help-0

[lone heart]

@worthy verge Has your question been resolved?

[worthy verge]

nvm

i got it

lol

.close

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[rugged flax]

I've already graphed them, I'm just struggling with finding intersections with a and b and I did a bunch of spaghetti math and it doesn't factor so I'm like...

<@&286206848099549185>

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@rugged flax Has your question been resolved?

[rigid smelt]

is your calculator capable of solving a quartic?

if so then there is no need for factoring

[rugged flax]

Yeah I used that to check

[rigid smelt]

ok so if your calculator is capable of solving a whole quartic equation, all you need to do is to input your equation into the calculator and solve

after all, it asks you to use a calculator

[rugged flax]

nvm I messed up, I got it

.close

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[graceful plinth]

.open

Do these mean the same thing?

[graceful plinth]

<@&286206848099549185>

[little nimbus]

Yes they do @graceful plinth

and please wait a little bit before pining helpers, alright? (the rule is 15 mins)

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[lavish pier]

im quite confused i just need someone to explain to me how the index of A ends up being 14

[abstract fractal]

What have you tried

[lavish pier]

3 x -2 = 6

-6*

a^-6 = a^1/6

correct?

[abstract fractal]

No

-6 isn't the same number as 1/6

a^(-6) = 1/(a^6)

[lavish pier]

,rotate

[ocean seal]

Couldn't find an attached image in the last 10 messages.

Aug 14, 2022, 10:52 AM

[lavish pier]

,rotate

[lavish pier]

<@&286206848099549185>

[abstract fractal]

What are you still stuck on

[lavish pier]

i got 64 b^20 / 9a^22

i want to know if its right

[abstract fractal]

How

[lavish pier]

how did u get something else

[abstract fractal]

Try answering my question first

[lavish pier]

ok

take 81 out of root

becomes 9

[abstract fractal]

And?

[lavish pier]

4 becomes 64

[abstract fractal]

Yep. What else?

[lavish pier]

b^-8 moves up to numerator

and becomes positive

[abstract fractal]

81 isn't the only thing inside the square root

[lavish pier]

8 + 12

how do i take the rest out of the rot

root

[abstract fractal]

Same thing you did with 81

81 is 9² so √81 = 9

[lavish pier]

what about the a

so a ^4

[abstract fractal]

Not a^4

(a^4)^2 = a^8

[lavish pier]

6

[abstract fractal]

No

[lavish pier]

8

[abstract fractal]

(a^6)^2 is not a^16

[lavish pier]

8

and then b is -4

?

[abstract fractal]

I'd be much more comfortable if you would refrain from spitballing numbers. It would make it seem less like guessing. Anyways, yes

[lavish pier]

so 64 b^16 / 9a^14

?

[abstract fractal]

Why b^20?

[lavish pier]

4+16

wait

my bad

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[lone heart]

@pale reef Has your question been resolved?

[marsh rapids]

Have you done question 1 ?

The answer should be yes

Since Q2 is asked

[lone heart]

@pale reef Has your question been resolved?

[pale reef]

qn 1 is unrelated to q2

[copper stone]

where are you struggling ?

[pale reef]

Determine whether U satisfies vector space axiom 7

idk how im supposed to start solving it

[copper stone]

let u = (x , y) and v = (x' , y') then calculate k(u+v) and ku + kv

if you get the same result then the axiom is satisfied

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[rain trench]

Hey could someone please assist me thanks

[rain trench]

Would this be true or false just wondering

[trim wagon]

Would what be true or false?

[rain trench]

Idk man I’m wondering whether it’s true or false but I say it’s true

What do you say @trim wagon

[trim wagon]

Thats a odd notation

Is it addition?

It looks like

If so then yes

Wait a minute

[rain trench]

Also would this be right or incorrect :/?

[trim wagon]

Is that a test?

[rain trench]

Nah it’s a task

[trim wagon]

Task 👀

[rain trench]

Yeah I’m online

[trim wagon]

I can see that

[rain trench]

But going back to physical school next year

[trim wagon]

What kinda task?

[rain trench]

Nah for tests I wouldn’t take screenshots I can get zero

[rain trench]

Simultaneous equations revision

[trim wagon]

So isn’t there answers for you to check if it is right or incorrect

[rain trench]

Nah there isn’t 😭

We go through task tomorrow

[rain trench]

That’s all I need help with 🙂

<@&286206848099549185>

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@rain trench Has your question been resolved?

[lone heart]

@rain trench Has your question been resolved?

[rain trench]

<@&286206848099549185>

<@&286206848099549185>

[lone heart]

@rain trench Has your question been resolved?

[rain trench]

Close.

.close

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[solid imp]

Hi

So there are 2 sin fonctions

The one underneath is:

and the highest one is:

they touch each other at x = 0.5

and to find c of the upper fonction they did all this

wich I dont get

Why did they only fill out the 125 they found for y

and not fill in x equals 0.5

here

nvm i think i understand what to do

.close

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[trim oracle]

Why can you replace e^xsinx with y?

