help-10

[sage geode]

Ofc because |3| = 3 > 2

No absolute value is never negative

That's the point of its definition I guess

3

Yes

|3| = 3

Also |-3| = 3

Because generally |a| = |-a|

|ab| = |a|*|b|

Yup

[obtuse pebble]

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[sage geode]

Np

[obtuse pebble]

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[lean flicker]

Given that f(x)=cosx and g(x)=squareroot(10+x), what is the value of g(f(x))

[lean flicker]

i tried putting f(x) into g

[silk galleon]

Yeah thats all u have to do

[strong vale]

then what happened

[lean flicker]

g(cosx) = squareroot (10+cosx)

then idk what to do next

[strong vale]

you've done homie

[lean flicker]

really

[strong vale]

yup lol

[lean flicker]

thats the end

oh wow

okay

[strong vale]

no more homework

woo

[lean flicker]

haha

thanks man

.close

[obtuse pebble]

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[timid silo]

f(x) = (7x2 − 6x)ex

[timid silo]

Differentiate.
f(x) = (7x^2 − 6x)e^x

how do I start with this???

[sage geode]

Do you know the product rule?

[timid silo]

no i missed class today

[spiral maple]

have you reached out to your teacher?

or anyone who was in class?

[timid silo]

im tryna learn it my self why does that matter?

[spiral maple]

cause your teacher's job is to help you learn

[timid silo]

nah thats not what he does

i learn my self

[unique solstice]

Reasonable

[sage geode]

Basically product rule states that derivative of f*g is

f'*g + fg'

[sudden dome]

Product rule:
f(x) = g(x)h(x)
f'(x) = g'(x)h(x) + g(x)h'(x)
Apply this

[timid silo]

ok ty

debo join boice

voice chat

[sudden dome]

If you are interested in the derivation and explanation of the different rules for differentiation, you can use this url:
https://www.xplusa.com/?action=showtheory&theory=3b1dd229-f431-4119-9cf5-b003e4adcfa2

[sudden dome]

Which one?

[timid silo]

mathematics

[sudden dome]

Thanks

[obtuse pebble]

@timid silo Has your question been resolved?

[obtuse pebble]

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[fallow needle]

If I have two triangles : one small and the other bigger but both have the same proportions how can i found out the proportion itself

[nocturne minnow]

Create a proportion, with a side from the small and one from the big triangle

[fallow needle]

Can i attach the picture of the triangles themselves

ive already found out the X and Y

[nocturne minnow]

,rotate

[fallow needle]

X is 8 and Y is 12

How can I easily find out the proportions?

Any formula or way to do kt

[nocturne minnow]

You know that the proportion is 9/12 or 3/4 so the ratio between the small and large is 3/4

[fallow needle]

Ohhhh yes of course I get you now

For the 6/8 divide both by two you get 3/4

for 9/12 do the same thing but with three (a common factor)

Then you get the proportions

Thank you man

I get it now

[nocturne minnow]

That's how you were suppose to solve it $$\frac{9}{12} = \frac{6}{x}$$

Solve for x

[fallow needle]

Yeah I did that to find out the X and Y

How did you get a 3 though

[warm shale]

dldh06

[nocturne minnow]

Typo

[fallow needle]

Yes I did that in my textbook

At school

To find out the X and Y

I only added that proportion question for myself to understand it better

[nocturne minnow]

The proportion is just that equation

[fallow needle]

Oh

I get it now

Thank you man

.close

[obtuse pebble]

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[timid silo]

how do i show

[novel knoll]

Tried taking log?

[timid silo]

nop

how would it simplify the left side?

[novel knoll]

n*log(…)?

[timid silo]

oh uh lets see

over the root terms?

[novel knoll]

Yes? That is just basic log properties

[timid silo]

no idea what to do from hereon

[novel knoll]

What?

log(a^b)=?

[timid silo]

um

blog(a)

[balmy mortar]

a*b they mean

[novel knoll]

So where did what you write come from?

[balmy mortar]

youve applied log rules incorrectly

[novel knoll]

No I mean a^b

[balmy mortar]

oh that too

god

[timid silo]

eeeeeeh

[novel knoll]

a is everything inside the parenthesis

b is n

[timid silo]

oh ock

[novel knoll]

It gives this, like you said

[timid silo]

oki

so log(nthsqrt(x)) != (1/n) * log(x)?

[novel knoll]

What?

[timid silo]

eeeeeh

like dis uwu

[novel knoll]

That is not what you have

Reread your expression (and review log laws)

[timid silo]

ock 😦

haha this must be it ewe

with the n on the root

but it looks even scarier now

[balmy mortar]

look.

You keep applying log laws incorrectly

[timid silo]

*looks at neko ears

[balmy mortar]

Youre taking the log of the entire left hand side term

[timid silo]

aaaah

and uuh

now we uuuh

ok now this uuh

[novel knoll]

Don’t assume what you want to prove

And missing a limit

[timid silo]

yea always write the limit when taking it at the end

cuz lazy uwu

.close

[obtuse pebble]

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[digital island]

Hey I'm having some trouble with finding a tangent to a parametric curve. My curve is c(t)=(e^t,t^2). I assumed that I could find the tangent by taking derivatives so that I have c'(t)=(e^t, 2t). Now a tangent should be position from c(t) + c'(t)*t_2 where t represents the t value for which the tangent is to be created and t_2 is a scalar which is needed for a line equation.

