help-0

[echo socket]

And, either way, you could tell that the integral is 0 by just looking at it since it's an odd function being integrated over a symmetric interval

[lone heart]

@scenic wing Has your question been resolved?

[lone heart]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• 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>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[fossil tide]

what is the derivative of e^(1-x)

[long axle]

What’ve u trid#es

Tried

[fossil tide]

i thought it was itself because i thought d/dx(e^x) = e^x

solutions say its negative i dont undertsand how

[long axle]

Right, but then there’s chain rule

e^(1-x) * (1-x)’

e^(1-x) * -1

[fossil tide]

why do i have to use the chain rule here

[long axle]

-e^(1-x)

The exponent is a function

[fossil tide]

sorry i think im mostly confused on when the chain rule is used

[long axle]

$[e^{f(x)}]’ = e^{f(x)} \cdot f’(x)$

[ocean seal]

Stephen

[long axle]

It’s always used, you just don’t see it sometimes

For example

$[e^x]’ = e^x \cdot [x]’ = e^x \cdot 1 = e^x$

[fossil tide]

oh

[ocean seal]

Stephen

[fossil tide]

.close

[lone heart]

Channel closed

Closed by @fossil tide

Use .reopen if this was a mistake.

[lone heart]

Available help channel!

Send your question here to claim the channel.

Remember:
• 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>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[vast stump]

<@&286206848099549185> hi, i dont understand anyth from this question

[lone heart]

Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.

[vast stump]

<@&286206848099549185>

[lone heart]

@vast stump Has your question been resolved?

[dire tiger]

See this solution for first part

[vast stump]

ahh

[dire tiger]

Is it clear

[vast stump]

yep

im abit confused abt the part b

part b of the question

[lone heart]

@vast stump Has your question been resolved?

[lone heart]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• 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>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[signal shale]

x = 122 ?

[alpine sable]

a car travels a disctance of 52000 m is 15 minute whereas a train covers 65km in 45 minutes find the ratio of thier speeds

[storm ridge]

! occupied

[lone heart]

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).

[round iris]

Did you try finding both in km/minute and comparing them?

[lone heart]

@signal shale Has your question been resolved?

[runic hedge]

It's not their channel btw

[signal shale]

anyone ?

[runic hedge]

No guarantee i can help, but can you give a clearer picture of whats been written?

I see 3 & 4 at the bottom but can't read the rest

[signal shale]

that's just the sides

doesn't really matter

[runic hedge]

Ahh i see

What's the middle say?

[signal shale]

that's the total angle

here's a clear image I guess

[naive sorrel]

u know inscribed angle theorem?

[signal shale]

yh

some of them

[naive sorrel]

there's only one

[signal shale]

there's a ton

of them

[naive sorrel]

well there's only one theorem

[signal shale]

yeah

my bad

[naive sorrel]

so basically u know the circle arc measures add up to 360

[signal shale]

but what ive learned it only taught about triangles and 4 sides

yeah

[naive sorrel]

ok

do u know that an inscribed angle's degree measure is half the arc it inscribes

[signal shale]

I have no idea what are you talking about

[charred jewel]

idk if its correct but i got 128

[naive sorrel]

have u seen this b4

[signal shale]

yh

but this is a 4 side

6

[naive sorrel]

yeah it doesn't matter

[signal shale]

howd you get it

[naive sorrel]

an angle is an angle

[charred jewel]

just make a new line on the middle

[signal shale]

soo what does this has to do with the question

[charred jewel]

thats how i did it but idk if its right

might be making shit up

[signal shale]

i've never learnt anything about

dividing like that

[charred jewel]

yeah but dividing it like that gives you a quadrilateral in a circle

[naive sorrel]

yeah I got 128

I used different wY

way

so basically

the red arc is double the 127°

so it's 254°

and the blue arc is double the 105°

so it's 210°

but the circle can only add up to 360°

so the overlap

is

464-360

= 104

so

[signal shale]

how do you know the red arc is double the 127

[naive sorrel]

x° is 1/2(360° - overlap arc)

x° = 1/2(360°-104) = 128°

[naive sorrel]

I'll show u

[charred jewel]

its a skill you naturally develop when doing geometry problems

drawing these lines sometimes help simplify the problem into something doable

[signal shale]

so there's more than 1 way to solve this huh

[charred jewel]

yeah

[signal shale]

can you show me how you also do it if you dont mind with your line dividing method shioshi

[charred jewel]

yeah

[naive sorrel]

inscribed angle

and central angle

[signal shale]

oh I see

what;s the

center x for tho

[naive sorrel]

that's the central angle

[signal shale]

127 x 2 right

[naive sorrel]

yea

[signal shale]

the center

[naive sorrel]

it is

and the arc is 127*2

[signal shale]

then what do I do after that

[charred jewel]

anyways so you have a 6 sided shape here inside the circle right, you draw a line through the middle two points

now you have two shapes with only 4 sides, and since those 4 sides all touch the circle, you know that opposite angles add to 180

then go from there

[signal shale]

do I divide

the 105 into 2 too ?

[charred jewel]

no

[signal shale]

what happens to it then

[charred jewel]

you know that if you have a shape with 4 sides, and all of them touches the circle, then opposite angles add to 180?

[signal shale]

yeah

corners

[signal shale]

you mean ?

[charred jewel]

yeah

now whats the blue angle

[signal shale]

its gotta be

180-127

[charred jewel]

you have 127 on the opposite side

yep

and since that whole angle is 105

you have the other side angle right?

