help-0

[abstract current]

.

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[sick tangle]

i need help

[tacit arch]

use definition of stationary point

and f(0) = -5

[sick tangle]

f,(x)=0?

[tacit arch]

do you know what the x value is for the y-axis ?

[sick tangle]

yes

4 and 3

[tacit arch]

oh you were replying to a different message

f'(x), not f,(x)

[sick tangle]

my apostrophe button is broken xd

thats why i used a comma instead

[tacit arch]

yea so use f'(x) = 0 to get an equation for your unknowns. then integrate f'(x) to get a form of f(x) up to a constant and use the "curve meets y-axis at -5" to solve for the other constant

[sick tangle]

ok ill see what i get to

.solved

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[fallen nimbus]

How did the 5 arc tan turn into 5/2 arctan

[gray isle]

they made a mistake,
they should've had 5/2 instead of 5 initially

[fallen nimbus]

ohh thank u

.close

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[sick tangle]

markscheme to part b:

[sick tangle]

question:

my question is regarding to part b

[sick tangle]

the part all in orange

i dont get at all.

how did an equation like that go into such factorised form

[sour verge]

Aren’t they just expanding the equation given in b?

And then on the right they rewrite the equation you get from the integral

Hence how they conclude that they are identical

[polar ivy]

So the arrow should really be pointing like this:

[sick tangle]

ohhh i see

[sick tangle]

i see

ty guys

.solved

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[small horizon]

Having trouble figuring out how to get to right hand end of first line to the second line

[small horizon]

How do i consolidate E into one term, and split T into two?

[naive valley]

after exponentiating, you have something of the form A = (E + B) / (E - B), right?

[small horizon]

Yes.

[naive valley]

ok, multiply both sides by (E - B), which gives you:
A(E - B) = E + B

put the E stuff on one side and the non-E stuff on the other:

AE - E = AB + B

E(A - 1) = B(A + 1)

E = B(A+1)/(A-1)

(using A and B here instead of the nastier expressions makes it easier to see what's going on, you can plug in A and B at the end)

[small horizon]

Ahhhh

Thank you!

[naive valley]

yw

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[vapid steppe]

is the answer 1 or 4

[vapid steppe]

im between 1 and 4

[naive valley]

don't you generally want to use a surface whose normal vectors are parallel with the field?

[vapid steppe]

ye

[naive valley]

is 1 or 2 going to do that for you?

[vapid steppe]

i thought it was like gauss's law only works if the charge is inside the surface

ohh wait

[naive valley]

yea, that would be true in both cases if the sphere and cube are large enough

[vapid steppe]

i misinterpreted the question

[naive valley]

but if you want to use it to find the field, you need to use a surface which has normal vectors parallel with the direction you know the field will point (by the geometry of the situation)

[vapid steppe]

so 1 and 2 dont work?

[naive valley]

1 certainly won't work, the field is not going to radiate out spherically from a cube

is it going to radiate "cubically"?

[vapid steppe]

no

[naive valley]

right

so neither one will work

[vapid steppe]

oh ok ty

[naive valley]

yw

[vapid steppe]

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[austere charm]

Yo so how tf I even do this

Ik it's B or C because of the equal

Just use a test point?

[patent vale]

you know which one it is because of the side the inequality is facing

[austere charm]

Could I just say plug in a point like -2 -2

And then see from there

[patent vale]

ok just look at the inequality and is it highlighting the part less than the equation or more than the equation

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[wheat badge]

can someone explain to me why d hat is unbiased- i was under the impression dhat was the stat

[broken pivot]

I'm pretty sure $\hat d$ \textit{is} biased.

[ocean seal]

King Leo

[wheat badge]

thats what i was thinking but a friend told me oposite

i thought it was biased because wouldnt the probability be equal to mean if it was unbiased- idk where the statistic falls into play here

[broken pivot]

A sample is unbiased if it properly reflects the population

[junior vigil]

if the expected value of an estimator of a parameter=parameter, then we call the estimator unbiased

if this is not the case, then its biased

[left hearth]

yes, you are right. Just use a test point and you get the C option as correct

[wheat badge]

yes but here isnt it saying d hat represents the statistic?

[wheat badge]

OHHH

okayyy iseee

thanks moose micheal

[junior vigil]

np

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[alpine sable]

Help

[alpine sable]

Can someone help me step by step just 10-17

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[steel parrot]

can someone help me? How to find the domain of composite function f(g(x))?

[steel parrot]

$f(x)=\sqrt{x-4}$

and $g(x)=1/x$

[ocean seal]

Odd_the_Wolf

[steel parrot]

the domain of g(x) is (-inf, 0)U(0, inf)

But I am not sure how to find domain of sqrt((1/x)-4).

[ocean seal]

Odd_the_Wolf

[alpine sable]

for f(x) to be real, what do you think we should do?

ensure that the number inside the square root is greater than or equal to 0 right?

[steel parrot]

the inside must be >=0

yes.

