help-0

[shut mantle]

power of -x

I'm not sure how to change these to a log tbh

[golden canyon]

You can substitute u = e^x

Since e^-x = 1 / e^x

[shut mantle]

so it would become 8/u - u=2?

[full frost]

yes and then solve for u and then substitute back

[shut mantle]

ahh okay

Ahh I think I got it

Thank you so much :)

.close

[lone heart]

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[woven rose]

how do you find a vector c1 c2 and c3?

[lone heart]

@woven rose Has your question been resolved?

[lone heart]

@woven rose Has your question been resolved?

[lone heart]

@woven rose Has your question been resolved?

[lone heart]

@woven rose Has your question been resolved?

[upbeat hornet]

what does it say in English?

[woven rose]

That We have a vector b1 b2 and b3, which are linear Independent and have the basis b1 b2 b3 and the subspace u = span b1b2b3. Then We also have a C =c1c2c3 which is another basis for U and has the basisshiftmatrix Pb<-c

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[placid spire]

im bad at integration lol

how did they do this

why does it become 1 over -0,98 etc

i know that 1,2 is just a factor so its not integrated

[upbeat hornet]

because they took the antiderivative of it

[placid spire]

u got any formula on how to do it

[upbeat hornet]

it is the antiderivative of exp(Ax)

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[rocky atlas]

If ax^2+bx+c=k is an identity, then is a=b=0 and c=k?

[rocky atlas]

k is a constant here

[vital goblet]

Is this your homework or for hdnerstnwidnf

Understanding ?

[rocky atlas]

Understanding

Question for understanding purpose only

[vital goblet]

Ok then

Do you know quadratic formula

[rocky atlas]

ax^2+bx+c

[vital goblet]

Good job

What do you understand from this formula

[rocky atlas]

that a is coefficient of x^2 and b is coefficient of b and c is coefficient of x^0

[rocky atlas]

Am I right

[vital goblet]

yes correct

now tell me in your own words, the question you posted, what do you think it means now

doesnt have to be correct

[rocky atlas]

It means $$ax^2+bx+c=k$$ is true for all $$x \in R$$

[ocean seal]

Calamity

[vital goblet]

umm kinda youre not fully right though

let me explain

[rocky atlas]

Oh

[rocky atlas]

Yes please

[vital goblet]

for this formula you asked a question on, this is an identity and it holds all true values of x and a,b,c must satisfy certain conditions

[rocky atlas]

Yes

[vital goblet]

what is the coefficient of x^2

[rocky atlas]

a

[vital goblet]

yea a=0

[rocky atlas]

Oh

[vital goblet]

and coeff of x ?

[rocky atlas]

b=0

[vital goblet]

yea b=0

and the constant term ?

[rocky atlas]

c=k

[vital goblet]

exactly you got it

[rocky atlas]

Oh

Constant term will be c-k

And c-k=0

Yeah I got it

[vital goblet]

so this ax2+bx+c is an identity, so this equation reduces c=k where c is the constant and k is also constant

thats it

[rocky atlas]

Thank you!

.close

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[copper pendant]

can anyone help me with this please

[ocean hawk]

you're given the roots of the function, so what does that tell you?

[copper pendant]

(b)

i mean

[ocean hawk]

?

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[silent vault]

.reopen

Exercise in context about functions and limits, I haven't seen derivatives yet.

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[grizzled musk]

Can someone solve this for z

[grizzled musk]

I get the wrong answer every single time

<@&286206848099549185>

[woeful loom]

take it one side at a time. what do you get when you find a.b?

[grizzled musk]

What

[woeful loom]

a*b

[grizzled musk]

3+2z

[woeful loom]

the dot product

[grizzled musk]

This

[woeful loom]

i think you should get 1+2z

[grizzled musk]

No?

Im srry

[woeful loom]

(1 * -1)+(-1 * -2)+(2 * z) = -1+2+2z

[grizzled musk]

Your right

And what about other side

[woeful loom]

maybe thats all youre missing

[grizzled musk]

Still

Nope

[woeful loom]

whats the magnitude of a?

[grizzled musk]

3

[woeful loom]

awesome. and what do you get for |b|?

[grizzled musk]

Just z

[woeful loom]

how do you get just z? can you show your work?

[grizzled musk]

Is this correct

[woeful loom]

I believe you should be getting $\sqrt{2+z^2}$

[ocean seal]

Roald Amundsen (Paul)

[grizzled musk]

Of

[woeful loom]

$\sqrt{(-1)^2+(-1)^2+z^2}$

[grizzled musk]

Im so stupid

[ocean seal]

Roald Amundsen (Paul)

[grizzled musk]

Omg

[woeful loom]

everyone makes mistakes!

and then you know that cos45 = \sqrt{2}/2

That might all you were missing

[grizzled musk]

Can u stay with me just so i see its correct

Its correct thx

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[frosty lark]

Stuck trying to prove this

[silent vault]

.reopen

[frosty lark]

My definitions I believe I’m using is… a vector space over R is a non empty set V with a rule for * and * that satisfies the ten axioms …

And a subset U of R^n is called a subspace of R^n if the zero vector in the set U , If V,W is an element of U, then V+W is an element of U and If V is an element of U and C is an element of R the cV is an element of U

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[alpine sable]

it is about elliptic curves. This is a general formula.
$$y^2 \equiv x^3 + a \cdot x + b \bmod{p} $$
In addition, it must hold:
$$4a^3 + 27b^2 ≠ 0 mod p$$
$$4a^3 + 27b^2 ≢ 0 mod p$$
Which notation is correct? Is the not equal correct or the not equal with the 3 lines?

