help-17

[marble harbor]

yea i know

theta

the angle

r is the hypotenuse kinda

[viral copper]

r is actually the modulus

[marble harbor]

ah

yea im stupid its in the picture

😭

|z| = r

[viral copper]

nah lol dw one step at a time

yeah

so now can you tell me what the modulus of this is

[marble harbor]

oh is it (2cospi/6)^5?

[viral copper]

yes

simplify that

[marble harbor]

(sqrt 3 )^ 5

i think

[viral copper]

yeah

[marble harbor]

oh wow

which is

also

9sqrt 3

which is one of the answers

[viral copper]

yes

[marble harbor]

thanks man

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[vocal sleet]

@stuck maple Has your question been resolved?

[vocal sleet]

@stuck maple Has your question been resolved?

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[vast shale]

could someone help me

[strong olive]

!ask

[pale perch]

!da2a

[vocal sleet]

No need to ask “Can I ask…?” or “Does anyone know about…?”—it’s faster for everyone if you just ask your question! See https://dontasktoask.com/

[vocal sleet]

No need to ask “Can I ask…?” or “Does anyone know about…?”—it’s faster for everyone if you just ask your question! See https://dontasktoask.com/

[pale perch]

jinx

[vast shale]

kk one sec im just uploading what i wrote so far

idk where to go from here

would it be c= 11/3? and b=3

idk

[pale perch]

that seems fine to me

made any attempts?

[vast shale]

not yet idk where to start

[pale perch]

my hint would be use logs

they seem to be set up so you can choose nice bases here too

[vast shale]

okok tysm

[pale perch]

np

[vast shale]

for c) i got 7 and 5 i just wanted to make sure this was correct

i mean -5

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[humble carbon]

this is a hole right?

and can sm1 explain if theres continuality or isnt

[floral pike]

"continuity"

[silk osprey]

there isn’t because the function at 3 doesn’t equal the limit as the function approaches 3

[floral pike]

This function is not contintuous (does not have continuity) because you have to lift your pencil when you get to x=3

this is called a "point" or "jump" discontinuity

[humble carbon]

thank you i like this explanation

would this be considered a jump as well?

i'd believe so cause its going from -2 to 2 at x=4

[silk osprey]

yes

[humble carbon]

can you elaborate on this a little more for the first problem?

what does the function = at 3?

the limit is 0 though right?

[silk osprey]

look at the values of the function close to x=3

the limit from both sides approaches y=0

[humble carbon]

Yea

so thats the limit

[silk osprey]

but if u notice there’s an open circle

indicating that the function≠0 at x=3

instead there’s a closed circle above it

so the function at 3=1

1≠0

so since the lim as x approaches 3 of the function does not equal the function itself at x=3 then there must be some sort of discontinuity

[humble carbon]

OH

THAT MAKES

SENSE

THANK YOU

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[buoyant latch]

For this question part b and c I dont get

[buoyant latch]

When you squareroot smth is the answer not both + and -

[distant eagle]

No

[buoyant latch]

Oh

How so

[empty frigate]

well

for every positive real number, there are exactly two real numbers that square to it

[distant eagle]

(Not in this context)

[empty frigate]

3 and -3 both square to 9 for instance

[buoyant latch]

Yeah true

[empty frigate]

but having the symbol $\sqrt9$ denote two numbers simultaneously just turns out to be confusing and inconvenient

[twin meteor]

bee [it/its]

[empty frigate]

so often what you do is just declare that that means the positive one

[buoyant latch]

How would I know when to do that and when to not

??

Wait

I think I am going insane 😭

Did someone say something

Honestly

I should sleep, I havent slept in two days and I am starting to lose it now

I'll figure this out later

Thanks!

[empty frigate]

i think generally if it's not explicitly stated you can assume the square root symbol is just referring to the positive one
or in the case of complex numbers there's a more general concept called the "principal" square root, so for instance sqrt(-1) would refer to just i and not also -i

[empty frigate]

yes

someone said something and then deleted it

[buoyant latch]

OKAY

I WAS WORRIED 😭

[buoyant latch]

Ohhh

[empty frigate]

the usual notation to get both square roots at once if someone does happen to want that would be to write $\pm\sqrt x$

[twin meteor]

bee [it/its]

[buoyant latch]

okay

Okay okay I get it

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[restive tinsel]

If
g(x) = 3x + 1
and
h(x) = 9x2 + 6x + 7,
find a function f such that
f ∘ g = h.
(Think about what operations you would have to perform on the formula for g to end up with the formula for h.)

[restive tinsel]

......

is it not as simple as dividing h(x) by g(x)?

[sharp lynx]

it is not

[restive tinsel]

so how do I proceed?