[signal shale]

yh

105-53 = 52

[charred jewel]

now that angle is opposite to x

[signal shale]

180-52

[charred jewel]

you see that?

yes

[signal shale]

I see it now thanks

[charred jewel]

side question, where are you from cause i see the question is in malay

[signal shale]

malaysia

[charred jewel]

ayy same brother

which form are you

[signal shale]

3

[charred jewel]

i see

[signal shale]

what about you

[charred jewel]

oh i already graduated

first year uni

[naive sorrel]

red arc = (127*2)°
blue arc = (105*2)°

overlap between the arcs = (red  arc+blue arc) - (360°)
= 104°

x° = (1/2)(circle - (overlap arc))
x° = (1/2)(360° - (104°))
x° = 128°```

[signal shale]

oh damn

[signal shale]

thanks il look into this too

[signal shale]

why do you add the red and the blue arc's

[naive sorrel]

because if you add them it includes the overlap

and then if you subtract the circle you get only the overlap

because the overlap is counted twice when u add the red and blue

so when u subtract the circle its only counted once and nothing else is counted

so u get the overlap degree measure

[signal shale]

what about the x calculation? I can't seem to be getting it especially about the 1/2

[naive sorrel]

because if u look at the picture

x is inscribing the arc of the whole circle - the overlap

so it's 1/2 the arc measure of (whole circle - the overlap)

[signal shale]

oh so theres another center for

the x we're looking for ?

that's why its 1/2 ?

[naive sorrel]

there's only one center of circle

maybe picture helps

[signal shale]

yhh I get the 1/2 thing

[naive sorrel]

so basically I just find the overlap between the red and blue arcs because x = 1/2 (circle - overlap)

[signal shale]

I see, thank you. Is this method useable in other questions with different amount of sides too?

[naive sorrel]

yes

side not mater

it's about the fact that the angle is inscribed in the circle

[signal shale]

alr thanks man I appreciate the assistance

this is one of the hardest topic this year for me

.close

[lone heart]

Channel closed

Closed by @signal shale

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• 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>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[finite glen]

how to say if x and y are independent

[lone heart]

@finite glen Has your question been resolved?

[finite glen]

<@&286206848099549185>

[lone heart]

@finite glen Has your question been resolved?

[lone heart]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• 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>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[jagged crow]

solving expoential equations with no logs

[fickle tinsel]

$16^{-3r} = 16*4$
From there notice any common powers?

[ocean seal]

7aman

[jagged crow]

four

[fickle tinsel]

So simplify both sides in terms of base 4 and that'll solve for the exponent

[jagged crow]

so it's 4^-3r = 4?

[fickle tinsel]

$(4^2)^{-3r} = (4^2)*4$

[ocean seal]

7aman

[jagged crow]

ok i see

and then it's -3r = 4

what should i do

[upbeat onyx]

This isn't exactly it. You can simplify both sides of the equation to a single term.

[jagged crow]

i got rid of 4^2 on both sides

[upbeat onyx]

Which leaves you with what for an equation?

[jagged crow]

-3r = 4?

and then i think i should do -4/3 as the final answer

[upbeat onyx]

You're comparing a power to an integer here

[jagged crow]

o

should i radical it?

[upbeat onyx]

Let's think of it this way:

Do you know how to rewrite, let's say, (4^2)^2?

[jagged crow]

sure

[upbeat onyx]

What would it be

[jagged crow]

256

[upbeat onyx]

If we wanted to keep the power

4^(?)

[jagged crow]

4^4

[upbeat onyx]

Right. So you can do the same with the left side and multiply the exponents together

So (4^2)^(-3r) would become?

[jagged crow]

(4^-5)^r?

[upbeat onyx]

Well you multiply it

So 2×(-3r)

[jagged crow]

why did it turn into 2x

or 2

[upbeat onyx]

It's a multiply sign

[jagged crow]

i see

[upbeat onyx]

x vs ×

So on the left, you're left with 4^(-6r)

[jagged crow]

mhm i get it

[upbeat onyx]

And then on the right, you can combine that into one term too

[jagged crow]

16*4

or 256

[upbeat onyx]

If we wanted to keep the powers

[jagged crow]

64

[upbeat onyx]

64=4^(?)

[jagged crow]

4^3

[upbeat onyx]

Right

So now we have

$4^{-6r}=4^3$

[ocean seal]

Narutoes

[jagged crow]

get rid of the fours

[upbeat onyx]

Well you said without logs, but in a normal situation, yeah

[jagged crow]

what do we do without logs

[upbeat onyx]

You can just set the exponents equal to each other since it is obvious they need to be equal since you have the same bases.

Basically the same as a log4 without calling it a log4

[jagged crow]

ok

thanks man

.close

[lone heart]

Channel closed

Closed by @jagged crow

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• 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>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[lament pilot]

can someone help me with this please (question b). I have repeatedly found that k = -3/2

[lament pilot]

this is my working:

[lone heart]

@lament pilot Has your question been resolved?

[lone heart]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• 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>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[old sinew]

I need to solve the polynomial $z^2+(2-i)z-2i$

[slate jolt]

you dont know how to solve quadratics?

[old sinew]

I used the quadratic equation

and i reached \frac

[slate jolt]

also z=0 is an obvious root here you dont need quad equation

you can factorize by z

right away

[ocean seal]

Dubs

[old sinew]

Sorry typo

[slate jolt]

ok

so yeah quad equation

[old sinew]

I reached $\frac{-(2-i) \pm \sqrt{3+4i}}{2}$

[ocean seal]

Dubs

[slate jolt]

yeah ok

so what?

[old sinew]

how do i proceed from here?

[slate jolt]

why would you need to proceed?

