help-13

[hollow garnet]

But what if it was like still same powers but the coefficients were like 2 on top and 1 on the bottom

Would the limit be 2 or would it be square root of 2?

[cedar kiln]

@hollow garnet Has your question been resolved?

[hollow garnet]

Thanks

.close

[cedar kiln]

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[dusky sparrow]

An embarassing situation:

I have forgotten how to simplify using common denominators and I need a "fool proof" way of doing that.

[dusky sparrow]

if i want to put these together without having to do painful work

[bright bridge]

numerators?

[dusky sparrow]

no, denominator

[bright bridge]

you add

[bright bridge]

this is common numerators?

[dusky sparrow]

no

[bright bridge]

wa

[dusky sparrow]

i want to know how to get the common denominator*

💀

[bright bridge]

ohhhh

that makes sense

[dusky sparrow]

ah

Because my book does not make sense

[bright bridge]

well first

make it

(2x+1)/(2x) + (2x+1)/(x+2)

[violet night]

$\frac{a}{b}+\frac{c}{d} = \frac{a \cdot d}{b \cdot d} + \frac{c \cdot b}{d \cdot b}$

[wraith dagger]

Clarkie

[bright bridge]

oh

[dusky sparrow]

that's how you get it?

[bright bridge]

i did not know that

[velvet mortar]

Step 1: Factor everything as much as possible in the denominator
Step 2: take what's common (let's say it's X).
Step 3: take what's leftover (let's say Y)
Step 4: common denominator is X * Y

Can you factor 2x and/or x+2 any further?

[dusky sparrow]

well you could write it as x(2)

but

not really in this case

[velvet mortar]

No?

[bright bridge]

what

[velvet mortar]

Oh

[violet night]

you can right 2x as x(2) yes

but

[dusky sparrow]

it's already as simple as it gets, algebraically

so

[velvet mortar]

In this case it's pretty simple

Nothing is common

Everything is leftover

[violet night]

why is 2x+2-1 not simplified to 2x+1

[velvet mortar]

So you just multiply the two

[dusky sparrow]

oh my bad

i forgot

[velvet mortar]

But in other cases you might need to follow the steps I provides

[dusky sparrow]

i didnt want the subtraction there

so

[velvet mortar]

What subtraction?

What are you talking out?

[violet night]

looks fine

now get it over the same denominator (thats the entire purpose) and evaluate the numerator

[dusky sparrow]

eh

i get it now

[violet night]

im confused

[velvet mortar]

..

[dusky sparrow]

And I am confused as well

this can also be simplified further

[violet night]

????????????????????????????????

yes

[dusky sparrow]

Well did I do it?

well

this was rather embarassing

[violet night]

stop

[violet night]

how is this right side fraction equal to 1 near the bottom?

[dusky sparrow]

for some reason it was

💀

switching the terms around, you can see why

[violet night]

that is

not 1

[dusky sparrow]

that is certainly 1.....

i mean look

[violet night]

WHAT

ok I hope im not going insane

[dusky sparrow]

am i being trolled by math

💀

[violet night]

how is 2x+2 = x+2???

,w is 2 * 3 + 2 = 3 + 2

[velvet mortar]

Should I tag moderators?

[wraith dagger]

Results provided by WolframAlpha

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

Requested by Clarkie#5208

[velvet mortar]

This is getting out of hand

[dusky sparrow]

this isn't getting out of hand

we're trying to investigate what the hell is going on

and here I am very confused what I did wrong

[velvet mortar]

Mockery of mathematics

[dusky sparrow]

...

[violet night]

well

[dusky sparrow]

not worth calling the mods over

[violet night]

blame yourself for posting a bunch of garbage and losing the entire train of working

with 15 thousand incorrect steps

[dusky sparrow]

but i thought i did it correctly

[velvet mortar]

Just explain how that's 1

[violet night]

^^^

[velvet mortar]

And we good

[violet night]

in which world

in what number system

[dusky sparrow]

yep

not 1

[violet night]

why do you have to expand to see THAT??

[dusky sparrow]

because I can't see that

[violet night]

HOW

[dusky sparrow]

and here I thought I could:

cross (2x+2)
cross 2x

on both denominator and numerator

[violet night]

HOW IS 2x + 2 = x + 2

[dusky sparrow]

simple act of being blind

[violet night]

so you don't have to expand it

just get better glasses

[dusky sparrow]

no dude

i need better eyes

💀

[violet night]

ok go back to your original problem and do it correctly this time

[dusky sparrow]

oka

[violet night]

remember that getting a common denominator has the purpose of putting both the numerators over the same denominator

[dusky sparrow]

now im just going to expand everything

and i guess i could simplify this using the QD-formula

[violet night]

yes

good job

but keep the denominator factorized

no reason to expand it

[dusky sparrow]

ah, because if i want to solve an equation then

[violet night]

yes

[dusky sparrow]

multiplying it would be easier

[violet night]

its easier

[dusky sparrow]

idk why i did that, but i had an instict to be simple as possible

[violet night]

and in that instinct you made it less simple

[dusky sparrow]

💀

hate it

[velvet mortar]

Hejsan

Glad påsk!

