help-10

[hardy widget]

What is a?

[fallen mica]

a as in 2y + 18x = 3

[hardy widget]

If you're referring to the slope/gradient of the line, then yes.

[fallen mica]

ahhh so take the derivative of y^8x^2=5 then set it equal to the slope of the line for a

[fallen mica]

is it alright if I show you the work to see if I did it correctly? (when i complete it)

[hardy widget]

👍

[fallen mica]

Ok so I took the derivative of y^8x^2. Would I then set dy/dx equal to the slope of 2y+18x = 3?

[hardy widget]

you can simplify your derivative

,w \frac{-2xy^8}{8y^7 x^2}

oh bot down smh

oh well

exponent rules go brrrrr

[fallen mica]

so i simplify dy/dx even further?

[hardy widget]

I mean it makes your life easier so

I don't see why not

[fallen mica]

Something like this ?

[hardy widget]

✅

the rest is just

algebra soup

[fallen mica]

ic. so i would set equal to the slope and solve for x (or y)?

[hardy widget]

you're gonna have to deal with a system

[fallen mica]

like a system of equations?

[hardy widget]

da

[fallen mica]

could you possibly elaborate i'm a little lost

[hardy widget]

1. needs to have the slope
2. needs to lie on the curve

each of these gives you an equation in x and y

and together they make a system

which I don't feel like explaining how to solve cause algebra soup is boring lol, hence why I was so vague

[fallen mica]

I think i might know what to do now thank you for the help! Would it be the same process for the perpendicular line?

[hardy widget]

same logic with the slope and stuff

just not the same condition as with parallel

negative reciprocal slope

[fallen mica]

ic okok thank you !

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[obtuse pebble]

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[timid silo]

Im really lost on drawing the shadow

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[finite echo]

i'm having trouble finding polynomials with multiplicities

[finite echo]

for 13, i feel like i had it going

but it just didnt seem to add up at the end and i got 2 different values for k

maybe it was some subtraction error but im not sure 😭

for 14, i feel like im misunderstanding the problem

how many zeroes are there exactly ?

[obtuse pebble]

@finite echo Has your question been resolved?

[finite echo]

<@&286206848099549185> if someone could help please 🥲

[obtuse pebble]

@finite echo Has your question been resolved?

[finite echo]

.clouse

.close

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[dull delta]

Hey, I am not sure which test to use for this problem

[dull delta]

I have tried the ratio test but to no avail

I can show my work so far, I have taken two different approaches to this problem

In this approach, I thought splitting it up would help

but not even that worked

I hit a brick wall since I have no way of canceling things out without it resulting in infinity over infinity

😭

<@&286206848099549185> Hey, would anyone here be willing to help me with a problem involving infinite series (calc 2 stuff)? I would greatly appreciate any and all help

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[fierce solar]

im trying to figure out how my professor simplified this

[fierce solar]

im doing a recursion problem in discrete math and he changed

2(3^n-1 + 3^n-2... 3^0)

into

2(1-3^n/1-3)

which simplified into 3^n -1

[obtuse pebble]

@fierce solar Has your question been resolved?

[obtuse pebble]

@fierce solar Has your question been resolved?

[timid silo]

geometric series formula

[fierce solar]

ok

im trying to understnad this pictur e

[untold cove]

I feel like my uni uses the exact same thing

[fierce solar]

i havent seen this before

ok i see

alright thank you

[timid silo]

ye

[fierce solar]

1 question

if the equation is rsn

instead of sn

[timid silo]

hmm

[fierce solar]

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[royal basin]

ok so this is kind of a reverse engineering question that i am thinking about bc i want to generate some diophantine equation problems for my students to solve...

given three linearly independent vectors u, v, w in Z^3, i want to create a diophantine equation of the form a_1 x_1 + a_2 x_2 + a_3 x_3 = b whose solution set is {u + sv + tw | s, t in Z}.

is this always possible? and if so, how can i do it?

[royal basin]

i need to create 20 such equations, so u, v and w are going to vary.

[obtuse pebble]

@royal basin Has your question been resolved?

[teal girder]

Hey I don't have a math question but I want to get into math to be good at it and I'm 10th grade I may have some stuff that I don't quite remember but I don't want to start it all over what to do?

[royal basin]

@teal girder #discussion or #math-discussion

[teal girder]

Oh sorry than😅

[royal basin]

okay fuck it im not getting an answer here

.close

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[timid silo]

Calculate the value of T if ratio of the distance travelled in the first T seconds to the total distance travelled in 60 seconds is 2:3.

[timid silo]

I have no idea on how to solve this😅

[obtuse pebble]

@timid silo Has your question been resolved?

[timid silo]

<@&286206848099549185>

[obtuse pebble]

@timid silo Has your question been resolved?

[tranquil arch]

distance is the area under the curve

[timid silo]

Ik but what will the equation be?

[tranquil arch]

first you can find the total distance

[timid silo]

½(15)(40) + 40(T-15) =

[tranquil arch]

=$\frac{2}{3} \times (\frac{1}{2}\times15 \times 40+(60-15)\times 40)$

[warm shale]

秋水

[timid silo]

Ah I see

Will the answer of tht be the final answer for the question?

