help-23

[pale remnant]

thx!

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@odd topaz Has your question been resolved?

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[junior tapir]

Im not sure how to solve these

Mainly the last one

[thin bridge]

(g + f)(x) = g(x) + f(x)

[junior tapir]

Ohhhh

Okay I got them

Thank youu

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[fickle trail]

am I on the right track here?

x_2 = S

after -2R1 + R2 -> R2
i got
4 1 -3 0 0 0

[final halo]

looks fine yeah

[fickle trail]

so for R1 it's 4x_1 + 2x_2 = -3

then I solve for x_1

I get x_1 = -3/4 - 1/4 S

-3/4 does not have S, -1/4 does have S

for 0 0 0
I get x_2 = 0 + S

0 does not have S, S does have S

not sure if my terminology makes sense

is there a name for this format?

[final halo]

0 is constant, s depends on s

[fickle trail]

yeah, that's the wording I am looking for

[final halo]

yeah its an equation of a line

[fickle trail]

wait so basically in this matrix format, you can read it as two unique equations?

but they are related, hence the same variables x_1 and x_2

so we call it a "system" of equations?

and we can only write it in matrix format because they use the same variables

[final halo]

sure

[fickle trail]

we call this a vector, a matrix, or something else entirely?

variable matrix?

we call this a constant matrix?

and we call this a dependent matrix?

[final halo]

(something)x1 matrices are called vectors

[fickle trail]

1 x row (any length) 0 x column

or
0 x row 1 x column (any length)

= vector?

[final halo]

one column, arbitrary rows is a vector

[fickle trail]

what do you mean by arbitrary?

[final halo]

i dont care how many rows it has its still a vector

[fickle trail]

yeah

x1
x2
x3
x4
x5

for example

that's a vector

[final halo]

it is

[fickle trail]

but [x1 x2 x3 x4 x5] is also a vector?

[final halo]

no

[fickle trail]

ooo

only applies to 1x column

interesting

[final halo]

yes

people call those covectors

[fickle trail]

ah OK

[final halo]

in practice you identify them to be the same, usually just because typing row vectors is easier

but they really are distinct things

[fickle trail]

and a vector is just a point, iirc, on cartesian plane for example

[final halo]

pretty much

[fickle trail]

would SVG (Scalable Vector Graphics) have anything Math related? or they just happen to share the same name (vector) but are not related, code and math wise.

another one with "matrix" in the code

interesting..

https://developer.mozilla.org/en-US/docs/Web/SVG/Attribute/transform

this looks like Math

[final halo]

pretty much anything graphical runs on linear algebra

wait until you hear how many matrix calculations happen in video games

[fickle trail]

https://tenor.com/view/albion-online-elevate-albion-albion-tv-albion-clap-gif-24206083

https://tenor.com/view/angry-make-my-explode-head-mad-gif-14261446

humans: 15 minutes struggling through one matrix calculation on a single core CPU
computers: billions of matrix calculations per second on a multi-core CPU

[final halo]

wait until you also learn that the actual universe pretty much runs on linear algebra

quantum mechanics is a big game of linear algebra

[fickle trail]

I was asking a question earlier kinda related to that, lemme see if I can find it

@final halo not sure if this question even makes sense lol
i think when we get that far out into space-time, our basic understanding of things start to melt away pretty quickly lol
https://discordapp.com/channels/268882317391429632/908076393198419988/1108485532062851144

[final halo]

yeah ive no idea what you're on about there

[fickle trail]

bending planes

to meet up at more than one unique point

[final halo]

why would you bend planes

[fickle trail]

but less than infinite

space-time, don't ask me mannn, it's the universe

isn't that how wormholes work?

black holes

very common we just don't know them well enough

https://tenor.com/view/huh-geicos-caveman-3doors-down-let-me-be-myself-song-wait-what-gif-20064762

[final halo]

i think you're taking the whole bend a paper and punch a hole through it thing too literally

and what that has to do with solutions to system of equations i have no idea

[fickle trail]

but that's literally how linear algebra was taught to us in class, taking some pieces of paper and showing where they meet

[final halo]

yes, explicitly not bending them

because in a 3x3 system, each equation is the equation of a plane

[fickle trail]

https://tenor.com/view/balls-warp-3d-gif-9225226

i just assumed this mesh was called a plane, or something along those lines - what do we call it instead?

[final halo]

its bent so its not a plane

its just some surface

[fickle trail]

oh.. https://www.quora.com/Is-spacetime-actually-planar-a-sheet-or-is-it-more-accurately-represented-by-this-picture#:~:text=Space time is three dimensional,describe said effect to laymen.

"spacetime" = 4 dimensions, with the fourth dimension being Time

[final halo]

yeah again don't take this too literally

spacetime has a certain metric, a different notion of "distance" between points

which is what makes the geometry of it weird

[fickle trail]

it's so trippy. but it's real. but we are so disconnected from it. almost everyone goes through life for only a fraction of a second thinking about this stuff
makes you wonder if there is life out there that truly understands it, extremely well, and has seen the edge of the universe

https://www.youtube.com/watch?v=-ZgUjVcEuyc

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[real mountain]

How do I solve it?

