help-10

[hazy junco]

yea

[teal turret]

That’s the same as f(0)+g(0) iirc

Try that

[hazy junco]

so the answer is 0?

[teal turret]

Do u know what f(0) means?

[hazy junco]

not really

[teal turret]

So to get f(0), u go to the graph and look for the graph of f. Once you’ve found it, find which y-value the graph intercepts when x=0

Do u get it or need an example

[hazy junco]

so 2

[teal turret]

Yes

Now find g(0)

[hazy junco]

is it f(2)+g(4)

[teal turret]

Nono

Just find g(0) first

[hazy junco]

4

[teal turret]

Yes

So we have f(0) which is 2 and g(0) which is 4

[hazy junco]

yes

[teal turret]

Then what’s f(0)+ g(0)

[hazy junco]

2+4

got it

[teal turret]

Yep

Is it right?

[hazy junco]

so (f-g) would be -2?

[hazy junco]

yes

[teal turret]

Yes, f(0)-g(0)=-2

Check it and see if ur right

[hazy junco]

Yes it was thanks

[teal turret]

Cool

Np

[obtuse pebble]

@hazy junco Has your question been resolved?

[obtuse pebble]

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[marsh pulsar]

ok guys be honest ..

what are divides relations in set theory?

[steel goblet]

whoops sorry

[marsh pulsar]

grrr

[steel goblet]

ill move one sec

[marsh pulsar]

good luck

[steel goblet]

thank you!

[obtuse pebble]

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[hard quartz]

How do I write this as a potency with the base 3

[brisk grove]

9 = 3^2

use exponent rules

[hard quartz]

So 3^2^8?

[abstract flame]

not quite

2^8 seems a little big

[hard quartz]

I don’t really get it

[abstract flame]

doesn't it

(a^b)^c=a^(bc)

use that rule

[hard quartz]

Alright will try

[hard quartz]

Thank you, I get it now! 3^-4

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[shut spoke]

Can someone tell me what do I do with sin 5 ∅ and csc ∅ cuz I seriously have no idea

[lost plaza]

k

question for u

[shut spoke]

Um yes?

[lost plaza]

hard

I'm so laptop so

[shut spoke]

If ur asking a question start a channel

[lost plaza]

k

how start channel

[cloud forum]

can somone help me

[cedar lichen]

#❓how-to-get-help

[shut spoke]

Can anyone help me with this?

[cedar lichen]

Holy shit everyone's stealing your channel, huh

[shut spoke]

It's not that I care honestly but I just want to get answer cuz this question is abit confusing

[cedar lichen]

What have you tried

[shut spoke]

Well I have tried using the last 4 geometry lessons nothing seemed to really fit with this question as the first unit is about similarity and I definitely did not take anything in trigonometry that can back this up

And algebra is out of the question

[cedar lichen]

What do you know about intersecting chords?

[shut spoke]

Co x do = bo x ao (atleast this is the rule that we supposedly should solve this with)

[cedar lichen]

And what happens if you sub in the values?

[shut spoke]

Sin and csc are different not really numbers wouldn't they be added as variables?

This wouldn't help solve the question at all we would have 3 different variables

[cedar lichen]

Just trust me

Pretty please 🥺

Things will cancel

[shut spoke]

How can we even multiply the csc with sin?

[cedar lichen]

What's the definition of csc?

[shut spoke]

Havent got to that point yet in trigonometry

[cedar lichen]

csc x = 1/sinx

Gotta go, use that

[shut spoke]

Okayyy

Okay I seriously did not get how we will solve this with two variables Inside and no absolute term

[cedar lichen]

@shut spoke I'm back

What do you have rn

Tag me when you return

[shut spoke]

I'm back but after we considered 2csc(x) = 2sin(x) how will we approach this afterwards?

[shut spoke]

Okay

[cedar lichen]

How did you get 2cscx = 2sinx

[shut spoke]

oh sorry mis understood

So wait 2 csc = 2 over sin(x)?

[cedar lichen]

Yes

[shut spoke]

Tysm

.close

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[steep stratus]

Help

😔

[obtuse pebble]

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[hazy junco]

help please

anyone

?

.close

[obtuse pebble]

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[delicate cliff]

Hi I'm pretty lost on how I would solve for the interval?

[delicate cliff]

I tried plugging in 1.1 and 1.2 into the equation but it seems like that wasn't the best approach

and same for 1 and 2 above

<@&286206848099549185>

i need help

[hardy widget]

the intervals should have endpoints that are the inputs

no?

[delicate cliff]

i'm not too sure by what you mean

?

[brisk grove]

Yeah. since f(1) < 0 < f(2), you know there is a number c between 1 and 2 such that f(c) = 0.

So there is a root between 1 and 2. A root means a point where the y value is 0.

[brisk grove]

Try understand what exactly this means

[delicate cliff]

so x is the root and y is 0?

?

so

?