[digital island]

However when I plot this with geogebra, the results suggest that there's something wrong with my method

[balmy mortar]

you want dy/dx

and use y = mx + c

Not sure what c'(t) represents ngl

no ok i get u

can u try with implicit and see if u get diff answer?

the 2 methods should correspond anyways

===
I'm still not entirely sure about c'(t) tbh

c'(t) = (x'(t), y'(t))

It might be some calculation error, should be fine

c'(t) = (e^t, 2t)

[digital island]

Hmm, I'm yet not that good at transforming parametric curves to f(x)+g(y) + h(x,y)=0 notation.

[balmy mortar]

r u sure your answer is wrong

[flat anvil]

isn't ur problem that you need to plot the tangent to some point on the curve?

[balmy mortar]

never used geogebra

[flat anvil]

,w parametric plot (e^t, t^2) and (e^t, 2t)

[balmy mortar]

no?

[warm shale]

Wolfram Alpha doesn't understand your query!
Perhaps try rephrasing your question?
Click here to refine your query online

Requested by Yottachad#0445

[flat anvil]

what

[balmy mortar]

why r u plotting derivative

[flat anvil]

isn't that what he said to do

[balmy mortar]

no

the tangent equation isnt that

[flat anvil]

so just to make sure.... he wants a tangent LINE

[balmy mortar]

yh

[flat anvil]

so he needs a point of tangency....

[balmy mortar]

check op post

[flat anvil]

because in a line the slope is constant....

[balmy mortar]

they have the write eq

right

[flat anvil]

yes

[balmy mortar]

(e^t, t^2) + k(e^t, 2t)

[flat anvil]

so then i guess he inputted it wrong

cuz that whole thing should be right

[digital island]

Yeah trying to find the equation for a tangent without knowing the exact point for which the tangent is to be created. A more general approach. End goal is to use that to find the t value and the tangent line which goes through a point which isn't on c(t)

I'll try to provide images, a moment

[flat anvil]

your equation is rhgt

right*

[balmy mortar]

T_t : (x, y) = (e^t, t^2) + k(e^t, 2t)

this is the parametric tangent line

[flat anvil]

@digital island

https://www.desmos.com/calculator/3ujfohspvt

let a = t1 and t = t2

now its the same equation

so u must've inputted it wrong into geogebra

[digital island]

Yeah on my 6th(?) attempt I got it right

Thanks for the help. I really appreciate it. I'm usually decent with geometry but this 5th year uni course on parametric curves is a bit harder than I expected it to be.

.close

[obtuse pebble]

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[alpine raven]

I have an hermitian space $E$, $dim(E) = n$. We let $F = E²$ such that for all $X\in F$, there exists $X_1, X_2 \in E$ such that $X=(X_1, X_2)$
We have an orthonormal basis $(e_i)_{1\leq i\leq n}$ of $E$.
How can I find an orthonormal basis of $F$ ?

[warm shale]

Herels

[tardy epoch]

does gram schmidt work?

[alpine raven]

not really, I don't have the value for each vector in the basis

I'm trying to derive an expression of an orthonormal basis of F with the basis of E

[tardy epoch]

$(e_i, e_j) / \sqrt{2}$?

[warm shale]

riemann

[alpine raven]

🤔

[tardy epoch]

or probably proportional to $1 / \sqrt{n}$

[warm shale]

riemann

[alpine raven]

the base is already orthonormal so I dont know why you are doing this tho

[tardy epoch]

no wait the $e_i$ already have that

[warm shale]

riemann

[tardy epoch]

yea, just try the initial suggestion with root 2

so it's just the cartesian product of the E bases vectors

[alpine raven]

yea but that looks too easy

[tardy epoch]

ship it

I'm probably missing a lot. You also need to calculate the Hermitian form on F according to definition 3.4.10
https://math.berkeley.edu/~gmelvin/math110su12/math110su12notes_p110-119.pdf

[alpine raven]

no need, I already proved that (F, w) is an hermitian space, with w the hermitian form

[obtuse pebble]

@alpine raven Has your question been resolved?

[alpine raven]

<@&286206848099549185>

[timid silo]

hi

what class is this for

[obtuse pebble]

@alpine raven Has your question been resolved?

[obtuse pebble]

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[lavish void]

whats thebest approach to modelling the best procedure

[obtuse pebble]

@lavish void Has your question been resolved?

[obtuse pebble]

@lavish void Has your question been resolved?

[obtuse pebble]

@lavish void Has your question been resolved?

[obtuse pebble]

@lavish void Has your question been resolved?

[worthy drum]

That's a lot of reading

[obtuse pebble]

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[distant cave]

$$\sin \left(20\right)\cdot \sin \left(30\right)=\sin \left(10\right)\cdot \sin \left(100\right)$$

[warm shale]

Theophania

[distant cave]

how do i prove this

[vagrant gale]

Calculate it

[distant cave]

$\sin \left(20\right)\sin \left(30\right)=\sin \left(10\right)\sin \left(100\right)$

[quaint glen]

you can write sin(30) and sin(100) in another way that might be more illuminating

[warm shale]

Theophania

[quaint glen]

assuming this is all degrees

[vagrant gale]

,,sin(10)sin^2(10) maybe?

[warm shale]

JWCfive

[quaint glen]

the right hand side isn't that if that's what you're asking

[vagrant gale]

I don’t like trigonometry lmao

[quaint glen]

ok

[distant cave]

Then why are you here burying my posts, refrain thanks.

[vagrant gale]

What?

[distant cave]

$$\sin \left(2x\right)=2\sin \left(x\right)\cos \left(x\right)$$

[warm shale]

Theophania

[distant cave]

is this an identity i am supposed to use?

