help-13

[vivid valley]

yes

oh so if you put the limits in

its just 0?

[regal oak]

don't put them as such

this will get reduced to 2ax^2 ryt ??

[vivid valley]

wait where did the log go?

[regal oak]

using formula 3

log(ax^2+1)/ax^2 = 1

[vivid valley]

ohhhhh okay because you separated them

yes okay

[regal oak]

so now the numerator simplifies to 2ax^2

[vivid valley]

which you can differentiate later?

once you have the bottom

[regal oak]

now do the same with denominator using formula 5

and tell me wt u get

[vivid valley]

okay

thank you

[regal oak]

my pleasure
we are not done yet so ya continue

[vivid valley]

yep so i got -1

[regal oak]

no no loll
u'll be getting -x^2

[vivid valley]

hang on

ill show my working

[regal oak]

no no it isn't like that loll

[vivid valley]

oh my bad

[regal oak]

how do u say this is 1 ?

lemme show u the actual working

[vivid valley]

rule 5

in your list

i assumed that e^x = e^x^2

[regal oak]

get this ?

[vivid valley]

yes but how did you know to use x^2

[regal oak]

bcos the power of e is x^2

[vivid valley]

ohhhhh

okay

i understand now

[regal oak]

so in the numerator we've like 2ax^2 and denominator we've -x^2
so ig u've the answer there

as -2a

[vivid valley]

thats what the calculator had for my final answer

thank you so much man

[regal oak]

my pleasure
if u still had any doubt feel free to dm if u close

[vivid valley]

thank you! Legend

!close

[cedar kiln]

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[bronze violet]

A company has a policy of retiring company cars; this policy looks at number of miles driven, purpose of trips, style of car and other features. The distribution of the number of months in service for the fleet of cars is bell-shaped and has a mean of 50 months and a standard deviation of 10 months. Using the 68-95-99.7 rule, what is the approximate percentage of cars that remain in service between 60 and 70 months?

[lethal jackal]

!status

[cedar kiln]

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

[bronze violet]

1

[lethal jackal]

you have absolutely nothing?

[bronze violet]

ive never done this before i have no idea where to start

[lethal jackal]

have you learned anything about it in class

[bronze violet]

no this is the first time im learning about this

[lethal jackal]

do you know what the 68-95-99.7 rule is

[bronze violet]

kind of its like the bell with three lines and theres different percentages for it right?

[lethal jackal]

I suggest you read your course notes

if you don't know the words in the question, then chances are you don't know the stuff that was taught

or try reading the textbook

[bronze violet]

we werent given a textbook it was a course using wamap

its an assignment i have to redo .close

[lethal jackal]

is there any text you're supposed to read

any reference material

because starting from nothing is really not where you're supposed to be

[bronze violet]

no my teacher didnt give us anything

there was a link to a video but it went to nowhere

.close

[cedar kiln]

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[vivid valley]

Looking to evaluate this limit. I am trying to use the following Limit rule but cant work out the algebra to get the 2023 to the numerator. Any help would be greatly appreciated.

[tropic oxide]

you can write your thing as $\paren{\frac{n+2023}{n}}^{-2n}$

[wraith dagger]

Ann

[vivid valley]

oh. my. god.

thank you

.close

[cedar kiln]

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[cedar kiln]

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[finite rivet]

Can anyone help with these

[cedar kiln]

Please don't occupy multiple help channels.

[finite rivet]

<@&286206848099549185>

.close

[cedar kiln]

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[left zodiac]

plss help

[tame wraith]

draw

the graph

of the reigion

[left zodiac]

then?

[tame wraith]

re write the reigion

interms of x

instead of y

youll have to split it up though

[cedar kiln]

@left zodiac Has your question been resolved?

[cedar kiln]

@left zodiac Has your question been resolved?

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[native pewter]

How do I answer question 1?

[cedar kiln]

@native pewter Has your question been resolved?

[cedar kiln]

@native pewter Has your question been resolved?

[cedar kiln]

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[spark flame]

um guys?

[spark flame]

anyone here?

[crimson sedge]

send your question

[spark flame]

I need help\

I need a guide or sumn like that

Can someone explain fractions

[crimson sedge]

Ah, there you go

[spark flame]

like all of fractions

pretty much all that a grade 7 student needs

[crimson sedge]

All of them? I mean we're here to explain math, sure, but didn't you learn at least some of it at school?

[spark flame]

no time to judge 😭

[livid hound]

you can start with googling fractions

[crimson sedge]

Like typically we'd get a question like "I don't understand why this works like that" or something but explaining the entirety of fractions is different

[crimson sedge]

I'm not judging, I'm expressing confusion

[livid hound]

rather than have us regurgitate readily available content

[spark flame]

okayy well umm

[livid hound]

and then come back if there are parts you don't understand

[spark flame]

explain improper fractions and how to solve em

[livid hound]

wdym by "solve them"

[spark flame]

yk like addition or sub

[livid hound]

improper fractions should be left as improper fractions

[spark flame]

I heard you need to find lcms?

[tranquil oracle]

have you heard of the pizza analogy

[crimson sedge]

Depends what you want to do

[tranquil oracle]

so 3/2 is like you have 3 pizza halves and so on

[livid hound]

lcms are related to combining fractions through addition/subtraction

[spark flame]

so, you basically find a common number of two or more numbers isnt that right?