[old sinew]

the solutions are -2 and i

it seems

[slate jolt]

,w z^2 +(2-i)z -2i

[ocean seal]

Results provided by WolframAlpha

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

Requested by b__n

[slate jolt]

ok

maybe write 3+4i in exponential notation

so you can take the root

easily

im just double checkinh your calculations

[old sinew]

exponential notation isn't nice

like won't look nice

[old sinew]

please

I reached $\frac{-(2-i) \pm \sqrt{(2-i)^2 +8i}}{2}$

[ocean seal]

Dubs

[old sinew]

I reached $\frac{-(2-i) \pm \sqrt{4-4i-1+8i}}{2}$

[ocean seal]

Dubs

[old sinew]

I reached $\frac{-(2-i) \pm \sqrt{3+4i}{2}$

[slate jolt]

ok but i think exp notation is your only way out

[old sinew]

but my textbook writes it soo trivially

letme show

Example 3 section 1.5 proves qudratic formula for complex coefficents

[slate jolt]

maybe you need to find a a^2 +2ab + b^2

inside the root

[old sinew]

like inside root, it's of some square?

[slate jolt]

it probably is since it simplifies

,w 3+4i exponential notation

[ocean seal]

Wolfram Alpha doesn't understand your query!
Perhaps try rephrasing your question?
Click here to refine your query online

Requested by b__n

[slate jolt]

,w 3+4i

[ocean seal]

Results provided by WolframAlpha

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

Requested by b__n

[slate jolt]

ok it suckd

[old sinew]

let me show the problem 21 they talking about

it's sort of mental trick it seems

3+4i= (a+ib)^2 they saying

[slate jolt]

yeah it is true

any complex number is the square of some other complex number

[old sinew]

can you explain the stratergy ?

i don't think i get it

[slate jolt]

(a+ib)^2 = (a^2-b^2) + 2ab i

[old sinew]

yes

[slate jolt]

so if you have c+id

and want to find the sqrt

you want (a+ib)^2 = (a^2-b^2) + 2ab i = c+i d

so identify imaginary and real parts

[old sinew]

so we look for two numbers a,b such that a^2-b^2 =c , 2ab=d?

[slate jolt]

yes

[old sinew]

make sense

so for 3+4i

a=2, b=1 works

thus 2+i is a root

the other root is -(2+i)

[slate jolt]

uh no

this gives you a simplification

of the sqrt

in your formula

[old sinew]

yes, but If I'm just looking for the root of 3+4i

isn't it 2+i and -2-i ?

since (2+i)^2 = 3+4i, clearly 2+i is a root of 3+4i right?

[slate jolt]

oh yeah the dqrt

sqrt

root= solution of a polynomial in my mind

[old sinew]

I reached $\frac{-(2-i) \pm \sqrt{3+4i}}{2}$ = $\frac{-(2-i) \pm (2+i)}{2}$

[ocean seal]

Dubs

[old sinew]

got it

z=-2 or i

[lone heart]

@old sinew Has your question been resolved?

[lone heart]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• 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>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[wary marsh]

This graph is a periodic graph for y = x in Fourier series

,rotate

[lone heart]

Channel closed

Channel closed due to the original message being deleted.
If you did not intend to do this, please open a new help channel,
as this action is irreversible, and this channel may abruptly lock.

[wary marsh]

I wanna oh

[lone heart]

Available help channel!

Send your question here to claim the channel.

Remember:
• 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>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[torn spade]

6 questions to ask but same topic

[tall topaz]

compute g(2) first

then do f(whatever g(2) is)

[torn spade]

uhhh idk

idk how to

[tall topaz]

for g(2) put 2 into the x in the expression for g(x)

,, g(2) = 2 \cdot 2^3 +1

[ocean seal]

Pure

[torn spade]

so g(2) = 17?

[tall topaz]

yes

[torn spade]

since x is 2

but im not sure what is the answer of f(g(2))

[tall topaz]

since g(2) = 17

you need to compete

compute f(17)

[torn spade]

i got 49

[tall topaz]

,, f(17) = 3\cdot \textcolor{red}{17} - 2

yes

[ocean seal]

Pure

[torn spade]

17 times 3 is 51 then minus 2 is 7 squared

[tall topaz]

yes

[torn spade]

.close

[lone heart]

Channel closed

Closed by @torn spade

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• 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>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[alpine sable]

help

[alpine sable]

help me

[slate jolt]

how do you find the turning point of a quadratic?

[alpine sable]

formula like -b/2a and Vertex y = b²-4ac/2a

bythe way what is the question about

I didint understand

who can help

me

[slate jolt]

start by finding the turning point

and then find a k

such that the turning point is on the y axis

meaning that its x cordinate is =0

and same for Q5 but the y cordinate= 0

[junior vigil]

@alpine sable

[alpine sable]

ok thanks

[lone heart]

@alpine sable Has your question been resolved?

[lone heart]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• 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>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[vivid roost]

https://gyazo.com/c3f831b5315e5708b658fcfe57ae5e34 how do i approach this?

[lone heart]

@vivid roost Has your question been resolved?

[vivid roost]

<@&286206848099549185>

[alpine sable]

Hey!

[vivid roost]

hi 🙂

[alpine sable]

What math are you taking

[vivid roost]

this is stats and probability

[alpine sable]

Alr

Lemme see if I can get a helper on you

[vivid roost]

okay thanks so much

[alpine sable]

We are very low on helpers rn

XD

[vivid roost]

ahhh

[lone heart]

@vivid roost Has your question been resolved?

[lone heart]

@vivid roost Has your question been resolved?

[lone heart]

@vivid roost Has your question been resolved?

[brisk quartz]

To find the expected value for the number of years of experience from the employees of this department, we will use the joint probability distribution given by $ f(x_i, y_j) $. The expected value of Y is computed as:

,tex $ E[Y] = \sum y_j f(x_i, y_j) $

[ocean seal]

kurenai_5h

[lone heart]

@vivid roost Has your question been resolved?