[dusky sparrow]

glad påsk på dig med

[dusky sparrow]

and, yeah, i don't think expanding this would be fun everytime you solve an equation

saves some pencil graphite

but, i get it now

[cedar kiln]

@dusky sparrow Has your question been resolved?

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[cedar kiln]

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[spice python]

Think im just having a dumb moment but how did they go from the second line to the third line

how do you work out 4x . 108/x^2

i thought they would have to have common denomenator

ohhh

wait

they took 4x/1

so its basically 4x/1 . 106/x^2 which gives 432x/x^2

that was a dumb moment from me had a lil brain fart there

.close

[cedar kiln]

Channel closed

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[cedar kiln]

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[junior timber]

question 4

*14

not sure if I got my areas correct

could someone double check for me?

I substances thé non shaded regions but my answer isn’t on the pick an answer

[crimson sedge]

ur answer is there

[junior timber]

yes i know

i got an answer but its not on there

[crimson sedge]

no i meant it is there

the area of ur shaded regions subtracted from the areas you have written down should give u the area

and it is listed as one of the options

[junior timber]

oh

[crimson sedge]

okay

first and foremost

what is the area of the whole rectangle

[junior timber]

60

[crimson sedge]

right

so u dont want to include the 16 and 9

so what is 60 subtracted from 16 and 9

[junior timber]

ohh 35

[crimson sedge]

yeppie

[junior timber]

wait so how did i mess up then

[crimson sedge]

what did u do?

[junior timber]

idk i think i calculated wrong then

[crimson sedge]

i dont think u wrote the area calculations in there

[crimson sedge]

maybe share it?

[junior timber]

i did like 60-(16-9)

i think maybe i did like 60-6-9

[crimson sedge]

see

it should be 60-(16+9)

[junior timber]

ohhh

[crimson sedge]

because like

think about it

you have a total of 60

and u want to remove the 16 and 9 together

key word together

[junior timber]

ohh

could u help with 15?

so the shaded area is a isoscelene

[crimson sedge]

by u doing 60-(16-9) you have basically shrunk the unshaded area and then subtracted the shaded area, 60, from that

[crimson sedge]

sure

[junior timber]

tytyt

[crimson sedge]

yes

[junior timber]

then what

[crimson sedge]

i would say u can start by proving that the triangle DAB is equal to triangle DCB

well maybe u dont even need to do that since they explicitly say it is a square

[junior timber]

yea

[crimson sedge]

well, what is angle DPQ

[junior timber]

right angle i think

[crimson sedge]

yes

you just said it is an isosceles

which means..

[junior timber]

uhh

idk

this?

wait nvm we dont rlyl have numbers

theres no point on usuing the √2x

[crimson sedge]

Okay sorry, i think i was kinda steering u in the wrong direction

okay so for now

Let's assume AB = 1

the side of the square

[junior timber]

yea

[crimson sedge]

@junior timber what is the relationship between the diagonal of a square and its sides

[junior timber]

uhh

wdym

like BP = BA?

[crimson sedge]

no like in general

if u knew the length of one side of a square

how would u find the diagonal of it

[junior timber]

like 1x : 2x: x√3?

[crimson sedge]

nono

okay so it is basically

[
d= \s 2 a
]
with $a$ being the side of the square and $d$ being the diagonal

[junior timber]

oh

[crimson sedge]

thats just the general formula for it

[junior timber]

whats d tho

[crimson sedge]

the diagonal

like

[junior timber]

ohhh

a is area?

[crimson sedge]

no the side of the square

[junior timber]

ohh

[crimson sedge]

yeah so is this fine?

[junior timber]

yea

[crimson sedge]

okay i am just gonna repost this because its just way up now

we said AB = 1

[crimson sedge]

what is DB knowing this

shu?