[sharp lynx]

following the hint would be a good place to start

[restive tinsel]

there is no hint

[sharp lynx]

the bit in the parenthesis is a hint

[restive tinsel]

I don't understand

f(g(x))

so it would be f(3x+1)

[sharp lynx]

indeed

for example, if f(x) = 3x, then f(g(x)) = 9x+3

the 9 coefficient matches, so that's getting close

[restive tinsel]

3x^2? but the 6x wouldn't match up

[sharp lynx]

what's 3x^2?

[restive tinsel]

9x^2 + 6x +1?

[sharp lynx]

careful

if f(x) = 3x^2, f(g(x)) has a leading term of 27x^2, not 9x^2

[sharp lynx]

this also didn't answer my question, but whatever

[restive tinsel]

1/3x^2?

[sharp lynx]

if you're asking if f(x) = 1/3x^2, then I'd ask you to compute f(g(x)) and find out

[restive tinsel]

3x^2 + 2x + 1/3 ?

can u not be blunt?

just please teach me the way

[sharp lynx]

there's not really a "way" aside from either trial and error, or some pattern recognition

[restive tinsel]

go back to the start then?

[sharp lynx]

g involves a 3x term, while h leads with 9x^2. How can you go from 3x to 9x^2?

[restive tinsel]

3x

[sharp lynx]

so if f(x) = 3x, what is f(g(x))?

[restive tinsel]

3(3x+1)

but that doesn't yield a square for the first one

[sharp lynx]

indeed

you need to do something to 3x such that it becomes 9x^2

[restive tinsel]

(3x)^2?

[sharp lynx]

i'd prefer if you were more explicit

do you mean f(x) = (3x)^2?

[restive tinsel]

sure

but if u plug in 3x+1

[sharp lynx]

this is the result of f(x) = 3x. Does squaring this give you a 9x^2?

[restive tinsel]

it becomes 81x^2

[sharp lynx]

note that you suggested f(x) = 9x^2, and your coefficient was 9 times too large

so what can you do to remedy this?

[restive tinsel]

just make it f(x) = x^2?

[sharp lynx]

perhaps

if so, what is f(g(x))?

[restive tinsel]

(3x+1)^2

I feel dumb

[sharp lynx]

expand this

[restive tinsel]

f(x) = x^2 + 6

(3x+1)^2 is 9x^2 + 6x +1

[sharp lynx]

indeed

[restive tinsel]

okie ty

[sharp lynx]

x^2 + 6 looks good to me

[restive tinsel]

.close

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[vast shale]

Elp

[rough zenith]

What are the questions

[vast shale]

Ignore the explanation pary

I dot have to explain it

[pale arch]

I jave tried but i cant get the right ans

[vast shale]

Nice name

[vocal sleet]

@vast shale Has your question been resolved?

[rapid escarp]

i think u need to multiply both of the variables by 3

im not sure if ur supposed to add or multiply them

thats one of the equations in the system tho

[vocal sleet]

@vast shale Has your question been resolved?

[floral halo]

I need some help lol

[civic lintel]

what have you tried

wait

[floral halo]

nah it is fine hold on wait that is not the question

[civic lintel]

someone else is using this channel

[floral halo]

yeah i just realized so i deleted it

i will move somewhere else

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[knotty gull]

Could someone pls explain me why does DA = b - CD

[flat whale]

b = AC

AC = DA + CD

[knotty gull]

Is B(bcosx, bsinx) a point ?

And is A(a,0) also a point

And how do we know that x and y of point B is bcosx and bsinx and how do we know that the x and y of point A is a and 0

Based on the Pythagorean theorem, c^2 = a^2 + b^2 right
and if so, how we know that a^2 = (bcosx-a)^2 and b^2 = (bsinx-0)^2 ?

[knotty gull]

Could you pls help me with this

<@&286206848099549185>

[silk osprey]

do u mean (bcosx,bsinx)

B is a point with those coordinates

[silk osprey]

yes

[silk osprey]

well the y coordinate is zero because it’s on the x axis and it just goes at some distance a

which gives the x coordinate

[silk osprey]

and u can use trig cosx=horizontal distance/hypotenuse

horizontal distance is our x coordinate

and hypotenuse is b

so horizontal distance =bcosx

the same can be said for sinx

but instead of horizontal distance it’s vertical distance

[knotty gull]

ok i understand it now, thank you!!

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[scenic ruin]

if speed represents a quantity

[scenic ruin]

velocity represents the same quantity & direction

why isn't the speed of any point on a parametric curve (u(t), v(t)) just |v'/u'|

[hushed pewter]

Why would it be |v'/u'|?

[scenic ruin]

the instantaneous rate of change at any point is v'/u'

[hushed pewter]

Oh you mean dy/dx

dy/dx is just the rate of change of y in respect to x

velocity is rate of change of position in respect to time

Two completely different things

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[novel wedge]

x^4 + 8x

[novel wedge]

How do i factor this?

