help-33

[rugged cobalt]

intersections of subsets that are already in the sigma algebra

[weary temple]

So say $B = \cup_{i \in \mathbb{N}} A_i$ then $B^c = \cap_{i \in \mathbb{N}} A_i^c$

[elfin berry]

Yeetus

[devout mauve]

we know that the A_i form a partition

what is A_1^C

[rugged cobalt]

yes and every A^c is in the sigma algebra

[devout mauve]

$\bigcup$ and $\bigcap$ btw

[elfin berry]

Denascite

[rugged cobalt]

yes iknow

[weary temple]

Oh yes I am sorry, the partition is countable, the unions in the sigma algebra can be finite

[weary temple]

Just X\A_1 right?

[devout mauve]

yes

but now use that the A_i are a partition

[weary temple]

Oh should that be the union of every A_i except A_1?

[devout mauve]

yes

[rugged cobalt]

if $A_1^C \cup A_2^C \in F$ then what would happen if you use demorgans law

[elfin berry]

Køter

[devout mauve]

you said that F is all the possible unions. or is it generated by all the possible unions?

[weary temple]

Not generated, that is the next question. Let me write is using mathematical symbols because my english is a bit poor sometimes and maybe it is causing confusion

Given is the sigma algebra $\mathcal{F} = { \bigcup_{i \in I} A_i | I \subseteq \mathbb{N}}$ is the sigma algebra where $A_n$ is an element of $\mathcal{C}$ which is just the countable partition of $X$

[elfin berry]

Yeetus

[rugged cobalt]

if $A_1^C \cup A_2^C \in F$ then what would happen if you use demorgans law

[elfin berry]

Køter

[weary temple]

That gives $A_1 \cap A_2$

[elfin berry]

Yeetus

[rugged cobalt]

yes and that has to be in F right?

[weary temple]

How so?

[rugged cobalt]

cause its closed under complements

[weary temple]

F contains countable unions only

[weary temple]

I am trying to proof that the given sigma algebra is closed under complements

I can't assume it is true to proof it is true

[rugged cobalt]

no im saying each of them are

[weary temple]

Oh yes right

If you mean A_1 in F then A_1^c in F

[rugged cobalt]

yes but you did it on $A_1^C \cup A_2^C$

[elfin berry]

Køter

[rugged cobalt]

which is just one element in F

sothe complement of that element is obviously also in F

[weary temple]

Right but the intersection of A_1 and A_2 is not guaranteed to be in F right? Sure I can take A_1^C \cup A_2^C and that is indeed contained in F but I am trying to proof that its complement is too

Or am I missing something here

[devout mauve]

lets take a step back

the A_i are a partition

so what is the complement of A_1 cup A_2

[weary temple]

That would be A_1^c cap A_2^c

By DeMorgans

[devout mauve]

not what I'm going for here

partition

[weary temple]

Oh in terms of partition you mean

Well earlier we said that the complement of A_1, because of the partition, is just equal to the union of all A_i except for A_1

So likewise for A_2

?

[devout mauve]

so that shows that the complement of A_1 is in F, yes

same for A_2

but I want (A_1 cup A_2)^C

I want to write this as a union of some of the A_i

how

[weary temple]

So ehmm $\bigcup_{i \neq 1} A_i \cap \bigcup_{i \neq 2} A_i$?

Woops

[elfin berry]

Yeetus

[devout mauve]

no

still not what I want

stop focusing on A_1 and A_2 on their own

dont use demorgan

[weary temple]

Oh don't use demorgans

Let me think

Oh I think I got it

Would be $\bigcup_{i \neq 1, 2} A_i $?

Hello texit?

[devout mauve]

no spaces

before the dollar sign

[weary temple]

$\bigcup_{i \neq 1, 2} A_i$

[elfin berry]

Yeetus

[devout mauve]

yes

and is that in F?

[weary temple]

That is in F yes

[devout mauve]

and now show that the complement of $\bigcup_{i\in I} A_i$ is in F

[elfin berry]

Denascite

[weary temple]

Well we just get $\bigcup_{i\not\in I} A_i$ right?

[elfin berry]

Yeetus

[devout mauve]

probably better to write it as $\bigcup_{i\in\bN\setminus I} A_i$ but yes

[elfin berry]

Denascite

[weary temple]

Yeah was gonna say

Notation wise that doesn't seem quite accurate lol

But thank you. I think I've got it!

Took me a bit to realise lol

I shall close it now

.close

[marsh citrus]

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[random gust]

Should I factor here?