[junior timber]

its √2a

[crimson sedge]

yea

but what is a in our case

okay the variable names are just confusing u

[junior timber]

a is DA

[crimson sedge]

the formula is:
Diagonal = side*sqrt(2)

[crimson sedge]

right

so like

[crimson sedge]

I said AB = 1 here right

so what is DA

[junior timber]

DA = BP

[crimson sedge]

okay sure

so all sides of a square are equal right?

we said AB = 1 which is also equal to DA

[crimson sedge]

now, can you tell me what the diagonal is

[junior timber]

1.41

[crimson sedge]

dont approximate just leave it the same in square root form because ur options are also in square root

so anyways yeah it is sqrt(2)

now

what is PB equal to? give me a number if u can

[junior timber]

1

[crimson sedge]

yep

so now

what is DP

remember the two numbers u just got

[junior timber]

0.41

[crimson sedge]

yea but again dont approximate

its sqrt(2) -1

[junior timber]

ohh

sqrt(2) -1^2?

[crimson sedge]

now

find the area of the triangle

[crimson sedge]

[junior timber]

but we dont have height

[crimson sedge]

you do

[junior timber]

wait what

[crimson sedge]

the triangle is rotated

but the height is the same thing as if it wasn't rotated

[junior timber]

ohh wait

A = ½ × b × h

so

1/2 * √2-1 * √2-1

?

[crimson sedge]

dont forget parentheses

[junior timber]

oh right

[crimson sedge]

but yeah

[junior timber]

so that equals too

1/2 (√2-1)^2

[crimson sedge]

yeppiee

[junior timber]

could u possibly

if u have time

with one more

[crimson sedge]

lmaoo

keep them coming eh

[junior timber]

tyty

[crimson sedge]

did u understand the idea

[junior timber]

yes

[crimson sedge]

of what we just did though

[crimson sedge]

by the way

the reason we made this choice is simple

[crimson sedge]

its because the area of the square under the assumption that AB=1 is also 1

[junior timber]

okk

[crimson sedge]

uh

[junior timber]

[crimson sedge]

oh right

u just draw a rectangle

[eternal quest]

I need help with area of composite shapes @junior timber

[junior timber]

??

[junior timber]

how

[junior timber]

my guy this is my help channel

[crimson sedge]

so try doing that and label this new point idk W

what is the length of WP and the angle of OWP

[junior timber]

but thats not the radius

[crimson sedge]

it is not

but we will get there

[junior timber]

oh ok

[crimson sedge]

sooo

[crimson sedge]

try doing this

[junior timber]

angle is 90

[crimson sedge]

yes

[junior timber]

Wp is 15

[crimson sedge]

yes

now draw a line making OP

[junior timber]

okk so WO -s 6

*is

[crimson sedge]

u dont know that

at least yet

you know that AW is the same as PN which is 9

[junior timber]

well 15 - 9

is 6

[crimson sedge]

yea but 15 is for AN and PW

anyways trust me u r like

almost done with the geometry

just keep going a bit

so lets label everything we have so far

first

[junior timber]

okk

[crimson sedge]

Call the radius some variable x

tell me the following:

AN = ?
AW = ?
WP = ?
OW = ?
OP = ?
(dont solve anything, if it is something u dont know then use the x for radius)

[junior timber]

AN = 15
AW = 9
OW = 6
OP = 16

approx 16

[crimson sedge]

nono dont pick numbers for the radius

again just leave it as x

[junior timber]

huh what

[crimson sedge]

we dont know it and we are going to find it out

[junior timber]

oh ok

[crimson sedge]

thats the whole point of what we are doing haha

anyways rewrite OP and OW

in terms of x

you know x is the radius

[junior timber]

yes

[crimson sedge]

yeah so can you do that?

um are u still here

[junior timber]

yea sorry

[junior timber]

15 - x

ok wait

[crimson sedge]

errr

almost!

[junior timber]

√15^2-(x-15)^2

[crimson sedge]

heh? where did that come from

[junior timber]

the line OP

u can use pythagorean to find it

[crimson sedge]

yes thats the idea but

[crimson sedge]

.

what is OP

in the circle

[junior timber]

x

[crimson sedge]

right

[junior timber]

ohh

[crimson sedge]

so OP = x

okay

[junior timber]

oops

[crimson sedge]

now

x-15 is wrong too

what is PN

[junior timber]

9

[crimson sedge]

right

what is AW

[junior timber]

9

[crimson sedge]

okay our radius is x right?

[junior timber]

ye

[crimson sedge]

so OW is?

in terms of x

[junior timber]

x - 9

[crimson sedge]

yeppie!!

okay so one last thing before we stop with the dreadful geometry

what is WP

[junior timber]

15

[crimson sedge]

right !!

now

write down what Pythagorean theorem is gonna look like

in this case

dont solve anything

just write it out for now

[junior timber]

√a^2 + b^2 = c^2

[crimson sedge]

yes

[junior timber]

now

√(x-9)^2 + 15^2 = x^2

?