.close

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[tribal root]

I'm doing a physics practice question and I'm stuck on the math calculations, basically have no idea how to finish the calculation to get the appropriate units

The first equation is a kinematics equation, and the second is the rearranged version to solve for a (acceleration)

-(27.8m/s)^2 is because v2 is 0m/s, so v1 just becomes negative

How do I finish the calculation and get the right units (m/s^2)

[royal shard]

in the top we have (m/s)^2

which is m^2/s^2

dividing by m we get m/s^2

[tribal root]

Ahhh that's what I was confused about

I wasn't sure how the exponent would affect the units

Thanks a lot man, I appreciate it

.close

[obtuse pebble]

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[barren summit]

X

[barren summit]

What is the negation of "exactly one of x or y is odd"

is it "x and y have the same parity"

ok

.close

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[barren summit]

X

[barren summit]

what is the negation of "everything I know in mathematics"

"something I know in mathematics that is true but is actually false" ?

[formal orchid]

Maybe something like "everything I don't know in mathematics"...?

[sinful bane]

something i dont know

[civic zealot]

that's not a statement with any truth value to negate.

[barren summit]

But listen

what if I have the statement: "square root of two is irrational"

Every statement can be rewritten such that P=>Q

[civic zealot]

if it's a statement with a truth value, yes

If i say "trees" you can't turn that into an implication, it doesn't have any truth value

'everything I know in mathematics' isn't a complete statement
"everything I know in mathematics is true"
"Everything I know is in mathematics"
Would be examples of statements with truth value.

[obtuse pebble]

@barren summit Has your question been resolved?

[barren summit]

"everything I know in mathematics", i.e. "everything I know to be true in mathematics"

idk

maybe you are right

[civic zealot]

Your statement is equivalent to “everything I know about math”

Basically you have “∀x∈M”
There’s no implication though

[obtuse pebble]

@barren summit Has your question been resolved?

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[obtuse pebble]

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[hallow sandal]

can yall help with physics also?

[twin sapphire]

ask your question first but maybe if it involves mostly maths

or if its basic physics

[wooden cipher]

there is a physics server if you want more people willing to help out

check #old-network

[obtuse pebble]

@hallow sandal Has your question been resolved?

[obtuse pebble]

@hallow sandal Has your question been resolved?

[hallow sandal]

.close

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[dusk turtle]

How to solve?

[summer stone]

do you know about the quotient rule or product rule?

[dusk turtle]

Yes my professor started by taking a cos out from the top to equal

1-sin^2 cos^2 / sin^2

and then im lost

[summer stone]

what is the quotient rule?

what is the formula for it?

[dusk turtle]

Supposed to use trigonometricc integrals

[summer stone]

its a derivative tho 👀

[dusk turtle]

hi di lo over lo di hi

XD

[dusk turtle]

Yeah this was the easy one

It started out

csc^2 cos^3

I just converted it to cos^3 / sin^2

[summer stone]

and your asking how to solve this, right?

[dusk turtle]

Yes

[summer stone]

quotient rule

[dusk turtle]

Ok

Thank you

[summer stone]

:)

[dusk turtle]

.close

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[dense agate]

How do I add and subtract binomials

[dense agate]

?

[twin sapphire]

wdym?

like (x+2)+(3x-1)?

[dense agate]

Ya like, (-7x + 5) - (-4x + 6)

[stable rain]

um remove it from the brackets first

then group like terms

[twin sapphire]

yeah you can remove the brackets

[stable rain]

notice that theres a negative, uve to * that with the terms inside

[dense agate]

How do i distribute?

[stable rain]

multiply - to each element in the ()

• (-4x + 6)

[dense agate]

u mean -1?

[stable rain]

ye

[dense agate]

-1 * -4x and 6?

[stable rain]

yes

[dense agate]

is that just -4x?

[stable rain]

um

negative * negative = positive

[dense agate]

so 4x

[stable rain]

yes

[dense agate]

negative * positive = ?

[stable rain]

neg

[dense agate]

positive * negative = ?

[stable rain]

neg

[dense agate]

how do u get a pos then

[stable rain]

neg*neg

or pos*pos

eg

1*1=1

or

(-1)*(-1)=1

[dense agate]

so it will be -6

[stable rain]

-1 * 6

yes

[dense agate]

ok

whats the nest step

next

[stable rain]

so whats the expression now

[dense agate]

-7x + 5 - 4x -6

right

[stable rain]

Ya like, (-7x + 5) - (-4x + 6)

i copy pasted

um no

the 4x shld be positive

[dense agate]

oh

ok

its positive 4

so now i do

[stable rain]

yes

so whats the exp now

[dense agate]

-7x + 4x

[stable rain]

no the

[dense agate]

and then 5 + 6

[stable rain]

ensure thing

put it in 1 line

[dense agate]

what?

[stable rain]

(-7x + 5) - (-4x + 6)

[dense agate]

yea

[stable rain]

put the whole exp in 1 line

[dense agate]

-7x + 5 + 4x - 6

[stable rain]

yes

so now u group like terms

[dense agate]

so

-7x and +4x

i add them

[stable rain]

yes

what do u get

[dense agate]

uh

-3x?

u there

[stable rain]

yes

yes

[dense agate]

is that correct?

-3x

[stable rain]

yes

[dense agate]

ok

so

i do

5 + 6

11

[stable rain]

-7x + 5 + 4x - 6

its -6

[dense agate]

oh yeah

5 - 6

=

-1

[stable rain]

ye

[dense agate]

so

the

answer is

[stable rain]

:ap

:ap

[dense agate]

-3x -1

?