[vagrant gale]

I’m literally just trying to help…

[distant cave]

@vagrant gale Don't. You give others who know Trigonometry a false impression that you're helping the student, we only ran in circles last time and my original post got buried.

[quaint glen]

absolutely

[balmy mortar]

call mod when u see troll

[vagrant gale]

Where is the false impression?

[vagrant gale]

I’m not trolling though

[distant cave]

$$2\sin \left(10\right)\cos \left(10\right)\cdot 2\sin \left(15\right)\cos \left(15\right)$$
$$=2\sin \left(5\right)\cos \left(5\right)\cdot 2\sin \left(50\right)\cos \left(50\right)$$

[warm shale]

Theophania

[distant cave]

Hmm

$$2\sin \left(10\right)\cos \left(10\right)\cdot \sin \left(30\right)$$

[warm shale]

Theophania

[distant cave]

Or this…

[quaint glen]

the problem is that you aren't really helping, even if you might genuinely be trying to help you clearly dont know the subject well enough to provide accurate and reliable advice

[quaint glen]

you should be more clear in writing what exactly you're doing

is this what you've turned the lhs into?

[distant cave]

this one is, yes

[quaint glen]

what's $\sin(30^{\circ})$?

[distant cave]

and sin(30) = 1/2

[quaint glen]

ok, so that leaves you with what

[warm shale]

Sneaky

[distant cave]

$$\frac{2\sin \left(10\right)\cos \left(10\right)}{2}=2\sin \left(5\right)\cos \left(5\right)\cdot 2\sin \left(50\right)\cos \left(50\right)$$

[warm shale]

Theophania

[distant cave]

so we've this, right?

[quaint glen]

nope

[distant cave]

or this

$$\frac{2\sin \left(10\right)\cos \left(10\right)}{2}=\sin \left(10\right)\cdot \sin \left(100\right)$$

[warm shale]

Theophania

[quaint glen]

This is true and completes the proof, but it doesn't feel completely sufficient, like you're missing some of the most important steps of the proof. Make it clear that this is drawn from cancelling the 2's and from the fact that cos(10)=sin(100)

[distant cave]

ok

where did you get cos(10) from

[short spruce]

you wrote it lmfao

[distant cave]

$$\sin \left(20\right)\cdot \sin \left(30\right)=\sin \left(10\right)\cdot \sin \left(100\right)$$

[warm shale]

Theophania

[distant cave]

this is what we had in the beginning

idk about cos 10

[twilit loom]

note that $$\sin{30}=\frac12$$ and $$\sin(90^\circ+\theta)=\cos{\theta}$$

[distant cave]

referring to this?

[short spruce]

yes

[warm shale]

dino

[short spruce]

referring to the only cosine you wrote

[distant cave]

Make it clear that this is drawn from cancelling the 2's and from the fact that cos(10)=sin(100)
but how is cos(10) = sin(100)

[short spruce]

this

[distant cave]

oh, it's from sin(90+v)=cos v

$$\sin \left(30\right)=\frac{1}{2}$$
$$2\sin \left(10\right)\cos \left(10\right)\cdot \frac{1}{2}=\sin \left(10\right)\cdot \sin \left(100\right)$$
$$\frac{2\sin \left(10\right)\cos \left(10\right)}{2}=\sin \left(10\right)\cdot \sin \left(100\right)$$
$$\frac{2\sin \left(10\right)\sin \left(100\right)}{2}=\sin \left(10\right)\cdot \sin \left(100\right)$$

[warm shale]

Theophania

[distant cave]

Now what

[short spruce]

what do you think

there's only one thing left to do

[distant cave]

oh yeah

cancel the 2

.close

[obtuse pebble]

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[oak pond]

Find two numbers whose sum is 4 and multiple is 8

[obtuse pebble]

Please don't occupy multiple help channels.

[balmy mortar]

No spam.

[obtuse pebble]

@oak pond Has your question been resolved?

[timid silo]

x+y = 4
xy = 8
Solve.

There are probably more than 1 solution.

[timid silo]

Or just write down all the possibilities.

Actually nah, that won't work.

[obtuse pebble]

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[lyric pier]

can anyone help me solve this equation?

[short spruce]

what have you tried

[lyric pier]

i tried to set t2 = 2x -1

[short spruce]

?

[lyric pier]

idk

[raven spire]

substitution: $t^2 = 2x -1$

[warm shale]

Ansh

[raven spire]

what expression did you get from that?

[lyric pier]

so that i can replace it maybe

[raven spire]

Yeah I understand... Go ahead, do the substitution and tell me what you get

the equation in terms of "t"

[lyric pier]

ok

wait how to write square root

[raven spire]

XD

You don't have a square root in the equation you get

Just substitute: $x = \frac{t^2 + 1}{2}$ and you'll be fine as long as you simplify

[warm shale]

Ansh

[lyric pier]

ok thanks i got it

.close

[obtuse pebble]

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[warm lance]

Yesterday I had a test with complex numbers. Eq: 4throot(1+sqrt(3)i), they asked me to graph it which i did and they asked to state what property was used

[warm lance]

Anyone has an idea?

[obtuse pebble]

@warm lance Has your question been resolved?

[obtuse pebble]

@warm lance Has your question been resolved?

[obtuse pebble]

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[timid silo]

@sharp granite change your pfp it's NSFW

[sick pelican]

why you minimodding him lol

he will change if he got caught anyways

[timid silo]

<@&268886789983436800>

[ocean topaz]

.close

[obtuse pebble]

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[fierce siren]

lol

[obtuse pebble]

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[minor ingot]

Hey how do i deriviate this?

