help-26

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[buoyant schooner]

any ideas how?

[buoyant schooner]

lim n-> inf*

[fallow vigil]

tried anything?

[buoyant schooner]

no, I actually don't know even how to start

it makes no sense for me

[fallow vigil]

ok so try taking 7^n out

see what u can do with that

and another hint y we're doing this-> 2/7<1

[buoyant schooner]

wait, so now I have something like this, right?

[fallow vigil]

yupp

[buoyant schooner]

so it means that it's 7*sqrt(1)

[fallow vigil]

yes

[buoyant schooner]

okay, so I get it but

why not 2^n?

oohhh

okay

XD

get it

[fallow vigil]

ok so now do u know the log approach to limits?

[buoyant schooner]

yea, thanks mate

luv u

[fallow vigil]

like i'm not sure of the exact name

oh nice so u got it?

[buoyant schooner]

yup

[fallow vigil]

gg

[buoyant schooner]

thank you very much

.close

[topaz sinew]

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[fallow vigil]

np :))

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[serene meadow]

It seems wrong

But it seems right too

a to the power b to the c is equal to a to the power bc ?

Or am I making stuff up on my own

[unique seal]

$(a^b)^c = a^{bc}\
a^{(b^c)} \neq a^{bc}$

[thorny flame]

Dogecode

[serene meadow]

Ahhh

Me dumb

I got confused

Sorry

[unique seal]

parentheses are important

[unique seal]

np

[serene meadow]

Thanks for helping

[unique seal]

np

[serene meadow]

.close

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[neon iron]

I need to help expressing my idea symbolically

[neon iron]

Let there be a set called S where it has elements of 1 to n

Then let there be subsets of S denoted as

T¹ , T²,T³ all the way up to T(n)

Such that they each aren't equal

[drifting swift]

did you mean for those to be subscripts and not superscripts?

[neon iron]

Yeah subscripts but my phone doesn't have it

[drifting swift]

ok

so you have S = 1:n and a family of n distinct subsets of S that you call T_1, T_2, ..., T_n

continue

[neon iron]

Such thr each distinct subset is divided into varying sizes

For example

If u had Set s to be 1,2,3,4

Then the distinct subsets would have a cardinality each of 3

But must be distinct

So u get

1,2,3

1,2,4

1,3 ,4

2,3,4

And u take the first row

And u split into into new sizes of subsets

So Size 0 would be empty set

Size 1 would be

{1} ,{2} ,{3}

Size 2 would be

{1,2}, {1,3}, {2,3}

Size 3 would be

{1,2,3}

And for each size you find the product in each individual subset and add them

So for Size 0

It's element multiple would be 1

Size 1

Would be

2+3+6=11

Size 3 would be 6

And u do the same for the rest of rows

How do I express this as notation

I made an attempt here

But I'm not sure it makes sense

<@&286206848099549185>

[drifting swift]

well this notation does look valid

you look at the subsets of 1:n that have k elements and do not contain a particular element s, and you take the sum of each subset's product

your notation does make sense.

[neon iron]

But icl I don't understand it

Ah tht makes sense thx

So "/{s}" means it doesn't contain a particular element set

?

[drifting swift]

no, you're overthinking it

\ is the symbol for set difference

A \ B is the set of all things that are in A but not in B

[neon iron]

Ah

But then how would I show that u split that subset into different sizes of subsets

[drifting swift]

??

now you've stopped making sense.

[neon iron]

Like you get a subset 1,2,3

And you split that further into sizes

Like size 0 is empty set

Size 1 is {1} ,{2} ,{3}

[drifting swift]

well presumably the size of the subsets you're summing over (T in your notation) is what you're denoting with k

[neon iron]

So how do I show k varies

[drifting swift]

what do you want to do with the sums for various k

just consider them separately?

or what

[topaz sinew]

@neon iron Has your question been resolved?

[neon iron]

I wanted to split the set further into sets with varying cardinality from 0 to n

[neon iron]

It's all right I was overthinking it

I understand now thx

Lll

Lol

[topaz sinew]

@neon iron Has your question been resolved?

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[neon iron]

hi could anyone help me on how to answer the 'regions increasing/decrseasing, regions concave up or down and sketch of the graph' thanks in advance

[neon iron]

this is my work so far:

[sturdy oracle]

Nice work

[narrow torrent]

caluclus

[neon iron]

thank you, im not sure if it is right tho?

[sturdy oracle]

I can't open it on mobile

Well let's start with the first

[neon iron]

can you open them now?

[sturdy oracle]

Yeah

[neon iron]

ya so finished the first three steps but idk how to do the last three...

regions increasing/decrseasing, regions concave up or down and sketch of the graph

[neon iron]

and im not sure if i even did the first steps right😂

[sturdy oracle]

Vertical asymptote is x = 0

Not VA = infinity

For regions, first find the derivative of $\frac{e^{x}}{x^{2}}$

[thorny flame]

Umbraleviathan

[neon iron]

so is the computation wrong?