[stable rain]

it wasnt gg thru earlier :c

yes

💕

[dense agate]

ok

thx

[stable rain]

np

[dense agate]

cya

[stable rain]

cya

💕

[dense agate]

.close

[obtuse pebble]

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[rigid lintel]

that looks like torture

[trail sparrow]

everything

theta alpha and beta

yea thats easy

its just 56

theta is 68

ik just confused with beta and alpha

[twin sapphire]

is there something else we need to know about triangle PST?

because like it could be anything

from just the drawing

[stable rain]

cong tri

[trail sparrow]

no

there are nothing

[twin sapphire]

oh yeah

[stable rain]

prob S and T are tangents

[trail sparrow]

what is tangent?

[twin sapphire]

thats what i suspected

[stable rain]

i dont think u can solve it if they arent

[trail sparrow]

what is tangent?

[stable rain]

https://www.varsitytutors.com/hotmath/hotmath_help/topics/tangent-to-a-circle#:~:text=A tangent to a circle,at the point of tangency.

touches 1 point

[trail sparrow]

oh yea it touches

[twin sapphire]

a more useful definition for a circle

a tangeant line is orthogonalm to the radius

and touches the circle

[trail sparrow]

yes it touches

so how would i find alpha

[stable rain]

use this

[trail sparrow]

so beta = theta?

[stable rain]

um

no

[twin sapphire]

no but use the fact that a+b+c = 180° if a b and c are the angles of atriangle

on well chosen triangles

and using the fact in this drawing that the orange line cuts beta in 2

[trail sparrow]

yeah but how does that finds beta?

[twin sapphire]

if you do it on two good triangles

you'll have 2 equations with 2 unknowns

and you can solve that with a little bit of algebra

[trail sparrow]

wait i think i know

thank you

do i close this channel?

[twin sapphire]

which triangles did you chose?

just to be sure

[trail sparrow]

no i remembered something that my teacher tought

hold on ill just draw a diagram

and i can find 2x by halfing 56

[twin sapphire]

wel ok

[trail sparrow]

okay thanks

so do i close this channel?

[twin sapphire]

you can if you want

its yours

[obtuse pebble]

@trail sparrow Has your question been resolved?

[obtuse pebble]

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[neat sedge]

I know normally how to find the average rate of change given a function, but not in this scenario. I'm completely lost.

[fierce lagoon]

Youre expect to see the pattern

The rate of change of $g(x)$ over $[{\color{lime}{a}}, {\color{cyan}{a+h}}]$ is expressed as $4a + 2h$.

You're given [{\color{lime}{2}}, {\color{cyan}{3}}]$

[warm shale]

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

[fierce lagoon]

@neat sedge so you're expected to see this connection and set a system of equations

[neat sedge]

Hmmm

I've been on this problem for over 45 minutes and I haven't found anything. I haven't done this kind of stuff in over 3 years and the lesson we were given had no examples like this.

[fierce lagoon]

Well the colors should highlight something pretty evident

The components of the interval are color coded by similarity. So perhaps you should set up a system of equations based on color

[neat sedge]

As in something like 2 = a, 3 = a+h, so 3 = 2 + h ? meaning h = 1

[fierce lagoon]

Yup!

[neat sedge]

so it becomes 4(2) +2(1) ?

My entire issue was I didnt want to assume I could just plug in the 2 and 3 into the other interval

[fierce lagoon]

Yeah

[fierce lagoon]

You can assume that similar components of something are equal to each other

Like if a/b = c/d, then it is a valid assumption that a = c, b = d

It may not be true, but you could make that assumption until proven false

[neat sedge]

I see, well thank you very much, I appreciate it.

.close

[obtuse pebble]

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[sterile thistle]

how do i solve for the second half of the answer?

[sterile thistle]

I understand how to find 9, but im stuck on the part inside the parenthesis

[obtuse pebble]

@sterile thistle Has your question been resolved?

[stable rain]

,w solve log2(x+2) = log2(2x-7)

[warm shale]

Results provided by WolframAlpha

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

Requested by Circle#0025

[stable rain]

no clue

[obtuse pebble]

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[grizzled geyser]

I'm so confused right now can someone explain what I did wrong

[obtuse pebble]

@grizzled geyser Has your question been resolved?

[grizzled geyser]

.close

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[ionic warren]

How to solve 589_ divided by 7 = _8_2

[stable rain]

what are the _

[ionic warren]

Missing numbers

[timid silo]

Is it supposed to be same like a variable

[ionic warren]

M I S S I N G N U M B E R S

[stable rain]

..

bit rude

[ionic warren]

Sorry 😦

I'm honestly just stuck on all of this

Hello?

Anyone here?

<@&286206848099549185>

😦

I'm sorry 😦

.close

[obtuse pebble]

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[sullen slate]

@ionic warren 5894 divided by 7 = 0842

[obtuse pebble]

✅

[ionic warren]

Thank you!

[sullen slate]

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[ionic warren]

.close

[obtuse pebble]

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[grand oxide]

How do you memorize trig formulas for quizzes?