I know sin squared plus cos squared equals 1

oh wait

think I got it

just factor to get sin squared minus cos squared

.close

[marsh citrus]

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[marsh citrus]

What step are you on?
1. I don't know where to begin
2. I have begun but got stuck midway
3. I got an answer but I'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above

[cerulean meadow]

1

I dont know the pattern

and I dont kknow how to find it

[marsh citrus]

@cerulean meadow Has your question been resolved?

[cerulean meadow]

<@&286206848099549185>

[marsh citrus]

@cerulean meadow Has your question been resolved?

[cerulean meadow]

...

2 times in a row no help

whatever

[marsh citrus]

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[jovial ingot]

can someone help me plz 🙏🙏

[marsh citrus]

@jovial ingot Has your question been resolved?

[jovial ingot]

someone

anyone

[flat raft]

so substitute

[lilac bane]

Hmm

Why did you divide by 5?

@jovial ingot

Meir is nowhere to be found

[marsh citrus]

@jovial ingot Has your question been resolved?

[marsh citrus]

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[crystal owl]

i need help with this

[crystal owl]

how do i find

the

answer

[keen stump]

@crystal owl still need help?

[crystal owl]

no

im good

.close

[marsh citrus]

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[safe oriole]

Hey

[safe oriole]

#help-31 message

I want to ellaborate in this answer that I was given

To make it clear. As long as you meassure the distance between two lines

With multiple lines, but with a consistent slope a.k.a stepness, if the distance is kept the same they are perpendicular

[lilac quiver]

Why does lim as x approaches 0 of (ln(x))^2 approach infinity?

[safe oriole]

@lilac quiver Repost it in an available channel

(he already did, dw)

[marsh citrus]

@safe oriole Has your question been resolved?

[still temple]

no

if they have the same slope they aren’t perpendicular

[safe oriole]

This contradicts with the answer I was originally given

[still temple]

How

[still temple]

?

[safe oriole]

#help-31 message

Or maybe I understood it wrong

[still temple]

no thats correct

parallel means same slope

[still temple]

you said perpendicular here

[safe oriole]

Sorry, wrong wording

I wasn't talking about the ones crossing with the same slope

I was talking about the ones that 'were crossed'

Let me draw it rq

[still temple]

parallel or not parallel?

im confused what you mean lol

[safe oriole]

If the red ones have the same slope

[still temple]

they are parallel yes

[safe oriole]

And the distance between the two points at which they meet with the yellow is the same

[still temple]

red and red

[safe oriole]

The yellow ones should be parallel aswell

Thats my point

[still temple]

okay

[safe oriole]

Sorry for the bad wording, didn't even realize it was that bad xd

[still temple]

Whats the question im a bit lost lol

[safe oriole]

About the definition of parallelism

[still temple]

what about it?

[safe oriole]

I didn't understand at first what was the distance being kept the same

Throughout two lines

[safe oriole]

So considering red lines have same slope, this may be what it means

[still temple]

You get like a straight line can be modeled by the equation y=mx+c

where c is a constant

[safe oriole]

My level of math is pre-algebra, sorry I don't understand what you mean

[still temple]

If you have two lines

oh

[safe oriole]

Hence why I don't understand what it means that two lines are parallel

[still temple]

parallel just means the slope of the two lines are the same

they go up/down by the same amount

[safe oriole]

OOOH

I understand

I don't know how I didn't originally got it

But thank you

.close

[marsh citrus]

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[primal ore]

hewo

[quaint hill]

@primal ore don't abuse help channels

.close

[marsh citrus]

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[cerulean meadow]

How do you write the equation for a pattern thats difference between numbers changes

[cerulean meadow]

for instance

2, 5, 10, 17

+3, + 5, +7

I see that its increasing by 2

(The difference)

But how to write this

i forgot

[still temple]

half the 2nd difference is the coefficient of ur x^2 term

[cerulean meadow]

?

[still temple]

so like 2/1 = 1

x^2

[cerulean meadow]

the second difference is 5 tho

[still temple]

i mean like difference of difference

[cerulean meadow]

ok

they are all 2

then

the difference of difference

nvm i found the equation

its

y = n^2 + 1

[still temple]

yea

[cerulean meadow]

ok

how to find the equation for the nth term

in this pattern

nvm

.close

[marsh citrus]

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[viral halo]

idk where to start

thank you

.close

[marsh citrus]

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[marsh citrus]

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[copper ice]

what did i do wrong here? isnt the numerator supposed to be 1 degree lower than denominator, which in this case is x instead of the constant 🤨

[copper ice]

i am trying to Partial Fraction Decomposition

[high pine]

just B/x^2

in fact you'll get right answer tho, just B = 0

[devout mauve]

Bx+C is a linear polynomial which is one degree lower than x^2 which is quadratic

[copper ice]

but i cant get the A and B constant

here ill send my attempt

[devout mauve]

oh I didnt look closely enough. if the factor is repeated then it's just a constant

[proud ice]

Get rid of B. Keep just C

[copper ice]

aha, okay

[proud ice]

$\frac{A}{x}+\frac{Bx+C}{x^2}=\frac{A+B}{x}+\frac{C}{x^2}$

Ah right texbot is dead

[copper ice]

f

.close

[marsh citrus]

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[dusty rose]

I can't find 2 numbers which the product of is 5 while the sum is also 5

How do I go about factorizing problems like this?

