help-0

[rocky dock]

because infinity is included in the one above..

[glass lichen]

cause you don't go to -inf vertically

you're bounded below by -2

it'd be infinity if it went to infinity

[rocky dock]

i still dont quite get your point

what do you mean bounded below by -2?

[glass lichen]

the asymptote prevents f from getting lower than -2

[wary stream]

The reason he moved the 3x first is to get rid of the negatives, less signs to handle. Moving the -3x to the other side, makes it positive 3x, moving the 2 to the other side, the 3x is still negative while the 2 becomes a negative value

[sudden tulip]

Anyone have any bright idea for parrt ii

[manic halo]

you can say that the sides of the rectangle are x and 24-2x

now write the equation for area

and solve the quadratic inequality set to greater that 27cm^2

[sudden tulip]

oh

[keen sluice]

What xyz

[wary stream]

What kind of assignment is this?

[keen sluice]

Geomotry circles assignment

It’s my friends idk

[wary stream]

A test?

[keen sluice]

No

[keen sluice]

What is the answer

[agile charm]

can someone help me with this?

[keen sluice]

I’m in the middle of being helped

Bruh

[agile charm]

ok

[wary stream]

Not sure, you can easily look up the equation that can help with that

[agile charm]

what about this one

[compact pawn]

Expand the equation then use the vertex relation to find y coordinate

[karmic scroll]

Determine the area and the centroid (x. y) of the area

https://imgur.com/PHMHsSf

idk what to do

help

[rigid smelt]

Do you know how to find the area?

[sudden tulip]

?

[stuck herald]

This ones easy but I cannot find this anywhere in my notes. What is the biggest and smallest segment?

Disregard the work from above

[ionic jewel]

the length of a line is directly proportional to the angle opposite it

so in a triangle, the side opposite the largest angle is the largest side

etc

although this might end with you just picking a value for the middle line then using law of sines to solve for all the lines

I dont see a trick but I imagine there could be one

[stuck herald]

But for segment AC, it has both a 57 degree and 61 degree angle

And we haven’t learned the law of sines in this course.

[manic halo]

solving a quadratic inequality is basically just solving the quadratic equation, then stating the values of x for which y<0.
-2x^2 + 24x > 27
2x^2 -24x +27 < 0
Here's a graph of the function from your question

so x belongs to (1.257, 10.743)

[ionic jewel]

AB > CB > AC = AC (from the other triangle) > AD > DC

you can use only the one fact I told you to get this ^

by comparing the a sides by using their opposite angles

[stuck herald]

Ok that makes sense. Thank you

[arctic swan]

I am confusion

[manic halo]

which part are you confused on?

Assuming your statement to be in the form "if A then B", the contrapositive is "if not B, then not A"

the converse is just the reverse: "if B then A"

the contrapositive and the original are logically equivalent statements, meaning proving one true, also proves the other

but the converse is not logically equivalent, thus proving it true does not necessarily prove the original true

[scenic crystal]

Hey! I have an algebraic equation like this - x/150 * 3 = x/50 Why x/50 is equal to x/150 * 3?

[manic halo]

x/150 * 3 = 3x/150

you simplify the fraction by dividing both numerator and denominator by 3

then you get x/50

[vale wigeon]

3/150 = 1/50

[sullen pagoda]

has anybody here done a roller coaster project for calculus? involves multiple functions in the shape of a roller coaster that have matching first and secon derivatives at the connecting points

[stone hatch]

help

[thorn kindle]

Consider the juxtaposition of this shape with itself such that you would have an infinite grid of parallelograms

Or even just a single 2×2 grid rather

[stone hatch]

ik how to do it but idk what to do when y has 2 infront of it

[thorn kindle]

Set up the equation

[stone hatch]

k

208 then idk what to do with the 2y

[lilac nest]

2y is not 208 but half of that, since you have 2y two times

[stone hatch]

so 104 is the answer or do i have to half it again since there are 2

[lilac nest]

Yeah

[stone hatch]

ohhhh ok

thank you

[lilac nest]

2y=104 --> y=52

👍

[snow lion]

How does this work

Also translation:

Given point P(-7, 2). The point P is being rotated around the center C(-2, 2) over an angle of -180 degrees. Give the position of P.

[manic halo]

this should help you to approach the problem

[snow lion]

Wait why’d it be in radians?

[manic halo]

radius*

[snow lion]

Why’d I need the radius?

[manic halo]

because it said it rotated 180 around a center

meaning it forms a semi-circle

to find the new point you just subtract value of radius from center, as shown in diagram

[mild cargo]

What’s up nerds

I’m looking for a blockchain dev who can help me build the next doge

Dogecoin

[vale wigeon]

wrong place

[manic halo]

sry bout the diagram btw, the number scale is in reverse lol

[lilac nest]

Wrong channel and wrong discord

[snow lion]

lol

[snow lion]

amd the radius is C*P?

[manic halo]

its the difference of the x values of C and P

[mild cargo]

Do you guys have like a business channel where I can post my ideas and get feedback

?

[snow lion]

Which does?

[manic halo]

-2 -(-7) = 5

radius is 5

[snow lion]

Sooooo

(5, 2)?

Is the new position of P?

[lilac nest]

No

[snow lion]

darn

[lilac nest]

You have to do -2+5

[snow lion]

What

[lilac nest]

Since the center c is at -2

[lilac nest]

To find the X point sorry

[snow lion]

What my brain

[lilac nest]

Y=2 akways

[snow lion]

Do you mean that this calculation is wrong?

[dull shuttle]

How to know area of a circle

[lilac nest]

X it's 5 units from the center in the opposite direction

[lilac nest]

No

That is the calculation to find the radius

[snow lion]

Of the X?