[lavish remnant]

what is 24/8

[real mountain]

3?

[lavish remnant]

Correct

[lavish remnant]

What is this

[real mountain]

m^-3?

[lavish remnant]

Correct

what is this?

[real mountain]

put m^3 in the denominator?

[lavish remnant]

sure

it's m^-3

[real mountain]

Yep

[lavish remnant]

you should be able to figure out the last part n

[real mountain]

yep you actually mentioned 24/8 which I stupidly looked over and didn’t simplify

[lavish remnant]

If you didn't know

[real mountain]

Mhm!

Thanks very much I think I can figure the rest out myself

Have a nice day! God bless! Jesus loves you

[lavish remnant]

Jesus doesn't exist

[real mountain]

He does, and He loves you. Have a nice day, and thanks for helping

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[lavish remnant]

What's your question

[calm comet]

how to find the answer. I'm confused on where to start

[worthy hemlock]

You're given the area of the circle, find the radius

Then use that to find the circumference

[calm comet]

so r =√(A / π)

[worthy hemlock]

Yes

[calm comet]

so r=5pi?

[worthy hemlock]

No

You do 25pi/pi, what does that equal to?

[calm comet]

25

but isn't it 25pi^2?

[worthy hemlock]

I think that's an error

It's 25pi inches^2

[calm comet]

wait I mean that the original thing is 25pi^2/pi

[worthy hemlock]

I think that's an error
It's 25pi inches^2

[calm comet]

oh ok

so r=sqrt25pi^2/pi

[worthy hemlock]

What did I tell you, it is not 25pi^2 inches, it is 25pi inches^2

[calm comet]

so do I just ignore the pi^2 thing for now?

[worthy hemlock]

it is 25pi inches^2

25pi inches^2

Why are you still saying pi^2

[calm comet]

Sorry. So how do I divide 25Pi/pi ?

would it just be 25?

[worthy hemlock]

Yes

[calm comet]

so r=25

[worthy hemlock]

No

[worthy hemlock]

.

[calm comet]

wait

r=5

so c=31.41

[worthy hemlock]

Keep in terms of pi

[calm comet]

10pi

[worthy hemlock]

And that's a option, right?

[calm comet]

yes

Hey I have another problem that I haven't been able to understand for days.

if you don't mind could I post it here?

[worthy hemlock]

Then ask

[worthy hemlock]

How can you represent at least 25 feet long as an inequality?

[calm comet]

<_

[worthy hemlock]

One, that's not an inequality

Two, what does at least mean, is it more or less than 25?

[calm comet]

I'm not sure how to do at least with my keyboard so _<x<

[worthy hemlock]

<= or >=

Greater than or equal to and less than or equal to respectively

[calm comet]

That's smart

so how do I go about solving this?

I don't know where to start at all.

[worthy hemlock]

what does at least mean, is it more or less than 25

[calm comet]

<=25<=50

[worthy hemlock]

I actually miss reread the question

You have 3 pieces of rope, and a total of 110 feet

Rope 1 is 25 feet, how much is left?

[calm comet]

85ft

[worthy hemlock]

Rope 2, can be as small as 25 feet and at most 50 feet, do you get that?

[calm comet]

yes

so <=x<=50

[worthy hemlock]

Fyi, the question is asking for the inequality for rope 3

[calm comet]

yes, I just don't know what the steps are to solving it

[worthy hemlock]

So if rope 2 has to be a minimum of 25 feet, how much rope is left?

[calm comet]

85

[worthy hemlock]

Not quite

You used 25 of the 110 feet for rope 1

[calm comet]

60 cause of rope one

[worthy hemlock]

Yes

And if the most rope 2 is 50 feet, how much rope it left for rope 3?

[calm comet]

35

[worthy hemlock]

So for rope 3, you can make a rope that can be a minimum of 35 feet and at most 60 feet, right?

[calm comet]

yes

[worthy hemlock]

Can you make the inequality based on that?

[calm comet]

yes

35<=x<=60

[worthy hemlock]

And is there an answer choice that represents that?

[calm comet]

So we got that by guaranteeing that you subtract at least 50 and at most 75

yes

[worthy hemlock]

Yes

[calm comet]

Thank you good sir

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[calm comet]

I'm not sure what the first steps are to find it. I tried making x+y=5050

then I just didn't know what to do

[keen comet]

What does Last Tuesday, 2,200 people entered the petting zoo mean?

