help-38

[shy nacelle]

Answer is c

[solid kiln]

Result:

77

[acoustic flint]

a

[torpid magnet]

how

what am i supposed to do with 77

[shy nacelle]

see 2pi

Returns you to same angle

A full rotation

[torpid magnet]

i see 2pi

How

[shy nacelle]

so upto 76 pi its 0° angle

[torpid magnet]

how do u know that

im sorry i know i already went through this class i just forgot how to do this completely

[acoustic flint]

You said it here

[shy nacelle]

I think thats what the question is asking for

[torpid magnet]

but how can i convert 76pi to degrees

like idk just for the sake of understanding

[acoustic flint]

You have to start working in radians

[shy nacelle]

76 pi = 76 ×180°

= 38 × 360°

So 38 full rotations

[torpid magnet]

yeah

but we want 180 so one more rotation

so 77

[shy nacelle]

And then 77

[shy nacelle]

Yeahh

[torpid magnet]

uea

thank you so much

[shy nacelle]

Welcome !

[torpid magnet]

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[chilly sphinx]

Example

[woven nova]

what exactly is the issue?

[tardy hemlock]

@chilly sphinx

[chilly sphinx]

I dont get waht to do

[woven nova]

you have two equations
to solve them, one technique is to solve each equation to the same thing
in this case they were solved for y
and since y=y, they got 2x-1=-x+2

and then they solve for x to get x

doing so will find x values, for which y is the same in both equations

[chilly sphinx]

Hm

[woven nova]

so for example in 2 a), you would divide the second equation by 3, so that both are solved for y
you can alternatively multiply the first equation by 3, so that both are solved for 3y and then set the sides equal

[chilly sphinx]

Would be easier to multiply first one no?

[woven nova]

yes

[chilly sphinx]

Alright so ill write that down rq and then ill tell u what i got

The only hard part for me is getting the y to a same value

[woven nova]

können übrigens auch gerne deutsch reden haha

[chilly sphinx]

O

Gerne doch

Ist es auch möglich das Gleichsetzungsverfahren mit dem x zu machen?

Nur so eine Frage

[woven nova]

ja, das geht auch

Im allgemeinen versucht man damit eine Gleichung zu erhalten, die nur noch von einer Variablen abhängt, sodass man diese lösen kann
Welche Variable das dann ist ist komplett egal

[chilly sphinx]

also ist x 4

Und die setze ich dann in eine x variable rein

Um y herauszufinden

Oder?

@woven nova

[woven nova]

4 dürfte nicht ganz richtig sein

3y=6x-12
3y=-2x+12
6x-12=-2x+12
8x=24
x=3

aber ja, dann einfach in irgendein x einsetzen

[chilly sphinx]

A

[woven nova]

welche gleichung ist dann auch egal, weil wir ja gerade Lösungen suchen, wo beide Gleichungen gleichzeitig erfüllt sind

[chilly sphinx]

Als ich +2x gerechnet habe habe ich es nicht auf die 6 addiert

[woven nova]

ahhh

mir passiert manchmal dass ich denke 24/8=4 hehe

[chilly sphinx]

Y=2

[woven nova]

👍

[chilly sphinx]

Ich rechne mal weiter

Mache jetzt b und c und pinge dich gleich

Oder wenn ich Schwierigkeiten habe

Nur um sicherzugehen bei b sind ja beide x und beide y gleich also kann man sich eins davon aussuchen

Kann ich bei b nicht einfach die 65 auf die andere seite bringen

Und dann +y

Also -65 und dann +y

@woven nova

[woven nova]

yo, das geht 👍

also
x-y=65
x-y-65=0
x-65=y

[chilly sphinx]

Ja

Okay

X=86?

Y=21

[woven nova]

yep 👍

[chilly sphinx]

Kannst du mir c erklären

Da kann man es deutlich mit x machen aber ich weiß nicht wie das funktioniert

A

Habe auf die falsche

Aufgaben

Geschaut

Lol

Aber bei d

Kann man es mit x machen

Wie?

@woven nova

[woven nova]

wir verschieben einfach das 5x auf die andere Seite

und dann wieder gleichsetzen

[chilly sphinx]

Huh

5y?

Also geht es doch nicht mit x oder was

[woven nova]

doch

yoah wir haben bei der d ja: x+5y=-7
das gibt uns: x=-5y-7

dann haben wir nach x gelöst

somit können wir dann gleichsetzen

[chilly sphinx]

Nur das hat mich verwirrt

Okay

Ist -0,75 richtig?

Oder halt -6/8

Also y

Und x dann 1,25?

