help-0

[hidden fable]

you just write in LaTex

it's a type of software to make documents. (usually related to math/science, since it allows you to add formulas and such)

[wanton tusk]

it’s so confusing 😭

but I’ll try to understand it

[hidden fable]

https://discordapp.com/channels/268882317391429632/840667252793802752/882140079672418305

https://www.learnlatex.org/

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[timid brook]

Hi! can anyone help me with this homework of mine?

[wanton tusk]

AUB means everything in A and B

A intersecting B means everything that’s common between A and B

A-B = elements in A that not in B

[wanton tusk]

B-A same concept

A’ means everything that’s not in A

B’ everything that’s not in B

[timid brook]

ohh ok thank you!

[timid brook]

for the A intersecting with B, is the middle numbers included?

[wanton tusk]

yes it is only the middle numbers (:

bec that’s what common between A and B

[timid brook]

ok thank you!

[timid brook]

for the complement, you mean everything especially the numbers outside and the middle numbers?

[wanton tusk]

not the middle numbers

bec they’re inside A as well

for A’ we want the numbers outside and the numbers inside B

[timid brook]

ohh ok thank you!

.close

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✅

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[silk pelican]

When doing Pythagorean theorem, can you have a negative. Say im given the values x = -2 and y = square root 3, would I be left with -1 or 7?

[rose sigil]

I kinda want to say no to both of those but... more detail?

[silk pelican]

What do you mean?

[rose sigil]

what exactly are you asking should be -1 or 7?

[silk pelican]

If im given an x value = -2 and a y value = square root 3 and I am looking for r, I have to do Pythagorean theorem.

So when I do

Does the -2 stay negative and my solution becomes -1?

Or does it become positive and my solution becomes 7?

[wanton tusk]

have a pic?

[rose sigil]

the length of the line connecting (-2, 0) and (0, sqrt(3)) is sqrt(7), not 7

[wanton tusk]

yep

the base will be -ve here

[silk pelican]

Okay, thanks.

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[silk pelican]

Hi, if I have the equation -6x - y = 0 and know x < or equal to 0, it would be in quadrant 3?

[alpine sable]

well do you know what the original equation looks like?

ie solve for y

y = -6x does not lie in quadrant 3 or 1 btw...

[silk pelican]

All im given is what I told you. It is my terminal side and I need to graph and find all trigonometric functions

And im a bit confused

[alpine sable]

ok so, the graph looks like this

and we want to see where values for x<=0 lie

we just look to the left of the y axis, and see the line goes through quadrant 2

remember, quadrants are counterclockwise from top right if you were confused on thjat

[silk pelican]

So would my graph look like this? And then for my trigonometric functions, say for csc, it would be - square root 37 over 6?

[alpine sable]

ohh your doing triangles and stuff i see

[silk pelican]

Yeah I am a bit confused about what your messages above mean

[alpine sable]

ignore those i thought you were asking something esle

[silk pelican]

Okay

[alpine sable]

im still not sure what you mean by -6x -y = 0

do you mean -6, -1?

something like this?

[silk pelican]

Thats whats asked of me

[alpine sable]

do you have picture of question by chance unless what you wrote is the exact wording

[silk pelican]

Yes I will send the exact wording

Sketch the least positive angle ø and find the value of the specified trigonometric functions of ø if the terminal side of an angle ø in standard position is defined by -6x - y = 0, x< or equal to 0

@alpine sable

[alpine sable]

since x < 0, we try x=-1

so
-6(-1) - y = 0
y = 6

so our point is (-1, 6)

we know that r = sqrt(x^2 + y^2)

we solve for r with our given point

[silk pelican]

ty

I get it now

[silk pelican]

wait hold on, so did you get positive 6 because you moved 6 to the other side?

[alpine sable]

i moved the y

and -6 * -1 is positve 6

[silk pelican]

Okay, ty

[alpine sable]

yea once u get r you know that
sin(theta) = y / r
cos(theta) = x / r
and tan(theta) = y / x

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[lost coral]

whats wrong here?

[rigid smelt]

the mistake was that you assumed sqrt(x^6)=x^3, this is not always true

it's true for positive x, the limit is not going to a location where x is positive

[lost coral]

sorry i dont understand what your say

[lost coral]

what do you mean?

(-1)^3 = -1

[rigid smelt]

what i'm saying is, yes sqrt(x^6)=|x^3|, now you just need to break up that absolute value according to your limit

[lost coral]

sorry im getting confused

give me a sec

-x^3?

ow okay

thank you

.close

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[nimble mulch]

how do I do this

[nimble mulch]

I tried simplifying it but cant eliminate u and q

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[last tangle]

how would i motivate that $max(a+b,c+d) \leq max(a,c) + max(b,d)$ ? it makes sense to me intuitively but i can't come up with a proof

[ocean seal]

Rœmer

[last tangle]

or is it just checking cases?

a,b,c,d being positive real numbers btw

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[lavish pier]

Could someone help me with 14b I’m a little confused

[vale wigeon]

draw a rectangle on paper

and think about what the largest circle that can fit inside it will look like

[lavish pier]

So the area of the rectangle is 619.5 cm

And I tried doing this equation

[vale wigeon]

no, the area of the rectangle is not 619.5 centimeters,

[lavish pier]

619.5 = r^2 *pi

[vale wigeon]

and also this does not answer my question at all

you did not do what i asked you to do

i suppose that i did not ask you to show the results

but it would be nice if you showed the results

or admitted that you didn't do as i asked

[lavish pier]

Woke up on the wrong side this morning?

