help-38

[wraith hinge]

help

[wraith hinge]

help me find the radius of convergence

i think g is infinity and h is 2

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[marsh forum]

None of these are in REF, right?

[marsh forum]

Wait

oops

I think 1 is in REF

or not

nvm

[chrome talon]

whats your reasoning in each case, why are they not?

[marsh forum]

Y/N

Ok, so for one , the row containing all 0s in NOT the bottom most row

[chrome talon]

yeah, right

[marsh forum]

For 2, the leading element of row 2 , must be 1. But on second thought, that's also the last row. So it's probably in RREF

[chrome talon]

what about the leading element of row 1?

[marsh forum]

Ah

Right, that should have been $2$

[solid kiln]

(why am i here )= idk

[chrome talon]

zero rows dont count

[marsh forum]

*should have been 1

So it's just in REF

[chrome talon]

right

[marsh forum]

Now, here 1 is i RREF

[chrome talon]

is it though?

[marsh forum]

I mean the leading entry is 1

the first non-zero entry is to the right of the first

Oh

Right

It's just in REF

[chrome talon]

idk about the exact definition you are using, but dont all leading elements need to also have zeros in its columns?

[marsh forum]

Let me send my defn

I'll be right back

[amber python]

condition 2 isn't always imposed on REF

that changes some answers

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@marsh forum Has your question been resolved?

[marsh forum]

Sorry, had to collect my laundry, will be back in 5

[marsh forum]

So d is in REF

as in e

f isn't in REF?

would this be right

[chrome talon]

is the first really row echelon form?

[marsh forum]

Oh yeah

It isn't

[nova spire]

b is not ref?

Also neither for f? What does that mean

Either it's ref of not

[marsh forum]

I meant not REF

my bad

[nova spire]

Ok and second thing

b is not REF?

Also no mention of rref

[marsh forum]

No?

The leading element should be 1

these are the defns I'm working with

[nova spire]

Yes ok

Very weird def

[marsh forum]

.close

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[ocean latch]

guys can someone help

[ocean latch]

ive been trying

the info is too less

[trim jolt]

Show your work, and if possible, explain where you are stuck.

The purpose of this server is to help you learn, not to hand out answers. Do not ask someone to give you the answer directly.

As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.

[main sigil]

This is what i meant

Well that's not a boring rule

that's the rule that ensures that people will actually learn something here

[ocean latch]

how

the answer aint four lmao

also stop flexing, absolutely noone gives a shit

me after giving the wrong answer

[main sigil]

alright calm down

@ocean latch Have you drawn a diagram already?

[ocean latch]

bro this guy kinda weird, is most prolly a kid, so ye its fine

[ocean latch]

yes

[main sigil]

alright

[ocean latch]

yes

i joined ic and ib and ia

not that its helping but ye

[main sigil]

call the radius of the incircle r

!nogpt

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Please do not trust ChatGPT or similar AI tools for mathematical tasks, as they often generate output which "sounds correct" but has numerous factual or logical errors. Use of these AI tools to answer other people's help questions is strictly against server rules (see #rules).

[main sigil]

read #rules

and please don't try to help until you do so

[split chasm]

<@&268886789983436800>

[main sigil]

thanks

[ocean latch]

bro you're a kid using ai for sums, these ai's mess up simple calcs, you're helping noone, go away

bro got erased

anyways lets get back to the sum

[ocean latch]

alright

[main sigil]

so the purple line is what we are trying to find

[ocean latch]

yes

[main sigil]

blue lines are the radia

drawn at 3 different places

Firstly, can you actually find the radius?

as a number

[ocean latch]

yep, i gotta admit tho that I never drew a circle

i thought incentre is the interection of all angle bisectors

[main sigil]

It's also the center of the inscribed circle

[ocean latch]

we know the blue line is root 8

[main sigil]

Good

[ocean latch]

wait is that a square

[main sigil]

Maybe

try thinking about the angles there

are they all 90°?

[ocean latch]

only 1 is

oh wait tangents

so 2 more are 90

[main sigil]

correct

and what about the last one?

[ocean latch]

so the 4th one gotta be 90 too

[main sigil]

correct

the next condition is that all sides should be equal

[ocean latch]

so pythagoras now?

[main sigil]

It will actually suffice if we show that 2 neighboring sides are equal

[main sigil]

not yet, but soon

[ocean latch]

oh

[main sigil]

do you know why does it have all sides equal?

[ocean latch]

because its a ssquare

wait but it can be a rectangle to

[main sigil]

right

[ocean latch]

shit

[main sigil]

we dont know that its a square yet

we know that all angles are 90°, so it is a rectnagle

[ocean latch]

oh wait because 2 adjacent sides are equal

radius right

[main sigil]

Correct!