[stoic saddle]

pay closer attention to the expression you've got here

it is not a quadratic in anything as written

it takes a little bit of work to make it that

[sterile rock]

trig identities?

[smoky plover]

||Use the fact that sin^2x=1-cos^2x||

[stoic saddle]

...well, that got spoiled.

[sterile rock]

...

[dusty rose]

lmao

[smoky plover]

…

[dusty rose]

I didn't see it it's ok

.close

[marsh citrus]

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[unborn cargo]

im abit confused about how to factor this

[worthy trellis]

!status

[marsh citrus]

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2. I have begun but got stuck midway
3. I got an answer but I'm told it's wrong
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6. None of the above

@unborn cargo Has your question been resolved?

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[marsh citrus]

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[marsh citrus]

What step are you on?
1. I don't know where to begin
2. I have begun but got stuck midway
3. I got an answer but I'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above

[bright garnet]

1

[spice drum]

you can convert the recurrence relation into an explicit form for the total money after n years

so after n years how much money is there

[bright garnet]

wait so

20000 = 800n?

wait no

[spice drum]

not quite

[bright garnet]

20000 + 800n

[spice drum]

not quite very close

wait no you're right my bad

okay nice so then

[bright garnet]

oh right then

20000 + 800n = 30000

[spice drum]

yep exactly

[bright garnet]

alright thanks

[spice drum]

and then round your answer up

if it isnt a whole number

[bright garnet]

got 12.5

so that'll be 13

wait

why round up when its in money

i mean time

doesnt it mean it'll tkae 12 years and 6 months

[spice drum]

no because the interest is paid annually

[bright garnet]

ooh shit

dam dude u right

u right

for c

how do i figure out the percentage

i remember doin this but i forgot

[marsh citrus]

@bright garnet Has your question been resolved?

[bright garnet]

.close

[marsh citrus]

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[fallen frigate]

what does it mean when sigma has something after it

[fallen frigate]

there's no limits or anything

[tacit fjord]

just omitted

likely obvious from context or something

or just a generic summation

[fallen frigate]

like

I have many values of x

graphing thingy

and it said Ex

E is summation

[nova totem]

Sum of all the x values

Sigma could also be a variable

Needs more context

[fallen frigate]

ok

also

@tacit fjord could please help me in my forum called Linear Trend Line I need some help on scatter plotting

[marsh citrus]

@fallen frigate Has your question been resolved?

[fallen frigate]

.close

[marsh citrus]

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[deep bane]

Ok, I am curious

[deep bane]

How can I solve this further

[high pine]

take out x^2 under the square roots in the denom

and x in the numerator

[deep bane]

Yeah well what would result

X plus or times the square root of AX

When I take out the x squared

Alright, what now?

Is this what you were going for?

Are you still there?

[high pine]

that's not what I meant

[deep bane]

Alright, then how do I take the square root of x squared out

I would think it makes x plus square root of ax

But based on what I heard earlier, that is wrong

[deep bane]

Is that it?

I don’t think we can simplify any further or figure out where it’s going so easy (because of all the variables)

[high pine]

from here it's easy to get the result since x cancels out

a/x and b/x goes to 0 as x goes to inf

[marsh citrus]

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[cobalt sentinel]

been struggling with this problem, no clue where to start. any help would be appreciated

[marsh citrus]

@cobalt sentinel Has your question been resolved?

[cobalt sentinel]

maybe my question'd be better in multivarcalc

.close

[marsh citrus]

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[long cape]

would these be equal? |y| and f(|x|)?

trying to understand this graph

[high pine]

if y = f(x) ?

[long cape]

well, by the way I have been taught it does

but anyways, I guess I'm trying to understand the relationship here. it's a piecewise function

absolute

https://www.desmos.com/calculator/dmo3wz8uko

[high pine]

|y| = x means y = -x or y = x, that's all in fact, but x >= 0

[long cape]

ah I see, so y can still be negative on the graph

just x can't

[high pine]

yes, it's because absolute value is nonnegative

[long cape]

the inverse, y = |x|
y cannot be negative, but x can

[high pine]

it's like y = |x| but axes are swapped

[long cape]

that's the way I normally see it, as a piecewise

but maybe |y|=x isn't even a piecewise

by definition it's not even a function

or is it still considered piecewise?