[vale wigeon]

ok, this is a little crude but it will do

do you see how this circle touches two opposite sides of the rectangle?

[lavish pier]

Yes

[vale wigeon]

do you see how the width of the sheet is in fact the diameter of this circle?

if the circle were any larger then it would not fit on the sheet.

[lavish pier]

So

10.5

Would be the radius of the largest circle

That can possibly fit in this paper?

[vale wigeon]

yes

10.5 cm

[lavish pier]

Ok

Thank you

[vale wigeon]

and the area of your sheet, by the way, surely ought to be 619.5 cm**^2** and not 619.5 cm

[lavish pier]

Yep

Well if I said area surely you would assume I mean cm ^2

Attempted 14d but got 78 percent instead

@vale wigeon

[vale wigeon]

what did you get for the area of the circle and for that of the sheet?

[lavish pier]

So for the circle I got 346.36

Cm^2

[vale wigeon]

,calc pi * 10.5^2

[ocean seal]

Result:

346.36059005827

[vale wigeon]

and for the sheet?

[lavish pier]

And for the rectangle sheet I got 619.5 cm ^2

[vale wigeon]

,calc 29.5 * 21

[ocean seal]

Result:

619.5

[vale wigeon]

,calc 346.36/619.5

[ocean seal]

Result:

0.55909604519774

[lavish pier]

Oh

I subtracted them to get the area of the outskirts

Because I thought that was the new total area of the shape

Because the circle overlaps the rectangle

@vale wigeon

Completely confused on question 15b

<@&286206848099549185>

[vale wigeon]

draw it out

draw the original square, then mark the midpoint on each side, then connect those into a smaller square, then find that square's area

[lavish pier]

Yeah

I did do that

Is the next square going to be half of the current squares area

@vale wigeon

[vale wigeon]

yes, and this it not hard to prove.

[lavish pier]

What about f and g

I did f and I got 12.5 percent could you correct me if I’m wrong

[vale wigeon]

it's 1/8 of the original square's area so yes you are correct

[lavish pier]

And g I’m not exactly sure how they get 1000 cm 2

@vale wigeon

<@&286206848099549185>

<@&286206848099549185>

[vale wigeon]

you should not ping helpers twice

or do YOU want to be spammed with pings

anyway

hang on

somethings wrong here

the area of the red square is 800 cm^2

[lavish pier]

That’s what I’m proposing

[vale wigeon]

how can the total area of the red regions, which form a subset of this square, be greater than that?

[lavish pier]

Then I read it again and I saw combined figure

But even with the additional you would get 1400

Maybe a typo in the book

But I doubt they would add such an easy question like that if it was 800

@vale wigeon

[vale wigeon]

what else do you want me to say here

[lavish pier]

Is it a typo or something else at play

?

[vale wigeon]

as far as i can tell it's a typo or other gross error

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[lavish pier]

May someone help me with this question

[lavish pier]

For a i got 3.39 but I’m not sure if I’m correct or not

And for b I got 1.63

Could someone correct me if I’m wrong and show me the way

<@&286206848099549185>

[wind cloak]

Do you know the formula

For the area of a sector

Yes I will help you even though I'm not in the mood xd

[worldly spear]

its not

the formula is Area= r^2 * α/2

which α is in radians

a) u need to turn degree to radians, then put them in formula. r gives the answer

[wind cloak]

You can just do $\frac{\theta}{360^{\circ}}$ instead of radians right?

[ocean seal]

NEONPerseus

[worldly spear]

they are not the same i guess

for the b) part you need to use the formula of arc length which is L = r * α

then use it in Area formula

@lavish pier

α must be radians

if u need better explanation tag me

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[lavish pier]

What I’ve never learnt that also it gives us the angle not radian

[worn fox]

<@&268886789983436800>

[worldly spear]

ok then you can use (angle/360) * π * r^2 for area

and for arc length you have (angle/360) * 2 * π * r

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[woven gull]

4x + 2y = 116

[unborn warren]

2x+y=58?

[woven gull]

wait we need 2 eqns

[unborn warren]

yeah

[neon scarab]

Look at the final goal. We need the number of animals.
So in (a), we should start from considering these number as our main variables.

Let p = number of pigs, c = number of chickens

First sentence: Total of the two combined is 35
so p + c = 35 … (1)

2nd sentence: Combined they have 116 legs.

This can get a bit tricky.
We need to consider that,

• Each pig has 4 legs. If we have p count of pigs, then count of pigs’ legs is 4p

• Each chicken has 2 legs. Count of chicken legs is then equal to 2c.