[elfin surge]

@novel wedge

How old are you?

[novel wedge]

17

[elfin surge]

Ok

[novel wedge]

Wait why?

[elfin surge]

take x common

[elfin surge]

help me explain better?

[novel wedge]

x(x^3 +8)

[waxen hawk]

That shit

Is x^3 + 2^3

[novel wedge]

yeah so i get like x(x+2)(x^2 - 2x + 4)

[waxen hawk]

a^3 + b^ 3 = (a+b) (a^2 -ab + b ^2)

Exactly

[novel wedge]

When i entered that into my work tho it says its wrong

[waxen hawk]

Factor your shit out

It can be simplified

Further

Don’t you notice that (a-b)^2 shit

[novel wedge]

oh perfect square

[waxen hawk]

Exactly

[elfin surge]

Why does shit have to be in each of your sentence

lol

[waxen hawk]

I don’t know, since it is a casual conversation?

[elfin surge]

Yeah but it's weird

[waxen hawk]

Wdym

[novel wedge]

I find it funny

[elfin surge]

nothing

[elfin surge]

cool

[novel wedge]

.close

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[lucid bane]

Contraposition could be useful method

same as contrapositive

proof by contrapositive

maybe

or proof by cases

contradiction could also work. I think ultimately it relies on using the prime factorization

OH

PIGEONHOLE

you have 3 numbers

and 2 primes

well, if its a multiple of 10, technically it could have more

but overall you could say 2^m * 5^n * j=a * b * c where m,n>0 and j not a multiple of 2 or 5

but you can still pigeonhole a,b,c to the prime factors of 2 and 5

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[gloomy osprey]

Help

[gloomy osprey]

I have done a

Question 10

[proven garden]

Notice that the perpendicular bisector and AD intersect at D

So solve the simultaneously equations

[vocal sleet]

@gloomy osprey Has your question been resolved?

[gloomy osprey]

I tried

But my x coordinate is way off

[proven garden]

Part a answer is wrong

The perpendicular bisector obviously have positive slope

Remember that slope of perpendicular lines have slopes that multiplies to -1

[gloomy osprey]

Ohh

I’m dumb

Thank you

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[prime rover]

hi

[prime rover]

i need help with this question

on question 2) i have 2

and on question 4) i have -pi/3

on the question 5 i think its -pi/2

but on the first question i am clueless

!help

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To ask for mathematics help on this server, please open your own help channel or help thread. See #❓how-to-get-help for instructions.

[dull bear]

Select the factors of P given P(x) = 0 at the points mentioned?

[prime rover]

how do u mean?

[prime rover]

idk what its called in english but itsnt like i need to use the chair to solve this one?

otherwise idk how i need to solve it

[dull bear]

Like polynomial division?

[prime rover]

yea

[dull bear]

I was asking what the question is asking you - assumedly that you’re supposed to select from the list which are factors of the original polynomial

[prime rover]

Mark the polynomials that divide

Management:
have the solutions

and

this is the translation of the question

[dull bear]

For which, the factor theorem may be useful

[prime rover]

i was thinking about everyone of them

beside z-1

[dull bear]

Which says something like $(x - a)$ is a factor of $P$ if and only if $P(a) = 0$

[twin meteor]

@dull bear

[prime rover]

so its correct?

alright thx mate

.close

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[civic bolt]

The perimeter of one triangle is 11/13 of the perimeter of the other similar triangle. The difference between two corresponding sides is 1 m. Find these pages

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[deep pine]

I need help with b

[deep pine]

It says find the area of the following shapes

[rancid tree]

Hey, I need help too!

Where do I go?

[deep pine]

another forum

[rancid tree]

Where is that?

[deep pine]

Go to math help available

click one of em

[rancid tree]

Alright, thank you!

[deep pine]

np bro

[rancid tree]

Sorry for interfering as well!

[deep pine]

all good

[deep pine]

^

[bold hound]

For a, we can calculate the volume by using the base and height

So we get the height

Any ideas on how?

[deep pine]

I know how to do a

[bold hound]

Oh didnt see

[deep pine]

isn’t the height 12.2

or no?

[bold hound]

No

You are given s, but need H

We can use pythagoras

[deep pine]

ok

wait how

[bold hound]

We are given s, need H

What is the third side?

[deep pine]

that’s what I’m trying to figure out

what is it

I see H and s

but not bottom side

do I divide a by 2

[bold hound]

Yes

👍

[deep pine]

ok

then I multiply by 4

and find the base

what about for question b

[bold hound]

Why did you multiply by 4?

