help-27

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[wide bluff]

stuck

[restive river]

can't u prove using ven diagrams

?

I mean, is it allowed

[wide bluff]

no rigorous

i tried venn diagram

but idk if i am right

cuz what i got is A = B = C

using venn

i am doing case making idk if its valid

[restive river]

ohh

[wide bluff]

this is UG math proofs course ok

[restive river]

yeah I know

alright

assume an element that belongs to B

[wide bluff]

i am unable to write english

idk how to prove

in case 2 B is subset of C

in case 1 however it does not need to be

[restive river]

say k belongs to B. Now if k belongs to B, then it also belongs to AUB. That means it also belongs to AUC since AUB=AUC. Then this means k either belongs to A too, or C too. If k belongs to A then, it also belongs to A intersection C. if k belongs to C then B is a subset of C and it also belongs to B intersection C. Therefore, either way one of the condition is true. Now imagine some other element p which belongs to C. Repeat the step but with the other set (B). You will end up with the same conclusion. It means that the first element u chose, k and the other, p, both are equal or the two sets are equal

[brisk totem]

!nosols

[devout snow]

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.

[wide bluff]

but if k does not belong to B k can still be in AUB cuz it can be in A

[restive river]

k belongs to B since we assumed it

that's the assumption

and we showed that it also belongs to C, with the given conditions

then we took some other element, p which belonged to C by assumption

and we showed that it also belongs to B

[wide bluff]

after we said x belong to AUC

we split into two cases

but there can be

3 cases

x belongs to A

x belongs to C

and x belongs to both

infact even intially there can be a case that x does not belong to AUC

[devout snow]

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[restive river]

I’m not sure how to find the bigger triangle chord area

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@restive river Has your question been resolved?

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@restive river Has your question been resolved?

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@restive river Has your question been resolved?

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@restive river Has your question been resolved?

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[supple knot]

average velocity is (final position - initial position) / time traveled

no

you did final position - intermediate position

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[sonic remnant]

Just solved it nvm

[stuck field]

.close

[pseudo basin]

.close (op stated he no longer needs help)

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[viral sonnet]

Umm

[viral sonnet]

Hello?

[winter patrol]

greetings, if you have a math question skip the pleasantries and just ask

[pseudo basin]

hello, do you have a math question to ask?

[viral sonnet]

How the fuzz is suddenly changes from the 1st row to the 2nd row??

Or i supposed to say line?

I dunno... not native tho...

[dusky drift]

dude

open the brackets

by multiplication

you notice a pattern

[winter patrol]

consider first distributing the p to the second expression
(write out the first few ... then the last few terms)
then below that write the result of the distribution of the -1, keeping terms of the same power aligned

[dusky drift]

of cancellation of terms

@viral sonnet

[viral sonnet]

Im here

Thinking

And

Writing

[dusky drift]

dude its simple

just multiply p with the terms in the second bracket

it will increase power of each term by one

now

mutiply -1 with each term

then subtract

[viral sonnet]

It

Will

[dusky drift]

from the terms with the power increased by one

[viral sonnet]

Leave

The

-p^14

And

p^42

[dusky drift]

so how will you write this

[viral sonnet]

Uhhh...

Pardon me?

You mean...

p^42 - p^14 ?

[dusky drift]

Yes

correct

[viral sonnet]

Hmmmmmmmmmmm

[dusky drift]

did you find this on your own or just copied

[viral sonnet]

Whaat refers to "this"?

Im sory

[dusky drift]

p^42-p^14

[viral sonnet]

I found it on my own

[dusky drift]

Nice

any other doubt?

[viral sonnet]

Maybe...

[dusky drift]

[viral sonnet]

Since p x p^n equals to p^n+1

[dusky drift]

yes

[viral sonnet]

Right?

Yes

Well

Makes sense

Thx

Thx very much for the brain boost! @dusky drift @winter patrol

I think we will meet again XD

.close

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[heady tulip]

A is a square matrix

[heady tulip]

status: -1, don't even know where to start

god has forsaken us

oh

i + sum of a^k's

nvm

god hasn't forsaken us

.close

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[restive river]

$( (f \circ f)(x) = x^2 + \frac{1}{4} ) \
Replace ( x ) with ( \frac{1}{2} ) to find ( (f \circ f)\left(\frac{1}{2}\right): ) \
( (f \circ f)\left(\frac{1}{2}\right) = f\left(f\left(\frac{1}{2}\right)\right) ) \
Use the relation ( (f \circ f)(x) = x^2 + \frac{1}{4} ) to substitute in the expression: \
( f\left(\frac{1}{2}\right)^2 + \frac{1}{4} = \frac{1}{2^2} + \frac{1}{4} ) \
Subtract ( \frac{1}{4} ) from both sides of the equation: \
( f\left(\frac{1}{2}\right)^2 = \frac{1}{4} ) \
Take the square root of both sides: \
( f\left(\frac{1}{2}\right) = \pm \frac{1}{2} )$

[woven radish]