[sturdy oracle]

No, your answers's incorrect

Your computation is right

[neon iron]

ohhh okok

[sturdy oracle]

You just gave an incorrect answer lol

Well

You stated the answer incorrectly

[neon iron]

so should i just change the infinity signs to zero

[sturdy oracle]

VA is x = 0

[neon iron]

so x approaches 0 is equal to 0?

[sturdy oracle]

no, it's infinity

Which means that there's a vertical asymptote at x = 0

[neon iron]

ohhh okay

[sturdy oracle]

But do this

This will tell you where the first equation increases/decreases

[neon iron]

i got for the first derivative is = e^x(x-2) / x^3

[sturdy oracle]

check your denominator

Wait actually

Sorry yeah you're correct

I just read it incorrectly

[neon iron]

but how does the derivative tell you where increases/decreases? ahha im dumb loolll

[sturdy oracle]

So when f'(x) > 0, f(x) is increasing

When f'(x) < 0, f(x) is decreasing

[neon iron]

ohhh

so do i make f'(x) =0 and then solve

[sturdy oracle]

So find critical points and set up a number line

Yeah

Find where f'(x) = 0

[neon iron]

ya i got x=2

[sturdy oracle]

Yup

You gotta find critical points now

It is where f'(x) = 0 and undefined

Where is f'(x) undefined

[neon iron]

how do i do that😭

[sturdy oracle]

_ _

[neon iron]

wdym by where its undefined

[sturdy oracle]

Like

When f'(x) = a/0

a is any thing

[neon iron]

wait im confused so do i solve for a?

[sturdy oracle]

No

You know what I mean by undefined right

It's where f'(x) would compute to an impossible number, such as a/0 where a is any number

The important thing is it is when the denominator = 0

[neon iron]

ohh okay

so wouldnt the ciritcal point just be x=2

[sturdy oracle]

No

Because f'(x) is undefined at x = 0

[neon iron]

im confused on how to actually find the critical points; so do i take the derivative and set it to zero, or the start fucntion and make it equal to zero

and then what would i do after that

pls help😭

[sturdy oracle]

okay so

you have $\frac{e^{x}\left(x-2\right)}{x^{3}}$

[thorny flame]

Umbraleviathan

[sturdy oracle]

correct

Critical Points are were f'(x) = 0 or undefined

you've found where f'(x) = 0

from looking at the function, where would $\frac{e^{x}\left(x-2\right)}{x^{3}}$ be undefined?

[thorny flame]

Umbraleviathan

[neon iron]

so when i made f'(x)=0 i made e^x=0 and got that it was undefined or no solution, and x-2=0 was x=2

[sturdy oracle]

okay but

a function is undefined when it computes a complex number or division by 0

that means that the denominator = 0

looking at f'(x), the denominator is...?

[neon iron]

x^3

[sturdy oracle]

yeah

so set that equal to 0

what is x

[neon iron]

so that would be x=0

[sturdy oracle]

yeah

so f'(x) = 0 at x = 2
f'(x) is undefined when x = 0

0 and 2 are your critical points

[neon iron]

ohhh okok tysm that makes sm sense now

[sturdy oracle]

have you been taught how to do sign analysis

[neon iron]

no whats that

[sturdy oracle]

its basically a number line

so f' <-------------[0]----------------------[2]----------------->

and youre going to check the sign of a computed point

well

so

what a value between 0 and 2

[neon iron]

1?

[sturdy oracle]

yeah

so find f'(1)

[neon iron]

how would i do that

[sturdy oracle]

literally plug in 1 for x

[neon iron]

i think i did smth wrong i got -e

[sturdy oracle]

yeah thats right

is that number positive or negative

[neon iron]

negative

[sturdy oracle]

good

so the region from [0, 2] for f'(x) is negative

<-------------[0]----------(negative)-----[2]----------------->

[neon iron]

ohhhhhhh

[sturdy oracle]

now check a number between -infinity and 0

[neon iron]

any number?

[sturdy oracle]

any

could be -1

-e

-2929409142359023529

any

[neon iron]

i got 3/e

[sturdy oracle]

for which number

[neon iron]

-1

[sturdy oracle]

yeah

3/e is a positive number

so f' <---(positive)--[0]----------(negative)-----[2]----------------->

try the last section on your own

[neon iron]

so between 2 and infinity?

i plugged in f'(4) and got e^4 / 32

[sturdy oracle]

yeah

[neon iron]

then i said the region from (2, positive infinty) for f'(x) is positive since e^4 / 32 is a positive number

[sturdy oracle]

mmhm

so now

f' <---(positive)--[0]----------(negative)-----[2]-------(positive---->

with that info

where is f(x) increasing

on which domains

[neon iron]

increasing on (−∞,0),(2,∞) ?

