help-0

[shadow mango]

height=4 base=4

[inland shale]

yeah im blind

[shadow mango]

substitute

[inland shale]

sorry

[inland shale]

16

answetr

[shadow mango]

yeah

[inland shale]

ok

tysn

tysm

bro

shut up

mind ur own buisness

smh

ur story is sussy baka

thats how u know ur a 3rd grader

moron

oH mY gOd SuSsY bAkA

tlike shut up that phrase is for idiots istg its so annoying

[spark zenith]

$\frac {5}{6}x$

[ocean seal]

Avocadoman

[spark zenith]

Ok

[inland shale]

smfd

[spark zenith]

hmm

$35-30x=49$

[ocean seal]

Avocadoman

[shell widget]

@inland shale smfd?

[alpine sable]

Can I use this channel?

[shell widget]

yes

[alpine sable]

What’s the mistake?

[spark zenith]

I dont do your homework

[shell widget]

@spark zenith He didnt ask you to

[alpine sable]

What a troll

[spark zenith]

Idc

[remote heron]

did you factor 2x-1 as 2(2x-1)?

[shell widget]

<@&268886789983436800>

kick this @spark zenith

[spark zenith]

just pinged 4 dude

[alpine sable]

What do you mean jan

[remote heron]

oh, i see

sorry

[small bear]

you forgot to change the sign of the 6, you have -5x-(-6)

[remote heron]

but i think you may have sign error

ye

[small bear]

second fraction, numerator

[alpine sable]

Why is it -(-6)?

[remote heron]

2(2x-1)-(5x-6) = 4x-2-5x**+**6

the negative gets distributed to the entire numerator

not just the first term

[alpine sable]

I see

[remote heron]

you can factor out the negative before you combine to avoid the problem, and turn it into addition

but this can create sign errors too lol

[alpine sable]

Ah sad

So whenever I have to combine and it has two negative I jusy change it to a positive?

[remote heron]

well the negative before the fraction applies to the whole thing is the problem

nothing is really being changed

[alpine sable]

Oh

Wait could you explain it to me

[remote heron]

so $-\frac{5x-6}{6}$

[ocean seal]

jan Niku

[remote heron]

this is the same as $-\left( \frac{5x}{6} - \frac{6}{6}\right)$

[ocean seal]

jan Niku

[remote heron]

sound reasonable?

just splitting on that sign

the same process you did above in your solution, but backwards, instead of combination its splitting

[alpine sable]

so is it -5x+6/6?

then?

[remote heron]

like $-\left( \frac{5x}{6} - \frac{6}{6}\right) = \frac{-5x}{6} + \frac{6}{6}$

[ocean seal]

jan Niku

[remote heron]

the negative sign is really a factor of negative one

so it follows the distributive property too, just like all numbers

well all products i guess

[alpine sable]

is this = to -5x+6/6?

[remote heron]

it is, id really really use parens in what youre typing

but it is if i get what you mean

[alpine sable]

ahh ok

ty

[remote heron]

• ( (5x-6)/6 )

this is how id type it

is this what you mean?

$\frac{4x-2}{6} + (-1)\left( \frac{5x}{6} + \frac{6}{6} \right)$

[ocean seal]

jan Niku

[remote heron]

this is what i mean with the factor, btw

maybe written this way its more clear what is happening

just like $a(b+c) = ab+ac$

[ocean seal]

jan Niku

[remote heron]

critically nothing is changing, its just distributive property in action

[alpine sable]

thanks for the help

[remote heron]

np

[alpine sable]

would that be 11?

f(6) = 11 doesn't make any sense

[glass lichen]

how come it doesnt?

[alpine sable]

idk if thats the right answer tho

[glass lichen]

it is

[alpine sable]

or am i over thinking it

[glass lichen]

f(6)=11

if that function is f(x)

[wary badge]

Anyone Need my Help?

[elfin talon]

Yeah, -x is short for -1x, -(x-y) is short for -1(x-y), which if you distribute you’re gonna get -x+y

[alpine sable]

ok i was scaring myself this is my first pre-calc quiz lol

@glass lichen thanks man

[elfin talon]

Just substitute in-line rather than doing it mentally if you’re in doubt

[alpine sable]

alright

[elfin talon]

f(6) = 6^2 - 4(6) - 1 = 36 - 24 - 1= 11

[alpine sable]

]

this is a function right?

[shell widget]

Yes, because for every "x" value, there is at most one "y" value.

[hot wedge]

hey this is only gonna take a second, but what specific math topic is this?

[shell widget]

Could be factorization/quadratic expressions

[alpine sable]

Ok, thanks

[topaz scaffold]

Rational functions maybe too

[hot wedge]

o

ok

[summer adder]

can i use this channel ?

[topaz scaffold]

Yea sure

[alpine sable]

Do polynomial division for that

[topaz scaffold]

It's not the ones where x is dependent of y

[hot wedge]

what i do there is just plug in each answer choice for x and see what equals to 0

[topaz scaffold]

So where the y value has no effect on the x

[topaz scaffold]

You could factor the top

[summer adder]

A,B

right ?

[hot wedge]

ok

ty

[topaz scaffold]

I'm unsure about b tbh

[summer adder]

these are tricky questions

😩

[topaz scaffold]

I think there might be a possible dependence for b

Again, I'm not completely sure so don't take my word for it lol

[summer adder]

can i ask more questions ?

😄

[topaz scaffold]

[summer adder]

Central Theorem Limit:

The sampling distribution of the mean approximately
follows a normal distribution if the sample size is large.---->true

The sampling distribution of the mean follows approximately
a normal distribution if the standard error of the sampling distribution is small.---->true

The mean of the sampling distribution of means
is exactly equal to the population mean.------>false

[topaz scaffold]

I'm heading to lunch soon so I won't be answer tho

Hopefully someone else can help

[summer adder]

okey

thank's anyway

[alpine sable]

would this dilate by 2?

horizontally?