[alpine sable]

yupadoodly do

[steel parrot]

so I got 1/x-4 >= 0

[alpine sable]

then how do you think we should find the domain from here?

mmmhmmm

$$\frac{1}{x} - 4 \geq 0$$

[ocean seal]

Edmund Cloudsley

[steel parrot]

should I combine them into one fraction?

[alpine sable]

Not required. This is a very simple inequality

$$\frac{1}{x} \geq 4$$

[ocean seal]

Edmund Cloudsley

[alpine sable]

$$\frac{1}{4} \geq x$$

[ocean seal]

Edmund Cloudsley

[alpine sable]

$$x \leq \frac{1}{4}$$

[steel parrot]

oh we can do that?

[ocean seal]

Edmund Cloudsley

[alpine sable]

yeah course why not

[steel parrot]

what if x is negative?

[alpine sable]

oh yeah sorry I forgot about that yes

it makes sense to combine them into one fraction

$$\frac{1 - 4x}{x} \geq 0$$

[ocean seal]

Edmund Cloudsley

[alpine sable]

now you can just do sign analysis

the critical points are x = 0

and x = 1/4

[steel parrot]

if x<0, it is negative>0.

[alpine sable]

yes

if its between 0 and 1/4 its greater than 0

if its more than 1/4 its less than 0

therefore

$$x \in ]0, \frac{1}{4}]$$

[ocean seal]

Edmund Cloudsley

[alpine sable]

where 1/4 is included

and 0 is not included

good job pointing out the negative numbers thing. I totally forgot about that lol

[steel parrot]

is that the answer for the domain of f(g(x))?

[alpine sable]

yup

[steel parrot]

one more question.

[alpine sable]

sure go ahead

[steel parrot]

so $$f(g(x)) =\sqrt{\frac{1}{x}-4}$$

[ocean seal]

Odd_the_Wolf

[alpine sable]

yeah

that is true

[steel parrot]

oh wait, I think I got it.

[alpine sable]

okay sure

also instead of writing f(g(x))

even though I know it is widely accepted

you may want to write it as

[steel parrot]

my confusion was if x goes to infinite, wouldn't it also work.

[alpine sable]

$$(f \circ g) (x)$$

[ocean seal]

Edmund Cloudsley

[alpine sable]

yeah it would not

let's see why

$$\lim_{x \to +\infty} \frac{1}{x} - 4$$

[ocean seal]

Edmund Cloudsley

[alpine sable]

as you have larger and larger values for x

1/x would become 0

let's see this in action

,w calculate 1/1000000 - 4

[ocean seal]

Results provided by WolframAlpha

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

Requested by alison_burg3r5

[alpine sable]

this number is almost equal to -4

therefore infinity wouldn't work

[steel parrot]

ok. thank you!

[alpine sable]

perfect

happy to help

[steel parrot]

.close

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[last vault]

how do i know when to use like the case of finding if theres another angle with sine rule and cosine rule

[topaz sage]

?

[last vault]

like

uk when u use cosine or sine rue

[topaz sage]

!xy

[lone heart]

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.

[topaz sage]

Depends on the question.

[last vault]

ok the answer is a degree

i dont rlly have a pic

but theres 2 answers possible

when u use the sine or cosine rule

idk how to identify when theres 2 answers

[alpine sable]

Arae you talking about the ambiguous case of sine?

[last vault]

hmmm i think so

[alpine sable]

https://www.youtube.com/watch?v=RCyjglaJo5w

watch this

[last vault]

is this the same w cosine

i cant remember fully but its like 360 - answer or smth

[woven kestrel]

yes

well

for sine it's pi - answer

and answer

[last vault]

pi?

[woven kestrel]

for cos it's +-answer

[last vault]

isnt it 180

[woven kestrel]

in radians

same thing as 180

[last vault]

oh

ye i havent memorised radians yet

[paper mango]

just remember 180° = pi

:]

or 2pi = 360°

[last vault]

whats 1 degree in radians

[paper mango]

but yeah sin(x) = sin(pi - x)

[paper mango]

1° = pi/180

pi/180 is the conversion factor

[topaz sage]

radians and degrees are linearly related

[last vault]

would that be for cosine so cos(x)=cos(2pi - x)

[paper mango]

and 1 = 180/pi°

[paper mango]

cos(x) = cos(-x)

[paper mango]

but yes also true

since cos(-x) = cos(2pi-x) = cos(4pi-x) = ...

[last vault]

wait if u use the cosine rule to find an angle would there be 2 answers possible?