[royal basin]

generally you don't

commit a few basic ones to memory (pythagoras, angle sum/diff/double, that sorta thing)

derive all else from those

[grand oxide]

My teacher says that memorizing trig formulas is preparation for calculus

[royal basin]

nyeh...

memorization is not sth to put that much effort into when it comes to math

[grand oxide]

So is it yes?

[royal basin]

don't memorize blindly

did your teacher give you a list of formulas they would like you to memorize

[grand oxide]

Yes

[royal basin]

show

[grand oxide]

Ok

[royal basin]

very likely there's only a few key ones there and everything else can be derived from them

cutting down on the memory load

[grand oxide]

https://tutorial.math.lamar.edu/pdf/Trig_Cheat_Sheet_Reduced.pdf

Is it better to do some math exercises in textbook than watching his lectures?

[high lily]

do combo of both?

[royal basin]

yeah porque no los dos

[grand oxide]

I am not sure his lectures are kinda delaying

[royal basin]

the more you practice with these formulas the more they will cement themselves in your mind

[grand oxide]

Ok

[high lily]

imo the most pesky would be the sum ↔️product formulas

[grand oxide]

Memorizing sum to products formulas is complicated?

[high lily]

depends on who you are,

[grand oxide]

Ok

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[feral cosmos]

What is the domain for |y| = 4 - x

[feral cosmos]

I got the answer: (- infinity, infinity)

or would it be (- infinity, 4]

[narrow fiber]

Yes that is correct

[final thunder]

Yea x can’t be more than 4

[feral cosmos]

okay

it's because the absolute value of a number has to be positive correct?

[final thunder]

Yes

[feral cosmos]

thanks!

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[final thunder]

Np

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[spiral bobcat]

Math is not mathing what am i supposed to put in this

[fiery oar]

if three rings collectively give 4, each outer ring is 4/3 as 4 is split by the three rings, then for the other gaps simply add the two 4/3s together

[spiral bobcat]

Its a set thing idk what ur talking abt

[fiery oar]

oh damn my mistake, sorry i didnt realize

[spiral bobcat]

Ah its ok

[fiery oar]

so you see the value for each of the singular games, 20 play scrabble, 27 billiard and i cant see how many play chess

those values are your outer ring values as those are the values for just people playing the single games

[spiral bobcat]

No i mean the one in the middle

Its the only one not filled

[fiery oar]

do you mean the top middle? the very centre has a 4 in it

[spiral bobcat]

Yes

[fiery oar]

ah alright

[spiral bobcat]

Its just so hard trying to guess stuff

[fiery oar]

say you make each outer ring one of the games, one of the numbers will give you the two games that cross each other

[spiral bobcat]

Its the medal question

[fiery oar]

could you show the full paper?

[spiral bobcat]

I tried to capture the whole thing

[obtuse pebble]

@spiral bobcat Has your question been resolved?

[obtuse pebble]

@spiral bobcat Has your question been resolved?

[obtuse pebble]

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[echo knoll]

$P(A\cap B’) = 0.32$ $P(A’\cap B) = 0.11$ and $P(A\cup B) = 0.65$

[warm shale]

Krispeh

[echo knoll]

How can I find P(A) and P(B)?

[wild swallow]

write P(A ∪ B) in terms of other stuff that you can find

[echo knoll]

How can I do that?

[wild swallow]

well you could start with inclusion-exclusion

[echo knoll]

elaborate pls

[wild swallow]

do you know the principle of inclusion-exclusion?

[echo knoll]

Never heard of it.

[wild swallow]

P(A ∪ B) = P(A) + P(B) - P(A ∩ B)

[echo knoll]

ohh okay

no I seen that

[stable rain]

so this is what its called

[wild swallow]

well its usually just called PIE

[echo knoll]

I know that yea..

[gilded needle]

think about how A∩B relates to the three sets whose probabilities are given

[stable rain]

first time hearing it

[echo knoll]

Makes sense

[wild swallow]

you're probably also gonna need the total probability formula

[echo knoll]

which one is that?

[wild swallow]

P(A) = P(A ∩ B) + P(A ∩ B')

obviously also works with A and B switched

[echo knoll]

never seen that one lemme note it down

[wild swallow]

youve probably used it before

[echo knoll]

Maybe in a different form with the eqn written in terms of $P(A\cap B)$

[warm shale]

Krispeh

[wild swallow]

like say for example

you want to calculate the probability of it being cold today or something

so you go probability of it being cold today and it rained yesterday + probability of it being cold today and it was sunny yesterday

[echo knoll]

mhmm

[obtuse pebble]

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[stoic dove]

For a probability space (Ω, P) we say that an outcome ω ∈ Ω is an atom if P({ω}) > 0.
a) Show that there are at most n atoms with P({ω}) ≥ 1/n.
b) Show that each probability space has at most a countable number of atoms.

[royal basin]

didnt you ask about part a several days ago?

[stoic dove]

I did, I need help with b

a) was just for context

[royal basin]

ok

well, have you made any progress?

perhaps a similar contradiction proof?

or maybe some more sophisticated cardinality argument

[stoic dove]

Not really I’ve tried showing P is injective

[royal basin]

not only would that not have helped you at all it's not even true in generla

general*

denote by At(P) the set of all atoms of P, and denote by A_n the set of all atoms whose probability is at least 1/n.

you have shown in part (a) that $|A_n| \leq n$ for all $n \in \bN$.