[strange raven]

I'm currently learning abstract algebra as a physics major who is weak at proofs​
I'm like goddamn anxious​
Very much anxious​

[alpine sable]

You'll be alright

Did i do something wrong?

[undone dock]

If you plug it in you get$(-3)^2 - 4(-3) -1$

[ocean seal]

K.

[alpine sable]

crap

[last moth]

Does this mean this channel is free now? I am having a trouble understanding a bit more advanced problem. I am reading der Warden's Algebra to get to know modern abstract Algebra.

In a paragraph about determinants it is defined elegantly as a polylineal antisymmetric form of vector space over a given field o. And one of the intermediate equalities puzzles me, specifically that it always equals 1 for the vectors of the basis, i.e. $D(x_i) = 1$. However I am struggling to prove this without using the representation as list of elements of o, in which case proof is trivial as a sum $\sum \pm x^i y^j z^k\cdot \ldots$ has only a single non-zero term. Is there a way to prove this without going to this representation? I have troubles with this because it gives a circular dependency since you assume that determinant will be the same for in any transformed basis, but you use this property (det=1) to prove basis invariance. Thank you!

[ocean seal]

Artej

[dreamy cedar]

You should probably ask questions like these in #groups-rings-fields

Most of the people advanced enough to answer these questions dont usually check these channels

[last moth]

will do, thanks, sorry I am new to this server

[dreamy cedar]

Np

see #get-advanced-access

[late monolith]

The area of ​​a square is: 50x (2 above x) - 180xy
(2 above y) + 162y (4 above y). Calculate the perimeter of said square

I need some help, pls

[shadow mango]

you have two equations over here, are both of these values of the area?

sharing a picture of the question would be helpful if possible

[late monolith]

A picture would be the same (Im spanish) I just translate it to english.

[shadow mango]

ooh alright

are those two equations the area of the same square?

[late monolith]

Yes same square

[ocean seal]

Mochi

[shadow mango]

@late monolith right?

[late monolith]

Let me check rq

Aight it is

Ty

[shadow mango]

cool shall we proceed?

[late monolith]

Sure

One last question

[shadow mango]

um this is the same eqn you have....we still have to find the perimeter-

[late monolith]

im dumb then

[shadow mango]

we have to calculate the perimeter, I just rewrote the area eqn for it to be clear

[late monolith]

oh ok

[shadow mango]

that's the question isn't it

[late monolith]

yeah find the perimeter

[shadow mango]

cool

now let the side of our square be "a"

then $a^{2} = 50x^{2} - 180xy^{2} + 162y^{4}$

[ocean seal]

Mochi

[late monolith]

k

[shadow mango]

hence $a = \sqrt{50x^{2} - 180xy^{2} + 162y^{4}}$

[ocean seal]

Mochi

[shadow mango]

now we have to factorise the equation to get "a" (which is the side of our square)

do you think you can try that?

[late monolith]

50x - 180 xy + 162y (2 above y)

[shadow mango]

no-

[late monolith]

pain

[shadow mango]

its in the form $x^{2} - 2xy +y^{2}$ right?

[ocean seal]

Mochi

[late monolith]

oo

Is that it?

[alpine sable]

@spark zenith thanks? 😆

[shadow mango]

$a = \sqrt{50x^{2} - 180xy^{2} + 162y^{4}}$

[ocean seal]

Mochi

[shadow mango]

$a = \sqrt{(5\sqrt{2}-9\sqrt{2})^{2}}$

[ocean seal]

Mochi

[shadow mango]

$a = 5\sqrt{2}-9\sqrt{2}$

[ocean seal]

Mochi

[shadow mango]

that's the side of your square

I presume you can find the perimeter on your own now?

[late monolith]

Yea thx

[shadow mango]

np

[alpine sable]

how do I prove convergence here? (direct comparison)

[kindred herald]

What's this "tg" term?

[alpine sable]

tan

[kindred herald]

I'd use small-angle approximation maybe... that way, you get rid of the tg and interpret the tg-inner part as a small value in radians

and then the ratio test

[undone sentinel]

How

[alpine sable]

ok thanks

Where does 81/4 come from?

20 + 1/4 is not 81/4 is it?

[kindred herald]

it is. expand fraction by 4

[alpine sable]

Sorry could you show me?

[kindred herald]

yeah. Every number is a "fraction". Therefore, you can always expand.
20 = 20/1 = 20 * 4 / 4

[ocean seal]

Edwin25

[alpine sable]

How do you use the bot

[ocean seal]

Edwin25

[alpine sable]

$\latex$

[ocean seal]