[high pine]

word 'piecewise' rather refers to function, so I'd say it's not

[long cape]

OK

https://www.desmos.com/calculator/5gfyfexqbd

this is also one I havent seen before

even power on y and x

[high pine]

that's |y| = |x|

[long cape]

odd power on y and x gives one linear

|y| = |x| would give two linears?

or the impression of that

[high pine]

|y| = |x| gives 4 cases:

1. y >= 0, x >= 0
2. y < 0, x >= 0
3. y >=0, x < 0
4. y < 0, x < 0

[long cape]

but why is it this? |y| = |x|

isn't it y^2 = x^2?

[high pine]

1. y = x (for x >= 0)
2. -y = x ---> y = -x (for x >= 0)
3. y = -x (for x < 0)
4. -y = -x ---> y = x (for x < 0)

that's why it produces the graph

y^2 = x^2 is same thing

[long cape]

OK

.close

[marsh citrus]

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[rich fable]

So here I entered the value in wolfram alpha

And based off of that info

I said it does not span R^3

What would I have to do to find c1 and c2

@civic blade

Could u help me???

[nova totem]

Don't ping individual people

[rich fable]

Nah he helped me before

Thats why i was asking

[bright jay]

Even if they helped before, you still shouldn't ping individual people

[rich fable]

Idk bout that srry

[marsh citrus]

@rich fable Has your question been resolved?

[civic blade]

I don’t mind

I’m not home right now

I’m driving

I’ll reply in like half an hour

[rich fable]

Tyty

[civic blade]

hmmm

,w RowReduce[{{15,26,52,x}, {7,13,26,y}, {21,40,78,z}}]

,w 2+2

wtf

@elfin berry

offline rip

so it's just z-3y and x-2y

but to my understanding, this does span R3

[rich fable]

Yea ur right

It needs a row of zeroes

To not span r^3

Right

And a non zero constant on the right hand side

[civic blade]

wym by this

[rich fable]

For the reduced

Row echelon

Form

[civic blade]

the rank of a matrix is the dimension of the span of its rows (which is equal to the dimension of the span of its columns)

[rich fable]

Im goin based off of my txtbook but u prolly know more

Its says

It needs a row of zeroes and a constant on the right hand side

To not span r^3

[rich fable]

This one I got C and D

What do I do to get the fill in the blanks

It it just a,b,c,d

Or is there an actual value

[civic blade]

a row of zeroes means that, that row was a linear combination of the other two

so yeah if ur matrix is 3x3 and u have a zero row, ur matrix's vectors don't span R3

but they instead span R2

since the rank of that matrix would be 2

[civic blade]

lemme see ur work

[rich fable]

Yea gimme a sec

[civic blade]

uhm

I'm not sure what ur doing tbh

what is this

[rich fable]

Multiplying 3 first to second

For that one

Subtracting 29 first to 3rd

And multiplying 31 1st to fourth

[marsh citrus]

@rich fable Has your question been resolved?

[marsh citrus]

@rich fable Has your question been resolved?

[marsh citrus]

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[crude wadi]

Is this correct?

[mystic minnow]

$\frac{\log(1+3x)}{3x}$?

[elfin berry]

Zybikron

[crude wadi]

Is that 1?

[mystic minnow]

no

[crude wadi]

Then what is the answer

[mystic minnow]

I don't know what you're trying to do, so I have no idea

[crude wadi]

Alrught

Thx

Just needed to know if it was 1

[marsh citrus]

@crude wadi Has your question been resolved?

[marsh citrus]

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[limpid wadi]

Hi

[limpid wadi]

Unit: Substituting info equations

Can someone tell me where I went wrong?

[flat raft]

not really, because you haven't said anything about what you did

[marsh citrus]

@limpid wadi Has your question been resolved?

[limpid wadi]

I timed the box with the Income and worked backwards from 200

[flat raft]

don't know what that means

[limpid wadi]

Oh I’ll show my working out later

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[sick bloom]

Hello I've been curious about something, So essentially I need to know how much possible combinations is possible but if a letter, for example, is used another letter is unusable, I want to know if something has two components but their two components can't be repeated (look at the example pic if I'm confusing) how many possible combinations can there be and is there a formula for it, since I have a problem with 19 taken 4 at time but you can't use one thing if you've used another

[marsh citrus]

@sick bloom Has your question been resolved?

[sick bloom]

<@&286206848099549185>

[marsh citrus]

@sick bloom Has your question been resolved?