V=1/3 a^2 H

[deep pine]

I’m not trying to find the volume

the total area

[bold hound]

Ohhhh
My bad

Oh yeah then you dont need H, sorry for the confusion

Then you probably also got
8.5^2 for base
And 4 times 0.5 * 8.5*12.2 right?

[deep pine]

yes

what about question b

I really need help with that one

[bold hound]

For the base, we can use pythagoras

We are given a triangle with 2 sides
Using pythagoras we can get the height,base is given

[deep pine]

wait

I thought that was only for right triangles

ty

I needed to make sure

[bold hound]

It is

[deep pine]

the base

?

or the sides

[bold hound]

Oh wait

Yeah sry, i dont know why i cant think right now...

[deep pine]

wym

what did u do wrong

[bold hound]

Cant use pythagoras there

[deep pine]

ok

so what do I do

[bold hound]

<@&286206848099549185>

He needs help with part b) and my brain isnt on yet

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@deep pine Has your question been resolved?

[vocal sleet]

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[deft orchid]

Hi

[deft orchid]

Wtf

[half light]

Can someone please give me advice for this question

I’m not sure if I did it right

Question 11

[deft orchid]

I don’t even know what that is

Are you a math major

[dull bear]

Looks fine to me

[half light]

.close

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[foggy wave]

I can not figure out 21

[pale perch]

whyd they go and drive off a cliff smh

what have you tried?

[foggy wave]

t= square root of 2•50/25

Idk tho

[pale perch]

i get the 2*50, but why 25

[foggy wave]

idk I was using the equations my teacher gave us

[pale perch]

s=ut+0.5at^2?

[sonic zinc]

(to make lives of students harder ;))

[sonic zinc]

Projectile motion ?

Do u know thAT ?

formulas wont work everytime yk

[foggy wave]

nah

what equation should I use

[pale perch]

50=0t+0.5gt^2

the only issue with what you had was the 25, g is not 25, at least not on this planet

[foggy wave]

Ok

[pale perch]

you then just apply the projection time to the horizontal velocity and youll get horizontal distance travelled

[foggy wave]

Would it be 79.75

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[crimson jetty]

test

[crimson jetty]

.close

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[crimson jetty]

I typed out a question in #help-28. I need it to unlock to access it again, so just recycling channels. Sorry for the spam & ignore

[crimson jetty]

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[river minnow]

Are you sure that X^2 is -2^3?

Right, fix that and the rest will be fine

Yes

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[dreamy forge]

Given a convex cyclic quadrilateral ABCD (where alpha=60°; beta=110° and the diagonal |BD|=m), find the formula of the radius of the circumscribed circle using m.

Can anyone help me? I have no idea how to go about this.

[dreamy forge]

The solution is apparently (sqrt3/3)*m, but idk how to get it

This is how it should look like but, idk how to even start

Wait

Hold up

Perhaps?

Did it

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[late rune]

who can help solve my homeworl

[pale perch]

you can

and i shall assist

whats the problemo

[vocal sleet]

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[lyric fjord]

!status

[vocal sleet]

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

[feral aurora]

3

I don’t understand how to do the question

[lyric fjord]

keep this in mind

[limber glade]

6/x=4/9

Alternate Interior angles are equal

[elfin surge]

use similarity of triangles

[lyric fjord]

you could imagine it like this

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[timber marlin]

i am confused as to what they want from me here

[timber marlin]

oh wait i made a typo

.close

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[urban laurel]

$\nabla_{\overrightarrow{v}}f\left(\overrightarrow{a}\right) = \lim_{h\to 0} \frac{f\left(\overrightarrow{a} + h\overrightarrow{v}\right)-f\left(\overrightarrow{a}\right)}{h} \$ Why is $\nabla_{2\overrightarrow{v}}f = 2\nabla_{\overrightarrow{v}}f$ ?

[twin meteor]

Adam Chebil

[urban laurel]

h --> 0 so no matter what the magnitude of the vector is, it's going to be equal to the directional derivative with respect to the unit vector, right ??

[graceful surge]

Consider u = 2h

u still goes to zero
h = u/2

(f(a+uv)-f(a))/(u/2)

[twin meteor]

Adam Chebil

[urban laurel]

so ur proof doesn't work in this case ?

[graceful surge]

What exactly do you mean?

[twin meteor]

Adam Chebil

[graceful surge]

How does it not work?

[urban laurel]

wait is u not a vector in this case ?

so you substituted u=2h (as a variable) ?

[graceful surge]

Yeah

[urban laurel]

got it

thnx

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[snow scaffold]

hi, how can i prove that this is a whole number?