[calm comet]

2200 is the amount of people the zoo which is also the amount of people which had to pay a fee

[keen comet]

Can you write an equation

[calm comet]

x+y=5050

[calm comet]

To be honest, I'm not sure. This time I have some sort of grasp on what to do, but I am a little confused

[keen comet]

Can you write an equation that represents Last Tuesday, 2,200 people entered the petting zoo

For one, 5050 is not 2200

[calm comet]

2200y?

the point of intercection is (1500,700)

[tardy garden]

yeah, the answer is 1500

[safe radish]

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

[tardy garden]

oop ok

so what i'd do is write two equations, just as you did

and then for one of them i'd isolate y

so u have 4y = 5050-1.5x
you can isolate y and get
y = 1262.5-0.375x

and you have the equation that says x+y=2200

so you replace y with 1262.5-0.375x and isolate x, and it should give you 1500

[calm comet]

so 1500 children went in the zoo?

[tardy garden]

yes

[calm comet]

This isn't making sense to me

x could be both 1500 and 700 children and both answers would still technically work

wait

ya never mind

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[fathom walrus]

yo can anyone help

[fathom walrus]

<@&286206848099549185>

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[gleaming trench]

Can you use excel?

[fathom walrus]

nope

[sage shore]

What is your question?

You don't know how to compute the mean, var, and std?

Or you did, you just want to compare

[fathom walrus]

this

[sage shore]

Okayy

Let's start with the mean

[fathom walrus]

alright

[sage shore]

If I tell you what is the mean of 1 and 2

What would you say?

[fathom walrus]

theres a mean for 1 and 2?

[sage shore]

yeah, basically mean means the "midpoint" between 1 and 2

it's like the average of 1 and 2

What is it, for 1 and 2?

It's 1.5 right?

[fathom walrus]

yeah

[sage shore]

Allright

Now, if I tell you

What is the mean of 1 and 2 and 3

What would you say?

[fathom walrus]

1?

[sage shore]

it's 2

2 is in between

[fathom walrus]

ohhhhh

[sage shore]

Just like 1.5 was between 1 and 2

You see

[fathom walrus]

okay i see

[sage shore]

We have a formula for this

It is 2 because

We simply added them

1+2+3=6

Then divided by how many of them (3)

So 6/3=2

[fathom walrus]

ohh

[sage shore]

2 is the mean

[fathom walrus]

give me another example

[sage shore]

The same way, if I give you now: 4, 6, 10, 15

What is their mean?

[fathom walrus]

8.75?

[sage shore]

exactly!

[fathom walrus]

yey

[sage shore]

Now you're ready to tackle your original problem

[fathom walrus]

so i just have to add them

[sage shore]

in the same manner, you have 48 numbers

Their overall mean is just their sum

But divided by how many of them (48)

[fathom walrus]

so i just add all of them then devide to 48?

[sage shore]

Yes

[fathom walrus]

what about the variance and deviation of data

[sage shore]

The variance also has a formula to be applied directly

It needs the mean, which you already computed (8.9)

[fathom walrus]

alright

[sage shore]

So basically what you do is:

For each and every number in the table, you compute the difference between it and the mean

Next, square all of these differences

Next, sum all these squared differences

Last, divide this sum by 48

That will be your Variance

[fathom walrus]

how do i find the difference?

[sage shore]

The number in the table - The mean

You need to do it 48 times, for each and every number in the table

It's so lengthy I know right 😋

[fathom walrus]

thats too much work broo

ill let you know when im done so i can show it to you

so you can point out whats wrong

[sage shore]

Okayy

[fathom walrus]

so i just have to subtract the 8.9 to every number on the table

[sage shore]

Yes

Then follow the steps

[fathom walrus]

alright

[sage shore]

Subtract mean

Square all them differences

Sum all squared differences

Divide this sum by 48

[worthy hemlock]

This might be useful https://www.youtube.com/watch?v=deIQeQzPK08&ab_channel=TheOrganicChemistryTutor

[sage shore]

I tell you what I found

Variance = 4.5635

Sd = 2.136

[fathom walrus]

can you help me with this one now

[sage shore]

No idea what this is about

I never studied or encountered this lol

[fathom walrus]

ohh alright thank youu!

[sage shore]

Others will help with this

Welcome!

[fathom walrus]

ill just ask my friend

[worthy hemlock]

https://www.khanacademy.org/math/ap-statistics/xfb5d8e68:inference-categorical-proportions/idea-significance-tests/v/examples-of-null-and-alternative-hypotheses
Might be useful

[safe radish]

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[cunning bobcat]

how do you wite the form specified

[quasi bison]

do you know completing the square

[cunning bobcat]

no

nvm i got it

ty tho

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[safe radish]

Please don't occupy multiple help channels.

[vagrant furnace]

someone solve this pls 😭

[worthy hemlock]

Don't open multiple channels

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[ionic haven]

@whole acorn

[safe radish]

Please read #❓how-to-get-help

[worthy hemlock]

Two, this is a person

And also

[safe radish]

Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.

[ionic haven]

okay po sorry

noted po

[acoustic axle]

for the a one substitute values in x and see the point where both the values for y are same

thats the point of intersection of both the graphs

if you dont get the point while solving manually dw

plot the graph and at some point both the lines would intersect

[worthy hemlock]

Fyi #help-0

[acoustic axle]

oh sorry i didnt see

[safe radish]

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[real charm]

Trying to solve (e) but not sure how to find the CI for a variable from a pdf equation? Any ideas?