[lilac nest]

Now add that in the opposite direction to find the X of the new point

[snow lion]

so -5

[lilac nest]

Of the semicircle that forms rotating the point

[snow lion]

Right...

[lilac nest]

No, the center is (-2,2) so you have to add 5 to the X, which means X=-2+5

Which is 3

[snow lion]

So it's (3, 2) the new point?

That is the new P

[lilac nest]

Yeah

Is it clear?

[snow lion]

So this'd be the same but for the Y then?

[lilac nest]

Yes

[snow lion]

Let me think first

Before posting the answer

[lilac nest]

I was asking you to try to find the answer ahah

[snow lion]

2-(3)=-1?

Is the radius?

[lilac nest]

Why -2 at the beginning?

[snow lion]

Wrong 2

[lilac nest]

Yeah

So that is not -3

[snow lion]

I'm so good at math you'd not believe lmao

And add that to the original point which is Q and Q = (-2, 3) so that'd be (-2, 3-1) = (-2, 2)?

[lilac nest]

Maybe drawing a graph can help you understand the situation faster in this type of problems

[lilac nest]

Not to the original point but to the center

[lilac nest]

That's where you are rotating the point around

[snow lion]

So C = (-2, 2) and then add that to C so (-2, 2-1) = (-2, 1)?

[lilac nest]

Yep

[snow lion]

Man this is confusing lol

O(0, 0) and C(-2, 2) deg -180

So like

Both are different

So calculate for both?

[lilac nest]

Yes

[snow lion]

Wouldn't that just invert polarities?

(2, -2)?

[lilac nest]

If the center is (0;0) yes, in all the other cases no

Try to calculate that

[snow lion]

(2, -2) - (2, -2)?

Wouldn't that just make it zero again

wat

[lilac nest]

Take just the x

[snow lion]

Okay

[lilac nest]

It would be O-C=0-(-2)

[snow lion]

2-(2)?

=0

right?

[lilac nest]

Where is the other 2 from?

[lilac nest]

.

[snow lion]

Good point

Do you've to do C-O or O-C?

[lilac nest]

Try to draw that on a graph if you can

[snow lion]

If it's C-O it's 2 right?

[lilac nest]

It's the same

[snow lion]

how

[lilac nest]

What

[snow lion]

It'd be 2-0 or you'd get 0-2

which then 2 would be negative

[lilac nest]

Yeah I meant to just find the difference between the points

[snow lion]

But that'd make a difference, no?

[lilac nest]

It depends how you use that later

[snow lion]

Hm

[lilac nest]

Just do O-C for now

[snow lion]

0-(-2)

so 2

so the radius = 2

[lilac nest]

Yeah in the X axis

[snow lion]

And now do the Y?

[lilac nest]

Yeah

[snow lion]

so that'd be 0-(2)=-2

Ry

[lilac nest]

Yeah

[snow lion]

So now I've calculate the rotation thing

[lilac nest]

Then you have to subtract them both from the center C

[snow lion]

-2 + 2 -2 + 2?

so 0?

[lilac nest]

No (-2-2; 2-(-2))

[snow lion]

what

[lilac nest]

So (-4; 4)

You need to subtract them

[snow lion]

Right

So they add up

Because their polarities get inverted again

boi

[lilac nest]

Trust me that helps a lot, try if you can

[lilac nest]

Yes

[snow lion]

I don't know how to draw graphs what do you want from me lmao

[lilac nest]

I want to help you understand... You just have to plot the points on an X/Y graph

With their coordinates

[snow lion]

?

Now what

[lilac nest]

O is 0,0

[snow lion]

No this is a different question

But we can do 0,0 first ig

[lilac nest]

You basically need to find the "opposite" point of O. so you understand the signs of the coordinates better

[snow lion]

right

[alpine sable]

Ah, Desmos. A man of culture.

[lilac nest]

With C as center

You can easily see that it must be a positive y and a negative x

You calculate the differences like we did before and find the points with the help of the graph

[snow lion]

How

How can the graph help me

[lilac nest]

To understand the signs of X and Y and to understand wath the problem is asking for

[snow lion]

integer limit lol

Sorry for being bad at math I do try I swear

It's just hard to imagine rotation like that lel

[lilac nest]

Don't imagine rotating the point, just imagine finding the simmetrical point with C as center

[snow lion]

As much as I want that to help, it really doesn't

I've no idea what to do with that information

[lilac nest]

Try to plot the answer on the graph

And you will understand what I mean

[snow lion]

OH

That makes so much sense

damnit XD

[lilac nest]

Yeah

[snow lion]

I'm so dumb lmao

[lilac nest]

They are all on the same line but in opposite directions and same distances from C

Right?

[snow lion]

yea

So like

Also idk why they're both blue and dunno how to change that

[lilac nest]

Np

[snow lion]

It'd end somewhere here right?

[lilac nest]

Try to calculate the difference like we did before

[snow lion]

Just by pure eyeballing it

so Cx-Rx?

[lilac nest]

Yeah

[snow lion]

-2-(-7)=5

[lilac nest]

Yes

[snow lion]

And then Cy-Ry

[lilac nest]

Yeah

[snow lion]

2-(3)=-1

So the radius is (5, -1)?

[lilac nest]

It's not really the radius but you have to add those values to the center to find the opposite point

The radius is not a point so it doesn't have coordinates

[snow lion]

But?

[lilac nest]

Bc we were working on a line parallel to the X axis

And it's 5, not (5,y)

It's just a number

[snow lion]

Also add or subtract?