Fractal Morality

$\latex$
```Compilation error:```! Undefined control sequence.
<recently read> \latex 
                       
l.55 $\latex
            $
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.```

[alpine sable]

?

[sharp sable]

how do i do this

[sharp sable]

<@&286206848099549185>

[uncut tapir]

Do you know what the 5 number summary is?

[sharp sable]

nope

is it the Q1

Q2 and Q3

[alpine sable]

Khan Academy accepts this answer for the x-intercept 5/3, 0

it does not accept 1.666, 0

why?

they are the same thing, right?

[supple prawn]

They are slightly different, 5/3 is exact while 1.666 isn't.

Think of it like writing 1/3 as 0.333, what do you get if you multiply 0.333 • 3? It should equal 1 if they were the same thing.

[glass field]

in your book or online you can look up "polynomial division" and/or "long division"

[crimson obsidian]

so, let's say there's a betting game.
$50 in the pot so far.
I can contribute any dollar amount I want. My probability of winning is my bet divided by the pot's total size. So if I contribute $10, I have a 1/6 chance of winning (since the pot is now $60).
From what I understand, there is no ideal bet size for one individual bet. In other words, my expected value is the same at any amount. Is this right?

[mystic sinew]

bro theres another question still active

[mortal void]

what took so long to tell, i didnt did it with bad intentions

[mortal void]

happy now, man

[mystic sinew]

I wasn't talking to you?

[uncut tapir]

Yes. Min, lower quartile, median, upper quartile and max

[ivory otter]

Differentiate: $\ln(2x^3) = \frac{1}{x^3}$

is this correct?

[ocean seal]

MEOWBRO 父

[glass lichen]

no

chain rule

[crimson obsidian]

so, let's say there's a betting game.
$50 in the pot so far.
I can contribute any dollar amount I want. My probability of winning is my bet divided by the pot's total size. So if I contribute $10, I have a 1/6 chance of winning (since the pot is now $60).
From what I understand, there is no ideal bet size for one individual bet. In other words, my expected value is the same at any amount. Is this right?

[sleek yarrow]

I am losing my mind with this question

I have spent a solid 25 minutes on it

Can I have any help

[mortal void]

oh no, and here i deleted my all asked question

[mortal void]

the first one is a polynomial functions

cause there x's value is 0

and second one aswell

[ivory otter]

how do i know when to use Chain rule lol

[glass lichen]

when it's a composition of functions

[ivory otter]

ah

always?

[glass lichen]

yes.....

when it's a composition of functions you use the rule for it

like how you use power rule for a power function

[ivory otter]

i see ok

[glass lichen]

alternatively $\ln(2x^3)=\ln(2)+3\ln(x)$

[ocean seal]

Mosh

[ivory otter]

ima stick to chain

[glass lichen]

Ok...

[mortal void]

my brain gonna smash

[alpine sable]

im having trouble in linalg rn - i've been going in circles on this problem a few times now, could someone point me in the right direction/ first step with this? dont give me the answer, i wanna figure it out

[mortal void]

can someone help me on question 2

[alpine sable]

How do you simplify a^3+b^4/a^3+b^3

[glass lichen]

well 1st step is to, quite easily, note that $x_5=0$

[alpine sable]

wasn't there like a rule where you can combine them

[ocean seal]

Mosh

[alpine sable]

i got that part, i just didn’t know what to do from there lmao

do i just substitute that for all x5s?

[glass lichen]

yes, so you have the reduced system
$x_1-4x_3=8 \ x_2+7x_3-x_4=2$

[ocean seal]

Mosh

[glass lichen]

so you can then note that x_1 and x_2 will depend on x_3 and x_4

(alternatively, x_1 and x_2 are the pivot columns)

so x_3 and x_4 have to be free columns, since x_5 is already dealt with and they arent pivots

[ivory otter]

Hi mosh

"when it's a composition of functions"

thats when you said i can use chain rule

but what confuses me here is

doesnt 2x count as a function

so shouldnt sin(2x) also be able to be solved using chain rule?

[alpine sable]

ah okay cool gochu, so i dont need a finite answer for each variable? do i just define them in terms of each other?

@glass lichen

[glass lichen]

Yes, you define them by the free variables

[alpine sable]

okay cool makes sense - tysm

[glass lichen]

So you have a plane of solutions, which you parameterized by the free variables

[alpine sable]

those are some big words for sure

ah okay gochu

makes more sense now lmao im j kinda dumb

day 2 into linalg so im not there yet

[glass lichen]

But yeah, the things that aren't pivots are your free variables

[alpine sable]

bet

[astral harbor]

Why did they set the alternative hypothesis as h1:p<0.08? Why not p>0.08? The question didn't give us any claim to test so how did they use p<0.08?

[placid zinc]

I have no idea. Indeed, there's no claim anywhere on the question

@astral harbor

[weary grove]

Hello, I have a question

[glass field]

nice

[weary grove]

So I have this

Here is what I done

The right answer is

So the first part with the 7/100 is correct

But the second one not

And I don't know why

Do someone have an idea ?

[weary grove]

<@&286206848099549185>

[weary grove]

Lmao I was asking a question ahaha

But I think no one is connected (Or no one wants to solve my problem)

[mossy agate]

just use the identity and then make sin(a+b/2) and cos(a-b/2) zero this should give u the solutions

@weary grove use sinA + sinB = 2sin(a+b/2)cos(a-b/2)

[pastel schooner]

If I know angle A, D, and B. how do I find BD? I also only have side AB. Isnt there a ratio of angle and side to angle and side.

I was thinking about using side AB (which is known as 3) with angle D which is 90 degrees. To find side BD with known A value of 53.1 degrees

[weary grove]

I'm pretty sure there's more simple

We used to do these exercise without these formula

I think I just did a stupid mistake somewhere

Cuz I have one of the two solutions

[plush quest]

Idk where to start lol

[pastel schooner]