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

[restive river]

is this correct

[cosmic trail]

why is ff(1/2) = f(1/2)^2 + 1/4

oh nvm I see now

yeah I think it's correct

[restive river]

because you are substituting x

as 1/2

[cosmic trail]

f(1/2) you mean

[restive river]

yes

[winter patrol]

it looks like you're subbing in f(1/2) on the left but 1/2 on the right

[restive river]

oh wait

ok now i think its 3/4

i will show you my work

this looks correct

[winter patrol]

it looks like you're still conflating (f o f)(x) with f(x)

[restive river]

.close

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[fervent sundial]

hii, not sure if this is a dumb question lol but

[fervent sundial]

how to compare $\frac 12 + \frac 13 + \frac 14 + .. \frac 18$ to $\frac 75$

[woven radish]

kanna

[fervent sundial]

without actually computing the sum: 1/2 + 1/3 + 1/4 + ... + 1/8

[pseudo basin]

wdym "to 7/5"

oh

compare

mb

[fervent sundial]

right

[pseudo basin]

uhh

compare 5/2 + 5/3 + 5/4 + ... + 5/8 to 7?

calculate the first few terms

,calc 5/2 + 5/3 + 5/4

[woven radish]

Result:

5.4166666666667

[pseudo basin]

that work?

hm

[fervent sundial]

hmmm

[pseudo basin]

i was hoping it would exceed 7 but no

hold on tho

!xy

[devout snow]

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

[fervent sundial]

yeah it's exactly that

[pseudo basin]

"Compare this sum to 7/5, only you are forbidden from explicitly calculating this sum and will be executed if you do so"?

[uncut crow]

harmonic numbers

[pseudo basin]

feels like an odd restriction to me is all

[fervent sundial]

Quantity A: 1/2 + 1/3 + 1/4 + 1/5 + 1/6 + 1/7 + 1/8
Quantity B: 7/5

Then you're supposed to compare quantities, but yeah the side note was not actually computing quantity A

[fervent sundial]

hi

[pseudo basin]

i mean lets see

[fervent sundial]

i'm not sure but i've seen something about 1/5 * 7 = 7/5

[pseudo basin]

oh

oh huh right

[fervent sundial]

and something about QA > that

[pseudo basin]

the sum has 7 terms

yeah cause 1/x is concave

on (0,+∞)

[fervent sundial]

wait 😭 let me look up what a concave function is

oh yeah okay i know that

[fervent sundial]

wait so what about it?

[pseudo basin]

1/4 + 1/6 > 2/5

1/3 + 1/7 > 2/5

[fervent sundial]

wait okay i see how this works

wow okay thxx

[fervent sundial]

by the way do you know what the "1/5 * 7 = 7/5 and the sum of quantity A should be greater than that" could've meant?

I don't explicitly remember the details

just curious if it makes sense to you (with the little info i have)

i'm guessing it has something to do with median

if that helps

since i'm not really allowed to use calculus for these problems

[fervent sundial]

and i'm guessing this result follows from calc

since i learnt concavity in calc

unless i'm mistaken

[pseudo basin]

yes

[fervent sundial]

right, so is there a way to construct a reasoning which isn't calc

(this is like an algebra task 😭 )

i saw one of this but i don't get the rationale behind it

since it wasn't explicit enough

[pseudo basin]

AM-HM inequality?

idk tired

[fervent sundial]

you mean my pic is related to AM-HM?

[fervent sundial]

this thing

[fervent sundial]

owhh okay okay no worries then-

thanks for the concave thing, that's pretty neat

[toxic magnet]

One doubt

[fervent sundial]

?

[toxic magnet]

Answer for this?

[fervent sundial]

:V

#❓how-to-get-help

[toxic magnet]

K sry

[uncut crow]

this is dumb but...
1/2 + 1/6 = 2/3 > 3/5
1/3 + 1/4 + 1/5 > 1/5 + 1/5 + 1/5 = 3/5
1/7 + 1/8 > 1/8 + 1/8 = 1/4 > 1/5

[fervent sundial]

oh lol, wait was that reasoning based on this?

okay i see, nice thanks C;

[uncut crow]

what's that and this?

[fervent sundial]

the pic

[fervent sundial]

this

okay maybe not 😭

[fervent sundial]

but yes your reasoning makes sense

tyty

[uncut crow]

not sure what's happening in that pic

[fervent sundial]

yeah idk either lol

wait on second though

i'm missing what ann meant

😭

i thought i understood but hmm when i actually tried it myself i think i was assuming something

@uncut crow do you understand? i think ann's tired so not sure if i'm allowed to ask

1/3 + 1/7 > 2/5```

this with relation to concave functions^

is it this thing?

looks related

[drifting sierra]

1/x is convex, not concave

[drifting sierra]

It's the opposite of this

So 1/5 < (1/4 + 1/6)/2

(strictly convex)

[fervent sundial]

wait so convex is the U shape right?

and concave is the cap shaped thing

[drifting sierra]

Kinda yeah

[fervent sundial]

okay the naming is weird ig

[fervent sundial]

wait where did you get this? well i get the rhs

[drifting sierra]

People also use "concave up/down" but I don't like it

[uncut crow]

same

[fervent sundial]

yeah 😭i thought it was related

[drifting sierra]

x=4, y=6, (x+y)/2 = 5

[fervent sundial]

wait okay i’m blind

thought i saw f(x)

so like wait just to confirm the main point

,, f \qty(\frac{x_1 + x_2}{2}) \leq \frac{f(x_1) + f(x_2)}{2}

[woven radish]

kanna

[fervent sundial]

this is for midpoint convexity right?