[sturdy oracle]

closed brackets

but yes

njow

for concavity

you do the same thing but with f"(x)

if f"(x)< 0, the region is concave down
f"(x) > 0, the region is concave up

[neon iron]

ohh okok

[neon iron]

can i say its also decreasing on (0,2)

[sturdy oracle]

yes

[neon iron]

for f"(x) i got e^x(x^2-4x+6) / x^4; and when i made it equal to zero i got no solution...

[sturdy oracle]

mmhm

[neon iron]

oh wait am i supposed to substitute the value of x

[sturdy oracle]

where is undefined

[neon iron]

x^4 right

[sturdy oracle]

well

yeah when x^4 = 0

[neon iron]

so x=0

[sturdy oracle]

yeah

do you sign analysis again

[neon iron]

but what points would i do it with, zero and infinty?

[sturdy oracle]

just zero

[neon iron]

so idk if this is right but i got that it would be concave up on (-infinity,0) since f"(x) was positive and concave up again on (0, infinity ) because f"(x) was positive

[sturdy oracle]

yes

so

those are your answrs

increasing from (inf, 0) U [2, infinity)
decreasing from(0, 2]

Concave Up x =/= 0

[neon iron]

okok that makes sense

thank you SO much😭

[sturdy oracle]

np

[sturdy oracle]

also mb

[neon iron]

how would the graph look like?

also for the other problems; to find the HA do i just make the limit approaches - infity? and for VA i make it approaches 0?

[topaz sinew]

@neon iron Has your question been resolved?

[topaz sinew]

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[tawdry chasm]

Anyone know what's with this Excel glitch?

Just ignore anything but the formula builder, was just trying out the example

I move the parenthesis all over the place but it doesn't really seem to change much

[empty sail]

You have 845 typed in and the problem says 854

[tawdry chasm]

Yeah but that's from a different problem

What's in the formula bar is just the example on the left side

I always do the SQRT separately because I never never remember the order anyways

[empty sail]

You also need to multiply F2 by 1.96

[tawdry chasm]

Oh weird

[empty sail]

,w 1.96 * .007457

[thorny flame]

Results provided by WolframAlpha

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

Requested by dldh06#2659

[tawdry chasm]

Don't remember doing that before

This seems like such an inefficient way of teaching math, these online courses

[empty sail]

It's the formula, you just didn't apply all the steps into excel

[tawdry chasm]

I swear I've done questions similar to this, but every time the steps seem different

Replaced the steps with the regular questions

Oh missed one extra bit, still wrong

I swear I've done something like this one before

The steps just keep changing every time

.close

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[sharp sky]

I am stuck on part c)

[topaz sinew]

@sharp sky Has your question been resolved?

[neon iron]

@sturdy oracle

[topaz sinew]

@sharp sky Has your question been resolved?

[topaz sinew]

@sharp sky Has your question been resolved?

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[feral carbon]

If < 1 is 2x + 8 degrees and < 8 is x - 5 degrees, what is the value of x?

how do I get X?

[patent flax]

what is the relation between 1 and 4

and the relation between 4 and 8

[feral carbon]

they are congruent?

uhm.. should I ask someone else?

.close

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[gray basin]

I don’t understand, the postcode starts with 3, so how would I find the different postcodes available?

[drifting swift]

@gray basin is the format for postcodes known?

[gray basin]

Nope

[drifting swift]

then you can't.

[gray basin]

Oh..

[drifting swift]

if you don't know what postal codes are made of, then how can you hope to count them (or a subset of them)

different countries have different postal code formats

[gray basin]

Yh

[drifting swift]

canada for example has letter-digit-letter-digit-letter-digit
in russia it's 6 digits

so what is it where you're from?

[gray basin]

Australia has 4 digits

[drifting swift]

okay so then why did you say the format was unknown?

[gray basin]

Because it doesn’t say anywhere in the book

[drifting swift]

Victoria is the name of a state in Australia, is it not?

[gray basin]

Yes

[drifting swift]

given that you're from Australia, this reads to me as knowledge you're expected to have w/o it needing to be spelled out.

[gray basin]

Ye

[drifting swift]

so a postal code in australia consists of four digits

in our case the first digit is fixed

[gray basin]

Yes

[drifting swift]

how many ways are there to fill the rest?

[gray basin]

3 different ways?

[drifting swift]

why three?

[gray basin]

Actually no

Not 3

Mm..

[drifting swift]

your postal code looks like this: 3 _ _ _
in each blank, you can write one of 10 digits

[gray basin]

Oh so 10x10x10x10

[drifting swift]

why four factors?

why do you multiply four 10's together?

[gray basin]

To get the total different combinations

‘10x10x10’

My bad..

[drifting swift]

would have been better if you didn't use the letter x for multiplication everywhere but whatever

now it's correct at least

[gray basin]

What do I use then?