[flat raft]

yeah I can't read any of that, but you can group the letters together

[boreal bobcat]

Can you give more context about the questions please? I can help you regarding the combination related formulas

[flat raft]

and if then your requirement is that at most one in each group can be used, if you use that letter, multiply the number of combinations by the number of elements in that group

[sick bloom]

Let's say A needs 1 2, B needs 1 3, C needs 1 4, D needs 2 3, E needs 2 4, F needs 3 4

A, B, C can't be together in a set because they all have 1
A, D, E can't be together in a set because they all have 2
B, D, F can't be together in a set because they all have 3
C, E, F can't be together in a set because they all have 4

So AB is not allowed
But AF is allowed

[boreal bobcat]

Got it, so what's the issue now?

[sick bloom]

I can't seem to find a formula that can solve it, I can brute force it but for bigger samples that just isn't possible, nCr isn't accurately telling me the number either

[boreal bobcat]

Sorry, that didn't make sense, in the first case, you have only 6 distinct letters while it is 5 in the 2nd case

[sick bloom]

Those two are just two separate examples

They have no bearing on each other

[boreal bobcat]

What is the original question then?

[sick bloom]

What I'm trying to find is a formula

[sick bloom]

Is there a formula for this?

[boreal bobcat]

Formula for what? Can you state the specific question?

[sick bloom]

Is there a formula for combinations that if one letter is used some of the other letters can't be used in a set

[boreal bobcat]

I don't think there will be a one size fits all formula. However, depending on the question, a pattern can emerge which will then be your formula.

[sick bloom]

I see

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[orchid oracle]

The equation of the line should be in this form:

^ this is the equation of a line represented as the intersection of 2 planes

Ive tried constructing 2 planes, as I probably should, but I dont rly know with what I should construct them

😪

<@&286206848099549185> ?

Any helpers know Solid Geometry?

[flat raft]

liquid geometry

[orchid oracle]

🫠

[marsh citrus]

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[thorn wharf]

can someone please explain this to me, how do I know what l and l0 is?

and according this answer, the answer is 102 db, then how is it a violation?

[flat raft]

l0 is given

l is the intensity

not sure why it's in violation

[thorn wharf]

tyy

[thorn wharf]

it should be not in violation right?

[flat raft]

yeah

[thorn wharf]

tyy

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[limpid wadi]

Hii

[limpid wadi]

unit substituting into equations

I have no idea what’s going on!!

Please tag/ @ / mention me if u can help

[subtle urchin]

Substitute all the values given into the equation

And you should be able to solve for T

[limpid wadi]

How tho 😭

[subtle urchin]

For example Emma makes $205 in a week so I would be 205

[limpid wadi]

Hu 💀

I am Super Lost

[subtle urchin]

The question says Emma makes $205 a week, correct?

[limpid wadi]

Yes

Correct

[subtle urchin]

Alright they also say that I is her income

correct?

[limpid wadi]

Correct

[subtle urchin]

so I would be 205

[limpid wadi]

250 is I

[subtle urchin]

Yes

[limpid wadi]

Correct

[subtle urchin]

Do that for the rest

[limpid wadi]

I would have to take those values away from 250?

[subtle urchin]

No just substitute it first

you should be able to simplify the right

then solve for M

[limpid wadi]

Let me try

Correct? Incorrect? Getting somewhere?

@subtle urchin

[subtle urchin]

yes getting somewhere

but you forgot to include the meals

[limpid wadi]

How do I solve the meals since it’s taking away?

Because it’s -8M so would it be -8x5= -40?

[subtle urchin]

Yes

And remember there’s still a 100

Not sure if the answer is correct, the answer I got is 4

[marsh citrus]

@limpid wadi Has your question been resolved?

[limpid wadi]

So sorry I didn’t see this

Why 4?

Can u pls explain how u got 4

I got 3 before which was incorrect

[subtle urchin]

250 = 100 + 12(6) + 5T + 7(4) + 5(5) - 8(5)
Solving this you get T = 4

[limpid wadi]

Omg ur amazing

Thank youuu

I Must of miscalculated then

[subtle urchin]

yeah maybe

[limpid wadi]

Thank youuu

Have an amazing day!!’

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[marsh citrus]

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[rich fable]

For this one I inputted the value given into wolfram alpha

I shown the work above as well

And got C and E

[rich fable]

^

[obsidian shard]

just do gauss elimination

[rich fable]

Lemme try that

[rich fable]

What do I do after that

[marsh citrus]

@rich fable Has your question been resolved?

[marsh citrus]

@rich fable Has your question been resolved?

[rich fable]

<@&286206848099549185>

[rich fable]

<@&286206848099549185>

[marsh citrus]

@rich fable Has your question been resolved?