Hence 4p + 2c = 116 … (2)

(1), (2) gives you the equations for answering (a).

And solving them in (b) is algebra work, should not be as hard as figuring the equations out 😄

[woven gull]

sheesh

ok man

[unborn warren]

so for a

its

p+c=35

and

[woven gull]

12 chickens

and 23 pigs

[unborn warren]

4p + 2c = 116

[unborn warren]

how do i show working out for that tho

with algebra

[woven gull]

just solve it by substitution'

[unborn warren]

wdym

[woven gull]

substitute p in 2nd from 1st

wait lemme post a pic

[unborn warren]

kk

[woven gull]

put c in 1st equation

p=23

[unborn warren]

ty

i got it now

[woven gull]

k

[unborn warren]

.close

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[alpine sable]

who can help with physics

[chilly shore]

oof sorry

[alpine sable]

A train travels at a speed of 15m/s before increasing its speed and accelerating by 0.25m/s^2 over a distance of 300m. How long does the speed change take?

[karmic solstice]

I need science help too lol

[woven gull]

lol\

[chilly shore]

How about using the kinematic equations?

[alpine sable]

yea but i still dont understand

[chilly shore]

Given:
Vo (initial velocity) = 15m/s
a (Acceleration) = 0.25m/s²
So (initial distance) = 0
S ( Final distance) = 300 m

use the formula : S-So = Vot + 1/2 at²

[neon scarab]

$s = ut + (1/2)(at^2)$
You have the displacement, initial speed, and acceleration already. The problem then becomes a standard quadratic equation solving.

[woven gull]

what's the question?

[ocean seal]

jimmy1234

[chilly shore]

Yep

[karmic solstice]

Help me with Chemistry?

[wanton tusk]

HAHA ur pic is saved in my gallery

[karmic solstice]

Lmao

[woven gull]

its comes out to be quadratic equtn

[karmic solstice]

I sent the wrong question

[woven gull]

$t^2+120t+1600

[karmic solstice]

How name?

[woven gull]

?

im too far ffrom chemistry lol

br means bromine right?

[wanton tusk]

wha-

[karmic solstice]

Yes.

[wanton tusk]

hmmmm

[woven gull]

what u wanna calculate?

[karmic solstice]

What is the name of that compound?

[woven gull]

lol

too hi-fi for me

[wanton tusk]

I forgot everything already HAHAHA

[woven gull]

xD

[karmic solstice]

It’s ok

[wanton tusk]

OH

I think I got it

1-bromo-2,4,4-trimethylpentane

wait

idk if that’s right but I tried HAHAH

[woven gull]

holy shit

what's that?

[wanton tusk]

it’s organic chem iirc

[woven gull]

tri-meth-yl-pen-tane?

[wanton tusk]

yepp

[woven gull]

gets nervous

[wanton tusk]

those are the substituent grps and stuff

[woven gull]

looks like complicated stuff

[wanton tusk]

😭😭

I need to know this for my exams

[woven gull]

lool

[karmic solstice]

I don’t have answer.

I hate this topic bruh

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[silent sage]

I don't understand this. step. From what I know, all even powers of f(x)=sinx had the same range,

[bronze oracle]

Sorry

[silent sage]

No, I am sorry.

[neon scarab]

$\sin^2 \theta$ is a decimal btw 0 and 1. Since $\sin^8$ has more decimal factor than $\sin^2$, we then can claim that LHS $\leq$ RHS.

[ocean seal]

jimmy1234

[silent sage]

Ahhh...

wire

That makes perfect sense.. Thank you for your time and assistance.

.close

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[alpine sable]

Not sure where to start here

[alpine sable]

Completely forgotten everything over the summer haha

[woven gull]

lol

find some solutions for the equation

then plug it into equations and find k

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[wanton tusk]

can mayb try making y the subj of the 2nd eqn and sub that into the first eqn,, then discriminant = 0

[alpine sable]

Go it, thanks @wanton tusk @woven gull

.close

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[alpine sable]

14: Suppose that 55% of all adults regularly consume coffee, 45% regularly consume carbonated soda, and 70% regularly consume at least one of two of these products. a) What is the probability that a randomly selected adult regularly consumes both coffee and soda? b) What is the probability that a randomly selected adult doesn't regularly consume at least one of these two products?

[alpine sable]

I'm pretty sure I have my answer, but I want to double check

for a), we are given the Coffee union Soda = 70%

This is P(Coffee) + P(Soda) - P(Coffee intersect Soda)

As we know that the probabilities add up to 100%, the intersect must be 30% - meaning 30% of people consume both coffee and soda

[alpine sable]

for b) This is given by the "70% regularly consume at least one of two of these products", wouldn't that just be another 30%?

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[alpine sable]

I pirated a solutions manual and it had nothing for this either. Just want to be sure I'm not goofing up

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@alpine sable Has your question been resolved?

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[mortal river]

Hey quick question about 18 and 19

[mortal river]

Would these shaded regions and graphs not be identical? Just with 18’s graph having a range from 0-1 and 19’s having a range from 0-infinity?