Bc I thought we subtracted them before

Or am I being dumb

[lilac nest]

Don't use the radius anymore, ignore that and just imagine the distances

[snow lion]

right

[lilac nest]

You did that bc you subtract everything in the opposite order before, but always do C-R before and then C+X after

The graph helps you understand that you have to add, since you need to go in the opposite direction

[snow lion]

Wait so I did it all opposite

Wait what

[lilac nest]

You basically did something like a double negative, which is a positive anyway

[snow lion]

I guess that makes sense

[lilac nest]

Just always do that from now on if you're not 100% sure

[snow lion]

Sooooo C+X which'd be (2+5, 2+-1) = (7, 1)?

[lilac nest]

The X is -2+5

[frank onyx]

A cookie factory used 9.5 kilograms of chocolate chips to make 2 batches of cookies. How many kilograms of chocolate chips did they put in one batch?

[lilac nest]

Pay attention to the sign

[snow lion]

yeah woops my bad

[snow lion]

(-2+5, 2+-1) = (3, 1)?

[frank onyx]

A cookie factory used 9.5 kilograms of chocolate chips to make 2 batches of cookies. How many kilograms of chocolate chips did they put in one batch?

Help

[lilac nest]

Yeah

[frank onyx]

Could anyone help me

[snow lion]

Thanks :D

I finished the homework

And I understand it now

[frank onyx]

A cookie factory used 9.5 kilograms of chocolate chips to make 2 batches of cookies. How many kilograms of chocolate chips did they put in one batch?

[lilac nest]

Good job

[snow lion]

You're really desperate for that cookie factory lmao

[snow lion]

:D

[teal sapphire]

Lol I was waiting for wumpie to finish his question

[frank onyx]

Could u pls help

[teal sapphire]

Or their

[snow lion]

Sorry 👀

[teal sapphire]

For what

[lilac nest]

Or use one of the other 10 channels...

[snow lion]

^

[teal sapphire]

I have nothing against waiting

Hence I waited lol no harm

[lilac nest]

I was referring to aspect

[frank onyx]

Ohh ok

[teal sapphire]

Oh

[lilac nest]

Btw,now we can help you

[frank onyx]

Me?

[lilac nest]

Yes

[frank onyx]

Is it 4.25

4.25 x 2 = 9.5

[teal sapphire]

How can I find the component form of 5v+2u when v=<-7,11> and u= <20,-15>?

[lilac nest]

Yes

[teal sapphire]

Oops sorry

I’ll send it in another chat

[snow lion]

Oh no I don't like the looks of this

I've no idea what that is lol

[teal sapphire]

I’ve been trying to get the hang of it but it has me stumped

[snow lion]

Yeah I'd be too

[heavy canopy]

Can someone help me out with this one?

I did find the point where sin|x| is non differentiable

Which is 0

[ionic jewel]

ping me wherever you post this

[lilac nest]

You need to multiply the vectors

So

[snow lion]

Wait those are vectors?

Is that how you write down vectors?

[teal sapphire]

I thought I was supposed to subtract them ?

[ionic jewel]

yes those are vectors

that is a valid way to write them

[snow lion]

I did not know that and that might be very useful

[teal sapphire]

I’ve been subtracting -7 with -20

[lilac nest]

No you have to multiply the values by 5 and 2

[shut tartan]

someone help me

[lilac nest]

Since you have 5v+2u

[teal sapphire]

Okay I get you

I have to start by subtracting correct ?

<-7-20>

[ionic jewel]

man just said you have to multiply first why are you subtracting

[teal sapphire]

On my notes I have that I have to subtract each vector x1 and x2

Then vice versa with the y’s

[lilac nest]

So that means you would get <5(-7)-2(20) , 5(11)-2(-15)>

You have to use them like they are variables/points in a graph basically

[ionic jewel]

Andreas is probably how you want to think about it, although it's perfectly legal to calculate 5v then 2u, then subtract them

[snow lion]

Wait till you get Vector3's and Matrixes

[ionic jewel]

I would usually do it in two steps

[lilac nest]

Oh ok

[heavy canopy]

But wait v and u are seperate vectors. So shouldn't it be like:

If we let v vector be xi+yj

[ionic jewel]

you added the vectors, you should be subtracting

[heavy canopy]

And u vector be ai+bj

[teal sapphire]

Lol I’m confused

[lilac nest]

Yeah sorry I wrote one thing for the other

[heavy canopy]

We put those point in place of x, y and a, b and then subtract them? Idk of anyone got it-

[snow lion]

.

[shut tartan]

yo bunny please help me in #help-9 after ur done

[ionic jewel]

1. multiply vector v by 5
2. multiply vector u by 2
3. subtract the result of the second from the result of the first.

which of these steps is confusing?

[snow lion]

What does finding the component mean exactly?

[teal sapphire]

Okay I got it

[ionic jewel]

component form is just the normal form

i assume

[teal sapphire]

<-75,85>

Right ?

[ionic jewel]

,w 5(-7,11)-2(20,-15)

[ocean seal]

Results provided by WolframAlpha

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

Requested by 兔子#6562

[ionic jewel]

yep

[teal sapphire]

Oh okay I see what I did wrong

[ionic jewel]

👍

[snow lion]

Nice embed?

[teal sapphire]

I was trying to do the subtraction first

[snow lion]

Order of operations

Don't forget :3

[teal sapphire]

And not the multiplication of the 5v and 2i

[ionic jewel]

PEMDAS/BODMAS

[snow lion]

The what now

[heavy canopy]

Is the channel free now?