Channel closed

Closed by @vivid roost

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• 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>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[summer hemlock]

I need help with number 4

My teacher wants me to find 5 x's that would fit on that graph to graph the function

[pulsar spire]

seems like you got 4 dots so far

do one more x value

[summer hemlock]

idk how to make the graph a triangle though

[pulsar spire]

triangle? wym

[summer hemlock]

in a triangle shape

I mean v shape

[pulsar spire]

what would x = -3 give you

input that into your function

[summer hemlock]

-5

[pulsar spire]

2 - 3

isnt -5

[summer hemlock]

oh shoot I forgot to make it positive then subtract

-1

[pulsar spire]

do -4 after that, and you should get your v

[summer hemlock]

alright

ok thanks I get it now

I appreicate the help

.close

[lone heart]

Channel closed

Closed by @summer hemlock

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• 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>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[alpine sable]

how can i make this into a form that can utilize PFD

[naive valley]

factor the denominator?

[foggy pecan]

are you dealign with Laplace'a transformation to find orignal?

[alpine sable]

yes

[alpine sable]

having trouble with that

[foggy pecan]

$\frac{1}{s^{2}-4}=\frac{1}{\left( s-2 \right)\left( s+2 \right)}=\frac{1}{4}\left( \frac{1}{s-2} -\frac{1}{s+2}\right)\text{ then }\\\mathbb{L^{-1}}\left{F\left( s \right) \right}=\frac{1}{4}\left( e^{2t}-e^{-2t} \right)=\frac{1}{2}\sinh\left( 2t \right)$

[ocean seal]

Joanna Angel

[foggy pecan]

first you introduce the image F(s) as a sum of partial fractions

and next you get the Lapalce'a tables

adn you read it from there

finally i noticed it can be exprfesed as hyperbolic sine

but it is makeup haha )

so optional thing

[alpine sable]

damn i had no idea that it factors to (s-2)(s+2) oof

im silly

thanks

[hushed locust]

that's a difference of squares

[alpine sable]

yeah i just thought imaginary for some reason

no clue why

.close

[lone heart]

Channel closed

Closed by @crude ginkgo

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• 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>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[slow haven]

Hi, how can I begin to show if something like this converges?

I only know a few tests such as: finding the limit directly, ratio test (growth factor test), and the comparison test

oh and the sandwich theorem

but that isn't a test per say..

So, I am not sure how to show if this converges or not, although im almost certain it diverges?

[foggy pecan]

this sequence is divergent, since its limit does not exist, becasue there are two subsequences convvergent to different limits

[slow haven]

OH I FORGOT ABOUT THAT ONE

thank you very much mate

[foggy pecan]

🙂

[slow haven]

i am just wondering which two subsequences to take

[foggy pecan]

think ab sin

am sure you know when sin = 0

and

sin = 1

or sin = -1

hence think , how to write n =

$sinx=0\Leftrightarrow x=k\pi$

[ocean seal]

Joanna Angel

[slow haven]

okay that one makes sense

but im not sure how to pick another subsequence that doesn't just oscillate like the original one to be honest

[foggy pecan]

just think about what n must be inside the sine for it to just stay there kPi

then

n = 12k

[slow haven]

Yes

[foggy pecan]

ok

and now

$sinx=1\Leftrightarrow x=\frac{\pi}{2}+2k\pi$

[slow haven]

the subsequence converges to zero

[ocean seal]

Joanna Angel

[foggy pecan]

n= 6 + 24k, i think

[slow haven]

Ah.

and that converges to one

[foggy pecan]

🙂

[slow haven]

i just forgot about the periodicness!

thank you @foggy pecan very much!

[foggy pecan]

yes )

yvw )

[slow haven]

.close

[lone heart]

Channel closed

Closed by @slow haven

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• 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>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[craggy briar]

How do I do this problem?

[foggy pecan]

you need to use double integral

nd using iterated integrals

$\left| V \right|=\int_{0}^{2}dx\int_{2x}^{4}\left( x^{2}y+y^{2} \right)dy=...$

[ocean seal]

Joanna Angel

[foggy pecan]

it is very easy to calculate

[craggy briar]

oh gotcha

thank you

[foggy pecan]

yw 🙂

[ionic jewel]

I hate that the dx is there

[lone heart]

@craggy briar Has your question been resolved?

[lone heart]

@craggy briar Has your question been resolved?

[lone heart]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• 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>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[gilded galleon]

Flip 10 coins. What is the probability that there are an equal number of heads and tails or the first three flips are heads (or both)?
So the probability of equal number of heads is 252/2^10 which is C(10, 5) over total combinations of 10 coins flips
probability of first three flips being head is 1/2 * 1/2 * 1/2 = 1/8
so to get the probability i want i would subtract from 252 the values that are already considered by the 1/8 or the values that have first three head and equal number of heads and tails? so that would by C(7, 2) = 21. so the probability is either event is (252 - 21)/2^10 + 1/8????

[lone heart]

@gilded galleon Has your question been resolved?

[gilded galleon]

<@&286206848099549185>

🙏🙏🙏🙏🙏

[lone heart]

@gilded galleon Has your question been resolved?

[plucky sluice]

I got the same answer with a slightly different argument, so I'm pretty sure you're right

[lone heart]

@gilded galleon Has your question been resolved?

[gilded galleon]

ok 👍

/close

!close

.close

[lone heart]

Channel closed

Closed by @gilded galleon

Use .reopen if this was a mistake.

[plucky sluice]

.close

[lone heart]

Available help channel!

Send your question here to claim the channel.

