help-10

[worthy birch]

replace dx/(x+2) with du

[brave cargo]

So du is = dx ?

[worthy birch]

du = dx/(x+2)

@brave cargo

[worthy birch]

Oh

you meant that way

[brave cargo]

No wait

[worthy birch]

this is what you have to do

[brave cargo]

I

So the integral of u/(x+2) is u* Ln(x+2) right

[worthy birch]

you are getting it wrong

if you substitute dx = du*(x+2)

you have a variable x

and you are integrating with respect to 'u'

[brave cargo]

I dont understand what you mean

[worthy birch]

Hm

[brave cargo]

So its the last step im doing wrong ?

[worthy birch]

ye

we have this

[brave cargo]

Yes

Dx

We need somerjing for Dx

Which is du / x+2

[brave cargo]

Ohh

[worthy birch]

we took u = ln(x+2)

du = dx/(x+2)

replace those values

[brave cargo]

Sooo

I think u missed “u” in before Ln(x+1) right?

[worthy birch]

?

[brave cargo]

Wait I’m so confused

[worthy birch]

you get this integral

[brave cargo]

Yes

[worthy birch]

The thing is

[brave cargo]

But where is the u / x+2

[worthy birch]

you were substituing dx = du/(x+2)

but you are integrating with respect to u

you got a new variable

[brave cargo]

So this is wrong ?

We don’t integrate the bottom part?

[rocky pelican]

if you're integrating this in respect to u, u need to change everything in the integral that was x into u

[brave cargo]

First is the ln(x+2) is = u

[rocky pelican]

hang on

[brave cargo]

Then the integral of u / (x+2) is like saying u * ln(x+2)

So we have 2 of the ln(x+2)

[rocky pelican]

i think u do this question using by parts

[brave cargo]

No

Substitution

2. c

[rocky pelican]

i think ur supposed to make x+2 the u

not ln(x+2)

[brave cargo]

It says to the right substitute u=

If u look

U = ln(x+2)

Whyyy is this so hard 🤬

[worthy birch]

correct sub is u = ln(x+2)

[brave cargo]

How come du = 1?

[cinder wigeon]

He has taken u = x + 2

[brave cargo]

Yeeee

Okey!

Now i understand

[rocky pelican]

because derivative of x is 1

[rocky pelican]

i got lost here lol, u didn't make dx the subject of the u sub

[brave cargo]

Okey my bad

[rocky pelican]

no problem

[brave cargo]

But Now i get it! Thank you

[rocky pelican]

everyone make mistakes

[brave cargo]

🤣

Me espcially

.close

[obtuse pebble]

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[tiny zephyr]

is this correct what i am doing so far?

[high lily]

no

[tiny zephyr]

ok

this is what i have done

have i made a mistake in writing the first expression as a product of trig functions

[high lily]

that seems fine

[tiny zephyr]

the whole thing?

[high lily]

everything except for the last line

[tiny zephyr]

ah ok

i think i need to /2 first

or do i not move the sin5 to the rhs, and solve each term for 0, then combine them for general sol

[obtuse pebble]

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[tiny zephyr]

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[bleak mica]

i can tell what im doing wrong

[bleak mica]

its part (ii) i got the (i) correct

oh it shouldve been 6 + ln (√28/7) but i still don't get how to get the 16

[fathom light]

ln(4/√7)
2/2xln(4/√7)

Can you move ahead now?

[fathom light]

Also it will be 6+ln(4√7/7) , 4x√7 is not √28

[obtuse pebble]

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[bright bobcat]

I'm not sure what I am doing wrong

simplifying complex rational expressions

[ruby wyvern]

I would start doing that differently

i would make the denominator the same for the 2-2/a+3 and for the 1/a+3+ a/2

then you can use the "sandwich" rule

for example, you can write 2-2/a+3 as (2a+6-2)/a+3 => 2a+4/a+3

[bright bobcat]

where does the six come from

[ruby wyvern]

do you agree that 2 = 2a+6 / a+3

[bright bobcat]

I don't see how those two are equivalent

[ruby wyvern]

2 = 2 * (a+3)/(a+3)

since a+3/a+3 = 1

then they are euivalent

[bright bobcat]

Okay

[old lily]

what's 2 * (a+3)

[bright bobcat]

2a+6

[old lily]

what's $2 \cdot \frac{2}{a+3}$

[warm shale]

vie Torus

[bright bobcat]

4/2a+6

[old lily]

no

[bright bobcat]

what is it

[ruby wyvern]

imagine doing a fraction multiplication: 2/1 * 2/(a+3)

[bright bobcat]

right

4/(a+3)

[ruby wyvern]

yeah thats correct

[old lily]

what's $(a+3) \cdot \frac{2}{a+3}$

[warm shale]

vie Torus

[bright bobcat]

assuming its (a+3)/1 then it's 2(a+3)/(a+3)

[ruby wyvern]

try to simplify 2(a+3)/(a+3)

[bright bobcat]

2?