[rich fable]

@civic blade could you help me finish the one from yesterday

[obsidian shard]

Daamn, I didn't get any notification

[rich fable]

Its good man lol

[obsidian shard]

anyway, after guassian elimination, if you got a zero row then that means that they are linearly dependent

[rich fable]

Js a sec

Lemme send you my answer for gaussian elimination

[rich fable]

Is this correct

[obsidian shard]

Yes, it is correct

[rich fable]

So C should be an answer right

And E

Based off of that

[obsidian shard]

Is it multiselect?

[rich fable]

What is that

Multiselect

[obsidian shard]

As in multiple answers can be correct or is only one of the options correct?

[rich fable]

Multiple answers

[obsidian shard]

ah, yes then c and e are correct

[rich fable]

B is not an answer right

[rich fable]

How do I get the blank ones

Fill in the blank

[obsidian shard]

nope cause linear independence is a requirement for basis

[rich fable]

Alr good

[obsidian shard]

you need to solve Ax = 0

although, since you already have row reduced form, I think you should be able to use that directly

[rich fable]

What is Ax = 0 how do I set it up

[obsidian shard]

Also here for gauss elimination we usually do not use the augmented matrix

[rich fable]

What do we use

Then

[obsidian shard]

basically x is some element of R4 say x = (a, b, c, d) then we want to find x=(a, b, c, d) such that matrix multiplication of A with x should give zero

[rich fable]

Lemme check on wolfram alpha

[obsidian shard]

you can just solve for it though

assume the vector to be (a, b, c, d) then do a matrix multiplication ie

[obsidian shard]

this matrix call it M, then M*x and then equate it to 0

then solve for (a, b, c, d)

[rich fable]

I just have to solve ot

Right

Like systems of linear equations

[rich fable]

^^

[obsidian shard]

yep

[rich fable]

I got 4,7,-3,1

[obsidian shard]

that's weird

can you show your calculations

[rich fable]

Yea

I used a ti-84 to solve it

With matrices

[obsidian shard]

you can do it manually, probably faster

[rich fable]

Lemme do it manually then send u

[obsidian shard]

Yep, it was easier

Cause we just want one solution, you can let x=1

[rich fable]

Could you check this one

I alr did this

[obsidian shard]

Which one?

[rich fable]

Lemme send

Span

C1=x-2y

C2=z-3y

[obsidian shard]

It looks like it does span R3

[rich fable]

C1 and C2

U just input what it says

RowReduce [({15,26,52,x},(7,13,26,v},(21,40,78,2}}]

[obsidian shard]

c1 = x - 2y

c2 = -3y + z

[rich fable]

Yep ty

[obsidian shard]

alright then

use .close to close the channel if you're done

[rich fable]

.close

[marsh citrus]

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[dawn onyx]

Why does adding a point and a vector get you another point

[bleak reef]

just think of the vector as an arrow that the point goes along

[dawn onyx]

Can the coordinates you get not also be used as scalar components of the new vector

[bleak reef]

what do you mean by scalar components and new vector

[dawn onyx]

When you add a point like (x0,y0,z0) with the vector and its components (x1,y1,z1), you get a new point (x0+x1,y0+y1,z0+z1) but why is this a point

Why cant it be a new vector

[bleak reef]

why would it be a vector

it's just the transformation of x0,y0,z0

[dawn onyx]

Hmmm ok, i think I get

Thanks

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[celest granite]

√5−x(x−1)

[celest granite]

how do i integrate this

so basically i did it by parts

[simple forge]

Is the whole thing square rooted

[celest granite]

only 5-x

i did by pasrts but idk where i went wrong

[bright jay]

$\sqrt{5-x}(x-1)$?

[elfin berry]

dldh06

[simple forge]

Is this it

[celest granite]

yess

[marsh peak]

I would substitute for 5 - x

[simple forge]

Yeah substitute u=5-x

[celest granite]

I did this

But looks super wrong

[celest granite]

Should I do the u substitution method?

[simple forge]

Yeah

[celest granite]

Oh the signs are wrong for mine at the end
Forgot the minus
But that's the idea right

Is this correct

[simple forge]

U g

[celest granite]

That's right
How did u do it

[simple forge]

U=x-5 substitution then integrate then substitute x-5 back in for u

[celest granite]

Oh okay

[simple forge]

I mean 5-x sry

[celest granite]

Yea
Tbh I am lost where I went wrong

Why is it 5/2

Oh

I just got it

Thank you

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[lime wyvern]

How to find root

[lime wyvern]

<@&286206848099549185>

I need help asap

Using long division method

[pliant hill]

bro

wait 15 minutes

😭

[lime wyvern]

What does that mean

Put the largest digit on the right of 10 such that the product of the largest digit with the new number obtained does not exceed 266

What does it mean

<@&286206848099549185> helppppp I need help asap

Please

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[weary nexus]

is this off a test?