[crimson sedge]

yep !!

now

wait no

why do u have a square root there

[junior timber]

is it not?

[crimson sedge]

yes but u also have x^2 written

[junior timber]

ohh oops

[crimson sedge]

anyways u dont want the square root

[junior timber]

ohh

[crimson sedge]

leave it in the form of c^2 = a^2 +b^2

its time to do some algebruh

[junior timber]

okk

[crimson sedge]

so what is ur equation now

[junior timber]

x^2 = (x-9)^2+15^2

[crimson sedge]

yes !

what are we trying to find in that?

[junior timber]

x

[crimson sedge]

yes

[junior timber]

one second

[crimson sedge]

first

expand that binomial

[junior timber]

x

should be

16

sorry

17

[crimson sedge]

lmao that was fast

did u plug and chug it in a calculator

just kidding

anyways yes it is 17

good job woooo

[junior timber]

no i just get alegebra a lot faster cuz its the only thing i get

[crimson sedge]

lmaoo

[junior timber]

thats so fun :D

[crimson sedge]

yeah u got some nasty geometry questions

they are just

p a i n

[junior timber]

frr

[crimson sedge]

anyways did u get the process?

like

[junior timber]

wait so AO is 17

[crimson sedge]

if u r confused about anything just ask tbh

yea

[junior timber]

tyty

life saver

[crimson sedge]

lmaoo glad i was of help

[junior timber]

tytytytyty

[crimson sedge]

usually not that good with geometry questions because u guys have like

1 million rules i just dont remember anymore

[junior timber]

lol tyty tho

[crimson sedge]

but it turned out well with u which is good LOL

but yeah good luck with ur studies have a nice day :D

[junior timber]

tyy! u too!

.close

[cedar kiln]

Channel closed

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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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[merry tinsel]

can sm1 help me here

i starts at 10

im a bit confused

on how i would do this

[livid hound]

sum from i =10 to 100
= (sum from i =1 to 100) - (sum from i =1 to 9)

[umbral hornet]

yo could I possibly ask my question here?

[granite knoll]

!help

[cedar kiln]

Please read #❓how-to-get-help

[livid hound]

no

[umbral hornet]

!help

[cedar kiln]

Please read #❓how-to-get-help

[livid hound]

claim your own channel

[umbral hornet]

Oh

ok

sorry

[merry tinsel]

so i would have t odo that for every

thing

like i^3

i^2

right?

[livid hound]

yeh

[merry tinsel]

bruhhhh

ok thanks

.close

[cedar kiln]

Channel closed

Closed by @merry tinsel

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[dark gale]

Would anyone show me a way to solve number 37?

[dark gale]

Like how do you approach this problem? I was thinking on using comparison test, but I don’t really know how it really works.

[runic garnet]

Have u attempted integral test

[dark gale]

Does that counts as a comparison test? I thought only comparison test and limit comparison test were allowed

[runic garnet]

Oh oops my fault I didn’t read it said comparison sorry

[dark gale]

But I know that I need two things a series smaller than zero: Asubk and a smaller series Bsubk

,rotate

[dark gale]

Btw I’m sorry I meant to say n instead of k

[runic garnet]

Have u tried comparing it to the series 6k/5k^2 ?

[dark gale]

So first I don’t know if the given is supposed to be my Asubn or my Bsubn

[dark gale]

No. I hadn’t thought of that

[runic garnet]

O wait a second

[dark gale]

I have An answer key which I didn’t really understand. Would it be better if I show you and you try to explain it?

[runic garnet]

I can attempt to but I haven’t done this stuff in a while

[runic garnet]

Send it anyways

[dark gale]

Let’s try at least then. Thank you.

Is weird cause I thought that 1/n is bigger than the given series

Cause you plug in 1 and 2 to 1/n, it yields bigger Than the given series.

[runic garnet]

I think it’s cuz (disregarding the +2 in the denominator because it becomes negligible), the 6k/5k^2 simplifies to 1.2/k which is greater than 1/n

[dark gale]

Oh okey

[runic garnet]

I may be wrong, don’t take what I said as truth, just maybe that may be it lol

But yea I think that’s why they’re comparing to 1/n

Which is the harmonic, and we know is also divergent by p-series

[dark gale]

Well that would put the given as Asubn and the 1/k as Bsubn which means it diverges. Does that means that it needs more analysis?

The theorem says so

[runic garnet]

The given would be b_n and the 1/n would be a_n

[dark gale]

Oh yes you are right I mixed the signs.

