything clear?

[bronze kelp]

yea

ty 🙏

[half salmon]

Try proving this

Its always good to know or be able to prove formulas you re using

[bronze kelp]

1 more question before that

[half salmon]

go ahead

[bronze kelp]

for one in this form, what approach should i take

i pulled out 1/4 to try and get it in the geometric series form?

[half salmon]

Yep do that

what do you get?

[bronze kelp]

1/4(-3)^n

[half salmon]

You sure?

What do we want the powers to both be?

[bronze kelp]

n-1?

[half salmon]

yep

So thats already the case for -3 now do it for 4

take out the 1/4 like you said

[bronze kelp]

hmm

[half salmon]

Want me to show you

or do you want to think

[bronze kelp]

show me X_X

i can't think of any way

[half salmon]

((-3)^(n-1)) / (4 * 4^(n-1))

Hopefully you can do the rest

[bronze kelp]

howd it turn into -3/4

[half salmon]

It was (-3)^n-1 / 4^ n-1

[bronze kelp]

converges because abs(-3/4) < 1

[half salmon]

yes

[bronze kelp]

im confused

hows the n-1 getting to the bottom

and i thought we took out a 1/4?

wait

does taking out the 1/4 like

basically take out an n

[half salmon]

what's 4^(1) * 4^(n-1)

[bronze kelp]

4^n

[half salmon]

So you can split the 4^n in the original question to

4*4^(n-1)

Then just take that out of the fraction

and because both -3 and 4 have the same power

put them in the same bracket

[half salmon]

.

[bronze kelp]

ohh

are these still geoemtric series or a completely different thing

[cedar kiln]

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[zinc radish]

I need help with the following question.

By applying the Mean-Value Theorem to f(x)=cos(x)+x^2/2 on the interval [0,x], show that

cos(x)>1-x^2/2

for x>0. This inequality is also true for x<0. Why?

[zinc radish]

Shit, I am doomed.

[cedar kiln]

@zinc radish Has your question been resolved?

[zinc radish]

Ah yes, finally someone who can help me

[snow zodiac]

ah sorry

i misread your question

[dire geode]

have you read the mean value theorem yet? do you know what equation it gives you?

[zinc radish]

Yes I have

Although I have not been taught how to use it to prove inequalities

[zinc radish]

Bruh lol, it's alright.

[dense kayak]

well for the last part of the question, we know that cos x and x^2 are both even functions.

[zinc radish]

Yeah

And how do you prove the inequality using mean-value theorem?

[cedar kiln]

@zinc radish Has your question been resolved?

[dense kayak]

i'll echo riemann above ^^^
do you have the mvt equation on hand?

[zinc radish]

No

[dense kayak]

https://tutorial.math.lamar.edu/Classes/CalcI/MeanValueTheorem.aspx

second blue box

[zinc radish]

Okay and now?

[dense kayak]

well, set up that expression equation

then we can say something about f'(c)

note that c is strictly between 0 and x

mvt is ok? something like this

[wraith dagger]

citrusmunch

[cedar kiln]

@zinc radish Has your question been resolved?

[zinc radish]

My bad I was outside

So had no time

Well okay, the derivate would be

-sin(c)+c

How do I go from there?

[dense kayak]

i think the trick is to see that the derivative is strictly positive for any value of c > 0.

[zinc radish]

Okay

[cedar kiln]

@zinc radish Has your question been resolved?

[cedar kiln]

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[cedar kiln]

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[red yarrow]

why is the denominator of the second fraction squared

[cedar kiln]

@red yarrow Has your question been resolved?

[cedar kiln]

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[dusk goblet]

<@&268886789983436800> help this guy

🥱🥱

right

fooling absolutely no one bro

come again?

bro you’re trying to cheat

who are you calling names lol

just don’t cheat

right because chatgpt is horrible at solving math problems

and it has an image which would make it even more difficult to put into chatgpt

[broken mist]

Chat can take images but only the worse chat

[dusk goblet]

right and yet you still chose to come here

[broken mist]

The less worse chat can't sadly

[dusk goblet]

maybe brainly didn’t have it bro

why are you still here

<@&268886789983436800>

clearly a graded quiz

[cedar kiln]

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[cedar kiln]

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[prime island]

This answer key is probably right but I don't get 1 when I use the equation...