@woven nova

[woven nova]

3y-1=-7-5y
8y=-6
y=-6/8=-3/4
x=3y-1 = -9/4-1 = -13/4

,cal -3*3/4-1

,w -3*3/4-1

[solid kiln]

Results provided by WolframAlpha

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

Requested by machmut_

[chilly sphinx]

Oh

Habe mein Fehler gefunden

Hab das minus vergessen 🐧

Danke für die Hilfe den Rest schaffe ich auch alleine

@woven nova

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[woven nova]

alles klar 👍

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[hot mountain]

Need help solving

[kindred pier]

https://tenor.com/view/the-office-dwight-schrute-blurry-gif-19345833

[calm quarry]

Use chain rule

[hallow kite]

if y = 4^(something) then dy/dx = 4^(something) * ln(4) * d/dx(something)

does that say g(secx)?

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[hot mountain]

Yes

My answer

Can someone check

Please

<@&286206848099549185>

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[hot mountain]

.reopen

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✅

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[hot mountain]

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[atomic moat]

In the screenshot, there is provided a definition of an inclusion map, for an injection f:B->A, what does it mean for it to be defined by f(b) =b for all b is an element of B?

[atomic moat]

The highlighted area

What does it mean?

[lean prawn]

Say A={1, 2, 3, 4, 5} and B={1, 2, 3} (a subset of A)

Now the inclusion map would be f : B -> A such that

f(1) = 1
f(2) = 2
f(3) = 3

It's kind of like a generalization of an identity function

[hallow kite]

image you can sketch some region A, then there is some smaller region B contained in A where every point in B gets mapped to itself

[lean prawn]

an identity function is a type of inclusion map

But when you have an identity function it's always defined from some set to itself

but with an inclusion map the codomain can actually be bigger than the domain

so strictly speaking the inclusion map I gave above and the identity function g : B -> B such that

g(1) = 1
g(2) = 2
g(3) = 3

are different functions because they have different codomains

but they behave very similarly

[grim sparrow]

the domain must be a subset of the codomain with an inclusion map

[atomic moat]

i understand

thank you

[lean prawn]

no worries ^^

[grim sparrow]

!done

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[atomic moat]

did you get this from a book?

[atomic moat]

i had an additional question, sorry.

[grim sparrow]

sure

go ahead and ask

[lean prawn]

It was an original example albeit a very simple one

[atomic moat]

I had.

[grim sparrow]

oh, where?

[atomic moat]

i see.

[grim sparrow]

oh I see lol

[atomic moat]

thank you both

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[north hinge]

How does the 3 row equal -3

I understand .1 = -1

as that would 10/100 = 1/2

threfore -1

[wraith hinge]

$0.001 = 10^{-3}$, so $\log_{10}(10^{-3}) = -3\log_{10}(10) = -3$

[solid kiln]

45

[tulip inlet]

oh mb ty

[north hinge]

Okay the equation makes sense

but does -3log do anything

or 10^(10)

10^-3

= 1/1000

.001

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[bronze plover]

I'm pretty confused. I thought maybe I can do a line integral with the given vector over C, with C being a circle with radius 4 in the xy plane?

[bronze plover]

But it wasn't really working

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[bronze plover]

<@&286206848099549185>

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[safe bone]

Have you tried thinking through the problem?

[bronze plover]

I mean, I don't really know how to think about this

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@jade haven Has your question been resolved?

[smoky snow]

I don’t see a mistake

What do you mean well written ?

The train of thought is pretty clear yes

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[runic sphinx]

Guys help me out with it

[limpid dawn]

you leaked yourself btw

[runic sphinx]

Oh yeah

Not much

Mine ans is c not b

Can anyone tell me why is this happening

[eternal adder]

how did you get c?

[limpid dawn]

yeah how?

[limpid dawn]

did you apply the dot product rule?

for perpendicular vectors

[runic sphinx]

Yeah

Yeah

[limpid dawn]

how?

[runic sphinx]

And it is coming -1/2

Not1/2

See it

[limpid dawn]

you been coding for 21 hours 💀

[limpid dawn]

can you type what you did

[eternal adder]

it rolls over once you get to 24 more like 3 weeks 💀

[limpid dawn]

yours teps

ah ok

[limpid dawn]

how 2 x 8?

2i and 4i

[runic sphinx]

Oooooo

[eternal adder]

yeah, I think you swapped 2*8 and 3*-4 at some point

[runic sphinx]

Yeah

[limpid dawn]

Yeah

[runic sphinx]

Ok

I got it

Thanks

[limpid dawn]

yeah that's it

[runic sphinx]

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[mighty prism]

what progress have you made so far

!status

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@lethal fable Has your question been resolved?

[mighty prism]

bruh

what the heck am i looking at

[split chasm]

sign error in the first line

should have +7y, not -7y

(and don't be lazy with dropping the =0)

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[gray charm]

is this correct notation (in general)

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@gray charm Has your question been resolved?

[kindred pier]

Looks good

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[noble carbon]

need help on all of these-

anyone-

[split chasm]

do you know pythagoras' theorem

[noble carbon]

yes

a square + b square = c square

[split chasm]

try applying that for part a)

[noble carbon]

is the hyptenous length 3m??