[runic garnet]

But yes accordingly more analysis would be needed

I’m trying to figure out the answer key

[dark gale]

Well I guess cause if you do the limit comparison test, it states that if any diverges, the other one will too

[runic garnet]

Oh wait

If 1/n is the smaller series and that diverges

Then that must mean that the 6k/5k^2 + 2, which is the bigger series, must diverge right?

Does that make sense?

[runic garnet]

It’s the first statement of number 2 on here

I think the letters just mixed me up

If the small a_n diverges, then the big b_n diverges

Analogous to

If 1/n diverges(small), then 6k/(5k^2 + 2) diverges (big)

[dark gale]

Ohh I see

Oh so if the bigger one were to diverge and you don’t know if the small one does , then that’s when you do more analysis?

[runic garnet]

Yes 👍

[dark gale]

Okey. Thank you so much for your help. Have a good night.

.close

[cedar kiln]

Channel closed

Closed by @dark gale

Use .reopen if this was a mistake.

[runic garnet]

No problem

You too

[dark gale]

Thanks

[cedar kiln]

Available help channel!

Send your question here to claim the channel.

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• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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[crimson sedge]

If I choose 4 random integers (a,b,c,d) from the set [-2,2] What is the probability ad = bc?

[crimson sedge]

I made 2 cases

First, where zeroes are there

Secone, where zeroes aren't

[tropic oxide]

the random integers in question can coincide, yes?

[crimson sedge]

If you mean the same numbers, then yes.

[tropic oxide]

i.e. you're essentially just rolling a die with sides -2, -1, 0, 1 and 2 four times

ok

so what did you do afterward?

[crimson sedge]

For first, I got 81
For second I think I got 64

[tropic oxide]

81 what

[crimson sedge]

ways the equation can be balanced when 0 is there

[tropic oxide]

ok that looks correct

there are 9 ways to get a product of 0 from two rolls so yes there are 81 ways to do that

what about the other case?

i believe you might need to break it down further based on what the value of the product is -- just saying "nonzero" is not going to take you anywhere.

[crimson sedge]

I realized that the numbers can be flipped or the signs can be flipped and the equation will still hold true so I did

____
4*4=4*1

Because that's the number of possible products such that

The equation hold true

Does that look good?

A friend did solve it with finding the number of ways to get the products.
Like 0 = 81 ways
1 = whatever
And so on for -4 -2 -1 0 1 2 4

So that's why I am taking a different approach

[tropic oxide]

yes that looks like the correct approach to me

i don't understand yours

[crimson sedge]

How would you try to solve if you were not allowed to use my friend's method?

[tropic oxide]

question WHY one wasn't allowed to use your friend's method.

[cedar kiln]

@crimson sedge Has your question been resolved?

[crimson sedge]

Just to try out different approaches :p

[tropic oxide]

well for a formally different approach i would find the number of ways to get each possible product of two rolls, then find their probabilities, then take the sum of squares of that

[cedar kiln]

@crimson sedge Has your question been resolved?

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[crimson sedge]

For now ig

[cedar kiln]

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[final lily]

How do I find the force exerted on each testries

[dreamy tundra]

net torque at the center of mass of plank = 0
and
net force on the plank = 0

[cedar kiln]

@final lily Has your question been resolved?

[final lily]

Don't understand still

So ur saying its just gonna be 480N

For the first trestis

[dreamy tundra]

480 + 120 = N1 + N2 --> this would be the force equation
N1 * 2 = 480 * 1 + N2 * 2 --> This would be the torque equation along the center of mass of plank
[N1 == Normal at A and N2 = Normal at B]

[cedar kiln]

@final lily Has your question been resolved?

[cedar kiln]

@final lily Has your question been resolved?

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[covert island]

is the derivative of (1-x)^-2

[covert island]

is it not just -2(1-x)^-3 * -1

thats the first derivative right

.close

[cedar kiln]

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[opal basin]

Yes

[cedar kiln]

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[valid fossil]

can i ask my question here ? or

[steel heart]

you can

[valid fossil]

oh okay one second

[calm hedge]

As long as its maths related

[grave cloud]

What is your question ?:D

[valid fossil]

Im rly stuck with the calculation part on this one

i checked the answer for it on yt n stuff but they just keep answering it directly with the final answer

[steel heart]

use rules of exponent, remove sqrt and then just normal division

what's so complicated?