Is it maybe possible to use the distribution of U and the distributions of Wi found in (c) and (d) to find the distrib. of lambda?

[safe radish]

@real charm Has your question been resolved?

[safe radish]

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[lean otter]

Stuck on the last part i dont understand how u get to it

[uneven veldt]

Send the whole question

[timid pasture]

commutativity of multiplication

[cunning shard]

Yes

Took the i inside and brought the denominator outside

[lean otter]

Here is the whole question

[cunning shard]

^

[lean otter]

Ah ok

Tysm

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[serene kraken]

]

[serene kraken]

what is this

[lean otter]

D ?

[fast gazelle]

i'd guess Y D A K Z

[lean otter]

ye

[hasty wagon]

permutation?

[quasi bison]

best guess? they want you to rearrange the letters ADYZK in the same order as the numbers were rearranged from I to II

[serene kraken]

u getting better with this questions

[serene kraken]

i dont know

[serene kraken]

why?

[serene kraken]

oh good point

[quasi bison]

no it's just they are getting a bit more sane

[serene kraken]

same thing cuz if u practice these questions it will make sense to u

[quasi bison]

no this one objectively has some kind of immediately understandable logic to it

[serene kraken]

u didnt tell me how?

[fast gazelle]

this

[serene kraken]

can u explain more

[fast gazelle]

the way i thought about it was

comparing I and III

1 = A, 2 = D, 7 = Y, 4 = Z, 6 = K

so then looking at II

7 is Y, 2 is D, 1 is A, 6 is K, 4 is Z

Y D A K Z

[serene kraken]

haaa

okayy

thank u

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[whole acorn]

do you know the trig addition and subtraction identities?

try it

[twilit spindle]

then write $\sin(a+b)$ and $\sin(a-b)$ in reduced trigonometric form

[flat frigate]

XxMrFancyu2xX

[twilit spindle]

and subtract the results, you may get something you like

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[quasi sentinel]

if tana=-2a and tanb = -2b
what does tana-tanb/a+pi+b represent

[quasi sentinel]

im thinking of something similiar to average slope

[safe radish]

@quasi sentinel Has your question been resolved?

[velvet nebula]

are you missing any brackets?

[safe radish]

@quasi sentinel Has your question been resolved?

[quasi sentinel]

nah

(tana-tanb)/(a+pi+b)

[velvet nebula]

so, you were

well we can substitute to get (-2a+2b)/(a+pi+b)

[velvet nebula]

though we might want to solve what $a$ satisfies $\tan(a)=-2a$ and there are many solutions (you can plot $y=\tan(x),y=-2x$ and see the graphs intersect many times)

[flat frigate]

Element118

[velvet nebula]

,w tan(x)=-2x

[flat frigate]

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[quasi sentinel]

wait

ill just send you the full q

[velvet nebula]

so just differentiate $f(x)$ to get $f'(x)=\sin(x)+2x\cos(x)$, okay explains why you have $\tan(x)=-2x$ and you want points between 0 and $2\pi$, which we can see the two of them on the graph

[flat frigate]

Element118

[velvet nebula]

we have f increasing from 0 to alpha and f decreasing from alpha to beta, then increasing from beta to 2pi

for one, we can check numerically...

,w y=2x sin(x)+cos(x)

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[quasi sentinel]

ok

[velvet nebula]

one thing I would try out is to apply mean value theorem

[quasi sentinel]

how do i

change

a+pi+b

into a a-b form

[velvet nebula]

so we have $\frac{f(\beta)-f(\alpha)}{\beta-\alpha}=f'(t)$ for some t

[flat frigate]

Element118

[velvet nebula]

$f(\alpha)=\cos(\alpha)(2\alpha\tan(\alpha)+1)=\cos(\alpha)(-4\alpha^2+1)$

hmm, still kinda unclear whether I can do anything with this

[flat frigate]

Element118

[velvet nebula]

alternatively $f(\alpha)=\frac{\cos(2\alpha)}{\cos(\alpha)}$

[flat frigate]

Element118

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[dull breach]

Hello, I'm struggling to solve this statistics exercise. Wouldn't I need additional data?

[safe radish]

Please don't occupy multiple help channels.

[lofty temple]

I would say so yes

[dull breach]

alright, thanks!

.close

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[calm robin]

hi so i'm a gcse student and i'm really stuck on finding the gradient for this specific question, and i'm having trouble with trying to find out which line is the most accurate tangent

[severe ruin]

well first think about

what is a tangent line

youll find that

theres only one line on there that matches the definition

then find the slope and ur set

[final halo]

stop trolling in peoples channels

[lean otter]

hi dinara

i need help for a question

[safe radish]

Please read #❓how-to-get-help

[lean otter]

quadratic sequences

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[river hinge]

Hello

[river hinge]

I have to put this into 1 root

And I don't know what to do after the 2nd step.

[rain tangle]

root(a) = a^(1/2), just convert like this

and multiply

[river hinge]

Which a?

