help-23

[hot thistle]

do you know what "(x,y,z) is a member of V" means?

[halcyon plover]

Yes 3 elements

I just have to plug in the numbers to check

[halcyon plover]

Its talking about the set i. The problem

I plugged in the numbers and got B

.close

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[safe radish]

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[upbeat swan]

What the easiest and shortest math question that most people get wrong?

[thin bridge]

hard to say, depends what you mean by "most"

[upbeat swan]

most high schoolers

[thin bridge]

freshman's dream

[patent vine]

2+2 = fish

[upbeat swan]

thats too ez

[flat frigate]

Kihei

[upbeat swan]

lol

[thin bridge]

and this would be more suited in the discussion channels

[bold ferry]

you'd be surprised by how many people say 9

[upbeat swan]

nah i'd just get ignored

wanna see

whach #discussion

watch

[thin bridge]

since there's no actual math assistance required here, gonna close.

.close

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[upbeat swan]

@thin bridge look

they're trolling

anyway thx for the help

[safe radish]

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[patent musk]

@spiral bane

am i right with B here

[spiral bane]

why u ping me lol

[thin bridge]

show work

[spiral bane]

^

[patent musk]

jus saw you in a diff channel

thought you available lool

[spiral bane]

diff channel means I'm not available lol

but okay

send a pic of your work

[patent musk]

1/2bh = (1/2)(6√2)(3√2) = 18

[spiral bane]

you skipped a ton of steps

wheres the rest of the work

[patent musk]

is this not right???

the steps before wont een matter if this is wrong

[spiral bane]

i dont know cause i didnt work out the problem

if I can see the work before I can spot any errors

no point in me doing all the work if youve already done it

[patent musk]

the area is half the product of the base (AB) and height (CD)

[spiral bane]

i am aware

but you didnt show how you calculated those values

[patent musk]

.close

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[maiden barn]

I have functions: y^2 = 8x and y = x^2

[maiden barn]

They create an area which we rotate around Ox axis

That creates a 3D body which I have to find volume of

I understand that we have to find where these points cross eacher other:

x^2 = sqrt(8x)
x^4 = 8x
x^4 - 8x = 0
x(x^3 - 8) = 0

Where we have x_1 = 0 and x_2 = 2

Should I calculate it as

PI * integral{0, 2}[sqrt(8x) - x^2]^2dx

Or should I square each of them by themselves

So I get PI * integral{0,2}[8x - x^4]dx

[stray socket]

Square each one differently

I'm pretty sure

That's the washer method

Mmhm yeah you would square each one

[maiden barn]

But why am I doing so

I understand there's some leftover area we don't really include within our volume

Shouldn't I first get "what I am rotating" then rotate it

[stray socket]

https://calcworkshop.com/applications-integrals/washer-method/

[maiden barn]

I see

Thank you very much!

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[fresh birch]

Could some plz help me w this proof?

I’m pretty sure my 2nd and 3rd steps r incorrect

[safe radish]

@fresh birch Has your question been resolved?

[safe radish]

@fresh birch Has your question been resolved?

[safe radish]

@fresh birch Has your question been resolved?

[sudden nova]

Uhh

Notice angle FEC= angle ACE and angle and angle BFE= angle BAE

[safe radish]

@fresh birch Has your question been resolved?

[fresh birch]

Wait, so

How would the proof look?

What would go in step 2?

Angle FEC and ACE are congruent and angle BFE is congruent to angle BAE by the alternate interior angles theorem?

[fresh birch]

@sudden nova

Could u plz look at where I’ve written “right answer?”

I wanna know if that’s right

<@&286206848099549185>

Plz, it’s important

[fresh birch]

Someone plz help

[sudden nova]

That is the proof

[fresh birch]

Does mine look right?

[sudden nova]

Just say by Angle Angle both are similar qed

[fresh birch]

So yk where it says “right answer?”

Do all of the steps look right?

Even the reasons?

[sudden nova]

Should be correct.

[fresh birch]

This

Oh, all of it?

[sudden nova]

Wdym

[fresh birch]

Like, the second column

[sudden nova]

It depends on how specific you want it to be

[fresh birch]

I think they’re specific enough in this case

So everything looks good, right?

[sudden nova]

Should be correct

[fresh birch]

Thanks sm

Appreciate it

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@fresh birch Has your question been resolved?

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[supple monolith]

If we have: 2,4,4,5,5,7,9 the mean is 5 and the deviation is 2. My question is, isnt the standard deviation the same as the average deviation of all the values?

[quasi bison]

no

you might be talking about $\frac1n \sum |x_i - \bar x|$, but that is a different measure, and it is called the \textbf{mean absolute deviation}.

[flat frigate]

Ann

[supple monolith]

Okay, but doesn't the standard deviation tell us how spread out the values are from the mean?

[quasi bison]

sure does. but that alone is not enough to define the word "standard deviation" nor is it ever taken as a definition.