[main sigil]

also correct

[ocean latch]

oh

[main sigil]

so it is a square, and we just need to find it's diagonal

which can be done by pythagoras

[ocean latch]

oh yes

[ocean latch]

thanks for helping!

[main sigil]

You are welcome :)

[ocean latch]

.close

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[crisp dust]

Can yall help me prove ME is tangent to (o),apparently i need to follow the guidelines on the left to solve it but i js cant comprehend

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@crisp dust Has your question been resolved?

[crisp dust]

<@&286206848099549185>

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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.

[crisp dust]

Let (O) be the circle passing through four points 4, D, H, E and M are the midpoints of BC. Prove that ME is the next route of (O).

<@&286206848099549185> ...

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@crisp dust Has your question been resolved?

[crisp dust]

<@&286206848099549185> anyone..

[serene shale]

i’m sorry idk

[crisp dust]

damn

[crisp dust]

<@&286206848099549185> anyone.....

[slate relic]

I will try to help you

Let me just translate the exercice , cause i don't know what Next route mean

[crisp dust]

its tangent

like

prove ME is tangent to (O)

[slate relic]

ok better

and also the circle passes trought 4 points

and you say that they are midpoints of BC ?

[crisp dust]

no like

[slate relic]

what is BC ? in the first place ?

[crisp dust]

M is midpoint of BC

[slate relic]

ok

and what is BC ?

[crisp dust]

the circle pass through A,D,H,E

[slate relic]

ok ty

[crisp dust]

the stuffs on the left r clues to solve this

like i have to prove e1 = c1,c1 = a1,a1 = e3,e3 = e1 then like e3 + e2 = 90degree in order to have e1 + e2 = 90 degree

[slate relic]

i will try to do it later

I cant figure it out now

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[gentle sleet]

Why would they create a garbage state?

01 is a valid input is it not

I was thinking it should be like this

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[gentle sleet]

nvm the prof made a mistake I see what she meant now

.close

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[burnt mulch]

@brave pawn I saw your message - all good

[burnt mulch]

.close

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[worthy eagle]

[opaque jetty]

.close

[worthy eagle]

i was about to fix it

[opaque jetty]

oh fr?

[worthy eagle]

!msgdel

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[worthy eagle]

,, \lim_{L \to \infty} \sum_{n=0}^{L} \frac{sgn(b)|b|^{2n+1}e^{\frac{-b^2}{2}} - sgn(a)|a|^{2n+1}e^{\frac{-a^2}{2}}}{\prod_{k=0}^{n} (2k+1)} = \int_{a}^{b} e^{\frac{-x^2}{2}} , dx

[solid kiln]

Kokichi

[worthy eagle]

copy this

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[echo imp]

(countable intersection of open sets ) intersection close set = close set always ?

[echo imp]

to show it better. lets take a topological space X and $U_n \subseteq X$ for every n, also $C \subseteq X$ closed set. Then could we say that the set $A = \bigcap_n U_n \bigcap C$ is closed ?

[solid kiln]

whitefang

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[serene shale]

countable intersections of open sets could be a lot of things
for example, in R:
∩(-1/n, 1/n) = {0} which is closed
∩(-1, 1) = (-1, 1) which is open
∩(0, 1+1/n) = (0,1] which is neither open nor closed

[echo imp]

Yeah true

But if we take the intersection with a close set will the result be always close ?

[serene shale]

yes, i’ll give you a short proof.
First, suppose C_1, C_2, C_3, … is a countable collection of closed subsets of X. Then:

$$X\setminus\bigcap_{n=1}^{\infty}C_n= \bigcup_{n=1}^{\infty}\big(X\setminus C_n\big)$$

[solid kiln]

Ryan

[serene shale]

^That’s De Morgan’s law

Anyway, the right hand side is a union of open sets, and any union of open sets is open.

Therefore, the left-hand side, the complement of ∩C_n, is also open

Therefore, ∩C_n is closed.

More generally, any intersection of closed sets, even uncountably many closed sets, is also closed. The proof is identical

[echo imp]

Thank you! Now I am not sure if let's say D is Gδ and C is close then D∩C=A is always closed

[serene shale]

C could just be X and then D∩C = D

[serene shale]

and D can be closed, open, or neither, like i showed here

[echo imp]

Oh ok

Thanks again

.close

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[compact seal]

i need help on understanding decimals and geometry, i fr wanna recite in class but i js dont get stuff

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@compact seal Has your question been resolved?

[compact seal]

no omg

<@&286206848099549185>

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[glass gate]

ive got 4/203/1916/18 but idk what to do next

[blazing geode]

Hello

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[marsh forum]

So here,in question (b) upon adding subtracting eqn 3 from 1, and adding that to eqn 2, I'm getting 0=0. Does that mean infinitely many sol s?