[valid fossil]

idk i just keep getting a different answer

wait lemme show u the sets i did once

[tropic oxide]

,rcw

[tropic oxide]

ok i have three questions

1. where did this come from
2. are you required to do it by hand only
3. is the 1000 under the square root

[valid fossil]

1. its a calculation from a physics problem
2. yeah , they don't allow calculators in the exam
3. yeah it is under the root

I keep getting the same thing and the actual answer is different

@tropic oxide

can u like check if its correct ?

[tropic oxide]

no calculators at all wtf

[valid fossil]

the answer im supposed to get from calculating it is 0.9x10^-12

[valid fossil]

yeah lol

calculation errors can just get u neg points

[tropic oxide]

wait, how did you find sqrt(512) then

[valid fossil]

i used a calc for that , but there's a method for it and i was about to look it up

[tropic oxide]

also what's with the [sqrt(512) = -22.6]?

[valid fossil]

no its not -

just 22.6

[valid fossil]

i just wrote how i got the 22.6 there

in brackets

[tropic oxide]

what's the symbol before the minus or dash or whatever

[valid fossil]

the dots ?

[tropic oxide]

yes the dots

[valid fossil]

oh just like "=" thingy

[tropic oxide]

"= thingy"?

[valid fossil]

ye ye

[tropic oxide]

do you get points taken off for using the actual equals sign???

[valid fossil]

no no

i just wrote it like that lol

[tropic oxide]

yeah but why lmfao

[valid fossil]

idk its just like a habit ig

[tropic oxide]

anyway $\sqrt{512 \times 10^{-46}} = 22.6 \times 10^{-23}$

[wraith dagger]

Ann

[tropic oxide]

then break said habit

[valid fossil]

yeh

[valid fossil]

it is ?

how is it 10^-23

[tropic oxide]

sqrt(10^-46) = 10^(-46/2)

[valid fossil]

ohh

i didn't know we are supposed to do that

[tropic oxide]

anyway just for my own sanity

since something still seems to be up with all of this

,calc 6.63e-34 / sqrt(2 * 1.6e-14 * 1.6e-27 * 1000)

[wraith dagger]

Result:

2.9300737245418e-15

[tropic oxide]

you say you're SUPPOSED to get 0.9e-12?

or 9e-13 as it may well be

[valid fossil]

the answer is 0.9 x 10^-12 which is confusing..

[tropic oxide]

yeah, my point exactly.

[valid fossil]

ye ye

[tropic oxide]

so we must call into question one of two things

(a) the trustworthiness of the answer key
OR
(b) the calculations that led to this scientific-notation monster.

[valid fossil]

there

[tropic oxide]

[valid fossil]

its 6.63 x 10^34 doe

[tropic oxide]

,calc 6.63-34 / sqrt(2 * 1.6e-14 * 1.6e-27 * 1000)

[wraith dagger]

Result:

-1.5026019100214e+20

[tropic oxide]

er

typo

erased the wrong symbol

,calc 6.6e-34 / sqrt(2 * 1.6e-14 * 1.6e-27 * 1000)

[wraith dagger]

Result:

2.9168154723945e-15

[tropic oxide]

doesn't make much of a difference.

[valid fossil]

ye idk why im not getting it

[tropic oxide]

was there any funny business with the units of the physical quantities involved?

[valid fossil]

doesn't look like it

[tropic oxide]

something's up still

like... the numbers don't add up here

[valid fossil]

this was the question btw

[tropic oxide]

the answer key just spouts bullshit

[valid fossil]

this is the formula for it

and he directly jumped into the calc

and got 0.9

smth smth

[tropic oxide]

,w planck constant

[wraith dagger]

Results provided by WolframAlpha

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

Requested by Ann#0413

[tropic oxide]

ok yeah

1.6e-19 is the charge of the proton in coulombs

[valid fossil]

ye

[tropic oxide]

1.6e-27 is the mass of the proton in kilograms

so no funny business with units

by the looks of it

[valid fossil]

yeh

[tropic oxide]

1000 is just 1kV from the problem

okay so what the fuck

[valid fossil]

exactly 😭

[tropic oxide]

you're just expected to know that the grader wants you to do a fancy version of 2+2=5

[valid fossil]

i've wasted time on this

[tropic oxide]

do you have somebody to yell at / complain to

[valid fossil]

wot

[tropic oxide]

can you talk to your teacher about this

[valid fossil]

yea i can't but in a few days but my exam is before that which is a problem

ofweihfodhsflk okay thank you so much for helping out i will just pray that question won't pop up

[tropic oxide]

so you're stuck with an exam in which you can potentially be screwed over by such bullshit answer keys...