[supple monolith]

I know how it is computed. Basically one way is: sqrt(E(X^2) - (E(X))^2). So we get an idea on how spread out the values are from the mean, and here in the example we have 2. But if we only look at some values for instance 9, we see that the deviation from the mean is 4. So aren't we taking the average? Why is it defined the way it is which is sqrt(E(X^2) - (E(X))^2).

[supple monolith]

.

[quasi bison]

...

sorry, you have lost me.

[supple monolith]

Where?

[quasi bison]

But if we only look at some values, for instance 9, we see that the deviation from the mean is 4. So are we not taking the average?

this is kind of a non-sequitur

and it sounds like some odd patterns in this particular data set caught your attention in a deadlock

[supple monolith]

I basically wonder why it is defined the way it is because intuitively one might think that we look at all the values and take the average spread from the mean

[quasi bison]

again,

that gives you something different.

[supple monolith]

Yeah, I know but why is the standard deviation defined the way it is

Why sqrt(E(X^2) - (E(X))^2)

[quasi bison]

right. so you are looking for motivation as to why the stdev is defined as what it is.

[supple monolith]

yes, why did we choose this formula to be defined as the standard deviation

[quasi bison]

the stdev has a property not shared by the MAD: when you have two independent random variables X and Y, and consider their sum, their stdevs follow a sort of pythagorean theorem-like law: stdev(X+Y)^2 = stdev(X)^2 + stdev(Y)^2

or, since the square of standard deviation is frequently called the variance, you could say that variances of independent RVs add.

[supple monolith]

yeah okay, and the variance is also a value which show us how dispersed the data is in relation to the mean, but it is squared so big differences will be clearly indicated

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[loud jolt]

Pls help

[quasi bison]

,rccw

[loud jolt]

It's gotta be similar to this

[quasi bison]

@loud jolt have you made any progress?

oh

sorry, those messages just loaded...

[loud jolt]

I'm literally stuck there

I don't know what to do

[quasi bison]

are you able to graph the lines y=x and y=-x?

[loud jolt]

No

[quasi bison]

have you graphed any straight lines before...?

[loud jolt]

Yes

[quasi bison]

then what is making you unable to graph y=x?

[loud jolt]

Because I don't get it

[quasi bison]

don't get what?

[loud jolt]

How to get it similar to this

[quasi bison]

forget about any mimicry of the last question...

please do as you are instructed.

are you able to just graph the line y=x?

[loud jolt]

Ys

[quasi bison]

then do it.

are you able to graph the line y=-x on the same set of axes?

[loud jolt]

But it's so stupid Y=x is same as y=-x

[quasi bison]

no, y=x is not the same as y=-1.

no, y=x is not the same as y=-x.

those are two different lines.

[loud jolt]

They are the same

[quasi bison]

you think they are the same point-for-point?

[loud jolt]

They both go same way

[quasi bison]

those are a select few points on the line y=x.

[loud jolt]

Then show how to make Y=-x

Wait it's like this ain't

[quasi bison]

well, first draw an actual straight line through the points you've plotted so far. we still need the line y=x.

[loud jolt]

It's like this?

[quasi bison]

draw lines, not individual points.

i promise you that drawing some diagonal lines on the grid won't make your fingers fall off.

[loud jolt]

Well obviously but it's like this isn't

[quasi bison]

yes, "it" is "like this".

[loud jolt]

Then good I just needed to solve this problem

I'll do rest myself thanks

.close

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[foggy salmon]

wel

[safe radish]

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[wanton pendant]

For case 1, how come we can assume it’s unique solution for all values of k

And for the other cases, why do we check that the vector with K is linearly dependent with the original matrix?

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@wanton pendant Has your question been resolved?

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@wanton pendant Has your question been resolved?

[loud jolt]

I don't understand shit there but we🆙

<@&286206848099549185> help this guy

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[gentle bramble]

can someone explain this:

[gentle bramble]

when "-1" <f(x)<1, y=[f(x)]^2 is closer to x axis then y=f(x)

[faint seal]

try squaring some values of x between -1 and 1

you'll notice that they are always smaller than the original value

or the absolute value of the original value

$x^2 <= |x|$ for all $-1 \le x \le 1$

[flat frigate]

kheerii

[lean otter]

Use \leq in place of <=

[gentle bramble]

oh so like it means that the value of x will make the y=[f(x)]^2 closer to x?

[faint seal]

closer to the x axis

[gentle bramble]

can u explain what that means

[faint seal]

they said that to me, not to you

they're talking about the latex

dw about it

[gentle bramble]

ahh, and what about the second point in the pic ive sent

[gentle bramble]

ohh okk

[faint seal]

well

it's just the opposite of that

if you square some value greater than 1, it will be further away from 0

[gentle bramble]

ahhh okk thankss

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[unique valley]

For the second part I’m a bit confused, how do you find the Fourier sine series for an interval of [0,1], from my knowledge I’ve only worked with intervals of [-L,L]? Another question I have is when you do the Fourier sine series of cosh(y) isn’t it equal to 0 since cosh(y) is an even function you would rather be using the Fourier cosine series to define it?