[tribal oxide]

they didnt do that tho

[trim oracle]

Meant with y

[tribal oxide]

it probably has to do with ur original equation, maybe y was equal to this at the start?

[trim oracle]

Oh yeah it is

Thanks

/close

/thanks

.thanks

.close

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[elfin herald]

asking for x,where did i go wrong?

[gray isle]

poor writing/notation/flow,
your work is incomplete

[elfin herald]

how do we solve this?

would be helpful

[gray isle]

well applying appropriate laws led you to
8x-10 = 3x +6

[elfin herald]

yes

[gray isle]

this is just a linear equation of one variable

[elfin herald]

so

[gray isle]

something you should definitely know to solve by now

[elfin herald]

16/5?

[gray isle]

x = 16/5
yes

[elfin herald]

thank you so much

[gray isle]

I didn't do anything

[elfin herald]

may i ask one more question

.close

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[hot storm]

Consider the sets A = The set of all vowels in the English alphabet, B = The set of all consonants in the word "strychnine", C = The set of all distinct letters in the word "mañana", D = The set of all vowels in the word "HOOIAIOIA", and U = The set of all letters in the English alphabet including ñ. What is A′?
A′ = {b,d,f,g,j,k,l,p,q,v,w,x,z}

[hot storm]

I think I'm correct? right?

Since you just need to deduct some words

[gray isle]

is U supposed to be the universal set?

[hot storm]

Yes

[gray isle]

you're only being asked about the complement of A here

this has nothing to do with the sets B,C,D

[hot storm]

So it's basically a diversion because of the ñ to make me think that all the sets are included when in actuality it's just A?

[gray isle]

whut?

supposedly some of this info will be used for later questions

it's not there to trick you

[hot storm]

I see, alright. Thanks

.close

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[lone heart]

@noble kayak Has your question been resolved?

[noble kayak]

<@&286206848099549185>

[noble kayak]

<@&286206848099549185>

.close

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[hot storm]

I'm doing Cartesian Product with A = fine B = nine
AxB = {(f,n),(f,i),(f,n),(f,e), (in),(i,i),(i,n),(i,e), (n,n),(n,i),(n,n),(n,e), (e,n),(e,i),(e,n),(e,e)}

[hot storm]

Is this correct way of doing it?

[lone heart]

@hot storm Has your question been resolved?

[alpine sable]

looks right to me

but i think you mean A={f, i, n, e} and B={n, i, n, e}

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[tawdry sail]

will an angle bisector always look like this during a question

[tawdry sail]

so when u see something like this u should know that is an angle bisector

?

[wary stream]

Do you know what bisector means?

[tawdry sail]

uh

not really

[wary stream]

An angle bisector is a line or ray that divides an angle into two congruent angles

[real gazelle]

Yes, by definition of angle bisector

bisect = split into two equal pieces

angle bisector = a line that splits an angle into two equal pieces

[tawdry sail]

ah alright

thank u

.close

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[tawdry sail]

.reopen

[lone heart]

✅

[tawdry sail]

so line qs here is a bisector???

just not into equal parts?

[wary stream]

No

[real gazelle]

bisect always means into two equal parts

[tawdry sail]

ohh

ok

Thank you

.close

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[ivory oracle]

Why is the solution 0<p<8 when p parameter and x is a real number ? I dont get it from the discriminant i get 0 and 8 and from the graph i read that x>0 or x >8

[naive valley]

what did you get for the discriminant?

[ivory oracle]

D = P^2-8P and from that D=P(P-8)

[naive valley]

ok

and what requirement do you have for D in order for the polynomial to always be positive?

[ivory oracle]

P>0 or p<0 and i do it in 2 ways?

[naive valley]

what requirement for D, the discriminant?

can the polynomial have any real roots?

[ivory oracle]

Yes

That needs to be : D>0

[naive valley]

a real root would imply that $x^2 + px + 2p = 0$, right?

[ocean seal]

Bungo

[naive valley]

but you need $x^2 + px + 2p > 0$

[ocean seal]

Bungo

[naive valley]

for all x

[ivory oracle]

Yes

[naive valley]

therefore you want no real roots

therefore the discriminant must be ...?

[ivory oracle]

oh that its D<0

[naive valley]

yes

[ivory oracle]

Wait sorry my english is bad a bit can i do this quick again in sheet?

[naive valley]

sure

[ivory oracle]

Hm , and why i want no real roots? Thats not clear for me sorry

[naive valley]

if you had a real root say $x=x_0$, then you would have $x_0^2 + px_0 + 2p = 0$. But that violates the desired inequality $x^2 + px + 2p > 0$, which needs to be true for all $x$

[ocean seal]

Bungo

[ivory oracle]

And if i solve lets say x^2+x+2 > 0 , i solve it for =0 and read the graph where is it > 0

than whats happening here?