[ruby wyvern]

yep

[old lily]

what's $2(a+3) \cdot \frac{2}{a+3}$

[warm shale]

vie Torus

[bright bobcat]

4(a+3) / (a+3)

[old lily]

ambiguous

yes

(a+3) / (a+3) = ?

[bright bobcat]

1

[old lily]

4

[bright bobcat]

yes

[old lily]

what's $2(a+3) \cdot \frac{a}{2}$

[warm shale]

vie Torus

[bright bobcat]

2(a^2 + 3)/2

[old lily]

u sure?

[bright bobcat]

not exactly

2a(a+3)/2

[old lily]

$$ \frac{2a(a+3)}{2} $$

[warm shale]

vie Torus

[bright bobcat]

oh so it's just (a+3)

[old lily]

$$ = \frac{1}{2} \cdot 2a(a+3) $$

[warm shale]

vie Torus

[old lily]

wrong

[bright bobcat]

is it (a^2+3)

[old lily]

how

[bright bobcat]

distributing the a after dividing by 2

[old lily]

ok what do u get after dividng by 2

[bright bobcat]

a(a+3)

[old lily]

k then distbute

[bright bobcat]

this is where i am confuses is it (a^2+3) or is it just (a+3) or is it (a^2+3a)

[old lily]

you need to know how to distribute

x*(y + z) = x*y + x*z

[bright bobcat]

(a^2+3a)

[old lily]

yep

i think u might understand enough to retry ur question

[bright bobcat]

okay i will retry my question

[obtuse pebble]

@bright bobcat Has your question been resolved?

[bright bobcat]

<@&286206848099549185> i am still struggling with this problem

[ruby wyvern]

hey

[bright bobcat]

Hallo oliv

[ruby wyvern]

remember that 2 = 2*(a+3)/(a+3)?

substitute the 2 in the problem with 2*(a+3)/(a+3)

its still equivalent

2*(a+3)/(a+3) can be writed as 2a+6/a+3

then you will get the expression 2a+6/a+3 - 2/a+3

which is 2a+4/a+3

agree?

[bright bobcat]

yes

[ruby wyvern]

ok, now lets make the denominator the same for this part

we want 2(a+3) to the the denominator for both terms

we should do something with the a/2

since a+3/a+3 = 1, then its true that a/2 = (a/2) * (a+3/a+3)

which is a(a+3) / 2(a+3)

then, we also need to rewrite the 1/a+3, which can be writed as 2/2(a+3)

now, as both terms have the same denominator "2(a+3)"

wen can add them together

[ruby wyvern]

this expression id equal to a(a+3)+2 / 2(a+3)

now you can use the sandwich rule

(2a+4 / a+3) / (a(a+3)+2 / 2(a+3))

which is equal to this by that rule: (2a+4)(2(a+3)) / (a+3)(a(a+3)+2)

then you can cancell out some factors such as a+3

you will get something like 2(2a+4) / a(a+3)+2

u can leave the answer like that, but it also can be expanded

[bright bobcat]

i'm not exactly sure how we got 2(2a+4) / a(a+3)+2

[ruby wyvern]

im not sure if you are allowed to use this, but...

https://es.symbolab.com/ a calculator for algebra

[old lily]

i think u should do easier questions on algebraic manipulation

[bright bobcat]

this is the work i have to do for my class and it's due tonight. (I am allowed to work on it with other people btw)

i would rather get help at my college campus instead but its closed on sundays

[old lily]

depending on how far tonight is for u...
you know what they say, it's better to sharpen ur axe before u cut the tree

[bright bobcat]

well it's 2:40pm and it's due at 11:59pm

[old lily]

like 2hours sharpening + 1 hour cutting vs 4 hours cutting

[bright bobcat]

we went from factoring polynomials to this

what do you suggest

[old lily]

when u do questions don't guess

make sure ur absolutely sure that smth is true

then like work backwards on what u don't understand

[bright bobcat]

i haven't had to work with fractions in a long time

so i forgot a lot of how it goes

[ruby wyvern]

btw, here is a solution step by step by symbolab: https://www.symbolab.com/solver/step-by-step/\frac{\left(2-\frac{2}{a%2B3}\right)}{\frac{1}{a%2B3}%2B\frac{a}{2}}

it might be in spanish cuz its my first language

[old lily]

change es to en

[bright bobcat]

.close

[obtuse pebble]

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[tender hull]

Hi, I am a physics 110 student. I do not know how I got these two questions wrong and have been at it for a while. Can anyone help?

[orchid wind]

south does not always equal down

let me draw

[tender hull]

I had originally said down but it was counted wrong. I get three tries
Edit: OH, it only counts it right if both answers are correct. Mb

[orchid wind]

ye

i dont think its 48

[tender hull]

What I did was divide the weight by earth's g and then multiplied by Mars's g

What would you suggest?

[orchid wind]

find mass of box

on earth

oh

does it give you conversions

for lbs into newtons

and g on mars

or what

[tender hull]

I believe g on Mars is 3.72

and then a pound is about 4.45 N

Would the mass of the box on Earth be about 66.77kg?