[ionic jewel]

sure

[teal sapphire]

I had another question

But soya can have a turn I could wait

[shut tartan]

no its my turn

i was next

[snow lion]

;-;

[ionic jewel]

inb4 soya posts a high level question we can't answer

[snow lion]

lmao

[heavy canopy]

I need help with this one

[snow lion]

Oh yeah

Uhm

I got this graph

That's about it

[heavy canopy]

How can I solve it without this graph?💀

[ionic jewel]

oh yeah i have no idea how to do that one, absolute values are annoying

[heavy canopy]

Graph was like the last option

[snow lion]

Like idk man

I've no idea what this is honestly XD

[heavy canopy]

PLEASE THIS IS HIGH SCHOOL LEVEL

[snow lion]

how

[heavy canopy]

Because I'm in high school. I mean this is for my college entrance-

[snow lion]

I'm very confused

[heavy canopy]

I cannot solve it

I'm trying since yesterday

[snow lion]

Idk what it is man

It looks like OR statements

I'm a game dev not a mathmatician lmao

https://www.mathway.com/Algebra

Just try to yeet stuff in here potentially

[stark lantern]

iirc the usual method for such questions would be identifying values of interest(here it would be 0, 1, 2 and -1) and just checking if the derivative exists at those points. I think it should be differentiable at all other points

[snow lion]

Well this is the derivative

I think you've a problem Soya lmao

[stark lantern]

I mean you should find it using the limit definition of derivative to check, not by differentiating

if it turns out that the one-sided limits are equal(and finite) it's differentiable at the point

[snow lion]

Yes I definitely know what you mean

[heavy canopy]

Yes. I found those critical points but Idk how to proceed after that because if I check differentiabiltiy in the usual way, that is LHD and RHD then it would take a hell lot of time

[snow lion]

R u sure about that lmao

[heavy canopy]

🥲🥲

[snow lion]

.

[heavy canopy]

Differentiating it would require a lot of work.

[snow lion]

yip

[heavy canopy]

I'm so confused about this. Sigh

[snow lion]

/s

¯_(ツ)_/¯

[heavy canopy]

😃

[snow lion]

What's with the happy face

[heavy canopy]

It's a broken face. It's like "You know what life is good" but in a sarcastic way.

It just looks broken

[snow lion]

It's just a regular smiley but sure lmao

[heavy canopy]

Please I feel all smile faces look broken😭

[snow lion]

f

Hey at least you don't have to do this

It's not really worse

But still

It's still funny that it's so dumb that it doesn't fit okay lmao

[heavy canopy]

Matrices multiplication?

[snow lion]

ye

It's not hard

It's just a lot

[heavy canopy]

Oh yes I have to do this too lol

[snow lion]

oh fun

[heavy canopy]

It's just a lot of work.

[snow lion]

yea

That's why excel is amazing

[heavy canopy]

But it's easier than my question

[snow lion]

yes

[bitter kite]

is anyone online here?

[snow lion]

for sure lmao

[snow lion]

yes

[clever locust]

6x6 matrices have entered the chat

[ionic jewel]

no

[snow lion]

lol

[clever locust]

maybe

[snow lion]

Oh no

[bitter kite]

heres my problem

[snow lion]

Yours is like rocket science

[heavy canopy]

💀💀

[heavy canopy]

Trust me when I say this is for high school students

[snow lion]

I really don't lmao

[heavy canopy]

You can find the third side and then use Heron's formula

[bitter kite]

wut that-

[snow lion]

Good question

[clever locust]

Can't you just use base * height / 2?

[heavy canopy]

Heron's formula wait

[bitter kite]

i think its a scalene not a right triangle

[clever locust]

You don't need a right triangle for that

[heavy canopy]

Oh wait yeah THATS simple
Sorry. Take out the area of XWZ and subtract the area of XWY

[ionic jewel]

^

[snow lion]

Does this help?

[bitter kite]

ok

[snow lion]

I'm pretty sure it doesn't hold up

[heavy canopy]

Heron's formula is for scalene, actually any triangle

[clever locust]

You have the base of the triangle, which is the side YZ, so 6cm, then you have the height, which is XW, so 9cm, then just use base * height / 2

[bitter kite]

my teacher wanted 0.00 format thing or something like that

[snow lion]

You mean 2 decimals?

[bitter kite]

yes

[heavy canopy]

This helps?

[snow lion]

A = 53.13
B = 36.87
In that case

Not that it helps probably

[heavy canopy]

Why do you all have such simple questions?😭😭

[clever locust]

This is literally all you have to do

[snow lion]

Hey not my problem you decided to study rocket science

[heavy canopy]

It's not rocket science ISTG

[snow lion]

ISTG what

[clever locust]

What's the problem the two of you are struggling with?

[bitter kite]

jow do i get xwy

[ionic jewel]

1/2 b*h

[heavy canopy]

This one

[clever locust]

That problem just seems tedious

But really it just boils down to finding the zeros of x^2-x-2 and x, doesn't it?

Then using the definition there

[heavy canopy]

You have the base, you have the height.

And it's right angled triangle

[bitter kite]

oh yeah, right'

[clever locust]

Because those are the only points where the absolute value can mess it up

[heavy canopy]

Yes I found those points but Idk how to proceed after that

[clever locust]

The definition of the derivative

[heavy canopy]

I searched online and it said modulus changes its definition on 2 and not -1 and I have no idea what that means

[bitter kite]

thanks for that, @heavy canopy

[heavy canopy]

Or how is that possible

[heavy canopy]

No problem!

[clever locust]

I'm on my phone but let me type up the first step real quick so you get what you're supposed to do

[heavy canopy]

Okay!

[bitter kite]

damn my teacher posted another one

this

[north flower]

Line across from left and right corner?