[livid hound]

not directly related to improper fractions

you would consider lcms when trying to simplify something like
$$\frac12 + \frac13$$

[wraith dagger]

ℝamonov

[crimson sedge]

Depends on what you want to do

[livid hound]

look up the content

and then come back if there are parts you don't understand

[spark flame]

And then you divide the lcm with the upper numbers

[crimson sedge]

Depends on what you want to do
Literally you don't need to do anything if you're not given a problem

What are you trying to do?

Like, what's the goal?

[spark flame]

everything is so irrelevant

[spark flame]

I have finals in wednesday 😭😭😭😭

[crimson sedge]

Yeah I am not getting my message through
Suppose you have a paper that says the following:
"5/3, 2/5"
How would you solve this? You wouldn't, there is no problem, literally this is just 2 fractions

However, suppose you have a problem that says this instead:
"Add 5/3 and 2/5 together, then simplify"
Now you can solve this, because there is an actual problem

So, National, you are asking "Should I do this?" but I don't even know what problem you're trying to solve

[spark flame]

like guys, imma give you a simplify problem

kay?

[spark flame]

4/7 ÷ [1 2/7 - 3/14]

[livid hound]

is that supposed to be a mixed fraction?

[spark flame]

i didnt say its a mixed fraction

i dont even know if its a mixed fraction

[crimson sedge]

What does "1 2/7" mean?

[livid hound]

its your question

[spark flame]

12 by 7

[crimson sedge]

Ah, I see

[spark flame]

guys, i just copied a google grade 7 fraction simplify problem

[livid hound]

is that: \
a) $1\frac27$ \
b) $\frac{12}{7}$ \
c) something else

[wraith dagger]

ℝamonov

[crimson sedge]

@spark flame Whatever, we're gonna assume it's a regular fraction for now...

[spark flame]

yh sure

[crimson sedge]

So you'd first start by simplifying the terms in the parentheses: 12/7-3/14

[spark flame]

guys, just give me a detailed guide

[spark flame]

u huh

[crimson sedge]

Do you know how to add and subtract fractions together?

[spark flame]

finding their LCMs?

[crimson sedge]

Hmmm, that works

[spark flame]

I mean thats what we were taught

[crimson sedge]

Alright, let me give you a simpler one: 3/4+2/4

@spark flame Do you know how to do this one?

[spark flame]

12/4+2?

Is that it?

[crimson sedge]

Not quite sure how you reached that

[spark flame]

lcm of 3 and 4 is twelve

[crimson sedge]

Ah, I see, you know it's LCM but you don't know how to apply it

Then let me walk you through the intuition first, then we'll see how LCM comes in handy later

[spark flame]

then you divide 12 with 4 and 2

[spark flame]

sure

[crimson sedge]

Suppose you have 3 quarters of a pizza, plus 2 quarters of a pizza

How many quarters of a pizza total do you have?

[spark flame]

5?

[crimson sedge]

Yep

And how do you write 5 quarters in fraction notation?

[spark flame]

5/amount of total quarters of pizzas

[crimson sedge]

5 is the amount of total quarters of pizzas though

How do you write a quarter in fraction notation?

[spark flame]

1/4

hopefully

[crimson sedge]

Exactly, now how do you write 5 quarters?

[spark flame]

5/4?

[crimson sedge]

✅

That's 3/4+2/4 with barely any math

[spark flame]

weeee

[crimson sedge]

here's a different problem: 2/5+3/5

[spark flame]

barely??? 😭

[spark flame]

wait

[crimson sedge]

¯_(ツ)_/¯

[spark flame]

Im already stuck!

[crimson sedge]

@spark flame If you have 2 fifths of a pizza plus 3 fifths of a pizza, how many fifths total do you have?

[spark flame]

5

[crimson sedge]

And how do you write 5 fifths in fraction notation?

[spark flame]

wait like

look, arent we supposed to divide the denomators my 5? (i mistakenly put 6 there)

[crimson sedge]

You phrased it weird, but assuming you meant "put a 5 in the denominator", yes

[spark flame]

no, like wait lemme get u an example

5/6-1/3

5multiplying1-1multiplying2/6

3/6

we solved this in class today

5 by 6 subtracting 1 by 3

[crimson sedge]

Hmmm, sure

That's the case where the denominators aren't the same

As a rule of thumb, when the denominators are the same, it because pretty easy to add or subtract them

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

[wraith dagger]

Labyrinth

[spark flame]

I really really really regret not listening to my teachers

[crimson sedge]

If you have 3 quarters (3/4) of a pizza plus 2 quarters (2/4) of a pizza, you have 5 quarters (5/4) total. If you have 2 fifths (2/5) plus 3 fifths (3/5) of a pizza, you have 5 fifths total (5/5). This can be generalized

[spark flame]

Or Im just dumb in general

[crimson sedge]

Hmmm yes I can't believe the hundreds of millions of students worldwide currently struggling with this concept decided to all be dumb at once like what

[spark flame]

😭

[crimson sedge]

I hoped you'd find the sarcasm in my message

[spark flame]

ykw

lets go to sets

that seems easier

[crimson sedge]

Sets...? That's a weird jump to make, but sure

First, do you know what a set is?