[ocean seal]

ncs

[alpine sable]

its a matter of taste

if its clear that all the working is mod p, using = is fine

otherwise use congruence if you want to emphasise the difference between Z and Z/pZ

[lone heart]

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[alpine sable]

Thanks

[lone heart]

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[coral prairie]

state the amplitude, period, phase shift and vertical displacement for the trig function with equation y= -sin(20 + Pi/3)-2 . Use this information to graph. Please show a graph for at least -2π ≤ θ ≤ 2π.
Choose appropriately sized scales.

I need help with this

[distant cove]

Claimed man sorry

[coral prairie]

oh sorry

[dim wagon]

To start, you know that the shortest distance between a line and a plane is the perpendicular between them

[distant cove]

Yes sure

according to geogebra

it should be 2.63/2.66

but it's wrong

[dim wagon]

is the x not negative?

[distant cove]

no

it's x^2+z^2=1

[dim wagon]

It's written as -x^2+z^2=1, just wanted to make sure

[distant cove]

yes you are write
it's just a dash between

[lone heart]

@distant cove Has your question been resolved?

[dim wagon]

Have a hunch that I might be lost here but since you already have the answer scheme is the distance sqrt(765/29) which is about 5.14?

[distant cove]

no 😦

[dim wagon]

Yea, then apologies I don't think I'll be of much help here .. I was look oh just a plane and a line at first then realized it was smth else, tried to read up on this and it's beyond me

i think atp you can ping helpers

[lone heart]

@distant cove Has your question been resolved?

[distant cove]

Not yet

[distant cove]

Thank you anyway!

<@&286206848099549185>

[lone heart]

@distant cove Has your question been resolved?

[lone heart]

@distant cove Has your question been resolved?

[lone heart]

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[humble oak]

Hello, can someone help me walk through this example?

[humble oak]

I want to show that the transformation T(U) is a convex subset

[placid zinc]

I'll abuse notation here to say that T(A) is the range of T, when applied to A

a, b are in A
Naturally, T(a), T(b) are in T(A)

What about a + t(b - a)?

[humble oak]

Heres a part of the soln, I wne through it with my TA but I am so confused about the line where he writes suppose and everything below that

[humble oak]

yeah this is where I get lost

lemme try to break what you down line by line to make sure I understand

helloo

[placid zinc]

Heyo. Were you able to break that down?

[humble oak]

I think I am still lost like

I get what you are trying to say

Does that same logic apply to the picture I sent above?

Like that whole suppose line is very confusing to me

could u explain that?

[placid zinc]

Yeah that's what the "suppose" part is saying. T(u) is a set that contains every output of T

After T is applied to u

[humble oak]

Suppose a,b in T(u) = T(x) s.t x in U

[placid zinc]

T(u) = {T(x) | x \in u}

T(u) is the set of elements that take the form T(x), given x is an element of u

[humble oak]

ahhhhhhh

[placid zinc]

T(u) is the set of outputs of T.

[humble oak]

and then after

he says a = T(x) and b = T(y)

[placid zinc]

a is in T(u)
Which means that a is some output of T.

Let's define x as the input, which outputs a. That is, there exists an x such that T(x) = a.

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@humble oak Has your question been resolved?

[humble oak]

.close

[lone heart]

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[dawn quest]

can someone explain how to do this to me??
also, i know ive made a mistake somewhere in my work but not entirely sure where or how to get the correct answer

[lone heart]

@dawn quest Has your question been resolved?

[dawn quest]

<@&286206848099549185> 🙏

im begging yall please 😭 , this is due tomorrow and neither my friend or family know how to do it or explain

[fallen pilot]

Which part

[dawn quest]

B. i think ive done up to iii correct, but after that something went wrong and didnt add up

[fallen pilot]

i. is correct (although you didn't explain what the y-intercept represents)

ii. is correct

iii. is correct

I'm not sure about iv. That seems like a finance question maybe?

v. is correct

[dawn quest]

sadly yes lol, revenue. basically just which pair of numbers would give us the most sales and highest price

[fallen pilot]

Not sure how to do vi. either. Seems like another finance question. (I'm not sure what the "original revenue" is)

i., ii., iii., and v. look correct though.

[dawn quest]

okay thank you 🙏 at least i can move on to the others with some peace of mind lol

i appreciate it

[lone heart]

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[fervent briar]

how would you solve this

without a calculator

they provided an example

with csc

and it has its own formula

does this one have one too lol

[solemn juniper]

can you decompose 9pi/4 into something that looks like t + 2pi?

and the formula is the same, secant is also 2pi periodic

[fervent briar]

yea

i think so

[fervent briar]

pi/4 + 2pi

?

does that work

[solemn juniper]

yep

[foggy current]

note that $\sec x=\frac{1}{\cos x}$ so that you can use the angle sum identity for cosine

[ocean seal]

Math Is Fun

[fervent briar]

ok now thats confusing

which is faster

[solemn juniper]

well do you know the value of sec(pi/4)?