[tropic heart]

uh

just multiply eqn 1 with 3 and eqn 2 with 2 and add em

and you will get rid of x

and write y in terms of z

[marsh forum]

No, I'm not asking how to do it.

I'm getting 0=0

[tropic heart]

or z in terms of y and substitute in 3

[tropic heart]

calculation error

maybe

[earnest nymph]

if theres not calc error or way to get around that then yea its infinite

[marsh forum]

Subtrating equation 1 from 3, you get $-3x+4y-z=-5$

[solid kiln]

(why am i here )= idk

[earnest nymph]

im pretty sure sure theres an actual answer for this

try other ways

[marsh forum]

I could try Row reductions

[earnest nymph]

ye

i thinkkk…

try 1 and 3 and 1x3 - 2

[marsh forum]

wait

Row reductions give a system of 2 linear equations in 3 variables

Unless they are parallel, that does imply infinitely ,many solns

Just by looking at them , one can concldue that they arent

,w does -2x+3y+3z=-9;3x-4y+z=5;-5x+7y+2z=-14 have infinitely many solutions

[solid kiln]

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

Requested by physicsrocks

[marsh forum]

,w solve -2x+3y+3z=-9;3x-4y+z=5;-5x+7y+2z=-14

[solid kiln]

Results provided by WolframAlpha

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

Requested by physicsrocks

[grim sparrow]

the quick answer is yes

there will be infinite solutions

[marsh forum]

Ah, cool.

How would I do this using RREF?

Thanks!

[grim sparrow]

it's the same procedure as you've done before wdym

also I will be going back to my old profile in a bit lmao

okay am back to old profile lol

[marsh forum]

Uh, did you change your name?

and your pfp too>

[grim sparrow]

I did

[grim sparrow]

and I did

I was messing around in discussion about my first discord profile

and went back to it for a bit

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[blazing geode]

Fk

[blazing geode]

Fk

Shirt

W tf it means

Tf it means

What’s the meaning of the fk equation that get me fked

.close

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[graceful zenith]

Can I get help w this. It’s mathematical induction btw

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[drifting rose]

wrong discord I understand but since it is simple enough I feel like it could be solved here

[drifting rose]

how do I find the resistance?

[ionic pendant]

apply ohm's law

[violet gust]

Step one, find total resistance of circuit with Kirchoffs law

Step 2, use ohms law on the graph

[drifting rose]

V=IR?

[ionic pendant]

yes

[drifting rose]

but how do I know what the current is

or volt

oh wait

wait nvm no clue

[ionic pendant]

you have a graph showing both

[drifting rose]

yes

but how do I correlate that to a resistance?

I don't understand from reading the graph sorry

[ionic pendant]

ohm's law gives you voltage as a function of current, which is graphed

if we have V(I) = IR, what shape graph do we expect to see? what aspect of the graph does R affect?

[drifting rose]

the voltage?

[ionic pendant]

if i had a graph y = Rx, what kind of graph would it be? what would R represent?

[drifting rose]

the graident

[ionic pendant]

yes

we are using different variable names but the idea is the same

[drifting rose]

oh

but how do I find the numbers that correlate to that graident

wait I think I got it

thanks

.close

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[wraith hinge]

one digit ina 10 digit number is missing. What is the maximum number of ways that the missing digit could be filled so that the final number is divisible by 3

[wraith hinge]

sum of 9 digits (mod 3) could either be 0, 1, or 2 right?

in the case where the sum of digits (mod 3) = 0 then you have 4 ways

in the case where the sum of digits (mod 3) = 1 then you have 3 ways

in the case where the sum of digits (mod 3) = 2 then you have 3 ways

[shrewd ridge]

sure

[wraith hinge]

so the answer is 10?

[shrewd ridge]

it's 4

[wraith hinge]

how?

isn't it 4 + 3 + 3

[shrewd ridge]

like it's a fixed number

[wraith hinge]

oh bruh i need to take reading lessobns

[shrewd ridge]

it's unknown but it's not of two types at the same time

[wraith hinge]

maximum number of ways

tbh i read that as all possibilities

okay thanks

[trail ingot]

!Kiz__

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[wraith hinge]

slayyla 💅

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[dreamy loom]

So this is 2 glasses of water that get put into 1

And I have to find the temperature of this water

[dusty sleet]

Isn't this physics?

[dreamy loom]

True

But it just requires math to solve though right

[dusty sleet]

Of course, but do you find problems in solving because of the math part or because of the physics part?

[dreamy loom]

The math is what is challenging me here

Isnt there an equation or something

I feel like I had one in math class but cant recall

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[trail ether]

how can i derive this parabola formula

[trail ether]

i need to turn that formula into this

[trail ether]

from that to this

[trail ether]

like this but reversed :(

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[warped saddle]

Can someone explain the wording for the principle of mathematical induction? “Having obtained values of S⬇️n for n less than or equal to some integer k, ….