[split chasm]

no

how are you getting taht

[noble carbon]

cause the length is 3m?

[split chasm]

how?

what calculations did you make that lead to finding 3m as the length of the hypotenuse

[noble carbon]

it says it there-

'

LENGTH IS 3m

[split chasm]

length of the shelter is 3m, that isn't the hypotenuse (of the triangle)

they've provided a diagram for you

[noble carbon]

ohhhhhhhhhhhh wait i get it

stop help

i get it

thanks

can u help me with the part b?

[solemn thorn]

b is asking for surface area

[noble carbon]

how do u figure out that again?

[solemn thorn]

its the perimeter of the triangular base

times the length

and twice the area of the triangular base

[noble carbon]

huh

can u help me pls!

[solemn thorn]

whats the perimeter of the triangular base

[noble carbon]

6.8?

[solemn thorn]

actually firstly

whats the length of the hypotenuse

clearly you must have calculated it by now

[noble carbon]

2.8

[solemn thorn]

ok

now how do you calculate the perimeter of the triangular base

[noble carbon]

what do u mean by triangleer base?

like 2?

[solemn thorn]

i hope this is clear enough

thats the triangular base

now whats the perimeter of the triangular base

[noble carbon]

6.8

[solemn thorn]

good

now multiply it by the length

id prefer to call it height but according to the problem its the length

[noble carbon]

so 6.8 x 3?

[solemn thorn]

yea

[noble carbon]

20.4

[solemn thorn]

ok now calculate the area of the triangular base

[noble carbon]

1/2 x b x h

so

1/2 x 2 x 3

[solemn thorn]

the height is not 3

[noble carbon]

oh 2

mb

the area of triangulr base is 2
!

[solemn thorn]

ok

now notice how theres two triangular bases

one on each side

[noble carbon]

so times it by 2?

[solemn thorn]

yes

[noble carbon]

k

so 4?

are u there??

[solemn thorn]

im back

i was participating in the javelin contest

[solemn thorn]

ok now add it to the value you got

20.4

[noble carbon]

24.4

[solemn thorn]

ok now round it to what the question desires

btw the answer can also be 25 if you put the exact value of sqrt(8)

[noble carbon]

oh oki :)

that makes sense

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[gaunt temple]

how do you do this? find supremum and infimum

[gaunt temple]

i have no idea where to start

[shy nacelle]

Max and min ?

[gaunt temple]

the text says to find sup and inf

[wet dragon]

is B a subset of the real numbers

[gaunt temple]

Might be not sure

Can somebody please confirm?

[gaunt temple]

It doesnt say anything about it

But yes i suppose

[gaunt temple]

I used the AM GM inequality

Though I only proved that 4 is a lower bound of n/m + 4m/n, not the GREATEST lower bound

[wet dragon]

i think it is the greatest lower bound

cuz its greater than or equal to 4

so that means it can equal 4

it cant be less than 4

[gaunt temple]

greater or equal means that it could just be greater

I think

[wet dragon]

m = 1 n = 2

@gaunt temple

it can equal 4

so 4 should be the greatest lower bound

[gaunt temple]

Great

Thank you

[wet dragon]

ye

[gaunt temple]

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[hoary bison]

how do i do this?

[sturdy bloom]

how do i do this?

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3. I got an answer but I was told that it's wrong.
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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.
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[frail heron]

@hoary bison

[frail heron]

!occupied

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@hoary bison Has your question been resolved?

[hoary bison]

yes?

[hoary bison]

1

[frail heron]

Your status?

I see

Do you know how does g(x) look like?

[hoary bison]

graph?

[frail heron]

yeah

[hoary bison]

no i solve everything manually

[frail heron]

Same

[simple geode]

Try to make perfect square at the denominator then go with partial Integration

[hoary bison]

which denominator 😭😭

[simple geode]

It's just one way you could use substitution such as t

[frail heron]

[hoary bison]

im not getting ti 😭

can u guide from the beginning

[frail heron]

I solved it geometrically

[hoary bison]

graph?

[frail heron]

ye

Once you graph it, it’s pretty obvious

[hoary bison]

did u graph it on ur own?

[frail heron]

ofc

[hoary bison]

how do we make the graph

[frail heron]

This is g(x)

Do you agree?

[hoary bison]

YEAHH

then ?

[frail heron]

Let’s ignore 1/2h first

When replacing f(x) with f(1)

[frail heron]

The integration can be interpreted as " extend h to x positive and negative

[simple geode]

If manual answer what you were looking for

[hoary bison]

breaking my neck to see the images lawl ty thooo 😭😭

[hoary bison]

then?