[drifting sierra]

Yes

[fervent sundial]

and what’s the significance of the equality

strictly concave is just <?

[drifting sierra]

Oof transparent background

This is strictly convex

[fervent sundial]

okay i switched to light theme for that

[drifting sierra]

It means if you take two points on the graph and draw a line between them, every point on the graph with x coordinate between the two points is below the line

[fervent sundial]

mhm that makes sense yeah

[drifting sierra]

If it's not strictly convex but just convex, you can have linear segments

[fervent sundial]

i’m lost

wdym by linear segments?

you mean it’s like a discontinuous function?

[drifting sierra]

In the interval it's linear

But it's still convex overall

[fervent sundial]

oh in that case the slope is constant(?) so that’s where they have the equality condition..?

[drifting sierra]

Yes

Constant slope = linear

[fervent sundial]

fair enough, i guess that’s something new

the convexity part

thanks bro

nel*

[drifting sierra]

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[remote knoll]

I'd like some help answering part (b). Even after reading the mark scheme, I still do not understand the question. All I know is that:

H_0: X ~ B(4,0.5) is a suitable model
H_1: X ~ B(4,0.5) is not a suitable model

[remote knoll]

This is a screenshot of the mark scheme, but I have no idea how to decipher all that. All I know is that it concerns hypothesis testing.

[devout snow]

@remote knoll Has your question been resolved?

[devout snow]

@remote knoll Has your question been resolved?

[devout snow]

@remote knoll Has your question been resolved?

[devout snow]

@remote knoll Has your question been resolved?

[remote knoll]

I’m going to close it as I’ve been asked by the bot four times.

.close

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[static pollen]

where does -4(t-2)u(t-2) -4u(t-2) come from?

[supple knot]

use (a + b)^2 = a^2 + 2ab + b^2

[static pollen]

but (t-2+2)^2 is just t^2

how can i use that there

[supple knot]

don't use that if you want to understand

[supple knot]

use this

[static pollen]

on (t-2+2)^2 correct?

[forest shuttle]

why doesnt it just simplify t-2+2 straight away?

much easier

[static pollen]

wdym

[forest shuttle]

t - 2 + 2 = ...

t - a + a =

[static pollen]

yeah its t but how does it come up with the bottom thing

,rotate

[woven radish]

Couldn't find an attached image in the last 10 messages.

Jan 14, 2024, 9:11 PM

[static pollen]

@supple knot

,rotate

[supple knot]

nah

[static pollen]

bruh wdym nah

[supple knot]

they kept t-2 together

[supple knot]

you should do the same

[static pollen]

what??

@sullen island help

[static pollen]

factor out t so it becomes t(t-2)?

@supple knot another hint pleassssseeeeee

.close

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[coral wraith]

how do i prove this?

[devout snow]

@coral wraith Has your question been resolved?

[coral wraith]

Anyone?

<@&286206848099549185>

.close

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[coral wraith]

.reopen

[devout snow]

✅

[coral wraith]

Anyone please

[coral wraith]

<@&286206848099549185>

havent been able to find anything online about this either

[cinder coral]

What is the question ?

[coral wraith]

this

[devout snow]

@coral wraith Has your question been resolved?

[coral wraith]

anyone?!

[devout snow]

@coral wraith Has your question been resolved?

[coral wraith]

Anyone please

[soft nest]

I believe section 6 will help you https://forumgeom.fau.edu/FG2013volume13/FG201305.pdf

[coral wraith]

Thank you

[coral wraith]

.close

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[delicate arch]

can someone explain to me why this is solved by multiplying by the conjugate?? I'm not familiar with conjugates.

[dense lynx]

when you see (1 - cosx) or (1 - sinx) in a denominator of something, you usually multiply by conjugate because (1 - (sinx)^2) = (cosx)^2 and (1 - (cosx)^2) = (sinx)^2

[delicate arch]

that kind of makes sense but I still dont get the use of conjugates besides the fact that the trig identity where sinx^2 + cosx^2 = 1

[dense lynx]

that's pretty much the main reason i guess

having a (sinx)^2 or a (cosx)^2 is usually more pleasant to work with than a (1 - cosx) or something

[delicate arch]

ah okay

thanks 👍

.close

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[summer harbor]

is this correct

[summer harbor]

wait its still loading

[hidden dragon]

The question is not written well

[summer harbor]

wdym

im asking if like im doing the substitution right

cause like

idk how to get the value from here

[hidden dragon]

You're substituting for x=5?