[fervent briar]

Nope

[foggy current]

Steakanator's solution might be faster

[fervent briar]

how would i find sec (pi/4)

fast

[solemn juniper]

do you know the value of cos(pi/4)?

[foggy current]

you can use the 45-45-90 triangle for this, if you know it

[solemn juniper]

it seems to be the way they want it solved so i reckon it's the best path

[fervent briar]

wait

[fervent briar]

for

these

things

would memorizing

the unit circle help

[solemn juniper]

yes

[fervent briar]

cause i remember learning something about if u look on the unit circle sin = y or cos = y

i forgot

but something like that

is it possible u can list

[solemn juniper]

there are a few values of cos, sin and tan that you need to have memorized

[fervent briar]

the things again

[solemn juniper]

pi/4 is one of them

[fervent briar]

oh yeah pi/4 is like (sqrt2/2,sqrt2/2)

coordinate points or something

[solemn juniper]

so cos(pi/4) is

[fervent briar]

Idk

thats the problem

i rmbr the values

but i forgot what cos does

is it the x coordinate

y coordinate

x/y

y/x

[solemn juniper]

if you're looking at the unit circle, it'd be the x coordinate

[fervent briar]

Ohhh

i remember now

yes yes

cos is x value

sin is y

and tan is y/x

then everything else is the reciprocal

ty

[solemn juniper]

np

[fervent briar]

so this would be 1/(sqrt2/2)

correct?

[solemn juniper]

yes

[fervent briar]

since csc 9pi/4, u made me simplify it down to pi/4 + 2pi

so t is pi/4

and just use the unit circle

Ahh

i get it

@solemn juniper and the formula provided in this example

its universal right for other functions?

like sin, cos, tan, sec, and cot?

t+2pi

sorry just tryna study for a test last minute

[solemn juniper]

that's just the definition of periodic

[fervent briar]

Kk

ty

.close

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[silent vault]

.reopen

@lone heartreopen

[wary stream]

What are you trying to reopen?

[silent vault]

[silent vault]

I need to solve this

[silent vault]

.

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@silent vault Has your question been resolved?

[silent vault]

[lone heart]

@silent vault Has your question been resolved?

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[wild yew]

If it says yes or no

[wild yew]

What else could be deduced

I'm a bit confused on this question

[remote heron]

<@&268886789983436800>

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[quartz panther]

I found the inverse but i dont know how to find the domain

.close

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[neat lichen]

how can I see the mean from this graph

[quartz panther]

they are unskewed so you just look at the highest point of the graph no>?

[neat lichen]

so 0.8?

[naive valley]

with the technical caveat that if the tails are heavy enough (as in the Cauchy distribution) then the mean doesn't exist even though the pdf is symmetric

^but if you're not aware of this technicality, you can safely ignore it for now 😀

[quartz panther]

thats too smart for me

[neat lichen]

Sorry i forgot to mention that the question, is if A and B has the same mean.

[quartz panther]

o...

[naive valley]

I think that is a safe bet here: the graphs appear to both be symmetric about the same x value. If it's a trick question where there's some microscopic difference then that would just be stupid 😁

[neat lichen]

I was wondering if there was like a way to read the graphs. Like if you read from 0.5 u can see the mean or something like that

[naive valley]

they haven't even labeled any of the x values except for 1, so we don't even know what the scale is here (although probably it's 1 per tick, if they put the origin where the two axes cross)

there's no way to say what the mean is, but from the graphs we can deduce that both have the same mean

[neat lichen]

ahhh okay gotchu. Thanks a lot !

.close

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[slim gazelle]

<@&286206848099549185>

[hot bluff]

do you know the right answer?

[slim gazelle]

yeah

[hot bluff]

okay yeah i jsut checked my work

this is a law of sines problem but there are two triangles you must work out

[slim gazelle]

yeah

[hot bluff]

so where are you stuck

[slim gazelle]

2nd triangle

so I get 210.37 from the first one

[hot bluff]

did you find one side length for it yet

[slim gazelle]

and then

[hot bluff]

what's the length of TD

[slim gazelle]

210.37?

I think

[hot bluff]

i got a different answer

[slim gazelle]

oh

wait let me redo

yeah idk

what i did wrong

[hot bluff]

i like to use law of sines reciprocal because we still get the same answers and anytime we have a right triangle we immediately know sin 90 = 1 so we can compare directly to the length we do know

so we know DE = 346.4m

we know 2 angles

[slim gazelle]

yeah

[hot bluff]

outside angle of TDE is 63, and there is that line from DE, so we know 63 is a supplementary angle of a flat line or 180

[slim gazelle]

yeah

[hot bluff]

180 - 63 = 117

[slim gazelle]

so u get 117

[hot bluff]

then we find the final angle

(117 + 31) + x = 180

what is x

[slim gazelle]

32

[hot bluff]

perfect

so we have all the angles and one side

all we need to apply law of sines

can you set up the equalities for this now?

[slim gazelle]

yeah

wait

I think I know what I did wrong

I subtracted 63 from 90 instead of 180

[hot bluff]

remember this first triangle isn't a right triangle

no 90 anywhere

[slim gazelle]

yeah

[hot bluff]

second triangle will be a right triangle because to measure the true length of the eiffel tower we must have a vertical line bisecting it.