[marsh citrus]

@still temple Has your question been resolved?

[civic blade]

https://youtu.be/6zXosIaem04

[marsh citrus]

@still temple Has your question been resolved?

[marsh citrus]

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[tame cedar]

How do i do this problem?

[novel fjord]

how did you get that answer

[novel fjord]

seems your 32/9 transformed into a 33/9

@tame cedar

[tame cedar]

Ah where was this?

[novel fjord]

5th line down in the 3rd picture sent

after you multiply both sides by 3/pi

[tame cedar]

o

This the answer?

Oh and if it is, what decimal point should I go to

[novel fjord]

looks good, i'd keep it as 81/96pi

unless it asks for a decimal approximation

81/96pi is your exact answer

[tame cedar]

Yeah I can't exactly write "Pi" in here

~~ 0.26857396

[novel fjord]

is it saying it's wrong?

[tame cedar]

Uh not yet, but i sort of only have one try left

a shame that it doesn't say round to the what decimal point

[marsh citrus]

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[austere finch]

Where do i start with the question 7/2(m+12)=5/2(20+m) i am solving for m

[chrome widget]

multiply in bracket

then cross multiply

[austere finch]

thank you!

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[ivory oak]

aight so y bears at 075° from x, z is 50km from x on a bearing of 128°, y bears 040° from z, find the angle yxz

[ivory oak]

ok theres 3 parts to this, first bit is easy enough

I think at least

I don't really understand what the bearing of 128° is applying to to start with

[lilac bane]

Okay do you know your angles and their stuff?

[ivory oak]

this is all I have down rn

[lilac bane]

Okay that θ you have there

[ivory oak]

yes

[lilac bane]

Do you know how to get it?

As a value?

[ivory oak]

I mean it has to be something with the other bearing I was given which is why i want to understand where it goes

if it doesnt involve the other bearing somehow then no

[lilac bane]

Hmm

Okay so

Point X has 2 lines

XZ and XY

And each of those has a bearing with the North from standing on point X

[ivory oak]

yes

[lilac bane]

Now here's the special part: one bearing is bigger than the other

[ivory oak]

xz should be 128 but in the picture it doesnt look like that's 128

[lilac bane]

Mood

Not to scale moment

[ivory oak]

is that all it is 😭

it just does not look like that's right when iput that there

but ok

so then would I subtract 75 from the 128 to get what's inside the triangle

[lilac bane]

Yepppp

[ivory oak]

53

ok

[lilac bane]

Yeppo

Now you need 1 more angle

You can get it easily

[ivory oak]

yeah this triangle picture does not match the actual numbers 😭

makes more sense now

[lilac bane]

But you need some trick to get there

And it requires another point with 2 bearings pointing at it

We already used up point X

What point do you think has 2 bearings pointing at it?

[ivory oak]

y right

but

[lilac bane]

Yepo

[ivory oak]

40 from z and 53 from x

[lilac bane]

Yep

Imma teach you now how to use those bearings

Now

Let's revise something with the angle of a straight line

If we pick any point in a line, and measured the angle from one side till we reached the other side, what will that angle be?

[ivory oak]

a straight line is just 180

[lilac bane]

Yep

180°

That's when we start with 0°

If we had a 40° angle and we want to get the angle pointing on the other side, what would that angle look like?

If you're confused, please tell me

[ivory oak]

I get it but I dont get what other side you're asking me to find the angle to lol

[lilac bane]

Hmm it's better to visualize it

[ivory oak]

I get that the bit to the right of the 40° bearing is 50°, but I don't know how to fill in the bit to the left still

[lilac bane]

Wait

Imma show you what I mean

[ivory oak]

please do 😭

[lilac bane]

Okay here's the setup

I want you to use the straight line angle

And tell me the total angle pointing to the other side of the line

You start with 40°

[ivory oak]

oh so like the 180 plus the 40?

[lilac bane]

Yep

[ivory oak]

ok so thats just 220

[lilac bane]

Yepp

So if we have the angle to a line from one side and we wanted to find the angle to the other side, we just add 180 to it

Let's apply that to our question

We have bearing of Y from X as 53°

And bearing of Y from Z as 40°

We want the same concept

Let's call that concept the "back bearing" because it points to the back

The name can change in the future tho lol

Lemme make sure of how it is actually called

Yep it's called back bearing and it points to the back

Anyways

We want the back bearing of each of those bearings

[ivory oak]

ok

[lilac bane]

Back bearing of 53°?