[spark flame]

I mean its in the syllabus so yh

[spark flame]

a grp of well defined anything

[crimson sedge]

Sure, why not...

Let me remind you of 2 properties of sets

First, they are not ordered

{2,5} is the same set as {5,2}

[spark flame]

theyre equivalent sets

ik what a set is\

[crimson sedge]

Indeed

Second, duplicates don't count: {2,2} is the same as {2}

[spark flame]

i have absolutely no idea how solve a set problme

[spark flame]

agreed

[crimson sedge]

Depends on what the set problem is

[spark flame]

give me one

[crimson sedge]

Hmmm

Uh...

I don't have many ideas, let's just go through the different operations you can do on sets

[spark flame]

ok

[crimson sedge]

First, do you know what a union is?

[spark flame]

i dont think were taught that in 7 grade

[crimson sedge]

Honestly I'm a little surprised you're being taught sets at the same time as fractions but whatever

[spark flame]

its nepal what do you expect lmao

[crimson sedge]

A union is an operation that takes 2 sets (let's call them A and B) and spits out a set containing all the elements of A and all the elements of B

[spark flame]

as in a venn diagrm?

[crimson sedge]

For example: {2,5} union {3,5,6}={2,3,5,6}

[crimson sedge]

That is one way to visualize it, yes

[spark flame]

waae whaaa???

[crimson sedge]

?

[spark flame]

im sorry wat?

[crimson sedge]

A Venn diagram is just a way to visualize sets

[crimson sedge]

We're taking the set {2,5}, taking the set {3,5,6}, and spitting out a set that contains all the elements of the first one and all the elements of the second one

Perhaps you've not seen this kind of notation for sets before?

[spark flame]

nope

i dont thhink unions have been taught

[crimson sedge]

Here's a visualization. Ignore everything but the first 2 for now

The top left one shows you what a union looks like as a venn diagram

[spark flame]

the teacher hasnt taught us unions so it wont come in finals

[crimson sedge]

Hmmm, what have you been taught?

[spark flame]

simple operations like addition, subtraction, n stuff

[crimson sedge]

You can't really add or subtract sets though

I mean I guess there are analogs for sets but "addition" and "subtraction" are not names we use

[spark flame]

tell me on esets operation.

[crimson sedge]

I just did, a union is an example of an operation

Seriously though, what have you been taught?

@spark flame I have a feeling that what I'm teaching you is not what I'm supposed to be teaching you, but since the only detail you gave was "sets" I can only guess

Alright, I'm gonna go, so I recommend you close this help channel with .close and open a new one if you need further help

[spark flame]

lmao thankyou

lmma take help frm others

thank you for your co-op and time tho!

really appreciate it

.close

[cedar kiln]

Channel closed

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[fair mortar]

so

[fair mortar]

i have $x^{\sin x}$

[wraith dagger]

bettim

[fair mortar]

for what value of x would this be lowest?

[tropic oxide]

x^sin(x) = e^(sin(x) log(x))

minimize that

or rather

minimize sin(x)log(x)

[fair mortar]

is it when x approaches $n\pi$

[wraith dagger]

bettim

[tame wraith]

what even is the limit of sin(x)ln(x)

,w limit of sin(x)ln(x) as x tends to 0

[wraith dagger]

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Requested by doctor99268#2294

[tame wraith]

hmm

[fair mortar]

well if

lets say

$x \to \pi^+$

[lyric narwhal]

but log(x) can go infinitely negative

[wraith dagger]

bettim

[lyric narwhal]

and sin(x) is a bounded function

so it would go to -inf

[fair mortar]

then it will almost be negative infinity?

[fair mortar]

thats what i got by my intuition but i have no idea how to represent it as a solution

[tropic oxide]

that doesnt sound right. hold on.

,w graph y = sin(x) log(x)

[wraith dagger]

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Requested by Ann#0413

[tropic oxide]

oh wait right hm

oh yeah that makes sense in hindsight

yeah youre gonna have no global minimum on that one

[lyric narwhal]

it's just the sine wave

with

exponential decay

[tropic oxide]

not quite no

[lyric narwhal]

or exponential growth however you view it

[tropic oxide]

logarithmic growth

[fair mortar]

yes but you have any idea how to write a solution for this?

[lyric narwhal]

ah yea sorry

[tropic oxide]

e^(sin(x)log(x)) will alternate between x and x^-1

[lyric narwhal]

what

,w graph x^(sin(x)) for x from -20 to 20

[fair mortar]

because $\sin x \in [-1,1]$?

[wraith dagger]

bettim

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Requested by kheerii#8421

[tropic oxide]

uh yeah sure

i dont like that wording very much

but you get the idea somewhat

[fair mortar]

why isnt there any graph left of y axis?

i think - infty will occur of x values less than 0

[tropic oxide]

log(x) is undefined for negative x

[fair mortar]

oh right forgot

but the function doesnt have log?

[tropic oxide]

x^sin(x) = e^(sin(x) log(x))

equivalently negative numbers cannot be raised to noninteger exponents

so at best you could maybe have your function be defined at x = -npi/2 for natural n but that is cherrypicking

[fair mortar]

but taking random value of x in 3rd or 4th quad gives an answer in negative

lets say x= 210 (deg)

[tropic oxide]

so x = 7pi/6?