[slim gazelle]

so now do u do 346.4/sin32 = x/sin31

[hot bluff]

yep

so isolate x

then calculate

[slim gazelle]

so 346.4/sin32 x sin31 = x?

[hot bluff]

[346.4 sin(31)]/sin32

since this is all multiplication/division it doesn't matter what order you do this in

[slim gazelle]

yeah

[hot bluff]

whats our answer for length TD

also remember we don't round until the end

[slim gazelle]

k

so

336.6723975

[hot bluff]

good

now we have one length for our second triangle, and two angles

all we need to solve it

[slim gazelle]

so

sin63 = x/336

[hot bluff]

you got it mixed up try again

actually wait

yeah that should be right, isolate x

[slim gazelle]

so u diviide 336 by sin63?

[hot bluff]

look at your equation

how do we isolate x

[slim gazelle]

multiply

[hot bluff]

right

so what times what is x

[slim gazelle]

300

[hot bluff]

lol yes thats the answer

[slim gazelle]

yeah

oty

ty

[hot bluff]

whats our unit

[slim gazelle]

trig

[hot bluff]

300 miles?

[slim gazelle]

o

meters

[hot bluff]

300 cm?

[slim gazelle]

300 meters

[hot bluff]

boom

good job

[slim gazelle]

ty

[lone heart]

@slim gazelle Has your question been resolved?

[lone heart]

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[finite fiber]

difined integration

[alpine sable]

Yes.

[lone heart]

@finite fiber Has your question been resolved?

[wind cloak]

caculus

[lone heart]

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[median oar]

is this statement correct?

[lone heart]

@median oar Has your question been resolved?

[lone heart]

@median oar Has your question been resolved?

[turbid linden]

im legit crying over this someone helpme

ik it’s easier that what 90% of u guys are going but i cant physically do stats

[lone heart]

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[shadow sparrow]

Hello, I'm trying to figure out why this is handled this way, its what I squared in red

[shadow sparrow]

Why does it at this point start multiplying different values by both sides? It seems that its obviously meant to get the denominators to match so you can subtract the fractions by each other, but how does it decide to multiply one side by 11/11 and the other by 11+2h/11+2h?

[vale wigeon]

same as you would do for any other fraction addition

[shadow sparrow]

So its just doing it in a way that makes the denominators match in general?

[vale wigeon]

yes

also missing parentheses: (11+2h)/(11+2h)

[shadow sparrow]

iirc the rule is that you can multiply either side by any fraction to make the denominators match, as long as you multiply the numerator by the same on that side

?

So basically its just analyzing what value multiplied by both sides in the denominator will make the two match, and then you multiply the numerator by those same amounts on the corresponding side

Also the other question I have

[vale wigeon]

feels wordy

[shadow sparrow]

It just adds (h/1) all of a sudden

I understand that you can take the reciprocal of a fraction like this to multiply it outside of the other fraction, but where does the (h/1) come from?

[vale wigeon]

"why is h equal to h/1?" or "i understand why h = h/1 but why did they choose to write it that way?"

[shadow sparrow]

The former

Is it because h = 1?

[vale wigeon]

no

h is h

dividing a number by 1 leaves you with the same number you started with

[shadow sparrow]

So its solely for the purpose of using the rule that you can do the reciprocal thing

[vale wigeon]

pretty much

somewhat unnecessary imo

but not illegal

[shadow sparrow]

Yeah

This class is just confusing me

As I never was able to get a great handle on Algebra

So this just compounds that, because there are a lot of assumptions that are made when solving things

I think mainly I get confused with calculus because it seems there's a lot of, "Well.. We just do that because it lets us kinda skip over to this rule we can use to make the answer solvable"

Makes it sometimes feel like I have to guess to get the answer in the way they want me to

anyways, tyvm

.close

[lone heart]

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[wintry sage]

I’m a bit confused about the definitions of cycle, path, trail. Is the trail ABGA considered different to the trail AGBA? What about if we consider it a cycle, or a walk?

[vale wigeon]

can you show your class's defns of cycle, path, trail and walk

this is the kind of thing that may be inconsistent from author to author

[wintry sage]

Ah i see, let me find it real quick

I interpret this definition as meaning a walk, trail, and path with different ordered vertices is considered different

A cycle is defined as a subgraph with a vertex set and edge set as opposed to sequences, which I interpret as order not mattering

[vale wigeon]

ok then yeah ABGA and AGBA are different trails

they traverse the same cycle but in different directions

[wintry sage]

Thanks, just wanted to make sure I got that correctly

.close

[lone heart]

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[little sable]

Can anyone explain me why there are absolute brackets and 2 notation on the right side. The bold X is meant to be a matrix but I don't know what these other notations mean.

[mortal trellis]

$\norm{x}$ is the norm of $x$

[ocean seal]

Denascite

[mortal trellis]

do you know what norms are?

in this case its the so-called 2-norm

squared

[little sable]

oh okay

norm means the magnitude or length of a vector right

[vague coral]

yes

[little sable]

ok thanks for the info.

.close

[lone heart]

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[grizzled zephyr]

i cant understand the derivative of e^-x

[echo socket]

Do you know the derivative of e^x?