[hoary bison]

lemme seee

[frail heron]

Like this

[frail heron]

Then find the area between g(x) and x-axis

The intervals are 1-h and 1+h

[hoary bison]

from where did u get those tersm

[hoary bison]

oooooo

how did u find area

[frail heron]

Rectangle formula..

[hoary bison]

hold on

[simple geode]

Oo my bad it is a method called partial Integration in which when the denominator from like factor of 2 bracket you assume them as 2 factor or you could call it foresight hehe

[hoary bison]

what's that orange bar above x axis for?
and those green lines they're for x+h and x-h ?

[frail heron]

That’s a part of g(x)

[frail heron]

yes, the green line are x-h and x+h individually

[hoary bison]

where did u get x²-x+6 ? tahts my doubt

[hoary bison]

ohhhh

[simple geode]

Isn't it part of questions and numirator

[hoary bison]

you're asmwerjmg to @scenic loom 😭😭

[simple geode]

I just changed the way of how the question looks and

[hoary bison]

which is x-h and x+h cause idk which u considered as x

[frail heron]

x=1, as the question demands

[hoary bison]

OHHHHH

right

sorry

[hoary bison]

yeahhh

so area of which part? 😭

[frail heron]

Green line

[hoary bison]

ok so what will be the values of l and b?

[frail heron]

l?

[hoary bison]

you said rectangle formula no?

l×b

[frail heron]

yeah

[frail heron]

I suggest you give it a try first 🙂

[hoary bison]

im not getting ittr

[frail heron]

Take this as reference

[hoary bison]

here me out

you took it as 1-h and 1+h

so how do i find it's length and breadth 😭😭

what does "g(x) =0 otherwise" mean in question

what's the value of that orange bar

[frail heron]

It says if x is between-1 and 1

g(x) becomes 1

or else it becomes 0

[frail heron]

That’s how I graphed it

[hoary bison]

ohhhhhh

okokok

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[flat flower]

Of a moving object, the velocity v (in m/s) depends on the time (in seconds) in the time interval [0,4] is given by the formula: v(t) = 8- t*sqrt(t).
Calculate the average velocity in the time interval [0,4].

[flat flower]

I got -4,8 but answer says 4,8

[scarlet totem]

Can someone explain those problems to me please. I’m in 7th grade Germany if this is important.

[scenic roost]

4.8m/s?

[flat flower]

yh

[scenic roost]

can you show ur working

[scenic roost]

this channel is taken, please send your help message in an available help channel

[wraith hinge]

!occupied

[trim jolt]

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).

[scenic roost]

dang there was a command for that

[flat flower]

ok nvm

i got 4.8 now

[scenic roost]

lol ok

[flat flower]

just miscalculated it

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[rigid trail]

how do i find the x1 and x2 in vieta's formula

[scenic roost]

x1 and x2 are the roots of the quadratic you have

you can usually get that by factoring

or quadratic equation/formula

do you have a picture of the question

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[naive egret]

for a sequence like this is the formula this:?

[naive egret]

or is it a0

[pseudo bone]

What is a_0?

Its u_0, right?

[naive egret]

a subscript 0

yes

u_0

[pseudo bone]

$u_{n+1} = 5u_n$

[solid kiln]

fukwerint

[pseudo bone]

$u_{n+1} = 5*5u_{n-1}$

[solid kiln]

fukwerint

[pseudo bone]

$u_{n+1} = 5^3u_{n-2}$

[solid kiln]

fukwerint

[pseudo bone]

$u_{n+1} = 5^{n+1}u_{n-n}$

[naive egret]

uhh

[solid kiln]

fukwerint

[trim jolt]

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.

[naive egret]

Im just confused which one I should use for this question

[sweet hare]

what kind of sequence is it?

your formula is for an arithmetic sequence, isn't it?

[pseudo bone]

Neither

[naive egret]

oh wait is it a gp

wait yeah mb

Which one do I use

[pseudo bone]

You tell me

[naive egret]

The down one ig

[pseudo bone]

Just substitute n = 1 in both and see which works 😂

[naive egret]

But then do all sequences start with an index of 0?

Or like does it depend on the sequence

[pseudo bone]

It depends on the sequence

Its your choice

How you want to label

[naive egret]

So for this the first term is a0 so that means that is actually the first term

Okay so doesn't depend on the index but depends on whatever is first

[pseudo bone]

Yup

[naive egret]

Okay ty

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[noble ridge]

for this question, how do we know what the independent and dependent variables are? In this case, do we think of x as a function of both y and z or do we think of x as an independent variable?

[unique minnow]

It'll be considered a constant here, because you're specifically taking the derivative w.r.t. z.
It's a implicit differentiation here : take the derivative in z across the board and make sure to use the chain rule to get the dy/dz popping out.

[noble ridge]

but in general how do we know whether to consider something as a constant or an independent variable

what gives that away?