Remember:
• 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>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[knotty thunder]

How do I formally prove the 1st statement to be true.
I proved the 2nd statement to be false by counter example. It's when f(x) = x ** 2 and A = {1} and B = {-1}.

[knotty thunder]

I tested empirically through python. It seems that the 1st statement might be True, but how do I formally prove it to be True

[lone heart]

@knotty thunder Has your question been resolved?

[tribal haven]

pretty sure 1 is not true unless i'm misreading something big

[knotty thunder]

can u give me a counter example?

# not one to one
def f(x):
    return x**2

# one to one
def g(x):
    return x + 1

A = {-2, -3, -5, 3, 4, 5, 6}
B = {-5, 2, 3, 4, 0, 1}

# {f(x):x∈A}△{f(x):x∈B} is a subset of {f(x):x∈A△B}
# {f(x):x∈A△B} is a subset of {f(x):x∈A}△{f(x):x∈B}

# not one to one
f_expression1 = {f(x) for x in A} ^ {f(x) for x in B}
f_expression2 = {f(x) for x in (A ^ B)}

# one to one
g_expression1 = {g(x) for x in A} ^ {g(x) for x in B}
g_expression2 = {g(x) for x in (A ^ B)}

print(f_expression1.issubset(f_expression2), g_expression1.issubset(g_expression2))
print(f_expression2.issubset(f_expression1), g_expression2.issubset(g_expression1))

this is my python code on trying to find counter examples of the problem

[tribal haven]

ok i might be mistreading something big lmao

oh jesus christ ok yes i did

the proof is like 2 lines

i read equality instead of subset -_-

just argue from the definition of subset and use properties of symmetric difference

[knotty thunder]

hi can u give me ur proof? im still lost on wut to do lol

iknow the definition of a subset and symdi

but idk where to start

[tribal haven]

by definition of subset if A is a subset of B then every x in A is in B

so show that if x is the set on the left then it's in the set on the right, properties of symdiff will help

i guess contrapositive might be easier

[knotty thunder]

hmm im still lost. wut properties of symdiff r u using. i only know the propert a ^b = (a-b) u (b-a)

[tribal haven]

specifically $x \in A \triangle B \Rightarrow x \notin A \cap B$

[ocean seal]

IV

[tribal haven]

you might even be able to exhaustively prove this

since either x in A or not in A and similarly x in B or not in B
you can brute force all 4 cases for all x for both sides

[knotty thunder]

sdjkahjkdashjk my brain broke down 😭

hmm wait

how about for when we input something lets say that is from A and B.
is f(A and B) ^ f( A and B ) going to be the subset of {f(x):x∈A△B}

[tribal haven]

your left hand set is empty, so yes

[knotty thunder]

oh yea

hmm

so the statement is equivalent when is both true when the function is one to one

but if the f is not one to one

the 2nd statement is gonna go false

?

this is wut i get from trying to draw the sets and function on paper

idk how to formally write any proof

[tribal haven]

bijective function gives you equality
but if not bijective then it's a subset of

[knotty thunder]

oh yeah thats wut i found also

wait bijective is one to one right

[tribal haven]

the start of the logic begins with:

if $x \in LHS$ then either $ x \in A$ or $x \in B$. Without loss of generality assume $x \in A$ (or otherwise swap A and B's), then $\nexists y \in B: f(y) = f(x)$ (why?)

[ocean seal]

IV

[knotty thunder]

wait wut

but theres a case where y like that exists

if the function is not bijective

It's when f(x) = x ** 2 and A = {1} and B = {-1}.

i dont get it

wut u tryna say

sorry

can u explain a bit more

[tribal haven]

show that in this case x does not belong to LHS

that requires some amount of thought instead of straight up copying down properties

[lone heart]

@knotty thunder Has your question been resolved?

[lone heart]

Channel closed

Closed by @knotty thunder

Use .reopen if this was a mistake.

[lone heart]

Available help channel!

Send your question here to claim the channel.

Remember:
• 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>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[whole scaffold]

I need to help with this question. I need to find the reading of the voltmeter and the ammeter right after the switch is closed and after a long time, but I'm not really sure what to do with she solenoid and the capacitor

can anyone give me hints with what to do with those two?

[alpine sable]

All are uhh ideal voltmeters and ammeters?

[whole scaffold]

yes

[alpine sable]

What's mH ?

Unit of inductance is what google says

[whole scaffold]

just Henry? in 10^-3

?

yeah

from what i assume, at the estart i can just assume this as one single series circuit?

because the loop witht he inductor will not flow any current, and the one with v4 will also not flow, because the one with the capacitor provides almost no resistance

so it'll just be strictly flowing through in one single loop right after switch is turned on?

so v2 = v3 = v4 = 0

am i right so far?

so V1 is just 40V, cuz that's the only resistor in the circuit

but what is V5, is it also 0, or is it at 40

cuz isn't the voltage through a capacitor like, 0 immediately after the switch is turned on?

so V2 ~ V5 = 0 immeidately after, and V1 = 40

[night wren]

how the bound differs from the constraint function? And how does it affect the solution

[whole scaffold]

hey not to be that guy but i'm using this channel btw

[lone heart]

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).

[whole scaffold]

And then after a long time, the loop with capacitor is dead, the inductor just acts as a wire, so now its a parallel circuit?

so overall resistance is 50 + 100/3, so the current is I = 40/(250/3) = 0.48A

so V2 = V5 = 0

V1 = IR = 0.48(50) = 24V

and the voltage across both V3 and V4 is equal cuz they are in parallel, so its just 16V?