[tranquil arch]

yes

[timid silo]

Alright tqvm!

.close

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[molten mason]

Function analytic on set G but the integral isnt zero:

Integral(1/(z-1))dz over a circle |z|=0.5 when parametrised, gives us 2×pi×i not zero even though the function is analytic on the interior of the circle

[molten mason]

.close

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[tropic lantern]

Why is one = 4267/21 and the other = 4267 when x = 10??

[fierce lagoon]

Hm

,tex \polylongdiv{4x^3 + 2x^2 + 6x + 7}{2x+1}

[warm shale]

Umbraleviathan

[fierce lagoon]

Okay so you divided correctly

It should still be the same

,calc 2(10)^2 + 3 + 4/21

[warm shale]

Result:

203.19047619048

[fierce lagoon]

,calc 4267/21

[warm shale]

Result:

203.19047619048

[tropic lantern]

Ohhhhhh

[fierce lagoon]

Still the same

[tropic lantern]

Ok ok 👍

Tysm!

[stable rain]

amazing

wait crap

thats preamble amirite

[obtuse pebble]

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[steep vortex]

I’m a little confused as to the purpose of functions. Example is f(x) = 1-x+x^2

Does this mean every time I see an “x” I have to input 1-x+x^2 into it?

[steep vortex]

Or f(x) = x^2. Why even put the function notation to begin with? It seems redundant. Why can’t you just have the x^2 there without the function notation

[drifting wraith]

it's a shorthand

it lets you say f(12) instead of 1-12+12^2

[steep vortex]

So if I see f(12) anywhere in a equation, that replaces the shorthand?

[drifting wraith]

like, not all things do something, some are just naming

yes

[steep vortex]

So it could be a very long string?

If there were multiple functions then it could be like f(x) = 1-x+x^2
And then h(x) = x^4

So when you see h(3) you would input the h function and f(5) you input that one?

[drifting wraith]

right

[steep vortex]

Sometimes I don’t see the parentheses

And I see f= equation

Same thing?

[drifting wraith]

it probably takes an existing function and uses it as a template

h = g  ∘  f

h = f’

if there's actually an expression, that's weird, that's not a function

[raven spire]

f = f^2 + 0.25 is weird?

[drifting wraith]

yeah, that doesn't define a function f

[raven spire]

well, I'd say it's a constant function, is it not?

f(x) = 0.5?

[drifting wraith]

i suppose it defines a function f, while also being weird

[fierce lagoon]

Yeah

[stable rain]

D:

eh

f means like

f(x) or smt

lazy notation i guess

tho sometimes f(z)

or any other dummy var

hm mayb nor dummy var actually

more like

say f(x)=0

[orchid otter]

well, f is a function, it lets u image a graph under a certain condition, f(x)=x is the same as saying y=x

[stable rain]

g(x)=x

[orchid otter]

a function represents something

[stable rain]

h(x)=x

then we can say

f+g=h

i guess?

[orchid otter]

f(x)=x^2+12x+3
f= function
(x)=variable
x^2+12x+3=condition

if it was f(z)=x^2+12x+3, z=5

f(5)=x^2+12x+3 cuz z was ur variable

but if it was f(x)=x^2+12x+3, x=5
f(5)=88

cuz x was ur variable

@steep vortex

[obtuse pebble]

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[steep vortex]

Yes thank you

[obtuse pebble]

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[steep vortex]

Sorry for reopening but this confused me as I thought about it

[orchid otter]

which pary

part

[steep vortex]

Is this saying if x= 3 then 3=3?

How is it the same as y=x if the function only includes x terms?

[obtuse pebble]

@steep vortex Has your question been resolved?

[patent meadow]

y=x+3
is the same as saying : f(x)=x+3

[steep vortex]

Y-3=X is also f(x)=x+3?

Why not just write y=x+3 then I don’t get why I put a function

[patent meadow]

in this case
there are infinite inputs (domain)
you want to apply a process "function" which is x+3
to produce an output which is the answer to this function "f(x) or y"

[steep vortex]

So the difference is the function form forces you to input that equation wherever you see the function notation of f(x)?

[patent meadow]

its the same
there is rule a function that you apply on the input to produce an outcome

if i want f(3)
that means (3)+3 which is 6

you applied the function (x+3) on the input "3" to produce an output "6"

[steep vortex]

So anytime at all if I have a whole page of equations, everytime I see f(x) it has to be x+3 and this has to be defined before I begin?

And if there were other functions I need to know, it should be represented differently? Like f(y) would be something else

My problem is when they don’t use the function notation of “f” and it’s something like g(y) and I think it’s just (g times y)

[patent meadow]

it would be something like
f(x) and g(x) , h(x)

[steep vortex]

It will always be x?

And the notation would change?

Would I see something like let’s say x = 5 so

x(5-x) f(x) and then it would fully look like 5(5-5) (5+3) ?