[bitter kite]

hmmm

[north flower]

Yeah now that I think Abt it they would be fully equal

[lilac nest]

That would made the top triangles bigger than the bottom ones I think

[bitter kite]

i agree

[north flower]

Mhnm

Hmm let me see

[heavy canopy]

Wait I think it would be similar

[bitter kite]

but it would make the top one much more taller

[heavy canopy]

Since these are squares and that line would be dividing those squares in half

[heavy canopy]

It just looks like that

I think

[bitter kite]

i know but its much more long-

[north flower]

So the bottom vertex that the line of symmetry runs through, if we make it go directly to the top left so it makes a right triangle. Then from that point go to the midpoint of the bottom right line on the left side

Ill try to draw it

I'm and to geom tho tbf

[clever locust]

So you know that by definition, the derivative at a point $c$ is given by

$$f'(c)=\lim_{h\to0}\frac{f(c+h)-f(c)}{h}$$

Now since you're dealing with absolute values, you have to first find where $x^2-x-2=0$ and where $x=0$, because that's where the absolute value changes based on its piecewise definition. So I'll show you how do to at one of the zeros of $x^2-x-2$. We know that the zeros of this are $-1$ and $2$, so let's consider the derivative at $2$. Then we would have to consider the one-sided limits separately, yielding us

\begin{align*}
f'(2)&=\lim_{h\to0^+}\frac{f(2+h)-f(2)}{h}\
&=\lim_{h\to0^+}\frac{((2+h)^2-1)((2+h)^2-(2+h)-2)+\sin(2+h)-(2^2-1)((2)^2-2-2)-\sin(2)}{h}
\end{align*}

and

\begin{align*}
f'(2)&=\lim_{h\to0^-}\frac{f(2+h)-f(2)}{h}\
&=\lim_{h\to0^-}\frac{((2+h)^2-1)(-(2+h)^2+(2+h)+2)+\sin(2+h)-(2^2-1)((2)^2-2-2)-\sin(2)}{h}
\end{align*}

Then all you have to do is check if these limits are equal

@heavy canopy

[lilac nest]

I think I have it

[clever locust]

Wait that cut off lol

Let me fix it

[lilac nest]

@bitter kite

[clever locust]

That should be right

[bitter kite]

"dividing"

[lilac nest]

It's divided

[ocean seal]

Lorago

[clever locust]

Typing this on my phone was a really bad idea lol

Hopefully it's at least a bit readable

[bitter kite]

but idk if its allowed to be extended

[lilac nest]

Its not

[heavy canopy]

Ahh yess I knew this one. I didnt want to try it cause it would be too complicated. We are basically having a problem with the picewise function.
What I did was I let the the whole modulus thingy be h(x) and sin|x| to be g(x) Then I started solving h(x) separately @Lorago#9459

[ionic jewel]

you typed that on ur phone? what a legend

[clever locust]

Also did y'all start discussing other problems while I was typing that up?

[bitter kite]

yes

[heavy canopy]

Wow-

[lilac nest]

Go on #help-5

[bitter kite]

ok

[clever locust]

It's actually not as bad as it looks. You start off with a really annoying expression but a lot of terms should simplify right away since you're plugging in numbers for x from the get go

But yeah, just as you said the problem is it being a piecewise function

[bitter kite]

@heavy canopy am i correct?

[clever locust]

Which might not be clear immediately

[clever locust]

?

[heavy canopy]

Yep

[bitter kite]

thx

[heavy canopy]

You typed that all on your phone

[clever locust]

Yes, and I had to fix it a bunch of times because of that lol

[north flower]

This is so late

Could this work?

[clever locust]

Just woke up so it might not be the best

[heavy canopy]

Also one last question, we don't really have a problem x^2+1 ? It's basically the modulus function that's troubling us?

[lilac nest]

@north flower we found the solution, it's in #help-5

[heavy canopy]

*x^2-1

[north flower]

Alr

[clever locust]

Yeah exactly, for that one everything should be fine

Since it's already differentiable everywhere

And not piecewise defined

[heavy canopy]

Oo alright. I got it. I'll solve it further. Thank you!

I'll let you know.

[shut tartan]

The Toronto Maple Leafs have a 35% chance of winning their next hockey game, while the Montreal Canadiens have a 65% of winning their next game. The probability that they both win their next hockey game is 15%.

Benny was asked to draw a Venn diagram that reflects this scenario. His sketch is below.

Is Benny correct? If not, identify is error or errors and then create the correct Venn diagram.
the image is a venn diagram with 2 circles, left circle is 35% middle is 15% and the right circle is 65%

HELP ME

[clever locust]

Sounds good

[shut tartan]

HELP ME HOMIE

[clever locust]

Nah I'm going to have breakfast

[heavy canopy]

Wait I think I got ir

*it

Okay so @shut tartan

Benny is not correct

Basically subtract 15.

Id really know how to explain myself

[bitter kite]

If Bob ate my Pizza, how many miles will John run if my sister did the dishes?

[heavy canopy]

But its something related to A U B= A+ B- A N(intersection)B

[tight locust]

U

[merry coral]

👍

[merry coral]

answer is always 7

[bitter kite]

correct

[teal sapphire]

Hello how would I find a angle that is formed from two vectors ?

[ionic jewel]

dot product of two vectors is |a|*|b|*cos(theta)

[teal sapphire]

Vector v is <-12,5>

And vector w is <3,10>

[alpine sable]

use dot prod

[ocean seal]

ajuze

[teal sapphire]

Let me try and figure it out on notes

Would I have to figure out the magnitude for each vector ?

[ionic jewel]

yes

[icy trail]

if you have three numbers, 1, 2, 3
how many ways can you arrange them into 4 boxes, using all three numbers at least once and one number twice?
e.g. 1123, 1213, 2213 are all allowed but 1113 is not
i think i have an answer, not sure if it's right tho

[mellow hatch]

u got 18??