[paper mango]

depends on the problem

sometimes yes sometimes no

[last vault]

how would i know

[paper mango]

by the angles you get

[last vault]

ok so lets say angle i get is 50

[paper mango]

if you get the angles 50° and 310°, 310° won't make much sense in the context of a triangle

[alpine sable]

remember that

if $\sin (x) = \theta$
$$\text{1. } x = \pi - \arcsin{\theta} + 2 \pi k$$
$$\text{2. } x = \arcsin{\theta} + 2 \pi k$$

if $\cos (x) = \theta$
$$\text{1. } x = -\arccos{\theta} + 2 \pi k$$
$$\text{2. } x = \arccos{\theta} + 2 \pi k$$

if $\tan (x) = \theta$
$$\text{1. } x = \arctan{\theta} + \pi k$$

where $k \in \mathbb{Z}$

[last vault]

what

[ocean seal]

Edmund Cloudsley

[last vault]

i have no clue what on earth that means

hmm

what year is this

[alpine sable]

you were talking about multiple solutions right?

[last vault]

yes

[alpine sable]

this is how you find multiple solutions to a trig equation

[alpine sable]

year 10 i guess?

[last vault]

theres tan rule??

[alpine sable]

not that I am aware of

I am just not fully sure what you are asking

if you are asking about multiple solutions to a trig equation

[alpine sable]

this is how we do it

[last vault]

isnt arc only in circles

what if u get a triangle

[alpine sable]

arctan, arccos and arccsin are just the inverse functions of tan, cos and sine

[last vault]

oh

hmm i think i get it

ok ima try

[woven kestrel]

only if the problem is a trig related question where we consider a circle with solutions

otherwise +2kpi would usually not be included when we're dealing with a triangle problem

[alpine sable]

yes that is true

[woven kestrel]

yes, but it's not used as much as sine and cos rule

[last vault]

whats k

which is z?

[woven kestrel]

this is the law of tangents

but it's not used

as much

[last vault]

oh

[woven kestrel]

an integer

[last vault]

so for this since im only doing it with triangles i wouldnt need to include the 2pi k or pi k

[alpine sable]

yeah

[woven kestrel]

yes

[alpine sable]

I would really recommend watching this

[last vault]

yes im watching rn

[alpine sable]

It would help you to find the two solutions to an angle

oh perfect

good

[last vault]

for the sine law is it always given that there will be another angle in the triangle which is given

wait nvm

thats a dumb question

ok so for the vid

it talks abt if opposite is longer than the other one theres only 1 angle

but

for this isnt the opposite longer

and theres still 2 solutions

[woven kestrel]

The sine rule is used when we are given either two angles and one side, or two sides and a non-included angle (SSA). The cosine rule is used when we are given either three sides (SSS) or two sides and the included angle. (SAS)

[last vault]

i get that part

[grave matrix]

because "a" here refers to the edge whose opposite angle is known

[grave matrix]

So here, b is 4.0 and a is 3.5

[last vault]

oh i think i get what u mean

[grave matrix]

b is not < a here

[last vault]

the angle thats known u look at that one

[grave matrix]

yee

[last vault]

which then the known angle opposite is the one u see

okay okay

ty

[lone heart]

@last vault Has your question been resolved?

[last vault]

is there a way to know if there is another angle with cosine without using this formula

how do ik when to do it for cosine

[lone heart]

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[low basin]

How to determine If in point r=4 is min or max i dont want to count second deriviative

[lone heart]

@low basin Has your question been resolved?

[low basin]

<@&286206848099549185>

[fair acorn]

yes

[low basin]

.

[fair acorn]

wait

just hold on ok

i ll be back soon

[low basin]

👍🏾

[fair acorn]

sorry

[low basin]

<@&286206848099549185>

[lone heart]

@low basin Has your question been resolved?

[lone heart]

@low basin Has your question been resolved?

[lone heart]

@low basin Has your question been resolved?

[lone heart]

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[trail sierra]

help

[mental python]

!da2a

[lone heart]

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/

[broken pivot]

Is there a list of such shortcut commands

[forest marsh]

Probably

[summer dirge]

see #helpers-info

[broken pivot]

Thx

[lone heart]

@trail sierra Has your question been resolved?

[broken pivot]

@trail sierra whats your question

[trail sierra]

i need help solving some alegbra

Translations of Exponential Functions

[loud warren]

what if it's not about the question but the friends we made along the way?

[loud warren]

show your problem so we can help you 🙂

[broken pivot]

The duality of man

[trail sierra]

1sc

[fierce cipher]

!original

[lone heart]

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.

[trail sierra]

i need some examples i can use for Translations of Exponential Functions in every instance

[fierce cipher]

First, what is f(x)

[broken pivot]

Looking at the y-intercept can be helpful

Because $ab^0 = a$ for any real $b$

[ocean seal]

King Leo

[trail sierra]

hm

[cedar cove]

Whats the Error in the sollution

[tacit arch]

!occupied

[lone heart]

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).

[cedar cove]

?

[tacit arch]

read this

[cedar cove]

Hih

Huh

[trail sierra]

read ^

[lone heart]

@trail sierra Has your question been resolved?

[lone heart]

@trail sierra Has your question been resolved?

[lone heart]

@trail sierra Has your question been resolved?

[lone heart]

@trail sierra Has your question been resolved?