The function doesn’t replace every x term right? Just when I actually see the notation is what I’m wondering now

[patent meadow]

no
its like f(x) = (x^2 ) +3x+5

find f (5)

[steep vortex]

Ah I see ok

Ty

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[shadow hemlock]

Actually lost on how to proceed

I’m getting thsi wrong everytime

[timid silo]

well do it again

this is correct so far

[shadow hemlock]

My answer is very very wrong everytime

[timid silo]

ok then send the previous work

we can check for mistakes

[shadow hemlock]

I cut it up

The answer is what I’ve written below

x5^x… is the answer

[timid silo]

,rotate

[timid silo]

the 1st step is correct you have done it wrong in the 2nd step

with the 2nd part

[shadow hemlock]

What have I done wrong?, I think I forgot to multiply 5^xlog 5

[timid silo]

the 5^x (log5) part just disappeared

[shadow hemlock]

Yea

[timid silo]

yes

[shadow hemlock]

But besides that? It’s correct right?

[timid silo]

yes

[shadow hemlock]

Okay I’ll try to solve further

Thanks

[timid silo]

and you have written the answer incorrectly you are missing brackets

[shadow hemlock]

That too

[timid silo]

the close bracket

[shadow hemlock]

I did not finish writing it before I gave up

My bad on that

[shadow hemlock]

Thankyou

[timid silo]

welcome

[obtuse pebble]

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[carmine sparrow]

Hello, how does z = 2+exp(itheta) on the right-hand side?

[twin sapphire]

exp(i theta) is the unit circle right?

so if u want the unit circle shifted by two on the real line

you add two

and that gives you a circle of radius 1 with center (2,0)

[carmine sparrow]

Ah ok thanks. But isn't it true that |expitheta| = 1? so the constraint 1<1 doesnt hold

or its just there as the "edge"?

[obtuse pebble]

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[vague saffron]

What I dont understand about this

[vague saffron]

And it is probably very obvious

But if we do this

And lets say pr(a) = 0.10 and pr(b) = 0.15

Then if we take the probability of them both occuring by 0.1 * 0.15

And then divide by 0.15 again

We and up with pr(a | b) = 0.10 = pr(a)

or is pr(a and b) not 0.1 * 0.15?

For example

How does this make sense?

I understand the reasoning behind it, but not the equations

[tardy epoch]

This is only true if they're independent events

Bayes rule is only useful for conditional events

[vague saffron]

I had a feeling that was the case, but then could you show an example with equations where they are dependent?

Because I dont see how the equation works for dependent variables, this one

If you first multiply and then divide by the same value dont you always get the original value back?>

[tardy epoch]

https://www2.math.upenn.edu/~mmerling/math107 docs/practice on Bayes solutions.pdf

[obtuse pebble]

@vague saffron Has your question been resolved?

[vague saffron]

Ah this is perfect

Thanks a lot!

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[timid silo]

hello, how do i solve log2(192) - log2(12)

[timid silo]

i dont quite understand this problem

ooh thats what it was asking me for

i thought it was something else because im used to seeing log2 192

alright thank you a lot

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[graceful ore]

I need some help with maths it is about growth rate

[graceful ore]

Hold on let me show problem

f(x)=2/3x**3 -x^2 +2x+1/3. Question 1. Determine f'(x). I have done so my answer is 2x^2-2x+2. Question 2: Determine the equation for tangent to f in the point (1, f(1)). Answer: y=2x Question 3: Show that the graph of f has another tangent that is parallel, with the one you found in task b. Find the equation for this tangent.

[tardy epoch]

it's asking for another tangent line with the same slope

[graceful ore]

But how will I find that?

[timber fox]

use your gradient of your tangent and plug into your derivative

you should get 2 values for x

one will be 1 other will be x

[graceful ore]

what is gradient in this conetext?

[timber fox]

here, another tangent with same slop

and you found y=2x

slope is 2

[graceful ore]

I tried what you said but I literally just wrote same slope equation again

:('

[tardy epoch]

,w solve 2x^2 - 2x + 2 = 2

[warm shale]

Results provided by WolframAlpha

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

Requested by riemann#2529

[timber fox]

boom

ez clap

dont even need to solve it tbh

can just see from observation that your other x is 0

[graceful ore]

if x is 0 than tangent equation is y=2b

[timber fox]

is it

oh

u sure

idk about that one chief

did you get another y coord for your new x?

f(0) = ?

[graceful ore]

wait what ... No it is not 2b

[timber fox]

solve for another f(x) with your new x value and use your same gradient of 2 and you'll get your answer

[tardy epoch]

what is b here

[graceful ore]

wait, I get the 2x^2 - 2x + 2 part. But I don't understand why it equal to 2

[tardy epoch]

.

[tardy epoch]

Determine the equation for tangent to f in the point (1, f(1)). Answer: y=2x
you calculated it

[graceful ore]

Sorry not really a native speaker, but is the slope 2 in this case?

[tardy epoch]

yes

for any line in the form y = mx + b, m is the slope and the y-intercept is b

[obtuse pebble]

@graceful ore Has your question been resolved?