PEMDAS is your best friend.

P is the first step

which is parenthesis

[plush quest]

Ya

[pastel schooner]

So you must do this:

similar to 2(2-2x) .

but in this case it is a -1

[plush quest]

Wait what

You would make the 2 become negative and the -3x become 3x?

[pastel schooner]

Correct

[plush quest]

Ok

[pastel schooner]

So you get 9 - 2 + 3x = 6 + 2x - 5 - x

Now you Combine Like Terms

so you put the x's together and the numbers without a variable

[plush quest]

Ok

4x?

Um

[pastel schooner]

On the left side of the equation of 9 - 2 + 3x

you would combine 9 and -2 and leave 3x

[plush quest]

Ok

[pastel schooner]

so left side becomes 7 + 3x

[plush quest]

Ok

[pastel schooner]

the right side

of 6 + 2x - 5 - x

you combine 6 and -5

to become +1

[plush quest]

Ok

[pastel schooner]

and combine 2x and -x to become just x

cause 2x - x = x

so you get 1 + x on the right side

now including both left and right you get:

7 + 3x = 1 + x

[low topaz]

Is a pies Circumference over its Diameter equal to π

[plush quest]

Inverse operation of 7 now?

[pastel schooner]

now you make one side a variable, and the other side a number without a variable

7 + 3x = 1 + x so you minus 7 on the left and right to cancel 7

which gives you 3x = (1-7) + x

which is 3x = -6 + x

you minus the other x on the right side to the left side

so you get 3x - x = -6

which is 2x = -6

[plush quest]

Wait hold on

[pastel schooner]

now you devide by 2 on both sides to cancel that 2 on the left

so x = -3

[valid kite]

hi is this right? if not why?

[uncut tapir]

I guess so. You're basically saying that even though you have brackets around the second term you can still group the x^2 terms together

[valid kite]

i was just so nervopus cuz if i got that wrong i would have to redo everything xd

i knew it was right

I JUST had to double check-

[high lintel]

hello, could someone please help and explain this to me?

[uncut tapir]

Yeah, it's like a mass balance almost. You have two constraints at play, the total volume has to equal 10L and the concentration has to equal 20%

Your volume constraint is solved by just saying that if I add x litres of the 5% solution I need 10-x litres of the 40% solution

This always adds up to 10 with 0<=x<10

Then how to solve for the concentration? The mass you have in the 20% solution needs to equal the mass added from the 5% and 40%. You can see the mass added would equal concentration times volume

Hopefully this information explains the equation more, now you just have to solve it using standard algebra

[high lintel]

yup, helped

thanks

[strong minnow]

Hi I have a quick question that I may be over complicating. Suppose there are 8 pens in my book bag. Five are blue and 3 are black. If I reach in and randomly pull out a pen.

E: I pull out a blue pen F: I pull out a black pen

E and F would be complementary events correct ? My thinking because they have nothing in common and make up everything that could possible happen.

Please let me know if there is a flaw in my logic

[placid zinc]

Yes. You are 100% likely to do one of those two things.

[cinder mantle]

^

[fierce niche]

is there any good courses/sites to learn math? (math in general)

[slender marten]

TLMaths on YouTube is good.

[alpine sable]

Use the Distribution Property to rewrite and evaluate each expression.
6(525)

[wraith wraith]

@mossy snow can u help me

[alpine sable]

How do you use the distributive property to rewrite and evaluate 8*1.5

@bitter juniper

Are we allows to ask stats questions

[minor anchor]

1.5 is seperatable (is that a word??) into 1 and .5 (because 1 + .5 is 1.5), so 8 x 1.5 is the same as (8 x 1) + (8 x .5), so just add those together to get your answer.

x=* cuz two asterisks make italics and idk how to use latex lmao

[unborn dome]

can someone help me out with this?

[oak chasm]

@unborn dome Do you know how to calculate speed?

Like if I go 1/2 a mile in 3 hours, how fast am I going?

[unborn dome]

nope.

never took physics

dont think im expected to know that formula either

[oak chasm]

Well, they tell you above where you put in the answer.

[ocean seal]

Chai T. Rex

[oak chasm]

What is my change in position?

[unborn dome]

figured it out its just 69. 09 when you just plug in the equation @oak chasm

of 4.9(T)^2

for both t's

but the second part is a bit troubling

i dont want to say its getting closer to 70

or 69

68.60

[oak chasm]

Right.

Do you know derivatives?

[unborn dome]

so

68.6

@oak chasm

[smoky urchin]

ok this is kinda dumb but are all expressions with domain the set of all real numbers considered polynomials?

[oak chasm]

@unborn dome Yes, that's right. Velocity is the derivative of position, so you can either use a derivative or the derivative limit.

@smoky urchin No, 2ⁿ isn't a polynomial, but it can have the domain of all real numbers.

[smoky urchin]

ok thank

s

[oak chasm]

No problem.

[subtle elbow]

can someone help

[placid zinc]

15 for the first year
15(0.8) for the second year
15(0.8)² for the third year
ect

[languid stirrup]

please help

[subtle elbow]

i dont understand

[placid zinc]

What is not making sense about my explanation? What did you expect the second year to be?

[alpine sable]

i need help

i need dis to be algerbric expression: 3 times the sum of r and d squared increased by 2 times the sum of r and d squared

[placid zinc]

Channel is busy @alpine sable

[alpine sable]

k, sorry

[subtle elbow]

i just dont understand to be blatant.

the response you gave is confusing me

[alpine sable]

is it busy rn?

ok i think i can use it

my question is

I'm still confused about 9+10

what is the point of the descartes rule of signs?

[placid zinc]

Knowing the number of positive roots

[alpine sable]

i mean you only figure out the number of possible roots for positive, negative, and imaginary

[alpine sable]

so? you still need to find the roots itself

[placid zinc]

Do you?

[alpine sable]

yes

by the way im semi-new to the topic so don't judge