[warped saddle]

Sn is from Sn = (n(n+1))/2

[clear cloud]

You make the assumption that S_n is true, and show it implies that S_(n+1) ?

[warped saddle]

Nvm i figured it out

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[ebon warren]

in general, is -a/-b == a/b?

[burnt mulch]

Yes, as long as b isn’t zero

[ebon warren]

thanks

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[smoky plover]

Im so lost

[smoky plover]

is this correct so far

and what do I do for the rest

[verbal stream]

1 & 4 are vertical, not corresponding

And two angles that are on opposite sides of two lines are vertical

1 & 5 are corresponding

[smoky plover]

I redid it all and came out with this

<1 and <4 are verticle angles and are congruent
<3 and <6 are alternate interior angles and are congruent
<1 and <5 are corresponding angles and are congruent
<3 and <5 are consecutive interior angles and are supplementary
<2 and <7 are alternate exterior angles and are congruent

is that more correct?

[verbal stream]

No blud I just said 1 & 4 are vertical 😭

3 and 6 are alternate interior, not exterior

other than that it looks correct

[smoky plover]

sorryyyy

I thought vertical

like wasnt a option for this

but it prob is

im just being dumb

appreciate you brutha

[verbal stream]

np

[smoky plover]

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[feral hornet]

Am I doing these right so far? Especially the second one I'm not so sure about

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@feral hornet Has your question been resolved?

[feral hornet]

@limpid raft

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@feral hornet Has your question been resolved?

[burnt mulch]

To clarify, are the supplementary numbers picked from the winning numbers or from the remaining 39 numbers?

[feral hornet]

yeah thats what I found confusing as well

I mean it says they are picked without replacement, that each tikcet has 6 numbers

So i'm guessing they are picked from the remaining 39....

because none of the divisions say for eg 6 winning numbers and 2 supplementary for eg

[burnt mulch]

If this is your interpretation, then idk how your setup is relevant to that

[feral hornet]

im going with this now

and do you think its the right interpretation?

[burnt mulch]

I have no idea

your guess is as good as mine

Oh wait

does it want the individual probability for each division

I thought it meant all 6 at once

ok nvm

I retract my comment

lemme see

[burnt mulch]

yeah this looks fine

[feral hornet]

it does want all 6 later i think, like the probabiliy of winning any prize at all (but thats a later question)

[feral hornet]

and I'm not 100% sure how to go about that, maybe multiplying all the probabilities from the divisions together, and then dividing that by 1-itself

[burnt mulch]

that wouldn't work since not all of them are independent

ex. divisions 1 and 3

I would do casework on the hands that wouldn't work for any of them (consider the number of winning numbers and the number of supplementary numbers)

basically, consider the complement

[feral hornet]

what do you mean casework?

and yeah thats a good point about the independence

[burnt mulch]

list out the possibilities that fail

"casework" = consider cases

[feral hornet]

so take the complements of each division then add them together?

[burnt mulch]

the complements aren't necessarily disjoint either

[burnt mulch]

hence why I said any of them

it's gonna suck at least a little bit

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[gilded panther]

Can anyone help me with my trigonometry/ calculus homework

[wraith hinge]

Put the img

Let's see it

[wraith hinge]

Alr #8?

[gilded panther]

Yes 8

[wraith hinge]

So, we can start with 2 options: either remove fractions, or create a common denominator for both sides

[gilded panther]

Create an common denominator

Is easier right?

[wraith hinge]

Alr, so the best option is 12 for CD

Which you did, nice

[gilded panther]

Can we multiple every thing with 12 to get ride of bottom

[wraith hinge]

That works too

[gilded panther]

The top would multiple with 12 right

[wraith hinge]

The top would not change

And it can be solved from there

[gilded panther]

That’s right?

[earnest nymph]

yep

you can simplify the fraction tho

[gilded panther]

Oh cause 2 it’s the gcf

[earnest nymph]

yep

[gilded panther]

7

Would we use quadratic formula

[earnest nymph]

this is solvable without it

but if youre unsure, just do it

[barren tartan]

Bro

Multiply by 12

And then simplify

Cmon cuh

[earnest nymph]

he already did that q

[barren tartan]

Then solve

[gilded panther]

💀chill we only did one day of math and he haven’t show us how to do anything

But how could we do 7

[barren tartan]

Quadratic formula bruh

Or factor

[gilded panther]

💀

[barren tartan]

What's with the skull emoji

[earnest nymph]

you can def factorise this just looking at common factors

[pliant junco]

can use complete square?