[drifting swift]

asterisks

[gray basin]

Ok sure

[drifting swift]

with spacing or backslashes before them as appropriate so that discord does not eat them

10 * 10 * 10

[gray basin]

Yh ok sure

True

Ok thanks

.close

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[frigid gull]

im not sure how to calculate the inflection points

[frigid gull]

this is what i have

[lyric marsh]

point of inflexion is where concavity of a function changes, mathematically those points are a subset of points where the double derivative equals zero. after that, it's a good idea to check for values between the solutions to see if concavity actually changes or not

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[leaden tusk]

you've asked in like 4 different channels and have provided no work or attempts at anything

if you want help, give us something to help you with

luckily you're on a device that has access to billions of resources to help you

[wraith nova]

To complete this assignment, you may need to start from the beginning of class so you're able to understand the questions at least.

No lectures, no videos, no references?

[topaz sinew]

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[patent flax]

can anyone pls double-check my answer?

[patent flax]

I'm not sure

I'm thinking like the parts are right

the sizes are correct

but it's missing the data numbers and whatever

sigh.

.close

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[hushed solstice]

hello

[hushed solstice]

can you tell me how do i solve for this if i don't know the measure of the smaller triangle?

.close

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[mighty bear]

ok so if you got 20$ every 300 seconds how many would you get in 10 hours

[wary oak]

@mighty bear How many hours are 300 seconds?

[mighty bear]

im only asking bc im super sleep deprived and im not tryna do the math bc of how tired i am
but there are 5 min

hollup nvm im dumb as hell sry for wasting ur time

sorry bruh

[wary oak]

so 300 seconds are 300/60 = 5 minutes. in hours that is = 5/60 = 1/12 hours. so equivalently, we get 20$ every 1/12 hours. so in 1 hour we get 20$ * 12 = 240

[mighty bear]

thx i figured it out

.close

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[simple swallow]

Hello! I am not sure where this question stands in the pre- or during- or post- university ladder.

I've been thinking about the sun, how its angle to the ground changes through the day, and in a different manner for a different point on earth. I would like to figure out exactly what angle that is for a given time, day, and position on earth.

What is a sensible path to take for learning to do this kind of calculation?

[topaz sinew]

@simple swallow Has your question been resolved?

[thorn nova]

I can come up with a function that takes as parameters latitude and longitude

The knowledge involved is trig. and a lot of information about earth and sun orbit, their angular velocity, earth axis rotation

[topaz sinew]

@simple swallow Has your question been resolved?

[simple swallow]

I've never used trigonometry in a 3D space context. If I have a point A on a sphere, how do I get the angle between an axis and OA (O being the sphere's point of origin)?

Actually that seems pretty simple. I just need to take an extra step of xy plane -> now z axis

OK thanks @thorn nova @haughty fog ❤️ I'll go figure out the lat:long -> point on sphere bit elsewhere.

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[opaque brook]

<@&286206848099549185>

[opaque brook]

I just got a few algebra questions

[fallen wasp]

first, you can’t just ping helpers

second, you have to clarify your questions, not just say “i need help”, ask your questions and someone will help

can you read bro, there’s rules and they’re clear

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[rustic crow]

i have a quick question

[rustic crow]

what is the derivate of x/3

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[rustic crow]

ok i have another one tho

what is

the derivate ln^2(x)

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[rustic crow]

:)

[rustic crow]

I SOLVED IT NVM

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[delicate pike]

I have question

[delicate pike]

if I want to find the rank of a matrix by reducing it, does it have to be in rref or just ref?

I was looking at stuff online and people are saying u need it in row echelon form

The matrix I'm dealing with can be reduced down to a 3x3 identity matrix

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[stoic sable]

I have to find the missing variable from a parable using the given coordinates, but idk how to start, can someone pls help

[stoic sable]

All I have is
(X - 4)^2 - 4

I thought maybe I could solve it using
ax^2 + bx + c
But I got even more confused

No wait, I got it

Sorry mates

I misunderstood the work

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[frigid gull]

did i find the inverse correctly

[neon iron]

how did you get 2x = y^3

when you multiply 2 on both sides thats not what u get

[frigid gull]

multiplied 2 by both sides so 2 cancels out

[neon iron]

...

$$ \frac{2y^5}{y^2+2}$$

[thorny flame]

painful

[neon iron]

they don't cancel out

[frigid gull]

so how would i isolate y

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@frigid gull Has your question been resolved?

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@frigid gull Has your question been resolved?

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@frigid gull Has your question been resolved?

[regal tide]

@frigid gull I don't think it's possible to isolate y here

I've forgotten my maths, but I've got a feeling that the fact that you need to get the derivative of the inverse means that this is something to do with function identities

[sweet shard]

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[coarse thunder]

Helloppp

[coarse thunder]

Please

i= 8, ii=-12, iii=-12

This is what I got but I don’t think it’s right, idk how to do this

Hello

<@&286206848099549185>

[alpine mist]

no

the graphs are the graphs of the derivative and second derivative, not the function itself

Graph A (the first derivative) has a maximum at x = -8, but that is not where the maximum of f(x) is

[coarse thunder]

How would I solve this

[alpine mist]

how do you find a maximum from a derivative?