[graceful ore]

Okay I got the right answer. But how did you know that they were asking for another tangent line with the same slope?

[tardy epoch]

Show that the graph of f has another tangent that is parallel

[tardy epoch]

with the one you found in task b.

[graceful ore]

How did you know they were asking for another tangent line with the same slope?

Because based on what they said, I did not understand that

[tardy epoch]

do you know what parallel means?

[graceful ore]

yes. When perhaps two lines are equal with each other, but never meet

[tardy epoch]

when else?

are y=x and y=x+1 parallel?

[graceful ore]

No

[tardy epoch]

how do you know

[graceful ore]

Idk

[tardy epoch]

watch this
https://www.youtube.com/watch?v=yUzyhMb7OUI

[graceful ore]

Can you please send me video title? I normally don't watch things that are on youtube

[tardy epoch]

youtube is great for education

Parallel Lines in the Coordinate Plane: Lesson (Geometry Concepts)

[graceful ore]

It is, but I would rather stick with something that is FOSS worthy

[graceful ore]

thx

[tardy epoch]

uh then you're limiting yourself to your education

[timber fox]

YOUTUBE IS GOD TIER

dont insult my blackpenredpen

[graceful ore]

No sir, There are wonderful alternatives

Perhaps yewtu.be

https://yewtu.be/watch?v=yUzyhMb7OUI

[tardy epoch]

that's just the same video but embedded on a different site?

I don't think FOSS is what you think it is

[graceful ore]

Well, that could be for a whole another discussion. But I do get the parrelell lines stuff now properly

But what was the thing about y =x and y=x+1?

[tardy epoch]

seeing whether you understood what parallel lines are

[graceful ore]

So what about the conclusion? These lines were parrell right

[tardy epoch]

do you?

what do two distinct lines that are parallel have in common?

[graceful ore]

they are equal, but they don't meet

[tardy epoch]

But I do get the parrelell lines stuff now properly
no you don't

[tardy epoch]

this video really isn't that long. did you watch?

[graceful ore]

What am I missing?

[tardy epoch]

.

[graceful ore]

They never intersect

[tardy epoch]

that's true, but not enough

something about their slopes

[graceful ore]

Because of the lines do not intersect they move through the coordinates at same growth rate

[tardy epoch]

what's a formula for "same growth rate"

[graceful ore]

But I mean you can have two separete lines that does not intercept and does not necassarliy need to be parallell.

[tardy epoch]

you can't in 2 dimensions. if you'd watch the video you'd know

[graceful ore]

I did watch the video.

[tardy epoch]

i don't know what more to tell you. it's written on the slide in the video

[graceful ore]

you are probably asking for Delta x = 2/Delta y=2

[tardy epoch]

absolutely not

[graceful ore]

but what about here: here the slopes are equal two: y=x and y=x+1 right? The slope is 1

[tardy epoch]

yes

[graceful ore]

was it anything else?'

about the example

you gave

[tardy epoch]

no

[graceful ore]

hm interesting conversation. I will remember that thx for the help + @timber fox

!close

[timber fox]

remember to use youtube

.close

[obtuse pebble]

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[stoic fable]

to showing that the sequence of the partial sums is bounded

If we show it is bounded, we are done, but I’m not sure how to go about this. Any thoughts?

[timid silo]

wont A be finite?

(am I right to assume that N is fixed?)

[kind hawk]

"for any N > 2022"

[timid silo]

oh yeah Im dumb, thx

so A is probably not finite then

[obtuse pebble]

@stoic fable Has your question been resolved?

[timid silo]

,w x^(2021/2022)>x

[warm shale]

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[timid silo]

the first n terms must at worse be n^2021/2022

so maybe bound the sum using sum_n 1/(n^2021/2022)

or not, idk :/

[tardy epoch]

Might help to define

$A_N = {n \le N, n \in A}$

[warm shale]

riemann

[tardy epoch]

and then $A = \bigcup_{N=2023}^\infty A_N$

[warm shale]

riemann

[tardy epoch]

From here you can bound the cardinality of A and show it's finite.

[stoic fable]

Oh this looks promising! Any advice on how to bound the cardinality? (im trying to work on this rn, but let me know if you have any hints, ty)

[tardy epoch]

do the basic union bound

[obtuse pebble]

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[obtuse pebble]

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[final sandal]

here ive got some set notation questions and such but i have absolutely no idea why some things are not what i'd expect them to be

[final sandal]

for example 2c

why is 2c not including Q \

but it includes the space that P Q shares

(the top ones are answers from the textbook)

another example

for f i get the A intersecting B part

but why isnt A intersect B intersect C compliment not a, b and the space they share?

<@&286206848099549185>

[obtuse pebble]

@final sandal Has your question been resolved?

[oak bear]

Set notation is a really strict notation and everything on it should be stated correctly.

[final sandal]

what

[oak bear]

In 2c, it only tells you the relationship of P and R. It doesn't include Q.