[fair mortar]

nv

nvm

[fair mortar]

it gives positive extremes

so

$x \to n\pi$ is \infty$?

[wraith dagger]

bettim
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[tropic oxide]

you are going weird places.

[fair mortar]

$\lim_{x\to \pi} x^{\sin x}$

[wraith dagger]

bettim

[fair mortar]

yes idk lol this suks

[lyric narwhal]

you can just substitute here

since sin(pi) = 0

just stick to what Ann said

[fair mortar]

what if x = pi -h

[lyric narwhal]

write it as e^(sin(x) log(x))

[fair mortar]

right

[lyric narwhal]

then you have to minimise sin(x) log(x)

[fair mortar]

,w sin 0.999

[wraith dagger]

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Requested by bettim#9852

[lyric narwhal]

now sin(x) is a bounded function and log(x) can go down to -infinity

so you're left with e^-inf (bad notation but stick w me)

=0

[fair mortar]

so

$\frac{1}{e^{\infty}}$

which is 0?

[lyric narwhal]

correct

but that notation is not correct

it would be the limit

[wraith dagger]

bettim

[fair mortar]

right so

$\lim_{x\to \infty} \frac{1}{e^x}$?

[wraith dagger]

bettim

[lyric narwhal]

$x^{\sin x} = e^{(\sin(x)\log(x))}$

[wraith dagger]

kheerii

[lyric narwhal]

so you have to minimise the exponent

$\lim_{x\to 0+h} = -\infty$

where h is sufficiently close to zero

[wraith dagger]

kheerii

[fair mortar]

why is ther a limit?

[lyric narwhal]

that's true

you can just use h to denote that

basically x can't be zero

because sin(0) = 0

so you need a value of x extremely close to 0

I don't know how to write that

but you get what I mean

so you'd have $\lim_{x\to \infty} e^{(-x)} = 0$

[fair mortar]

and so 0^0 is not correct

[wraith dagger]

kheerii

[fair mortar]

what do you call it

indefinite form?

[lyric narwhal]

well

0^0 is usually = 1

[fair mortar]

is it tho?

[lyric narwhal]

yes

it is

[fair mortar]

okay

so how do i denote x

for which the function is zero?

x=0

thats it?

[lyric narwhal]

no

it would be a number extremely close to 0

[fair mortar]

so $\pm h$?

[wraith dagger]

bettim

[lyric narwhal]

,w x^(sin(x)) at x=0.00000000001

[wraith dagger]

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Requested by kheerii#8421

[lyric narwhal]

wait what

@tropic oxide can you help me out here

[fair mortar]

,w sin .000001

[wraith dagger]

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Requested by bettim#9852

[lyric narwhal]

yes, sin(x) = x for sufficiently small x

[fair mortar]

,w (.00001)^(0.00001)

[wraith dagger]

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Requested by bettim#9852

[fair mortar]

bro

i graphed it in desmos

[lyric narwhal]

,w graph x^sin(x)

[wraith dagger]

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Requested by kheerii#8421

[fair mortar]

the bigger the x the closer it gets to x axis

[lyric narwhal]

it does go down to zero

[fair mortar]

not exactly 0

graph it in desmos

https://www.desmos.com/calculator

[lyric narwhal]

yes I said it goes down to zero

I did not say it equals zero

[fair mortar]

the upper limit is infty

[lyric narwhal]

but I dont see where my logic is wrong

[fair mortar]

then what do i write the minimum value of the function?

[crystal raptor]

Your logic is scattered its hard to see what you're claiming

[lyric narwhal]

okay

so basically

we write x^sin(x) as e^(sin(x) log(x))

which reduces the problem down to minimising sin(x) log(x)

since sin(x) is a bounded function and log(x) goes down to infinity as x goes to 0

that means the minimum value of sin(x) log(x) is when x gets sufficiently close to zero, but not at zero

am I wrong in saying that?

[crystal raptor]

Why do you think the minimum should be at zero?

[lyric narwhal]

not at zero

because sin(0) = 0

this isn't even my question lmfao

[crystal raptor]

But there are points where this sin(x)log(x) is negative

[fair mortar]

the minimum value is zero

[lyric narwhal]

yea

[crystal raptor]

Of sin(x)log(x)?

It has no minimum

[lyric narwhal]

when x gets sufficiently close to 0

[fair mortar]

x^sinx

[lyric narwhal]

it would tend to -infinity no?

sin(x) log(x)

[crystal raptor]

x^sin(x) also has no minimum

[fair mortar]

what does that mean?

[lyric narwhal]

yes it does

it can't ever be negative

[fair mortar]

it will have negative values?

it is positive only

[crystal raptor]

This doesn't mean it must have a minmum

[fair mortar]

this is what i got

[crystal raptor]

1/x² is never negative but it has no minimum

[lyric narwhal]

it wont have a minimal point

[crystal raptor]

Those valleys get closer and closer to zero but never hit zero

[fair mortar]

so i conclude that larger the value of x, closer it is to zero?