[naive valley]

here we have a different approach, we are not solving for = 0 because we don't want the polynomial to ever be 0

we are looking for a condition that ensures that

and making the discriminant negative ensures that

if the discriminant is zero or positive then there will be real roots, so the polynomial will sometimes be zero

we don't want that

in other words:

discriminant < 0 if and only if polynomial is never zero

then:

to conclude that the polynomial is always > 0 we use the facts that (1) the polynomial is continuous and (2) the coefficient of x^2 is positive

[ivory oracle]

Okay

I get it now

Thanks to you

.close

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[charred crater]

I'm in life or death need of support

[charred crater]

I have an equation and I'm trying to find the recurrence of fixed points

3. (From lecture 2.1) Suppose you buy a 1 million dollar house with a 20% deposit and
   pay off $b per fortnight. The following recurrence calculates the mortgage after n
   fortnights
   Xn = Xn−1 + 0.002178Xn−1 − b
   where Xn denotes the dollar amount of the loan after n fortnights, and assumes the
   (current) national average 30-year fixed mortgage APR (yearly rate) of 5.820%.

(b) Determine the fixed points of this recurrence, and interpret these in terms of the
loan and repayments.
we are always given the fixed point of 0,0.

I've been stuck on this for hours and have given in to some support if possible

please someone

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@charred crater Has your question been resolved?

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[weak aurora]

Can someone explain how this turns into this using distributive property

Like i understand how to do it but I don’t understand it completely conceptual wise

Can someone prove it

[alpine sable]

$\frac{7007}{7}=\frac{7000+7}{7}=\frac{7000}{7}+\frac{7}{7}$

[ocean seal]

Toby

[weak aurora]

That makes so much more sense

Thank you!!

[alpine sable]

yw :)

[weak aurora]

Wait sorry how does it correlate to distributive property, isn’t distributive property like when you distribute values to one another for example 2(3+7x)=14x+6

[alpine sable]

yeah, we are distributing 1/7

[weak aurora]

sorry, i dont understand

[alpine sable]

instead of 2, we have 1/7

$\frac{1}{7}(7000+7)=\frac{1}{7}(7000)+\frac{1}{7}(7)=\frac{7000}{7}+\frac{7}{7}$

[ocean seal]

Toby

[weak aurora]

Ahhhh i see, thank you so much the visual helped a lot!!

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[restive hearth]

Why can we use n! to find the number of possible orders for n objects?

[restive hearth]

5! = 1x2x3x4x5.

I am not sure how I can word it to better help my brain grasp the concept.

[oak perch]

n choices for the first place, then. (n-1) choices left for the second place…

[marsh rapids]

5 choices on the first pick, 4 choices left on the 2nd pick, etc until 1 choice left for the last pick

[oak perch]

I better be rigorous: any bijection from {1,…,n} to itself. n choices of f(1). Then n-1 choices of f(2)…

[restive hearth]

Ah I see.

In a more general form, it accounts for all possibilities from 1 choice all the way up to n.

The numbers 1-10 are put in a hat. If the numbers are taken out one at a time, what is the probability they come out in ascending order?

How would you exactly tackle this problem?

[naive sorrel]

oh

woops

uh

did you see what i said

or should i resend

[restive hearth]

There is 3,628,800 possible ways to arrange numbers 1-10.

[naive sorrel]

maybe im wrong but factorial wouldnt help here

[worn fox]

how many of those ways are in ascending order?

[restive hearth]

I would assume 1?

[worn fox]

you would assume correct

you have everything you need

[restive hearth]

1/3,628,800?

[worn fox]

yeah

[restive hearth]

Ah I see, thank you!

[restive hearth]

Out of curiosity, would you like to explain your way please?

[naive sorrel]

you probably could make mine work but yeah his is better

oh ok

yeah

it is just factorial

i was thinking of the first number chance it is 1 it is 1/10

then second number being 2 is 1/9

and so forth

so its 1/(10!)

[restive hearth]

Yeah, I see.

There's only 1 outcome where the numbers are in ascending order.

Using the permutation formula, we can identify the total outcomes.

[lone heart]

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[lone heart]

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[tidal zealot]

|

[tidal zealot]

wht swhould i do

<@&286206848099549185>

[molten pivot]

Alright this isn't so bad

We just need to count the number of unique permutations of:
66644

[tidal zealot]

oakyy

[molten pivot]

And then multiply that by (1/6)^5

[tidal zealot]

so how would i calcaulte the permuatition

[molten pivot]

How many elements are in the list?

[tidal zealot]

5

[molten pivot]

Right, so that gives us 5! in the numerator

But that causes overcounting

Because we have repeat elements

[tidal zealot]

okay

[molten pivot]

So we need to correct for that overcounting somehow

[tidal zealot]

diveide by 3! and 2!

[molten pivot]

Yes

So our final answer is:
(1/6)^5 5!/(3! 2!)