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[plucky elk]

show the entire question, including part (i)

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[unique valley]

For the second part I’m a bit confused, how do you find the Fourier sine series for an interval of [0,1], from my knowledge I’ve only worked with intervals of [-L,L]? Another question I have is when you do the Fourier sine series of cosh(y) isn’t it equal to 0 since cosh(y) is an even function you would rather be using the Fourier cosine series to define it?

[unique valley]

Sorry it Timed-out

The first part is when they asked you to calculate the integrals explicitly

The second part is asking you to use the first part to find the Fourier sine series

[peak estuary]

you can always do a u-sub to get to [-L,L]

[unique valley]

U-sub on what integral?

And am I correct when I said that you can’t write a Fourier sine series for cosh

[safe radish]

@unique valley Has your question been resolved?

[peak estuary]

fourier series are defined on all kinds of intervals

on [0,1] cosh is not even

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[unique valley]

.reopen

[safe radish]

✅

[safe radish]

@unique valley Has your question been resolved?

[safe radish]

@unique valley Has your question been resolved?

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[misty crow]

How would I go about solving this?

[rotund wolf]

Expand cos(a - b)

[junior smelt]

quadrant information (and sin^2 + cos^2 = 1) allows you to find cos(a) and sin(b)

[safe radish]

@misty crow Has your question been resolved?

[misty crow]

I see so using the sum and difference formulas

[rotund wolf]

Yup and then apply what chartbit said

[misty crow]

Got it thanks.

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[halcyon plover]

Is the correct answer for this A

Bcz

When u take

The sum of the entries in row i

The sum of the elements in each row = 1

@junior smelt am I correct

Ty

[safe radish]

@halcyon plover Has your question been resolved?

[halcyon plover]

Based off of gaussian elimination I got k=2

Doing reduced row echelon

The bottom row is zero

So the columns are dependent

@junior smelt

[halcyon plover]

.close

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[supple monolith]

Hello great mathematicians.
So I would be grateful if someone could give me some application examples regarding derivative integrals, like following. What a possible application for that? Thanks in advance for your time

[frank glen]

Hmm

[safe radish]

@supple monolith Has your question been resolved?

[safe radish]

@supple monolith Has your question been resolved?

[safe radish]

@supple monolith Has your question been resolved?

[iron flare]

sorry, are you asking 'what are some applications of integration' specifically?

[supple monolith]

Hi, thanks for your time. No, my question is regarding derivative of integrals(Fundamental Theorem of Calculus Part 1). I know applications of integrals, and derivatives, but I don't know if that integral derivative is math exclusive, or we have some application in physics maybe?
Initial point of interest: https://openstax.org/books/calculus-volume-1/pages/5-3-the-fundamental-theorem-of-calculus

[iron flare]

sorry if this question is a little pedantic, i just want to make sure i'm answering the right thing:

you're asking what application the theorem linking differentiation and integration as inverse functions has in other fields like physics?

[supple monolith]

Sorry, I hope I could understand your question, but probably yes. I know we could alias an integral using a function, like the F(x), and I understand it comes handy when whole expression could be invoked by F(x). I also understand derivating indefinite integrals results the based function were integrated.
Now I cannot understand when finding a derivative of a definite integral is needed? Like given F(x).
I really appreciate your time, thanks.

[iron flare]

ah is your confusion 'okay, why did we need to even state this, does this have any use'?

all this theorem does is start off as a building block for what calculus actually is

so as a result, its application is pretty much everything integration is used in

the most simple and notable would be the physical relation between velocity and acceleration

more complex is its use in probability density and wavefunctions in quantum mechanics

[supple monolith]

Yes I see. So like integrating acceleration gives us velocity, and derivative velocity, the acceleration.
So if we assume that F(x) is actually acceleration function, so calling F(1) would give us velocity between 1, and 2, now I wonder what derivating F(x) would give us? I'm sorry if it's very unclear, I understand I may need to keep reading to grasp the releam behind it better. Thank you.

[iron flare]

rather v(t) = s'(t) and a(t) = v'(t)

so i suppose if you wanted to directly use the fundamental theorem of calculus)

the derivative of the integral of s(t) dt = s(t)
is equivalent to the derivative of v(t) = s(t)

where v refers to velocity, s refers to displacement and a acceleration

more generally though the sheer amount one can actually do with integration and calculus as a whole when understanding that they are inverse operations is immense
it unlocks further study into analysis both real and complex, physical relationships as simple as motion equations to stuff like lagrangians and energy equations, and is used plenty across statistics as well

[supple monolith]

I really appreciate your time for going through this. And it seems I have to re-study that calculus theorem subject(probably from other source). I hope I'm lucky to find some examples like one shared. Thank you so much.

.close

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[floral pulsar]

Help me for my studies

[spiral bane]

wrong server

[safe radish]

@floral pulsar Has your question been resolved?