[warm shale]

Ann

[royal basin]

and it should be clear that $\mathrm{At}(P) = \bigcup_{n=1}^{\infty} A_n$.

[warm shale]

Ann

[obtuse pebble]

@stoic dove Has your question been resolved?

[obtuse pebble]

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[wanton pecan]

Hello. I'm currently trying to write a program which requires I find the height value of that red point P. The corners all have their own different height values so I intend to get it by finding the blue point X, lerping between the height values of A and B using X, and then between the height values of X and C using P.

I, however, don't understand barycentric coordinates at all. Looking into them they seem to be the appropriate way to find X, and conveniently also give me t values for lerping, but I can't figure out how to actually do that since my vector math skills, if not just general math skills, are pretty bad 😅 I would really apricate someone helping walk me through this, though I must warn this probably won't be the easiest time.

[sage geode]

So you want to find the height value of P given what?

[wanton pecan]

I know the height values of A, B, and C, and I know the x and y positions of A, B, C, and P.

So to get that, I intend to get point X, lerp between A and B to get it's height, then lerp between X and C to get P's height.

[sage geode]

What do you mean by height value? As I see that's different from y position

[wanton pecan]

Yes. I've flattened this down to 2D for simplicity. Sorry for poorly explaining this 😅

[sage geode]

Ah so we're working in 3 dimensions?

[wanton pecan]

This is actually a part of a large grid, where each square is made of two triangles and each corner has it's own height value.

Mhmm!

[sage geode]

So are A, B and C like on the ground or is any of them elevated?

[wanton pecan]

All of them are elevated to different heights.

This is just looking at one triange of a map something more like this. Bigger of course, but you can see how I'm just taking one triangle from it. Each point in this has it's own elevation value.

A simple square mesh plane.

[sage geode]

Alright, two more questions though for clarification, so are X and P fixed points or do you want X to go from A to B?

And is P the midpoint of CX?

[wanton pecan]

from A to B. The point of getting X is so I have something I can find the height value of that is then in line with P and C. And no, P can be anywhere in the triangle.

If there's a way of skipping getting X and just go straight to the height value of P, I'm all for hearing it. That's just the solution I came up with to try minimise the maths 😅 I'm a programmer, you see. I'm used to avoiding doing the maths parts in favour of functions.

[sage geode]

Well it looks like what we could do instead of finding X is finding the equation representing the ABC plane

[wanton pecan]

It's probably simpler. I tried the lerp to avoid bringing equations into the ordeal, but since that's unavoidable then why not try that instead?

[sage geode]

What did you label the coordinates of A B and C to be?

[wanton pecan]

x, y, z
Z being height.

Or Y if that's easier. It honestly doesn't matter for this.

Let's go with Y, for height, actually 😅 Trying to think what's easiest for the little program I have here.

[sage geode]

I was gonna go with Z

I meant the x y and z values of those points btw

[wanton pecan]

Right. Ye that's actually easier. I get thrown a bit with how to handle 3D when I'm also compressing it to 2D like this.

Each square is 1, 1 and the height is random, so let's go with:

A: 1, 1, 4
B: 0, 0, 1
C: 1, 0, 3

[sage geode]

Okay the equation of the plane ABC can be represented by ax + by + cz = d, where a, b, c and d are coefficients such that the equation is satisfied for (1, 1, 4) (0, 0, 1) and (1, 0, 3)

[wanton pecan]

You might have to take that a little slower for me 😅 I've not really had to touch maths since school so a lot of that's slipped over time.

[sage geode]

So it means we can plug in values x=1 y=1 z=4, x=0 y=0 z=1 and x=1 y=0 z=3 into the equation and the equation will remain true

[sage geode]

Alright look generally an equation of a plane is of the form ax + by + cz = d

[wanton pecan]

what is the x y z in that ax + by + cz?

[sage geode]

We'll use that

[sage geode]

x y z coordinates of any points lying on that plane

The equation is showing the relationship between those coordinates

And a, b, c and d are unknowns

For now

We have to solve for them

[wanton pecan]

D being the point on the plane?

[sage geode]

No, d is just a number like other coefficients a, b and c

[wanton pecan]

Gotcha.

[sage geode]

Okay so firstly the plane ax + by + cz = d needs to go through the point (0, 0, 1), right?

[wanton pecan]

Yes, since that's point B.

[sage geode]

And if a plane goes through a point (0, 0, 1), it means that we can plug in values x=0 y=0 and z=1 into the equation freely

The equation will still hold

So a * 0 + b * 0 + c * 1 = d

Therefore c = d

Let's now rewrite the equation of the plane to be ax + by + cz = c, since c = d and it'll look simpler

[wanton pecan]

Alright, I follow.

[sage geode]

Now that we made sure that the (0, 0, 1) is on the plane, we go onto (1, 0, 3)

So, again, plug in values x=1 y=0 and z=3 to get that a + 3c = c

Therefore a = -2c

Let's again rewrite the equation to be -2cx + by + cz = c

And, as you guessed, now we plug in values x=1 y=1 and z=4

-2c + b + 4c = c

So b = 3c

So the equation is of the form -2cx + 3cy + cz = c

[wanton pecan]

Ok then. So what has this acheived?