[orchid wind]

you just do something lke

Weight on mars= weight on earth x gMars/gearth

[tender hull]

🤦‍♂️

[orchid wind]

so its just

[tender hull]

It was that simple

Let me see here

[orchid wind]

nvm i dont lioke that method

just convert lb into newtons

and find mass of box

and find weight of box in lbs on mars

and convert back to lb

[tender hull]

Imma try that

654.03N, mass=654.03N / 9.8m/s^2=66.77kg
66.77kg x 3.71m/s^2=247.17N
247.17N=55.56lbs?

[orchid wind]

ye its something like that

kind of bs question tho bc if u round anywhere

ur kinda screwed

[tender hull]

yeah

thanks for your help!
]

[obtuse pebble]

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[safe rampart]

Can someone help with this question

[safe rampart]

.close

[obtuse pebble]

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@remote coyote Has your question been resolved?

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[fringe canyon]

why doesnt my approach work the answer was supposed to be 75/4

[obtuse pebble]

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[exotic drift]

Is it possible for a system of two differential equations to have infinite number of repelling equilibrium points and no other equilibrium points at all?

[obtuse pebble]

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[forest sphinx]

Need help, dont know how to do this

[obtuse pebble]

Please don't occupy multiple help channels.

[lean yarrow]

Bruh is it occupied

Dang it☠️

[lost fjord]

yeah, @forest sphinx is occupying two channels?

#help-0 #help-10

[forest sphinx]

i dont see it

ok so i go there?

to 0?

[lost fjord]

its fine all g

[forest sphinx]

oh nevermind i found it thank u

[lean yarrow]

Can u close this one then I also need help lol

[lost fjord]

for this problem just fill in the values for A,B,C and check them

[forest sphinx]

do i say .close?

[lost fjord]

for each combination

[unreal musk]

(Also make sure you expand the math help to show all channels, so the arrow's pointing down like this)

[forest sphinx]

got it

.close

[obtuse pebble]

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[lost fjord]

but first check if consistent

[lean yarrow]

Alr

[unreal musk]

You'll still need to get a new one from the available section (but there aren't many atm )

[obtuse pebble]

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[fathom kindle]

Data management gr 12

this is the answer key

I dont understand how u get those numbers in column F

for row 11

TSSS = (.4)(0.45)(0.50)

i understand that, but i dont get the other rows

[obtuse pebble]

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.close

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[limpid hound]

Why does this show up as undefined?

[limpid hound]

Oh wait nevermind

sorry inequality

.close

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[timid silo]

Is this Right?

[obtuse pebble]

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[cunning citrus]

i drew the diagram is this right

[azure wraith]

Ye

[obtuse pebble]

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[honest flicker]

omg i forgor how logs work

[iron edge]

Damn

[upper shuttle]

ln(ab) = ln(a) + ln(b)

[honest flicker]

help

[rocky pelican]

negative infinity

[honest flicker]

wat is ln again

[dim yacht]

the natural log

log base e

[honest flicker]

wat does a log do

something withe exponents

like wat does it equal

[dim yacht]

it's the inverse of exponential functions

[honest flicker]

so like

it's e^(x^2-9)

[dim yacht]

no

[honest flicker]

oh

e^y = x^2-9

[dim yacht]

I lied nvm

lol

[dim yacht]

you just have to know what a log looks like graphically

and what it's behavior is

on a graph for this question

at least that's the only way I could solve it

[honest flicker]

Noo

[dim yacht]

put it into desmos

graph it

[honest flicker]

That's cheating

[dim yacht]

well you'll have to know what it looks like at some point lol

[honest flicker]

It is no calculator allow

It says to solve them without it

[hidden compass]

Well, either you know the behaviour or log or you can't do this exercise 😅

You can deduce it by the property of the exponential function, if you want

But I strongly suggest you to learn logs very well, properly

[honest flicker]

help

[hidden compass]

Look for the graph of a log

With base e

[honest flicker]

im not supposed to use a calculator

how to solve it with algebra

[chrome compass]

you are supposed to know what the graph of log(x) looks like

[hexed river]

,w plot ln x

[warm shale]

Results provided by WolframAlpha

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

Requested by ginger4557

[obtuse pebble]

@honest flicker Has your question been resolved?

[honest flicker]

idk wat to do now

[hexed river]

there are multiple ways

what would you say ln(x^2 - 9) is at x = 3

[honest flicker]

ln(0)

that is liek

undefine rightt

[hexed river]

yeah

[honest flicker]

Fr

[hexed river]

and now you want the limit coming from the positive side

and you can look back at the graph again if it helps but yeah

you basically have the answer almost

[honest flicker]

it's liek almost 0

i think

ln(almost 0)

[hexed river]

yeah

[honest flicker]

so liek it goes to neg inffinity

[hexed river]

ln(almost 0 but positive)

[honest flicker]

Fr

[hexed river]

perfect

[honest flicker]

Ty

.close

[obtuse pebble]

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[quiet moss]

Kind of physics but need help

[quiet moss]

It’s not homework

It’s practise questions for an aptitude test

[obtuse pebble]

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[upper shuttle]

why is the Frobenius map an automorphism?