[placid zinc]

Depends what your problem is. There's many circumstances where you may not care what the roots actually are, but are happy to know if they're positive or not

[alpine sable]

ok..... another question. what if a root of the polynomial is 0? would you have to factor it first before using the rule of signs?

[placid zinc]

Control theory has a problem like this, a system is "in control" if all roots are negative, which you can check with this theorem

[alpine sable]

oh i see

what about this:

[alpine sable]

.

[placid zinc]

Rule of signs should still work

Even without factoring

[alpine sable]

but it wouldn't tell you if the root is 0 right?

[placid zinc]

No it wouldn't.

[alpine sable]

then wouldn't the whole thing be messed up

[placid zinc]

"Whole thing"?

[alpine sable]

like say there were 2 positive roots and 2 negative roots

of a 5th degree polynomial

you wouldn't know if the last root was 0 or imaginary

[placid zinc]

But you would know how many positive and negative roots there are

[alpine sable]

yes

[placid zinc]

Indeed, rule of signs won't give you absolutely everything

[alpine sable]

but shouldn't there be a way to know if a root is 0 too?

[placid zinc]

But for pretty little effort, it does give you a lot

[west bronze]

checking if 0 is a root is easy, then you can just factor out the term of x with multiplicity and apply the criterion to the remaining polynomial

[alpine sable]

yes this was what i was asking

[west bronze]

you put in 0

[alpine sable]

true

[alpine sable]

oh wait im dumb you can do that pretty easily too

wait what do you mean "with multiplicity"

i know what multiplicity means just not in this case

[west bronze]

f(x) = x and f(x) = x^2 both have 0 as a root, but the 2nd one has "multiplicity 2" because you have to factor out x twice to get rid of it

for x^2 it makes sense to count 0 as a root twice

if you know complex numbers, this leads to the fundamental theorem of algebra, that a polynomial of degree d has exactly d roots where you count them with multiplicity

[alpine sable]

yes, i know that

[alpine sable]

yup i got that

but wdym by factoring with multiplicity

[west bronze]

consider f(x) = x^2 + x^3, it has 0 as a root but if you factor it as x*(x + x^2) the thing in the parentheses still has 0 as a root
to get rid of it you have to factor it as x^2*(1 + x), then the thing in parentheses only has -1 as a root

[alpine sable]

ah i see

so when you say factoring with multiplicity you just mean to factor out the x's as much as possible

if you can factor out x^2 then factor it out, rather than just x

right?

[west bronze]

yeah, there's a better way to describe it but I don't know how much you know and it requires more advanced stuff

[alpine sable]

i know everything up till algebra 2. in algebra 2, i know good chunk of it and i know some precalc too

barely any precalc tho

[west bronze]

this is stuff I encountered in ring theory

[alpine sable]

ok but i have no idea what that is

[west bronze]

upper undergraduate level I guess

[alpine sable]

nope

im not even in high

A particle of charge q0 is located at x=a y=b, and particle of same charge is located at x=-a and y=b. find electric force on particle of charge q* located at origin

Someone help me please

[west bronze]

maybe ask the physics server

[alpine sable]

Uhm

I can’t

So

¯_(ツ)_/¯

[west bronze]

it's linked in #old-network

[placid zinc]

Both particles put a force on the particle on the origin

[alpine sable]

i should do more science

[placid zinc]

You may have an equation for that force?
F = kc1c2/r²
Or something I don't remember it great

[alpine sable]

Uh

[alpine sable]

This is all the information I was given

[glass lichen]

That's electric force, yeah

though typically q for charges

[placid zinc]

Oh shi I did use c when q would be better

[glass lichen]

$F_E=\frac{kqQ}{r^2}$

[ocean seal]

Mosh

[placid zinc]

Ignoring the other particle for now, what force does the particle at (a,b) put on the origin?

[alpine sable]

uh

The electric force is located at the origin

[glass lichen]

forces arent located anywhere

there's a charge at the origin

[alpine sable]

I meant charge

[placid zinc]

More like, what's the magnitude of that force?

[alpine sable]

Yes

A particle of charge q0 is located at x=a y=b, and particle of same charge is located at x=-a and y=b. find electric force on particle of charge q* located at origin

Hm

[alpine sable]

This is the formula, right

?

[glass lichen]

Also if you haven't drawn a diagram... do so

[alpine sable]

K is Coulomb’s constant

[alpine sable]

;-;

[last sage]

#19

Nvm

[rapid grove]

@last sage u good?

[last sage]

Why

[rapid grove]

With the question

[last sage]

Can You help me

It sideways sorry

[wary stream]

,rotate

[last sage]

Help or no

[oak chasm]

@last sage What are the possible arrangements of 3, 5, and 7?

There are 357, 375, 537, 573, 735, and 753, right?

[last sage]

Yea

[oak chasm]

OK, so you fill them in to the blanks on the card on the right side of your problem, right?

Like the card has 753 as the arrangement.

[last sage]

Yea

[oak chasm]

It fills it into the blanks:

|-_ _ . _|
|-7 5 . 3|

What's |-75.3|?

[last sage]

Hmm

What does the lines mean on the left and right

[oak chasm]

Sorry, fixed a mistake above.

That means to take the absolute value of what's inside.

The absolute value leaves the value alone if it's not negative.

If it's negative, it takes away the negative sign.

|3| = 3

|0| = 0

|-5| = 5

[last sage]

Ohh

[oak chasm]

See how it leaves it alone if it's not negative and gets rid of the negative if it is negative?

[last sage]

Yea

[oak chasm]

OK, so here's what you can do.

Take the arrangements we got earlier.

Fill each of them into the blanks and get the final number after taking the absolute value.

[last sage]

What blanks

[oak chasm]

|-35.7|
|-37.5|
and so on

[oak chasm]

See the blanks on the far right?

In the grey?

[last sage]

Yea

[oak chasm]