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[meager vapor]

Given secant of theta is equal to the square root of 10 over 2, what is cos?

[lone heart]

@meager vapor Has your question been resolved?

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@meager vapor Has your question been resolved?

[blissful whale]

1/sec = cos

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[worthy solstice]

How do I find the limit of this as x approaches from the left of 3, right of 3, and from either side of 3?

[worthy solstice]

If I sub in 3 for x in the denominator I get an output of 0

[rustic coral]

Hint: $|x|=\begin{cases} x, x \geq 0 \ -x, x<0 \end{cases}

[ocean seal]

messy circle creation
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[rustic coral]

Use that to ||rewrite the denominator|| without the absolute value for each of the limits individually

[worthy solstice]

hmm

I still don't think I get it. The hint means that depending what number I sub into the denominator I'll get

1. number greater or equal to 0
2. if its negative I'll get an output that's less than 0

right?

[lone heart]

@worthy solstice Has your question been resolved?

[rustic coral]

yeah, note that by the same logic, $|x-3|=\begin{cases} x-3, x \geq 3 \ \ -(x-3), x<3 \end{cases}$

[ocean seal]

messy circle creation

[rustic coral]

meaning that as you approach $x=3$ from the right, $|x-3|=x-3$, and as you approach $x=3$ from the left, $|x-3|=-(x-3)$.

[ocean seal]

messy circle creation

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[digital steeple]

What kind of differential equation is this?

[digital steeple]

i can tell its a bernoulli substitution candidate at first

But that will lead to y getting negated from 3, and most Bernoulli depends on it if im not mistaken (since we pick that define our V, unless we can define V as 1)

[abstract fractal]

Isn't it seperable

[digital steeple]

I mean, yea it is

is any separable equation also linear?

[abstract fractal]

I don't think so necessarily

But this one looks linear

[digital steeple]

how do you tell its linear?

i remember its

y' + f(x)y = q(x)

[abstract fractal]

Subtract y √x from both sides and factor out a y

[digital steeple]

y' + y(3-root(x)) = 0

not further separable

so i dont think its linear

[abstract fractal]

Why not?

f(x) = 3 - √x

q(x) = 0

[digital steeple]

._.

i can define q(x) as 0

right...

yea that comes up often sure

thank you a lot for that clarification

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[wicked tree]

can someone help?

[abstract fractal]

Show your work

[wicked tree]

oh I integrated in my head

cos thats 5y-80

[abstract fractal]

5y - 80

Not 5t - 80

[wicked tree]

doesnt work either

[abstract fractal]

That's not how you solve a seperable differential equation

[mellow tusk]

but its y(t) so ig its t only

[abstract fractal]

If I said y' = y, that wouldn't mean y = y²/2

[wicked tree]

ohh

would that be 1/2y^2 = 5/2y^2-80y+C?

[abstract fractal]

No

https://youtu.be/DL-ozRGDlkY

[wicked tree]

hmmm

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[quartz pawn]

Here's the question

[quartz pawn]

How can I analyze the confidence interval and the hypothesis test to determine if I should reject H0 or not?

[lone heart]

@quartz pawn Has your question been resolved?

[quartz pawn]

<@&286206848099549185>

[lone heart]

@quartz pawn Has your question been resolved?

[solemn juniper]

If the value specified in H0 is not within the confidence interval, you reject H0 at that confidence level

[quartz pawn]

So H0 is 0
population mean is at minimum 0.0003
Also the p value is less than the significance level

So in this case I reject it because both the hypothesis test and the confidence interval both show there is insufficient evidence?
@solemn juniper

[solemn juniper]

You can reject it with either result, since one implies the other

If the interval contains the value in H0, the test will never reject

[quartz pawn]

Now with the normality assumption, given that my sample size is 80, do I need to be concerned about the normality assumption?

[solemn juniper]

Not really

[quartz pawn]

Why? What would give me reason to be concerned about it?

[solemn juniper]

Well for one, you're using the t distribution anyway, which mostly bypasses the need to worry too much about normality

But your sample size is large enough either way, you could use a z test and likely get the same result

[quartz pawn]

In a case that I would need to be concerned about normality?

Would that be if the data was heavily skewed in any way?

Or if the sample size was a small number?

[solemn juniper]

The smaller the sample size, the less safe you are

[quartz pawn]

Makes sense

Ok, thanks a ton ❤️

[solemn juniper]

Np

[quartz pawn]

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[latent patrol]

Can someone help explain how pearson managed to simplify ln(1/2) as 0? i keep getting -0.69314718056

[wary stream]

They didn't

ln(1/2) is a constant, aka some value so it just gets combined with the + C

Because ln(1/2) + C = C

Or some value

[latent patrol]

ahh it makes sense, just didnt think about including it. thanks!