[grizzled zephyr]

i just memorize it as e^x

but i dont know the reason

[echo socket]

Right, so, according to chain rule, the derivative of e^(-x) should be e^(-x) * [the derivative of -x]

[echo socket]

It's one of the definitions of e

[grizzled zephyr]

can you represent it in the chain rule so i understand more please? because chain rule is f'(g(x) * g'(x)

why is it power i mean

shouldnt it be e(-x) * -1

i hope u got me

[echo socket]

Yes, it is

[grizzled zephyr]

but there is no power

[echo socket]

Let's say f(x) = e^x and g(x) = -x

Then e^-x = f(g(x))

According to chain rule the derivative of f'(g(x)) * g'(x)

f'(x) is simply e^x, so f'(g(x)) turns into e^g(x) and e^(-x)

g'(x) = -1

So the final answer is -e^-x

[grizzled zephyr]

$\frac{d}{dx}\left(e{-x}\cdot -1\right)$

i mean like htis

chain rule doesnt take into account the power

f'(g(x) * g'(x)

[ocean seal]

Sprites

[echo socket]

[grizzled zephyr]

i know soryr

[echo socket]

How does e^-x turn into e - x

[grizzled zephyr]

i dont know

isnt e alone the f(x)

[echo socket]

No

[grizzled zephyr]

and g(x) is -x

then what

[echo socket]

f(x) = e^x

Not f(x) = e

[grizzled zephyr]

oh so g(x) is -1

[echo socket]

g'(x) is -1*

[grizzled zephyr]

ugh

ok thanks

[grizzled zephyr]

what about 2^sin2x

what is f(x) and g(x)

[echo socket]

Rewrite that as $e^{\ln2\sin{2x}}$

[ocean seal]

A Lonely Bean

[grizzled zephyr]

whaat

[echo socket]

Now $f(x) = e^x$ and $g(x) = \ln2\sin{2x}$

[ocean seal]

A Lonely Bean

[grizzled zephyr]

what is this theorm called

so i search it

[echo socket]

Definition of logarithms

[grizzled zephyr]

i just took this lesson

but it never illustrated this way

[echo socket]

Then it should simply mention the derivative of $a^x$ is $a^x\cdot\ln{a}$

[ocean seal]

A Lonely Bean

[grizzled zephyr]

so e^x is e^x multiply e?

[echo socket]

lne

Which is 1

[grizzled zephyr]

derivative of e^x is e^x tho

[echo socket]

Right

[grizzled zephyr]

you mean for non "e" bases?

[echo socket]

ln is log_e

[grizzled zephyr]

so derivative off 2^x is 2^x multiply ln(2)

[echo socket]

Yes

[grizzled zephyr]

thanks

[plain flame]

its because of the chain rule

$2^x = e^{x \ln (2)}$

[ocean seal]

heavy

[grizzled zephyr]

what about e^sinx

e^x is f(x)

sinx is g(x)

so e^x(sinx) * cosx?

f'(g(x) * g'(x)

@echo socket sorry for ping

[echo socket]

e^sinx * cosx

[grizzled zephyr]

why isnt f(x) = e^x

so f'(x) = e^x usinging chainrule is should be sinx * e^x

[echo socket]

It is

[grizzled zephyr]

like here

[echo socket]

No

f'(g(x)) is e^g(x)

And e^sinx

[grizzled zephyr]

so we should always consider the power

[echo socket]

Of course

[grizzled zephyr]

so its f'^(g(x)) if that makes sense

[echo socket]

No it's still f'(g(x))

[grizzled zephyr]

i think i got it lol

another question 😓

$\frac{d}{dx}\left(2^{sin2x}\right)$

[ocean seal]

Sprites

[grizzled zephyr]

i did 2^sin2x * ln(2)

but am wrong

[plain flame]

f(x) = 2^x

g(x) = sin(2x)

what is f'(g(x)) * g'(x)

[grizzled zephyr]

oh i should use chainrule in sin2x too?

so sinx * cos(2x)

[plain flame]

$\dv{x} \sin (2x) = 2 \cos (2x)$

[ocean seal]

heavy

[grizzled zephyr]

got it thanks

lol this is getting so confusing pardon me

[plain flame]

yeah

youll get used to it dont worry

[grizzled zephyr]

doesnt look like it , like i just solved this:

(sinx)^3x

I said f(x) = sinx
g(x) = 3x

so it should be cos^3x * 3

but it doesnt look like it

i wish I know what am doing wrong

[plain flame]

f(g(x)) is not sinx^3x if you define f and g like that

[grizzled zephyr]

so what am wrong in i dont get it

[plain flame]

with f(x) = sinx, g(x) = 3x you would have that f(g(x)) = sin(3x)

[grizzled zephyr]

oh so it differs with powers?

should like always when i have powers use lograthmic

differentiation

[plain flame]

yeah that works too

thats probably the easier way

[grizzled zephyr]

what means d/dx logx (e)

what is the derivative of e

0?

would be undefind then

[plain flame]

log base x of e?

[grizzled zephyr]

1 minute let me write it

$\frac{d}{dx}\left(\log _x\left(e\right)\right)$

[ocean seal]

Sprites

[plain flame]

are you sure you dont mean $\frac{d}{dx}\left(\log _e\left(x \right)\right)$

[ocean seal]

heavy

[grizzled zephyr]

no

[grizzled zephyr]

exactly like this

[plain flame]

aha

alright

[grizzled zephyr]

i like the "aha" moment i never got to experince

😭

[plain flame]

this is a tricky one

try to rewrite log_x(e)

with the change of base formula

[grizzled zephyr]

hmm i got no idea what you are talking about to be honest

[plain flame]

you can pick c to be any positive number

i suggest you pick c = e

a = x for you

and b = e

[grizzled zephyr]

so i write it as log 10 (e) / log 10 (x)?