[tidal zealot]

why do i multiply by 1/6^5

[molten pivot]

(1/6)^5 is the probability of any of the permutations occuring

5!/(3! 2!) is the number of permutations

Make sense?

[tidal zealot]

hmm, so there are 10 possible combinations

i dont really get it

so if there are 10 possible

then each permutation is 1/6^5

hence, 10 times 1/6^5

i think i get it

[molten pivot]

Yep

[tidal zealot]

.close

[lone heart]

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[tidal zealot]

what am i trying to find?

[real gazelle]

when is the speed of the particle decreasing?

[tidal zealot]

when tis below the t axis

[real gazelle]

No

[tidal zealot]

HMM!

wdym

so wehn?

[real gazelle]

do you understand what is being plotted

[tidal zealot]

its just showing what the velocity is, at various times

[real gazelle]

yup

what is the relationship between the speed and velocity

[tidal zealot]

idk

how does veloctuy and spseed relate

[real gazelle]

do you know what scalars and vectors are

[tidal zealot]

yeah

[real gazelle]

alright

speed is the magnitude of the velocity

do you know what that means

[tidal zealot]

so ur saying i get the length of the graph?

[real gazelle]

what do you mean by length of the graph

[tidal zealot]

*how woukdl i get the magnitude of the graph

[real gazelle]

well how would you get the magnitude of like, -8

[tidal zealot]

idk

is it a vector?

-8i + 0j?

[real gazelle]

yeah here v is a one dimensional vector

[tidal zealot]

$$sqrt((-8)^2+(0)^2)$$

[ocean seal]

jaxplaysgames

[real gazelle]

okay

what is that

[tidal zealot]

root 64

[molten pivot]

$$\sqrt((-8)^2+(0)^2)$$

[ocean seal]

Mr. Gamer

[molten pivot]

Remember the backslash

[tidal zealot]

oh

[tidal zealot]

8

[real gazelle]

okay what is root 64

okay yeah

so what is the magnitude of like

-9

if you want you can think of it like -9i (where i is a unit vector)

[tidal zealot]

okay

but am i finding the magnitude of the whole graph

• which specific points do i find the magnitudeof

[real gazelle]

yeah you find the magnitude of each point on the graph

the v coordinate

to get the speed

and then you can plot speed vs time

[tidal zealot]

why is this question so hard

its only one mark

[real gazelle]

it's not hard as long as you understand the relationship between velocity and speed

[molten pivot]

Speed = |Velocity|

That should help

So if you want the points where the speed is decreasing, you want the points where the velocity is getting closer to 0

[real gazelle]

it may help to plot a speed vs time graph so we can check if you are understanding properly

[molten pivot]

Meaning that the function and its first derivative should have opposite sign

[lone heart]

@tidal zealot Has your question been resolved?

[lone heart]

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[feral skiff]

evaluate the expression below if x = 3 and y = 4 2x - y + 3x
i have no clue how to do this

[alpine sable]

y=-x so (3,4) doesn't even exist on that line

unless you mean x=3 -> y=-3 and y=4-> x=-4

[feral skiff]

dang guess my math teacher rigged it

oh wait

ok that should be the equation i typed 1 letter wrong

[chrome plank]

It's an expression (not an equation)

"Evaluate ... if (variables)" means that you have to substitute those variables

So instead of x write 3 and instead of y write 4

@feral skiff

[feral skiff]

yes?

[chrome plank]

?

[feral skiff]

im so slow 😭

[chrome plank]

That's ok

[feral skiff]

so 2- 4 +3?

[chrome plank]

no, how did you find 2 and +3?

[feral skiff]

^

you told me to re write the numbers as they equal

[chrome plank]

Let me do it with x, then you will do it with y

[feral skiff]

ok👍

[chrome plank]

No nevermind, let's just do it together

[feral skiff]

ooook

[chrome plank]

2x - y + 3x, x = 3
2 * x - y + 3 * x

Instead of x, write 3
Let me know what you get

without doing any calculations

[feral skiff]

huh?

23

[chrome plank]

[feral skiff]

2*3?

[chrome plank]

All the expression

[feral skiff]

2*3-y+3 *3

it wont let me put astrik

[chrome plank]

write \* instead of * only

But you didn't substitute an x

[feral skiff]

oh

[wary stream]

Either write it surrounding in ` or add spaces around the *

So something like this 8 * 8 or 8*8

[chrome plank]

Yes that's good

Now do the same, but with y = 4

[feral skiff]

2*3-4+3 *3

[chrome plank]

Yes well done

Now evaluate that

[feral skiff]

15?

[chrome plank]

Are you sure?

[feral skiff]

hmmm

2*3 = 6-4 = 2 2+3= 5 and 5*3=15

[chrome plank]

No, multiplication first

[feral skiff]

oh yeah pemdas

[chrome plank]

Yes

[lapis sluice]

Not 2+3, 2+(3*3)

[feral skiff]

what?