<@&286206848099549185> anyone?

so to summarize for what i got
Right after switch is closed
V1: 40
V2 = V3 = V4 = V5 = 0

After long time
V1 = 24
V2 = V5 = 0
V3 = V4 = 16

So in terms of current, at the start, there's none through A2 and A3 so that's 0

A1 and A4 is equal cuz its current in a series circuit, so its just 40/50 = 0.8A

And then after long time, A4 is 0 cuz capacitor is fully charged

[whole scaffold]

A1 is 0.48 cuz of this

and because the resistors are 2:1, A2 = 0.16A and A3 = 0.32A

Did i do this correctly? anyone?

[golden gulch]

is the angular frequency (w) given in the question??

or frequency (f) given?

[whole scaffold]

???

[golden gulch]

Basically what happens is that when the switch is closed immediately, the current through inductor(solenoid) will be zero, as the nature of the inductor is to oppose the current, so, v2=v3=0 when switch is immediately closed.
Capacitor will start charging and hence current will flow in capacitor

after a long time at t=infinity, no current will flow in capacitor and current will flow in the branch having the solenoid. SO, V5=0 when t=infinity.

now after eliminating the elements according to the condition, we can find the ratio of impedences and hence current in each branch, for that we need frequency in order to find the impedence of the elements like capacitor and inductors,,.....

in order to find the Xl and Xc( impedences of inductor and capacitor respectively), we need frequency as
Xl=wl and Xc=1/wc where , w=2pif

[whole scaffold]

i feel like you are way overcomplicating this for my class

[golden gulch]

Well i ain't aware of the class you are present in, but i guess we cannot solve circuits having inductors or capacitors without the frequency of the circuit, as impedence cannot be found.

[whole scaffold]

hmm

alright

also another question

if a current is decreasing at a constant rate, and that rate is di/dt = -0.018A/s

do i treat that as negative or positive

like, its decreasing, but the rate is negative?

[golden gulch]

I guess u are talking about the inductor, the negative sign just denotes that the current is decreasing, so you will use negative sign while solving the equations.

[whole scaffold]

aight ty, gn 🙏

.close

[lone heart]

Channel closed

Closed by @whole scaffold

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• 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>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[whole scaffold]

I was doing this question earlier and I got three parts wrong, and I'm not sure where I got it wrong, so can someone check for me?

I had to find the values of the voltmeter and the ammeter right after the switch is turned on, and after the long time

here's my answers
Voltmeter at the start
V1 = 40V
V2 = V3 = V4 = V5 = 0V

After long time
V1 = 24V
V2 = V5 = 0V
V3 = V4 = 16V

Ammeter at the start
A1 = A3 = 0.8A
A2 = A4 = 0A

After long time
A1 = 0.48A
A2 = 0.16A
A3 = 0.32A
A4 = 0A

[whole scaffold]

all my logic is here if you want to see wehre I went wrong

🙏

[whole scaffold]

ok i realized two of my mistakes. i calculated A3 = 0A and A4 = 0.8A but i put my answers in wrong

The only other thing that i think could be wrong is V5 = 0

[stuck cape]

It seems to be question of physics

[whole scaffold]

cuz i thought it could be 40V, but i thought at the start, voltage through capacitance was 0

yeahhh, but i was told i can ask physics questions cuz physica is technically math :3

nvm

.close

[lone heart]

Channel closed

Closed by @whole scaffold

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• 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>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[alpine sable]

please can anyonje help me?

[lone heart]

@alpine sable Has your question been resolved?

[alpine sable]

.close

[lone heart]

Channel closed

Closed by @unborn abyss

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• 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>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[hollow trench]

4(x+1) + |x+4| < 2(2x+3)

[hollow trench]

Hello. Can someone help me with something?

I have this inequality and the exercise requests me to verify if 0 is a solution of the inequality

but I don't really understand

[pallid scarab]

replace x by 0, check if the statement you get is true

[hollow trench]

so 4(0+1) + |x+4| < 2(2 * 0 + 3)

4 + 4 < 0 + 6

8 < 6

nonoo

4 + | 0 + 4 | < 6

| 0 + 4 | < 2

-2 < 4 < 2

it doesn't maky any sense

am I wrong somewhere?

[pallid scarab]

no, you're not wrong

Remember, i asked you to check IF the statement is true

as the same as the question

so is the statement true or false?

[hollow trench]

so 0 can't be a solution because the " -2 < 4 < 2 " is false

so the whole statement is false

[pallid scarab]

It was already finished here btw

[hollow trench]

if I have absolute value don't I need to use the opposite of the number in the right in the left of the inequality?

[lament forge]

...that might be the correct thing to do in some circumstances but it's not something that a law of the universe requires you to do any time an absolute value exists anywhere

it is true that if x=0, then 4(x+1) + |x+4| = 8 and 2(2x+3) = 6, and so the statement 4(x+1) + |x+4| < 2(2x+3) is equivalent to the statement 8 < 6

[hollow trench]

soo... How can a stupid like me find if I need to use that "law"

Overall, the statement is false, at least I understood that

[lament forge]

...well it's just also true that |x| < y is the same as -y < x < y

so if you're trying to work out which x satisfy |x| < 4, turning that into "-4 < x < 4" is probably useful

if you want to know if |4| < 6, you can turn that into "-6 < 4 < 6" because it's still true that those are the same, but just computing that |4| = 4 so the statement is 4 < 6 is also valid

in general there isn't really ever only one way to solve something, any sequence of valid inferences will get you a correct answer

[hollow trench]

Thank you for the explanation and for your time! I really appreciate. I was a bit confused.

we can call this an "ugly" math problem, ig...

[lament forge]

...?
i don't see what's "ugly" about it

[hollow trench]

I usually call a problem "ugly" when I can't do it by myself, hehe, I am a strange person. However, even with the inegality resolved wrong, I still got the same answer.