[ivory oak]

is it 233 do I just add 180 directly

[lilac bane]

Yep

53° + 180° = 233°

Back bearing of YX is 233°

And previously we did the back bearing of 40°

Should be 220°

Now here's the part where

Things get super cool

We draw the 233° bearing, and then we draw the 220° bearing.

Something interesting happens

At the point Y

[ivory oak]

they meet the two lines?

I'm assuming

[lilac bane]

That's how it looks like

Notice how it feels similar to the earlier angle?

The triangle's inner angle

[ivory oak]

yes I see

so is that angle the difference of the back bearings

[lilac bane]

Yep

[ivory oak]

is 13° right that's a really small angle

[lilac bane]

Yeah don't worry lol

[ivory oak]

so 53+13 is 66, which means the last angle would be 114?? to add up to 180

[lilac bane]

Yep

Triangle completed :)

[ivory oak]

oh my god . I just went back to answer and the math page froze and refreshed with an entirely different question LOL

😭

ok I can figure it out at least tho

[lilac bane]

Well the tricks are in your sleeve now

[ivory oak]

yes thank you

[lilac bane]

You can control angles at your will

[ivory oak]

[marsh citrus]

@ivory oak Has your question been resolved?

Channel closed

Closed by @ivory oak

Use .reopen if this was a mistake.

[marsh citrus]

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[thorny onyx]

so sqrt 9-40x becomes (9-40x)^1/2

but how do i find g?

[main idol]

what's g

[thorny onyx]

is it going to be ((9-40x)^1/2)(g(x))

[jovial star]

You need to use differentiation

[thorny onyx]

yes chain rule right?

[main idol]

you're not answering the question

what's are you using g to represent

[thorny onyx]

is it the point (-1,7)

[jovial star]

Before that you need to use the power rule

[thorny onyx]

for which part?

[jovial star]

The sqrt

[thorny onyx]

i did

it becomes (9-40x)^1/2

[jovial star]

No

That is incorrect

[thorny onyx]

oh then what should it be?

[thorny onyx]

.

.close

[marsh citrus]

Channel closed

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[raw coral]

how do you do this? I have no idea how to do it or where to start.

[raw coral]

would a) be m`(t) is grams and minutes and m``(t) be milligrams and seconds?

for b) would that mean that the object's mass is increasing with respect to time

for c) would that mean the rate of at which the object is moving in size is decreasing?

.help

[marsh citrus]

Commands:
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consensus: .poll
factoids: .tag
help: .help

Type .help <command name> for more info on a command.

[raw coral]

.unsolved

.close

[marsh citrus]

Channel closed

Closed by @raw coral

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[analog sun]

How's the solution set is selected here?

[analog sun]

(Highlighted is the inequality given)

[glacial hedge]

The question is to find where it's positive ?

They rewrite is as a product to say it's positive iff it's (+)(+) or (-)(-)

As (+)(-) and (-)(+) give a negative product

[analog sun]

from (x>=2,x>=3)or(x<=2,x<=3)

how did they select x>=3 and x<=2 ?

[glacial hedge]

The pairs of inequalities are redundant

x >= 2 and x >= 3 is just x >= 3

The x >= 2 doesn't do anything

Same with the <= 2 one

[analog sun]

could you elaborate?

[glacial hedge]

if x >= 2 and 3 then x >= 3
If x >= 3 then x >= 2 and 3

So x >= 3 is the exact same constraint as x >= 2 and 3

So you lose no information by removing x >= 2

The x values that verify this are in [3, +inf[ either way

[analog sun]

Didn't understand, both statements are same I think

[naive stump]

if x had to be greater than 3 to be true

then isn’t it also implied that x had to be greater than any value less than 3

ie: 2

[analog sun]

yeah

[naive stump]

so like mateo said

u don’t need x>2 if u have x>3

but anyways

that doesn’t apply to solutions in the first place

[analog sun]

okay But how should I select from (x>=2,x>=3)or(x<=2,x<=3)

one expression from each?

[naive stump]

yeah

i don’t usually do it this way but i guess that works since it’s the intended working out on the image

it might be easier if u draw a graph to see where it is >= 0

[analog sun]

I don't know but I didn't understand I think. So from (x>=2,x>=3) we should select x>=2 here

but it was not chosen

if I choose x>=2 it automatically should include x>=3

and here x>=3 is chosen

[naive stump]

yes

however

if u choose x>=3

the solutions does not include between 2 to 3

they aren’t the same

[analog sun]

okay so anyways we need to make a graph that can make some sense

,w x^2-5x+6>=0

[elfin berry]

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[analog sun]

Many thanks @naive stump @glacial hedge 👍