[rain tangle]

cube root of a^5 = a^(5/3)

[river hinge]

nah

.close

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[weary timber]

Object A (with green rod) is moving on the Y axis 1 unit per second starting at 0,0,0.
Object B (with red and blue rod) is moving forward at a (-90--30)=-60degree angle at 0.5 unit per second.

I have added a recording of a simulation I have made.

Can someone please help explain to me why the green rod keeps touching the red one?

[weary timber]

I'm trying to figure out a way to calculate this.

So that I can modify the speed of Object B and find out the correct angle it should move.

<@&286206848099549185>

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@weary timber Has your question been resolved?

[weary timber]

No!

[safe radish]

@weary timber Has your question been resolved?

[weary timber]

Nein!

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@weary timber Has your question been resolved?

[gleaming trench]

So is the red rod orthogonal to the -60° line?

Also what’s the length of the green rod

From the y axis

@weary timber

[weary timber]

@gleaming trench yes it is orthogonal, i'll have to check the length of the green rod,

in this example it's the green rod about 2.3 long, or about 1.15 from the base of Object A.

i'm afraid I have to eyeball it because I found out it moves like that through trial and error

I can move the position of object A anywhere really and I would only need to adjust the length of the green rod so that it touches the red rod again and it would move in the same way

[weary timber]

Maybe this will help:

[fair hound]

all motion is relative, instead of considering two motions, place yourself in the frame of the point of intersection of the red and blue lines
now, consider the movement of the white point of the green line relative to you

notice how it goes parallel to the red line

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[indigo salmon]

can this graph be discontinuous? if so, at which numbers

[marsh walrus]

what have you tried or checked?

what does it mean for a function to be discontinuous? do any values for x jump out at you here?

[indigo salmon]

well, at first i thought of 3, since the first graph. however, i dont know if that would work because that is only if x does not equal to 3

u know wht im trying to say

[marsh walrus]

what class is this for?

[indigo salmon]

accelerated algebra 2 -> algebra 2 and precalc

[marsh walrus]

okay

can you tell me does this function have vertical asymptotes?

or is there a removable discontinuity

[indigo salmon]

honestly, not at the top of my head

[marsh walrus]

try graphing it

[indigo salmon]

okay ill try

[marsh walrus]

use desmos

[indigo salmon]

okok

does desmos support piecewise funtions?

[marsh walrus]

dont worry about the piecewise part

[indigo salmon]

ok

[marsh walrus]

just graph the first part of the piecewise function, tell me if it has a vertical asymptote

[indigo salmon]

am i doing anything wrong?

[marsh walrus]

do you think you can rewrite the function in some way to illuminate what is happening in the graph?

(think factoring)

[indigo salmon]

ohh wait didnt think about that

well i mean if you just factor it

it cancels out to (x+3)

[marsh walrus]

right

almost everywhere

but there is a consideration

where is $\frac{x^2-9}{x-3}$ not defined?

[flat frigate]

jan Niku

[indigo salmon]

what does that mean?

[marsh walrus]

like 1/x isnt defined at 0

(you cannot divide by 0)

[indigo salmon]

yeah

x cannot be 3

so theres a hole at three right

[marsh walrus]

but thats okay, right, its defined by the piecewise function there

the only question is if theres a jump

is the point (3,6) on that line?

if so, the single point fills in the hole

and the function is continuous, as its defined

[indigo salmon]

yeah it does state that

[indigo salmon]

it is

[marsh walrus]

[indigo salmon]

hmm can u summarize the question and answer again, i just want to make sure i learned it! sorry if its a struggle for u🙂

[marsh walrus]

well you asked if the function can be discontinuous

you found out that, if you factor the function, its a line

except for a point-discontinuity

so you checked if the piecewise function, which adds a point where its not defined, adds a point on the line or not

[indigo salmon]

ohh i get it

[marsh walrus]

[indigo salmon]

so there would be a blank hole on three, and instead there would be a filled hole at (3, 6)

correct?

[marsh walrus]

yea

and the piecewise thing

it doesnt necessarily have to fill that hole

you could define the function at x=3 with some other value

in that case, it would be discontinuous

but here, the point defined fills the point discontinuity

[marsh walrus]

like if instead, you defined f(x) = 8 at x=3 or whatever

youd have a jump-discontinuity

[indigo salmon]

got it! thanks so much

.close

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[lament rivet]

I don’t understand why the answer is undefined

Why can’t I just get rid of the radical by squaring

[half thunder]

Because it is positive square root

That is what that radical means

@lament rivet

it cannot be negative

[lament rivet]

Why can’t I do y+6=-7^2

The other problems look very similar but the answers are not undefined

[twilit harness]

the value of the square root must be positive

[twilit harness]

show them

[lament rivet]

Sorry it’s a bit of a mess

[twilit harness]

well the c one is similar to this question

[lament rivet]

Trying to figure that one out too lol

[twilit harness]

but there too a root is ignored because it gives a negative value for the radical

[languid vigil]

U still get a y value, but if u plug it back in the og equation, it doesnt work

[lament rivet]

am I stupid I still don’t get it

[plucky elk]

Plug in that y into the square root. What do you get?