[earnest nymph]

what have you tried

[gilded panther]

X = -6, 1 right

[barren tartan]

Just plug the fricking quadratic formula

[earnest nymph]

mmmmmm

[barren tartan]

Ofc u can do ctx

[earnest nymph]

no

[barren tartan]

Cts

[pliant junco]

?

[barren tartan]

-6 ain't a solution for 7 I think

[earnest nymph]

think about the multiples

first, break the 2 and 3 up into its factors

[gilded panther]

It’s-3 I didn’t divide right

[barren tartan]

Lemme actually solve it cuz yall to lazy to plug in a damn formula

[earnest nymph]

which is just 2 x 1 and 3 x 1

[earnest nymph]

yep

did you divide both of them by 2

-3 and 1/2

[barren tartan]

Aight

I got -3

And 1/2

I don't think u can factor it

In a nice way

[earnest nymph]

you can

[barren tartan]

Oh sht

I'm such a dumbass

[gilded panther]

💀i definitely feel like one

[earnest nymph]

nah its allg

at one point, maths is pattern recognition

you just gotta practice for it

[barren tartan]

I studied alg 1 2 years ago 💀

And I can't even factor the most basic ones

Like visually I didn't spot the trick

By just looking at it

I would have to use the traditional method

[gilded panther]

What would we do first

Do we try to break the square root first or combine the regular numbers

[earnest nymph]

def combine the like terms first

the square root wont be breakable just like that, so were going to add the numbers and then square both sides

[stray drum]

Add 14 on both sides, square to get rid of the root

[barren tartan]

Isolate sqrt expressions first

[gilded panther]

Like that so far right

[earnest nymph]

like that yra

[stray drum]

Yes

[earnest nymph]

then solve for x

[barren tartan]

Very good

[stray drum]

Now its trivial

[barren tartan]

Exactly

[earnest nymph]

youre going to get 2 answers, one of them isnt going to work

you have to check which one it is by subbing it back in

[barren tartan]

Yeah just plug them back In the original

And eradicate the negative

[gilded panther]

Am sorry am confused what do I do now

[barren tartan]

It's positive

[stray drum]

Sir

[barren tartan]

200

[gilded panther]

No

[stray drum]

Yes

[barren tartan]

Cmon dawg

Look again

[stray drum]

264-x^2

Dawg

[gilded panther]

🙏Ong am confused

[stray drum]

Just write it correctly on paper or else ur gonna get confused 😭

[barren tartan]

Yes bro

Ngl that handwriting needs work

To be blunt

Abt it

[stray drum]

Schlawg its 264-x^2=64

[gilded panther]

Yeah I have the same teacher as last year and he made an example saying he know who did it if you got bad handwriting like me

[stray drum]

If you subtract on both sides you get -x^2 = -200

Thats x^2=200

[barren tartan]

Sadge

[gilded panther]

If this wrong I new it on paper to see what I did wrong💀💀💀

[stray drum]

Its right

Now get rid of negatives

[barren tartan]

Exactly

Pull the negatives out of the paper

[gilded panther]

Oh it’s because we square them getting rid of the negative sign right

[barren tartan]

Bro

It's cuz

There's a negative sign

On both sides

[gilded panther]

💀

[stray drum]

Bro this is just ratios

Since slope is change in y over change in x

8/9=36000/x

[barren tartan]

Don't worry I know how to tackle these word problems

The trick

Is to read the english

And use Google translate to translate it into equations

[stray drum]

😭🙏

[gilded panther]

💀 I have an idea but it probably wrong but this is what yall said right or idk

💀💀💀

[stray drum]

Dawg

[gilded panther]

Ong I need it on paper cuz am just slow

[stray drum]

I dont even think I can help you here bro how do you even

You wrote down 3600😭

Its 36000

And why dont you have a variable x 😭

[stray drum]

Yes good

[gilded panther]

🙏here what you said right

Ight

[stray drum]

Now isolate x

Or

Actually

Just cross multiply if you learned that

[gilded panther]

Right?

[stray drum]

Man

[gilded panther]

My bad

[stray drum]

Its 8x=9*36000

Thats how cross multiplying works

[gilded panther]

(3 anit there)

[stray drum]

Ok

Now

Solve for x

[gilded panther]

Divide it by 8?