[minor ingot]

i have tryed doing something like this

but when checking for result in wolfram alpha i get this

what am i doing wrong?

[warped agate]

chain rule m8

(e^x)^2

first start from left

derivative of anything e is e

next x^2

derivative of x^2 is 2x

so 2x.e^x^2

[minor ingot]

doesnt this rule apply here?

[warped agate]

yes its the same

wat i told u rn

[minor ingot]

ou tnx

.close

[obtuse pebble]

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[warped agate]

np m8
gl

[obtuse pebble]

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[simple siren]

is my induction proof valid, if i prove for the base case, then assume its valid for all n, then prove it for n-1?

[junior inlet]

all n up to a number? no

all n larger than a number? probably

[simple siren]

I found this proof online, and its published by a state uni. https://facultyweb.kennesaw.edu/mlavrov/courses/graph-theory/lecture11.pdf
If its not valid in this manner, that means i have misinterpreted the induction step value, since they cant be wrong. Can you tell me for what value do they do the induction step on then?

im refering to thereom 1.2

[junior inlet]

well

according to my 5 seconds of reading

it assumes the statement is true for m-1 and proves that it's true for m

not what you said

(probably)

[simple siren]

ohh

i see

so assuming for n-1, and then proving it for n is valid, no matter what right?

since n is just (n-1)+1?

[sick pelican]

mathematical induction?

[junior inlet]

yep

[simple siren]

aight thx

.close

[obtuse pebble]

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[bold ingot]

spherical piece of gold with radius 3cm has been melted into a golden cylindrical decoration with height
being twice the length of its base radius. Find the base radius of this decoration: my hw. does anybody know some relation between them?

[thorn torrent]

Between what?

[bold ingot]

sphere and the cylinder

[thorn torrent]

Here a sphere is turned into a cylinder, so you can say that V_c = V_s, i.e. their volumes are equal.

[bold ingot]

ye got it, thank you!

[thorn torrent]

👍

[obtuse pebble]

@bold ingot Has your question been resolved?

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[simple siren]

.close

[obtuse pebble]

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[surreal moth]

for question 8a

how elimate t

x=2^t , do i use log2(x) = t?

[brave bramble]

I wouldn't include that. Note that you can write:
y = (2^t)² + 1

y = x² + 1

[surreal moth]

ohhh

understood

thank you alot

🙂

[brave bramble]

Np, feel free to ask if you have anything else

[surreal moth]

thanksss

@brave bramblecan u explain to me how to find the domain and range of that curve

oh wait, for domian, if i use log2(x) = t. then x >0 right?

cause if i used negative or 0 it will be undef and wont be real

so, the range is alos y> 0

right?

wait? i havent finished my question

[elfin sage]

Use tan to find the base of the triangle inside with 60°

Oh right

Sorry @surreal moth

[umbral ferry]

ok

[surreal moth]

is ok

can u help me with mine? @elfin sage

[elfin sage]

After you find the length of base just double it

[surreal moth]

il be finsih

[elfin sage]

Ok one sec

[surreal moth]

okkk

[elfin sage]

This is above my level I am sorry

I have not Yet studied Cartesian Plane

[surreal moth]

oh

thanks anywawys

@brave brambleu still there?

.close

[obtuse pebble]

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[obtuse pebble]

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[final citrus]

How did dV became that

Note: 4 pi r^2 is the surface area of a sphere

It makes sense that area*radius is Volume

[balmy mortar]

whats dV/dr

[final citrus]

Area

[balmy mortar]

what.

in letters

and numbers

[final citrus]

What

[balmy mortar]

???

ok whats the formula for volume

in terms of r

[final citrus]

r r r = area r

[balmy mortar]

???????

[final citrus]

Jk

4/3 pi r^3

[balmy mortar]

V = that

now whats dV/dr

[final citrus]

Oh cool

[balmy mortar]

then chain rule

[final citrus]

Yeah awesome

Thanks

.closd

.close

[obtuse pebble]

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@inner leaf Has your question been resolved?

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[scenic slate]

does 10 means 10 grade ?

[obtuse pebble]

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[fluid snow]

How do you prove that
$log(a^x) = x \cdot log(a)$

[warm shale]

Kepe

[raven spire]

I'm sure Shuri was just helping with something like that-

[balmy mortar]

they probably closed it early

this is the next step

@fluid snow are you not given this log property

if not uhhhh

[fluid snow]

i just want to know why this is, i have already heard that this is true

[balmy mortar]

I can at least show you why its true for integer x?

Cant think why for real x atm

[fluid snow]

oh, is it hard to prove?

I thought it was something basic

[balmy mortar]

no, i just cant think of it.

[timid silo]

From the definition, $log_b(x) = k$ implies $b^k = x$

[warm shale]

SKJJ

[fluid snow]

yeah

[nocturne minnow]

Would this help?
https://www.quora.com/Why-is-log-a-b-b-log-a

[balmy mortar]

i think SKJJ has it.

[warped agate]

https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:logs/x2ec2f6f830c9fb89:log-prop/a/justifying-the-logarithm-properties

[timid silo]

No I dont lmao

[balmy mortar]

u do what

substitute for x

From the definition, $log_b(x) = k$ implies $b^k = x$

[warm shale]

Shuri2060

[balmy mortar]

substitute y^z

or whatever for x

From the definition, $log_b(y^z) = k$ implies $b^k = y^z$

[warm shale]

Shuri2060

[balmy mortar]

then what next uhhh

kth root?