[lyric narwhal]

that isn't true

[fair mortar]

yes thats what i observed

[crystal raptor]

Yes so there is no minimum

[fair mortar]

why is that wrong?

[crystal raptor]

The larger the x value of a valley, the closer the value of the function is to zero

[lyric narwhal]

the valleys lie at (2n+1)pi

I believe

but anyway, what @crystal raptor said makes way more sense than what I said

just ignore everything I said

[fair mortar]

ah 😦

[fair mortar]

thanks

,w graph (sinx)^sinx

[wraith dagger]

Results provided by WolframAlpha

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

Requested by bettim#9852

[fair mortar]

lol this funny

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[lyric narwhal]

W

[fair mortar]

lots of W

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[lament pasture]

I have this as my answer I'd just like if someone can tell me if its reasonable

[crimson delta]

well the positive integer bit is not necessary

its enough that n is an integer

where did you use that p is prime

you didnt explicitly write it anywhere

[lament pasture]

I see

maybe I could use that to prove that if p|b^2 and p is prime then p| b

Otherwise how do you think I should include it

[crimson delta]

that is exactly the place where you need to use it

cause if p is not prime then p|b^2 does not necessarily imply p|b

[lament pasture]

Ok gotcha

otherwise is the proof good?

[crimson delta]

its fine

[lament pasture]

Perfect! Thanks

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[rancid prairie]

I need to give two examples for roots and two examples for powers using De Moivre's theorem

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[rancid prairie]

no

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[lime wagon]

what was the first step here?

[livid hound]

factorisation

[lime wagon]

shouldnt we get rid of the sqrt first

[livid hound]

not neceesary

if you can recognise that y is the square of sqrt(y),
the factorisation process is pretty much the same as the polynomials you're used to

[lime wagon]

i see that

what do you do after though

I assume you dont ude the quadratic formula

[livid hound]

cancel common factors, specficially the factor that would be responsible for the 0/0 indeterminate form

then plug in the specified value

what do you do after though
after what? after factorisation?

[lime wagon]

no I dont see how (sqrt(y))^2-4sqrt(y)+3=(sqrt(y)-1)(sqrt(y)-3)

[livid hound]

getting the factorisation of
$$y - 4\sqrt{y} +3$$
is not that different from factorising
$$(\this)^2 - 4(\this) + 3$$
$$x^2 - 4x + 3$$
use whatever factorisation techniques you know

[wraith dagger]

ℝamonov

[lime wagon]

ait lemme try

[livid hound]

(just like how x^2 is the square of x, y is the square of sqrt(y))

[lime wagon]

yeah but say i use the quadratic formula. Which is my b if I have 4*sqrt(y)

[lime wagon]

this is clear

[livid hound]

viewing that as a quadratic in sqrt(y)

the b would be the coefficent of sqrt(y)

[lime wagon]

so b=4

[livid hound]

no

[lime wagon]

damn

[livid hound]

you're ignoring the - sign

[lime wagon]

sure -4

and variable is sqrt(y)?

[livid hound]

you could view it like that

[lime wagon]

is there an easier way to factor this othar than the qf?

[livid hound]

sums and products

[lime wagon]

quicker I should sau

say

[livid hound]

the common factorisation techniques

since the quadratic is monic,
identify the pair of values that multiply to 3
and sum to -4

[lime wagon]

I know this technique of course, but the sqrt makes my life difficult

[livid hound]

makes no difference

(just like how x^2 is the square of x, y is the square of sqrt(y))

$$(\sqrt{y})^2 - 4\sqrt{y} +3$$
$$(\this)^2 - 4(\this) + 3$$
$$x^2 - 4x + 3$$

[wraith dagger]

ℝamonov

[livid hound]

the exact same technique applies

just instead of x,
you have (this) or sqrt(y)

[lime wagon]

so that would be -1 and -3

[livid hound]

yes, that's your pair of values

[lime wagon]

okay thanks

[livid hound]

and if the quadratic was
x^2 - 4x + 3
would you be able to use the values you identified to factorise that?

[lime wagon]

then it would be (x-1)(x-3)

[livid hound]

for the other two, as mentioned

just instead of x,
you have (this) or sqrt(y)
similarly their factorisations would be
(sqrt(y) -1)(sqrt(y) -3)
(this - 1)(this - 3)

[lime wagon]

yeah clear thanks!

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[ember mesa]

X_n = 1/2(x_(n-1))

[ember mesa]

how would I solve this recursive sequence

X_n = 1/2(x_(n-1))

[slow thicket]

Be careful with the fractions

Which one is it

[ember mesa]

the photo

[slow thicket]

Well yes but there are two interpretations

[ember mesa]

0.5(x_(n-1))

[slow thicket]

Okay

This is just a geometric series

[ember mesa]

ah thanks

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[viral stump]

1)both are arithmetic sequences so find the general formula and make them equal each other (0.25x+1.75=0.5x+0)
2)rearrange the equation and collect like terms (1.75=0.25x)
3)x=7

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[shadow agate]

idk where to begin

[violet flume]

https://www2.nau.edu/lrm22/lessons/mark_recapture/mark_recapture.html

theres a formula here

does that look familiar?