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[fresh birch]

For question #28 here, does anyone know why 0 isn’t an answer?

Here’s what the teacher posted

But I’m not sure what restriction allows u to eliminate x = 0

[worthy hemlock]

Plug in zero into the given expression, mainly 4x - 4, one

What do you get?

[fresh birch]

Oh, length can’t be negative, right?

But how do I know to plug it in?

[worthy hemlock]

You look for extraneous solutions

[fresh birch]

Do I always have to plug 0s in and only 0s, or will it never be an answer?

So I have to plug both solutions in regardless of whether one’s a 0?

[pine forge]

help

[safe radish]

Please read #❓how-to-get-help

[worthy hemlock]

Yes

[fresh birch]

Ah, I see

Thanks sm

[fresh birch]

What if I plug it in and get 0

For 2x for example

It’s not a negative, but it’s 0

Same thing?

[worthy hemlock]

Does it make sense for a side length to be a length of 0?

[fresh birch]

No

[worthy hemlock]

There's your answer

[fresh birch]

Thank u

Could u help me w #8?

@worthy hemlock

[worthy hemlock]

Similar triangles

[fresh birch]

So

Like

[fresh birch]

How would I go abt that?

[worthy hemlock]

You have two triangles in that diagram, create a proportion

[fresh birch]

10/x=24/x?

[worthy hemlock]

No

[fresh birch]

Then

Wait but don’t the corresponding sides need to match up?

[worthy hemlock]

You don't need to reply to every one of my messages

[fresh birch]

Sorry

So

[worthy hemlock]

Those are the triangles

[fresh birch]

Oh

So

But what abt the hypotenuse of the bigger triangle?

[worthy hemlock]

You can find it

[fresh birch]

I have 10/x=?/24

Oh yh

Nvm

Does 10/x=26/24 sound eight?

*right

[worthy hemlock]

Sure

[fresh birch]

I got abt 9.2

Also

How do I know that I’m working w the bigger triangle ?

[worthy hemlock]

Not sure what you are asking

[fresh birch]

Like how do u know that they’re similar

[worthy hemlock]

Because it had two right angles so 2 right triangles

[fresh birch]

R they similar in #30?

[worthy hemlock]

Something you need to recall

Hypotenuse-Leg (HL) Triangle Congruence Theorem

Wait not that one

That's for congruent

[fresh birch]

Yeah

[worthy hemlock]

But it shares a side and angle

[fresh birch]

The top one, right?

[worthy hemlock]

The right angle

[fresh birch]

Which one tho

The one at the top right

Or the bottom?

[worthy hemlock]

There's one labeled right angle

[fresh birch]

Sorry i was looking at the other one

[worthy hemlock]

You don't know anything about the angle at the top

[fresh birch]

Right so

That means they’re similar

Right?

?

I don’t think they’re similar @worthy hemlock

Plz help

I’ve got a test tmrw

Wait, I think I got it

I got 12 as my answer

Does that seem right?

<@&286206848099549185>

I just have one question

For #30, how do I know which side is 14-z as opposed to z?

Is it bc it’s drawn to be smaller here?

[lean otter]

You mean x?

Oh nvm

[safe radish]

@fresh birch Has your question been resolved?

[fresh birch]

Do u know?

[safe radish]

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[safe radish]

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[fiery socket]

does Fermat's Little Theorem work for a semiprime modulus?

[fiery socket]

For RSA

[safe radish]

@fiery socket Has your question been resolved?

[safe radish]

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[lean otter]

I understand the two straight lines I am going to have but I am confused where they should meet if that makes sense

[faint seal]

what is the question?

you have to graph this?

[lean otter]

oh sorry that would have been helpful

[lean otter]

correct

I have y = 3/2x - 1 and -3/2 + 5 but I am not sure where I should "limit" the two straight lines

for example g(x) = 3/2x -1 if x > something

[faint seal]

well

at what point does the absolute value change

[lean otter]

is it where they intersect?

[faint seal]

well yes

but

|1-x/2| has a turning point, so to speak

the point where 1-x/2 = 0

would be the intersecting point of the two lines

[lean otter]

ohhh, so when working with absolute values in your equation you get the turning point by* making the values inside the absolute value equal to zero

would this be the case for all functions with an absolute value?

[faint seal]

when there is one absolute value then yes

when there are multiple absolute values you have to separate it into more cases

[lean otter]

so for this, I would have essentially two turning points as x = +-1

[faint seal]

yes

you're right

[lean otter]

okay thank you, that clears a lot of problems up for me, I was stuck with finding where my turning points were

[faint seal]

no worries

[lean otter]

have a great evening / day where ever you are!

[faint seal]

ìt's 1am

💀

[lean otter]

have a great evening!