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[ionic cradle]

Hello, I wqas wondering if someone can help me understand how 2 /3 works. I am really confused what that number means. I know how to solve the actual problem but figuring out what this number is is stumping me. Thanks a lot

[wary stream]

https://www.youtube.com/watch?v=pxaUb8aaSx8&ab_channel=PocketRoni
Here's a video that could assist

[ionic cradle]

Thanks a lot man

[native cloud]

$\sqrt{3\cdot\left(2\cdot2\right)}=2\sqrt{3}$

[ocean seal]

AirToastie

[native cloud]

Square roots can take out squares

4 is a square of 2

So the 2 can come out

[ionic cradle]

.close

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[untold bane]

how do i find the five terms using division..

[proud pike]

what do you mean by "the five terms"?

[untold bane]

sorry i mean first five terms of the sequence

yes whoever answered the sum

[lunar dawn]

oh okay

well you have the equation

what's stopping you from plugging in 1 for n

[untold bane]

idk how to solve it

[wary stream]

$a_1$ is the first term

[ocean seal]

dldh06

[wary stream]

Plug in 1 for n, into the given expression, simplify

Repeat for the next numbers in the sequence

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[ocean turtle]

Could someone me with this problems. It's writing the coordinates of each point. Rn I'm so confused on what to do and lost. Like why is the point in #7 floating and like can they go bigger than the graph? I'm so confused. Could someone explain me how to do this plz.

[heady pollen]

a point is made up of three components, x y and z

in your tasks you have boxes

which show you the compononents

you can think of it as a box where one corner is the origin (0,0,0) and the opposite corner is your point

so what you really want are the side lengths

which you can read from the graph

just make sure to not mess up with positive and negative

[ocean turtle]

Ok so for z would be -3, z would be -2?

Wait

X will be -3

And z will be -2 since it's going down?

But how would we do y ? Because the little point is like floating in between numbers and isn't on a little line. And the dot goes beyond the arrow

For the y axis

Or would y be 4 ?

🤔

So would we only focus on the one touching the (0,0,0) and ignore the rest of the square to get our points?

[ocean turtle]

<@&286206848099549185>

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[ocean turtle]

.reopen

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✅

[ocean turtle]

<@&286206848099549185>

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[proven tendon]

hi guys i was doing a reading and was confused how they did the circled step

difference of squares is done on squared variables right?

so how did the turn b-a in to difference of squares and why do they root instead of squares?

[neon scarab]

Treat $a = (\sqrt{a})^2$ and $b = (\sqrt{b})^2$. Then you apply the identity.

[ocean seal]

jimmy1234

[proven tendon]

but how do we know to do that or why can we assume that?

also wht do we multiply by 1/(\sqrt{a})^2$ + $b = (\sqrt{b})^2$

[ocean seal]

Arm
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[proven tendon]

i get its to cancel out the positive differnece

but how does that work computationaly

how can we do LS RS if the RS is only 0?

[neon scarab]

Most likely book author does not think in the order as he write the step. He/she can be doing some thinking before that, and then formulate the proof so that things look “logical” between every successive step.

[proven tendon]

yeah maybe

this textbook has lots of interesting steps

they do three changes to a formula in one step confusing every student in my class

[neon scarab]

Currently you have $(\sqrt b + \sqrt a) \cdot (\sqrt b - \sqrt a) > 0$, and your goal is $\sqrt b - \sqrt a) > 0$, you then need to further eliminate the extra factor by muliplying $\dfrac{1}{\sqrt b + \sqrt a}$ to the current inequality.

[ocean seal]

jimmy1234

[proven tendon]

got it

thank you kind stranger 🙂

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[odd maple]

how can i solve this, nothing on youtube works its just giving me examples where A is x^2 not when A has a value bigger than 1 and its stunting me because the 2x^2 is where im at a loss

[proud pike]

if 2 y = 16, then what is y?

[odd maple]

8

2x is squared btw in case you missed that

.closed

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[glass sable]

I don’t know to solve this

[rose sigil]

the first floor to the third floor (if I'm getting the floor naming conventions right...) is 2 floor changes

so each floor change takes 41/2 seconds

the first floor to the sixth floor is 5 floor changes

does that help?

[glass sable]

Still a blank 😵‍💫

[rose sigil]

hmm...

if something takes 41/2 seconds, how long does it take to do it 5 times?

[glass sable]

Ohhhhhh so I multiply the 41/2 by 5

[rose sigil]

yep

[glass sable]

I get 102.5

[rose sigil]

sounds right

[glass sable]

Yup that’s right tyty

[rose sigil]

great

[glass sable]

.close

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[glass sable]

.reopen

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✅

[glass sable]

.close

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[dusk tendon]

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[turbid stag]

hi, i've got this question

[turbid stag]

matrix transformation, my question is, i've got a triangle, how do i write a transformation matrix for 3 vector matrix

this is the matrix

or GHI

that has to map to

ABC

[lone heart]

@turbid stag Has your question been resolved?