[final sandal]

still confused but alright

[oak bear]

If you want to include a notation with Q intersection on it at 2c, it should be (sorry for the lack of set notation. I'm too lazy to copy paste them) something like this -> (P or Q) and (P and not Q)

[final sandal]

what

so since q is not mentioned

q is not relevant?

then why is the space shared between P and Q still highlighted

[oak bear]

At which part

[final sandal]

2c

the part between P and Q

[oak bear]

Is this the key to correct?

[final sandal]

thats still shaded

the top 1 is the answer key

[oak bear]

I mean, the middle part is still a part of the P right>

There are still elements in P that happens to have the same elements as Q

[final sandal]

ig

should i just shade it in parts

accordig to instructions

and then see where they overlap

[oak bear]

Yes or use this as reference

I saw this at google

[final sandal]

how about

4f

[obtuse pebble]

@final sandal Has your question been resolved?

[oak bear]

I mean the picture is correct

(The overlap for A and B) And exclude C in the overlap

[obtuse pebble]

@final sandal Has your question been resolved?

[obtuse pebble]

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[uneven otter]

someone pls help me with this

[uneven otter]

how would I approach this

[mental plaza]

solve for dy/dx = 1

[pine sail]

"parallel to line"
That means, the tangent to your curve should have the same slope as the other line they've given.

[mental plaza]

SAME SLOP

HAHAHAH

[uneven otter]

ah

[mental plaza]

that was some gd autocorrect

[pine sail]

It wasn't, I genuinely missed an e.

[gilded needle]

it's all slop

[pine sail]

Cut me some slack you lot.

[mental plaza]

still amusing ;))

[uneven otter]

but for me to find the eqauation of the tangent line dont I also need the point?

[gilded needle]

it's not actually asking for the equation of the tangent line

indeed there are potentially multiple tangent lines here

"tangent line is parallel to the line..." means "tangent line has the same slope as the line..."

[uneven otter]

oh so since the slope is just 1

do I just find rthe derivative

and set it to = 1

[obtuse pebble]

@uneven otter Has your question been resolved?

[uneven otter]

<@&286206848099549185>

[obtuse pebble]

@uneven otter Has your question been resolved?

[uneven otter]

smh

.close

[obtuse pebble]

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[ionic egret]

I think the limit comparison test is what I should be using here, how should I choose a function to compare it with?

[ionic egret]

i tried divergence and ratio tests and thought root would be a bit dumb

[obtuse pebble]

@ionic egret Has your question been resolved?

[timid silo]

Integral

Test

[ionic egret]

huh my textbook gave a few examples of things to use and that wasn't one but ill try it

[timid silo]

Actually

I did figure it out

But basically integrate by parrs

Parts*

[ionic egret]

is it possible to do with limit comparison?

[timid silo]

Take u = lnx and dv = 1/x^p

Make the 6 go down from the ln and out of the integral

[timid silo]

I mean, then you have to check case by case

So

I'm giving you a general solution

Btw this is just a p series

I'm just giving you the rigorous way of finding out with the integral test

[timid silo]

ln(k) grows so slowly that it does not influence the fact of whether 1/k^p converges or not

But you have to prove that anyways

[ionic egret]

ah i see

.close

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[ruby skiff]

where did teh (n+1) / (n-1) come from

[elfin dune]

common factor

[timid silo]

They just factored out the (n-1)! And (n+1)!

[elfin dune]

(n-1)! is a common factor

[timid silo]

If factoring out a whole expression is hard to see, then replace it with a letter like u

[ruby skiff]

ah k

btw for this one how is it combinations?

why would it not be permiatations?

[timid silo]

Because you are more or less counting the various permutations possible with 5 distinct items

Which is what combinations are about

Well 4 ig

[ruby skiff]

oh so it does not matter what order they are picked up in

asl long as they have the same value

[frosty tiger]

well if i have one penny and one nickel, and you have one nickel and one penny, i would say we have the same sum of money (6 cents)

so yes order doesn’t matter

[obtuse pebble]

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[timid silo]

Hey anybody, I need some help with some Math homework regarding trig identities and algebra. I have some questions here that require proofing, and I honestly remember very little about how I'm to go about solving this. It already bugged me a lot when trigonometry, a subject I am good at, was then mixed with algebra expressions, something I'm not very good at, and I'm just trying to figure out some reliable methods for these types of questions.

[timid silo]

<@&286206848099549185>

[tardy epoch]

Pick one and work on it and show your attempt here

[timid silo]

That was 10. a)

[tardy epoch]

(a+b)/(c+b) does not equal a/c

You have to factor all terms in the numerator and denominator, not just cherry picked ones

(ab + ac)/(ad+ae)= (b+c)/(d+e)

Because a appears in all terms

[timid silo]

Like so?

Forget the lines across the top values, forgot to erase from earlier attempt

And then the (1+sin) cancels out, right?