[fluid snow]

oh, thank you

[balmy mortar]

oh yh i have it

kth root both sides

[warped agate]

np gl

[timid silo]

Idk man why am I not able to prove this 😔

[balmy mortar]

😢 ok ok ok

[nocturne minnow]

Found a pdf of a proof

[balmy mortar]

fine

[fluid snow]

thx!

[warped agate]

@balmy mortar lmao

[balmy mortar]

kth root right thing

then u have it

[timid silo]

ye

[warped agate]

ye

[timid silo]

I would prolly assume it and prove it and it would work then

but I cant get the nicer proof

[fluid snow]

thanks a lot!

[timid silo]

prolly the one in the khan academy video

okay i got it

[fluid snow]

.close

[obtuse pebble]

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[fallow lantern]

Hello there! can someone please help me?

[fallow lantern]

Can someone help me solve these questions?

Please guys I have 20 mins left

[velvet socket]

I would help you but I don't know this I kinda suck in math :(

[fallow lantern]

That alright thanks for trying though

<@&286206848099549185>

@lapis parcel

[fallow lantern]

<@&286206848099549185>

[spiral maple]

dont spam ping the role.

[fallow lantern]

??

[fallow lantern]

<@&286206848099549185>

[nocturne minnow]

It means don't repeatedly use the ping

You literally used that 3 times in 2 minutes

[scenic sundial]

dude stop spamming

[velvet socket]

I think he must spam cuz he has like 15 minutes left

[scenic sundial]

I guess this isa test? Become of spamming?

[nocturne minnow]

Not a test, some assignment that they procrastinated on

[fallow lantern]

What’s the ping

[velvet socket]

When you @ someone

[nocturne minnow]

The @Helper

[scenic sundial]

@ helpers is the ping

[fallow lantern]

What does a ping mean I pressed it because that’s what it says to do after 15 mins especially that I have 15 mins left 🥲

[nocturne minnow]

It meant use it once after you have waited 15 minutes with no help

[scenic sundial]

but you did @ helpers twice

[nocturne minnow]

Not use it 3 times in a row

[fallow lantern]

O

[fallow lantern]

But can u help me with this work??? Please

[nocturne minnow]

No, I don't want to help you

[fallow lantern]

Uh oo ok 😀

[scenic sundial]

this is not even math

[fallow lantern]

It is

[velvet socket]

It looks like math but some logic test

[fallow lantern]

I’m guessing no one can help 😦 ok

Thbx though

<@&286206848099549185>

<@&268886789983436800>

[ocean topaz]

hmm?

[upbeat plinth]

pls dont ping mods for help

[ocean topaz]

is this an exam?

[fallow lantern]

Oh ok

[upbeat plinth]

@ocean topaz literally the same guy

[ocean topaz]

[fallow lantern]

It’s suppose to be class work but idk but I really need help. So can you please help 🙂

[fallow lantern]

What?

[upbeat plinth]

nothing. just telling ed that u/metal/him were in another convo just minutes ago

[fallow lantern]

I was? 🤨

[spiral maple]

You were

[balmy mortar]

If people don't want to help, tough luck.

Your best bet is to make your teacher help or a classmate

[upbeat plinth]

ok but in all seriousness

[balmy mortar]

cus honestly its your teachers job to explain

not ours

[upbeat plinth]

the server is volunteer driven

[fallow lantern]

The teacher won’t help us and the students don’t know

[balmy mortar]

If the entire class doesnt know

[upbeat plinth]

helpers have lives. ur not guaranteed a reply each time, so pls be patient, wait for an available helper, and pls dont ping helpers multiple times

[fallow lantern]

Ya understood

[balmy mortar]

theres not much wrong with failing

then the teacher takes responsibility for not explaining

[fallow lantern]

There is a lot wrong with that 😟 I will get detention

So none of u understand this or just no one wants to help me? 😊 it fine though

[balmy mortar]

I dont want to spend 1 hr explaining something the teacher should have.

[spiral maple]

I personally don't want to help, as you flew off the handle when Ann tried to help you.

And you said you only had 40 minutes, which is likely up by now

[fallow lantern]

Lmao it is… I still have to do it it will mark my work as « late » now

[nocturne minnow]

If the entire class doesn't know, why will you be the one that gets detention?

[spiral maple]

Welp, shouldn't have procrastinated it then. Gl.

[unique solstice]

Procrastination station

[scenic sundial]

@fallow lantern @royal basin wanted to help you but you shut them out

[fallow lantern]

Because I was absent due to family issues and was unable to come to school missing the other work given, and this is the only opportunity I have to not fail the subject and get a 2 hour detention (kinda) on a Monday morning at 5 AM

[fallow lantern]

I’m ngl I don’t think I did that but I thought she was insulting me with the way they reply

[nocturne minnow]

Kinda sounds like a you problem, not an us problem

[fallow lantern]

Then next time don’t ask me why I will get detention if u don’t wanna hear it…

[spiral maple]

See?

[fallow lantern]

And plus I apologized for the misunderstanding

[scenic sundial]

can't you just chegg it?

[fallow lantern]

Sorry what?

[spiral maple]

bruh

[balmy mortar]

You miss material, it's usually your responsibility to catch up. If you can't, explain it to the teacher. If they refuse to understand... well that really would be poor luck.

[nocturne minnow]

[scenic sundial]

I agree ^

[fallow lantern]

Yeah and that’s why I joined this server to get a bit of help especially that someone told me to come to this invite

[fallow lantern]

And plus isn’t this a group to yk help each other out like idk why everyone is against me at this point

[nocturne minnow]

It also helps to see what you know too. If you come in blindly, no one is going to teach you an entire lesson, no one has time for that

[nocturne minnow]

A volunteer group. We choose if we want to help or not

[fallow lantern]

Fam I needed help with those questions specifically

[unique solstice]

Is this all about that rope question?