[upper shuttle]

in a finite group

[kind hawk]

you mean a finite field?

which part of the word automorphism are you not sure about

[upper shuttle]

yea finite field

no im not sure how to show that it is a bijection

[kind hawk]

you can give the inverse

[upper shuttle]

hm im not sure how to

thank you dena

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[keen tiger]

If this is the "circulation" around a circle C_R

Am I right in thinking that this is the total distance travelled by a particle as it moves through the circle

And also am I right in thinking that the total time it takes for that particle to traverse the circle is the integral $t = \int \frac{1}{u \cdot \theta} d\theta$

[warm shale]

trayan_b

[keen tiger]

im working in polar coordinates r,theta

[obtuse pebble]

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[edgy needle]

for this graphing question

do i find the turning points x intercepts by differentiating and making it equal 0

[rocky pelican]

that will find the local max and local min

[edgy needle]

and then i find the y intercepts by subbing back into original equation?

[rocky pelican]

you should work out the zeroes first

then find the turning points

and the point of inflexion

[edgy needle]

whats a point of inflexion

[rocky pelican]

the point where the curve's concaveness changes

that is when teh second derivative is 0

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[exotic knot]

I'm kind of curious what I'm doing wrong

Apparently, the answer is incorrect

[fathom light]

Can you show your work?

[coarse void]

it should be 9/10 pi ig

[exotic knot]

hang on, i'll try reworking it

9/10 Pi worked

how though?

[coarse void]

r=h/root3

v=(pi/9)*h^3

differentiate

[fathom light]

@coarse void Stop giving answers buddy, try to guide the person

You have done same in another channel

[coarse void]

oh sorry, new to this channel

[fathom light]

Guide them how you find relation between h and r

So that they can understand

[fathom light]

No worries

[exotic knot]

wait why is r = h/root3?

[coarse void]

equilateral triangle, use trigonometric relations

[exotic knot]

oh wait

i misread the question

makes sense now

i thought the equlateral one was the halfed triangle

thanks!

.close

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[magic locust]

Is there a strict format for how these should be represented? Can I simply write "∀e ∈ R n e > 0, En : 1/n < e" Does this mean the same thing? is there a better way to write it?

[rocky nymph]

∀e ∈ R n e > 0
what is the "n" before epsilon?

[magic locust]

and (intersection) is what i meant

[rocky nymph]

i would write

$\forall \epsilon \in (0, \infty)$

[magic locust]

I'm not sure of the notations to write or anything here tbf, google showed three notations for such that

[kind hawk]

nah

[rocky nymph]

or $\forall \epsilon \in \mathbb{R}^+$

[warm shale]

woomy

[rocky nymph]

but thats personal preference

[dry flint]

i use this one

[kind hawk]

R^+ is bad notation cause its also often used to include 0

just write eps > 0

[magic locust]

Hmm I wasn't sure if it could be written like that here, tbh i don't even understand the question i assume i am just simply supposed to write it down in tis manner right?

[magic locust]

oh hmm

[rocky nymph]

yea thats true

[drifting badger]

ε can't take on the value ∞.

[rocky nymph]

thats why its best to avoid it, or write $\mathbb{R}^*_+$

[kind hawk]

thats even worse

[warm shale]

woomy

[rocky nymph]

idk we learnt that notation for specifically not including 0

[kind hawk]

well ok with the star at the top, yes

[rocky nymph]

yea i fumbled

[kind hawk]

if you want some notation with the R, I'd recommend $\bR_{>0}$. its very clear

[warm shale]

Denascite

[rocky nymph]

why not this?

[rocky nymph]

that works better yea

[warm shale]

woomy

[magic locust]

There's no strict format to any of these right? As long as it conveys the message it is correct?

[rocky nymph]

im stupid i included infinity

lol

[rocky nymph]

practically yes

but there are different conventions

[magic locust]

Oh hmm

[rocky nymph]

as you want to be as clear as possible

[magic locust]

Yep 👀

[rocky nymph]

but i think that you can also just say for all epsilon > 0

without specifying in R

in majority of the cases

but maybe here you would preffer to specify

[magic locust]

hmm the sentence they gave specifically mentioned R so i assumed i would need to include all the info

[rocky nymph]

yea its better

[dry flint]

in my intro proofs classes they all use epsilon > 0 if that means anything

[rocky nymph]

I would probably write the following \
${\forall \epsilon \in \mathbb{R}_{>0} \exists n \in \mathbb{N} : \frac{1}{n} < \epsilon}$

[warm shale]

woomy

[rocky nymph]

sorry im horrible with latex

[drifting badger]

Well, it's a "write it as predicates and quantifiers" not "write it as the most standard predicates and quantifiers". So yes. Use what you want that conveys the message clearly.

[magic locust]

Oh hmm

[magic locust]

Also would i have to mention "∀e : e ∈ R n e > 0, En : 1/n < e" or is it already implied in the first case 💀 (They didn't really take much for us tbh, roughly a hour and half on this topic.)