[turbid stag]

<@&286206848099549185> could somone help me out?

also is the shape of my matrix correct?

idk if this is how the matrix is suppose ot be shaped

[rustic coral]

It should be 2 rows and 3 columns
But it looks like each element is being multiplied by 2, so idk if you can say multiplying by a scalar of 2 lol

[turbid stag]

nah bro that's too simple

so this matrix is enlarged and rotated 180

so its x2 and inversed

[rustic coral]

Oh wait I'm high lol

Well there you go

[turbid stag]

lmao how do i express that though

i just dont know how to express it

[turbid stag]

plus its a single matrix transformation

[rustic coral]

And then you can multiply the rotation matrix by the scalar

[turbid stag]

do i apply that to the whole matrix or do i apply that to each vector in ABC

[rustic coral]

I'd apply it to the transformation matrix

[turbid stag]

whats the transformation matrix lol, thats what im trying to find

"give a single matrix transformation that maps ABC onto GHI"

[rustic coral]

You use this to find the rotation of 180 then multiply it by 2?

lol

[turbid stag]

damn, do i apply that to every vector inside the matrix?

thats a big ass equation

[rustic coral]

Wdym...

[rustic coral]

Oh you mean multiply it out after

Well it appears to only want the transformation matrix, so prolly not

[turbid stag]

nah thats just one vector being rotated 180

you said, apply 180 rotation on ABC and then multiply that by 2

btw i've already done that for GHI

i just dont get the question tbh

[rustic coral]

Where did I say thst explicitly

[turbid stag]

.

[rustic coral]

The rotation matrix isn't the same as the matrix for the triangle

[rustic coral]

Here, the rotation matrix is the 1st one

[turbid stag]

yeye ik that

i just dunno what the question wants me to do

[rustic coral]

If yk that then everything else im saying should make sense tbh

[turbid stag]

bro idk what a "single matrix transformation" is

[rustic coral]

You take the matrix for each transformation

And combine them

By multiplying

[turbid stag]

im so sorry bro, ik you're trying real hard, could you pllssss say that in laymens?

[rustic coral]

Idk how else to make it simpler

Umm so if we wanted to go 90 counterclockwise then 180

You would multiply the 90 degree counterclockwise by the 180 degree mateix

To get a single one

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[alpine sable]

hi, can i get some@help on this did i found the right surface area of a cuboid

[alpine sable]

i can see that a cuboid has@got six sides in total and the front side is a rectangle hence you have six rectangles basicalli

can you mark it

[vale wigeon]

,calc 2 * (5 * 3 + 5 * 7 + 3 * 7)

[ocean seal]

Result:

142

[vale wigeon]

ah, you calculated 3*7 a second time instead of 5*7

[alpine sable]

i was expecting i would have done some where a mistake

would it be like dis

i took an incorrect height

so@now it gives 142

im sure it would work the same way for a cube too

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[alpine sable]

yes

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[silver onyx]

what is the range of cos inverse (|1-x^2|)

[mellow tusk]

x belongs to its domain?

[neon scarab]

$|1-x^2|$ is between 0 and 1.

[ocean seal]

jimmy1234

[silver onyx]

yes

then

[neon scarab]

Only angle in (I) and (IV) quadraint can be send to this range via cos

[silver onyx]

I might have made some silly mistakes somewhere

[silver onyx]

yes

+ve

[mellow tusk]

.

[neon scarab]

So the range is $(-\frac{\pi}{2}, \frac{\pi}{2})$.

[ocean seal]

jimmy1234

[mellow tusk]

um no

[silver onyx]

wrong

[mellow tusk]

its 0 to pi/2

both included

[silver onyx]

I got [0,pi/2]

yes

[silver onyx]

not given, probably ye

[neon scarab]

Yes shd be square bracket, and depends on whether you are asking from 0 to $2\pi$, or from $-\pi$ to $\pi$, the way to represent the full range can be different.

[ocean seal]

jimmy1234

[mellow tusk]

yeah this is only when x belongs to [-sqrt2,sqrt2], otherwise the function wont be defined

[silver onyx]

like cos y = |1-x^2|

[mellow tusk]

its modulus inside arccos

[silver onyx]

-1 <= |1-x^2| <= 1

I did like that and messed up

[mellow tusk]

0<=|1-x^2| <= 1

[silver onyx]

yea

[mellow tusk]

cause modulus cant be negative

[silver onyx]

I messed up

yep

I got now

suppose f(x) = log | log x|

then

[silver onyx]

@mellow tusk

like y = log |log x|

e^y = |log x|

[mellow tusk]

x should belong to (0,inf) here

[silver onyx]

well no

[silver onyx]

exclude 1

[mellow tusk]

why?

[mellow tusk]

no

yea mb exlude 1

[silver onyx]

it's (0,1) union (1, inf)

[mellow tusk]

so the range should be R right

[silver onyx]

log x would be 1

sorry

[mellow tusk]

x cant be 0

[silver onyx]

0

log 1 is 0

log 0 not possible ryt

[mellow tusk]

yea

[silver onyx]

log log 1

so not 1

[mellow tusk]

thats why 1 is not included

[silver onyx]

R - {1}

yes

[mellow tusk]

i mean the range could be 1

put x=e

[silver onyx]

that would be negative

@mellow tusk

[mellow tusk]

how

the base is e right?