[lone heart]

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[shrewd sail]

I dont understand how to solve this when the function is x^3. I tried it but i feel like something went wrong

[left orbit]

take h common and cross out num and den

[shrewd sail]

But is it to the point i got right?

[left orbit]

yeah looks about right

[shrewd sail]

Thanks. Im going to try again if i fail well i just come back :)

[left orbit]

sure

[shrewd sail]

.close

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[warped topaz]

I have some ideas on how to start this but im not really sure

Like I think I set x(t) and y(t) both equal to 0 and solve

0 = 2sin(t + pi/4)

arcsin(0) = t + pi/4

pi*k = t + pi/4

t = pi/4 + pi*k

and

0 = sin(-t - pi/4)

[icy plinth]

I just had a quick look, but i'd rewrite sin(-t-pi/4) as -pi(t+pi/4) since it that is what x(t) is

Also just have x(t)=y(t)

[exotic canopy]

sin(-t-pi/4) = -sin(t+pi/4)

so the whole figure is just a line

[warped topaz]

How come we can do that?

[icy plinth]

you need both of them to be 0

you said it yourself :D

[static girder]

technically you just have to check when sin(t + pi/4) becomes zero for t in [-pi, pi]

both x(t) = 0 and y(t) = 0 boil down to sin(t + pi/4) = 0

just graph sin(t) and shift it by pi/4 to the left and see how many times it crosses the x axis

[warped topaz]

But how does them both equaling zero mean we can set them equal?

Instead of set them each equal to zero

[static girder]

x(t) = y(t) = 0

they're not always equal but at the t's we're interested in, they are

[warped topaz]

Ok but why dont we need to set it equal to zero first? Before we set it x(t) = y(t)?

[static girder]

.

[warped topaz]

Like theyre not always equal to zero, right?

[static girder]

no but we set them to zero and solve for t

[warped topaz]

So was I right to set them equal to zero first?

[static girder]

yes

[warped topaz]

I was right the whole time yall were just confusing me 😂

But ok

They both equal sin(t + pi/4)

[warped topaz]

So t = pi/4 + pi*k right?

[static girder]

yes

[warped topaz]

And then I sub in values for k, and the values that are between pi and -pi are the times p passes through the origin right?

[static girder]

yes

[warped topaz]

Great thanks

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[graceful sparrow]

Show that f satisfies Cauchy-Riemann conditions on z=0 and show that the derivative does not exist in z=0

[graceful sparrow]

$u(x, y)=x^{3}-y^{3}, v(x, y)=x^{3}+y^{3}$

[ocean seal]

nick

[graceful sparrow]

$u_{x}(x,y)=3x^{2}, u_{y}(x, y)=-3y^{2}, v_{x}(x,y)=3x^{2}, v_{y}(x, y)=3y^{2}$

[ocean seal]

nick

[graceful sparrow]

$u_{x}(0, 0)=v_{y}(0, 0)=0, u_{y}(0, 0)=-v_{x}(0, 0)=0$

[ocean seal]

nick

[graceful sparrow]

satisfies C-R

how do I show the derivative does not exist in 0?

[lone heart]

@graceful sparrow Has your question been resolved?

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@graceful sparrow Has your question been resolved?

[lone heart]

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[muted locust]

can anyone help me with the logarithm?

[lone heart]

@muted locust Has your question been resolved?

[static bobcat]

multiply the powers out

u should get something like 5^log_5(...)

and recall that n^log_n(x) = x

[lone heart]

@muted locust Has your question been resolved?

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[warm garden]

Can yall help me find Y?

I need to use law of cosine but I don’t get it

[junior kraken]

Do you know trig ?

[warm garden]

It’s very faint ngl

Like I know some of it but not a lot

[junior kraken]

Can you say what's cos29°

[warm garden]

my calculator is broken do you know how to use the calculator on here

Like I use photomath

And it’s on radian instead of degrees

wait

[warm garden]

-0.748058

[junior kraken]

I didn't mean that

cos(theta) = Adjacent/Hypotenuse

[junior kraken]

This value is certainly wrong, all trig identities are positive in the first quadrant!

[warm garden]

Ikr

Idk how to get the calculator out of radian

[warm garden]

oh like

cos^-1?

[junior kraken]

Nah

cos(29°) = y/42

Observe this carefully!

[warm garden]

I gotta go sadly cause the bell is gonna ring

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[granite fiber]

Anyone can help me check my answer?

[little drum]

Just a sec.

mb @granite fiber 12k is correct.

however, don't you mean Delta x = 12k?