[lament forge]

idk what you mean by "resolved wrong"

you did it two different ways and both of them were correct

[hollow trench]

oh, I thought that without using this law isn't as correct as it is using it

Anyway. Thank you very much for your time! Have a great day!

.close

[lone heart]

Channel closed

Closed by @hollow trench

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• 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>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[novel widget]

hello, i saw a correction of an exam and at some point they give this equation
e^(1/α -1) = -α/(α - 1 )
α range is between 0.21 and 0.22 that make both left and right sides positive but how did they went from left side to the right side

[vale crag]

e^x is approximately 1+x, that's prolly what they did

is it $e^{\frac{1}{a-1}}$ or $e^{\frac1a -1}$ ?

[ocean seal]

aPlatypus

[vale crag]

@novel widget

[novel widget]

its the first one

1 / (α -1)

[vale crag]

$e^{\frac{1}{a-1}} \approx 1 + \frac{1}{a-1} = \frac{a}{a-1}$

[ocean seal]

aPlatypus

[vale crag]

I don't really see how they got their minus then

[novel widget]

α is ranged between 0.21 and 0.21
α -1 is negative while exponential is positive
i think the equation is incorrect

[vale crag]

yeah so they typo'd

a/(a-1) should be a correct approximation then

[novel widget]

this is really missed up ngl

[vale crag]

well it's not the first nor the last typo we'll ever do

[novel widget]

yeah i guess i will just ignore it for now, thanks

how can i close thi

s

[vale crag]

.close

type it yourself you'll see

[novel widget]

.close

[lone heart]

Channel closed

Closed by @novel widget

Use .reopen if this was a mistake.

[lone heart]

Available help channel!

Send your question here to claim the channel.

Remember:
• 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>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[thin sedge]

A

[thin sedge]

,rotate

[thin sedge]

Here’s what my teacher did

[storm ridge]

Step 2, x^-1 * x should be 1

[thin sedge]

Numerator, when he multiples xy why is it not xy^3+y^2

I know what it should be but I don’t understand why

[storm ridge]

Ok so

What does x^-1 mean

[thin sedge]

negative exponent or 1/x

[storm ridge]

1/x

x^-1 = 1/x^1

[thin sedge]

Mhm

[storm ridge]

And now if you multiply x

x/x=?

Another way to look at it would be that
x^-1 * x^1 = x^(-1+1) (why?)

[thin sedge]

Ohh

wait I’m writing ur stuff

okay

I get it

Thx

[storm ridge]

Np

[thin sedge]

.close

[lone heart]

Channel closed

Closed by @thin sedge

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• 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>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[exotic canopy]

i am investigating behaviour of nested functions of cosine

[exotic canopy]

i know that dottie number is what $$\cos^{(\infty)}(x)$$ stabilizes to (where $f^{(n)} = \underbrace{f(f(\cdots(}_{n \text{ times}}x)$) )

[ocean seal]

artemetra

[exotic canopy]

this is equivalent to what the sequence $a_n = \cos(a_{n-1})$ converges to

[ocean seal]

artemetra

[exotic canopy]

this function becomes a straight line

but

let's analyze $\cos^{(\infty)}(bx)$

$x$ is the variable, $b \in \bR$ is a parameter

[ocean seal]

artemetra

artemetra

[exotic canopy]

dottie number is the case b=1

[exotic canopy]

however, this function behaves very weirdly for different values of b

how/where can i study this weird behaviour?

ofc what i have here is an approximation because i have the function nested finitely many times

(although 70 times is a pretty good approximation)

the x/b argument is to keep the period of the function the same

[lone heart]

@exotic canopy Has your question been resolved?

[mellow grail]

Study as in? Its properties?

Well a good start is its fixed points

And to test if they r there u can use that banach point theorem

[mellow grail]

Taylor expansions, de movieres generalization, stability for different number systems, just to name a few

Also if u know how to (me also researching this topic so don't ask me how( u can design a differential equation if there exists one

@exotic canopy

[exotic canopy]

i see

it's just really difficult cuz these numbers are all transcendental

hm

,w taylor expansion of cos(cos(x))

[ocean seal]

Results provided by WolframAlpha

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

Requested by arte_m_etra

[exotic canopy]

bruh

[mellow grail]

Eh Taylor might be stupid. Wait no it is stupid

I suppose Fourier series would be...shittier

Hmm perhaps a slope field? It would be the slope field of y' = cos(by)

Because aPlaytpus and my research have told me that a_n = f(a_(n-1)) and, y' = f(y) are similar

So if u study one, the other will have similar properties

[mellow grail]

Also u would wanna know whether ur parameterized function cares about a_0

I think the graph can help with that

[exotic canopy]

that's true

[exotic canopy]

wdym?

[mellow grail]

Well when b=1 we know the sequence converges to a single value, no matter what a_0 (ie first value) u take. Does ur modified sequence show that too?

The word is constriction, I think

[mellow grail]

I just realised this is equivalent to checking for banach fixed point theorems validity on ur modified sequence

[exotic canopy]

hm

[exotic canopy]

oo i'll look into that

[mellow grail]

Is that a yes, a mhm, or a hmm?