[chrome plank]

If you are not familiar with that ignore it for now, but it's another way of saying in which order stuff should be calculated

[feral skiff]

2*3=6 6*3=18 18-4= 14+3=17

[chrome plank]

Why 6*3?

2*3 - 4 + 3*3

[feral skiff]

because its the next multiply thing

but multiplication comes before subtraction

[chrome plank]

Evaluate every multiplication

[feral skiff]

wat

2*3 = 6 3*3=9

[chrome plank]

Ok, so what's our original expression?

[feral skiff]

uhhh

well you see idk

[chrome plank]

It's much easier if you keep all the expression instead of splitting it into parts

Try again, evaluate only 2*3 and then copy the rest of the expression

[feral skiff]

wait so 2x3 isnt 6

[chrome plank]

It is

[feral skiff]

i was lied to my whole life

?

6-4+3 *3

[chrome plank]

Yes exactly!

[feral skiff]

oh dang

[chrome plank]

According to pemdas what should we do next?

[feral skiff]

uh more multiply

[chrome plank]

Ok, do the same thing

keep everything the same except the part you are calculating

[feral skiff]

6-4*3+3

oh

wait

[chrome plank]

(Continue from here, don't restart)

[feral skiff]

😕

[chrome plank]

Keep everything that is not what you are calculating the same,
change only what you are calculating

[feral skiff]

idk what im suppose to calculate

[chrome plank]

What does pemdas say?

[feral skiff]

multiply

[chrome plank]

Then multiply

[feral skiff]

3*6-4+3

[chrome plank]

Why did the * move?

[feral skiff]

because

[chrome plank]

6-4+3*3, what are we multiplying?

[feral skiff]

multyply first

[feral skiff]

idk

[chrome plank]

That means that multiplying is the first thing you should do, not that you should multiply the first terms

[feral skiff]

i quit ill take the f

.close

[lone heart]

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[chrome plank]

Bruh

we were multiplying 3 * 3

[wary stream]

Do you know order of operations?

[lone heart]

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[opal merlin]

How would you find the multiplicative inverse

[wary stream]

Yes

Because the multiplicative inverse is when it multiplies to 1

It is

[opal merlin]

is -0.25 supposed to be like 1/0.25

[gray isle]

no

[wary stream]

No, as I stated, it multiplies to equal 1

[opal merlin]

right

[wary stream]

So does -0.25 times 1/0.25 equal 1?

[gray isle]

-0.25 * 1/0.25 isn't 4

[opal merlin]

basically 0.25 times a number that equals 1

[gray isle]

the multiplicative inverse of $x$ is $\frac1x$

[ocean seal]

ℝamonov

[gray isle]

yes

[wary stream]

Also, here you said -0.25

[gray isle]

4 would be the multiplicative inverse of 0.25 but ^

[opal merlin]

.close

[lone heart]

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[alpine sable]

Can anybody help me with this?

[alpine sable]

I need help determining the limits of integration for theta and psi

Calculate the triple integral of $f(x,y,z) = z - 1$ in the set $B: (x-1)^2 + \frac{y^2}{2} + (z-1)^2 \le 1$ and $\sqrt{(x-1)^2 + \frac{y^2}{2}} +1 \le z$

[ocean seal]

Resendelay

[lone heart]

@alpine sable Has your question been resolved?

[alpine sable]

<@&286206848099549185> anyone?

[alpine sable]

.close

[lone heart]

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[alpine sable]

<@&286206848099549185> can someone walkthrough on how to do this graphing

[old horizon]

I think that you can add 4 to lhs and rhs and then open the modulus to get 2 equations

then plot the graph of the two ig

[alpine sable]

what is lhs and rhs

[old horizon]

left hand side

right hand side

[alpine sable]

ohh

[old horizon]

I mean things left to the equal sign and right to equal sign

but idk if the method of plotting this is correct

[alpine sable]

OK

[worthy verge]

its correct

but LHS has to be as it is

then negative the LHS abs val

so
x-4= whatever
4-x=whatever

so rhs is 0.5x +4 graph that out

then graph the lhs out but nothing can be below xacis

axis

should be a V line graph and another Positive gradient line

[old horizon]

yeah

[worthy verge]

[old horizon]

I meant this 4

[worthy verge]

yeye

tats what i meant

But tbh idk how ur supposed to get the answers from a graph

without a graph paper

If ur just sketching idts u can get values from it

Its way easier to solve the eq

x-4=0.5x+4
0.5x=8
x=16

4-x=0.5x+4
x=0

[old horizon]

yes

but in exams they do so

[worthy verge]

⬆️

[lone heart]

@alpine sable Has your question been resolved?

[gray isle]

graph
y = |x-4| - 4
and
y = x/2
identify where they intersect

[lone heart]

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[elder viper]

Hello,

[elder viper]

Let $\Omega=\mathbb{Z}$. Consider $\mathcal{T}$ the $\sigma$-algebra engendered by sets \$S_n={n,n+1,n+2}$ with $n\in\mathbb{Z}$. What are the elements of the $\sigma$-algebra $\mathcal{T}$?