[sage geode]

Huh, there's something wrong, wait let me check everything I did here

[sage geode]

Ah b = -c, my bad

So the equation is -2cx - cy + cz = c

Now, I know it may sound weird at first, but we can choose any value for c

Because as long as the proportions between the coefficients are the same, the equation will represent the same place

Let's pick c = 1

So the equation of the plane, finally, is -2x - y + z = 1

There z, the height value, for any point on the plane is equal to 2x + y + 1

So if the x and y coordinates of P are, let's say, P_x and P_y

Then P_z, the height value of P that we're looking for, is 2P_x + P_y + 1

Btw how is the point P "generated"? Just by picking random coordinates?

[wanton pecan]

Mhmm. So let's say 0.4, 0.7

[sage geode]

Then the height value is simply 2 * 0.4 + 0.7 + 1

[wanton pecan]

That's... huh, that's pretty interesting. Let me just go over that again in my head real quick.

That's actually a lot simpler than I thought it'd be, huh. Thank you.

Is there a name of this process I can look up? As well as actually implementing it, I need to explain the process a little. I get the process but not entirely how to describe it.

[sage geode]

Well the thing process is just finding a, b, c and d values such that (0, 0, 1), (1, 0, 3) and (1, 1, 4) points satisfy the equation ax + by + cz = d, not sure if that has a name on it

Perhaps you could look up "Finding equation of a plane given 3 points"

[wanton pecan]

Alright, thank you. This is actually helping me with a job application (thankfully not a maths heavy one). Thank you so much for taking your time to run some random guy through this. You have no idea just how lot I was on this beforehand.

[sage geode]

It's fine, you're welcome

[wanton pecan]

Have a nice day. 😃

[sage geode]

You too

[wanton pecan]

!solved

Oh wait it was

.close

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[shrewd ginkgo]

ok i need help

[shrewd ginkgo]

in

[shrewd ginkgo]

what is

x1 x u9

[devout sable]

can you post actual question

[royal basin]

x1 x u9 is a string of symbols

of length seven

[devout sable]

the photo

[royal basin]

apparently meaningless

[devout sable]

[shrewd ginkgo]

ooooohhhhhhhhhhhh

ok

thanks

2 x 5

[long plinth]

Stop the trolling nonsense, please. You've been posting nothing but that since you joined.

[shrewd ginkgo]

ok

i wont trol

from now on

me sorry

[long plinth]

.close

[obtuse pebble]

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[sacred root]

Hello

[sacred root]

How did he got e^{pi/2}??

[final thunder]

This is true when the inverse function takes the principle value

Consider this θ=arcsinx

Find expression of x in terms of cos

[sacred root]

$\theta = \arcsin(x)$

[warm shale]

Basudev

[sacred root]

90-t

??

[final thunder]

So $x = \sin(\theta) = \cos{(\frac{\pi}{2}-\theta)}$

Yeah?

[sacred root]

Ye

[final thunder]

Okay so $\arccos(x) = \frac{\pi}{2} - \theta$

Replace theta with arcsinx

Then we’re done

[warm shale]

Pure

Pure

[sacred root]

Ohhh

Ye I got it

So you get

arccos(x)=90-arcsin(x)

Then

arccos(x)+arcsin(x)=90

Thx for helping mam

*man

.close

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[final thunder]

Np

[obtuse pebble]

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[worldly thorn]

Help Needed

[final thunder]

You could do this by long division, or (better) inspection.

What have you tried

[obtuse pebble]

@worldly thorn Has your question been resolved?

[worldly thorn]

I did

one min

here @final thunder

[final thunder]

Okay nice

[worldly thorn]

need help at b bit

[fervent cradle]

if the remainder when (4x^3 + 17x^2 + 9x) is divided by (x^2 + 5x + 6) is 18

then the remainder when (4x^3 + 17x^2 + 9x - 18) is divided by (x^2 + 5x + 6) is 0

so (4x^3 + 17x^2 + 9x - 18) has (4x-3) and (x^2 + 5x + 6) as factors

[worldly thorn]

wait

could u explain me clearly?

@fervent cradle

[fervent cradle]

what don't you understand, specifically

[worldly thorn]

first we seperated (4x-3)(x^2+5x+6)

1st value we got as 4/3

so for 2nd equation should we use quad formula?

[worldly thorn]

.close

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[unreal herald]

Hi

[small thicket]

what r u stuck on

[unreal herald]

I dont know what to do with the 4 t shirts and 67.80

[small thicket]

well

the 4 t shirt information is kinda redundant

[unreal herald]

K

[small thicket]

just take 67.8 and add tax of 5.5% on top of taht

[unreal herald]

I dont see 73.3

[small thicket]

what exactly did u do to get

73.3

[unreal herald]

Yes

[small thicket]

because i got a different answer

no im not asking if u got that

how did u get 73.3

[unreal herald]

Arent you supposed to move the decimal of the percent like 2 times to the left

For 5.5

Or once

[small thicket]

wydm by moving the decimal

r u trying to change it into.