[stray drum]

Yes

[gilded panther]

X= 40,500

[stray drum]

Yes

Do you actually understand why we did that though

[gilded panther]

Yeah cross multi break them out of the /

I think I do

4

🙏 hope am not being too slow for you

[barren tartan]

Bro literally dipped

[gilded panther]

Am here

But it’s definitely understandable why he did

[barren tartan]

Don't talk down on urself like that

Anyway

U need to attempt the problems

Or else

You'll never get the concepts

[stray drum]

Bro i just had to take a shower 😭

Attempt the problems as well as you can and use online resources also

Especially for word problems they can seem confusing at first but sometimes its actually really simple

[gilded panther]

Oh I gotta h

Gotcha

Yeah I have no idea where to start

Well it’s an 🔺 and I tried making it an box

Because idk I was gonna do try to find the area square then divide by 2

But that’s dumb

Since it the perimeter

Chat gbt chat this which am confused

With the formula

Am gonna try to do this one rq

No clue

Am done with math tonight ( not with the paper just for tonight)

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[cosmic gate]

hello

[cosmic gate]

just a very quick question

is a lamina an object where the mass density is just 1

meaning that M is just the area of omega

[unique minnow]

I don't know that there is such a distinction. From what I know a lamina is just a closed surface on the plane with some surface density.

[violet gust]

Lamina s just a thin plate that is considered a 2d surface object in 3d

[cosmic gate]

oh ok

so there should be no height

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[clever chasm]

Could someone provide some context as why this conversion works?

[wind cloak]

change of base formula in reverse order

[clever chasm]

ah

i see it now

ty

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Please don't occupy multiple help channels.

[dim osprey]

got it till here

[cyan nebula]

Cos2A + sin2A =1

@dim osprey

Wait

[dim osprey]

got it

[cyan nebula]

Mk

[dim osprey]

$(\frac(cos^2A - Sin^2A)(cosA-sinA)$

damn i messed shit up

$(\frac(cos^2A - Sin^2A)/(cosA-sinA)$

[solid kiln]

Whenwhywhat

[dim osprey]

idk how to use this

imma learn

[cyan nebula]

Did u get it

@dim osprey

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[compact seal]

with solution too, i wanna understand and recite in class

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[compact seal]

<@&286206848099549185>

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[graceful cairn]

I'm relatively new to logarithmic equations, and I have been told that my solution of the problem (lg x)^2 = lg 4 is wrong. I am unable to understand what procedure I did do that was wrong, though..

[carmine spade]

this is the wrong step

$10^{(\log{x})^2} = 10^{(\log{x})(\log{x})} = \left(10^{\log{x}}\right)^{\log{x}}$

[solid kiln]

Acman

[carmine spade]

can you see now why this step doesnt work ? @graceful cairn

[graceful cairn]

Yeah, I do. There's got to be a hole in my understanding of the exponent rules

[carmine spade]

ok thats also not right, but its easy to think that

ill explain 2s

[graceful cairn]

take your time

[carmine spade]

when we see notation like $a^{b^c}$ we assume that its $a^{(b^c)}$ because otherwise it would be $(a^b)^c = a^{bc}$ and we would just write that simpler expression

[solid kiln]

Acman

[carmine spade]

does that make sense?

in this case we have $10^{(\log{x})^2} = 10^{\left((\log{x})^2\right)}$ instead of $\left(10^{\log{x}}\right)^2 = 10^{2\log{x}}$

[solid kiln]

Acman

[graceful cairn]

It does make sense. You're great at explaining. The question that remains is to know when the power rule applies and when it doesn't when it isn't made clear by the parantheses, but I think that context is the answer

like be able to identify if the power rule can be used or not

oops, my apologies, it's not the power rule but the xponent rule

[carmine spade]

if you ever see one of these 'power towers' always think about evaluating from the top down

e.g. $a^{b^{c^d}} = a^{\left(b^{\left(c^d\right)}\right)}$

[solid kiln]

Acman

[carmine spade]

unless other parenthesis are given that would indicate otherwise

[graceful cairn]

All right, that's clear. I should perhaps train at putting exponentiations in paranthesis when writing own equations, too, since I was the one who wrote the intial lines

[carmine spade]

yeah not a bad thing to have extra clarity

[bronze agate]

But it's not mandatory

[graceful cairn]

right, so it's only mandatory to put paranthesis when you want to underline that the exponent rule applies

[carmine spade]

parentheses would only be needed if you werent following this order

[graceful cairn]

makes sense, since aceman emphasised that we're automatically assuming

[graceful cairn]

yeah, that

[bronze agate]

You don't need to underline it. You assume that anyone who reads your writings that they understand it

[carmine spade]

so you might have $\left(a^b\right)^{c^d}= \left(a^b\right)^{(c^d)} = a^{b(c^d)}$

[solid kiln]

Acman

[graceful cairn]

i'm relatively new to logarithmic equations so it wouldn't hurt to put these for some of the first questions I solve for the sake of clarity, but i do understand now when it's mandatory and when it's not, thanks to you guys

you've been extremely helpful, i appreciate your time! Thanks for clarifying

[carmine spade]

nws ! happy to help

do you need help with your original question or do you want to go back and try it on your own

you can leave this channel open and come back in a bit if you need to

[graceful cairn]

i got the question from a book that first asks you to explore potential solving ways before proceeding with teaching you the theory for solving it + other logarithmic equations

i would therefore not bother you with the inital question before i get an understand of the theory/methods, so i'll close the ticket for now

thanks again, your help is deeply appreciated

.close

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[carmine spade]

all the best !