[summer harbor]

yeah

intermediate value theorem actually so im supposed to get 5 and 7

[summer harbor]

its specificiallt asking if there is 0

[hidden dragon]

Also is it 1/(2x) or x/2

[hidden dragon]

I see

Nvm it's x/2

[hidden dragon]

I see

Yeah h(5)=sin(-115/2)

If that was your question to check it's correct

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[meager yarrow]

“How many vectors can be determined by the sides of a regular pentagon”
The answer is not infinitely many but 10
Why is that?

[feral agate]

why would it be infinity?

[meager yarrow]

The sides aren’t parallel
So they so determine a whole plane which would be infinitely many vectors right?

[feral agate]

well I guess they mean the number of exact vectors you can define

[meager yarrow]

Hmm ok

.close

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[fluid flax]

A farmer wants to build a rectangular pen for his rabbits. We know that it only has 40 linear meters of metal fence.
a) Let's call x the width of the corral. Which algebraic expression will give us the value of the length? Write the function that allows you to calculate the area of the corral considering only the width x.
b) Calculate at what point the function you found in the previous section reaches its maximum. Deduce what the width x and what the length y must be so that the corral has the maximum area. What will this maximum area be?

[fluid flax]

i got witdh=10m and length=10m

can someone correct me if im right?

and the area=100m^2

[devout snow]

@fluid flax Has your question been resolved?

[fluid flax]

<@&286206848099549185>

[mint orbit]

Hi I’ll help you.

[fluid flax]

glad to hear that

[mint orbit]

Good job! 🙂

One thing to note is if you want to verify if something is a max or min without taking the second derivative then simply just examine the behaviour as I did by testing the instantaneous slope before and after the critical point

If f’ goes from - —> + we know its concave upwards therefore its a minimum

Conversely, if f’ goes from + —> - we know its concave downwards thus a maximum.

[fluid flax]

ok, tysm!😊

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[obsidian eagle]

how can i figure out a function of a parabola if i have 2 points that it travels through?

[timber pebble]

its not sufficient

a parabola is ax^2+bx+c

3 unknowns, so you need 3 points

[obsidian eagle]

this is what i have

[timber pebble]

idk how to interpret this

[timber pebble]

you cant figure out the parabola, but you can find one that works, its just not unique

[timber pebble]

heres the formula

so for two points $(x_1, y_1)$ and $(x_2, y_2)$ just solve the system \begin{align*} ax_1^2+bx_1+c &= y_1 \ ax_2^2+bx_2+c &= y_2 \end{align*}

[woven radish]

jan Niku

[obsidian eagle]

so this would be good?

[timber pebble]

so you can solve for 2, right?

you get C

but then you have an equation for unknowns A and B

[obsidian eagle]

yea, c=30, and what do i do afterwards

[timber pebble]

try to solve the other equation

[obsidian eagle]

so i get 90 000a+300b=60, and what then?

[timber pebble]

thats as much as you can solve it

this gives you a family of parabolas

because you only have 2 points

if it really doesnt matter which, you can elect a value for one of the coefficients

[south terrace]

how to solve this

[timber pebble]

and solve for the other

[south terrace]

?

how to get function from that

[obsidian eagle]

so for example, i can say that b=10?

[timber pebble]

sure

[obsidian eagle]

oh

wait a sec

nvm

thank you

[south terrace]

bro that is just not correct you get wrong answer

[timber pebble]

👁️

[south terrace]

try it yourself

[timber pebble]

it works fine?

https://www.desmos.com/calculator/phzbhzqjbc

https://www.desmos.com/calculator/mpd4j0wqyl

heres a more general one

[obsidian eagle]

how did you get that parabola?

how did you get B=0.8?

[devout snow]

@obsidian eagle Has your question been resolved?

[obsidian eagle]

no

[devout snow]

@obsidian eagle Has your question been resolved?

[obsidian eagle]

no

bro ghosted me

[devout snow]

@obsidian eagle Has your question been resolved?

[obsidian eagle]

noooo

bro ghosted me for like 2 hours already

[devout snow]

@obsidian eagle Has your question been resolved?

[devout snow]

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[jovial fractal]

why is the right rienmann sum correct but not the left

nvm im stupid

.close

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[violet zenith]

how do i determen?

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[junior cairn]

I need a quick help to solve this problem.

[mighty galleon]

Whats the whole question?

[junior cairn]

These are my working out (and attempt) on solving the questions.

[neat solstice]

what is the formula for decay you are using?

[junior cairn]

Final mass = 100 x (1-0.9)^t/10

[neat solstice]

have you heard of another formula before?

well

let's just say there is a way around this, but i dont think that is the purpose here

[junior cairn]

okay?

[neat solstice]

ok so, it says you have to estimate
so for that, i would just try out numbers for t and try to get close to 50

[junior cairn]

oh

[neat solstice]

also, for some clarity:
in your formula you are not using "half-life" you are using the time (10 years) it take for the substance to decay by 10%

[junior cairn]

yeah I realized that typo

oop....