[prime island]

i get 2 / root 5

im doing <6,5,5> dot (-2,1,2)/sqrt(5)

then I get 2/sqrt(5)

[hollow trail]

how do you get the magnitude of v as sqrt(5)?

[prime island]

o

my

fking god

this is the

third time

how am i even in calc

wtf

.close

[cedar kiln]

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[crimson sedge]

most accurately identifies the types of extrema in the graph?

[crimson sedge]

Is there is one relative maximum and one relative minimum?

[livid hound]

no

where do you think are the locations of those are and what is your reasoning

[crimson sedge]

One sec

[crimson sedge]

max is x = 1 and min is x =4

If im wrong im sorry

[livid hound]

and your reasoning?

[crimson sedge]

Hold up

It has to be one relative maximum and one relative minimum.

hard to explain

[livid hound]

try

what are you looking at when determining whether something is a relative min

[crimson sedge]

This is where I can solve the answer

[livid hound]

e.g would the point (-1,0) be a relative min
and if not, why?

[crimson sedge]

No, the point (-1,0) is not a relative minimum.
cause (-1,0) looks like the function is chan ging from increasing to decreasing

So i think the answer is one relative maximum and one relative minimum

[livid hound]

incorrect reasoning

[crimson sedge]

What do you mean

This is the way we are taught on khan academy

[livid hound]

increasing to decreasing indicates a relative max, which (-1,0) isn't either

what exactly did you read on khan?

[crimson sedge]

They give us a video then these questions

I go here when khan academy doesnt explain it to me good

[livid hound]

can you link which vid you watched

[crimson sedge]

https://www.khanacademy.org/math/ap-calculus-ab/ab-diff-analytical-applications-new/ab-5-4/v/testing-critical-points-for-local-extrema

Khan didnt explain this problem good.

[livid hound]

vid seems fine

you're pretty much looking for whether there are points where the stuff immediately to its left/right
are both lower or higher

[crimson sedge]

So my answer is correct?....

[livid hound]

not quite

you missed something

[crimson sedge]

I submitted it

It was correct

one relative maximum and one relative minimum.

That was the answer

ugh

.close

[cedar kiln]

Channel closed

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[livid hound]

submitted into khan?

[crimson sedge]

Yes,

Khan gives you points for right answers

[livid hound]

that's questionable

[crimson sedge]

No higher points higher levels

No mistakes = more points

[livid hound]

applying the properties of rel min/max
there would be another rel min

[cedar kiln]

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[coarse atlas]

in this question, is F onto?

[coarse atlas]

.

is that a valid counter example?

[dusk goblet]

2/3 is not in the domain

this function is from the integers to the integers

[coarse atlas]

right because it has to be an integer

therefore its a valid counter example

because for all integers

[loud gyro]

Why do you care about onto when you are asked about one-to-one?

[dusk goblet]

huh

[coarse atlas]

.

this was my thinking

so if your codomain contains 2

.

but that is not an integer

therefore its not onto

[loud gyro]

Yea, its valid. But you need to prove the one-to-one ness of the function for this argument

[coarse atlas]

.

[coarse atlas]

.

[loud gyro]

[coarse atlas]

is that right?

[loud gyro]

Also, mention that since the function is one-to-one, there can be only one possible value for n, which is n=2/3, which ends up to be outside the domain

just for the sake of completeness

[cedar kiln]

@coarse atlas Has your question been resolved?

[coarse atlas]

.

[loud gyro]

pretty much yeah

But I would understand it if the one who grades it doesnt give 100% for what you have written

[coarse atlas]

.

[loud gyro]

You need a reason to show that there isnt some other value within the domain that you havent missed

and that reason is the one-to-one nature of f(n)

[coarse atlas]

so I just need to add that because F is one to one, and 2/3 is not an integer, therefore it is not onto?

[loud gyro]

yes

[coarse atlas]

.

[cedar kiln]

@coarse atlas Has your question been resolved?

[cedar kiln]

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[crimson sedge]

can I have someone show me how to solve this? im confused on it.

[pastel vault]

where are you stuck?

[abstract locust]

try to draw the problem

draw a cartesian plane

[crimson sedge]

i drew it out and initially started by multiplying the 488 mph by 1.5 hours and 436 mph by 1.25 hours

but after that im stumped

[abstract locust]

that gives you the length of the lines