0.055?

[unreal herald]

Yes

No

0.55

[small thicket]

why 0.55

u r trying to change 5.5% into decimal form

[unreal herald]

Thats what i was told to do

[small thicket]

100% = 1, 10%=0.1, 1%=0.01

[small thicket]

thats what we r doing but u did it wrong

[unreal herald]

What was i supposed to do

[small thicket]

i told u

[small thicket]

^^'

im saying ur answer is wrong

[small thicket]

its not 0.55

check out conversions of percentages

https://txwes.edu/media/twu/content-assets/images/academics/academic-success-center/Quick-Guide-to-Percentages-and-Decimals.pdf

[unreal herald]

0.055?

[small thicket]

yes

so now what should be do

[unreal herald]

Ohh

Add?

Wait

Multiply

[small thicket]

multiply what

[obtuse pebble]

@unreal herald Has your question been resolved?

[obtuse pebble]

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[rigid lintel]

probability theory correct?

what is the total area under any distribution function

[obtuse pebble]

@dark storm Has your question been resolved?

[obtuse pebble]

@dark storm Has your question been resolved?

[obtuse pebble]

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[fickle bramble]

Hello! This is about logic. I have this given and I don't know where I got it wrong. It says that (p and q) implies r is logically equivalent to (p implies q) implies r. But that is not the case as you can see in my truth table. What did i do wrong?

[obtuse pebble]

@fickle bramble Has your question been resolved?

[fickle bramble]

<@&286206848099549185> sorry. but please help

[mossy salmon]

Looking

I haven't checked your whole truth table, but I checked your last row and my calculations agree

Maybe a typo in the problem?

[fickle bramble]

Could that be the case? I hope so.. I'll just have to ask my teacher about it then

thank you so much

[mossy salmon]

That's my suggestion yeah

[slim lake]

Wait False implies True is True?

[mossy salmon]

Unless I've missed something

Yes, under material implication

It's just the less-than-or-equal-to relation for bools

[cedar lichen]

It's vacuously true

[fickle bramble]

.closed

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[buoyant mortar]

How to prove that 5^2002 < 10^2001

[buoyant mortar]

Like

It sort of logical if we take one 5 out of left part

But how to hard prove it?

[buoyant mortar]

Like 5*5^2001 < 10^2001

[gloomy valve]

You can reduce the inequality to 5 < 2^(2001)

[buoyant mortar]

W8

You can divide them?

[gloomy valve]

Now that's easy to prove because 2^3 is already greater than 5 and 2^x is increasing

Yes you can assume it holds (first) and manipulate it however you wish to reduce it to a simpler form

[buoyant mortar]

Or how do you do that

Dont get it tbh

[buoyant mortar]

This one

Can you explain in math language xd..

[gloomy valve]

5^2002 < 10^2001
5^2002 < (5 * 2)^2001 = 5^2001 * 2^2001

5^1 < 2^2001

[buoyant mortar]

Ogh

Well

Ty ig ❤️

[gloomy valve]

np!

[buoyant mortar]

.close

[obtuse pebble]

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[barren summit]

X

[obtuse pebble]

Please don't occupy multiple help channels.

[barren summit]

?

anyway

[warm shale]

Tim O’Brien

[barren summit]

The case where $x$ is even is easy

But in the case where x is odd I am having trouble

[warm shale]

Tim O’Brien

[barren summit]

Is this enough for a contradiction? Feels kind of shady

[final thunder]

I think this looks good tbh

[barren summit]

i mean yeah, right? I clearly define k and c as integers before and treat them as such

but something about the division by 3 is unsettling

not all integers can be divided by 3

[final thunder]

But 3c and 3k clearly can be decided by 3

[barren summit]

yeah

true

rightfully so, but I will wait for 1 more reply here I guess before I close the channel to be sure

[final thunder]

Alright

[barren summit]

reminds me of something like this:
3 = 5
3*0 = 5*0
0 = 0
true, so 3=5

but i guess
3=5
3/3 = 5/3
1 = 5/3

1 is in Z, 5/3 is not in Z, contradiction, 3!=5

so it's fine Im pretty sure

[final thunder]

Yeah I’m pretty sure this proof works

[barren summit]

alright well wish me luck on my exam in. an hour, i hope this doesn't bite me in the. ass

.close

[obtuse pebble]

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[final thunder]

Lol good luck

[obtuse pebble]

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[blazing mason]

can this converge by DCT?

[alpine raven]

dct ?

[blazing mason]

direct comparison test

[obtuse pebble]

@blazing mason Has your question been resolved?

[obtuse pebble]

@blazing mason Has your question been resolved?

[obtuse pebble]

@blazing mason Has your question been resolved?

[midnight scaffold]

I thinknits possible, can't think of any series I'd compare it tho. It'd be better if you just used the integral convergence test

[obtuse pebble]

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[obtuse pebble]

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[mystic tendon]

Idk if it fits here

[mystic tendon]

But if uranium235 isotope gets fissioned to barium+krypton and some neutrons

the difference in mass will be converted to energy

correct?

but the question:

why? why does it not just even out? whats the cause for that difference? is this just a "god" given fact of how the universe+particles and stuff work?