[rocky nymph]

but other ways are: \
${\forall \epsilon \in (0;\infty)\ \exists n \in \mathbb{N} : \frac{1}{n} < \epsilon} \$
${\forall \epsilon > 0\ \exists n \in \mathbb{N} : \frac{1}{n} < \epsilon} $

[warm shale]

woomy

[rocky nymph]

i think having two ":" is abit overkill

[magic locust]

Yep hmm

[rocky nymph]

just directly specify what the conditions are

[drifting badger]

Most standard would probably be $\forall \varepsilon > 0, \exists n \in \mathbb{N}, 1/n < \varepsilon$.

[magic locust]

realistically all of them mean the same thing? in the first case would the forall quantifier apply to the second e? 🤔

[magic locust]

Oh hmm

[rocky nymph]

wouldnt you use : or | instead of the second comma?

[rocky nymph]

which case?

[magic locust]

Was about to ask that if the coma could be taken in the same meaning hmm

[rocky nymph]

tbh ive never used the comma so im not sure what it means, usually for "such that" i (personally) use : or | and i just use the commas so you can read set builder notation as you would read normal language

[magic locust]

∀e ∈ R n e > 0 (How there's the forall quantifier for the first e and then it repeating without it) though i guess realistically all of them mean the same thing idk, thanks though

[drifting badger]

https://tenor.com/view/no-no-gif-26414895

[magic locust]

Does the coma read as anything or is it just a separator?

[drifting badger]

We are not doing set builder notation.

[drifting badger]

Usually just read as "such that". Some people write "s.t.".

[rocky nymph]

oh yea

ohh i was confusing

[magic locust]

oh

[rocky nymph]

i was mixing the two

[magic locust]

is the colon usable here? or is it just for set builder?

[rocky nymph]

do you mean $\forall \varepsilon \in \mathbb{R} \land \varepsilon > 0$?

[warm shale]

woomy

[magic locust]

Hmm how there's the for all quantifier on the first epsilon and that it didn't apply to the second one, that's why i asked if i should have added the additional such that at the beginning~ Though i am fairly sure it makes no difference and i am just being idiotic

thanks though

✨

[rocky nymph]

sorry im back

no its fine

its the same variable

so you dont need to specify anything

but it reads weird to me

[magic locust]

hmm 👍

[rocky nymph]

thats why maybe you should just merge the two

and right $\mathbb{R}_{>0}$

[warm shale]

woomy

[rocky nymph]

write**

im stoopid

[obtuse pebble]

@magic locust Has your question been resolved?

[magic locust]

Why does it use implication in the first premise and then use and in the second case despite their sentences being identical, Can you write down implies as and in some manner? 🤔

"Mangoes are not sweet" can be writen as "M(y) -> -S(y)"

Actually nvm

Flowers are red can be written as F(x) ^ R(x) right?

[obtuse pebble]

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[sturdy plover]

Can anyone help me solve this?

[marsh geyser]

Solve?

[sturdy plover]

Like get a simpler form

[marsh geyser]

What have you tried?

[sturdy plover]

This is what I got

Idk what to do forward

[sturdy plover]

U still here?

[marsh geyser]

I would take a different approach

Can we go back to the beginning?

[sturdy plover]

Sure

[marsh geyser]

Do you agree that $1 = \sqrt[3]{1}$

[warm shale]

Samuel

[sturdy plover]

Yh

[marsh geyser]

Ok so we can cube the whole expression first

To get rid off cubic root

So you get $\frac{1}{\sqrt{5} - \sqrt{2}}$

[warm shale]

Samuel

[marsh geyser]

Agree?

[sturdy plover]

Yup

[marsh geyser]

Ok rationalize that

[sturdy plover]

Done

[marsh geyser]

Qhat u got

[marsh geyser]

Ok

We cubed the original

So now we need to undo that

Cubic root the whole expression

[sturdy plover]

Like this?

[marsh geyser]

Yes, but only one whole big cubic root

[marsh geyser]

Yes like this

You finished

You can rewrite that if you want like this $\sqrt[6]{\frac{7}{9} + \frac{2 \sqrt{10}}{9}}$

[warm shale]

Samuel

[marsh geyser]

But is not necessary

[sturdy plover]

Think I can leave it like this for now just to not make things harder

[marsh geyser]

U you reslize

The only thing i did after that is

Splitting inside cubic root in two fractions

And put the 3 inside the sqr root

But don’t worry too much about that

Now lets check if we did anything wrong

,w is 1/(sqrt5-sqrt2)^(1/3)=((sqrt5+sqrt2)/3)^(1/3)?

[warm shale]

Results provided by WolframAlpha

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

Requested by _arkimond_

[marsh geyser]

Perfect

[sturdy plover]

Nice 😃

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[upper shuttle]

how do i list all groups of order 16

[upper shuttle]

https://www.youtube.com/watch?v=TFl_dw6_pbI&list=PL8yHsr3EFj51pjBvvCPipgAT3SYpIiIsJ&index=18

i got this from this video

however what happens if say Z4 x Z4, are both not normal subgroups of G?

also is there a systematic way of doing it? whats the name?