[unique minnow]

In general you should assume that variables are independent unless (1) specified explictly (2) you can infer it. Here x isn't discussed at all, so it's a constant when taking the derivative w.r.t. z.
y isn't explicitly mentioned, but computing dy/dz tells you that they should be linked in some way.

[noble ridge]

ah ok makes sense

and yea ig the partial derivative tells me that y has to be a function of z and x

thanks!

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[prisma basalt]

i'm a bit lost here:

[prisma basalt]

im trying to write an algebraic expression for the distance from 0,0 to x,y

at first i thought the pythagorean theorem

(this is in euclidean distance)

[river willow]

yes

[prisma basalt]

that's it? i got it right?

[river willow]

yes

[prisma basalt]

what is an algebraic expression for the squared distance from 0,0 to x,y? does that mean the first part of this would by a+b=c and the second part is a^2+b^2=c^2?

[river willow]

wdym first part second part

[prisma basalt]

the first problem was "write an algebraic expression for the distance from 0,0 to x,y" and the second part is "what is an algebraic expression for the squared distance from 0,0 to x,y"

[river willow]

a+b=c never appears in pyt

[prisma basalt]

how would you define the difference between the distance from 0,0 to x,y and the squared distance from 0,0 to x,y

[river quest]

Hello

Am I free to ask question?

[river willow]

not here

[river quest]

Ok, where can I ask question?

[unique minnow]

#❓how-to-get-help

[prisma basalt]

if the first part of the problem is just the pythagorean theorem then i am stumped on the second part

[river willow]

try drawing a triangle first

[river quest]

Sorry, thank you so much

[prisma basalt]

one sec let me grab my scrap paper

ok, i drew a right triangle

[river willow]

where is x and y

[lean prawn]

In the first part you calculate the distance, in the second part you multiply that distance by itself

[prisma basalt]

0,0 i think

[prisma basalt]

so the first part is just a^2+b^2=c^2 and the second part is (c^2)^2? because you're basically mirroring the first operation which gives you the lengths of the sides of the triangles?

so am i right in thinking if you take c^2 and ^2 it again you would basically wind up with a square in some way i cant envision in my mind's eye

[lean prawn]

when they say "write an algebraic expression", they don't mean "write an equation whose solution is the distance", they mean "write an algebraic expression that evaluates to the distance"

[prisma basalt]

i feel dense but i dont grasp the distinction

[lean prawn]

x^2 + y^2 = c^2 is an equation where c is the distance

[prisma basalt]

i just googled it

[lean prawn]

but they're not asking for an equation

they're asking for the distance in terms of x and y

[prisma basalt]

an expression is a number, variable, or combination of thoe and operation symbols, and equation includes an = sign that connects two expressions

[lean prawn]

so you need to solve an equation and the solution of that equation is the answer

[lean prawn]

yes, exactly

[prisma basalt]

my initial thinking keeps going back to the method im sure is wrong which is (pretend this is subscript) (x2 - x1) + (y2-y1) but that's the taxi cab metric

and it wouldnt be a^2+b^2

(x-0)+(y-0)

no that cant be right

[lean prawn]

you can draw a diagram and a right triangle and use the pythagorean theorem to form an equation that the distance c must satisfy

[prisma basalt]

so then i was right in my thinking x^2+y^2 for the expression, and by not including the rest of the pyth theorem it answers the question without being an equation

thank you for your patience with me btw, it's been many years since ive been in school

many many years

[lean prawn]

no worries

but what question does the expression x^2+y^2 answer?

Like what geometric quantity is that equal to?

[prisma basalt]

the length of the hypotenuse which gives the distance from the point of origin (0,0) in euclidean distance, i think

[lean prawn]

The pythagorean theorem states that x^2 + y^2 is the square of the distance from (0, 0)

which is not the same as the distance itself

[prisma basalt]

am i missing something fundamental from early math

[lean prawn]

except in very specific cases, such as if x=1/sqrt(2) and y=1/sqrt(2)

[prisma basalt]

i have some gaps in my knowledge

[lean prawn]

Well have you done any exercises related to the pythagorean theorem recently?

[prisma basalt]

yes, on khan academy

[lean prawn]

do you ever remember taking a square root?

[prisma basalt]

it was back in 8th grade math

no

i think we've just identified another gap i need to work on

[lean prawn]

Square roots are pretty handy to understand

[river willow]

c is the hypotenuse or distance right?

what does c= ?

[prisma basalt]

c= the square of the hypotenuse, and to get the distance we would get the square root of c

so then if i take the distance from 0 like this

[river willow]

yes

[prisma basalt]

since the origin is 0,0 then (x - 0)^2 + (y - 0)^2

and then you

square root the answer for the distance?

[river willow]

yes

[prisma basalt]

to brush up on this on khan academy i should keep doing pyth theorem stuff?