[coarse thunder]

Yes the local maximum

And the inflection point

And the absolute maximum

[alpine mist]

I'm asking you, how do you find it?

[coarse thunder]

I’m not sure

I know how to do it when an equations is given

[alpine mist]

what do you do when an equation is given?

[coarse thunder]

But I don’t understand when it’s just graphs

I set it equal to zero once I find the derivative

[alpine mist]

ok, so the zeros of the derivative are important, then what?

[coarse thunder]

We use the first derivative test to find the extrema

[alpine mist]

So when the first derivative goes from positive to negative you have a max, right?

[coarse thunder]

Pretty sure

[alpine mist]

What that means graphically is, when the first derivative crosses the x-axis (going from positive to negative) then the function has a maximum

when the first derivative crosses the x-axis (going from negative to positive) then the function has a minimum

[coarse thunder]

So that would be -8 right?

Oh wait

[alpine mist]

Graph A has a maximum at -8, but that is not the function

[coarse thunder]

I mean -4

So -4 is right?

[alpine mist]

for a maximum yes

[coarse thunder]

Local maximum

So what’s the difference between local maximum and absolute maximum

Like part 3 of the question

[alpine mist]

local maximum is a maximum in that area. Absolute maximum is the highest value reached by the function

For iii, are there any other maximums?

(you can determine this from the first derivative)

[coarse thunder]

I don’t see any other than at -8

[alpine mist]

x = -8 doesn't give a maximum of the function

[coarse thunder]

But that’s where the graph A is at it’s highest?

[alpine mist]

graph A, yes. Not the funciton f(x)

[coarse thunder]

How would I do that

[alpine mist]

^

[coarse thunder]

Isn’t the graph suppose to be y=f(x)

[alpine mist]

read the very top sentence

graph A = f'(x)
graph B = f''(x)

[coarse thunder]

Oh ok

That makes more sense

English is not my first language

[alpine mist]

So since graph A = f'(x) crosses the x-axis from positive to negative at x=-4, you have x=-4 is a local maximum

[coarse thunder]

Ok yes I under stand that

[alpine mist]

Does graph A = f'(x) cross the x-axis anywhere else?

[coarse thunder]

No

At least not that we can see

[alpine mist]

ok, so that tells you that f(x) is increasing then decreasing with a max at x=-4
So is that an absolute maximum?

[coarse thunder]

Yes

Do we not have to use the second derivative graph?

[alpine mist]

yeah, this is one of those situations we have to assume we're being shown all the relevant information

[coarse thunder]

For any of the problems

[alpine mist]

not for 1 and 3

for 2, you use the second derivative test

[coarse thunder]

Ahh ok

[alpine mist]

This is basically the same as the first derivative test, but it tells you inflection points instead of max/min

[coarse thunder]

Ooh ok

So I’m looking for when x=0 on graph b right?

[alpine mist]

you're looking for when it crosses the x-axis

[coarse thunder]

And that would be -8 right?

[alpine mist]

so x = -8 is an inflection point

[coarse thunder]

Oh ok

Thank you so much for being patient and helping me I really appreciate it🥺🥺

[alpine mist]

no problem

[coarse thunder]

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[half crescent]

Yo, financial math question, when calculating forward rates in the interest of finding monthly returns, do we calculate using an input of annual spot rates and just use the resulting forward rate each month, or is there conversion to be done so the rates can be used monthly?

[hollow bone]

I dont know how it is done IRL but the two methods definitely dont have the same results

[half crescent]

sweet cheers

[hollow bone]

if you have an amount X and gain y percent over a year, you have X*(1+(y/100)) by the end of the year, but you cant compute that same thing for each month, if you do you'll get the same result as if you computed the first method for 12 years

so yeah you have to find a monthly rate that is different

such that (1+y/100) = (1+m/100)^12 where m is the monthly rate and y is the yearly rate

so if you do 12 times the computation monthly you get X(1+m/100)^12 ( = X(1+y/100))

[half crescent]

right

[hollow bone]

it would not work since the rates of growth are exponential and not linear

your method would work if you gained the same each month

(it can be what actually happens in real life idk about that)

but if you want to have a monthly rate, the good equation is what i wrote earlier

(1+y/100) = (1+m/100)^12

solve for m

[half crescent]

ahhh fair enough

cheers for the help!

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[loud raven]

Can somebody check if my answer is right ?

[loud raven]

<@&286206848099549185>

[patent flax]

you're good

at calculations

from what I see

as for if your answers are correct

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@loud raven Has your question been resolved?