For your y, sqrt(y+6) = ?

[sweet thicket]

@lament rivet choose a number whether negative or postive

[lament rivet]

Any number?

[sweet thicket]

yeah,

[lament rivet]

14

[vague slate]

Is √(y+6) + 10 = 3 the question?

[lament rivet]

Yes

[vague slate]

So you got your answer?

[sweet thicket]

okay square number 14 u would get a postive number 196
again if u choose -14 and square it u would get 196

so, square of a number is always postive

if u do sqrt(196) u would get 14.
but there is no real number for sqrt(-196).

because square of a number is always postive in a real number

@lament rivet did u understand the statement?

uhh, there is more I want to say but did u understand the statement that I said

[lament rivet]

Yes I understand

[vague slate]

I guess y = 43
?

[sweet thicket]

okay, now @lament rivet this is from my book just read this section and u would understand why ur question is uhh, undefined

If u don't understand the section I will say in nutshell

4 can be made of two number one is 2 squared. and other is -2square.

but the sqrt(4) states that only postive of that number should be written

so, sqrt(4) cannot be -2

this is call principal nth root

@lament rivet if u are still struggling with the question u can ask : P

[lament rivet]

Why is y+6 negative

[fresh plume]

hello i will try to help, can you ask the question again?

[sweet thicket]

if u solve the equation u would get some value for y but if u put that value to the equation again it will be sqrt(-y) of something

it called extraneous solution

again from my textboox

[lament rivet]

Ok hold on one sec

[sweet thicket]

$$ \sqrt{y+6} + 10 = 3 $$
$$ \sqrt{y+6} = 3 - 10 $$
$$ \sqrt{y+6} = -7 $$
sqaring both side
$$ y+6 = 49 $$
$$ y = 49 - 6 $$
$$ y = 43 $$
now checking the equation by putting the value of y in equation
$$ \sqrt{43 + 6} + 10 = 3 $$
$$ \sqrt{49} + 10 = 3 $$
$$ 7 + 10 = 3 $$
$$ 17 = 3 $$
which is false

so the answer should be undefined

[fresh plume]

um small mistake with latex. use {} instead of ()

[sweet thicket]

okay

[fresh plume]

for example, $\sqrt{y+6}+10=3$

[flat frigate]

Parzival

JXHN

[lament rivet]

This helps

[sweet thicket]

first time using latex

[fresh plume]

aight no probs

[sweet thicket]

I have seen other helpers using it so, i just geting gist of it lol

@lament rivet bascially whenever their is radical equation check all the value if it satisfy or not

[lament rivet]

How are you able to recognize that it is undefined without going through that whole process

[sweet thicket]

I can't u just said the answer is undefined

so for every value of y it cannot satify the equation again check all your answer for radical problem

[lament rivet]

Thank you that helps

[sweet thicket]

anyway type .close

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[weary iron]

I’m stuck on these last two

[pastel verge]

think about dot product of (a+b) with itself

[weary iron]

Don’t vector a and vector b have to be going the same direction to equal magnitude of the sum?

<@&286206848099549185>

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[tall pumice]

Real Analysis/Calculus
I have the following question:
Given a series(sequence?) of continuous functions (f_n) in [0,1] which converge pointwise to the function f(x)=0 in [0,1] - let us define:
a_n = the integral of f_n(x) between 0 and 1
Prove/disprove that a_n is bound.

[tall pumice]

I though I managed to prove that the series is bound but apparently not necessarily. I'd gladly show it but unfortunately its not in English.
On that note though, can anyone give me an example of a sequence of functions which converge pointwise to 0 but they don't uniformally(?) converge?

[plucky elk]

Counterexample exists. Try constructing a sequence of functions that has height that grows unbounded, but the support (domain where f isn't zero) converges to zero

[plucky elk]

The integral is also unbounded so there's an error in your proof

[tall pumice]

Yeah I figured as much

[tall pumice]

I can almost imagine one (I'm not sure I can think of a concrete one though atm)
Even then though, I feel like the integral should converge?

well idk if converge is the right terminology

Moreso, decrease as n approaches infinity

[plucky elk]

No point in feeling, write down some examples

[tall pumice]

I can't think of one, otherwise I would've done so already

[plucky elk]

.

What did you do with this hint in the two minutes I gave it to you

[tall pumice]

That's not a hint though lol

Nothing I haven't thought of already, at least

Unless I don't know what a domain means

Which is also possible

[plucky elk]

What examples did you try

[plucky elk]

Support is what matters, not domain

[tall pumice]

I tried constructing an example where the integral is 1/x

Or rather the expression of it

Sorry, my math English isn't great

[tall pumice]

Not sure I understand that part either, care to elaborate?

[plucky elk]

http://wiki.gis.com/wiki/index.php/Support_(mathematics)

[tall pumice]

Oh, literal support

I think I've seen one already

[plucky elk]

Uh huh and what examples did you try

[tall pumice]

Like this?