[shadow agate]

not in the slightest

not for the brits

[violet flume]

well what formula are you to use

[shadow agate]

idk never did this

im doing probabi;ity rn

<@&286206848099549185>

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[shadow agate]

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[muted bear]

What is the other series

[eternal knot]

I believe this is solved using the Ratio Test; however, I'm having trouble with the algebra to get rid of the factorial

[eternal knot]

They're solved separately I believe

[muted bear]

Oh

You can use the factorial that factorial grows a lot faster

[eternal knot]

so the limit as n approaches infinity goes to zero?

because the denominator is always larger?

[sage forge]

You can devide this by n! And argue pretty quickly that lim of ratio goes to 0

[sage forge]

Also what you could have done here is noting that 1/(n+n!) < 1/(n!) and then use the ratio test

[eternal knot]

So use the comparison test and solve (1/(n!)) using the ratio test?

[sage forge]

Yes

Majorante

[eternal knot]

Cool I'll do the comparison thing but how do you divide by n!? do they cancel out?

I'm always slow on the algebra stuff

[sage forge]

That is how you could continue from your last line

[eternal knot]

so like this?

[sage forge]

n/(n!) = 1/((n-1)!)

No ☹️

You need to devide everything in a sum

Just as you'd do with normal fractions

[eternal knot]

sorry i'm still lost

[eternal knot]

I get this though

I just don't know how to apply that to the problem

[sage forge]

Sorry, that I need to ask. But do you know how to reduce fractions?

[eternal knot]

I probably need to jog my memory on that

by that you mean stuff like 3/6 = 1/2?

[sage forge]

Yes

[sage forge]

And this is also a fraction, which can be reduced by n!

[sage forge]

You know devide everything in numerator and denominator by n! ?

[eternal knot]

ok so the numerator would be (n/n!) + (1/n!) + n+1

[sage forge]

Yes 👍

[eternal knot]

and the denom would be (n/n!) + n + 1?

ok I get it

nice!

thanks

[sage forge]

Wait

denom would be ((n+1)/n!) + n + 1?

Like that 🙂

[eternal knot]

did I fix it?

wait no fuck

I edited the numerator by accident

[sage forge]

Your numerator was correct. In the denominator you made a tiny mistake, which doesn't really change the result though

[eternal knot]

denom would be (n/n!) + (1/n!) + (n+1) ?

[sage forge]

Yeah, you can write it like that, too

[eternal knot]

and then simplify like this

[sage forge]

Note that n/(n!) = 1/(n-1)! and that goes to 0 as n goes to infinity

[eternal knot]

gotcha 👍

[sage forge]

Yes 🙂

[eternal knot]

thanks brotha

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[sage forge]

You're welcome

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[frozen forge]

Hey guys, my exercise is to sketch the polar curve of the function r = pi θ - θ^2, and I am supposed to identify the limits of all values of θ such that r = r(θ) > 0

[frozen forge]

I have tried googling, can’t find anything similar to this equation

[cedar kiln]

@frozen forge Has your question been resolved?

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@frozen forge Has your question been resolved?

[static fern]

im guessing that for the graphing part, we get a spiral-looking thing, with some kind of strange behavior near the origin

desmos gives this:

[frozen forge]

figured it out, thank you.

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[mighty mortar]

Why the chain rule is applied while differentiating t^2 here?

[mighty mortar]

t^2 should be just 2t

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[soft sigil]

Help

[soft sigil]

A straight highway leads to the foot of a tower. A man standing at the top of the tower observes a car at an angle of depression of 30°, which is approaching the foot of the tower with a uniform speed. Six seconds later, the angle of depression of the car is found to be 60°. Find the time taken by the car to reach the foot of the tower from this

point.

<@&286206848099549185>

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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.

[soft sigil]

Ok bot

[crimson sedge]

i.e. $t_\text{at foot}=3,\mathrm{s}$ after he was at depression angle 60°.

[wraith dagger]

Landau08

[soft sigil]

Mine was also write

3s

Problem is solution is bit confusing

I marked solution green

.close

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[stray pasture]

i'm a bit confused on
(b)(ii)
Specifically, how was -1.6 obtained

[long arrow]

,calc 80 * (-0.02)

[wraith dagger]

Result:

-1.6

[long arrow]

(by the chain rule ⛓️ )

[stray pasture]

please explain the chain rule

nvm

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[fading viper]

Hello how would I do 9b?

[digital cliff]

is 12cm the circumference?

[fading viper]

I'm not too sure tbh

[digital cliff]

hmm, anyway the formula for the area of the curved section of a cylinder is circumference * height in any case

[fading viper]

Ah that makes sense

Yes 12 is circumference then

Thanks

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[solid mesa]

sup, i have this question (answers are included yes) why would you do (2^-2)^2-1/2x? i would never think of that. is there any specific reason for it or do you really gotta know it?