💀

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[lean otter]

Graphing

[lean otter]

I need help with the first one on the table of y and x

[limber jewel]

What have you tried

[lean otter]

I am doing a big paper and this question is 7 out of 15 graphs that I need to complete tables and plot them

And I think I may be confusing myself because of all teh past ones I jist did

[limber jewel]

Just substitute x=-4 in the f(x) so you get a value that is the 'y' you are trying to get

f(-2)=-2+2(-4)

And then.. i think you'll get it

[lean otter]

My brain is tired so Im gonna collect my thinking here

So -2 + 2 x -4

So 2 x -4 equals -8

Plus -2 is -10

Is that the answer for the first one @limber jewel

[limber jewel]

Yup thats right

[lean otter]

Thanks!

And then there's 0

So is it just -2

Multiplication won't work

[safe radish]

@lean otter Has your question been resolved?

[misty bay]

multiplication does work

2 x 0 = 0

[safe radish]

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[broken wagon]

i need help with solving the equations:

a. x+15+3x-2x < 31-2 x+4
b. 2(x-3)-(x+6) > 4x+(x+2)

[limber jewel]

Try putting like terms together

That would help in simplifying the inequality

[broken wagon]

what do you mean

[limber jewel]

Like in the first one
x+15+3x-2x is just 2x+15 and its right hand side is -2x+35 and you can put the numerical terms on one side of the inequality and variables on one side

[broken wagon]

right okay

[final bay]

Like why would you write x+x when 2x is easier and clearer

[broken wagon]

yeah i understood

[limber jewel]

Which gives you 2x+15<-2x+35
And then it becomes 4x<20

Then solve for x

[broken wagon]

where does 4x<20 come from sorry?

[final bay]

Algebra

[broken wagon]

oh wait nvm

i got it

[limber jewel]

Taking the -2x to the right side it becomes +2x as we add two positive quantities the inequality does change direction

[broken wagon]

alright x<5

[limber jewel]

Yup

Try the second one i think you'd get it

[broken wagon]

ill give it a try

[limber jewel]

I'll check the answer , tell me your final answer

[broken wagon]

nah im lost

😅

[final bay]

Have u expanded the brackets

[broken wagon]

i forgot how to do it tbh

[final bay]

a(b+c)=ab+ac

[limber jewel]

2(x-3) is just 2x-6 and so we have 2x-6+x+6

Which is just x on the left side of the inequality

[final bay]

you messsed up the signs hel

[broken wagon]

its 2(x+3)

[limber jewel]

My bad now its right

[final bay]

No it’s not check the Q again

[limber jewel]

Ya so you multiply 2 with each term

So 2*x+2(3)

[broken wagon]

oh i did the question wrong the first time sorry

[limber jewel]

So thats 2x+6

[broken wagon]

its supposed to be 2(x+3)

[limber jewel]

Even if you got the question wrong that was still solvable to be honest

[broken wagon]

oh right

[limber jewel]

If its 2(x+3) its becomes 2x+6

So the left side becomes 2x+6-x+6

Its just x+12 on the left

[broken wagon]

i thought it would be x² or something

-x²*

[limber jewel]

Only if it was x(x)

But here there's no multiplication involved

[broken wagon]

right okay so what are we doing to make it just be 1 x

im confused

[limber jewel]

My bad i messed up the signs above

Let me get it clearer this time

The left side is 2(x+3)-(x+6)
Which is 2x+6-x-6

2x-x is 1x

You get it?

[broken wagon]

but its still 2x in the front?

[limber jewel]

1+2 is the same as 2+1 so you can just rearrange(as long as you dont change signs)

[worthy hemlock]

Aka commutative property

[broken wagon]

wait so what were doing isnt multiplying the x's in this? (x+3)-(x+6)

[limber jewel]

No no no we are subtracting

[limber jewel]

Yup

[broken wagon]

but to write it out wouldnt it need to be multiplied?

is anyone able to write it on paper with explenation of what actually is being done

[limber jewel]

Ok give me a sec

[broken wagon]

thank you

[broken wagon]

wait you can do - *x?

[limber jewel]

• just means -1

[broken wagon]

right so its -1*x?

[limber jewel]

So you're multiplying by -1

Yup

[broken wagon]

right thats what was confusing me i think

i was thinking you had to do x * x and x* 6

[limber jewel]

That happens a lot when you hurry so see the question carefully , and process it slowly

[broken wagon]

right okay i got just x now

ill try the other side quickly

[limber jewel]

Ok give it a try

[broken wagon]

what i got was x>5x+2

probably wrong tho

[limber jewel]

Ya

Its right

[broken wagon]

okay so what do i need to do after this

[limber jewel]

Now you simplify further

Put all the x's together and the numbers together

[broken wagon]

how would that be

[limber jewel]

Look at it from the fourth line

[broken wagon]

how does it go from -4x to positive x?