[hushed pewter]

Square root of a square

[vast shale]

translate please

[snow scaffold]

prove that its a whole number

[hushed pewter]

Just be sure you don't get tricked by one sneaky detail

[vast shale]

okay

[snow scaffold]

rn i can only get this far, i know that one is negative and one is positive

[dreamy forge]

Think of how to rewrite the first one so you dont need the absolute sign and still get the same value

[snow scaffold]

okay!

like this?

[dreamy forge]

Exactly

Now think about the second one. Is there anything you need to modify to bring it out of the absolute value sign?

Or is it good as is and can just be rewritten without the absolutes?

[snow scaffold]

i dont think theres anything to modify

[dreamy forge]

True

[snow scaffold]

is it because its a positive number

[dreamy forge]

Yes. With absolutes you get the difference between the two values in this case.
3<2*sqrt(3), so to get the difference you need to subtract the smaller number (3) from the bigger one (2*sqrt(3)).

Meaning 2*sqrt(3) - 3

4>2*sqrt(3), therefore the difference (which must be positive, which is why you use absolutes) is 4-2*sqrt(3)

[snow scaffold]

okay it makes more sense now

ill just do a few more questions

but thank u for ur help

i appreciate it

.close

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[twin citrus]

why in the proof it is required for epsilon to be equal to 0 ar 0 ? where do we need epsilon(0)=0 in this proof

?

[dusty umbra]

The underlined line is to avoid a divide by zero error right?

[twin citrus]

that is my question where we need it

[dusty umbra]

because without that definition when delta x=0 epsilon would be undefined

and therefore non continuous

[twin citrus]

where do we need that?

why do we need epsilon to be continuous at 0

[dusty umbra]

It's not about it being continuous at zero

its about it having a value at zero

[twin citrus]

on which line in this proof it is required?

to have value at zero

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@twin citrus Has your question been resolved?

[twin citrus]

<@&286206848099549185>

[twin citrus]

.close

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[deft vault]

Need help understanding unit conversion

[vast shale]

ok here is the secret on how to perform ANY unit conversion, no matter what it is

[deft vault]

I’m listening

[vast shale]

you can employ this to the problems you have

think of whats happening when you do unit conversions as multiplying by 1

say, for the sake of example, we want to convert 3 hours to minutes

[deft vault]

Okay

Perfect example unit also

[vast shale]

<siunitx>
You know that $\qty1{hour} = \qty{60}{minutes}$

[vast shale]

so, say, we divide both sides by 60 minutes

<siunitx>
we get $\ds \f{\qty1{hour}}{\qty{60}{minutes}} = 1$

[vast shale]

now, here is the neat part, we can totally flip this fraction and it would still remain 1

<siunitx>
so $\ds \f{\qty1{hour}}{\qty{60}{minutes}} = 1 = \f{\qty{60}{minutes}}{\qty1{hour}}$

[vast shale]

so this is amazing

so what you should do when you are trying to perform unit conversions is to basically think of the units as variables you need to eliminate and modify

<siunitx> so we have $\qty3{hours}$

[vast shale]

what we can do is multiply this by 1

multiplying by 1 doesnt change anything of course

<siunitx>but the thing is, [
\qty3{hours} \cd 1 = \qty3{hours}\cd \f{\qty1{hour}}{\qty{60}{minutes}} = \qty3{hours} \cd\f{\qty{60}{minutes}}{\qty1{hour}}]

[deft vault]

So then how would I solve a question like this one

[vast shale]

you could do either of those

BUT you have to think of what logically makes sense

you want to eliminate the hour unit

so you need to choose latter as the hours cancel

so you can employ this for pretty much any dimensionless conversion

[vast shale]

ok sure

lets work on that

do you get the idea of my example though?

[deft vault]

Yeah I do but these more confusing units are what I’m having trouble with

And like

What do I do with the number in front

[vast shale]

okay, no worries, its the same strategy pretty much

[deft vault]

So for this example its 254.7 in front

[vast shale]

so like first, tell me the relationship between feet and inches, and beta and gamma

[wicked axle]

this thing is both intuitive and smart lol, i think once u practice these a few times, you won't even have to think

[deft vault]

Yeah yeah I think so too

So the relationship according to the conversion chart

12 in = 1 ft

[wicked axle]

start with basic symbols nd u will build ur intuition for hard ones

[deft vault]

1.1 gamma = 1 Y

[vast shale]

u mean 1.1 beta

but okay

[deft vault]

Yeah

[wicked axle]

tht is something you have to remember or use chart for

[vast shale]

so you notice how in ur problem it is given cubed yes?

[deft vault]

I don’t know what those thingies are called

Yes

[wicked axle]

she cn solve it by putting their values ig

[vast shale]

<siunitx>
so what you should do is cube both sides of $\qty1{\beta} = \qty{1.1}{\gamma}$

[vast shale]

can you try doing that?