[valid fossil]

even if it does i remember it anyways

lmao

[valid fossil]

💀 yea-

frick this im going chemistry

how do i close it

this channel

.close

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[hexed mesa]

Didn’t understand what’s the question ngl

[steel heart]

,rotate

[steel heart]

@hexed mesa can you send full ques so that i can understand context

[hexed mesa]

That’s legit the whole question ☠️

It’s about Arcs and Chords but the whole question is “Find BD”

[steel heart]

what is to find then?

what is given?

[hexed mesa]

It gave me this circle ⭕️

Only

[steel heart]

CD = 4 or CF = 4

[hexed mesa]

CF

[steel heart]

then tell me what is radius

i am asking u to find radius

[hexed mesa]

Bro that’s the whole question is about

Oh wait

Radius is 6

[steel heart]

its not @hexed mesa

lemme give u a hint

[hexed mesa]

Okay

[steel heart]

radius is distance of centre from point on circle

[hexed mesa]

I know

10?

[steel heart]

is C located on circle?

[steel heart]

yes

now find AD

[hexed mesa]

If AF (the radius) is 10 , shouldn’t AD be 10 as well?

[steel heart]

yes

find cd now

hint: pythagora

[hexed mesa]

Hm

Wait imma afk rq

[cedar kiln]

@hexed mesa Has your question been resolved?

[cedar kiln]

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[novel stone]

convergence for a series of functions

[novel stone]

Hi! I want to make sure I solved this correctly

I need to prove that the convergence set of this series is R (the set of real numbers)

I got omega = superior limit of (x+1)^2 / x^2

which is 1

and (1+/(1 + x^2)) < 1, so the series is absolute convergent

(I used Abel Cauchy Hadamard Theorem)

[cedar kiln]

@novel stone Has your question been resolved?

[novel stone]

<@&286206848099549185>

[steel heart]

yes?

[novel stone]

if I want to prove the convergence of this series

do I use Abel Cauchy Hadamard's theorem?

just making sure

I am dumb, nvm

sorry for bothering you

.close

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[solar tendon]

How do i solve for the derivative of the funtction f(x) with respect to x?

[solar tendon]

with that equation

[granite knoll]

quotient rule

[solar tendon]

I did this what now

[short blade]

are you being asked to use the formal definition of a derivative?

are you allowed to use the quotient rule?

[solar tendon]

My teacher had not discussed that so i guess not

[short blade]

ok

make the fractions on the top into a single fraction

as in, give them a common denominator

[solar tendon]

Ok

[solar tendon]

this is correct right?

[short blade]

yes, with a limit

[solar tendon]

correct?

idk i suck at fractions

maybe this?

[granite knoll]

closer but still not quite

pay attention to signs

[solar tendon]

Oh right

[granite knoll]

left numerator is not right

[solar tendon]

??

[granite knoll]

yes, looks right

[solar tendon]

OK i multiplied and cancelled stuff in the numerator

What now?

Is this the final answer?

since h=0

[granite knoll]

yes

[solar tendon]

yes

epik

i can now sleep

thanks you all.

.close

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[gray obsidian]

if x + 1/x = 5 , what is x^7 + 1/(x^7)?

[south tundra]

You are most likely expected to consider the expansion of (x + 1/x)^7

[short blade]

there's an easier way

[gray obsidian]

so i should raise both sides to the 7th power and then isolate x^7 + 1/x^7?

[short blade]

mutliply the first equation by x

[gray obsidian]

ok

[south tundra]

Yeah you can solve for x

Boring though

[short blade]

this is inadvisable

[crimson sedge]

Hi

[gray obsidian]

so what should i do

[short blade]

multiply the first equation by x like i said earlier

[south tundra]

They have already advised you to solve for x

[gray obsidian]

x^2 + 1/x^2 =5x

[short blade]

check your second term again

what is x * (1/x)?

[gray obsidian]

sry 1

[short blade]

ye

[gray obsidian]

x^2 +1=5x

[short blade]

this should be a familiar setup to you

[gray obsidian]

k thx

.close

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[robust belfry]

Hello, I'm having some trouble interpreting this question:

[robust belfry]

specifically im struggling with understanding my professors construction of the cantor set

he starts by saying let C,a,0 = [0,1] = J0, and then says let C,a,1 be J0/I01, where I01 is the "open middle interval of length a/3"

what I'm not understanding is the middle interval being of length a/3

normally the cantor set is just constant trimestering of length 1/3 so im finding this a little strange

[cedar kiln]

@robust belfry Has your question been resolved?

[robust belfry]

<@&286206848099549185>

[storm mural]

it's generalized

the case where alpha = 1 is the normal cantor set

[robust belfry]

im aware i just dont follow what he precisely means with open middle interval of length a/3

is he just saying take the halfpoint of your interval and remove the open interval of length a/3 centered aroudn the halfpoint?