OK, they filled in 753 there, right?

And that's |-75.3|, right?

[last sage]

Ya

[alpine sable]

his mistake was ignoring the absolute value sign

[oak chasm]

OK, what if they fill in 357?

[alpine sable]

then it's the smallest number

[oak chasm]

What does that look like when it's filled in?

[alpine sable]

|-35.7|

[oak chasm]

@alpine sable One of the rules is to not just give the answer.

[alpine sable]

what grade are you in

[last sage]

There are 357, 375, 537, 573, 735, and 753,

[oak chasm]

Right.

So, fill in 357 to the blanks.

What do you get?

|- _ _ . _|

[alpine sable]

what grade are you in rex

[last sage]

|-35.7|

[oak chasm]

Good, and take the absolute value.

What do you get?

[last sage]

35.7

[alpine sable]

35.7

[oak chasm]

Good.

Now do the next arrangement 375.

What's that after you fill in the blanks?

[last sage]

|-37.5|??

[oak chasm]

Good.

Now take the absolute value.

What do you get?

[last sage]

37.5

[oak chasm]

Good.

Now fill in the blank and then take the absolute value for the rest of the arrangements.

Write down the blank-filled part. Write down the absolute value.
Go to the next one.

Find out what the lowest value is.

[last sage]

Then what do I do

Oh

35.7

[oak chasm]

OK, good.

So, that's the answer to the lowest value.

Now, what did the student do wrong?

They picked 753, right?

Why did they pick that?

[last sage]

Hmm

What about B

[oak chasm]

Oh, that was B.

You found the arrangement with the lowest absolute value, right?

[alpine sable]

why is this true?

im so confused

[oak chasm]

@alpine sable Sorry, channel is busy.

[alpine sable]

oh mb

[last sage]

Wait what

Least possible number the card can show

[oak chasm]

Right.

So, when you fill in 357, you get |-35.7|, right?

And the value of that is 35.7, right?

So, if you fill in 357, the value the card shows is 35.7.

Fill in all the arrangements. See what the absolute values are. Find out what the lowest absolute value is.

That's the lowest value the card can show.

Does that make sense?

[last sage]

Hmm

[wary badge]

@alpine sable we will not help u in exams

[last sage]

What do I write

[oak chasm]

What was the arrangement with the lowest absolute value?

[wary badge]

Guys don't Help those who asks answers for their exams if u did then u broke a rule

[last sage]

35.7

[last sage]

She been teaching me

[alpine sable]

its homework wtf???

and i already got the question right

and i asked why

[wary badge]

:sus:

[oak chasm]

@last sage Good, so that's the lowest value you can get on the card (when you fill it in with 357).

[wary badge]

Aren't u are lying?

[alpine sable]

why would i ask for the proof of an answer if i was cheating on an exam

[last sage]

So I write 35.7

[alpine sable]

why does that make any semblance of sense

[oak chasm]

@last sage Yes, that's the lowest value the card can show, right?

[last sage]

Yea

[wary badge]

Ok I trust u

[last sage]

Sorry I was confused

[oak chasm]

No problem.

[alpine sable]

pog

[oak chasm]

@last sage Now for part A, what did the student do wrong when they chose 753?

[last sage]

I put the mistake was ignoring the absolute value sign

[oak chasm]

OK, that sounds good.

[last sage]

If you plot the point -8.85 on a number line, would you place it to the left or right of -8.8? Explain.

[oak chasm]

Well, what side is the left?

The side with lesser numbers or greater numbers?

[last sage]

Wowlet me see

It doesn’t say

#23

[oak chasm]

No, I mean, how does the number line get written?

You write a line that goes left to right, right?

Then you write the numbers from left to right, right?

[last sage]

Middle is 0 left is negative right is positive

[oak chasm]

Right, so the farther left you go, the lesser the numbers are, right?

[last sage]

I thinks

[oak chasm]

And the farther right you go, the greater the numbers are, right?

Well, look at the number line I put above.

Start at 5.

Go left.

All the numbers are less than 5, right?

4 then 3 then 2 then 1.

[last sage]

Ok

[oak chasm]

Start at 5.

Go right.

6 then 7 then 8 then 9.

All the numbers are greater, right?

[last sage]

Yes

[oak chasm]

So, is -8.85 less than -8.8 or is -8.85 greater than -8.8?

[last sage]

Greater

[oak chasm]

Why do you think so?

[last sage]

Because 8.80 is less

[oak chasm]

OK, now let's think about -2 and -1 on the number line.

2 is greater than 1, right?

But how is it when they're negative?

The number line goes -3, -2, -1, 0, 1, 2, 3, right?

So, -2 is left of -1, which means it's less.

2 is right of 1, which means it's greater.

See how the number line shows that it's backwards with negative numbers?

[last sage]

Yes

[oak chasm]

OK, so is -8.85 less than -8.8 or greater than it?

Remember that negative numbers are in backwards order: -3, then -2, then -1 instead of 1, then 2, then 3.

[last sage]

Lesss

[oak chasm]

Is lesser to the left or to the right?

[last sage]

Left

[oak chasm]

OK, there's your answer.

[last sage]

Thanks for your help

Good night

[oak chasm]

You're welcome. You too.

[stable coyote]

Anyone here know ODEs?

[alpine sable]

Can you represent $2^{x+c}$ as a dilation instead of a translation?

[ocean seal]

Jeed

[oak chasm]

@stable coyote I don't, but some do. Find an empty #questions channel and ask your question or try in #multivariable-calculus.

@alpine sable What does a dilation do to the graph?

[alpine sable]

stretches/compresses, thats why I dont think its possible

[oak chasm]

Vertically or horizontally?

[alpine sable]

it can be either

[oak chasm]

OK, vertically, you multiply the entire expression by something.

[alpine sable]

yeah

[oak chasm]

Horizontally, you multiply the x part by something.

[ocean seal]

Chai T. Rex

[alpine sable]

yeah I know that, but how do you dilate the function so its the same as a translation

doesn't seem possible

[oak chasm]

A vertical dilation can't move the minimum value up or down.

You can, however move the thing to the left or right.

[ocean seal]

Chai T. Rex