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[subtle ether]

How dyu work out part d

[main sigil]

You probably found out that f(x) = 0 has a root x = -3

that means f(-3) = 0

and we need to find some x, such that f(x-5) = 0

[subtle ether]

oh shit is it the way where u just

plug in random numbers

oh

actually

x- 5 = -3

so x = -2

[bronze agate]

yes

[subtle ether]

my algebra is wrong

my brain is fried

whats - 3 + 5

its 2 innit

ok thanks

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[subtle ether]

.reopen

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✅

[subtle ether]

can someone eplain to me how to do part c?

they differentiate in mark schee

but I don't understand why

Like finding turning points

but i dont get it graphically

[simple finch]

the line y = k has to be within the area captured by the two turning points of curve C, for it to cut the curve C at three distinct points...

if you sketch the curve C on a paper, it becomes pretty clear

[subtle ether]

shit I didn't read that it was a line

I thought it was another cubic graph for some reason

thanks

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[main sigil]

Am I stupid, or does f(x) = -x not work?

[main sigil]

f(f(x)^2 + f(y)) = f((-x)^2 - y) = f(x^2 - y) = y - x^2
xf(x) + y = - x^2 - y

oh wait

I got it

nvm

.close

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[cosmic gate]

hello

[cosmic gate]

does anyone know why the order of the bounds are what they are for h(y) and k(y)

this is the graph

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[cosmic gate]

<@&286206848099549185>

[cosmic gate]

<@&286206848099549185>

[wooden remnant]

Where are you stuck?

[cosmic gate]

.

[wooden remnant]

O sry hadnt seen that line woops

This is the area we are integrating in the second part of the integral

These are the directions we are integrating in

Obviously for y this is just from 0 to 1 but your question was about the x bounds

The green funxtion here is the upper bound k(y) and the red line is the lower bound h(y) (area we integrate i have colored in yellow)

Does this answer your question or did you mean something else?

@cosmic gate ?

[cosmic gate]

i was wondering as to why k(y) is the upper bound

[wooden remnant]

Because we are integrating this way

For example when we are integrating a normal function y(x) from x = a to x=b and we know b>a we integrate as $\int_a^b dx$

[solid kiln]

thijs2725

[wooden remnant]

The only difference this time is that we dont have 2 points a and b but 2 functions h(y) and k(y)
k(y)>h(y) so now the integral will be $\int_{h(y)}^{k(y)} dx$

[solid kiln]

thijs2725

[wooden remnant]

Is it more clear now?

[cosmic gate]

yeah but the only thing is that i thought since k(y) was lower than h(y) on the relevant interval, it would be the opposite?

[wooden remnant]

No k(y) is the one above h(y) within the interval

Otherwise it would indeed be the opposite

At least when they are defined like you have written here

But are rhese f(y) and g(y) correct? Because they look switched

[cosmic gate]

they are correct

[wooden remnant]

Would that be to make it positive because the -4 to 0 integral is negative?

[cosmic gate]

ummm from what i understand they are simply the boundary curves as y varies between 0 and -4

[wooden remnant]

Nvm this that isnt the case

[wooden remnant]

It looks strange because it is the opposite of the h and k functions orientation

[cosmic gate]

yeah they are multiple answers to this

this is another one

[wooden remnant]

O woops i now see the negative sign in front of the sqrt

My mistake

That explains it

[cosmic gate]

thanks for your help

i think i get the general gist of everything

[wooden remnant]

👍

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[rich stag]

should i do like in degree mode or radian mode

[gaunt wave]

radians

Although with 0 it doesn't really matter, since 0 rads = 0 degrees

[uncut aspen]

both should yield similar answers, but in calculus you always use radians with trig

[rich stag]

oki

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[timber bronze]

how do i do this question?