[plain flame]

yeah that also works

[grizzled zephyr]

then what

[plain flame]

but i would recommend you write log_e(e)/log_e(x)

because log_e(e) = 1

log_e = ln

[grizzled zephyr]

so it would be ln / log_e(x)?

[plain flame]

1/ln(x)

[grizzled zephyr]

so we want the derivative of 1/(lnx)

[plain flame]

yes

because log_x(e) = 1/ln(x)

just rewritten

now you need to use the chain rule again

[grizzled zephyr]

could you complete solving it please because my mind is dead

[plain flame]

let f(x) = 1/x

and g(x) = ln(x)

then you know that f'(x) = -1/x^2 by the power rule

and we also know that g'(x) = 1/x

so therefore f'(g(x))g'(x) = -1/(xln(x)^2)

$-\dfrac{1}{x\ln^2\left(x\right)}$

[grizzled zephyr]

thanks alot i got it

[ocean seal]

heavy

[lone heart]

@grizzled zephyr Has your question been resolved?

[lone heart]

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[hasty flax]

i have a question

[hasty flax]

how is Uxx -sin x

@mental coyote

.close

[lone heart]

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[restive dock]

I dont understand this question

[restive dock]

circles and semi circles arent one to one

do i have to describe a transformation the creates a quadrant instead?

How would I word that in this instance?

[upbeat hornet]

yes
edit: you need to write out what restrictions must be on a general function for it to be one-to-one

[restive dock]

What does that mean? restrictions?

that one x input equals one y output?

Am i to describe the characteristics of a one-to-one function

[upbeat hornet]

possibly something like this

[restive dock]

thats a one to one?

[upbeat hornet]

No, this is an example of a restriction, not necessarily the answer to your question

[last ether]

One-to-one usually refers to monotonicallt increasing or monotonically decreasing (on an interval)

[restive dock]

Oh, so i need to write more than one yeah

[restive dock]

i see ok

I have another question is it ok to post here again?

[upbeat hornet]

Have you resolved this one?

[restive dock]

I think, but are there any more restrictions besides the one you posted and umbraleviatn said?

[upbeat hornet]

The one I sent isn’t a restriction for injective(another name for one-to-one) functions. It is just an example of what a restriction is supposed to look like for something else

[restive dock]

would these qualify?

[upbeat hornet]

This is a restriction for the inverse, not injectivity. But it is close, you just have to add a bit and change a bit

[restive dock]

Would these be better?

[upbeat hornet]

“category”? “monomorphism”? are you taking category theory?

[restive dock]

No i just looked it up

[upbeat hornet]

if you read them carefully, the latter image has only statements which are rephrasings of “f is injective”, or they involve terms in category theory

[upbeat hornet]

this is almost the answer

[restive dock]

what do i have to change?

[upbeat hornet]

Do you understand what the three statements are defining?

[upbeat hornet]

this is it, you have to describe some conditions that every injective function must satisfy

[restive dock]

ok i understand

[restive dock]

its talking about inverse functions rite

[upbeat hornet]

yes, which are linked to injective functions but not the same

[restive dock]

Okay

I think i somewhat understand

A function is one to one if no two elements in the domain of f correspond to the same element in the range of f rite

[upbeat hornet]

Try writing that using symbols
edit: you don’t need to, but you can try anyway

[restive dock]

ummmmmm

[upbeat hornet]

never mind then, your answer should be good enough

[restive dock]

f(x1) = f(x2) implies x1 = x2 ??

[restive dock]

Ok wait

[upbeat hornet]

Spot on

[restive dock]

WOW thanks

ok let me summarise all this

[upbeat hornet]

you figured this out yourself?

[restive dock]

I looked at my school booklet

[upbeat hornet]

You’ll need to learn it anyway

google just gave you

“ō̶̕n̵̑̂e̴͊͑-̵̩̈́t̶̃̃o̴͑̍-̷̋̍o̶͋̈́n̶̏̌ě̴̹ ̷̄͑f̶̆͋ü̴͆n̶̒̔c̸̛̿t̴̛͙i̴̒̔o̵͒̒n̶̰͝s̵͑̊ ̸̈́͘à̴͗r̵̿͛ë̵́̈́ ̴́͘e̴͑̀x̸̂͝a̴͑͒c̵̆̎t̷̂̅l̸̊̔ẏ̴̛ ̸̱͗t̵̽ͅh̷͛̿e̴̚͠ ̸̛͝m̷͗͑o̷͒͌ń̶̚ȍ̷̙ḿ̶̍o̸̎́r̴̾̄p̷̙̉h̶̋̇i̷̅͛s̴̉͝m̴̋͛s̴̒ in the category Set of sets”

when you were just trying to do homework

[restive dock]

A function is one to one if no two elements in the domain of f correspond to the same element in the range of f
f(x1) = f(x2) implies x1 = x2
The domain and the range of an injective function are equivalent sets
The injective function follows a reflexive, symmetric, and transitive property
If a function is one to one, its graph will either be always increasing or always decreasing.