[oak chasm]

A vertical dilation will move the original graph to the left or right by the exponent on 2 you multiply the entire output by.

Does that make sense?

[tight locust]

dilation

[alpine sable]

oh, im just trying to think why a vertical dilation is equivalent to a translation parallel to x, its not like that in any other functions I've studied

[oak chasm]

Because it converts to an addition on the input.

By the exponent laws.

[alpine sable]

ohhh, right

[astral dagger]

post your question on #multivariable-calculus , maybe I can help you

[oak chasm]

That doesn't happen with many functions.

[astral dagger]

I hope

[chrome spade]

Hello i have a question about probability, im not sure how conditional probability works

https://gyazo.com/bc2821f3a782dffa795923686ae1871c

[alpine sable]

@alpine sableThe difference occurs because vertical dilations occur when we scale the output of a function, whereas horizontal dilations occur when we scale the input of a function.

[chrome spade]

I don't understand why to get P(T|C') we calculate it as 1- P(T' | C')

why is it not 1-P(T|C)?

[oak chasm]

Well, P(A|B) means to use B as the universe and get P(A).

So, P(A') = 1 - P(A) in a universe.

So, P(A') in the universe of B is also 1 - P(A) in the universe of B.

So, P(A'|B) = 1 - P(A|B).

Does that make sense?

@chrome spade

[wary badge]

degree of f(x) = 0 is undrfined? why explain

[placid zinc]

What would you rather it be?

[alpine sable]

studying for a test + really bad at math, wondering how to do this properly? dont rlly know how to use powers + these

like idk where the -4x and the +1 came from in the answer

i assume he multiplied -1 by -1 cuz powers and got the +1

lesson name?

but for the 4x^2 - 4x i dont know

[wary stream]

You FOIL

[alpine sable]

doesnt have one just picked it up from notes

[wary stream]

F: First, I: Inner, O: Outer, L: Last

[alpine sable]

use foil

yes

erm

[wary stream]

$$2x*2x = 4x^2$$

[ocean seal]

dldh06

[alpine sable]

works like that

i see

hm

i thought 2x . 2x would end up being just 4x

is it cuz of the power that it becomes 4x^2?

[wary stream]

And $$(2x*-1)+(-1*2x) = -4x$$

[ocean seal]

dldh06

[wary stream]

No, it's x^2

$$x*x = x^2$$

[ocean seal]

dldh06

[civic sable]

Sorry y'all, does anyone have the join link/button to the server? My friend wants to get in

[alpine sable]

https://discord.gg/AhEJ2bzh

[civic sable]

ahh thank u sm

[alpine sable]

ok so, 2x-1^2

2x x 2x = 4x^2

-1 x -1 = +1

and then for the 4x in the middle

[alpine sable]

not sure how to get this one

[wary stream]

Don't use x as multiplication signs, it gets confusing

[alpine sable]

yeah ik

do i use

period

[wary stream]

Star

$*$

[ocean seal]

dldh06

[dawn galleon]

😮

[alpine sable]

o ok

[dawn galleon]

2+2

is 4

-1

[astral dagger]

also (\cdot) is a good choice

[ocean seal]

SubGui

[wary stream]

The outer terms plus the inner terms

[alpine sable]

right so yeah 2x * 2x = 4x^2, then the -1 * -1 its +1

uh lemme see

never used FOIl

[wary stream]

FOIL

[alpine sable]

speaking of foil I have one foil question too

I’ll wait

so would the outer term be the power? cuz theres no 2nd equation

[astral dagger]

go to #help-4

it's free

[wary stream]

$$(a + b)(c + d)$$
The outer terms would be a and d while the inner terms are b and c
$$(2x-1)(2x-1)$$ So the outer is 2x and -1 while the inner is -1 and 2x

[ocean seal]

dldh06

[alpine sable]

okay

so if it was (3x-1)^2

id do 3x * 3x for 9x^2

-1 * -1 for +2

but then i still need the middle number

which is

[alpine sable]

.

[wary stream]

$$(3x-1)^2=(3x-1)(3x-1)$$

[ocean seal]

dldh06

[alpine sable]

so the middle number is -6x just checked on calculator

still need to figure out the process hoe

[wary stream]

We told you, the FOIL method

[alpine sable]

can i just add the 1st term together?

[wary stream]

No

https://www.youtube.com/watch?v=ZMLFfTX615w&ab_channel=KhanAcademy

Here's a video on the FOIL method

[alpine sable]

does it show an example with a power only

yeah ive done this method before

but like

not really with the powers

3x * 2 = 9x^2

-1 * 2 = +1 i got this from the foil method by using the powers for each term

[wary stream]

The concept of FOIL works with multiplying a binomial and binomial

[alpine sable]

but in terms of how he got the -6x

[wary stream]

If you understand how FOIL works, you just apply it with $$(3x-1)(3x-1)$$

[ocean seal]

dldh06

[alpine sable]

wait i think i might get it

(3x-1)(3x-1)
3x * 3x = 9x^2
3x * -1 = -3x
-1 * 3x = -3x
-1 * -1 = 1

9x^2 -3x - 3x + 1 combine the like terms (i think theyre called) and you get -6x

so 9x^2 - 6x + 1

[wary stream]

Yes

[alpine sable]

bruhhh

i never expected to figure that out

now i gotta somehow hope it sticks in my head for my test

thanks

[wary stream]

I mean, it's the FOIL method

[alpine sable]

the reason i didnt get it is because

ig i didnt visualize it right

(3x-1)(3x-1)

when i did it like this its a lot easier instead of just multiplying each term by 2

[radiant ferry]

somebody help me

my brain has been melting doing this quesiton

[wary stream]

Is that the whole question?

[radiant ferry]

yea pretty much

[wary stream]

What exactly is the goal?

[radiant ferry]

the stars is just either x + divide or -

and somehow the answer is 11

[wary stream]

Oh, you need to figure out what operations to use to get 11?

[radiant ferry]

yea

[gaunt magnet]

<@&268886789983436800>

i would like to report

@glass lichen

[radiant ferry]

what has he done?

[wary stream]

I'm confused now

[gaunt magnet]

he called me a dick

last month

[radiant ferry]

oh damn

[radiant ferry]

yes but my brain was melting

[wary stream]

I meant to Usman

[radiant ferry]

oy dmadna

bruhhh

🥶

[wary stream]

Not exactly 100% sure, but found this site, it helps solve it for you
https://www.dcode.fr/missing-operators-equation-solver

[radiant ferry]

hmm

[west hearth]

Why can lhopital’s rule be applied multiple times

[wind quest]