Bro I'm a fucking dumbass, Idk why I just forgot that factoring exists

https://tenor.com/view/fell-off-the-chair-conner-bobay-coughing-uncomfortable-losing-balance-off-the-chair-gif-20669617

Thanks for the help lol

I'm good now

Stress made me overthink things ig

!close

.close

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[timid silo]

xd

[obtuse pebble]

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[vernal bobcat]

how do you get from that to this

what does the ability_i = (whatever is there) mean

[obtuse pebble]

@vernal bobcat Has your question been resolved?

[novel knoll]

What are you confused about? They wrote ln(wages_i) several times

How do you understand that then?

[novel knoll]

Get what? u_i= what they say just by looking at the true relation

[vernal bobcat]

second off

I am confused about ability_i = d_o + d_1educi+ u_i

what does this exactly mean

[novel knoll]

Same as beta its just some numbers?

But since not the same we use another letter

[vernal bobcat]

ohh right

thanks

hmm

:D.

@novel knoll

could you explain how that got to that? if you would able to

[novel knoll]

Cov properties

cov(aX+b,Y)=a * cov(X,Y)

where X and Y are RV and a, b constants

[vernal bobcat]

why is y1 brought out and nnot Yo.

ohh the cov because its constant

Yo and Ei = 0?

they didnt put that in the steps

guess its self explanatory

ty

[obtuse pebble]

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[obtuse pebble]

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[worn breach]

a

[worn breach]

so how do i simplify

to make g the subject of

m = 2fg / g-c

i dont see any way

[unique spear]

multiply g-c on both sides

[worn breach]

i did

[unique spear]

and you should be able to rearrange the term so that you can factor g out of two terms

simple

[worn breach]

i dont see any way

m(g-c) = 2fg

[unique spear]

now expand it

[worn breach]

if i do m is common

[unique spear]

And?

Why is that a concern?

we can rearrange the terms

[worn breach]

OH

im dum

thx

[unique spear]

so that we can factor g out of two terms

[worn breach]

thanks

i lack thinking

:>

[unique spear]

@worn breach type .close when you’re done

[worn breach]

.close

[obtuse pebble]

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[tawny fog]

It is just
-x^2-14x-5

Right?

Or we have to factor it

Or we have to take -1 common cause I never solved this type of question in my entire life

[tranquil helm]

,w x^2+14x-7=0

[warm shale]

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Requested by AdityaSenpai#0379

[tawny fog]

?

[tranquil helm]

this is your given equation after simplification

[tawny fog]

Yes but why =0

,w factor -x^2-14x-5

[warm shale]

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Requested by 𝓐𝓡𝓝𝓐𝓑 𝓟𝓐𝓛#6985

[tranquil helm]

oh I missed that

[tawny fog]

Yes

[tranquil helm]

but then how this can be a question of equation if there is no = 0

[tawny fog]

This is the real problem

[tawny fog]

Sorry expression

I think it is 6 graders questions and I forgot the concepts 😂 I can literally play with this expression but I didn't understand the question what we have to do?

[tranquil helm]

lol

hey can you tell me how to use latex here? I am a noob in this server

[tawny fog]

Oh ok

$ use this sign

From the start to end

You could make mistakes

Like for square root

$\sqrt{x}$

[tranquil helm]

lemme try

[warm shale]

𝓐𝓡𝓝𝓐𝓑 𝓟𝓐𝓛

[tawny fog]

You could use this

[tranquil helm]

$3x

${4x^2}

[tawny fog]

In ending

[tranquil helm]

oh

${4x^2}$

[tawny fog]

You have to use that in ending also

[warm shale]

AdityaSenpai

[tranquil helm]

nice...

thanks!

[tawny fog]

Good

And for fractions

Use

$\frac{1}{3}$

[warm shale]

𝓐𝓡𝓝𝓐𝓑 𝓟𝓐𝓛

[tawny fog]

Like this

For cube root

$\sqrt[3]{x}$

[warm shale]

𝓐𝓡𝓝𝓐𝓑 𝓟𝓐𝓛

[tranquil helm]

ok ok I know that, m quite familiar with latex

[tawny fog]

Okk

[tawny fog]

Could you help me in that

[tawny fog]

Anyone

[obtuse pebble]

@tawny fog Has your question been resolved?

[obtuse pebble]

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[vague elk]

heyo! can i use khz in the formula for wavelength or do i have to convert it first to hz?
v10^8 m/s / [f]630kHz = λ

[obtuse pebble]

@vague elk Has your question been resolved?

[vague elk]

<@&286206848099549185>

[obtuse pebble]

@vague elk Has your question been resolved?

[obtuse pebble]

@vague elk Has your question been resolved?

[obtuse pebble]

@vague elk Has your question been resolved?

[lethal sand]

You would have to convert it to Hz to keep the unit for wavelength as meters. Basically, hertz in another way of saying is just times/sec, so m/s divided by Hz would give you meter

[obtuse pebble]

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[tepid fractal]

Hi I need to prove that for epsilon >0

[tepid fractal]

I tried to rearrenge the term so I had something like (n+2)/|n-3|

but now I am kinda stuck

[tardy epoch]

looks like you rearranged incorrectly

[tepid fractal]

so its not: (2n^2+n-4)/(n^2-3) - (2n^2-6)/(n^2-3) = (2n^2-2n^2+2-4+6)/(n^2-3)?