[timber bronze]

i guess i just dont really understand the notation the answer options are in, i know you have to do a binomial expoansion

is the top number just the exponent of the (1+x)^n and the bottom number is the exponent in the binomial youre choosing

i assume so because the answer is E but can someone confirm please

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[pearl lotus]

It's asking for the Taylor series expansion of the function at x = 0

And the coeff of x^5 in that expansion

[timber bronze]

yeah i get that

you need binomial for this question

i just dont know how to read the binomial notation

[pearl lotus]

what exactly

[timber bronze]

well the answers are written as two numbers on top of each other in a bracket

this is binomial

[timber bronze]

i just need someone to confirm if this is true

[pearl lotus]

By the top number you mean n! Well not exactly
The exponent of x in (1+x) ⁿ is n-r and exponent of 1 in the same is r and the gen coeff is nCr

[timber bronze]

well i explained my reasoning above and it gives me the right answer sooo

i know the top number has to be 1/5 and i assumed the bottom number is 4 because it would give you the term for x^4

that multiplied by the x in f(x) gives you x^5

[pearl lotus]

ok as you wish

[timber bronze]

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[weak vigil]

Hey, can someone explain to me why in the derivative of $\sec^{-1}{x}$ we have a modulus? in the result, ie

[solid kiln]

PianoDolphin

[weak vigil]

$\frac{1}{\abs{x}\sqrt{x^2 -1}}$

[solid kiln]

PianoDolphin

[weak vigil]

why is there that modulas, I know that one reason is because the function always increasing

but then why do I have to take that into account from outside and manually put the modulo symbol

why did that symbol not just appear naturally while deriving it

where did I assume something or skip past something?

My derivation also is not very standard because I do not understand implicit differentiation yet so I haven't used it

I mean I did differentiate both the sides by the logic that if for two functions f(x) and g(x) , if f(x) = g(x), then their derivatives will also be equal because the value of the function at each point will be equal

[ionic pendant]

https://math.libretexts.org/Bookshelves/Calculus/Supplemental_Modules_(Calculus)/Differential_Calculus/Differential_Calculus_(Seeburger)/Derivatives_of_the_Inverse_Trigonometric_Functions

[weak vigil]

Thank you

I am not sure I understand it tho

I am weak at all this d/dx stuff

I just write g(x)`

I don't think I have ever used d/dx much, hence I am problem understanding implicit diffentiation as well cause there they use dy/dx and I don't know what that means

But I will get it

thank you

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[inland dew]

quick q about interest calculation
this is compound right?

[inland dew]

compounded daily

it would be P(1 + r/365)^365

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[tame mica]

what is euclidean geometry?

[tame mica]

or more what isn't euclidean geometry?

[jaunty scarab]

Euclidean geometry is derived from 5 specific axioms, contained in The Elements

[maiden hare]

Elliptic geometry, hyperbolic geometry, Riemannian geometry (over a non-planar smooth manifold), ... are not Euclidean

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[tame mica]

Are 3d objects euclidean?

Like are there any real world non euclidean objects?

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[spice fulcrum]

what have you tried?

[brazen gazelle]

deriving

but i forgot how to get maximums

[violet gust]

There is a test for checking the maximum. What is that test?

[brazen gazelle]

isnt it first derivatigve test

[violet gust]

use that

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[brisk forum]

anyoen know how to figure part B and C out?

[worldly wing]

the domain is the set of possible values of x, and the range is the set of possible values of y

[brisk forum]

yes i know what a domain and range is

but how do i change the parametric domain to a cartesian domain

answers are these, doesnt really explain how it got to it tho

[fleet bear]

Well, what values can sin t take when 0 <= t <= 2pi?

[brisk forum]

thats what im asking....

not sure how to get the domain of the parametric curve to a cartesian domain

[fleet bear]

Hmm, so if I asked what the range of sin x is, what would you say?

[brisk forum]

the range of sin x -1, 1

[fleet bear]

Correct. Are you aware that sin x is a periodic function?

In simple terms, the function "repeats" the values it takes in the same order

[brisk forum]

yes

[fleet bear]

Great! Now, I'll just tell this bit. Every 2pi, sin x repeats its output, meaning it takes all the values in its range in any 2pi interval. So the range of sin x, (where x in 0, 2pi) is still -1, 1

That's pretty roundabout way to explain it tbh. It's usually just something you learn when trig functions are introduced in pre-calculus

[brisk forum]

i get what a sin graph looks like and is usual given domain and range

the question asks for the domain and range of the given parametric curve, in a cartesian plane

because the last part of the question is going to ask you to graph the function in a cartesian plane

[brisk forum]

and yes that is correct, the range will always be [-1,1] because the sin graph repeats

as the period is 2pi

the domain is given in the question yes, but in terms of "t" which is the domain in the parametric curve

[fleet bear]

"The domain of the parametric curve" is "set of values of x it takes"

x is given by some function of t, therefore the set of values of x it takes is just the range of that function of t

[brisk forum]

ahh alright

that makes more sense

[fleet bear]

Epic

[brisk forum]

thanks

[fleet bear]

No problem!

[brisk forum]

im just tryna rush everything bc i got some test tomorrow

[fleet bear]

Fair enough mate, good luck 👍

[brisk forum]

ty

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[smoky yacht]

<@&286206848099549185>

Plz tell me how to solve it....

[fathom idol]

Why

Help?

[smoky yacht]

Yea

Plz

[fathom idol]

Ok