You've written Del y = 12k tho~

[granite fiber]

Oh ya tq for that

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[rugged acorn]

Why is this not working

[tight pier]

Mein Lieber, wie funktioniert (a+b)² richtig

[rugged acorn]

So hatte ich’s davor

Ergebnis ist aber falsch

[tight pier]

das ist schiefgegangen im 2. Schritt schon

Schau dir mal die Binomischen Formeln richtig an

[tight pier]

Du hättest hier
[ x+6 = (x-4)+2\cdot 2\sqrt{x-4} +4 ]

[rugged acorn]

uff

[tight pier]

Und was du hier machen kannst ist, du bringst alles auf die andere Seite außer Wurzel(x-4)

und dann schaust du ob du nochmal quadrieren darfst, um die endgültig die Wurzel loszuwerden

[rugged acorn]

verstehe leider nicht so ganz, wie ich da hinkomme

[tight pier]

(a+b)² = a²+2ab+b²

a = sqrt(x-4)
b = 2

[rugged acorn]

Sieht das so dann ausgeschrieben aus ?

[tight pier]

du vergisst den 2ab term

[tight pier]

,, \left ( \sqrt{x+6} \right )^2 = \left (\sqrt{x-4} \right )^2 + 2 \cdot \sqrt{x-4} \cdot 2 + 2^2

[rugged acorn]

achso also die 2 mit in die klammer

Wusste nicht, dass ich die sqrt(x-4) als ein Ganzes beachten muss, aber so sollte es ja dann klappen

[tight pier]

jetzt ists richtig

[rugged acorn]

jawohll jz kam ich aufs ergebnis

dankeee

[lone heart]

@rugged acorn Has your question been resolved?

[lone heart]

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[waxen turtle]

Am I doing the B. Right so far

I think it is wrong idk

[buoyant saddle]

bro you need a new pencil

and yea what you’ve written is not a point

you’re supposed to differentiate implicitly to solve for y’

seems like you did that in part a so i’m not sure why you didn’t do that for part b

[lucid osprey]

Bro

[buoyant saddle]

Bro

[lucid osprey]

Is that implicit diffrentiation

What course are you taking

[waxen turtle]

Yes

[waxen turtle]

calc

[waxen turtle]

😭

[lucid osprey]

Ah I thought A level maths for a sec

[waxen turtle]

Idk wat that means

[buoyant saddle]

some british shit

[lucid osprey]

True

[lone heart]

@waxen turtle Has your question been resolved?

[waxen turtle]

How to do

[buoyant saddle]

$y’ = -\frac{3x^2-9y}{3y^2-9x}$

[ocean seal]

knief

[buoyant saddle]

did you get this

[waxen turtle]

Wdym

[buoyant saddle]

bro where did you go for 20 minutes

[waxen turtle]

I never simplified it i just plugged it in immediately after getting the derivative

[waxen turtle]

I WAS GOING TO CLASS

[buoyant saddle]

ok well simplify it

[waxen turtle]

Y

[buoyant saddle]

to find the vertical tangent

[waxen turtle]

how

[buoyant saddle]

i mean its clear from the graph where it is but

[buoyant saddle]

denominator = 0

[waxen turtle]

booo

[waxen turtle]

I got + on the yop

Yop

Top

[buoyant saddle]

no you didn't

you got 9y - 3x^2 on the top

[waxen turtle]

😔

Fr

[buoyant saddle]

yes?

[waxen turtle]

Fr

[buoyant saddle]

notice how i have a - out front

[waxen turtle]

Umm but I do too

[buoyant saddle]

-(3x^2-9y) = 9y-3x^2

[waxen turtle]

And it's still the other way

[buoyant saddle]

bruh

your writing is illegible

[waxen turtle]

I only have a negative on the 3x^2

[buoyant saddle]

you wrote

$3x^2 + 3y^2\dv{y}{x} - 9y - 9x\dv{y}{x} = 0$

[ocean seal]

knief

[buoyant saddle]

move the 3x^2 and 9y over

then divide by 3y^2 - 9x

you get what i got bruh

[waxen turtle]

help

[buoyant saddle]

yep

[waxen turtle]

Don't you subtract the 3x^2 and then add 9x

where the extra negative from

[buoyant saddle]

add 9y

[buoyant saddle]

same shit as this my guy

[waxen turtle]

Umm I don't have 9y

[buoyant saddle]

i put that negative there because the way i found dy/dx is different

i use a different method

which requires some multivariable calc knowledge

[buoyant saddle]

ya do

you literally wrote it brother

[waxen turtle]

no where

[buoyant saddle]

first line

[waxen turtle]

Oh

On my paper it says X

Omg

😭 😭

[buoyant saddle]

yea no idea what went on below that

consider organizing your work

[waxen turtle]

I plugged in 4 2

[buoyant saddle]

and please write in a pen or a sharpened pencil

[buoyant saddle]

sure, whatever that means

oh you mean the point

[waxen turtle]

Fr

[buoyant saddle]

word

[waxen turtle]

Fr

[buoyant saddle]

go on

[waxen turtle]

OK

So do I the denominator thing bow

Now

To the bototm

[buoyant saddle]

yep

divide that bitch by 3 first tbh

[buoyant saddle]

here

common factor of 3

$y' = \frac{3y-x^2}{y^2-3x}$

[ocean seal]

knief

[waxen turtle]

OK

Wat do I solve for

[waxen turtle]

Ty

Do I solve for x

[buoyant saddle]

in what?