[ocean seal]

Chad

[naive valley]

hint: what is $S_n \setminus S_{n+1}$?

[ocean seal]

Bungo

[elder viper]

{n, n+1, n+2} \ {n+1, n+2, n+3}

so {n, n+3}?

[vale wigeon]

no

\ is difference, not symmetric difference

also it's generated not engendered (unless you're a baguette)

[elder viper]

im sorry it was originally baguette

[vale wigeon]

the difference you were asked for is {n}

[elder viper]

yeah so it's single

singleton

so apparently i have to do union for all

[naive valley]

So $\mathcal T$ contains all the singletons. What can you conclude?

[ocean seal]

Bungo

[elder viper]

i would think that it's Z

wait no

P(z) but only singleton

[naive valley]

what does the notation P(z) mean?

[elder viper]

uh oh power set

[naive valley]

what does it mean to say "power set but only singleton"?

[elder viper]

ohhhhh

because it's sigma

so i can do union because it's stable

and then i shouold get the power set right

[naive valley]

there is a key detail..

[elder viper]

disjoint?

[naive valley]

you need to use the fact that $\Omega = \mathbb Z$ is ...?

[ocean seal]

Bungo

[elder viper]

a sigma algebra

?

[naive valley]

no

[elder viper]

damn

[naive valley]

it's the underlying set, not a sigma algebra

what is its cardinality, and why does that matter?

[elder viper]

oh yes so it's the bigger

its cardinality is infinity no?

[naive valley]

what kind of infinity?

[elder viper]

that you can count so the word is

in english uh

[naive valley]

haha just countable

yes that is correct

why is that important here?

[elder viper]

because there is like a prerequisite for union and it has to be countable for the sigma algebra to be stable with union?

[naive valley]

yes, sigma algebras are closed under countable unions

not necessarily uncountable unions

Z is countable, so all of its subsets are also countable

[elder viper]

i see

[naive valley]

which means?

[elder viper]

that i can union the subsets

and union the already unioned stuff and then i get power set

[naive valley]

well what specifically do you take the union of?

in order to conclude that the generated sigma algebra is the power set?

you need to make the argument clearer

[elder viper]

i start with singletons at first right?

and i believe they have to be disjoint

yeah im not sure about this part

[naive valley]

yeah any two distinct singletons are disjoint, each one only contains one point

[elder viper]

i'm just not sure about the way it builds up

from singleton to eventually the underlying set

[naive valley]

well given a set A, how would you build it using singletons?

[elder viper]

i could combine the singleton two by two

[naive valley]

hm, why two by two?

take a concrete example, say A = {1,2,3}. How would you construct that from singletons?

[elder viper]

so i have like {1}, {2}, {3}

and then {1, 2}, {1, 3}, {2, 3}

and then {1, 2, 3}

so

i use union and

yeah I don't know how to put it in words im sorry

i take all possible unions with 1 element and then i get two element sets

and i take all possible unions again with the two element sets

and i guess it doesn't matter if a set is here twice because i could just remove it

[elder viper]

and then i get {1, 2, 3}

i don't know how i could mathematically put this out in a formula

[naive valley]

it's a bit simpler than what you are describing

given any set, all you need to do is take the union of the singletons that are contained in the set

formally, for any $A \subseteq \mathbb Z$, we have $A = \bigcup_{n \in A}{n}$

[ocean seal]

Bungo

[naive valley]

the key thing to note here is that it's a countable union

which is important because sigma algebras are only closed under countable unions, not necessarily under uncountable unions

[elder viper]

hm

alright, i'll work up on that formula

i'm a bit skeptical about whether it really works and i think that's the problem

thank you

[lone heart]

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[weary void]

how do i solve

[weary void]

i know reflection is

i don't think i understand the reflection part

[lone heart]

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[tidal zealot]

c

[tidal zealot]

any cluew on what to do

[tight locust]

so you get 0 tails, 21.9% of the time

you get 1 tail, 42.7% of the time

2 tails, 29.2% of the time

[tidal zealot]

yeah

[tight locust]

3 tails, 6.2% of the time

multiply each result by its probability of occurring and then add them all together to get the weighted mean

[tidal zealot]

okay

once i get the mean then what

[tight locust]

then that's your answer

[tidal zealot]

i got 1.197

[tidal zealot]

r u sure

[tight locust]

hold on nvm i misread the problem

[tidal zealot]

so how am i susposed to approach this?

[tight locust]

try finding the total number of tails over all trials and dividing it by the total number of trials

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@tidal zealot Has your question been resolved?

[lone heart]

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[potent rain]

How can I know this is true by the mid point (0,2) and min point (3,-6)?

I had y = 8sin(pi*x/6)+2

So close except the amplitude is negative in reality.