[silver onyx]

ye

[mellow tusk]

so at x=+e, fx=1

+e

eh typos

logloge=log1=0

[silver onyx]

log e to the base e is 1 ryt

something ain't ryt

[mellow tusk]

ya

[silver onyx]

so answer is R-{1}

ryt

[mellow tusk]

um

[silver onyx]

e is 2.7

[mellow tusk]

at e^e, fx=1

[silver onyx]

try putting 1

[mellow tusk]

log(eloge)=loge=1

[silver onyx]

hmm

domain should be R-{1}

nk

R+

more like (0,inf)-{1} should be domain ryt

[mellow tusk]

ya

this is the domain, and the range is R for this domain

[silver onyx]

I think answer key wrong

@mellow tusk ok thanks

[mellow tusk]

np

[silver onyx]

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[silver onyx]

@mellow tusk no class today?

[mellow tusk]

i have a class in an hour

[silver onyx]

oh ok all the best, hue

[lone heart]

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[silver onyx]

1 doubt

[silver onyx]

umm if like a random function f(x) = x^2+3x-1 then find number of distinct roots of f(f(x))

how do I start this??

anyone?

[vale wigeon]

you are asked to solve the equation f(f(x)) = 0

[silver onyx]

okay

[vale wigeon]

[f(x)]^2 + 3f(x) - 1 = 0 in your case

[silver onyx]

f(x) = y can we asuume

[vale wigeon]

ok sure

[silver onyx]

yep

[vale wigeon]

substitute that

you will have a quadratic in y

solve for y

[silver onyx]

y^2 + 3y - 1 =0

[vale wigeon]

??

where are you getting that from

[silver onyx]

2

[vale wigeon]

the equation y^2 + 3y - 1 = 0 does indeed have two solutions, but you need to get those solutions themselves to progress further...

[silver onyx]

yea

how to do

that's my doubt

[vale wigeon]

do you know how to solve quadratic equations

[silver onyx]

yes

[vale wigeon]

ok then do that

[silver onyx]

ok 1 min

[vale wigeon]

solve the quadratic equation y^2 + 3y - 1 = 0 for y

[silver onyx]

@vale wigeon

[vale wigeon]

yes

ok

[silver onyx]

that's like 0.3

?

[vale wigeon]

now you need to find the number of solutions for each of the following two equations
x^2 + 3x - 1 = (-3 - sqrt(13))/2
x^2 + 3x - 1 = (-3 + sqrt(13))/2

and add the solution counts for those

[silver onyx]

and -3.3

[silver onyx]

oh

oh okay

[silver onyx]

how do we do that

[vale wigeon]

calculate the discriminant and note its sign...

[silver onyx]

ok

[silver onyx]

one is positive and other negative

[vale wigeon]

i'm going to assume you calculated things correctly

ok now you need to remember how to tell the number of roots of a quadratic from its discriminant

[silver onyx]

think so

[silver onyx]

what

[silver onyx]

how

[vale wigeon]

you know, it's really really REALLY annoying when you ping me 3 times in a row

if the discriminant is positive then there are 2 roots, if the discriminant is zero then there is 1 root and if the discriminant is negative then there are no roots

[silver onyx]

I'm sorry

I will not ping from now

[silver onyx]

so there are 2 roots

oopps I am so sorry

it became habit to reply while ping

[silver onyx]

then?

[vale wigeon]

now you need to find the number of solutions for each of the following two equations
x^2 + 3x - 1 = (-3 - sqrt(13))/2
x^2 + 3x - 1 = (-3 + sqrt(13))/2
and add the solution counts for those

[silver onyx]

2

then over ryt

[lone heart]

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[lapis crow]

help on hw

[lone heart]

@lapis crow Has your question been resolved?

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[paper terrace]

the answer key says db/dt = 26

so idk if that's right or not

i dont understand why it wouldnt just be 4*(-1/2)*4

[worn fox]

Product rule

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[quasi creek]

hello why is it that -72 + (-30) + 10

[quasi creek]

is -92?

and not 112?

[vale wigeon]

how are you getting 112?

[quasi creek]

i add -72 + -30

[vale wigeon]

and you got what

[quasi creek]

which is 102

[vale wigeon]

no it isn't

[quasi creek]

and then added 10

lol

what

[vale wigeon]

-72 + -30 = -102

[quasi creek]

o

dang i really have to study

[keen pasture]

Negative signs do exist

[quasi creek]

i thought that if u add 2 negatives

they make a positive

o_O

[vale wigeon]

it's with multiplication that this happens

[quasi creek]

oh

[vale wigeon]

a negative times a negative is a positive

[quasi creek]

damn im dumb

alr thank u for ze help

[keen pasture]

Let's say I owe someone 72 dollars and I lent myself another 30 dollars. That would not make my balance positive

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[lone heart]

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[digital steeple]

Can someone explain to me how I can use a Z transform with d'alemberds theorem to prove if a function converges / when it converges?