[wicked axle]

just put 1.1 beta for gamma

[deft vault]

So then gamma cubed = beta cubed?

[vast shale]

yes

but you have to account for the 1 and 1.1

[wicked axle]

won't tht be easier?

[vast shale]

so what is 1.1 cubed

you can use a calculator for that if you want

[wicked axle]

1.33

[deft vault]

It would be that?

[vast shale]

1.331

but ok

[wicked axle]

i was close :)

[deft vault]

I don’t wanna sound dumb but

How do I cube something

[wicked axle]

1.1 x 1.1 x 1.1

[deft vault]

Ohhhh

Got it

[vast shale]

<siunitx>[ \qty1{\beta} = \qty{1.1}{\gamma} \Iff \qty1{\beta^3} = \qty{1.331}{\gamma^3}]

[vast shale]

all clear?

[deft vault]

Where does the 1 after the 33 come from

[vast shale]

,calc (1.1)^3

[twin meteor]

Result:

1.331

[deft vault]

Also I am not touching the number in front yet?

[vast shale]

thats just what it evaluates to

1.33 is incorrect

[deft vault]

Oh

[vast shale]

what is?

[deft vault]

Wait

[wicked axle]

wht is pi?

[deft vault]

So the number in front is the total?

[vast shale]

what do you mean by the 'total'?

[deft vault]

254.7

[vast shale]

it basically scales it

like

im 50 kilograms

im 100 kilograms

[wicked axle]

just like value of pi is 3.14
1.1 x 1.1 x 1.1 = 1.331

[vast shale]

it just assigns a value on "how much" of that unit the thing you are considering is

[deft vault]

Okay

[vast shale]

its been 100 hours since i took my exam

[wicked axle]

wwhich 1

[vast shale]

So back to what we were saying

<siunitx>[
\qty{1.331}{\gamma^3} = \qty1{\beta^3} \
\qty1{feet} = \qty{12}{inch}
]

this is what we are considering

[wicked axle]

how u make those so quickly

also beta cubed

[deft vault]

Okay

[vast shale]

<siunitx>
anyways @deft vault lets consider your problem again of [
254.8,\f{\t{inches}}{\beta^3}
]

[vast shale]

so i want you to recognise

lets start with the inches

we want to transform the inches to feet

[deft vault]

12 inches per foot

[vast shale]

so by our multiplying by 1 analogy

should we be multiplying by 1 feet/12 inch or 12 inch/1 feet?

which one eliminates the inches do you think?

[deft vault]

Um

The second one

[wicked axle]

think

[vast shale]

are you sure tho?

[deft vault]

No

[vast shale]

multiplying by that gets you inches^2/feet

does that sound logical

[wicked axle]

so relatable

[deft vault]

Im really bad at math T_T

It hurts my brain

[wicked axle]

ok look, what is x/x

x divided by x

[deft vault]

What

https://tenor.com/view/cat-huh-meme-gif-27557281

[wicked axle]

1?

[deft vault]

Yeah definitely

[wicked axle]

okay

so we canceled x right

[deft vault]

Yeah

[wicked axle]

by dividing it by x

[wicked axle]

back to the question

[deft vault]

Teach it to me like I’m 5 years old

[wicked axle]

umm

[deft vault]

Lol

Okay so so so

1 foot divided by 12 inches

Would cancel out because both are technically the same

[wicked axle]

sure this time?

[deft vault]

Is that correct?

[vast shale]

what cancels out?

[deft vault]

The inches

[vast shale]

yes

great

[wicked axle]

Yay!

finally

[vast shale]

you are getting the hang of it

[deft vault]

Okay okay

So the feet cancels out the inches

So then does the beta cancel out the alpha too?

[vast shale]

ok the way you word it is extremely bad

[deft vault]

Oh

[vast shale]

the feet are not cancelling the inches

the inches are cancelling the inches

[deft vault]

Yes

[vast shale]

again, think of them as variables

you are looking to eliminate the inch

so you want something inch/inch = 1

[deft vault]

Think of it like it’s multiplying by 1

[vast shale]

1 feet/12 inches does that

[deft vault]

Right?

[vast shale]

yes exactly

[deft vault]

Okay

Okay okay

[wicked axle]

i hv a much simple strategy that should work

no need for these complications

[wicked axle]

you want your answer in feet/gamma cubed right

just put inch = feet/12 and beta = gamma/1.1

then with just basic calculations you get the answer

[deft vault]

The / is divided by or times

[wicked axle]

divided

• = multiply

ok?

[deft vault]

I will generate a new example

[wicked axle]

ok, first try urself

[deft vault]

So I have 965.9 as the number in front

Let me do math

Okay so it wants me to convert cm to feet

So I would first convert 1 cm to 1 inch

And then 12 inches by 1 ft

[wicked axle]

👍 😄

[deft vault]

What do I do with the number in front 965.9

Also this wants me to convert backwards also

[wicked axle]

keep it as it is

[wicked axle]

?