[exotic canopy]

the last one

[mellow grail]

I see

[exotic canopy]

the answer is kinda

it's periodic

it doesn't converge to one value

but it converges to one interval

[mellow grail]

https://youtu.be/qHnXE_h5c2M?si=GoMtUEl0o4Pg-GMP

This very briefly covers the banach fixed pt theorem

And studies ur sequence for b=1

[exotic canopy]

yeah i know it's properties for b=1

[exotic canopy]

it's just that the way this function changes over b

[mellow grail]

Eh? I think as n approaches infinity it becomes denser so it ends up approaching a value just above 0.5

[mellow grail]

Changes over b...partial differentiation

[exotic canopy]

this kinda reminds me of logistic map for some reason

[mellow grail]

Isn't that for like exponentials

And that reminds me u can even use the imaginary definition of cosine here, see if it gives something interesting

[mellow grail]

Well I don't know much about it, just heard that it's connected to a variety of phenomenon

[exotic canopy]

oooo right right

wait

$\cos(\theta) = \frac{e^{i\theta}+e^{-i\theta}}{2}$

[ocean seal]

artemetra

[exotic canopy]

so

$\cos(\cos(\theta)) = \frac{e^{i\cos(\theta)}+e^{-i\cos(\theta)}}{2}$

[ocean seal]

artemetra

[exotic canopy]

$\cos(\cos(\theta)) = \frac{e^{i(\frac{e^{i\theta}+e^{-i\theta}}{2})}+e^{-i(\frac{e^{i\theta}+e^{-i\theta}}{2})}}{2}$

[ocean seal]

artemetra

[exotic canopy]

anyways

i think i'll come back once i have a proper question

[exotic canopy]

thanks bro

.close

[lone heart]

Channel closed

Closed by @exotic canopy

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• 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>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[meager temple]

I need help solving this question. I got no clue how to solve it

[meager temple]

i dont know how i can decide on the third length of a triangle

[snow cobalt]

Triangle inequality

Sum of 2 sides has to be greater than the third

Can't be equal

[meager temple]

so the third side should be less than 6+4?

[north perch]

yeah

[meager temple]

so itll be 10>BC

but then wont it mean that all the options can be BC

[north perch]

the difference of 2 sides is lesser then third side

there's also this property

[meager temple]

🤨

i do not understand

do i make the inequality 6+4>BC or 6-4>BC

[north perch]

sorry mb

6-4<BC

[meager temple]

that means it cannot be 2 yes?

[north perch]

yep

[meager temple]

and this is called triangle inequality?

difference of two sides must be less than the third side?

[north perch]

yes

[meager temple]

lemme check if its correct on the answer sheet rq

alright nice

thank you grey

.close

[lone heart]

Channel closed

Closed by @meager temple

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• 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>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[idle willow]

if i have

4h/9/h

can I eliminate the h?

[exotic canopy]

yes

[idle willow]

but

directly?

[exotic canopy]

$\frac{4h}{\frac{9}{h}}$?

[ocean seal]

artemetra

[idle willow]

no

[exotic canopy]

this?

[idle willow]

4h/9/h/1 i think

[exotic canopy]

what

write it down and send

[idle willow]

ok

[exotic canopy]

ah

still cancels out

[idle willow]

can i ask another quick question

if i want to change them to multiply
4/h * h/1 is that possible right?

[idle willow]

can you explain me why they can cancel out?

[exotic canopy]

imagine the 5 wasn't there

[idle willow]

wow

okay okay

[exotic canopy]

$\frac{4h}{h}$

[ocean seal]

artemetra

[idle willow]

thanks ❤️

[exotic canopy]

wdym?

[idle willow]

there is something that mathematician do

is pass double fraction to multiply one fraction with the other one

i dont know how is that named

[exotic canopy]

you mean like $\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \cdot \frac{d}{c}$?

[idle willow]

no i mean

[charred summit]

You can think about it as
$$(4h \over 5) \over h$$
$$\frac{4h}{5}\over h$$
$$\frac{4h}{5}\times \frac1{h}$$

[ocean seal]

artemetra

[exotic canopy]

this?

[idle willow]

this

i know

i am stupid but i have examen monday haha

and im studying basics

[exotic canopy]

yes

that's correct

[idle willow]

because basics are important

okay thanks artemetra

[exotic canopy]

no problem

[idle willow]

seeinglike this i can eliminate the h without remorse

hahaha

well thank and happy december first

.close

[lone heart]

Channel closed

Closed by @idle willow

Use .reopen if this was a mistake.

[idle willow]

.reopen

[lone heart]

✅

[idle willow]

@exotic canopy i can't to cancel the h because upside h is substractin

right?

[deep condor]

I mean

You could just write it as (1/h)-1

[idle willow]

the thing is i need to eliminate the h

[deep condor]

Not really possible here, you're going to have at least one h remaining

[idle willow]

.close

[lone heart]

Channel closed

Closed by @idle willow

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• 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>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[alpine sable]

can someone explain this?

[devout helm]

if you expand it entirely there will be some zeroes after 7 like 14670000000000000..

[alpine sable]

oh my god 😭

[alpine sable]

[
1467 \cd 10^{?}
]

[alpine sable]

what is ?

99?

yeah

so

how many zeros

OHHH

99 ZEROS?

yes

bro my dumbass thought i had to write down 99 zeros

in the qn

thank you so much'!

is this correct

and how do we simplify fully btww

[alpine sable]

okay

one big question

did you write [
\s[3]{\f62} \tss{or} \f{\s[3]6}2
]

[alpine sable]

???

what the fuck?

okay but you get the idea, which one of those did u write?

[alpine sable]

both 😭

[alpine sable]

this

[alpine sable]

and this

what u wrote doesnt really show it well

you have to be clear

they are very different

[alpine sable]

for [
2p^{\f13} = 6
]
what is the step you do?

[alpine sable]

is this correct?

i rewrote

it

[alpine sable]

yeah now this is correct

[alpine sable]

this is wrong

what u wrote

but anyways

like

[alpine sable]

is it correct if the qn asked for indices? just wondering

[
\p{abc}^n = a^n\cd b^n\cd c^n
]