.close

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[midnight vortex]

Hello

[midnight vortex]

can someone help me with this

In a class of 27 students, 11 are bilingual. A group of 6 students are randomly chosen to be ambassadors to the local elementary schools.

a) What is the probability that exactly 4 of the students chosen are bilingual? Round your answer to the nearest percent
b) How many bilingual students would you expect to choose

[plain vapor]

If im not wrong, should be (11/27)^4 *(16/27)^2

The a question

[midnight vortex]

yes

[plain vapor]

Oh

Forgot x100

[midnight vortex]

I wrote

(11 choose 4) (16 choose 2)/ (27choose 6)

[plain vapor]

Ok different approach

Should be correct

Let me check

Yes yours is right

Dont look at mine

[midnight vortex]

so for b I got (bilingual/total) (6 students in the group)

[plain vapor]

Seems right

Even just by logic getting 2.44 seems right

[midnight vortex]

2.44

whats the total in this case

[plain vapor]

I would say between 2 or 3, but if you want to round its 2

Closer to 2, so its more probable

[midnight vortex]

yes what would the total be here

what would the equation look like

[plain vapor]

Its just 11/27*6

No?

[midnight vortex]

yes

thanks

so just to breakdown

to solve this question

[plain vapor]

Well you did all by yourself, but your welcome

[midnight vortex]

can you help me with another question please

[plain vapor]

You can use a calculator to do this exercise, right?

[midnight vortex]

yes

[plain vapor]

Lets see, im not really good in statistic but i may help

[midnight vortex]

ok so for the previous question

What is the probability that exactly 4 of the students chosen are bilingual? Round your answer to the nearest percent

the solution we got was 2.44

[plain vapor]

No

Thay was the 2nd solution

[midnight vortex]

wait what

so what was the first than

[plain vapor]

About 13%

Which makes sense to be honest

Cant you do it by yourself?

[midnight vortex]

sorry my calc isnt as advanced

[plain vapor]

Ohd

Do you know how to write choose without the c itself

Its quite handy

[midnight vortex]

so the probability of 4 students being bilingual is 13%

[plain vapor]

Yes

[midnight vortex]

alright

now for this next one

Research has shown that 62% percent of teenagers pass the G2 driver’s test on their first try. Ten teenagers who take the test are randomly surveyed.

What is the probability that at least two (2) teenagers passed the G2 test on their first try? Give your answer as a percent rounded to two decimal places.

so I partially did most of this question

[plain vapor]

Let me check something

[midnight vortex]

ok

@plain vapor are you still there

[plain vapor]

I got 99.83%

[midnight vortex]

oh thanks goodness

[plain vapor]

Could it be correct

[midnight vortex]

for

how did you get that

[plain vapor]

Wait i wanna check sometinh els

Else

Ok

I used binomial distribution formula

Do you know it

[midnight vortex]

yes

[plain vapor]

Since it asked from 2 up

I just calculated the probability of only 1 or 0 passing it

And then removed those 2 percentages from 100%

[midnight vortex]

ok

so

I wrote

[plain vapor]

Did you get the same result

[midnight vortex]

The probability of at least two teens is as the same as 1 - the probability of 1 or 0 teens passing

[plain vapor]

Exactly what i did

[midnight vortex]

ok

[plain vapor]

I just used %

[midnight vortex]

what did u get

[plain vapor]

0.9983 in decimal

[midnight vortex]

the odds of first teen passing + the odds of second teen failing

0.62* 0.38= 0.2356

[plain vapor]

????

[midnight vortex]

=23.56%

[plain vapor]

What is this

[midnight vortex]

this is how we learned it

im breaking it down

[plain vapor]

Ok

[midnight vortex]

can you show me what you did on paper or something please

[plain vapor]

Ok

[midnight vortex]

alright thanks

[midnight vortex]

can you explain please

[plain vapor]

I think i miscalculated before

I got 0.9989

[plain vapor]

Its just binomial distribution

You said you knew it

[midnight vortex]

I do know it

so what does 0.9989 mean in this case

[plain vapor]

Its the answer

99. 89%

[midnight vortex]

I got it thanks I had wrote it as 99%

Thanks TOSI

[plain vapor]

Np

Anywaus

[midnight vortex]

can you help me on one last question

[plain vapor]

I really need to referesh my statistic knowledge

[plain vapor]

Ok

[midnight vortex]

perfect

[plain vapor]

Hm i dont get this

[midnight vortex]

can you please help me on this one

I litterally didnt get it

@plain vapor are you there

@plain vapor please come back

<@&286206848099549185> anyone know how to help me with this question

.clsoe

.close

[obtuse pebble]

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[tight bison]

Please help with limit of sin(tan(x))/x as x approaches 0.

[tight bison]

I tried the squeeze theorem but that didn't really work.