[waxen turtle]

The bottom

wehn it's equal to to 0

[buoyant saddle]

sure

then what

[waxen turtle]

And then like plug in

To the original

[buoyant saddle]

sure

[waxen turtle]

And find the point

Yayayaya

OK

I got (y^2)/3

@buoyant saddle is that right

[buoyant saddle]

yes but go on

[waxen turtle]

Okii

[buoyant saddle]

did you get it yet

[waxen turtle]

Mb i had to go to my next clas

[buoyant saddle]

bruh

[waxen turtle]

How to go from here

Do I take out a y^3

And eviscerate it

[buoyant saddle]

$y^3\left(\frac{y^3}{27} - 2\right) = 0$

[ocean seal]

knief

[waxen turtle]

Fr

[buoyant saddle]

so you have two factors

use the zero product property

set each factor to zero

[waxen turtle]

OK IM AT

y^3=54

[buoyant saddle]

yea

go on

whats y

and whats x

[waxen turtle]

do I simplify the third root of 54

[buoyant saddle]

you can

factor the 27

perfect cube

[waxen turtle]

OK 9√2

[buoyant saddle]

uhhh

no

[waxen turtle]

Oh

OK third root of 2

Right

[buoyant saddle]

still no

why 9?

cube root of 27 = ?

[waxen turtle]

oh 3

[buoyant saddle]

yep

now you have y

find x

[waxen turtle]

OK 3 times third root of 2

idk how to do that

liek

Wat is a cube root times a cube root

do I combine it into cube root of 4

[buoyant saddle]

you mean for y^2/3?

[waxen turtle]

Yes

[buoyant saddle]

then yea

what's your final answer

[waxen turtle]

OK

[buoyant saddle]

OK

[waxen turtle]

Is 0 also an answer

[buoyant saddle]

seeing as they said at what point, i'd say no

because its 0/0

problematic

im guessing they just want the one you got

[waxen turtle]

How to do this

[waxen turtle]

On the answer key it says 0,0 is the other one

[buoyant saddle]

find y' then y''

[buoyant saddle]

yea i mean you can include it

[waxen turtle]

It says in terms of x and y wat does that mean

I never show respect to y

[buoyant saddle]

an expression containing y and x

[waxen turtle]

All my homies hate y

Oh

[buoyant saddle]

what did you get

[waxen turtle]

Also on the other one how do I make 3 • third root of 4

Bcuz like cant you make it 9/3 • third root of 4 /3

and that's like 3 times something divided by 3

how did the 3 stay

[buoyant saddle]

$\frac{(3\sqrt[3]{2})^2}{3} = \frac{9\sqrt[3]{2} \cdot \sqrt[3]{2}}{3} = 3\sqrt[3]{4}$

[ocean seal]

knief

[buoyant saddle]

also you can think of adding exponents if youd like

you get 2^{1/3} * 2^{1/3} = 2^{2/3} = 4^{1/3}

[buoyant saddle]

9/3

[waxen turtle]

ya but like isn't the root also divided by 3

Oh nvm

Im thinking of addition

OK LEMME TRY THE NEXT ONE

[buoyant saddle]

i have to go

but

[waxen turtle]

NOOOOOO

[buoyant saddle]

you'll have some ugly shit

i can write it out

and you can check

[waxen turtle]

Okii

[buoyant saddle]

$\dv{y}{x} = \frac{5x}{2y}$

[ocean seal]

knief

[buoyant saddle]

$y'' = \frac{(2y)(5) - (5x)(2y')}{(2y)^2}$

[ocean seal]

knief

[buoyant saddle]

$y'' = \frac{5y - \frac{25x^2}{2y}}{2y^2}$

[ocean seal]

knief

[buoyant saddle]

$y'' = \frac{10y^2 - 25x^2}{4y^3}$

[ocean seal]

knief

[waxen turtle]

wat do I do after i get the first deerviavie

[buoyant saddle]

boom

[buoyant saddle]

differentiate that dy/dx

to get the second derivative

[waxen turtle]

okii

Ty

.close

[buoyant saddle]

quotient rule

[lone heart]

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[sly fossil]

What am I doing wrong on this fraction decomposition I don’t get it.

[glossy river]

hmm

let me solve on my notepad and tell you

[tough relic]

$\frac{A}{(x-1)^2}+\frac{B}{x-1}+\frac{C}{x+1}$

[ocean seal]

GoldBarley

[sly fossil]

Why though, if I write (x-1)^2 then there shouldn’t be another (x-1)

And shouldn’t the numerator on the first fraction be a first degree polynomial?