Or am I misreading

[plucky elk]

That does have support that tends to zero on [0, pi] yes

But that sequence of functions does not grow unbounded

[tall pumice]

Yeah, moreso in the concept of support

Have never heard of the term until now

[tall pumice]

Err.. lemme see

[plucky elk]

It's not necessary to be familiar with the term support, just convenient to talk about

[tall pumice]

Wait, if the height grows unbounded at some x, how does the function converge pointwise at x?

It just occurred to me I tried that but they thought it's impossible

Like, by definition

"For every x and epsilon there exists an N where for every n > N: |f_n(x)| < epsilon"

Innit?

So said "Unbound point of x" has to shrink to at least "0 + epsilon" for some large N?

Yeah that's probably where I missed something, surely

[plucky elk]

this sequence almost converges pointwise to 0

[tall pumice]

Right, because at pi/2 the function will always be err.. 1?

So it doesn't really work

But if it didn't, and "conformed" to the rest of the function, I could probably say that it even uniformly converges

Which is sort of what I don't understand - how can a function converge pointwise in a "[a,b]" part (in contrary to (a,b) for example) and a single continouous* "limit function"

[plucky elk]

could probably say that it even uniformly converges
you're not given this. that's exactly why a counterexample exists.

[tall pumice]

Yeah but to me the two sound identical under these circumstances

If you can take every single x and make it so |f_n(x)| < epsilon for a large enough n, what's the difference at that point?

I know of the classic x^n example but this only works in (0,1), otherwise the limit function isn't continuous

So I'm once again stuck without a counterexample

[plucky elk]

you still haven't suggested a sequence that grows unbounded

[tall pumice]

Nevermind

.close

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[rose glacier]

pls help

[rose glacier]

someone help me cuz i am confused

[safe radish]

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

[lean otter]

!show

[safe radish]

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

[rose glacier]

.close

[safe radish]

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[glacial pawn]

can any one help

[glacial pawn]

question 2 ist about drawing the x y axis on the g(x)

[safe radish]

@glacial pawn Has your question been resolved?

[safe radish]

@glacial pawn Has your question been resolved?

[safe radish]

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[flat frigate]

antrep

antrep

[lean otter]

I dont see why it is obvious that you can exchange limits here

I think the way to solve this is to find u by solving the ODE

[safe radish]

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[safe radish]

Please don't occupy multiple help channels.

[daring forge]

overwhelming

it has a maximum point at (171 , 1096.5)

it has a period of 365

it is cos

the amplitude is (1096.5-382.5)/2=357

so 357cos(x)+382.5

x is a multiple of pi

[copper pewter]

First please close your other channel

[daring forge]

if x=pi then the period is 2

i cant find it

it disappeared

[copper pewter]

#help-33

[daring forge]

the channels keep dissapearing

anyways, 365/2=182.5

so 357cos(pi/182.5x)+382.5

[copper pewter]

Yeah

What's wrong about it

That's the same one I got

[daring forge]

so did i do it right??

[copper pewter]

Wait wait

I put x with pi

So u get 2 first then u divide after

[daring forge]

i think if i just have x it has a period of 2pi

so if i write pi*x

the period will be 2pi/pi=2

and i want 365

so if i just multiply by 365 i get double what i need

[copper pewter]

Yeah this is right

[daring forge]

so i write 182.5

the problem looked intimidating but when i wrote it down it felt easier

[copper pewter]

Which is right, but u can't just shift x for no reason

U got 2 then u shifted x so it's no longer 2

[daring forge]

yeah

but wait i also need phase shift

need get -171

[copper pewter]

Done?

[daring forge]

no

i need to phase shift it by -171

is this correct

[copper pewter]

Not the one I did but probably correct, lemme check

I'll try to rearrange mine

[daring forge]

the maximum point is correct

[copper pewter]

Yeah it's mine rearranged

It works, also with the shift

[daring forge]

what did you do

[copper pewter]

Just redid the same thing

[daring forge]

ah yes

[copper pewter]

Less thinking

[daring forge]

i just factored to make phase shift easier

[copper pewter]

I was lazy

Like me normally

Okay so put L(x) as this and we done right

[daring forge]

bet

[copper pewter]

I don't think ur missing anything

[daring forge]

well see

if i get it wrong there is more to learn

noone is forcing me to do this, so a mistake isnt a bad thing

[copper pewter]

Yeah yeah if ur done u can close

I need to sleep

[daring forge]

it was right, thanks

[copper pewter]

Please check it first tho

W

[daring forge]

W

[copper pewter]

K bye have a good one

[daring forge]

good night man

[copper pewter]

Close the channel, don't forgor

[daring forge]

ofc

.close

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[little dagger]

q6 pls

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@little dagger Has your question been resolved?

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@little dagger Has your question been resolved?

[tardy lark]

What is this ? Is this math or electrical engineering or something else ?