[icy trail]

no i got more than that

[merry coral]

3! * 3

would not account for everything

[icy trail]

i did
3! * 4 choose 2

[mellow hatch]

3 x 3 x2 shud be the right one..

[mellow hatch]

yes

[mellow hatch]

4 choose 2 why?

[icy trail]

because there's that many ways to choose where the two repeated numbers go

but actually

that would count things twice?

[mellow hatch]

don't overthink..
Just put 4 boxes
Count how many ways u can place those numbers in first box
then do for the second
similarly for 3 and 4

[merry coral]

actually I think it is 3! * 3

[mellow hatch]

thats correct I guess

[merry coral]

lets do it with 2

a b b

a a b

a b a

b a b

[icy trail]

this is a different question?

[merry coral]

2! * 2

[icy trail]

n! * n maybe

[merry coral]

lets do it with 1

a a

1! * 1

[merry coral]

think so

with 0:

0!*0

[ionic jewel]

0! = 1, but that doesnt really matter

[mellow hatch]

generally , if u have n numbers , n+1 spaces , with the condition
n ways to put the number in first box
n ways again to put the numbers in second box (2nd repetition)
n-1 ways to put the number in third box
n-2 ways in next box
so on... upto 1
so simplifying will give us n! x n

[merry coral]

wait thats confusing

lol

[lilac hazel]

Where can i ask someone for help

[ionic jewel]

literally any channel without an active conversation

[merry coral]

paradox

[lilac hazel]

Oh so not here?

[merry coral]

here lol

[mellow hatch]

not a big thing.. because u have no number and only 1 space , u can't really place twice of the number

[lilac hazel]

just part b

If someone could explain it, that’d be great

[ionic jewel]

whats the answer to a

[lilac hazel]

n^2 + 2

[ionic jewel]

p^2 + 2= 123,
p^2 = 121
p = 11

(11)^2-2(11)-120 = 121 - 22 - 120 not 0

[mellow hatch]

is that right?

[ionic jewel]

guess i went wrong somewhere

[lilac hazel]

yeaa

[mellow hatch]

I get n^2 - 2n + 3

[ionic jewel]

n^2+2 seems to work assuming u start at n=0

[lilac hazel]

yep

[mellow hatch]

oh kk

[lilac hazel]

I literally cannot wrap my head around that question

Part A and C were easy

B messed with my head fsr

[mellow hatch]

then u should use p-1 right?

not p

u'll get 12 (sorry i got p-1 = 11)

[ionic jewel]

100-20-120 is also not equal to 0

[lilac hazel]

Yea

[ionic jewel]

,w p^2-2p-120=0

[ocean seal]

Results provided by WolframAlpha

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

Requested by 兔子#6562

[ionic jewel]

12

[lilac hazel]

Yea i got that for part C

[ionic jewel]

so you have to shift it the other way

[lilac hazel]

wdym

[mellow hatch]

p-1 = 11

[ionic jewel]

^

[solid ocean]

what is the objective function of the support vector machine with logsitc

[lilac hazel]

huhh

[mellow hatch]

substitute p-1 instead of p

p = +/- 11 + 1

[lilac hazel]

p^-1? or p^1?

[mellow hatch]

p-1 , since u assumed the first term n to be = 0 , not powers of p

[lilac hazel]

Oh yea tru

i think i get it now

Should we factorize it

Or did i confuse myself again

[mellow hatch]

don't confuse .
For them pth term = 123 , but for us , we have assumed n = 0 , pth term = p-1 th term
substitute p-1 in n^2 +2 and equate it to 123
get the value of p

then substitute in the given quadratic

thats how u prove it

[lilac hazel]

oh makes sense

Yeayea

thanksss

So simply find one of the P terms, substitute it into the given equation, and show how it equals 0

finally

@mellow hatch thanks mate

adios

[spring elm]

im not quite sure how to solve this lol

[ionic jewel]

5 oz = 91.7% of the total

[mellow hatch]

welcome dude!!

[spring elm]

can you explain how u came to that conclusion

[jovial knoll]

hey

anyone know how to solve this

0, 5, -3, 5, -3, ?, 4, 3, 8, -4, 1, 3, ?, 7, 9, 6, ?, 8, 2, 3, 3, 5, 4, 7, 9

[vague coral]

is it a sequence or something ?

[jovial knoll]

the pattern is hard as fuck to find

idek

[vague coral]

hmmm hard patterns

[jovial knoll]

yep

i tried everything

this is something that requires you to think outside the box

[vague coral]

at the second question mark its 5

[ionic jewel]

oh good poinit

thats wrong

[spring elm]

yea i was a bit confused haha

[ionic jewel]

its (75%)*(5 oz) = 91.9% (of the 22carat mixture)

[ionic jewel]

the best part about sequences is you can make it be whatever you want

[vague coral]

^

[gaunt wedge]

lmao

[jovial knoll]

yep

[spring elm]

how would i find how much pure gold is mixed in though

[gaunt wedge]

91.7 no?

[ionic jewel]

okay here

we have 5oz of 18 carat gold

that means its 3/4 * 5 oz of gold

15/4

and 5/4 oz of not-gold

we want the ratio of gold/total stuff = 0.919

(15/4+x)/(15/4+x+5/4) = 0.919

,w (15/4+x)/(15/4+x+5/4) = 0.919

[ocean seal]

Results provided by WolframAlpha

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

Requested by 兔子#6562

[ionic jewel]

add 10 oz of gold I sps

[spring elm]

ohhhh okay thank you so much

[delicate mango]

i got gf(x) = x-5 for b

but for c, i thought it was {x|x ∈ ℝ}
but it is {x|x ≤ -√5 or x ≥ √5, x ∈ ℝ}

why is that

[alpine sable]

Hello

Can someone help me

[gleaming granite]

for part c it asks for f(g(x))

[quaint trout]

@delicate mango fg(x) = sqrt(x^2-5) and you cannot take the sqry of a negative number, so you need x^2-5 >= 0

[delicate mango]

ohhh so the square outside of sqrt doesnt cancel the sqrt ?