[river willow]

can you write down the answer so i can check

[prisma basalt]

write an algabraic expression for the distance from (0,0) to (x,y) would be √(x-0)^2 + (y-0)^2 write an algebraic expression for the squared distance from (0,0) to (x,y) would be (x-0)^2 + (y-0)^2

[river willow]

i hope you got it right

sqrt(x^2+y^2)

it covers both ok

[prisma basalt]

i think i understand

thanks for your patience and help

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[river willow]

🍞

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[true olive]

Im having trouble constructing the ranges for tan(x)

[true olive]

so I know that there are 2 cases here

the top being positive and the bottom being negative or the top being negative and the bottom being positive

so it simplifies to

$\tan x \ge -\sqrt 3 \ \tan x \le -1$

[solid kiln]

nashira._.

[true olive]

and

$\tan x \le -\sqrt 3 \ \tan x \ge -1$

[solid kiln]

nashira._.

[true olive]

so I tried to solve these 2 series of equations and I cannot seem to correctly get the ranges of tan

[signal bobcat]

u can make 2 tables and see when the top is negative and when the bottom is negative and compare the two tables

@true olive

and what u do in cases of periodic functions is you look at the range [0,2pi]

and then add $+k \cdot 2\pi , k\in \mathbb{Z}$

[solid kiln]

spookyspaghetti

[trim jolt]

@true olive Has your question been resolved?

[true olive]

the problem in this case is that some of the answers are in the negative domain

here is the answer

[signal bobcat]

oh then u look in this interval my bad [-pi/2 , pi/2]

and then u can see u add +k*pi , K in Z

[true olive]

now how do I construct the intervals for tan? cause ik they are kinda different to cosine and sine

[true olive]

since tan is only negative in the second and fourth quadrants, how can I translate that to make the answer that's where Im so stuck

[signal bobcat]

u look at the interval $[\frac{-\pi}{2} , \frac{\pi}{2}]$ this way u have all the values than tan can have in the intervall

[solid kiln]

spookyspaghetti

[true olive]

shit im still not getting it

[true olive]

How would I plot a unit circle from the negative domain in this case?

[signal bobcat]

wdym plot a unit circle from the negative domain ?

[true olive]

like u know the way the unit circle will start from 0 to 2pi? is there a way to now show it from -pi/2?

[signal bobcat]

no u just only look at that part of the circle

the u can look at the 4th quadrant as negative angles

so the 4th quadrant is from 0 to -pi/2

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@true olive Has your question been resolved?

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@true olive Has your question been resolved?

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[nova pumice]

Am I currently doing this right?

[nova pumice]

I am REQUIRED to use difference quotient

Find derivative

[trim jolt]

@nova pumice Has your question been resolved?

[nova pumice]

<@&286206848099549185>

[river willow]

are u finding derivative?

[nova pumice]

Yes

[river willow]

what are u differentiating? and why is there a x^2+3

[nova pumice]

f(x) = (it wasnt written in)

[nova pumice]

because there is

?

[river willow]

the question had no x^2+3?

[nova pumice]

it has one

im confused

[river willow]

what is f(x)?

[nova pumice]

that equation for 4

It’s suppose to be this

[river willow]

oh, 4x/(x^2+2) with respect to x at 2?\

[nova pumice]

yes

[river willow]

ok i get u want it to have the same denominator at the top right?

[nova pumice]

yes

but i feel like theress a easier

way to do it

[river willow]

but there should not be a +3, it should all be +2

yea um let me think about it. but i think it will be a bit long either way

[nova pumice]

yea

someone did it like this

but i dont understand it

(the bottom one)

[river willow]

let how to get from the second to the last?

[nova pumice]

yeah

[river willow]

let
a=(x+h)^2+2
b=x^2+2

the denominator is abh

got that?

[nova pumice]

i understand the top part

but i dont get the denominator

like why is it thisfrom that big expression

i dont get it

[river willow]

its abh

[nova pumice]

could you elaborate please

[river willow]

its from the denominators of the previous stuff

ok first ignore the h

the h at the bottom i mean

[nova pumice]

okay

[river willow]

actually let me just give another example

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

[solid kiln]

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

[river willow]

and notice both denominators are bd so we can combine them

$\frac{ad-bc}{bd}$

[solid kiln]

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

[nova pumice]

i see

[nova pumice]

what are we combining here though? I understand this because they are on both sides but why (x^2+2)h

[river willow]

its similar but do this

and we have a /h below so we add that h at the end

[nova pumice]

ohhh ok thank you

[nova pumice]

and now do i just miltiply everything here?

[river willow]

probably at the top yea, at the bottom you probably leave it as it is

[nova pumice]

eye eye

[river willow]

and u try to factor something and cancel stuff at the top and bottom probably?

[nova pumice]

ill try it

[nova pumice]

Unsure where to go now

Do I just factor a h out of everything on the top?