is the surface area of an ellipsoid hard to derive?

[radiant ferry]

HOLY SHEET THIS IS AMAZING

THANKKKYOUUUU

[void grove]

Question 11 A

[wary stream]

Do you know how to find average?

[void grove]

Yes

[shadow mango]

Can you show what formula or method you use to find it?

[void grove]

So I add the given numbers then divide

[wary stream]

Divide by what exactly?

[void grove]

The amount of numbers

[wary stream]

And that is?

[void grove]

for q 11?

[wary stream]

Yes

[void grove]

20

10+30=40

[shadow mango]

huh?

[void grove]

Divide by 2

[shadow mango]

no no

[wary stream]

What? No

[void grove]

See Im very stupid

[shadow mango]

Here they ask to find the average of a number 'x' and 10

they've already found the average to be 30

[void grove]

Yes

[wary stream]

Average is founded by, the sum of the values, divided by how many terms there are

[void grove]

Correct @wary stream

[shadow mango]

yup so you substitute here
our values are x and 10
average = 30

[wary stream]

Some value and 10 give an average of 30, what is that value?

[void grove]

Oh so 50

The answer would be 50

[shadow mango]

yeah

[void grove]

Oh I misread that completely!

Thank you guys so much!!

That helps a ton!

[naive musk]

how to solve this? what would be the answer?

[rigid smelt]

try to solve the inequality seperately

solve (x^2+ax-2)/(x^2+x+1)<2 and (x^2 +ax-2)/(x^2+x+1)>-3 and then combine the solutions

[naive musk]

i tried but i was not able to reach the answer

[rigid smelt]

show your work?

[naive musk]

yes i just solved the each part and i got these but after that i'm not sure what to do

[rigid smelt]

use quadratic formula

[rigid smelt]

and the fact that the coefficient a of ax^2 + bx + c determines the concavity of the parabola shape

oh actually nvm

a better way is

[naive musk]

yes it wull be an upside open parabola without touching the x axis

[rigid smelt]

oh wait a minute

you made some mistake

[naive musk]

okey

[rigid smelt]

a mistake to be more specific

[rigid smelt]

this one is not true

oh nvm

miscalculated

ok so, heres a thing, the both of these quadratics are facing upwards correct?

so a fact is that there will always exist an x such that its sign is positive

now the question however wants that for every x it is positive

[naive musk]

yes

[rigid smelt]

so basically, think about the graph, the parabola will always stay in the positive y region if it never crosses the x-axis

[naive musk]

yes

[rigid smelt]

meaning the quadratic will always be positive if it has no roots

[naive musk]

yes no real roots

[rigid smelt]

so how do you make sure that the quadratic has no roots?

[naive musk]

because it is strictly greater than zero

[rigid smelt]

i know that but how do we make sure that happens?

what do we use to restrict a?

||hint: discriminant||

[naive musk]

ah yea !

[rigid smelt]

so, just make sure that the discriminant of both quadratics are always less than 0

and thats your condition for a

[shell widget]

Yes

[naive musk]

yes

[shell widget]

"No. of times the graph of the polynomial crosses the x-axis"

doesnt matter

[naive musk]

thanks @rigid smelt

[alpine sable]

Yo how do I do this?

This is a question on my homework

[waxen spruce]

Hello, is the 3b1b and ocw enough to learn linera algebra?

[alpine sable]

someone pls help

I have to turn this in an hour

[nimble cave]

middle term splitting

[alpine sable]

Try breaking the 17y into 2 other things

[shadow mango]

split 17y into two things

[alpine sable]

||Namely 15y + 2y||

There was an example for this but I was confused.

[waxen spruce]

i think u factor it by groupoing

[alpine sable]

it said something about pq

And 15x2

This is not the answer. but the answer format should be something like this

[waxen spruce]

(15y+2)(y+1)

?????

[alpine sable]

Yes

[split oriole]

Try middle term split

[ionic jewel]

yes, but I'd grab a textbook too for practice problems and such

[alpine sable]

Yes

[nimble cave]

wait no it won't work

[waxen spruce]

ty ty may i ask how u learned it o

[nimble cave]

the factor will be (15y+2) (y+1)

[alpine sable]

OHH I GET IT NOW

[ionic jewel]

i took a course at my high school, but I've watched both of your mentioned lectures/series

[alpine sable]

Thanks for the middle term split formula.. I searched it up

[waxen spruce]

What grade did u take the course

[ionic jewel]

12

[waxen spruce]

Sheesh

Ok thanks man I will do that

[ionic jewel]

i think most math oriented people do it either then or first year of college

[waxen spruce]

True

[ionic jewel]

otherwise a bit behind second year is still on track

alright good luck

[waxen spruce]

Ok thats good im in 10th grade and I like Math

[ionic jewel]

precalc?

[waxen spruce]

No im taking AB calc

I took precalc in 9th

[alpine sable]

how is that possible lol

[ionic jewel]

yeah okay that's faster than me so you are fine

[waxen spruce]

I did geo in summer

[waxen spruce]

Bet

[alpine sable]

what about Algebra 1 & 2??

[ionic jewel]

bunch of people in my school just were a year ahead

[alpine sable]

I did Geo in summer too

[waxen spruce]

i took alg 1 in 7th and in 8th i did alg 2

[waxen spruce]

Yea its commonplace where i am

[alpine sable]

Wait wth those actually count?

[ionic jewel]

precalc is a stupid class anyways

[waxen spruce]

Fr

[waxen spruce]

Wym yea

[alpine sable]

I mean if the teacher is good then the class can be good

[ionic jewel]

no

[waxen spruce]

rare

[ionic jewel]

i mean yes but the curriculum is bad

common core at leadt

[waxen spruce]

we skipped the fun stuff bc it would take "too much time"

😐

[ionic jewel]

like I'm convinced i learned nothing that class, wish i was just a year ahead

speaking of being far ahead in math i knew a guy that took differential equations in 9th grade then started college math at the local college

[waxen spruce]

All i remmebr is limacon

[waxen spruce]

🧠 ???? wtf

[alpine sable]

What the f

[glacial hedge]

Uhhhh What am i doing wrong with this problem