[loud raven]

8 that correct

I’m very new to this concept

[patent flax]

8 is not correct from what I see

it can be simplifed

Consider that as $\frac{15}{6} \times \frac{x^7}{x^3}$

[thorny flame]

hellblaze_skyfire

[loud raven]

It didn’t ask to simplify any further

But yes I am correct in a sense of way I didn’t simplify

[patent flax]

you need to simplify

[loud raven]

I will thanks

[patent flax]

it is a requirement for every teacher

[loud raven]

I never thought of it like this

But rest are correct right ?

Most are correct.?

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[tropic tiger]

I need help with this.
I tried to do it but i just end up only changing the position from (-4/9)pwr-6 into (-9/4)pwr6 and I dont know what to do

please ping me btw

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@tropic tiger Has your question been resolved?

[drifting swift]

okay first off

this symbol: ^ exists

(-4/9)^6

second: this question is poorly stated. both x = -4/9, y=6 and x = -9/4, y=6 are valid answers to it, among others, and yet the question is phrased as if there were only one correct answer

so it is not your fault

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[kind mantle]

Using Polya's theorem or otherwise
how do I find the coefficient of of $r^4yb$

[thorny flame]

melon lord

[kind mantle]

I know the answer is supposed to be 5

but how do I work out the answer to be 5?

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[kind mantle]

<@&286206848099549185>

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[kind mantle]

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[honest oyster]

yo

[honest oyster]

wolfram doesnt simplify the answer to pm 1 for some reason

does that mean my answer is wrong

i feel like its supposed to be plus minus 1 becoz if its not plus one, its negative one and if u graph it it proves it correct

but wolfram doesnt simplify it for some reason and even if i manually input "simplify... (the expression)" it still wont show pm 1

any help?

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[night flax]

How do i prove this ? tks

[night flax]

question d

transitive

my idea is

introducing new tuple

and somehow find the relation with (y1,y2)(z1,z2) and (x1,x2)(z1,z2)

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[celest yoke]

where would i go to learn math properly? School takes too long and i would rather get everything start up and move on past my grade at some point

[empty sail]

Khan Academy is good

[celest yoke]

Thank you. I'll start there

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[timber schooner]

how do I calculate holdaiy pay

[grim jacinth]

I believe you can calculate pay per day and then apply that for 1 year - 4 weeks

[timber schooner]

huh

[neon iron]

@timber schooner

82460 / 365

• 28

[timber schooner]

ok

then?

I got 6325.69863

[timber schooner]

<@&286206848099549185>

[neon iron]

Sounds right

[timber schooner]

wrong

this is the answer

how do you get that answer tho

😭

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[cursive flax]

,w calc 82460/365*28

[thorny flame]

Results provided by WolframAlpha

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

Requested by hoi#0323

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[deft elbow]

Hi guys, which test would you use to check convergence? Limit Test?

[viscid thistle]

homie, for loads of large values,it’s almost 1

I’d be surprised if something that’s infinitely going to one converges

[median temple]

cos(1/n) tends towards 1

[viscid thistle]

yeah

[median temple]

1-cos(1/n) tends towards 0

it has at least a chance of converging

[viscid thistle]

oh

1-

Sorry,

I didn’t see that part

[median temple]

that was pretty big to miss, but no worries, it happens

[unique tundra]

the necessary condition for convergence is met but not the sufficient one

[median temple]

yes

[unique tundra]

root test and quotient crit doesnt work

its = 1

[viscid thistle]

it was indeed, I’m stupid

[median temple]

Personally I would just use an limited development/equivalence

[unique tundra]

so maybe just use: $-1\leq \cos(\frac{1}{n})\leq 1$

[thorny flame]

Big xdddd

[deft elbow]

Squeezing theorem?

[viscid thistle]

oh yeah

[median temple]

What?

0 ≤ 1-cos(1/n) ≤ 2, and ?

[deft elbow]

Ah, ok, nevermind

[viscid thistle]

so if
f(x) <= g(x) <=h(x)

[viscid thistle]

no x terms

nvm

you can’t squeeze

[deft elbow]

Ok, maybe I can use Alternating Series Test?

[median temple]

It's not alternating

[deft elbow]

Huh, ok

[median temple]

In fact, every term is strictly positive

[unique tundra]

we are talking about sequences not funcitons

[median temple]

Squeeze theorem also works for sequences

[unique tundra]

but squeezing theorem could work yes

[median temple]

Not sure how in this case

[deft elbow]

So, I guess we left with Limit Test or Integral Test no?

[median temple]

If any one of these is likely to succeed it's probably the integral test

But I can't be sure, I have other tools which would solve this problem

[unique tundra]

$a_n\leq b_n\leq c_n\newline a_n=0\quad b_n=1-\cos(\frac{1}{n})\quad c_n=..$

[thorny flame]

Big xdddd

[median temple]

(ones that you may not know of/may not be allowed to use)

[deft elbow]

Yeah, I guess so, I'm still in Calculus 2 so 🙂

[median temple]

(if a_n=0 you're just using the comparison test here)

[unique tundra]

yes

[deft elbow]

You mean direct comparison test?