[storm mural]

open = does not contain its endpoints

ye

[robust belfry]

cool thanks .close

.close

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[bright bridge]

whats the question

[lavish plank]

c is cos s is sin

ctheta5= -0.5 lookslike startig pt

<@&286206848099549185>

[storm mural]

from ctheta5 you can also get ctheta5d6 and stheta5
then you can get stheta4 and therefore ctheta4

etc

[lavish plank]

is it radians or degrees etc

[storm mural]

um probably doesn't matter

[lavish plank]

what is inverse cos of -0.5

[storm mural]

does it say give your answer in radians

[lavish plank]

think degrees, no but examples are in deg

[storm mural]

unit circle
cos is the x value of the point
what degree gets you there

[lavish plank]

etc

i usually use a calc. never understood circle

[storm mural]

well then use a calc now

[lavish plank]

will do.cant find aha

120deg

[storm mural]

yes

[storm mural]

^

[cedar kiln]

@lavish plank Has your question been resolved?

[cedar kiln]

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[junior timber]

idk what this quesiton means

[crimson sedge]

basically is asking u to find the ratio of two lengths

[junior timber]

okk

[crimson sedge]

like if length AD was 1

and AC was 2

then it is 1:2 or just simply 1/2

[junior timber]

oh ok

[crimson sedge]

anyways u r like

on the right track

with what u have written down

what is angle ADB

[junior timber]

right angle

[crimson sedge]

yeah

so like you know what BAD and ADB are

can you recover what ABD is

[junior timber]

wdym

like right triangle?

or the angle of ABD

[crimson sedge]

yes

[junior timber]

oh ok

[crimson sedge]

just what the angle of ABD is

[junior timber]

its 30

[crimson sedge]

yeah

that by effect tells u DBC to be what

[junior timber]

30

[crimson sedge]

are u sure

its a right angle right

[junior timber]

yea

[crimson sedge]

like ABC totally

[junior timber]

and ABC is right triangle too

and ABD is 30

so 90 - 30 is 60

[crimson sedge]

yep!

u got it

okay angle hunting is over

so now

do u remember what the 30-60-90 triangle is

[junior timber]

yes

x, 2x, x√3

[crimson sedge]

okay so like, try to notate each triangle using that

but remember, you have to use different variables (x,y,z) for different triangles

because they are all different in lengths

[junior timber]

yea

[crimson sedge]

yeah

so whats ur progress

[junior timber]

ok so

AB can bex

be x

AD is y

DC is z

BD is a

and BC is b

[crimson sedge]

okay hmm maybe this method will be harder to follow and explain

[junior timber]

oh ok

[crimson sedge]

okay let's try to do it a step at a time instead of all at once

just notate what triangle ABD is

knowing your 30-60-90 triangle

[junior timber]

okk

[crimson sedge]

sorry typo

so yeah, just stick to x for now but, what are ur sides for ABD now

[junior timber]

x, 2x, x√3

?

[crimson sedge]

Yep!

okay so what is BD

[junior timber]

x√3

i think

or its 2x

[crimson sedge]

yeah its this

[junior timber]

oh ok

[crimson sedge]

okay so now

i want u to keep this in mind

now switch to triangle DBC

you want to do this exact same process

so you know BD is x*sqrt(3) right?

and it is opposite to the 30 angle

so like we are going to introduce another variable y for the side lengths of triangle DBC

[junior timber]

oh ok

[crimson sedge]

so in the 30-60-90 triangle

when the side is opposite to angle 30

what is it

[junior timber]

waht opposite

[crimson sedge]

okay so let me rephrase

if u were looking at triangle DBC

and u wanted to find what BD is

what would u write it down as knowing the 30-60-90 triangle

[junior timber]

isnt it x√3?

[crimson sedge]

yes! thats right

but lets pretend we did not know it is that

imagine if u were looking at triangle DBC on its own with nothing else

what would u write DB as

[junior timber]

uhhh

idk

[crimson sedge]

u did it above haha

[crimson sedge]

here

its the same thing

but for triangle DBC

[junior timber]

ohh

it would be x

[crimson sedge]

yess !!

but

we defined x for the sides of triangle ABD right

[crimson sedge]

here

so lets put a new variable such as y for triangle DBC

okay so what is side DB now?

[crimson sedge]

remember this

[crimson sedge]

and this

[junior timber]

yea okk

[crimson sedge]

btw do u prefer like any other method of helping?

[junior timber]

im still a little confused