[limber jewel]

Divide both sides by -4

You get -4x/-4 in the left

And its 2/-4 in the right

The left becomes x and the right becomes -1/4

But if we multiply or divide by negative number the inequality changes direction

So it becomes x<-1/2

[broken wagon]

might need you to write it on paper again

if you can

[limber jewel]

Give me a sec

[broken wagon]

x<-2/4 is the same as x<-1/2

[limber jewel]

Yup

[broken wagon]

i think i understood it then

[limber jewel]

Cheers then

[broken wagon]

wait when do i know when to switch the side > goes to

[limber jewel]

Just remember when you multiply or divide by a negative number you switch signs

[broken wagon]

alright ill try to remember that

[broken wagon]

yeah okay i got it, thank you very much

[limber jewel]

Np

[broken wagon]

.close

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[patent vault]

i drew this diagram. i know that triangles COD and AOB are similar. and i could probably use the triangles that have have a base on AC. besides that, im stuck. any hints?

[patent vault]

anyone? <@&286206848099549185>

[lean otter]

think about the areas of triangle ACD and BCD

[patent vault]

ooooh. they are congruent right?

since they have the same base and the same height

[lean otter]

maybe not congurent

but yes, they have the same area

[patent vault]

sorry right

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[patent vault]

how can i solve this?

[patent vault]

i dont want a full solution

[lean otter]

maybe start by finding the centre of triangle OLM

[patent vault]

its poorly drawn but

[lean otter]

call the red dot C

do you see why angle LCM is important?

[patent vault]

oh wait of triangle OLM

thats here

and i dont see why its important

[lean otter]

by centre, i mean the intersection of all the medians (the lines that bisects the sides)

how does this relate to the centre of the small circle?

[patent vault]

is it exactly the center of the small circle?

[lean otter]

yeah

so we need to find the angle LCM

I think LCMO is a kite?

[patent vault]

seems like it

does that help us?

[lean otter]

idk, still thinking about it

[patent vault]

take your time

[lean otter]

oh wait

[lean otter]

OC = LC

since we know angle LOC already, we know everything

[safe radish]

@patent vault Has your question been resolved?

[patent vault]

do we know it?

[lean otter]

OC bisects angle LOM

(since it's a kite)

[karmic hedge]

this is not true, the circumcenter is the center of the smaller circle, not the centroid.

[lean otter]

oh

yeah

mb

[karmic hedge]

assuming c is the circumcenter, we can find LCM by inscribed angle theorem, and then we subtract 360 to find LOM

[patent vault]

but LCM isn't an inscribed angle

[karmic hedge]

LOM is, and we know LOM=78

[patent vault]

oh yeah

LCM is 78/2 then

,calc 78/2

[flat frigate]

Result:

39

[patent vault]

oh that's smart thanks

[patent vault]

360-39=321 which is wrong

[karmic hedge]

it’s 360-78*2

just by looking you can tell 321 is wrong, so you should’ve checked your work again

[patent vault]

oh you multiply by 2

,calc 360-78*2

[flat frigate]

Result:

204

[patent vault]

.close

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[novel cargo]

Can someone explain the 2nd and last line?

[novel cargo]

I’m guessing they split the integral so the 50 is coming from the integral of x dx from 10 to 0

But then ngl I don’t even know what the hell [x] dx integral is

[mellow rune]

they def did this

idk abt the integral of that

[novel cargo]

If only I had a lecturer capable of actually explaining stuff

[zinc berry]

The easiest way is to just draw the picture and calculate the integral without the fundamental theorem.

[novel cargo]

I don’t get that at all

I think the lecturer spent 95% of the time doing this but it just looked like scribbles to me

[zinc berry]

[x] is just a step function. So draw the picture and directly find the area or break it up into 10 integrals from 0 to 1, from 1 to 2 etc

[novel cargo]

I don’t understand what I’m supposed to be drawing tho 😭

[zinc berry]

The graph of f(x) = [x] from 0 to 10

[novel cargo]

Is it like a ladder?

So is it jumping up 1 every time?

Also are you saying to partition it and then work out the sum?

Isn’t that the long way? Seems way more complex

[safe radish]

@novel cargo Has your question been resolved?

[safe radish]

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[autumn vine]

The fraction confused me

[novel cargo]

Vanilla is 1/2 of all sales

[autumn vine]

mhm

[novel cargo]

1/2 means a half

[autumn vine]

which is 0.5

[novel cargo]

Yes

So 90*0.5

[autumn vine]

45

[novel cargo]

And what’s strawberry?

[autumn vine]

1/3

[novel cargo]

So how many scoops

[autumn vine]

80

nvm

90

[novel cargo]

No

90 is the total scoops

1/3 of 90 is the strawberry scoops

[autumn vine]

30

[novel cargo]

Yes

So what’s the difference

[autumn vine]

vanila is 15 more than strawberry

[novel cargo]

Correct

[autumn vine]

so 15 is the scoops?