[unique tundra]

but i dont think we can find anything for c_n

[median temple]

You can, as a matter of fact, but you need some limited taylor expansions

Or at least find a way to turn them into inequalities

[deft elbow]

Hmm, maybe we can. show that its absolutely convergent?

[median temple]

All terms are positive, so it's going to change exactly nothing

[deft elbow]

I remember, in case of cosines, we mostly used that and used 1 instead of cosine

[median temple]

Yeah, but here that inequality won't help you get any meaningful bound

[deft elbow]

Ok, I think the right way is to use integral test

We split into 2 integrals right?

[median temple]

In what way

[deft elbow]

I mean, separately integral of 1, minus the integral of cos(1/x)

[median temple]

Those diverge

The integral of 1 from, say 1 to infinity, is infinity

[deft elbow]

Oh, sorry, i forgot, indefinite integral

[median temple]

And likewise with the integral of cos(1/x) since that tends towards 1

[deft elbow]

With integration by parts

[median temple]

I've tried things on the integral, but we're left with something that might be equally as hard

[deft elbow]

Hmm

Strange, so lets check.
Ratio test is useless
Root test is useless
Alternating series test can not be used
Term test gives no information
Integral test is unpredictably hard
What we have left? 😅

[median temple]

Well, if you can check whether $\lim_{x\to 0} \frac{1-\cos(x)}{x^2}$ converges you have yourself an answer

[thorny flame]

Syst3ms

[deft elbow]

How we got this equation?

I mean, how its related?

[median temple]

I did the change of variables x=1/t in the integral

[deft elbow]

Oh, ok

[median temple]

$\int_1^{+\infty} (1-\cos(\frac1{t}))dt = \int_0^1 \frac{1-\cos(x)}{x^2} dx$

[thorny flame]

Syst3ms

[median temple]

But I can also solve this problem with the exact same tools, which leads me to believe you'll have trouble doing it with the ones at your disposal

[deft elbow]

Okay, we leave this question for now, will check office hour, maybe professor solved something similar, thanks guys

Btw, this seems to be easier 😄 , its ratio test right?

[median temple]

Let me check

Yeah, that works

[deft elbow]

Guessed it 😆 , now, need to write solution

.close

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[brazen aspen]

HN Geometry Class, SOH CAH TOA Triangle Word Problem

A museum is displaying a large sculpture (on the ground floor) in its high-ceilinged rotunda. Thomas is looking at it from the second floor. His angle of elevation to the top of the sculpture is 21 degrees and his angle of depression to its bottom is 42 degrees. If the horizontal distance from Thomas to the sculpture is 24 feet, how tall is the sculpture?

I can't visualize how to draw a model for this. Help pls (if u can draw a model that would help a bunch)

[brazen aspen]

after some further thinking i solved it

.close

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[opal rampart]

I'm looking for someone who can help me create a formula for calculating if something is above an average and how it should be valued

[opal rampart]

For example

if its 1000 value

and 25 daily sales and the average daily sales is 50
it removes 5% of the 1000 value

or if the daily sales for that item is 80 and the average for everything is 50

its like maybe 2-3% raise in the 1000 value

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[topaz sinew]

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[neon iron]

I forgot what topic this was

[leaden tusk]

tranglie

what does $\tan^{-1}\left(\frac{a}{b}\right)$ represent?

[thorny flame]

a disappointing son

[neon iron]

Idk

[leaden tusk]

do you know what inverse trig is used to find?

[neon iron]

Nope

I wasn’t in class for more then a week and I come back to this

I have no idea what this is

[leaden tusk]

perhaps go over notes?

maybe look at your textbook?

[neon iron]

At school 💀

What do I do now

@leaden tusk

[leaden tusk]

youtube?

i'm not gonna tell you the answer, if you want to learn a topic, that's on you

[neon iron]

What topic is that

[leaden tusk]

trig and inverse trig functions

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[narrow torrent]

Given $f(x)$ and $g(y)$, prove that:
$\int\int(\left f(x)g(y) \right) dx dy = (\left\int f(x) dx\right) (\left\int g(y) dy\right)$

[thorny flame]

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

[sweet shard]

do you just use the definition of the iterated integral

should be similar to
https://math.stackexchange.com/a/549929/142904

[narrow torrent]

lol

that was less complicated than i thought

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[mighty epoch]

what you trying to do?

okay but which topic does this fall under?

but you haven't given the topic this falls under

like is it sequences?

series?

calculus?

what does this professor teach you?

convergence test?

what was your test on?

so most likely this question is asking for you to test for convergence

okay

so do you know your convergence tests?

this seems like a p-series

so I think it was using the integral test

good luck!!!

hopefully next year is not that bad.

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[neon iron]

how to calculate probability?

[grim jacinth]

It's not that hard to read

[neon iron]

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[undone fog]

i've got this, but im unsure of how to continue from here

how is it even possible to find the heading of the airplane?