Since the denominator is 2nd

[tough relic]

No, that works for irreducible quadratics like x^2+1 or x^2+9

For $(x-a)^n\\$
$\frac{A}{(x-a)^n}+\frac{B}{(x-a)^{n-1}}+\text{...}+\frac{Z}{x-a}$

[gray isle]

A/(x-1)^2 + B/(x-1) could be expressed in the form (Mx + N)/(x-1)^2
it's just easier to integrate if you split it like that

[tough relic]

Nevermind :(

[ocean seal]

GoldBarley

[lone heart]

@sly fossil Has your question been resolved?

[lone heart]

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[tall sparrow]

Can somebody explain how the angle is negative pi/6 ?

arctan(1/sqrt(3)) is pi/6 for reference

I know it's because the pi/6 is in the wrong quadrant but I'm just confused on the process of getting that to negative pi/6

[little drum]

$w = 8\left(\frac{\sqrt{3}}{2} + i\frac{-1}{2}\right)$

[little drum]

so cos theta > 0, sin theta < 0

the only quadrant I'm aware of where this happens is the fourth quadrant :)

[tall sparrow]

How does this explain that the angle is negative pi/6 and not pi/6 ?

Wait never mind I realised that I put it into my calculator wrong.

.close

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[glad glacier]

need some help with this exercise (Jacobson Basic Alg I, 2.10 Q1)

my understanding of the setup is that if P(x) = x^2+x+1, then P(w) needs to satisfy P(w)=0. However, upon verifying, this does not seem to be the case. Could I check if there is any flaw in my understanding (?)

[lone heart]

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[glad glacier]

unlucky

[vale crag]

yeah you might have to reopen a channel, a scammer posted a link just before you

[glad glacier]

yeah no worries

[vale crag]

it got deleted

[glad glacier]

saw it haha

[lone heart]

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[eager kraken]

help me plz

[eager kraken]

liner approximation then use ur answer to find

[gray isle]

what have you tried?

[eager kraken]

i

used f(xo) + f'(xo)(x-xo)

to find LA so first part done

but im just confused about 2nd part how it tells me to use my answer to find 3sqrt1.2

i got 1 + 1/3(x-0)

for LA formula first part

[gray isle]

for what value of x
will (x + 1)^(1/3) = cbrt(1.2)

[eager kraken]

am not sure sorry

[gray isle]

don't overthink

[eager kraken]

is this jsut algebra

cube both sides

i rly dot know

[gray isle]

you can if you want

[eager kraken]

kk

[gray isle]

but not really even needed

[eager kraken]

bc tbh idk whats the goal we didnt really do smth like this

what she told me to do is take the number from the square root

and put it in x so it becomes

1 + 1/3(1.2 - 0)

but i dont think thats right

[gray isle]

no

x isn't 1.2

[eager kraken]

i got x + 1 = 1.2

so x = 0.2 ?

[gray isle]

yes

[eager kraken]

oh so just put 0.2 instead of 1.2 ?

[gray isle]

yes

[eager kraken]

1.06 which is equal to cbrt1.2

ohh

[gray isle]

approximately

[eager kraken]

yes

but

some quesitons lile this it just makes u sub in the number lemme find one

[gray isle]

depends on your function

[eager kraken]

yeah in organic chemistry tutor video he just took the number inside

it was a normal square root tho

not cubed

or does it not make a difference

[gray isle]

here your function is
f(x) = cbrt(x + 1)
and you want the approximation of
cbrt(1.2)

makes no difference they type of function, what matters is what's inside

[eager kraken]

Bro

i compeltely forgot

that 1/3 is acube rooot

whoops

wait so lemme show u

something like this

all we did was replace x with 1 even tho its cos1

[gray isle]

yeh, because you have
cos(just x with no other crap attached)

[eager kraken]

ohh

and this one too lemem find

use answer to find sin(3)

[gray isle]

same

[eager kraken]

ohh alr

and how to tell the differences again like what to do

[gray isle]

yeh, because you have
sin(just x with no other crap attached)

compare your function with what they want

[eager kraken]

kk

and last one hold up

this is the one from the organic chemistry

all i did was sub in the 3.99 and it worked got a close answer

LA = 2 + 1/4(x-4)

[gray isle]

yes

[eager kraken]

but its just confusing me a bit

how come we didnt od the same thing with the cube root

[gray isle]

because you didn't have just x under the root

you had x+1

[eager kraken]

wait so we just set f(x) to the given thing ?

[gray isle]

yeh

[eager kraken]

sqrtx = sqrt3.99

ohhhh

we only set when its for roots ?

[gray isle]

same principle applies

you want the input to be the same whatever it may be

just x
x + 2
x + 1
or w/e

g(h(x)) , and they want you to approximate g(7)
use the value of x where h(x) = 7

[eager kraken]

ohhhhhhhh

i remmeber this

composite funciton or something like that right

[gray isle]

if it's just g(x)
x = 7 and ur done
if you have g(x -6)
then you want
x - 6 = 7
etc

I'm just using composites to try and be general

[eager kraken]

nah its fine it makes more sense now

thx

if am confused with anything ill see if ur available myabe in a channel to help me thank you a lot

have a nice day

.close

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[sweet island]

first one

[sweet island]

hardest equation system i found yet, gotta prove its impossible

i tryed all possible manners

but there is always a little bit that verifies the equation

[high rapids]

,rotate

[lone heart]

@sweet island Has your question been resolved?