[river willow]

hm yea u can cancel one h

[nova pumice]

What now

[river willow]

actually

wait

u can just

[nova pumice]

ok

[river willow]

not do this from the start

just let x=2

hahahaha

[nova pumice]

It’s not how she wants us to do it 😭

[river willow]

oh

u have to find the derivative first?

[nova pumice]

Yes

[river willow]

rewrite the top

combine the x^2

factor out 4 and see if u can factorise it more

[nova pumice]

I don’t think there is anything else I can do

[river willow]

err

the top should be 4(2-xh-x^2)

[nova pumice]

Oh yeah

[river willow]

anyway yea ive no idea how to continue

good luck

[nova pumice]

Tanks

[nova pumice]

.close

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[nova pumice]

.reopen

[trim jolt]

✅

[nova pumice]

how do i solve this

[past river]

You should split the fraction

[nova pumice]

how

[past river]

Using addition properties

[frail heron]

Just divide the numerator and the denominator with x^3

[past river]

That also works

[frail heron]

yeah, but I’m still curious about your solution

Could you proceed?

@past river

[nova pumice]

im sorry how? 😭

-9/3

?

[frail heron]

No, look carefully

The numerator is -9x^4 -1

[nova pumice]

yes

[past river]

Just split it into ||-3x - 1/(3x^3) and by the linearity of the limit operator you get two limits. One goes to -inf, one to 0||

Spoilers Light, don‘t check if you want to work it out yourself

[nova pumice]

regardless what you just said doesnt make sense for me anyways

[frail heron]

Ty, didn’t come up with it that the first glance

[past river]

Well then you can proceed with SkyAndNight‘s way if you understand that better

No hard feelings haha

[frail heron]

You divided it incorrectly

[nova pumice]

ok divide the whole thing

[frail heron]

You’re supposed to get -9x-1/3 in the end

[nova pumice]

yeah

sorry

[frail heron]

It’s ok

[nova pumice]

oka

[nova pumice]

(what do i do from there)?

uh

🇸🇰

.close

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[nova pumice]

.reopen

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✅

[nova pumice]

im trying to find derivitive with difference quotient

am i doing it right

[nova pumice]

<@&286206848099549185>

[half mural]

lemme check

[nova pumice]

amen

[half mural]

the answer should be -3

[nova pumice]

i got that too at the bottom

[half mural]

you could solve it easier

there is a formula

[nova pumice]

im aware but my teacher

specifically

wants me to use that

🇸🇰

[half mural]

ahhh okay

[nova pumice]

wrong emoji

💀

i also asked because photomath said it was -6

which i thought was odd

[half mural]

get the derivative first and u could just plug in 1

i mean replace x by 1

[nova pumice]

yea

thats what i did

i got -3

[half mural]

nice

[nova pumice]

i didnt think photomath could be wrong

lol

my bad

[half mural]

do you know formula to solve this?

[nova pumice]

fx+h-fx

over

h

[half mural]

ah no no

not the first principle

[nova pumice]

?

[half mural]

d/dx (a/f)

[nova pumice]

ah sorry i dont even know what

d

is

we just got introduced to derivatives

im sorry

[half mural]

oh thats okay

gl

[nova pumice]

np

i love u

.close

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[half mural]

so btw d is differential

[nova pumice]

oka

[nova pumice]

.reopen

[trim jolt]

✅

[nova pumice]

do i just plug in 7

[neon pine]

If you just plug in 7 then you should carefully observe the outcome

[neon pine]

If you put 7 what will be your outcome?

[nova pumice]

21/0

(infinity)

[neon pine]

So, what is anything divided by 0?

[nova pumice]

inf

[neon pine]

Yeha. Got it.

So what you observe is that when the x = 7 something undefined and infinite things are happening. So limit is saying you to approach towards 7 and observe your outcome.

[neon pine]

To observe what's happening if x approaches toward 7 You can apply L hospital's theorem.

[nova pumice]

okay tanks

one more question

how would i solve this if the rational function was top heavy?

[neon pine]

Do you know what's L hospital theorem says?

[nova pumice]

oops

wrong eomoji

💀

ono

[neon pine]

Okay listen. L hospital theorem is applicable for any differentiable function.

[nova pumice]

ok

[worldly wing]

We don’t suggest using l’hopital’s rule though

It’s not a good way to understand limits

[worldly wing]

You can divide the numerator and denominator by the highest power of x (i.e x^2)

[nova pumice]

oh i see

thank

[neon pine]

It is if you can visualize what is slopes are doing at that point of time.

[worldly wing]

But OP clearly can’t, which is why they’re asking the question…

[neon pine]

Ooooo

Then it's okay to do algebra manipulation 😋

Sorry

[worldly wing]

In general, we almost never encourage using L’hopital’s rule for limits on this server

Even though it’s a good tool for limits, if you introduce that too early many don’t even bother learning actual limit manipulation techniques

[nova pumice]

Can u help me with these two pls then I go sleep 💤

[neon pine]

yeha. actually understanding the standard limits is important before learning what the slopes of the functions are behaving.