[neat solstice]

and some other things:
there is another formula which we can actually derive from your formula

Let's assume after a certain time T (which will be the half time), the substance decayed by 50 percent, so we get:
$$N(t)=N_0\cdot (1-0.5)^{t/T_{1/2}}$$
$$N(t)=N_0\cdot 0.5^{t/T_{1/2}}$$
$$N(t)=N_0\cdot e^{\ln(1/2)\cdot t/T_{1/2}}$$
$$N(t)=N_0\cdot e^{-\ln(2)\cdot t/T_{1/2}}$$

[woven radish]

Martin

[neat solstice]

ok now it looks good

to find out the exact value for the half life T_1/2, we can now do
N(T_1/2)=0.5 N_0

(but that is not what you are supposed to do here, you should just try out some numbers)

sry for taking a little detour haha

[junior cairn]

I see

What's N_0 in this case? ;-;

wait

it's 100

[neat solstice]

N(t) is the amount of substance
N_0 is the starting amount, correct

[junior cairn]

I thought the rate was 0.9? ;-;

[neat solstice]

0.9 after 10 years

[junior cairn]

oh

[neat solstice]

actually

sry for the confusion, what we would actually want to do is use the 0.9

N(10)=0.9 N_0

[junior cairn]

Trial and error means that I have to keep guessing right?

[neat solstice]

yeah

you already got N(60)

and spoiler: N(70) is below 50

and yes, the middle is not a bad next guess

[junior cairn]

66?

[neat solstice]

with your formula:

,w 100*(1-0.1)^(66/10)

[woven radish]

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[junior cairn]

so it's correct...

[neat solstice]

well

its a good approximation

,w 100*(1-0.1)^(65/10)

[woven radish]

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[neat solstice]

,w 100*(1-0.1)^(65.5/10)

[woven radish]

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[junior cairn]

I mean, I could take 65, since it asks for nearest year

[neat solstice]

yeah true

btw

[junior cairn]

hm?

[neat solstice]

if we would go through with finding the exact value, we would get this

,w 100*(1-0.1)^(65.7881/10)

[woven radish]

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[junior cairn]

Those are quite a lot of calculations ;-;

[neat solstice]

yeah haha

[junior cairn]

Honestly

[junior cairn]

I cannot recognize what you are trying to do in here

me dumb

[neat solstice]

here, we derived another formula which takes in the half life
this one is usually used

in the picture you mentioned, we apply our knowledge N(10)=0.9 N_0
that gives us an equation where we can get the value of T_1/2 without guessing

[junior cairn]

I know this is dumb question to ask

how do I put that into the calculator? (Or is it NOT suppose to)

[neat solstice]

you mean the -10 ln(2) / ln(0.9) ?

[junior cairn]

uhhh....

Maybe way before that? ;-;

[neat solstice]

which equation did you have in mind?

[junior cairn]

I cannot translate all of these equations ㅠㅠ (aside from 'N(t)' being the final mass, N_10 being 100), I'm a bit confused on what e^ln(1/2) * t/T_1/2

[neat solstice]

ahh i see

have you heard of the exponential function?

ah wait

you have used ln yourself

so you must have used e^x before right?

[junior cairn]

If its for only when writing down my working out, I've never

What grade am I suppose to know this knowledge? ;-;

surely not 10th grade right???

[neat solstice]

well, we used N(t)=N_0 * e^( -ln(2) * t / T_1/2 )
as a stepping stone
we used the fact that we already know N(10)=0.9 N_0
in order to get T_1/2

and to in the end put it into the calculator, a good idea is to use brackets
my idea there is "better a bracket to many than one to few"

and i think your calculator should have a button "e^x" or "e^[]"

[junior cairn]

oh ye it does

[neat solstice]

and for ln, most have a button called "log_[] ()" and one called "ln()" or "ln x"
sometimes you can write "ln x" by pressing shift and the normal log one

[junior cairn]

mine already has natural log button, 'ln'

[neat solstice]

and if you are at home doing homework, you could also use WolframAlpha instead
idk what calculator you are using, some are more easy to understand

[junior cairn]

I'm using Casio, fx-82AU PLUS II

[neat solstice]

ah i see

oh thats a nice one though

it can write fractions etc nicely right? thats a huge win

[junior cairn]

ye! :D

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[maiden crescent]

How do I integrate this without expanding?

[supple knot]

why don't you want to expand

[full cosmos]

What about u - subs

[lilac pebble]

are you trying to solve the integral?

I CAN DO THIS

[maiden crescent]

I just need to remember how to do it without expanding in case I get a question with a higher exponent

[supple knot]

!xy

[devout snow]

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

[lilac pebble]

its just 0

[supple knot]

which one of these have higher exponents that you need to do

none of them look remotely related to 1b)

[supple knot]

which is what you asked here.

[maiden crescent]

I mean there’s this one but the function inside is linear so it’s easy

I’d just like to know how you do it without expanding in case unless in impractical or impossible

[lilac pebble]

does pascals triangle work?

[thin inlet]

u-sub

[maiden crescent]

How do you do that

[thin inlet]

https://tutorial.math.lamar.edu/classes/calci/substitutionruleindefinite.aspx

https://tutorial.math.lamar.edu/classes/calci/SubstitutionRuleDefinite.aspx

[thin inlet]

let u=(5-2x)

[crisp niche]

your exercises from the book show that they do not need to be calculated using substitution, I am speaking from a methodical perspective

[maiden crescent]

Ok thanks everyone

.close

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[patent marsh]

did you have an actual math question?