[solid mesa]

i did this:

oh yeah, i forgot to mention the actual question; i have to rewrite the given formula to a • b^x

[cosmic steppe]

Using exponent properties, $(2^{-2})^{2 - \frac12x} = 2^{-2\parens{2-\frac12x}}$

[wraith dagger]

Umbraleviathan

[solid mesa]

huh

[crimson sedge]

Hey geis

so basically

[velvet mortar]

You multiplied instead of divide

[crimson sedge]

You don't have to do it

It's just simpler

Because exponents can be multiplied

for example

2^2^2 = 2^2 x 2

so by turning a fraction into a singular number to the power of the negative exponent

we can then multiply that negative exponent but other exponents

does that make sense

[solid mesa]

no but thats because i don’t know all the math translations in my language, I’ll translate it in a bit and let you know

[crimson sedge]

what is ur language

[solid mesa]

dutch

You don’t have to do it, though

[crimson sedge]

do you speak german

or french

nah I speak french and a little german

[solid mesa]

i would say I’m more fluent in English than in English

I kind of understand it i just have to put some stuff together

Ok let me ask a stupid question

What’s the difference between exponent and to the power of

[cosmic steppe]

You know that property where $(a^b)^c = a^{bc}$, right

[wraith dagger]

Umbraleviathan

[cosmic steppe]

They used that

[crimson sedge]

same thing

exponent is just the power

exponent = power

[solid mesa]

yeah but is that required to get the right anwser?

[cosmic steppe]

Yeah

[solid mesa]

ah yeah figured

[cosmic steppe]

It's how I would do it

[crimson sedge]

It's not

but it's a main in the ass otherwise

[solid mesa]

Is there any way to know to know when to use that or do you need to get experience to get that

[crimson sedge]

yes there is a way to know

read the question of what you're trying to solve

[solid mesa]

hmmm i see

but i do have the same formula thats asked

it’s just not the correct answer

[solid mesa]

because this was my answer^

[crimson sedge]

Okay look here's the first thing to understand

you don't have to flip the equation at that point

You can flip later, flipping then is just foresight of something you're eventually going to do

but if you don't understand why

you don't have to flip

[solid mesa]

You mean like flipping Y and whats after = or

[crimson sedge]

flipping the fraction

1/ 2^2 to 2^-2

[solid mesa]

ohh yeah

my bad that was a translation problem

so you have to flip the fraction

[crimson sedge]

you don't

[solid mesa]

i feel so stupid right now

[crimson sedge]

ok do you understand this

[solid mesa]

yes

[crimson sedge]

ok and do you understand that

[solid mesa]

oh my god

Im so stupid

[crimson sedge]

god finally

Nah just kidding haha

[solid mesa]

i forgot the minus

nah you got the right to say that dude

lmao this is so funny looking back

thanks for the help bro

It was such an easy question i just wrote it down incorrectly

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[nova snow]

What would the domain and range of a circle be?

[quartz frost]

depends on how you define it

y in terms of x
or
y in terms of angle

[nova snow]

Uh

Like

h,k

In terms of that if that makes sense

[quartz frost]

what are h and k?

[nova snow]

like the equation of a circle

[quartz frost]

can you give an example?

[nova snow]

(x-h)^2 + (y-k)^2 = r^2

[quartz frost]

ah ok

the circle will be moved by h horizontally and by k vertically

let's consider h and k to be 0 first

in this case, the domain would be [-r, r]

since that are all the possible x values

the domain would also be [-r, r]

is that clear? or is that weird

like, why this is the case

[nova snow]

[-r,r] refer to the positive and negative radius?

[quartz frost]

yes, the interval starting at the negative radius, going to the positive radius

[nova snow]

Oh okay

I thought the domain would be like [h,k] or something

[quartz frost]

yeah, we set h and k to 0
to check for the most simple case

here we can see domain(red) and range(blue)

now if we consider h and k to not be 0, the circle moves

[nova snow]

Does the range include h,k?

[quartz frost]

it will

let's look at the case where k=0 and h is not 0

h is the movement in x direction

the domain is still red and range is blue

so what we are really doing is:
by moving the circle by h, we are also moving the domain by h

previously we had [-r, r] as the domain
moving this by h, we get [-r+h, r+h]

which is the same we can see in the picture

[nova snow]

ohhh alright

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[obtuse hinge]

I've tried getting the net force on the system and finding acceleration. Then applying that to get force from m2 to m3 but it doesnt seem to work 😦

[obtuse hinge]

$F{net}=656-0.79.8(31+12+22)=210.1$

$\implies a{net}=210.1/(31+12+22)=3.2323$

$F_{32}=123.2323-129.8*0.7=-43.5323N$

[wraith dagger]

ミョーみ

[obtuse hinge]

what did i do wrong

[cedar kiln]

@obtuse hinge Has your question been resolved?

[obtuse hinge]

$F{net}=656-0.79.8(31+12+22)=210.1$

$\implies a{net}=210.1/(31+12+22)=3.2323$

$F_{32}=223.2323+229.8*0.7=222.0308N$

is this right?

[wraith dagger]

ミョーみ

[cedar kiln]

@obtuse hinge Has your question been resolved?

[cedar kiln]

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[lament cobalt]

hello

[lament cobalt]

how can i do the one on the bottom

for #2

[cedar kiln]

@lament cobalt Has your question been resolved?

[cedar kiln]

@lament cobalt Has your question been resolved?