[digital steeple]

I studied it again and again, but I can't make sense of z transform properly with that

Like someone help me dumb down what I see

To be exact, I don't understand the second half at all

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[wintry path]

-5p - 28/5 = -4?

the first step

[silver onyx]

how 28/5

[wintry path]

idk

possibly -5 times 3/5

i used -5 to time the denominator

[silver onyx]

thats - 15/5

= - 3

so - 5p - 3= - 4

[wintry path]

how

[silver onyx]

what is 5*3

[wintry path]

alr so i got -5p = -1

[wintry path]

15

[silver onyx]

yes

[wintry path]

oh we time the numerator?

alr

[silver onyx]

yes

[wintry path]

havent done it for a while

and p = -1/5

wait no

it's p=1/5

[silver onyx]

yes

[wintry path]

alr thx

[silver onyx]

ok

close it

[wintry path]

.close

[lone heart]

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[foggy urchin]

Need help with Q2,3 and 4 . I've already solved 2 and 3 but i'm not sure if my answers are correct so I want to double check

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[wide shale]

Hi, Im learning about ideals, and I think I understand the basic definitions, but its difficult to find examples online, specifically with rings of polynomials. One example I have is that sqrt(<y^2-X^3-X^2,y>) = <x(x+1),y>. How do we know, explicitly, that this is the radical? Also just making sure I have the notation correct, <f,g> denotes a system of polynomial equations where f,g = 0 yes? Meaning in the example, that y^2 = x^3+x^2 and y=0. Correct?

[mortal trellis]

<f,g> denotes the ideal generated by the polynomials f and g

that essentially amounts to setting them equal to 0

but it's still an ideal, not a system of equations

[wide shale]

right, so a collection of points where f,g = 0 that satisfy the definition of an ideal

[mortal trellis]

no

the set of polynomials of the form p*f+q*g

[wide shale]

ah right, because an ideal is a subset of the polynomial ring (in this case), so its elements must be polynomials

@mortal trellis Could you also elaborate, explicitly, on the example of the radical above? How would you show that the radical is indeed equal to <x(x+1),y>?

[mortal trellis]

honestly not sure, not super familiar with radicals of ideals

[wide shale]

Ok, thanks for letting me know! I'll sit tight and wait for someone else to chime in

but thanks for your input!

[lone heart]

@wide shale Has your question been resolved?

[lone heart]

@wide shale Has your question been resolved?

[lone heart]

@wide shale Has your question been resolved?

[lone heart]

@wide shale Has your question been resolved?

[mortal trellis]

I guess it's probably better if you get yourself the advanced role and head over to #groups-rings-fields

[weary wyvern]

That would be ideal

[wide shale]

done!

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[dawn quail]

Why does the graph have solid and empty dots?

I don’t understand why each blue line is exactly 1 unit long with the same marking, solid dot on left empty dot on right

Never seen this before.. maybe someone can fill me in?

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[ornate condor]

what about it...

yea its trivial

[waxen flame]

A trivial solution occurs when you have a solution that is all zeroes.

[ornate condor]

i mean

the only soln is the trivial soln

i dont think u call the matrix trivial

[waxen flame]

No, it is parametric so it has an infinite number of solutions.

In this augmented matrix, you have a vector that is R3. There is no way to determine the value of the third element of the vector. Because of this, the third element of the vector becomes part of the solution for the first and second element. In other words, the first and second element are dependent on the third element.

There are no limits on what that third element can equal, ergo there are infinite solutions.

\begin{align*}
x_1 + \frac{9}{2}x_3 &= 0\
x_1 &= -\frac{9}{2}x_3
\end{align*}

[ocean seal]

Kookiemon

[waxen flame]

Yes.

yw

[lone heart]

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[rustic meadow]

I'm having trouble getting started on this.

[rustic meadow]

I thought North and south could cancel 17 paces and all we would be left is the total 10 paces north and 37 paces northwest

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[dreamy osprey]

how to I convert mass to mols?

[vale wigeon]

pedantic answer: you don't, because mass and amount of substance are different quantities and are not interconvertible

non-pedantic answer: you'll need to know the molar mass of the chemical you're working with

[dreamy osprey]

A 35.9 g sample of Ca(NO3)2 contains _____ moles of nitrate ions.

so I got this problem

[vale wigeon]

ok

,w Ca(NO3)2 molar mass

[dreamy osprey]

do i get the molar mass by the atomic number under the elements and add?

[ocean seal]

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Requested by Ann#0413

[vale wigeon]

no

you need to know the molar mass of each element, and add those (and also keep track of how many of each element you have in the molecule)

[dreamy osprey]

is O's 16?

[vale wigeon]

iirc yes

i had WA do it for you just now anyway

[dreamy osprey]

So I do add all of their atomic numbers

[vale wigeon]

no

the atomic number of oxygen is 8

[dreamy osprey]

whoops wrong one

[vale wigeon]

but its molar mass is 16 (g/mol)

[dreamy osprey]

atomic mass right?

[vale wigeon]

.

[dreamy osprey]

ok so N takes up 28 g/mol of the total

do I divide that by the total?

[vale wigeon]

i think you are overthinking it right now