[little dagger]

its discrete maths

[tardy lark]

oh nice

Gl

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[junior wagon]

I’m not sure whether it is the second one?

By elimination, I think the last 2 are wrong since it looks like those are the arc length formulas

But I’m just not sure about the bounds

Actually, I think it not not any of them..

I’m confused

When you set r=0, it should give 7pi/6 and 11pi/6

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[karmic ore]

The two triangles are similar what is the value of x?

[dull sequoia]

What does triangle similarity tell you about the relationship of the sides?

[karmic ore]

.close

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[lean thorn]

did you figure it out?

[karmic ore]

yes!

it was 10

😎

[lean thorn]

yep that's what I got too

well done 🙂

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[pallid oar]

Any help is appreciated

[pallid oar]

.close

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[mint veldt]

I thought that if the limit increases/decreases without bounds that the limit doesn't exist?

[mint veldt]

but my professor said that for j, it just = - infin but didn't say anything about the limit not existing here

[thin bridge]

technically the limit doesn't exist
but being able to indicate that approaches a signed infinity is more meaningful

[mint veldt]

oh okay

that's sort of odd to me

I don't know if I like that

[light shoal]

it is a standard and useful distinction, whether or not you like it 😀

btw, i don't know if this situation applies to you, but there's a well defined notion of "extended real numbers" wherein +infinity and -infinity are perfectly legal numbers with some restrictions (infinity minus infinity is still undefined), and in that system, a limit that approaches +infinity or -infinity is actually convergent, not divergent

[mint veldt]

hmmm

I'm not sure if we've talked about that so probably not

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[candid wadi]

Can anyone please help?

[quasi bison]

!status

[safe radish]

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

[candid wadi]

1

[quasi bison]

divide both sides by 4^(2x) and recognize the equation as almost quadratic

[candid wadi]

I got really long answer

[earnest wagon]

Dividing both sides by 3 also may work

[plucky elk]

!show

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

[quasi bison]

just now?

[limpid jolt]

hi

[quasi bison]

@limpid jolt hello. if you want help for your own question, open your own help channel ( #❓how-to-get-help for instructions). if you just want to chat, go to #discussion or #chill

[limpid jolt]

ok

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[daring forge]

can someone give me a hint

[lavish remnant]

law of sines

tangent

[daring forge]

i think i got it

33.14 roughly?

[flat frigate]

Result:

0.54671585749209

[daring forge]

and then inverse sin

[novel sandal]

yeah looks right

[copper pewter]

Yeah

I have no idea how to inverse sin on this

[daring forge]

lol

[copper pewter]

,calc sin(33.14 deg)

[flat frigate]

Result:

0.54668666587762

[copper pewter]

Yeah

[daring forge]

it makes sense because the 4 things that are displayed are the ones for the law of sines

[copper pewter]

Mhm

U can close if u understand, which u seem to have done

[daring forge]

thanks

was just about to, just saw you typing

.close

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[winged forge]

How do I do this?:

Convert the formulas where you express b in a.

2b - 9a = 24

[twilit spindle]

you can manipulate variables the same you can numbers

[thin bridge]

have you ever solved equations with only one variable before?

e.g. can you solve
2x + 7 = 103

[winged forge]

only with + not -

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@winged forge Has your question been resolved?

[pulsar pecan]

can you solve 2x - 7 = 103?

[sweet thicket]

the question is bascially asking to find the value of b. Meaning b should be left alone in one side and other expression in other side in your case:
$$ 2b - 9a = 24 $$
$$ 2b = 24 + 9a $$
$$ b = \frac{24+9a}{2}$$
you should use basic algebraic mainpulation to solve it

[flat frigate]

JXHN

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[full lotus]

I need to find the values of the Domain of fx where the eq of the tangent is y = 2x - 1

option c right?

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[final plinth]

A

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[quasi sentinel]

is there a way to check the number of tangent lines that can be made on a function from a certain point algebraically

[quasi sentinel]

for instance (x²-3x+2)e^x

and i selected a random point

[hushed minnow]

well if the function is differentiable at a given point, there is only one tangent line at that point

if it's not, then there is zero tangent lines

[quasi sentinel]

the point doesnt have to be on the function

it can be anywhere

[hushed minnow]

I don't follow, can you show an example?

[quasi sentinel]

theres 1

[hushed minnow]

I see, well you can calculate the derivative and then just check for how many different values it intersects with the point

[quasi sentinel]

huh

so f'(a)=b

is this what ur saying?

ngl that doesnt make sense

[hushed minnow]

Formula for a line tangent at x is f'(x)x - f(x) right

like ax + b = y

[quasi sentinel]

f'(a)(x-a)+f(a)

but the point is outside the function

so the a can change

wait

oh

ok

[hushed minnow]

then check if you get b for a

for point (a,b)

[quasi sentinel]

how do i check the range

for example

when x<a 2 tangents
when a<x<b 3 tangents etc

[quasi sentinel]

what if the function isnt a polynomial function

[quasi sentinel]

like this one

i cant solve transcentdal equations or whatever its called

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