[quaint trout]

I don't understand what you mean

[gleaming granite]

no there are two terms (x^2) and (5) seperated by a minus sign

[delicate mango]

6×85+4?

[delicate mango]

i still cant make sense of this

[quaint trout]

What do you think fg(x) is if not what I said?

[delicate mango]

oh wait

i got ittttt

omggg

i thought it was gf(x)

alrighttt thanks @quaint trout @gleaming granite

[quaint trout]

@delicate mango hold up

Even if it were gf(x), the range would not be R

[delicate mango]

it is... because its a linear function

[quaint trout]

It would be {x in R: x >= 2}

It is a linear function, but it is a linear function on this domain.

[gleaming granite]

[quaint trout]

When you find gf(x), you are right that it simplifies into a linear function. But by the definition of gf(x), you must first be able to put x into f and then put f(x) into g.

[delicate mango]

wait that means you have to take the domain of gf(x) from the range of f(x) only?

[quaint trout]

Since f is only defined for x >= 2, you cannot put a smaller x into f

[flint ocean]

wannna play minecraft join this SpaceCraftCity.aternos.me join this too https://discord.gg/aCz8SrBGAJ

[quaint trout]

dom(gf) = {x: x in dom(f) and f(x) in dom(g)}. Normally you have that f(x) is always in dom(g), then it becomes dom(gf) = dom(f)

[delicate mango]

i see

if its fg(x) then the domain should be in g(x) rite

[quaint trout]

I don't understand what that means

[delicate mango]

if its fg(x) then the domain should be in the range of g(x) right

[quaint trout]

The domain should be a subset of the domain of g

The range of g is only relevant in that you need the image of that subset to be contained in the domain of f

[delicate mango]

ohh i got itt

thank youu

[vague nova]

im in university for engineering and i cant figure out what DF is for the second triangle

worst moment of my life

is it 6 or 4?? i think its 4

would u solve it by finding AC by adding AF with FC to get 6 and then know that 6 is 1/2 of 12 therefore DF is double AF which is 4

[gray isle]

,rotate

[gray isle]

printer issues?

[vague nova]

a friend on disc sent me it like that i tried to explain it to him

im pretty sure its a cutoff 2

for AF

[gray isle]

yeh, it'll be 4

[vague nova]

thank you !

[alpine sable]

how do i work this out?

The price of the computer is $1550 including 10% GST.
The amount of GST paid when purchasing this computer is closest to:

im really having trouble with these financial questions

[gray isle]

let the base price of the computer be x,
express the gst in terms of x
express the total price in terms of x
solve for x

[alpine sable]

wait

what?

[vale wigeon]

have you done any algebra before?

[alpine sable]

yeah but its just abit confusing since we dont really use that much algerbra in financial arithmetic

what is did was 10% of 1550 which is 155

but apparently thats wrong

because b is the correct answer

although wouldnt 10% of 1550 just be the amount of gst

idk

[quaint trout]

What they mean is that you are paying 10% on the original price

So if the price without GST is X, you are paying 10% * X in GST

They are not saying that 10% of the final price is GST

Do you understand the difference?

[alpine sable]

i didnt say $10 is the final price did i?

[quaint trout]

It was a typo, which I corrected

If you want to be snarky, I can go

[alpine sable]

oh oki

nono i was just confused

[quaint trout]

Okay

[alpine sable]

lmao wasnt being snarkey

[quaint trout]

Sounded that way a little

But it's fine

Do you understand the difference?

[alpine sable]

the price without GST would be 1550-155?

[quaint trout]

No

You are assuming that the GST is 155

Which is wrong

[alpine sable]

oh

[quaint trout]

Let me give an example

Let's say an apple costs $4 without tax, but tax is 25%

Then 25% of $4 is $1, so with tax the apple costs $5

[alpine sable]

yes

[quaint trout]

But 25% of $5 is not $1

That's because the tax percentage is given on the original price, not the price with tax

[alpine sable]

alright

but this doesnt give original price

[quaint trout]

Yes

[alpine sable]

its with 10% gst included

[quaint trout]

@delicate mango ask elsewhere

@alpine sable yes, so you need to think a little.

[alpine sable]

oh im sorry

[delicate mango]

alright

[quaint trout]

If I tell you that something costs $100 and you need to pay 20% in tax

How much does it cost with tax? And how do you work it out

How you work it out is the important part

[alpine sable]

5?

ahh idk

1 min

[quaint trout]

Okay

Ping me

[alpine sable]

let me try and figure it out

[quaint trout]

I want to know, if I give you a price without tax and I give you a tax percentage, how do you work out the price with tax?

[alpine sable]

20?

$20?

[quaint trout]

Okay

So how did you work that out?

[alpine sable]

well

100/20

=5

100/5=20

[quaint trout]

Why do you do 100/20?

I don't get it

[alpine sable]

idk

just though 100

and 20

100/20

thought*

[quaint trout]

If something costs X dollars and you have to pay r % in tax

Remember that r % means r/100

[alpine sable]

ohh

yes i remember

[quaint trout]

Then the tax is X * r / 100

Does that make sense?