[timid silo]

1 is the answer

[gloomy valve]

try l'hospital

[tight bison]

yes! and why?

but i need to solve it without : (

[gloomy valve]

ah

[timid silo]

sin(tan(x)) / x = (sin(tan(x))/tan(x)) * tan(x) / x

[tardy epoch]

it's not really helpful to just give away answers. try explaining and giving hints instead

[gloomy valve]

can you use taylor series of tanx around x=0?

[timid silo]

yea sorry I am new here. Will give steps properly

[tight bison]

we didn't "learn" that yet

[tardy epoch]

all good. appreciate it

[timid silo]

Now since x-> 0 => tan(x) -> 0

[tardy epoch]

i think this is the intended way to do the problem

[timid silo]

lets take y = tanx => y->0 as tanx -> 0

(sin(tan(x))/tan(x)) * tan(x) / x = (lt y->0 (siny/y)) * (lt x->0 (tanx/x)) = 1 * 1 = 1

[tight bison]

okay ima try it

i dont see it yet

Wow okay i get it

damn that's a cool way to solve that

thanks

.close

[obtuse pebble]

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[obtuse pebble]

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[fast canyon]

Are the probabilities to the folllowing two questions not 1 and 0.99 ?

100% of people who have covid-19 receive a positive test but also that 1% of people who are not sick with covid-19 will receive a positve test

[drifting wraith]

it's 1 for 2.2

the other one is something non round

um

i don't see anything that counts as prior, it has to be impossible

[fast canyon]

thats what im thinking

[drifting wraith]

i mean you can assume 50%

i don;t know what's the probability that they assumed 50%

hehe

they could assume 1/100,000 maybe too

1. they expect the answer to be "not enough data"
2. they expect 50% assumption
3. they expect 1/1000000 assumption

gotta roll with the one that's most likely

[fast canyon]

hmmm

the 50% assumption?

[drifting wraith]

that 50% of the population has covid

[fast canyon]

definitely the 1/1000000 assumption

but that would mean its 0.99

but single digit rounded that 1

also

[timid silo]

can you pls google confusion matrix

you can understand from it quite clearly and then try out the problem

[drifting wraith]

it's ~0.0001 with 1/1000000 assumption

[obtuse pebble]

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[amber trout]

haha you got sparx hw too

[abstract geyser]

a, b >= 0

[obtuse pebble]

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[arctic grove]

ty

[obtuse pebble]

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[timid silo]

can someone help me understand what r and n is

[timid silo]

i dont even get what it means ngl

[obtuse pebble]

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[timid silo]

Hello

[timid silo]

Is this correct?

The last one would be 1/(3n-2)(3n+1)?

For P(n)

[obtuse pebble]

@timid silo Has your question been resolved?

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[meager wolf]

i completely forgot how to do this typa question

<@&286206848099549185>

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[next lantern]

what do i even do

[obtuse pebble]

@next lantern Has your question been resolved?

[next lantern]

.close

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[eternal mortar]

hi again😭😭 this is something different though it’s still considering slopes.

okay so: this is a graphing math project and I’m VERY confused on how to find the slopes in this graph, basically, we have to find two vertical lines, horizontal lines, positive slope, and negative slope. I’m so confused on how to find the horizontal, vertical, positive, and negative but mostly horizontal and vertical. I’m so so confused😭

[merry peak]

what are you trying to do

are those corners supposed to be curved

or what

[eternal mortar]

our teacher told us to draw a pixelated image of something (this is a cat skull, not particularly my choice but it’s a whole story) and then get the vertical, horizontal, etc. slopes
here’s the sheet for it😅

[merry peak]

firstly

what you drew was not a function

secondly

why did you make the lines like corners

[zenith raft]

wow your teacher is awesome

[eternal mortar]

LOLL IKR

[eternal mortar]

she told us to make it all pixelated and that’s how it looked😭

[merry peak]

ok

tbh IDK what the question is asking

positive slope equations? f(x)=x, f(x)=2x

negative slope equations? f(x)=-x, f(x)=-2x

horizontal line? f(x)=1, f(x)=2

vertical line? f(y)=1, f(y)=2

is that right

[merry peak]

did she give an example

of what you should do

[eternal mortar]

unfortunately no🥲

[merry peak]

ok

anyway

I think she just wanted you to draw a function

that isn't weird

just like a function

[eternal mortar]

oh

WELL TYSM

.close

[obtuse pebble]

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[arctic girder]

help

[arctic girder]

with transformations

3^(-0.5x-1) -5

[urban patrol]

what

that's not a proper question

[arctic girder]

im supposed to graph this

but im not getting it right

I created a table of values with the base function

[urban patrol]

just plug in x values

And connect the dots with a curvw

[arctic girder]

im not supposed to do it that way

im supposed to apply them to the base

for x i got

-2x-1

[urban patrol]

like logarithms

[arctic girder]

and y-5

but my points arent matching when i graph

[obtuse pebble]

@arctic girder Has your question been resolved?

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@arctic girder Has your question been resolved?

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[primal dust]

i need help with this

[random depot]

What is e^ln

[fierce lagoon]

What's the relationship between e and ln

Also is this homework