[little drum]

Let x = π/2 - y. Given inequalities are:

sin 2y + cos y ≥ 0

=> tan y/2 > √3 => y/2 in (π/3, π/2) U (4π/3, 3π/2)
(cos y)(sin y + 1/2) ≥ 0```

Check the bottom inequality with above intervals and seek a common solution

You'll be able to crack it

Well there's no soln sadly so :c

[sweet island]

that's the solution

it is impossible just had to prove it

thank you very much

[lone heart]

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[pine pumice]

How does the second shape cover the first without overlaps?

[cinder compass]

are you sure it's possible

[polar ivy]

what is defined as an overlap?

[ocean fossil]

How can something cover something else without overlapping

[pine pumice]

I mean how can shape 2 cover shape one without overlapping on itself

[cinder compass]

i think they mean filling it with tiles

one square goes to one square

[ocean fossil]

Can you rephrase? What does covering and overlapping mean

[polar ivy]

Oh, it need to cover the entire shape?

[ocean fossil]

Is the goal to make a square?

[pine pumice]

Yes it needs to cover shape 1

[cinder compass]

no

[pine pumice]

Shape 1 is not a perfect square

It’s part of a quiz for a 9 year old but I can’t seem to do it 😭

[ocean fossil]

It is not possible, chess board pattern

Unless I'm tripping

Are you allowed to mirror it

[fallen verge]

no need

[pine pumice]

Can’t mirror it

[fallen verge]

112
1322
4335
4455

[prime badge]

it doesn;t become different if you mirror it

[prime badge]

amazing

[ocean fossil]

I might be high

[pine pumice]

That’s the full question

[ocean fossil]

😭

[pine pumice]

And that’s the answer

It says you can’t mirror it

[ocean fossil]

AMC?

Format looks similar

[pine pumice]

It’s from a maths challenge for my little sister lol

Ohhhh

[ocean fossil]

From where

[pine pumice]

Thanks

First mathematics challenge

[little drum]

!done

[lone heart]

If you are done with this channel, please mark your problem as solved by typing .close

[pine pumice]

.close

[lone heart]

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[lone heart]

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[quartz crown]

Information given, find the limit of square root of "a"

[dull lintel]

lim fonksiyonu tanımlanmış mı

[quartz crown]

limit x sonsuza giderken

[dull lintel]

<@&268886789983436800>

[dull lintel]

x yok ki

[quartz crown]

Aman

n işte

[junior vigil]

<@&268886789983436800>

[urban swan]

first of all do you know how to solve the limit? what have you tried? im assuming lim is n tends to inf

[quartz crown]

It is

I do solve limits but i stucked on this one

[urban swan]

note that what is inside the ln looks very similar to (1 + 1/x)^x

which we know is e

we can ignore ln and consider it at the end

inside the brackets can be rewritten as 1 + 1/((3n+1)/a)

note that multiplying anything by 1 doesn't change anything, at exponent, at base, at anything really

so we can multiply and divide by (3n+1)/a at the exponent

did you get this step?

[quartz crown]

We do this to the exponent 2n-1?

[urban swan]

yes

we are basically multiplying by 1

[quartz crown]

Okay

[urban swan]

multiplying 2n-1 by (a(3n+1))/(a(3n+1))

which is technically 1

[urban swan]

now apply this

we have 3n+1 over a both in the denominator in the brackets and on the exponent

that becomes e and we still have a weird exponend

we will get e^(a(2n-1)/(3n+1))

now ln gets rid of the e

and you just solve that limit = 4

a will just be a constant btw

so lim sqrt(a) the lim can be ignored

[quartz crown]

What do i do now

@urban swan

[urban swan]

lets rewrite that as this

same thing

[urban swan]

note you have the same thing on denominator and exponent

you know that for lim x-> inf (1+1/x)^x = e

instead of x we have (3n+1)/a

[quartz crown]

OH OKAY

GOT IT

[urban swan]

awesome

hope it was clear

[dull lintel]

it's really god tier shit wow

[quartz crown]

TYSM

<3

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[cinder iron]

I don't get it

[broken pivot]

$\mathrm{deg}$ returns the degree of a polynomial.

[ocean seal]

King Leo

[cinder iron]

Why degree of P(x) in the example is less than degree of Q(x) though (that's what the original example looks like as you can see)

they somehow converted the example function in an integral so the hypothesis above could be used

[static bobcat]

the first statement seems unrelated to the second. the first one merely shows that if that condition is satisfied, u can use long division to make ur integral easier perhaps

[lone heart]

@cinder iron Has your question been resolved?

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[plush valve]

I forgot 90 60 30

what do u do with the leg again