[supple knot]

just a spam. mods have been pingededed

[dire forge]

.close

Oh already closed

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[whole storm]

i need help on understanding the second question and how they solved n for 128 and how they found a1

for qusetion 2 please

[whole storm]

@blissful jasper

<@&286206848099549185>

[sage burrow]

144-128=16, 160-144=16, 176-160=16, ...

[devout snow]

@whole storm Has your question been resolved?

[blissful jasper]

We know the difference in this sequence we are just not sure how we would arrive at the first term of this sequence when we don't know how many terms are in the sequence.
<@&286206848099549185>

[sage burrow]

thats not solvable without additional info. maybe you should assume that the first element is not negativ or is greater 0, or ...

[blissful jasper]

Oh yeah sorry about that forgot to add where the first term is greater than or equal to zero.

My apologies.

[sage burrow]

so how many times can you subtract 16 from 128 then?

[blissful jasper]

8 times.

So their are 8 terms that came before 128?

[sage burrow]

i would say so.

[blissful jasper]

Thank you

This has been helpful.

.solved

Not how it works lol

[sage burrow]

type .close

[blissful jasper]

Ty

.close

[sage burrow]

maybe seaturtle has to cloes it.

[blissful jasper]

Oh yeah probably

@whole storm

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[vague obsidian]

i don't even know where to start : (

anyone wanna guide me?

[cloud remnant]

Do you know about $tan(x) = cot(\frac{\pi}{2} - x)$

[woven radish]

Shockshwat

[vague obsidian]

i know about it's degree version

is it the

cot(90-x)?

[cloud remnant]

yes

Put X = 1 and convert tan(89) (at the end of the series) to cot 1 and see what happens

[vague obsidian]

hmmm

tan 1, tan 2, tan 3, ..., cot 1

i don't get it, sorry

[cloud remnant]

What is tan1 x cot1

[vague obsidian]

1

oh

OH

so every pair

of first and end

is 1

so

since we're multiplying

the whole sequence

is = 1?

[cloud remnant]

Yes

[vague obsidian]

wait where did we get x = 1 tho

is it the "x as 1"

[cloud remnant]

i think so

[vague obsidian]

i see

so basically

y = 1?

[cloud remnant]

yeah

[vague obsidian]

wowwwwwwww

it's that easy

lol

[cloud remnant]

yep

[vague obsidian]

thank you

[cloud remnant]

np

[vague obsidian]

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[native trout]

(1st year undergrad LinAlg)
I've gotten this far with a) but can't work out how to actually deduce the basis. Does the relation at the bottom mean that B is a valid basis as you can simply use the same arbitrary constants but multiplied by -1 to span V, or have I completely misunderstood it?

[devout snow]

@native trout Has your question been resolved?

[native trout]

<@&286206848099549185>

[sand isle]

im tryna sleep bro

[sand isle]

Bro

Maths got self love now

I'm done

[native trout]

😭

[devout snow]

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[devout snow]

@native trout Has your question been resolved?

[native trout]

.close

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[spiral dagger]

find the constant term

can i simplify it to

(x^4-2x^3-9x^2+2x+8)(1/2) then get 4

[hasty saffron]

You needn't expand the entire thing tho

[spiral dagger]

why

but does it still work

[hasty saffron]

to get the constant term you can just multiply all the numbers together

[hasty saffron]

It does, yes

But it's longer

[spiral dagger]

2 x 1 x -1 x -4?

[hasty saffron]

Yes, do you see why tho?

[long elk]

Divide by 2?

[spiral dagger]

by a half yes

172

1/2

[spiral dagger]

because they cancel out and give 0

[hasty saffron]

No coz

[spiral dagger]

but

?

[hasty saffron]

While expanding, you multiply all the terms right? You can just filter out the terms which you're not multiplying with x

For example in
(x+2)(x+1), you do x(x+1)+2(x+1)

Now the first term after expansion will have some power of x, since you're multiplying with x

The second term after expansion won't have all terms in form of x

[spiral dagger]

Why can you do that

[hasty saffron]

Coz we are only after the constant term

And while expanding, you're multiplying terms with x in it, you can completely ignore that

[hasty saffron]

Now in this, that's possible only when you multiply (2)(1)(-1)(-4)

[spiral dagger]

then divide by half?

[hasty saffron]

Yeah

[spiral dagger]

can we call the fraction for a factor

1/2

[hasty saffron]

Factor of?

[spiral dagger]

or is term the right word

[hasty saffron]

1/2 is a constant term, yes

Which is multiplied

Not too much sure about the right term

[spiral dagger]

alright thx

.close

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[crude geyser]

Who can help

[crude geyser]

It is a paralellogram

[long elk]

Adjacent angles are supplementary

Opposite are equal..what help do you need in this lol

[crude geyser]

Finding the X and Y

[thin fern]

they just told you how to find x and y...