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[slate basin]

Suppose that I have a polytope

$\mathcal{S} = \left{ \text{diag}(k) \cdot x \mid k \in [\eta_1, 1] \times \cdots \times [\eta_n, 1] \right}$

where all $\eta_i \in(0,1]$ (known)

I need to define sufficient conditions so that

$ \mathcal{S} \subset C$

Where C is a convex set. Is the only method to do it verifying that all the vertices of S are in C? Is there any more efficient method?

[kind hawk]

$ around the latex bits

[warm shale]

Drun

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[pastel sphinx]

Plot the points on a graph, draw a line between all the points

count everytime there's a change in direction

[honest flicker]

Umm im supposed to use intermediate value theorem

[unreal musk]

In which case, how many times do you change from positive to negative, or vice versa?

[honest flicker]

liek 2

[unreal musk]

Do you have all of them? where are those changes you've spotted?

[honest flicker]

Oh 3

[unreal musk]

Yep

So each of those points, because you're continuous, IVT says you take all intermediate values in between those changes... including 0

And of course, you're at rest when your velocity is 0

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[void quartz]

intersecting chords theorem

[obtuse pebble]

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[faint gorge]

hi, i have a exam tommorow and i need help studying (its on quadratics)

[faint gorge]

im tryna get a 70 atleast

here are the topics 1. Using first or second differences to determine if a relation is linear or quadratic.
2. From a factored equation, find the zeros or x-intercepts, the axis of symmetry, the vertex and graph the parabola.
3. From a given parabola, find the key features such as vertex, the axis of symmetry, the direction of opening, state the max or min
value, the y-intercept and the x-intercepts.
4. Given the key features like above in #3, use them to draw the parabola. A grid will be given.
5. Determine the equation in Factored Form of a quadratic relation given the x-intercepts (zeros), vertex, a point, and/or the y-intercept.
.
6. Application (word problems) of quadratic relations. .
7. Changing a quadratic equation from Factored Form into the Standard Form. State the y-intercept of the relation.

[subtle sinew]

Try using khan academy

[faint gorge]

i used that when i was a kid didnt really learn anything from it tbh

is there any other tips for studying?

[subtle sinew]

Look back at your notes

Do practice problems

I suggested Khan because it has good practice

[faint gorge]

can you help me with each topic?

i dont know how to do most of them

[subtle sinew]

No because I don't have time to help with all that, and probably others too. If you have specific problems that you get stuck on, ask that and someone can help

[faint gorge]

oh ok

[subtle sinew]

But do what I suggested, look at your notes, look up videos, use khan for practice problems

[faint gorge]

yup forsure

<@&286206848099549185>

can someone help on all of them tho

[obtuse pebble]

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.

[obtuse pebble]

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[fast vale]

.

With

[fast vale]

I dont understand the delta A/A part, Im just following my lecture notes

But I dont know how to solve the problem as a whole

<@&286206848099549185>

[dim root]

I assume the shape is a sphere.

If so make an equation where you get the rate of volume change and surface area change by change in r
And then you can understand your prof proof

Next time please type the question down in letters. Pictures are hard to read when they are written by a drunk doctor

[fast vale]

I think proofs are higher level math than this, this questions is supposed to be similar to this

[obtuse pebble]

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@fast vale Has your question been resolved?

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@fast vale Has your question been resolved?

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[fathom flicker]

I want to use that R is commutative to say this sum is equal to swtiching adj(M)(i,j) * M(1,i) in the summand
so this is equal to adj(M)_(i,j)M
but I am confused, because just because M is a matrix over R, and R is commutative, doesn't mean that matrix multiplication commutes
but it seems like this would imply that it does
what is going on?

M is a matrix over the commutative ring R

and adj(M) is the adjoint matrix

nvm I see

.close

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[twilit quiver]

Any way to remember the trig ratios quick?, aside from the trig hand trick

[high lily]

hand trick is pretty good
what are you expecting?

practice and use them enough and you'll know without looking

[twilit quiver]

Hmm alright

But what if I'd need to go above

90

Is it where I use the reference angle?

[high lily]

yes

[twilit quiver]

Do you perhaps have any resources / videos on more in-depth abt the 6 trigonometric ratios?

Due to the limited schedule my teacher usually just skims through it, without giving any background knowledge

[obtuse pebble]

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[civic kettle]

I'm not certain but

If 13.5 mg = 5ml

and a guy needs 46 tablets of 13.5 mg

Then total ml should be 5×46?

Forget what I said then

Let me see

If this is correct

The answer is around

183 after rounding off

Uh I see

I probably can't think of this question through now

I'm no help

You can wait for other helpers or ping them after 15mins

[obtuse pebble]

@ripe hare Has your question been resolved?

[civic kettle]

You can just send it

I'll reply if I can help

[obtuse pebble]

@ripe hare Has your question been resolved?

[opal gyro]

What do you think the answer is?

Oh, this looks like it's for an exam? Or homework?

[opal gyro]

how do you think you would go about solving the first fill in the blank?

[obtuse pebble]

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[hardy scroll]

how do u derive this

[fathom light]

Do you mean how do you find derivative?