[cedar kiln]

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[crimson sedge]

<@&286206848099549185>

yeah

so i dont

what?

understand the question

oh lemme explain

ok

there is a rectangular painting

which is fit into a rectangular frame ok

ye

so now, the total are of the rectangular painting + the frame is 1200cm²

ye

It's simple

and the painting is 600cm^2

yeah

and u subtract

now u need to find the width of the frame

so i get 600cm^2 but then the frame

width wonr fit

bc the factors

of 600

wait

which r the closest are 40 and 15

ok

(x+30)(20+x)=1200

no

(30+2x)(20+2x) = 1200

Why??

did u forget

there are 2 sides

so 2x

i mean 2 widths and 2 lengths

wait so after i expland it

Does it matter since it's rectangle

it does

i bring the 1200 to the LHS and use null factor law

Yeah yeah

I get it now lol

yeah

So width is 5cm

bruh

no ans

ye i get it now

nah i alr got the answer

b4

!nools

!nosols

[cedar kiln]

As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.

[crimson sedge]

ty for ur help

Oh I see I'm new to the server lol

me too

i learnt this from a guy just now

Haha cool

[crimson sedge]

ye

ping me always ill be there to u help u out

alr ty

.close

[cedar kiln]

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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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[still hedge]

my answer is -0.69

but I am not sure

[violet flume]

is it right

[crimson sedge]

do u need in decimal form?

or as it is as root

[still hedge]

I need it rounded to the nearest hundredth

[crimson sedge]

oh

[still hedge]

if I get this wrong I gotta redo the entire thing 😦

so its a clutch kinda thing

[crimson sedge]

lol

let me check wait

[still hedge]

yeah its cringe if u get 4 problems wrong then u gotta redo all 15 problems

[crimson sedge]

damn!

[still hedge]

and if I am on 15/15 and get the 4th one wrong its cringe

and I am on 15/15 with no lifes left rn

[crimson sedge]

hmm

can u tell me how did u get -0.69

[still hedge]

I plug in the average rate of change with the formula right?

[crimson sedge]

uhh

what formula

[still hedge]

x2-x1/x2-x1?

right?

am I tripping

[crimson sedge]

im sorry

this is out of my portion

[cosmic steppe]

Yeah you would

That's the average slope formula

[crimson sedge]

and tbh

i dont know

[still hedge]

or do I plug in -9 and -1

[cosmic steppe]

Average rate is $\frac{f(x_2) - f(x_1)}{x_2 - x_1}$, which you used. So you should be fine assuming you computed it correctly

[wraith dagger]

Umbraleviathan

[cosmic steppe]

But lemme check myself

[still hedge]

please I am shitting myself thinking about if I get it wrong

[cosmic steppe]

Show your work

Like actual work

[radiant topaz]

how did you configured to get red with black background

[cosmic steppe]

Because you're close but it's not quite what I got

[still hedge]

(-1)-(-9)/(-1)-(-9)

[cosmic steppe]

Preamble

[crimson sedge]

no

[cosmic steppe]

Oh no no no you need to use the formula correctly

[cosmic steppe]

Use what I gave you

[crimson sedge]

f(x) function

put the values of x in f(x) = root -8 + 6

[radiant topaz]

mind explaining in #bots

[cosmic steppe]

Ngl I needed help with it. Probably ask someone else because I forgot

Lemme see if I can fetch it

[still hedge]

oh yeah when I plug in the stuff I get sqrt of 14 and sqrt of 70 for my answers

[crimson sedge]

i dont think so

since -8 (x1 ) + 6

[still hedge]

so its sqrt of 14-sqrt of 70/sqrt of 14-sqrt of 70

[crimson sedge]

is equal to -8 (-9) + 6

ahh man

i think its 2 / - 8

[cosmic steppe]

You're still not plugging it in correctly

[crimson sedge]

which is -0.25

[still hedge]

what am I doing wrong

[cosmic steppe]

Nor is Boruto

What is f(-9)

And what is f(-1)

[still hedge]

x1 and x2

[cosmic steppe]

I want the numerical value.

Of f(-9) and f(-1)

[crimson sedge]

lemme do it rq

[cosmic steppe]

Keep them under the radical

[cosmic steppe]

i got it.

[crimson sedge]

its root 72 for x1

[still hedge]

what do you mean keep it under the radical?

[crimson sedge]

and root 14 for x2

when sub these

[cosmic steppe]

Boruto you aren't even doing it correctly either

Bro you're confusing him more

[crimson sedge]

wdym

nvm ill shut my mouth

[still hedge]

so I plug in x1 and x2 into the formula right

when I plug in -9 I get sqrt of 78

[cosmic steppe]

Recall your average slope formula. $\frac{y_2 - y_1}{x_2 - x_1}$. The $y$ refers to the OUTPUT and $x$ refers to inputs. The subscripts just tell you which respective output and input

[crimson sedge]

this guy didnt understand still

[wraith dagger]

Umbraleviathan

[cosmic steppe]

You're given you want the secant between x = -9 and x = -1

So x1 = -9 and x2 = -1

[crimson sedge]

put the x values in f(x) = root -8x + 6

right?

[cosmic steppe]

If y's are the respective output, then:

y1 = f(x1) = f(-9)
y2 = f(x2) = f(-1)

[crimson sedge]

yeah

[still hedge]

so when I plug in the x values I get sqrt of 78 and sqrt of 14

[crimson sedge]

yeah

[still hedge]

for -9 and -1

[crimson sedge]

yeah