Thats what ive done so far

Is this right

[lone heart]

@restive dock Has your question been resolved?

[upbeat hornet]

“the domain and the range of an injective function are equivalent sets” and “the injective function follows a refl., sym., transitive property’ are wrong

[lone heart]

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[bold sinew]

Idk how to do this

[bold sinew]

We have to find the distance traveled in meters

[median oar]

Convert minutes to s

Then convert cm to m

[mossy mulch]

2 minutes= 120 second

[bold sinew]

Yea

[mossy mulch]

because its m/s

Now if he travels for 120 second

find 8*10^5 and divide it by 120

and there you have your answer

[bold sinew]

Ok

Tysm

[mossy mulch]

no problem

[restive dock]

wdym

[bold sinew]

. Close

[mossy mulch]

.close

You dont put a space

@bold sinew

[bold sinew]

Ohhh yes

Sorry

.close

[lone heart]

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[upbeat hornet]

consider f: (0,1) —> (10,11) defined by f(x) = x + 10

and the third statement doesn’t make sense

[restive dock]

thats trye

[restive dock]

what would be a more suitable statement?

[upbeat hornet]

the second statement is just wrong

[restive dock]

ok so i just leave it as
A function is one to one if no two elements in the domain of f correspond to the same element in the range of f
f(x1) = f(x2) implies x1 = x2
If a function is one to one, its graph will either be always increasing or always decreasing.

[upbeat hornet]

looks right to me(the third statement technically only applies in the reals but you won’t see many functions beyond the reals anyway)

[restive dock]

Thank you so much bro, i really appreciate your patience

[lone heart]

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[median oar]

Can you always “graph” functions?

[upbeat hornet]

What do you mean?

[median oar]

If a function is one to one, its graph will either be always increasing or always decreasing.

That seems to imply you can graph every one to one function no?

[upbeat hornet]

Every relation of x and y can be graphed

[worn fox]

depends what you mean by graph, good luck "graphing" a dirichlet function

[median oar]

I’m trying to imagine a graph in 4D

I mean that function isn’t one to one at all

[upbeat hornet]

well, if you define a graph to be a set of points in the plane, then every relation has a graph

[median oar]

I’m trying to imagine the graph of complex conjugate

[worn fox]

graphs of complex functions usually involve colour

[upbeat hornet]

or multiple dimensions

[median oar]

That’s why I’m currently attempting to imagine a 4D graph

It is not going very well

[median oar]

Hard to imagine 4D where they are paired

[upbeat hornet]

about this, what are those pictures actually showing if dirichlet functions are so pathological?

[worn fox]

as good an approximation as we can display ig?

[median oar]

That’s not the complex conjugate is it?

[worn fox]

philosophically you can never truly display a mathematical object, platonism and all that

its not no just some complex function

[fast lichen]

how would you imagine something 4d 💀

isnt it impossible

[worn fox]

you could have a before and after picture of the complex plane filled with pretty colours before and after applying complex conjugate

[median oar]

I have no troubles imagining n-dimensions

[upbeat hornet]

probably not, since complex analysis exists

[median oar]

I do have trouble trying to pair up the dimensions

[upbeat hornet]

then what you have to do here is imagine n dimensional graph and then let n = 4

[fast lichen]

i mean like visually

[median oar]

The accuracy of my imagination is up for interpretation but I think it’s fine

[median oar]

Yeah but I somehow have to make them “paired up”

[worn fox]

what are you trying to pair up?

[median oar]

The a and b of a + ib

Wait a minute can’t you graph complex conjugate in 3d

The a doesn’t change

[worn fox]

https://www.youtube.com/watch?v=1l411zv5iFA

this looks like a good video at a glance

whole section on 3D and 4D plots

[median oar]

So a z+y = 0 would be the graph of complex conjugate

For w = x + iy and w* = x + iz

Now how do we reason that it is monotonously increasing/decreasing

I suppose in the direction of y and z they are monotonic

[worn fox]

complex numbers arent well ordered so you've have to decide what you mean by that

i think i mean total ordering

this is above my paygrade sorry axiom of choice lovers

[median oar]

There is no choice

And I’m still struggling to imagine 2 planes being orthogonal to each other

[worn fox]

yes of course you are

[median oar]

Do you have any ideas

[worn fox]

no, our brains cant do it

[median oar]

😦 alright thanks guys

.close

[lone heart]

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[gusty coral]

Why does A need to have a pivot in every row for Ax=b to have a solution for every b? I thought it needed to have a pivot in every column.

[median oar]

Both needs to be true

If A didn’t have a pivot on a row (meaning it is all 0’s) then if b is not 0 on that row your system is inconsistent

You’d get some sort of 0 = 1 case

[worn fox]

(so not both, just rows)

pivots on every column give you a unique solution

[median oar]

Ah

That

Good catch

[lone heart]

@gusty coral Has your question been resolved?

[wild trail]

Isn't this assuming that we're doing row reduction?

[worn fox]

what else would you be doing?

[wild trail]

yeaah, that's what is usually done but nothing stops you from column reduction (wrong)

[worn fox]

column operations do not preserve the system

[wild trail]

I.. How tf did I forgot, my bad

[worn fox]

its probably because when you're doing things like computing dets, you can do either

[wild trail]

yes, yes

[gusty coral]

so, a pivot in every column give me a unique solution, pivot in every row makes it consistent?