[novel cargo]

Read the question

[autumn vine]

so yup

[novel cargo]

It asks for how many more vanilla than strawberry

So yes

Your answer is 15

[autumn vine]

yup

Thank you

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[peak crane]

How do u do this

[misty bay]

,rccw

[misty bay]

did u seriously close ur previous channel

and open another LOL

I told u: observe that $10^{\log (1.08^{10})} = 1.08^{10}$ and also that $\log (1.08^{10}) = 10 \log 1.08$

[peak crane]

Lol

[flat frigate]

Saccharine

[peak crane]

What do I do with 10log1.08

That’s the part I’m stuck on

[misty bay]

can you calculate that

[peak crane]

Wdym

We can’t use a calculator

[misty bay]

can you calculate 10 log 1.08

[peak crane]

Isn’t it just 1.08^10

[misty bay]

yeah but calculating that is difficult

don't you understand that your job is to actually calculate 1.08^10

[peak crane]

Then what’s the other way to calculate

[peak crane]

Yea

But idk how the answer is 2.16

Wait

Would u divide 10 by 0.334

[misty bay]

no

[peak crane]

Then what

[misty bay]

I said this

do you understand what that log table lets you calculate?

[peak crane]

Yes

[misty bay]

what does it let you calculate

[peak crane]

🤣

Lol

I knew I were gonna ask that

I don’t know how to explain it

[misty bay]

it's not a particularly difficult explanation

why do they print the log table

it's to give you the values of certain types of calculations

[peak crane]

Yea that

[misty bay]

what are those calculations

[peak crane]

.

Calculations are for the logs

[misty bay]

what does that mean

[peak crane]

No clue

Okay why does this matter

I needa find the answer

10log1.08

What do u do

[misty bay]

because if you knew

what these calculations were and why they mattered

perhaps you'd be able to figure it out

[peak crane]

Okay

Now that u explained it

Let’s move on

[misty bay]

I didn't

[peak crane]

Bruh

[misty bay]

I asked you what calculations a log table lets you do quickly without a calculator

you didn't answer

[peak crane]

I have no clue

[misty bay]

probably should think about that for a little

what do the values on a log table mean

[peak crane]

It’s to perform bigger calculations without a calculator

Please

I wana sleep

[misty bay]

what do the values on a log table mean

[peak crane]

Let’s just go through this

It means

Logarithms

[misty bay]

idk if a whole table means "logarithms"

[peak crane]

The results

It means the Logarithm of a number is the exponent to which the base must be raised to produce that number

[misty bay]

okay you just defined logarithm

not very helpful

[peak crane]

Bruh

[misty bay]

what does a log table help you do

like why do you have a log table

what's useful about it

[peak crane]

It helps u find the values easier

Without having to use a calculator

And more precise answer

[misty bay]

no

what specific thing does it let you calculate

[peak crane]

Wdym

[peak crane]

Values

Bro

10log1.08

[misty bay]

that's like saying "it lets you calculate numbers"

meaningless

[peak crane]

10log0.334

What’s next

Bro

Your not very helpful right now

[misty bay]

yes I am

[peak crane]

Idk what your asking for

What’s after 10log1.08

[misty bay]

what might you use a times table for?

[peak crane]

To find the value of specific nunbers

Like 4x4

[misty bay]

wdym by this

numbers have values

[peak crane]

To find the results

Is what I mean

[misty bay]

results of what

[peak crane]

Nunbers

Number

[misty bay]

what does a "result of number" even mean

Just biject it to a planar semigroup whose elements are Cauchy Turing machines

[peak crane]

Bro what

Please

Explain to me

[misty bay]

what does a times table do?

the log table is the same idea

[peak crane]

Wdym what does it do

It does what it’s supposed to do

Which is make it easier

[misty bay]

make what easier

[peak crane]

To SOLVE

Omg

[misty bay]

solve what

[peak crane]

Bro

Are u gonna help me or not

I’ll ask someone else

[misty bay]

ok

[peak crane]

Okay

.closd

.closd

.close

[safe radish]

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[north raven]

would we say a function has a horizontal asymptote y=a if f(infinity)=a?

[misty bay]

f(infinity) makes little sense

[hexed dune]

its better if you said limit as x -> infinity f(x) = a.

[safe radish]

@north raven Has your question been resolved?

[north raven]

cool

riemann integration can't be hindered by jump discontinuities/sharp corners right?

bc we'd be able to compute f(x) at all points

would removable discontinuities possibly hinder it?

since we won't be able to compute f(x) at the discontinuity

[safe radish]

@north raven Has your question been resolved?

[peak wigeon]

IS ANYONE OF CLASS9

[safe radish]

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[worthy hemlock]

Class of 19?

09?

99?

89?

[safe radish]

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[icy nymph]

how do I graph a line that does not exist at x=4 on desmos?

[icy nymph]

like this i mean

is it possible?