[fallow lantern]

Yeah and I didn’t force you to reply or anything you are the one choosing to do that

[balmy mortar]

I struggle to see what you have trouble understanding. From your previous conversation with Ann. If it is the meaning of certain words, try looking them up.

[fallow lantern]

Yeah

[nocturne minnow]

Did you take the effort to figure out what you missed?

[unique solstice]

I mean that's not really an entire lesson anyone would have to teach

[balmy mortar]

Or tell us exactly which part is troubling you

[unique solstice]

That's a thinking problem

[nocturne minnow]

To understand the concepts you are lacking?

[scenic sundial]

Are you in the USA?

[balmy mortar]

If you don't know what a regular polygon is, I suggest looking it up

or a right angled triangle

Or a factor

like rlly, idk

[fallow lantern]

I understand that I don’t know how to figure out the how to answer the thinking skills of the knots and to name tu games using 3,4,5

[balmy mortar]

Draw on a piece of paper

with ruler

A knot just marks a length if unit 1

[scenic sundial]

start with this

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

[fallow lantern]

Tbh at this moment I need a way of answers to know the lesson, first time I learn this if I’m honest

[fallow lantern]

Alr

[obtuse pebble]

@fallow lantern Has your question been resolved?

[obtuse pebble]

@fallow lantern Has your question been resolved?

[obtuse pebble]

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[west sierra]

My question is related to conceptual clearing. Are every indeterminate forms in existence undefined? Just like 1/0?

[sage geode]

Well I mean the word indeterminate by itself means "Not defined" so yeah

If you were wondering about the limit then still limit of form 1/0 don't exist

[west sierra]

I see that m@kes sense!

[sage geode]

But in other cases limits may exist

Or may not

Depends on the function

[west sierra]

Then I've another question!Does having gap in continuous function does not mean the function's value at that gap is undefined or indeterminate?

Like in f(x)= 1/x we have gap at x=0

[sage geode]

Continuous functions can not have gaps

[west sierra]

I mean gaps due to which continuous functions are not continuous lol

[sage geode]

Why'd you call them continuous then

[west sierra]

If not for those gaps

Let's call them discontinuous then

[unique solstice]

Isn't a function that has a gap not on its domain still continuous

[west sierra]

So if a indeterminate forms that comes in a function means that function is discontinuous?

[sage geode]

For example if you have a function (x^2 - 4)/(x - 2)

Then it has indeterminate value at 2, right?

[west sierra]

ye

[sage geode]

But what you can do to make it continuous is

Say that

[west sierra]

Take factors

And cancel

[sage geode]

f(x) = (x^2 - 4)/(x - 2) for x that aren't 2
and
f(x) = 4 for x = 2

[sage geode]

Those can't cancel at x = 2 still

[west sierra]

Yeah

[sage geode]

But here yeah you can factor and cancel in the first part

[sage geode]

Notice that this function is different from just the (x^2 - 4)/(x - 2)

Because it's defined at 2

[west sierra]

Means if they are in algebra we can cancel out factor but if we plug x value we cant do same

[west sierra]

Yeah that makes sense

Btw

in x^2-4/x-2, if we plug x= 2 it becomes 2^2-4/2-2, can't we still factor 2^2-4 into (2+2)(2-2)

[sage geode]

Yes so you'll have (2 + 2)*0/0

[west sierra]

0 cancels out each other

[sage geode]

You can't cancel out 0's (because cancelling means dividing basically)

[west sierra]

Oh

[west sierra]

Wait

[sage geode]

If you could cancel 0's, then you could say that 0/0 = 1 and 0/0 = 2*0/0 = 2

So 1 = 2?

[west sierra]

No

[sage geode]

Yeah this is why you can't cancel 0's

[west sierra]

I see

So back to my original question, if a function is indeterminate at x=something then is it also undefined at x= something?

[sage geode]

Yeah, pretty much

[west sierra]

Ohk

You said that unlike 1/0 there are some indeterminate forms whose limit exist

What are they?

0/0 is one of them

[sage geode]

Yes for example limit of (x^2 - 4)/(x - 2) exists as x approaches 2, despite it not being defined for x = 2

x^2 - 4 approaches 0 and x - 2 approaches 0

So you have limit of a form 0/0

Or for example infinity/infinity

[west sierra]

Yeah!

[sage geode]

Take limit of (2x + 3)/(x^2 - 5) as x approaches infinity

It's just 0

[west sierra]

Yes

.close

[obtuse pebble]

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[nocturne minnow]

Try it with a simple example, $2^{2x} + 2^{2x}$ and see if you they add or not

[warm shale]

dldh06

[timid silo]

This is exponet rules... hmmm

It's gonna be like 2x^2x+1??

[nocturne minnow]

I'm saying that if you did your way, it would be 2 * 2^(4x), right?

Using the original expression, plug in x = 1, see if the simplified equals the non simplified

[timid silo]

Good point they're different

So when you add the exponents stay the same

[nocturne minnow]

So then does that answer your question on if you add the exponents?

[nocturne minnow]

Yes

[timid silo]

Yeah, ty man

.close

[obtuse pebble]

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[nocturne minnow]

It's always best to come up with a simple example, to test

[obtuse pebble]

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[timid silo]

can someone help me with this question

[obtuse pebble]

@timid silo Has your question been resolved?