[deft vault]

So 1.12 & to Y

[wicked axle]

ig

[wicked axle]

idk it's 3 am for me rn

😴

[wicked axle]

u cn do it, just put values from table

cn i go to sleep if u don't mind me leaving midway

[deft vault]

That’s fine

[wicked axle]

😊 cya, also gl

[deft vault]

.close

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[hollow prism]

So I'm stuck at here right now:
[1 2 3 :1]
[0 -1 a-6 : 0]

^ imagine that is an augmented matrix

what value of a do i need?

@rugged orchid you helped me before, is it a != 6?

[pale perch]

that seems sensible enough

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[remote yacht]

guys can someone help me with this

[vocal sleet]

@remote yacht Has your question been resolved?

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@remote yacht Has your question been resolved?

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@remote yacht Has your question been resolved?

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@remote yacht Has your question been resolved?

What step are you on?
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2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
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[cinder oyster]

plzzzzzzzzzzzzzzzzzz

i keep getting it wrong

like theres 8 squared a's

[mild flower]

cube root

so look for triplets not pairs

[cinder oyster]

Ohhh

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[little imp]

Hi, I am trying to solve this question, but I feel lost on trying to solve it.

deviation of the total noise. Suppose that we have a cooled CCD so that dark current is negligible
with an amplifier noise source having a standard deviation of three electrons. Photon noise is
also present as described in class. Assume that all noise sources are independent.```
What minimum signal (in electrons) is required so that the standard deviation of the amplifier noise is ten percent of the standard deviation of the total noise? If it helps, this is the equation

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[vast shale]

how do i properly plug this into my calculator

i am confused with the part where it says sin^2

i have a ti-84

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[zinc quail]

What's the general approach for determining the left/right hand side limits? E.g. if I'm confronted with a function that's not some simple polynomial, such as f(x)=log(x+1)/sin(πx) for x->1

[thin vale]

@mighty nacelle

[thin vale]

Is sin(pi x) continuous?

[zinc quail]

Si

both are for x>-1

[thin vale]

then doesn't the limit of the function approaching any point, equal the value of the function at that point

by the definition of continuity

and if the limit of the function exists at any given point, don't the left and right hand limits agree at that point?

by the definition of the two-sided limit

[zinc quail]

Sry had to switch trains

But sin(π)=0

so we divide by zero

yet log(x+1)=log(2)≠0 nor inf/-inf

[thin vale]

I didn't realize you had edited your original question, I thought you were asking about the limit of sin(pi x) as x->1

[zinc quail]

formerly it was log(x)/sin(πx) but I realized I'd just use l'hopital

[thin vale]

Alright well

you're right that log(2) != 0

this limit doesn't exist for that reason

whereas it might've saved you in the case of log(x) it doesn't here

if this limit existed

it will be equal to the limit of the numerator / limit of the denominator

which is undefined

[zinc quail]

but the left/right side limits must exist

[thin vale]

they do exist

well

they actually don't

they go off to +/- inf

since sin(pi x) will pick up a sign if you come from the right vs. the left

[zinc quail]

well then they exist, just diverging

[zinc quail]

So the actual approach would be? I presume inserting x=1 yielding log(2)/0, no indeterminate form. sin(πx) approaches 0 from the positive on the left and negative on the right

log(1+x) is positive on either side when approaching log(2)

thereby left side limit is ∞ and right side limit is -∞?

doesnt feel like a proper proof though @thin vale

[thin vale]

It suffices to show that either the left or right hand limit doesn't exist to show that the entire limit also doesn't exist

So pick a side

show it doesn't exist

You can do it by epsilon delta

Negate the definition

and prove it that way

[zinc quail]

We defined it in a way where ∞ and -∞ count as existing limits

[thin vale]

So you would say that

lim x->0 1/|x| exists?

[zinc quail]

yes, we'd say it's ∞

Since left/right agree

[thin vale]

interesting okay well then just prove both sides don't exist

should be fairly straightforward

or not don't exist I guess

but don't agree

I'm used to tending to infinity being DNE

[zinc quail]

If I have another form where for instance a function approaches ∞⁰, what would be suitable in that case

[thin vale]

suitable as what?

[zinc quail]

suitable for determining left/right hand side limits

[obsidian stream]

No sensible Calculus course should ever says a limit exists and equals infinity. You should read your notes very carefully.