[crude geyser]

What?

[long elk]

NO OFFENSE but may i ask what grade you are in?

[crude geyser]

9

I got class with sophomore so is hard for me

[long elk]

Sorry pal, you need to think a little. Opposite angles are equal and adjacent ones is 180

[thin fern]

You mean opposite angles are equal

[crude geyser]

No I mean I gotta find the x and Y

Or is the answer is 180

[long elk]

Sry

[frozen aurora]

yes, they are giving you hints

what's the angle opposite to 56?

[crude geyser]

56

[frozen aurora]

like where is it

well yes but do you understand where it is on the diagram

[crude geyser]

Yea

The opposite angle

[frozen aurora]

so take the measure of that angle and set it equal to 56

and solve

[crude geyser]

Alr thx I was confuse thought it was 5b

[frozen aurora]

same lol

[devout snow]

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[jaunty niche]

Hey can you help me find the domain of this parabola. F(x) = (x+3)^2 / (x-1)(x+2). Would the domain still be all real numbers?

[long elk]

Yes, excluding 1 and -2

[jaunty niche]

Ok thank u!

[long elk]

Do you know why tho

[dense lynx]

by the way this is not a parabola

this is something we usually call a rational function

[long elk]

Hey, um do you know when we have such type of thing in integration...we divide it and put it in a form like Px + Qx/Fx or something?

[dense lynx]

oh what about it? 👀

[wooden veldt]

#help-1 dont intrude on others channels

[long elk]

Idk whats px, qx and fx are and frequently misplace quotient for remainder and stuff..

Sorry asked it out of blue...but i just wanted to know how to solve that type of problems

[lusty sapphire]

It's not a parabola, just fyi.

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[dense lynx]

so normally polynomial division f(x) divided by g(x) is done like this

f(x) / g(x)
is equal to Q(x) + R(x)/g(x)

f is dividend; g is divisor; Q is quotient; R is remainder

[dense lynx]

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[untold ridge]

Hi , I don't know what to do

[untold ridge]

I need the value of "A"

[devout snow]

@untold ridge Has your question been resolved?

[devout snow]

@untold ridge Has your question been resolved?

[frosty mantle]

can you elaborate

what do you mean by the value of A

what level of math is this

it would help to see the original question

[untold ridge]

mmm

tha question is in spanish

[frosty mantle]

still would be helpful

[frosty mantle]

what level of math is this

[untold ridge]

well, im at the academy, this exercise are pre-university

[frosty mantle]

like

algebra? or calculus?

[untold ridge]

It's trigonometry

[frosty mantle]

have you done calculus yet

[untold ridge]

nop

[red viper]

try manipulating with m^2 and A^2

[untold ridge]

thank you

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[fossil cobalt]

I dont understand how to choose what number goes where in the set equations

[devout snow]

@fossil cobalt Has your question been resolved?

[fossil cobalt]

<@&286206848099549185>

[uneven notch]

a,b both?

[fossil cobalt]

Yes please

I looked at the answer sheet but still understand why it was that answer

[uneven notch]

easy-to-understand approach will be

can you write down the general form of cubic function?

with the unknown coefficients

[fossil cobalt]

F(x) = ax^3 + bx^2 + cx + d

This one ?

[uneven notch]

yes

if zeros are 1,-2,-5 then F(1)=F(-2)=F(-5)=0

and you can get one more equation with y-intercept information

which would make you able to calc coefficients

this is easy-to-understand, hard to actually calc

[fossil cobalt]

Yeah

[uneven notch]

the easy-to-solve one is

if cubjc function has 3 zeros a,b and c

then you can write down F(x)=k(x-a)(x-b)(x-c) where k is unkown constant

[smoky nimbus]

It's easier to use the factored form of the equation, which is in the form of $f(x) = a(x - x_1)(x - x_2)(x - x_3) ...$

[woven radish]

CaptainNova22

[smoky nimbus]

Where x1, x2, x3 are the roots of the equation

Then you can use the y intercept to find a

[fossil cobalt]

Do i just plug in all the numbers and find a ?

[uneven notch]

y-intercept happens when x=0

so you can write "y-intercept is 10" as F(0)=10

[fossil cobalt]

Oh I see now omg thank you

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[fervent sundial]

Hi, could someone help me with how to do this?

[fervent sundial]

No clue where to start

[raven rover]

what does lcm of 2 numbers mean?

[fervent sundial]

well you pick out the highest power of each prime factor from the two numbers

[thin fern]

LCM is least common multiple

[thin fern]

You can use this as a strategy for this problem

[raven rover]

exactly and the lcm here is r²s⁴t² what now

try doing something with small numbers and let me know what you observe

[fervent sundial]

so:
q | p
1 | r^2s^4t^2
r | r^2s^4t^2
r^2 | r^2s^4t^2
.
.
.

do i just keep adding stuffs lol

[raven rover]

uh

[fervent sundial]

this was supposed to be like a table btw

[raven rover]

look

ill provide you a hint

$p = r^a \cdot s^b \cdot t^c$

[woven radish]

feirynatural

[raven rover]

$q = r^x \cdot s^y \cdot t^z$

[woven radish]

feirynatural

[raven rover]

the exponent of r,s,t doesn't exceed 2, 4 and 2 respectively

it can be either less or equivalent

now its time for you to make combinations

[fervent sundial]

what is a combinatorial argument for this?