Even if I try the equation 2 = -6 + a to find if it's negative it doesn't help (midline = min value + amplitude)

a = 8

[lone heart]

@potent rain Has your question been resolved?

[potent rain]

<@&286206848099549185>

[naive valley]

well if you plug in x=3 into your formula you get y = 8sin(pi/2)+2, which equals 10, not -6

is there more context to the question? there are infinitely many sine curves that pass through those two points

[potent rain]

I'm constructing sinusoidal equations

So the answer is yes = -8sin(pi*x/6)+2

But I don't know how to tell that it's a vertical reflection at all

Especially without a graph

[naive valley]

they're not giving you enough conditions to conclude that y = -8sin(pi*x/6)+2

yes, that's a solution that works but there are many others

like they don't say that there can't be one or more periods of the sine before reaching the minimum at (3,-6)

[potent rain]

Khan academy constantly gives me questions I can't solve. Worse, they offer a video that's irrelevant.

I'm sick of everywhere I go, people "explain" how to do something and it doesn't give a full explanation.

It's like, here's how to drive. Just press the accelerator pedal and move the steering wheel.

Easy!

But I'm not moving, why? Oh there's no answer on the internet.

[lone heart]

@potent rain Has your question been resolved?

[lone heart]

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[quasi rapids]

Hi guys, looking for help to calculate the meters of the redline (not necessary precisely, but at least (~2-5cm correct)

[burnt ravine]

Sir, you have a scale

Find a ruler and just measure then make a ratio with reference

On my screen the 4,63 line measure 7,5 cm

and the unknown red line measure 5,1 cm

Then you can affirm ... ?

[quasi rapids]

isn't that all messed up with screen res?

[burnt ravine]

You wanted an approximation so no it's not

[quasi rapids]

should be about 3,14 then

but yea thought it was more than messed up due to screen res

[burnt ravine]

👏

[burnt ravine]

Then print it in A3 format

Jesus format

5k

[quasi rapids]

thanks

.close

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[white pike]

Hey helpers, i need help i have been given a linear graph, and a line is drawn through it, how do I calculate the gradient of this line shown??

[keen pasture]

Delta y/ Delta x

[white pike]

no clue what that means im sorry this topic just started with us

[slender gull]

(y_2-y_1)/(x_2-x_1)

[white pike]

im still very confused with the formula

lemme send pic

actually nvm thanks guys ik how to do this

.close

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[keen pasture]

Didn't you have a blue name once?

[slender gull]

I did, now I don't.

Haven't been active for a while now.

[keen pasture]

OK :(

[lone heart]

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[sand star]

Am I correct with this ?

[slender gull]

nope

like you can verify your answer by plugging in values that you claim to be in the solution.
An example:
You can check the expression's value at x = 2, which is in your solution (according to you) you see that 0/7 that is 0, is not > 0

So show your work that led to what you got.

[sand star]

So to get the answer do I just have to trial or error each number ?

[slender gull]

Obviously not.

There are ways of doing this. I illustrated the example, only and only to show your answer isn't correct.

[sand star]

Ohh alright

[slender gull]

Before I tell you how to do it, you tell me you did it?

[sand star]

So I make sure that the denominator is not gonna equal to 0

[slender gull]

That's right.

[sand star]

And the nominator should be 0 or negative

[slender gull]

numerator should be zero or negative

why

[sand star]

I mean shouldn’t

[slender gull]

why?

I mean, numerator shouldn't be zero. Okay, why not negative?

[sand star]

Ohh umm I thought it will make the whole value negative but now I think about it

If the denominator also negative

[slender gull]

Exactly.

[sand star]

Then it should be fine

[slender gull]

You get it.

So, can you solve an inequality like that?

[sand star]

Umm what do you mean by that , what inequalities am I solving ? What I am thinking of is it should be any values over 2 or under -2

[slender gull]

Well no that is not how it works. Can you solve something like

(x+1)(x-2) > 0

[sand star]

Like x <-1 x>2?

[slender gull]

yes

How about (x+1)/(x-2) > 0

[sand star]

Same answe r?

[slender gull]

Yes, so essentially you can solve inequalities.

For your original question. Factorise it first.

[sand star]

Like this ?

[slender gull]

More.

Factorise it into linear factors.

[sand star]

D

Is there more to factorise ?

[slender gull]

yes (x^2-1) is also factoriseable

[slate sleet]

hey i have an int calc problem in my channel see if you can help me

[slender gull]

@slate sleet do not beg for help in others' channels.

Wait for someone to help you.

[slate sleet]

ok👍

[slate sleet]

do check it out yourself tho once

[slender gull]

Now, have you solved something of this sort before?

From what I know, you probably haven't. You should check out videos that deal with such examples.

[sand star]

Umm alright what kind of keyword should I search ?

[slender gull]

“Inequalities”
“ Rational inequalities ”
“ Wave curve method for inequalities ”

Probably.

Anything like this.