[nova pumice]

(Idk what to do if it’s bottom heavy)

[worldly wing]

What do you mean by bottom heavy?

[neon pine]

factorize tge denomenator ig

[nova pumice]

Degree on bottom is heavier

Than numerator

[worldly wing]

The second one can just be solved by simple substitution, there’s no indeterminate form there

[neon pine]

its same both are x^2

[worldly wing]

If that’s the case then as x tends to infinity the limit is 0

You can see this again by dividing the numerator and denominator by the largest power of x (i.e x^3)

[nova pumice]

And if it was negative infinity?

[worldly wing]

Same thing

[nova pumice]

It would still be 0

[worldly wing]

Yes

[nova pumice]

So I can just plug in 5 for x normally?

[worldly wing]

And if the degree is larger on the numerator then it goes to + or - infinity

[worldly wing]

Yeah

There’s no discontinuity

[nova pumice]

How would I know if there was one (sorry I am slow

[worldly wing]

If the denominator was becoming 0 at x=5 then there’s a discontinuity

There are many examples

For example in the floor/greatest integer function there’s a discontinuity at every integer

A polynomial is continuous everywhere

A rational function of two polynomials (like the one you have) has discontinuities wherever the denominator becomes zero

[nova pumice]

Ok thank

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[neon pine]

How can I calculate this?

[scenic roost]

do you know the power of log rule

[neon pine]

I just actually forgot that.

[scenic roost]

$b^{log_b{x}}=x$

[neon pine]

Btw I just saw you asking a question of function. 🙃

[neon pine]

b is the base here ig

[neon pine]

Can you just say me that how it is derived

[solid kiln]

Amby

[scenic roost]

yep

i was figuirng out how to get the bot to do that

[neon pine]

If you are free for a moment can you teach me how you can write and that bot beautifully converts into a mathmatical font.

[neon pine]

Like this @scenic roost

[scenic roost]

https://www.youtube.com/watch?v=YkGaRTxvIC8

[neon pine]

Ok I will Watch this

[scenic roost]

search up latex math equation tutorials

theres a whole bunch on there

[neon pine]

The latex code is converted by the bot right?

[neon pine]

Btw the ans is 7 here right?

[scenic roost]

yep

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[scenic roost]

https://tenor.com/bZP3r.gif

[scenic roost]

.close

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[neon pine]

$2^{\log_{2} 7} = 7$

[solid kiln]

Avirup

[scenic roost]

👏

do that in #latex-testing tho

[neon pine]

I did it. Yay

[scenic roost]

.close

[neon pine]

Ok ok

[scenic roost]

good job tho

[neon pine]

Why I can't use them? Why those channels are blocked for me

Are they blocked for you too @scenic roost

Do you what is happening? Regarding this @scenic roost

[scenic roost]

.close

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[restive spire]

according to a video i found on youtube on finding the lcm of fractions, the answer for the first item is 12/5

[restive spire]

but why is it not 6/5? when i try to solve it, it seems to me that 6/5 is the lower answer that is a multiple of all three given fractions

[cedar flower]

it's because 4/20 isn't simplified; if you for example turn 2/5 into 4/10, then you get a hcf of 10 and your lcm is 12/10 = 6/5
if you turn it into 8/20, you get a hcf of 10 again but a lcm of (8, 3, 4) = 24 = 12/5 again

if you do it to 2/5, 3/10, 1/5 then you get an lcm of 6/5

[restive spire]

oh wow, that's crazy. so that means, your lcm changes if your fractions aren't in reduced form?

[cedar flower]

No, sorry - the results you get from this technique change but the lcm is always 6/5

Should've been clearer

[restive spire]

ohh ok. so, am i right in saying that to use the technique properly, u have to first reduce all the fractions to get the right answer?

[cedar flower]

If you don't fully simplify your fractions then it seems weird things happen

[restive spire]

ooooh alright, i think i got it

thank you!

.close

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[rapid horizon]

Is there any short formula like this series have?

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[wraith hinge]

idk u should do it

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[wraith hinge]

,rotate

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[shrewd vessel]

I'm guessing you need to find the basis matrices of W

[wraith hinge]

Basis matrices?

[shrewd vessel]

I'm not too sure tbh but my guess would be write the general matrix in W as a linear combination of n matrices (and those would be the basis matrices that span the subspace W) where n would then be the dimension

[rapid horizon]

What should I do for a+b+c?

[shrewd vessel]

separate the matrix into n number of matrices (where you need to figure out what n is), where each of them only depend on one of a,b,c

[rapid horizon]

a

c

1×1

[shrewd vessel]

1x1?