[hardy scroll]

yes

[teal turret]

ln y = 5ln(3x^2 -5) - 0.5ln(6x+1)
y' = y[(30x/(3x^2 - 5)) - 3/(6x+1)]

[hardy scroll]

is this the final answer?

i thought you use quotient rule

[teal turret]

i used logarithmic differentiation

u dont have to use quotient rule

[hardy scroll]

oh im not on that yet 😭

ty tho

[teal turret]

are u allowed to use it even if u havent learned it

if not, just do quotient rule

[hardy scroll]

no i think i can only use quotient, product, chain, and power

[teal turret]

👍

[hardy scroll]

its confusing with quotient rule tho cuz im left with a fraction on the numerator and im not sure how to remove that

[teal turret]

show me ur work

[hardy scroll]

alr one sec

[teal turret]

alr lemme take a look

yes so what you have done so far is correct

now what fraction are u referring to

u should do some simplification and factoring btw

[hardy scroll]

this one, doesnt it become 3/(6x+1)^1/2

[teal turret]

wdym by 'become

[hardy scroll]

not become but like doesnt it basically mean that it is a fraction when its raised by ^-1/2

[teal turret]

yes, thats an equivalent form

but before we deal with that

can u do some factoring and simplification of the answer

for example the denominator

what does that simplify to

[hardy scroll]

wouldnt the exponent just become 1?

[teal turret]

sorry i didnt see this

but yea

and then factoring in the numerator, we'd get

$\frac {3(3x^2 -5)^4[10x(6x + 1)^{0.5} - (3x^2 - 5)(6x+1)^{-0.5}]}{6x+1}$

[hardy scroll]

ohhh

would that be the final answer?

[obtuse pebble]

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[coral cloak]

Assume there are 1000 people in a room. If the probability that you're born in any day of the year is 1/365, what's the probability that exactly two people share their birthday in this room?

[coral cloak]

Note this is different from the probability that at least two people share their birthday

I tried calculating the probability that two random people share a birthday, 1/365 x 1/365

And then multiplying that by the number of possible pairs with 1000 people

1000*999/2

But the end result is larger than 1, can't be right

[sudden wadi]

what did you get for this

[coral cloak]

0.0000075

[obtuse pebble]

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[obtuse pebble]

@coral cloak Has your question been resolved?

[obtuse pebble]

@coral cloak Has your question been resolved?

[obtuse pebble]

@coral cloak Has your question been resolved?

[void quartz]

i found 24.258%

if you have the answer, tell me if its correct or not

if it actually is, ill explain how i got it

[obtuse pebble]

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[tawdry vortex]

hey

would g be positive here

since the ball is going down

but to be honest i like making my y coordinate upwards

[tame python]

then youll have to choose a side
if y points upwards, g accelerates in the opposite direction, so negative acceleration
if y points downwards, g accelerates in the same direction, so positive acceleration

[tawdry vortex]

so

g will be negative for me always

aslong as i do upwards y

[tame python]

yep

either that or you can manually insert in - signs into all your questions and have g itself be positive

so instead of like "F = mg", youd have "F = -mg and g is positive"

or instead of "a = g", youd have "a = -g and g is positive"

this also isnt really a good choice since you have to manually write in the - sign anyways

[whole forum]

the = or - sign is only usually there to show direction (in mechanics), so when the question asks for magnitude it doesnt rlly matter which you use, remove it anyways

heavy emphasis on mechanics only

[tawdry vortex]

thnx

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[lost steeple]

I wan tot negate this statement "I have a friend all of whose former boyfriends had at least two siblings with exactly three different vowels in their name."

The answer says the negation of this statement is:

"Each of my friends has a former boyfriend who had at most one siblings with exactly three different vowels in their name."

I don't understand why "exactly three different vowels in their name" written as "more or less than three vowels in their name".

[tepid yoke]

Opposite of exactly is not exactly, or equivalently, more or less

[obtuse pebble]

@lost steeple Has your question been resolved?

[lost steeple]

what is the opposite of exactly then?

[obtuse pebble]

@lost steeple Has your question been resolved?

[balmy beacon]

the opposite of having (exactly) 3 vowels in your name is having any number of vowels in your name which isn't 3

"exactly 3 vowels" : vowels = 3
"more or less than 3 vowels" : vowels =/= 3

[lost steeple]

the answer is “each of my friends has a former boyfriend who had at most one siblings with exactly three different vowels in their name”

apperanlty we dont negate exactly in this sentence

i want to know why

[balmy beacon]

oh nvm i read it wrong💀

[lost steeple]

lol its ok

[balmy beacon]

i think (sibling(s) with exactly three different vowels in their name) is its own object in this case

[obtuse pebble]

@lost steeple Has your question been resolved?

[lost steeple]

but how do i know that

how can i figure that out on my own

[obtuse pebble]

@lost steeple Has your question been resolved?

[obtuse pebble]

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[timid silo]

i need help with this question

[trim lily]

sure

[scenic vapor]

Do you remember the range of arctan(x)?