[sand star]

I actually do understand th4 method of point of interest

But the denominator is kinda confusing

Like the point of interest is -2 And 2 and -1 and 1 right ?

[slender gull]

I'm unsure about that terminology. I don't follow “interest” wdym?

[sand star]

Ohh umm alright cause I search on those videos mostly they talked about point of interest

Which is where the values =0

[slender gull]

Okay got you.

So yes +-2 +-1 and 0 would be the interest values as you say it.

After that you more or less start from the right end, and just kind of keep alternating postive and negative sign. (As long as you have the inequality written in a standard way, i.e factorised into linear factors and the coefficient of x being > 0 each time.)

[sand star]

I have been trial and erroring using the point of interest

Will this be correct ？

[slender gull]

You don't do that. Once you have all the linear factors. Set them all equal to zero each time, to get the values.

[sand star]

Umm I am really confuse cause this is what I did

And the video suggest after that you plug in the values between the point of interest to find out it is negative and positive

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[lavish glacier]

I have a solution to answer i tried before

[lavish glacier]

but have no clue wtf they are doing

can someone explain it a lil bit

original question

[worn fox]

Repeated use of:

[lavish glacier]

x=e^ln(x)

[worn fox]

Exactly

Twice

[lavish glacier]

does exp mean exponential aka part of this is to the power of

[worn fox]

It's exp(stuff)=e^(stuff)

[lavish glacier]

how do they get the log^2?

[worn fox]

Good question im not sure, some kind of approximation for small x I imagine

[lavish glacier]

bruh

ty man does explain a bit but uni is so dumb lol

.close

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[glad mural]

can anyone help

[nocturne dove]

Just take the LCM

And cancel x+4 from the numerator and the denominator.

[glad mural]

LCM of (1/4 + 1/x)?

[nocturne dove]

Yep

Just like adding fractions

1/x+1/4=(x+4)/4x

[glad mural]

ohh i see

thank you

[nocturne dove]

Np

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[solid imp]

Hi, why are there 2 D's?

[worn fox]

There are two quadratics

Before and after dividing by 2

They have the same solutions

But different discriminants

Not sure why they bothered working out the first one D=16

[solid imp]

huh

but when i try to get the 16

I somehow get 36

[worn fox]

Yeah actually I have no idea what 16 is for

Maybe typo they meant 36

[solid imp]

does the 16 have anything to do with the next step?

btw of = or

[burnt ravine]

ew u use degree instead of radians

[alpine sable]

wdym by cosa=-1 OF cosa=1/2

[solid imp]

It is the solution so am not using it

[worn fox]

Not rly you can get those from D=9

Or just factoring

[solid imp]

alright i will try working on it further myself

thanks for your time

[worn fox]

Of is probs or in their language

[solid imp]

^^

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[alpine sable]

lol in their language isnt it eng

[solid imp]

dutch

[worn fox]

? Lol

People can speak more than one language

[alpine sable]

okk

no he did not say it i sin dutch

[alpine sable]

huh?

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[lament basalt]

Prove:

[alpine sable]

use that $sin^2(x)=1-cos^2(x)$

difference of squares

[ocean seal]

Normal Zeta

[alpine sable]

and $sin^4(x)=(sin^2(x))^2$

[ocean seal]

Normal Zeta

[alpine sable]

so $(1-cos^2(x))^2-cos^4(x)$

[ocean seal]

Normal Zeta

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@lament basalt Has your question been resolved?

[lament basalt]

How is sin^2 x = 1 - cos^2 x?

Is that a rule?

[alpine sable]

that's the pythagorean identity $sin^2+cos^2=1$

[ocean seal]

Normal Zeta

[lament basalt]

[lament basalt]

That's pretty big brain moment, thanks

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[heady finch]

Guys what am I doing wrong here

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@heady finch Has your question been resolved?

[heady finch]

<@&286206848099549185>

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[heady finch]

.close

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[weary void]

how do you get the highlighted bit from the previous line

i understand that sin(2*(x/2))= 2sin(1/2x)

anyone?

this is proof by inductiond

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[weary void]

.close

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[deft kettle]

The least distance, of sum of distances of two points from a third point which satisfies the eqn of the line, HAS to be their midpoint right?
Well am given an equation 3x+2y+10=0 with two points ON it namely A(4,2) and B(2,4) and am asked to find the minimum sum of distances from some point P which satisfies the condition of the line, ie AP+PB should hold the least value possible... When i took the midpoint of AB out, i got (3,3) and for some reason this point doesnt satisfy the eqn of the line...why?!

[deft kettle]

there can be only one line through two points, and the midpoint LIES on the line made by the two points then how come am not getting the answer?

and not just the midpoint i mean, any point b/w A and B should satisfy right

[oak perch]

Not just midpoint, any point on that line segment

[deft kettle]

yes yes

[oak perch]

So just the length of that line segment

[deft kettle]

oh i think i got the answer

however i still dont get why does the midpoint not satisfy the eqn

[oak perch]

? It satisfies