[timid silo]

@nocturne minnow so is that a yes

[nocturne minnow]

I don't recall any of this stuff

[timid silo]

ok thanks ig

[obtuse pebble]

@patent moth Has your question been resolved?

[obtuse pebble]

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[timid silo]

.close

[obtuse pebble]

Channel closed

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[harsh badge]

I need help with example 3

I don’t understand how to find the limits of integration

Where is pi/2 from

<@&286206848099549185>

[timid silo]

Can you figure it out at what value of x, will the function sin(2x) = 0 ?

Similarly 2cos(2x)

[timid silo]

..

[harsh badge]

0

[timid silo]

Noo

sin(x) is 0 at x = π
So, sin(2x) is 0 at x = π/2

[harsh badge]

Is this from the unit circle?

[timid silo]

See this

[harsh badge]

Yes

[timid silo]

So here sin(x) is 0 at x = π

sin(2x) will be 0 at π/2

[harsh badge]

Yeah

Ok

Is this from the unit circle

[timid silo]

Wdym?

[harsh badge]

Do I have to memorize the unit circle

[obtuse pebble]

@harsh badge Has your question been resolved?

[timid silo]

Prob should.... its not that complicated

[hazy marlin]

you could use the identity of sin2x if it helps you see the solution

[obtuse pebble]

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[meager sorrel]

not sure how to do this

[timid silo]

hello, i don't understand how u do an induction question when there isn't an equals sign

[meager sorrel]

when I differentiate x=sin^2Θ I get dx = 1/2x+1/4cosΘ dΘ, but idk how to use that to cancel whatever terms to get the integral to become what it asked me

[meager sorrel]

copy paste that into #help-22 because it is available and this one isn't

[balmy mortar]

Let's see

$$\dv{x}{\theta}=\sin2\theta$$

[warm shale]

Shuri2060

[balmy mortar]

$$\int\sqrt{\frac{x}{1-x}}\dd{x} = \int\sqrt{\frac{\sin^2\theta}{\cos^2\theta}} \dv{x}{\theta}\dd{\theta}$$

[warm shale]

Shuri2060

[meager sorrel]

yes I got that

[meager sorrel]

I don't get this

[balmy mortar]

isnt it

2 cos sin

writing like that probably doesnt help ofc

[meager sorrel]

sin2Θ = 2cosΘsinΘ

[balmy mortar]

$$=\int \tan\theta (2\cos\theta\sin\theta)\dd{\theta}$$

[warm shale]

Shuri2060

[balmy mortar]

which is what you need

[meager sorrel]

but x=sin^2(Θ) not sin2Θ

[balmy mortar]

???

breh, check what dx/dtheta is

[meager sorrel]

um

[balmy mortar]

2cs ?

[meager sorrel]

how

[balmy mortar]

what

chain rule?

[meager sorrel]

that's a double angle formula

[balmy mortar]

???????///

$$x = \sin^2\theta$$

[warm shale]

Shuri2060

[balmy mortar]

ok?

$$\dv{x}{\theta} = \dv{\theta}\sin^2\theta$$

[warm shale]

Shuri2060

[meager sorrel]

ye and sin^2(Θ) = 1/2(1+cos2Θ)

[balmy mortar]

what?????

why would u do that

literally bring the power down

reduce power

and differentiate inside

[meager sorrel]

oh

[balmy mortar]

Chain rule

[balmy mortar]

heck is this 👀

[meager sorrel]

double angle formula

[balmy mortar]

probably gets you to same answer anyways but uhhhhhhh

wait are you sureee thats right???

$$\cos2\theta = 1 - 2\sin^2\theta$$

[warm shale]

Shuri2060

[balmy mortar]

yh no, that's not right

(and u dont need it)

[meager sorrel]

i got it from here

[balmy mortar]

u wrote +

[meager sorrel]

oh ye my bad

i always get confused

[balmy mortar]

You only need to remember 1 double angle formula for cos

and derive the rest

[meager sorrel]

ok so I use chain rule and get, dx = 2cosΘsin^2(Θ)

[balmy mortar]

i usually just remember cos^2 - sin^2

[balmy mortar]

no way.

btw is this Step?

[meager sorrel]

what is step

[balmy mortar]

idk, where is that question from

just past exam for your school?

[meager sorrel]

ocr is an a level exam board

it's from an ocr exam paper

[balmy mortar]

ok well yh, just try avoiding making mistakes like tht 😂

[balmy mortar]

.

If u make mistakes like that, then try writing out the chain rule fully

until u dont need to

[meager sorrel]

but if u=sinΘ then i am doing u'*u^2

[balmy mortar]

$$\dv{x}{\theta} = \dv{\theta}\sin^2\theta$$

[warm shale]

Shuri2060

[balmy mortar]

what no

$$\dv{x}{\theta} = \dv{\theta}u^2$$

[warm shale]

Shuri2060

[balmy mortar]

$$\dv{x}{\theta} = \dv{u}{u}\dv{\theta}u^2$$

[warm shale]

Shuri2060

[balmy mortar]

$$\dv{x}{\theta} = \dv{u}{\theta}\dv{u}u^2$$

That's how i write the chain rule fully to make sure i dont f up

Its just 'swapping the denominator'

[warm shale]

Shuri2060

[balmy mortar]

And if I make typo, its obvious 😂

[meager sorrel]

yeah

so dx/dΘ = cosΘ* 2u

where u = sinΘ

so dx/dΘ = 2cosΘsinΘ

[balmy mortar]

yh and u get there

[meager sorrel]

ok so the integral becomes sinΘ/cosΘ * 2sinΘcosΘ dΘ

which is 2sin^2(Θ)

thanks

[unique solstice]

Capital theta

[meager sorrel]

i just copied this idk

.close

[obtuse pebble]

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[willow fiber]

Just wanna check to see if I’ve done this correct

[hoary coral]

could you show the question in a)?