[obtuse pebble]

@mystic tendon Has your question been resolved?

[mystic tendon]

¿?

[obtuse pebble]

@mystic tendon Has your question been resolved?

[obtuse pebble]

@mystic tendon Has your question been resolved?

[obtuse pebble]

@mystic tendon Has your question been resolved?

[mystic tendon]

.close

[obtuse pebble]

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[obtuse pebble]

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[fading musk]

How to factorize bc(b+c)-ca(c-a)+ab(a+b) using factor theorem

[fading musk]

I let b=-c

And got b+c=0

[obtuse pebble]

@fading musk Has your question been resolved?

[obtuse pebble]

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[stiff saffron]

I already matched the bases , and I don't know how shall I continue due the square root of 3

[stiff saffron]

that's what I got now

or this

it's the same

[final thunder]

$\sqrt{a} = a^\frac{1}{2}$ a is positive

[warm shale]

Pure

[grand garden]

whats the goal? find all real x that satisfy the inequality?

[stiff saffron]

yeap

I don't know what to do with the square root

[timid silo]

Someone just told you

[stiff saffron]

I didn't understand

,

OH

I did it

wait

ok nevermind I don't get it

[timid silo]

replace a by 3 and it's still true

[stiff saffron]

so

?

[timid silo]

square root is power 1/2

Yeah

[stiff saffron]

and then, I multiplied 1/2 by x?

ups

1/2.x ?

[grand garden]

ye

what does the ineq become then

[stiff saffron]

?

[grand garden]

you can mash the threes on the right hand side together

[timid silo]

I would rather simplify a bit further

[stiff saffron]

?

[timid silo]

no

[stiff saffron]

dang

[grand garden]

huh?

[stiff saffron]

then how it is, the bases are already equal right?

[grand garden]

why is $\log_3( 3\cdot 3^{-x})=-x$ in your steps?

[stiff saffron]

shouldn't I just pass to the exponents?

[warm shale]

alshfik

[stiff saffron]

log?

we aren't working with logarithms

[grand garden]

thats the function you applied to both sides in the first step in this image

[stiff saffron]

I didn't know that

it's like that how the inequalities are solved right?

[grand garden]

yeah you were doing fine

[stiff saffron]

till where

[grand garden]

this

[stiff saffron]

that come from here

right?

[grand garden]

$\log_3 (3^{\frac{1}{2}x})=\frac{1}{2}x$ is fine though

[warm shale]

alshfik

[stiff saffron]

where the 1/2x from the right come from?

[grand garden]

definition of logarithm?

[stiff saffron]

logarithm, the exponent or power to which a base must be raised to yield a given number. Expressed mathematically, x is the logarithm of n to the base b if bx = n, in which case one writes x = logb n. For example, 23 = 8; therefore, 3 is the logarithm of 8 to base 2, or 3 = log2 8.

oh

[grand garden]

try to simplify $3 \cdot 3^{-x}$ using $a=a^1$

[warm shale]

alshfik

[stiff saffron]

3^{\frac{1}{2}}\cdot x\ge3^{1}\cdot3^{-x}

why

$3^{\frac{1}{2}}\cdot x\ge3^{1}\cdot3^{-x}

I don't get the bot either

however

?

[grand garden]

$dollars on both sides$

[warm shale]

alshfik

[stiff saffron]

oh ok

$\frac{1}{2}\cdot x\ge1-x$

[grand garden]

the right hand side is fine right now, but what happened to the left

[warm shale]

by_melody

[stiff saffron]

?

[grand garden]

why'd the x fall lol

[stiff saffron]

mistake of the machine

[stiff saffron]

it stays like this right?

the exponents I mean

[grand garden]

good job! you should also note, if you don't already know, that $3^1 \cdot 3^{-x}=3^{1-x}$

[warm shale]

alshfik

[stiff saffron]

yeah, I write it like this in my notebook

just the right part

..

OH

I didn't get it

ok

both part are the same

so at the end it's just two 3 instead of three 3

[grand garden]

as an additional comment, you can apply $log_3$ to both sides of the inequality (while still keeping the new inequality vlaid) because $log_3(x)$ is an increasing function

[warm shale]

alshfik

[stiff saffron]

I didn't study logarithms yet, you could teach me how to use them?

[grand garden]

are you able to work with this then?

[stiff saffron]

I don't know what I should do with the 1/2x

[grand garden]

add $x$ to both sides, are you able to work with that

[warm shale]

alshfik

[stiff saffron]

add x to both side? how? shouldn't I just do $\frac{1}{2}\cdot x+x-1\ge0$

[warm shale]

by_melody

[grand garden]

uh sure, you didn't need to do anything with the $1$ thouh

[warm shale]

alshfik

[grand garden]

there are like terms now! add them!

[stiff saffron]

how?

,

$1\ \frac{1}{2}x-1\ge0$

[warm shale]

by_melody

[stiff saffron]

?

[grand garden]

uh oh, no

what's $1+\frac{1}{2}$

[warm shale]

alshfik

[stiff saffron]

nothing, mb, I don't know how to do it

I thought it was the result between the two x's