[worn fox]

for any b yes

[gusty coral]

great ty!!

[worn fox]

eh well you can't be inconsistent and have a unique solution

but near enough

just an edge case

[surreal meadow]

is A square?

[gusty coral]

no it says A= m x n matrix

[remote dawn]

to post a question i just add it here and it gets assigned a channel?>

[surreal meadow]

no

go to one of the unoccupied channels

like #help-2

[gusty coral]

would that be different tho?

[remote dawn]

thank you

[wild trail]

For a unique solution the rank of the matrix must be equal to the augmented matrix which should be full rank

[lone heart]

@gusty coral Has your question been resolved?

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[modern lichen]

hello

is anyone there?

[alpine sable]

What is the question?

[modern lichen]

putting that in standard form for a circle

[modern lichen]

*elipse

[alpine sable]

Ah, right... Sanity check, can you write out the standard form for an ellipse?

[modern lichen]

x2/a2 + y2/b2 = 1

[alpine sable]

Almost, remember an ellipse doesn't have to be centered at the origin

[alpine sable]

Correct, now go ahead and expand this equation

Then it's just a matter of pattern matching

[alpine sable]

I meant the other equation

The standard form

[modern lichen]

o

they teach me another way to do it

the canonic one

[alpine sable]

To do what? Convert it to standard form?

[modern lichen]

yes

[alpine sable]

Prescriptivism smh my head /j

Okay more seriously, there is no such thing as the canonic way to do it

[modern lichen]

from general to standard form

yeah

[alpine sable]

Anyways use whatever method you want

[modern lichen]

yeah I'm using from general form to standard form

do you know how to use it?

[alpine sable]

What do you mean by "general form"?

[modern lichen]

https://www.youtube.com/watch?v=7WPH2X1C354

like this

[alpine sable]

Ah, I see

Either way there's no single way to convert from general form to standard form

But since you're asking the question I can only assume you don't know how to do it at all so I'm gonna show you my method

Which, as I said, starts by expanding the standard form

[modern lichen]

yeah

[alpine sable]

So I need you to expand out the standard form and show me what you get

[modern lichen]

So I did this first

organize x and y

in their order

[alpine sable]

Sure

[alpine sable]

Can you do that?

I'll be back in a bit

[modern lichen]

what

[alpine sable]

Can you expand out the standard form?

[modern lichen]

I don't know how to do it

Like this?

[alpine sable]

No

[alpine sable]

I mean take this equation

And expand it

You can even forget the question you have

Just focus on the standard form equation

[modern lichen]

ok...

[alpine sable]

@modern lichen So can you do it...?

[modern lichen]

Like this?

[alpine sable]

No

Stop going back to the question

Forget this equation you have right here entirely

[modern lichen]

but then how do you do it?

[alpine sable]

Just focus on this

This thing

Only

And expand it

[modern lichen]

but that's after no?

[alpine sable]

I don't know how you've been taught, but if I were to do it, I would expand this equation first

So that I could then pattern match

[modern lichen]

How would you expand this using this equation then?

Or you're telling me to use this one

I'm confused

[alpine sable]

Sorry for the response time

Do you know how to expand something of the form (x-h)^2?

When I say expanding I mean something like (x+y)^2=x^2+2xy+y^2

And 2(x+y)=2x+2y

That kind of stuff

[modern lichen]

oh

I haven't use that

[alpine sable]

What do you mean? That you don't know how to expand or that your method doesn't involve it?

[modern lichen]

no I haven't use it

[modern lichen]

I used this one

[alpine sable]

"I haven't use it" doesn't mean anything though

Oh right you mean the form

[modern lichen]

but do you want it that I use that one?

[modern lichen]

exactly

[alpine sable]

No, if what you learned to be the standard form is different you can use whatever form you want

Sure, use the other one if you want

Now expand it

@modern lichen Does 👍 mean you're doing it or you did it?

If you did it already I want you to show it

[modern lichen]

I'm doing it

[lone heart]

Channel closed

Closed due to the original message being deleted

[alpine sable]

.reopen

Bruh

.close

Man

Just ignore it... Once this channel closes we can claim it again

[lone heart]

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• Show your work, and if possible, explain where you are stuck.
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Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[alpine sable]

There it is

[alpine sable]

(in case you're coming across this this channel wasn't meant to close)

@modern lichen Are you stuck?

Pretty sure I lost them

Oh well...

.close

[lone heart]

Channel closed

Closed by @plain fable

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Remember:
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• Show your work, and if possible, explain where you are stuck.
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[molten reef]

Just an question im I supposed to multiply this or add? , the top only mind the red that I circled

[molten reef]

The ⁵ and ²

On number 3

[ocean hawk]

,tex .exp rules

[ocean seal]

cwatson

[molten reef]

I don't get those sadly mind explaining please?

Are those the solutions?

[ocean hawk]

no, they are rules

you are multiplying c^5 and c^2?

[molten reef]

How does that work?

Yes

[ocean hawk]

then look at the first rule, the "Product Rule"

[molten reef]

I see I get it now

Thank you!

.close

[lone heart]

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[real cipher]

what are the general method of solving these type of question sometimes i get multiple answer how do i know which is the right answers