[zinc quail]

I'm certain

[obsidian stream]

There is a difference between writing that a limit equals infinity, then assigning a specific meaning to that notation and saying "the limit exists and equals infinity"

[zinc quail]

We'd write f->∞ for x->...

not lim_f(x)=∞

We do separate them into "eigentlich" and "uneigentlich"

in German

where the first would stand for what you meant

and the latter extends it with {∞,-∞}

nywys I'm aware of the separation, I'm just uncertain how to determine the left/right hand side limits of functions that approach forms like ∞⁰, 0*∞, 0^∞ etc

for .../0 Austin has shown me

to just determine the sign for num & denom to find the limit

[zinc quail]

@obsidian stream do you know the approaches for forms like these? 🐛

[obsidian stream]

You usually just apply some algebraic manipulation until it is reduced to the case of 0/0 and then do it as usual.

or whatever ratio it might be

[zinc quail]

Could you show it for a sample?

Ok (1-cos(x))^(1/x)

for x->0

which approaches the form 0^∞

[vocal sleet]

@zinc quail Has your question been resolved?

[thin vale]

I think you should be able to find some examples like this online

maybe on youtube

[zinc quail]

am creating a table instead

[zinc quail]

.close

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[ionic marlin]

assuming you publish a video on youtube , 30 days before your video got 300 views and 60 likes. find the probability of getting 4 like tomorrow

[ionic marlin]

This is what I djd

Probability of getting a like when you get a view is 60/300

So p of getting 4 likes when you get a view is 1/5 ^4

And p of getting a view is 30/300

So shouldn't the answer be 1/5 ^4 /(1/10)

Or do we use binomial and say

N=10.p=60/300 and x = 4

[vocal sleet]

@ionic marlin Has your question been resolved?

[vocal sleet]

@ionic marlin Has your question been resolved?

[vocal sleet]

@ionic marlin Has your question been resolved?

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[odd lintel]

Can someone guide me through this improper integral? I've split it into two, and i'm now trying to solve the integral from 1 to infinity of that function. I have to determine whether this improper integral converges or not.

[odd lintel]

I've tried that the integral of 1/e^x converges, but the function e^-x * ln(x) isn't smaller than 1/e^x, so i couldnt use that comparison test.

[obsidian ore]

I tried by parts

but -e^-xlnx from inf to 0 doesnt even exist 😭

[inner osprey]

are you allowed to compare ln(x) with x

[odd lintel]

true but you have to split it from 0 to 1 and then 1 to infin

[obsidian ore]

wait what

why

[odd lintel]

bc ln(0) isnt defined right

[obsidian ore]

yep

[odd lintel]

no clue

i know that ln(x) << x

in terms of growth and thus values as well

but lnx is in the numerator so it makes it a bit trickier right

[inner osprey]

wdym

[odd lintel]

i thought you were hinting to compare with 1/x

[inner osprey]

that doesn’t make sense though

[odd lintel]

yeah because lnx is in the numerator

[inner osprey]

e^(-x) ln(x) < e^(-x) * x for the “x goes to infinity” limit

[odd lintel]

ah okay

and i have to prove that e^(-x) * x converges

[inner osprey]

yes

[odd lintel]

so that e^(-x)ln(x) is forced to converge

okay

.close

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[pulsar scroll]

I had a further question about c)

[pulsar scroll]

so, the answer is that {b} and {c} are minimal elements

and {a, b, c} is a maximal element

if I were to add a single {x} to A, is {a, b, c} still a maximal element and are {b}, {c}, {x} now minimal elements or is {x} now a maximal element because it is not a proper subset of any other set

also, if we were considering the subset relation on A = {{a}, {b}, {c}} are all the elements minimal or maximal elements? or both or neither

[vocal sleet]

@pulsar scroll Has your question been resolved?

[pulsar scroll]

<@&286206848099549185>

[pulsar scroll]

<@&286206848099549185>

[hybrid flicker]

{x} is both maximal and minimal because nothing contains it and nothing is smaller than it too

[hybrid flicker]

all elements are both

[cerulean compass]

Remind me what defines a maximal and minimal element for this set

[hybrid flicker]

maximal <=> nothing contains it (for subset)

minimal <=> it contains no other element (for subset)

[cerulean compass]

Ah right

[pulsar scroll]

do you mean there is no other element that can be a subset of the minimal element?

[hybrid flicker]

yes

[pulsar scroll]

thx

.close

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[fast moth]

okay uh

[fast moth]

now what do i do

oh

yay

[vast shale]

you occupied it

now its yours

[fast moth]

oohh thats cool

[vast shale]

post your question for starters

[fast moth]

well i kinda understand what i was looking at right here but the bottom par t confused me so i got stuck

like

idk if this is even what we r learning

[vast shale]

like

[fast moth]

my teacher quit bc she got hit so i didnt have a teacher for a couple months

[vast shale]

what do u not understand

is there even a question here

[fast moth]

i just got a new teacher but ive been in iss