[lean otter]

piecewise function

[hexed dune]

@icy nymph https://www.desmos.com/calculator/c3hoxtxz1l something like this

[lean otter]

or multiply it by (x-4)/(x-4) so theres a hole at x=4

[hexed dune]

where you just only use > < inequalities

around 4

not >=

or <=

[hexed dune]

that also works

[icy nymph]

ah ok. i was looking for a more general solution anyways, not specifically this graph but thanks

ig i'll just have to break it up

[lean otter]

multiply by (x-c)/(x-c) to add a hole at x=c

[icy nymph]

yea that works thanks

why does it not show it on the graph tho. i was hoping for a visualization for my notes actually lol

oh well, thats just a desmos being desmos. this works still thanks

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[crude lantern]

I don't understand why f(x) is 2 when x is -2

Pretty sure that 2(-2) +2 =-4+2
=-2

[icy lance]

do you know what the | | means?

[crude lantern]

No

[icy nymph]

|-x| = x

so |-2 | is 2

[crude lantern]

I see ok thanks

[icy nymph]

but note that |2| is still 2

so it just changes negative numbers to positive and positive stays the same

[crude lantern]

I will keep that in mind thanks

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[little sorrel]

how can i do this

[quasi bison]

integration along the y axis might do the trick

[little sorrel]

the equatiosn are already on the y axis

im just thinking if i could do it in one integration

or does it have to multiple

[light stone]

1 intiegration

[hollow siren]

You could integrate with respect to y or x. If you integrate with respect to y, you would only have 1 integral

[little sorrel]

would this be the equation

[light stone]

idk find out

if you get a reasonable answer, then probably yes

[little sorrel]

dont have answers

[light stone]

compute the integral

[hollow siren]

You don’t need to change the equations. It is already in terms of y

[little sorrel]

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[little sorrel]

how do i do (i)

[solid moat]

Do you know what is the definition of tangent?

[little sorrel]

touches eachother

[solid moat]

Mathematical definition?

[solid moat]

I know 😅 , but in terms of math?

[little sorrel]

idk man

just skip this

In geometry, the tangent line to a plane curve at a given point is the straight line that "just touches" the curve at that point. Leibniz defined it as the line through a pair of infinitely close points on the curve. Wikipedia

[solid moat]

You can't , the solution depends on it, tangent in mathematics means they have the same slope

[little sorrel]

ok

so what do i do to find b

or show it

[solid moat]

If they are tangent you need to show they have the same slope right?

[little sorrel]

ye

so i diff it to find gradient

but i dont have the value of x

[solid moat]

What is the slope of y=x+b?

[little sorrel]

1

[solid moat]

And what is the slope for the other y ?

[little sorrel]

would i diff the other y

and sub in x?

[solid moat]

What x?

[solid moat]

Is that how you find the slope for everything x?

[little sorrel]

to find the slope

given x value

[solid moat]

Ok so give me the slope equation for the other y

@little sorrel did you get it?

[little sorrel]

this?

[solid moat]

That is the equation of y, we want to find the slope equation for this y to see on what x we get the same slope

Did you learn how to diff?

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@little sorrel Has your question been resolved?

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[rotund salmon]

I should find all values for x with 0 <= x <= pi/2 for tan(3x) + tan(2x) = 0.
I tried with theorems and used that tan = sin/cos, but my equation gets longer and longer instead of finding a way to solve the problem.

[safe radish]

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

[lean otter]

you can use the fact that tan is pi periodic to avoid expanding everything out

[lean otter]

use trig identities

[lean otter]

also what's going on with your denominator?

just make it cos(2x)*cos(3x)

and since it's equal to 0 you can get rid of it

also cos(2x)sin(3x)+cos(3x)sin(2x)=0
just equals to sin(2x+3x)=0

now using the general solution method will give you the full answer

[rotund salmon]

Okay one moment, I will try

Okay, I made the denominator to cos(2x)*cos(3x), but what did you mean with "and since it's equal to 0 you can get rid of it"?

[lean otter]

(5x+1)/2=0

[lean otter]

5x+1=0

[rotund salmon]

Okay in other words you mean, I just have to find the solutions for sin(5x) thats equal to zero, because the denominator can't be zero?

[lean otter]

yeah but that's not the important part

the important part is how you get to sin(5x)

[rotund salmon]

okay like so:

So then should be the only solution for x. x = 0, because we are on the intervall [0, pi/2]

[lean otter]

take out the denominator

multiply both sides by cos3x cos2x

you're left with sin(5x)=0

[rotund salmon]

okay

I got it, thanks 🙂

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[zinc token]

hint: look at the denominator

that fraction is unreadable and I have no idea what you mean

if you cannot latex it write it out on a piece of paper

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[hazy elbow]

What do you want to achieve?

[gritty glacier]

simplify maybe lol

a^2/2-b^2/18

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[wise sky]

how do you write this as a piecewise function

[wise sky]

$$f(x) = |x-3| - |2x+1|$$

[flat frigate]

choufleur ❦

[proper creek]

remember the definition of the absolute value function

|x| = x, x>0; -x, x<0

apply that in this

[zinc token]

small caveat: you are missing 0

x when x>=0 will fix it

[proper creek]

yes indeed

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[peak crane]

How do u do this

Number 1