(a,x) = (0,2), (2,0), (2,1), (2,2), (1,2), and (2,2)

[raven rover]

did you do it for rest or no

[fervent sundial]

I could yeah

but this is bruteforcing, no?

now i do the same for (b,y) and (c,z)

[raven rover]

this is how you approach these type of problems

[uncut crow]

[fervent sundial]

[raven rover]

and multiply the respective combinations you got

do for (a,b,c)

then (x,y,z)

and multiply the combi you get

[uncut crow]

i think something is being overlooked here..

[raven rover]

make sure to remove overlaps

[fervent sundial]

yeah

where's the math in this question

my computer can do this

faster than me lol

[uncut crow]

this isn't quite right, the exponent on e.g. r in at least one of p or q needs to be 2

[raven rover]

yea indeed

i miss wrote

I am not really sure what you mean by 'where is the math'?

its more like case work problem

[fervent sundial]

i'm lost

well i did it for (a,x), (b,y) , and (c,z)

i didn't but i'm guessing the pattern still holds

6,10,6 combinations for each tuple

what does "do for (a,b,c) then (x,y,z)" mean?

[devout snow]

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[fervent sundial]

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[spring sundial]

can someone please explain why they are able to sum over all the divisors

Basically, are they saying that $F(d)=\sum\limits_{e\mid d}F(e)$

[woven radish]

Kalgar

[spring sundial]

how?

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@spring sundial Has your question been resolved?

[supple knot]

how what

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[weak cove]

For context

[gritty rune]

Can I get some help with question b

[weak cove]

!occupied

[devout snow]

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).

[supple knot]

austin can't catch a break

[weak cove]

Why

Why me

always

[gritty rune]

bc u smart

[weak cove]

I was wondering if someone could check my proof for this part of the problem. I was wondering if I made it clear enough why what I was showing with the region Omega was clearly proving what I wanted to prove

[supple knot]

just close and reopen

[weak cove]

.close

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[weak cove]

.reopen

[devout snow]

✅

[weak cove]

For context

I was wondering if someone could check my proof for this part of the problem. I was wondering if I made it clear enough why what I was showing with the region Omega was clearly proving what I wanted to prove

I think this is called Gauss's theorem

if that matters to anyone

Also I guess if anyone could check my reasoning for part (d) that'd be great too

[weak cove]

and for this it might be nice to include the divergence theorem for your viewing ease

<@&286206848099549185>

[devout snow]

@weak cove Has your question been resolved?

[devout snow]

@weak cove Has your question been resolved?

[devout snow]

@weak cove Has your question been resolved?

[weak cove]

NO @devout snow

[wooden veldt]

Confused, looks like you're just assuming Ω is a sphere with boundary

[weak cove]

no omega is the region in between some outer region being whatever we want and the interior region just being some sphere about the origin

like R is the region I want omega to be I think

[wicked turtle]

in (d): "the divergence theorem does not apply"
in (e): "by the divergence theorem"
how to reconcile these?

[weak cove]

for the divergence theorem

[weak cove]

in part (e), the origin is not included

so the divergence theorem does apply, because that is the only place where it is not C1

all other criterion are met

[wicked turtle]

wait, what is Omega then

[weak cove]

Okay so Omega is supposed to be like

draw a wacky region right whatever you want

(containing the origin in its interior)

and now draw another region being a sphere about the origin

and omega is the region in between those two

and those are supposed to be S1 and S2

I think

that's what I was going for

[wicked turtle]

oh, it's not really stated well

[weak cove]

Right I think that's my problem

[wooden veldt]

Yeah you've just said omega is a sphere with boundary

[weak cove]

Idk how to say it

[wicked turtle]

you say at the top that Omega is a region whose interior contains the origin
but now you're saying it doesn't contain the origin

[wooden veldt]

Idk how else you would interpret writing omega as a union of a sphere and its boundary lmao

[weak cove]

I said it was a regular region with piecewise smooth boundary whose interior contains the origin ?

[weak cove]

interior meaning like

not included but inside of

[wicked turtle]

you mean complement

haha

[weak cove]

not quite

[wooden veldt]

You wrote Ω = S1 U S2 where S1 is a sphere and S2 is its boundary

[wicked turtle]

well either the origin is in Omega or it's in the complement of Omega

[weak cove]

no S2 is the boundary of omega

I will draw what I mean

one sec

[wooden veldt]

Which is now a sphere 😭

[wicked turtle]

So are you really forming some Omega-prime which is Omega setminus (ball centered at origin)?

[weak cove]

omega is in between the blue region and the red sphere

so the boundary of omega

is the boundary of the blue region

union with the boundary of the sphere

I think is what I mean to write

[wicked turtle]

or rather, i guess, Omega = R \ (some small ball centered at 0)