[timid silo]

yess
-pi/2 to pi/2

[scenic vapor]

now what is [-pi/2] and [pi/2]

[timid silo]

-2 and 1

ohhhh

i think i got it now?
like it'll be -2, -1, 0 and 1
there's no range given in the options so those elements listed in the options are the best options

i hope my conclusion isn't wrong
thank you

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[river abyss]

could i have help with this question please

[fathom light]

Do you have a visual of what the question is saying?

I mean do you understand it visually

[river abyss]

yeah i do

i visualised it with paper

i just don’t get how to calculate the numbers

[fathom light]

Breadth= x-10

For first case 
Length of rectangle= circumference of cylinder 
(So find radius in terms of length)
Breadth= height of cylinder 

For second case 
Breadth of rectangle= circumference of cylinder 
(Find radius in terms of breadth)
Length = height of cylinder```

[river abyss]

could you explain a bit more please

[fathom light]

Let's take the first case , when you fold the rectangle along the length
The length will become the circumference of cylinder ends
And the breadth of rectangle will become height of cylinder. If you have understood it visually maybe draw a rectangle and then draw a cylinder that way it is easy to understand

See this @river abyss

First case

[river abyss]

yes

[fathom light]

Can you see breadth became height of cylinder

And length of rectangle is circumference

[river abyss]

yes I can see that now that part

[fathom light]

Now we assume length= x, so we can write
x = 2πr
r = x/2π

And breadth was x-10
So h = x-10
Now use the volume of cylinder formula

[obtuse pebble]

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[obtuse pebble]

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[edgy egret]

Hello, can someone help me with this question?

[edgy egret]

I keep getting 2alpha instead of alpha

[light flume]

i need a sanity check

|a| < a

[fossil crag]

|a| < alpha

[light flume]

oh

jesus my eyesight is bad

[fossil crag]

and triangular inequality won't help you to prove this

[brazen gorge]

show your work

[edgy egret]

Yes, it would be useful if I was trying to prove the implication in the opposite sense.

[edgy egret]

Hold on.

I think I need to separate the cases.

Like if |a|<alpha/2....

[fossil crag]

not those cases

more like

if (a+b)/2 > 0...

or if (a-b)/2 < 0...

[edgy egret]

Let me try that.

[fossil crag]

(you have 4 configurations)

[edgy egret]

Yes, thank you.

I got it.

[obtuse pebble]

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[lunar nymph]

For sequence a(n)=[2a(n-1)-1]/3, a(0)=4x-3, Rewrite a general formula

[obtuse pebble]

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[quartz idol]

.rotate

[quartz idol]

Thx

Idk where to start with this question

[frigid burrow]

Multiply by d

[timid silo]

find relation between them

[frigid burrow]

(common difference)

[timid silo]

yea or that

[quartz idol]

Will expanding on both sides work?

[timid silo]

no

[frigid burrow]

Show your work

If you are talking about taking LCM then pls no

[frigid burrow]

Good thinking

But instead multiply by d

Then say that d = a(r+1) - ar

[quartz idol]

Wat bout using Sn

[frigid burrow]

You don't need Sb

Sn

[quartz idol]

Ah ok

I think I get it

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[rose night]

<@&286206848099549185> I need help with a problem

[rose night]

Please prove all even numbers can be expressed in the form of 6x+6y+2 or 6x+6y-2 or 6x+6y

Please send me a help

[scenic vapor]

Case 1: If the even number is divisible by 6 then it can be written as 6x+6y,

Case 2: If the even number divided by 6 and has the remainder 2 then it can be written as 6x+6y+2

Case 3: If the even number divided by 6 and has the remainder 4 then it can be written as 6x+6y-2

[frigid burrow]

!15m

[obtuse pebble]

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.

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[rose night]

hey but i tried it and they said i need proper proof

[obtuse pebble]

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[worthy birch]

?

[fathom light]

Do you have any questions or doubts?

[obtuse pebble]

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.

[rose night]

.reopen

[worthy birch]

it isnt even closed

[rose night]

@scenic vapor I want u to prove that all even numbers can be expressed in the form of 6x+6y+2 or 6x+6y-2 or 6x+6ybut with realistic using more of a methodlogy than what u did earlier as they said its wrong

[frigid burrow]

! occupied

[obtuse pebble]

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).

[frigid burrow]

Damn so many rule breakers today

[rose night]

what?

im new

[obtuse pebble]

@spark jay Has your question been resolved?

[wraith barn]

<@&268886789983436800> , youre working hard today lmao

[upbeat plinth]

.close

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[fallow cove]

so why do we do tan(beta+gamma)?

[stone holly]

as we have to prove that

alpha = beta + gamma

you can also alpha - gamma = beta
then

tan(alpha - gamma) = tan(beta)

that will also get you to your answer

[acoustic reef]

Just we found the lhs by tan alpha = a/a and then we have to find rhs

[fallow cove]

oh

alr

thx

.close

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[signal dagger]

Can someone tell me how I could simplify this

[timid silo]

what have you done till now

[signal dagger]

Im repeating maths to be fair

not really good but i know most rules

[scenic vapor]

What rules of exponent can you apply here?

[warm shale]

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

[timid silo]

keep in mind these rules