So the final price is X + X * r /100

[alpine sable]

wait

what is X though

[quaint trout]

.

[alpine sable]

so x here would be 1550

?

[quaint trout]

I am not looking at your problem specifically

No

1550 here is the price with tax. X is the price without tax.

[alpine sable]

ok

see this is the problem

i dont know how to get the price without tax

[quaint trout]

I am explaining it to you

But you are ignoring my explanation lol

[alpine sable]

no im not

i just dont understand it

[quaint trout]

Well, that's what I'm asking

[alpine sable]

when you say here

i literally have no idea what you mean

[quaint trout]

Did you understand the previous part where I said the tax is X * r / 100?

[alpine sable]

is r=to rate or in this case GST?

[quaint trout]

r is the tax percentage

[alpine sable]

yes ok

so 10%

[quaint trout]

So if it's 20% then r is 20

If it's 10% then r is 10

[alpine sable]

yes

ok i get that part

[quaint trout]

Well

Price with Tax = Price without Tax + Tax

Price without tax is X

Tax is X * r / 100

So Price with Tax = X + X * r / 100

Does that make sense?

[alpine sable]

so for the question im asking

its

X * 10/100

[quaint trout]

The tax is yes

And the price with tax is?

[alpine sable]

so how do we find X

ohhh ok

[alpine sable]

hmm idk

[quaint trout]

what

You still haven't told me if you understand this part. I need you to confirm every time when I explain something if you understand it

[quaint trout]

.

[alpine sable]

no

as i said i dont understand what the X is or how to get it

[quaint trout]

The X is the price without tax.

[alpine sable]

maybe be we can use my example so i can understand it?

yes i know its the price without tax but idk how to get that

at the beggining i thought it was just 10% of the principal

[quaint trout]

You don't need to know what X is yet. You need to understand the formula.

[alpine sable]

but its not

then yes i understand the formula

but just not how to get X yet

[quaint trout]

Can you see that I can factor X out of X + X * r \ 100 to get X* (100+r)/100?

[alpine sable]

hmm

ok so

from this example

[quaint trout]

$X + X \times \frac{r}{100} = X \times \frac{100}{100} + X \times \frac{r}{100} = \frac{100X + rX}{100} = X \times \frac{100+r}{100}$

[ocean seal]

Lunasong the Supergay

[alpine sable]

it would be

1550/1.1=1409

1550-1409=141

right?

[quaint trout]

Yes

[alpine sable]

ok

[quaint trout]

Final Price = Initial Price * (r+100)/100

Initial Price = Final Price * 100 / (r+100)

I was trying to derive these 2 formulas for you

[alpine sable]

oh

i just thought of it as

Cost without GST = Cost with GST/1.1

and cost with= cost without x 1.1

vice versa

[quaint trout]

Yes, 100/(10+100) = 1/1.1

[alpine sable]

yay

thanks Lunasong the supergay

for teaching me*

[quaint trout]

np

[alpine sable]

sorry my engish is bad

[quaint trout]

It's okay

[alpine sable]

still learning

oh really?

thanks!

[quaint trout]

:)

[alpine sable]

🙂

eww ok thats creepy

i may have more questions but well see

(on different stuff)

[quaint trout]

Lol

[heady karma]

please somebody help

I barley studied angles

[hollow owl]

$f(x) = (\sqrt (x^2 + 1 ) -1) / x$

[vale wigeon]

$f(x) = \frac{\sqrt{x^2+1} - 1}{x}$

[ocean seal]

Ann

[vale wigeon]

did you mean this?

[hollow owl]

yes

[vale wigeon]

did you just decide to post this function here for fun?

[hollow owl]

no

now I write my quastion

[vale wigeon]

okay

[hollow owl]

I need to find lim when x=0

[vale wigeon]

okay

and have you made any progress on that front?

[hollow owl]

yes I move x outside of the sqrt

[vale wigeon]

you... what?

[hollow owl]

x*sqrt(1-1/x^2)

[vale wigeon]

?!

okay, did you mean x * sqrt(1 + 1/x^2)?

as in, you rewrote just the root as this?

[hollow owl]

yes

[vale wigeon]

this is going to be useless in your scenario

can i suggest multiplying & dividing by the conjugate instead?

[hollow owl]

sec let me try

[vale wigeon]

@keen citrus channel busy please move

[keen citrus]

oh

srry

sorry

[vale wigeon]

@hollow owl yes this is correct, now you can plug in x=0

[hollow owl]

(0/2) = 0

I did it correct?

did x=0 is discontinuity?

[vale wigeon]

yes you are correct, the limit is 0

[hollow owl]

Removable discontinuity

[vale wigeon]

your function had a removable discontinuity at x=0 yes

[hollow owl]

thanks!

[subtle mantle]

Biot-savart law moment

[alpine sable]

???

[subtle mantle]

It’s how you find the magnetic field produced by a closed loop of wire

Anyway

Finding y in terms of x

You know the total length right?

[alpine sable]

yes

[alpine sable]

2m

[subtle mantle]

Ok, so if you calculate the total length in terms of y and x using the formula for the circumference of a semicircle and then adding on the 3 sides of a rectangle, you know that has to be equal to 2m

[alpine sable]

idk what you mean

wait

[subtle mantle]

There’s derivatives in the question bro I KNOW you know how to find the perimeter of a semicircle

[alpine sable]

yes

sorry i didnt understand

yes

[subtle mantle]

It’s alright dw

[alpine sable]

im just stuck on the first one

[alpine sable]

bye 😫

[subtle mantle]

?

[alpine sable]

help me when?

[subtle mantle]

I am currently helping you.... lol....

[alpine sable]

ok

[alpine sable]

thanks, idk what to do next