[willow fiber]

Yeah

It’s just asking for the max height which should just be the vertex right

[hoary coral]

yeah it should be right

[willow fiber]

The time

[obtuse pebble]

@willow fiber Has your question been resolved?

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[regal tendon]

how do i solve this by hand

[regal tendon]

@timid silo go to #help-5

[flat anvil]

solve it like a normal system of equations

[regal tendon]

and how do you do that

[flat anvil]

well immediately you should notice that you could multiply the bottom row by 2/3

then add the two

[regal tendon]

yes

[flat anvil]

then you can use the rational roots theorem

to solve the cubic

[regal tendon]

so far im at $x^3+x^2-3x+1==0$

[warm shale]

erentar2002

[flat anvil]

1 equals

so now do u know the rational roots theorem?

there are also 2 tricks you can use

if the sum of all the coefficients equals 0, then 1 is a solution

if the sum of all the even coefficients - (the sum of all the odd coefficients) = 0 then -1 is a solution

[regal tendon]

can you link me to an explanation

[flat anvil]

of what? plug in one to any polynomial and you can see why

that is

$ax^2 + bx + c = 0$

[warm shale]

Yottachad

[flat anvil]

if we plug in one we get

$a + b + c = 0$

[warm shale]

Yottachad

[flat anvil]

so if the sum of the coefficients of the polynomial is 0, then 1 works

[regal tendon]

right yes

.close

[obtuse pebble]

Channel closed

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[regal tendon]

thanks bro

[flat anvil]

you're welcome

[obtuse pebble]

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[fervent axle]

I know you cant see the log base on denominator but whether it's 2 or 3 i can't tell what my first step should be

[balmy mortar]

What does intersect mean for the equations.

[fervent axle]

their y value is equal so i set them equal to each other

I suppose I meant a different step

acc I'll try smt new now

[balmy mortar]

ok.

[fervent axle]

sry 1 sec

[balmy mortar]

you set them equal to each other

[fervent axle]

I just remembered the log law with multiplication can be used

[balmy mortar]

👌

[fervent axle]

ty and sorry about that. got it

.close

[obtuse pebble]

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[obtuse pebble]

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[dry pebble]

So I've been figuring out on how to solve this and saw this on Google
https://www.mathway.com/popular-problems/Pre-Algebra/167344

The answer I only need is if this is what i should do step by step upon solving the problem if I am searching the right one to study and answer the question.

Our teacher is not active in class and always just leave things to do to us so I kinda need more self study to this

[tranquil pasture]

Can someone please help

[nocturne minnow]

Don't ask in an occupied channel

[vagrant gale]

smh

[balmy mortar]

I don't think this solves the components of each conic

[balmy mortar]

I'm honestly not familiar with this, you could cross check with wikipedia/videos?

I doubt it would be wrong.

[dry pebble]

i think i saw it

.close

[obtuse pebble]

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Use .reopen if this was a mistake.

[dry pebble]

ty

[obtuse pebble]

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[obsidian isle]

Vagene

[warped agate]

is that ur qn fr

[obsidian isle]

Bob?

[warped agate]

ok nvm

m8
if u wanna chat go to #chill

close this

.close typw

[obtuse pebble]

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[obtuse pebble]

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[raven vapor]

hello! how do you find reference angles? And how do you draw them in standard position?

[worthy drum]

The reference angle is the angle between the x-axis and the ray from the given angle

It will always be between 0 and 90 degrees

[raven vapor]

i'm using the unit circle as a reference, as advised by my teacher. sorry for the other question, but is the reference angle like

for example, for reference angle 60 deg. is the reference angle pi/3 or

[zenith zenith]

You can picture the reference angle as dropping a line to the x-axis if you have a line going out from the origin at a certain angle.

[zenith zenith]

Since this is under 90 degrees, yes, the reference angle is the same as the original.

[worthy drum]

You can still say "60 deg" since that is actually the angle between the x-axis and 60 deg

[zenith zenith]

Unless your teacher would like you to also convert to radians

[worthy drum]

True

[raven vapor]

ah thank you. so if im also asked to draw the given angles in standard position. would i draw it the same way as the unite circle does?

[worthy drum]

Yeppers

[raven vapor]

ok thank you!

[zenith zenith]

^ Standard position would mean starting from the positive x axis

[raven vapor]

.close

[obtuse pebble]

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[pliant phoenix]

Hey Can I get some help with this question shiro was helping me but they went afk and its due soon i made some progress but im not too sure

[pliant phoenix]

I got a

This is the eq btw

B is the tough one I need help with not too sure

[forest sinew]

hmmm

what if

,w x^4 + 8x^2 + 20 x^2 + 16x -5 = 0

[warm shale]

Results provided by WolframAlpha

Click here to refine your query online
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Requested by jan Niku#2119

[forest sinew]

n o

how about factor

does it work

$f(x) = x^2(x^2 + 8x + 16) = x^2 (x+4)^2$

[warm shale]

jan Niku

[pliant phoenix]

IM not too sure how I can help but ask And Ill try my best

[forest sinew]

im trying to think

[pliant phoenix]

idk how about equaling the two?

[forest sinew]

sure then what

[autumn adder]

When you find intersection points

You equal the two