[topaz sinew]

@undone fog Has your question been resolved?

[undone fog]

<@&286206848099549185> i'm really struggling with this 😭 if anyone could help please

[fluid phoenix]

are you sure that V_f = 1.8V_s? The distance they travel isn't the same

[undone fog]

The velocity of V_f is 1.8 times the Velocity of V_s right?

V_fast and V_slow

[fluid phoenix]

That would be the case if the distance traveled was the same

[undone fog]

😭

hmm

[fluid phoenix]

The question says that the time taken by the slower plane is 1.8x the faster plane

not velocity

[fluid phoenix]

if the distance were to be the same that would mean this

[undone fog]

i was given this for help my by TA

so they do travel the same distance right?

just the slower one takes 1.8 times as long

[fluid phoenix]

from what it looks like to me the slower plane travels a longer distance

but they are flying to the same cities

so yes its the same distance

[undone fog]

doesn't the wind offset this?

the crosswind

[fluid phoenix]

it should

that's what I'm thinking

[fluid phoenix]

but

[undone fog]

im so confused...

how would I even start solving the

angle?

because this ^

is a complete mess

[fluid phoenix]

mhm let me take a look

There are still things that bug me about this question, if the slower follows a heading that is 40 deg west of north, it isn't even gonna reach the destination and if it does it would have travelled a longer distance than the faster plane did

so we can't assume V_f = 1.8V_s

[undone fog]

im not sure why my TA put that then...

hmm

well the displacement is still the same right?

because both planes are tehcnically going straight?

https://youtu.be/VvPWp-zEYo8

kind of like this

[fluid phoenix]

mhm

[undone fog]

i feel like im doing all of this for nothing

[fluid phoenix]

ah yes their x components will be the same

since the crosswind is the same

equate those

[undone fog]

hmm

[fluid phoenix]

Vsx = Vs sin(40) = Vfx = 1.8Vs sin(theta)

[undone fog]

and i would just solve for theta there?

[fluid phoenix]

yes

Vs would cancel

[undone fog]

wait i get it because

omg 😭

i spent 3 hours on

okay hold on

[fluid phoenix]

yeah the crucial part is knowing that the velocity in the x direction is only due to the crosswind and is the same for both

[undone fog]

and now that i have the angle

solving the speed of the

plane should be easy?

[fluid phoenix]

yeah

[undone fog]

i find the x component of the slower one right

and since x components are the same

i use that and the angle i just got

to solve for the speed of the plane?

[fluid phoenix]

does the question ask for that?

[fluid phoenix]

ah part 2 yes

[undone fog]

thank you so much 😭

[fluid phoenix]

yes

[undone fog]

i had such a hard time with this one, so their x components are the same because of the crosswind, and since the magnitude is greater for the other plane, the only thing that can change is their y component

[fluid phoenix]

yes

but you need to find the y component I think that's the airspeed

[undone fog]

so airspeed isn't the magnitude?

its the y component?

[fluid phoenix]

wait no

[fluid phoenix]

Its the speed relative to the wind right?

and the wind in the north direction is 0

so you need to find the velocity in the north direction or the y component

[undone fog]

okay 😭 thank you

i understand it i think

[fluid phoenix]

if the wind was blowing north east you'd have to find the north component of wind speed

[undone fog]

so the y component of the slower plane is 160mph

[fluid phoenix]

yes

[undone fog]

ah okay

i understand it now 😭 thank you so much

[fluid phoenix]

[undone fog]

thank you that is so easy to understand now

okay good 😭

[undone fog]

i got about 351 mph for the y speed

i hope... that's

okay..

but anyway tysm for all your help!

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[split solstice]

idk if I did this right and its just

f^1 = 2x
f^2 = 4x
f^3 = 8x
f^n = 2^nx

[pulsar falcon]

Looks good

[split solstice]

Ok just checking

Thank you

.close

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[barren patrol]

I just completely forgot the formula for this type of question, how do I do this

[drifting swift]

there's no such thing as "the formula"

however, you might find the idea of the discriminant useful

[barren patrol]

sorry but i also completely forgot what that was so

[drifting swift]

would you like a reminder?

[barren patrol]

yes please

[drifting swift]

the discriminant of the quadratic polynomial ax^2 + bx + c is the expression b^2 - 4ac

the discriminant tells you how many real roots your polynomial has:
if b^2-4ac > 0, there are two real roots
if b^2-4ac = 0, there is one real root (a double root)
if b^2-4ac < 0, there are no real roots

to calculate the discriminant of your quadratic equation you will have to bring it into standard form first so that you can actually see the coefficients

[barren patrol]

OH THAT STUFF-

[barren patrol]

so i turn this thing into ax^2 + bx + c

then i put the numbers into the discriminant and make it >0

or >= 0

and then i just work it out from there?

[drifting swift]

well the coefficients aren't going to be numbers, they'll be expressions in terms of k

but other than that, yes.

[barren patrol]

omg ty