help-0

[alpine sable]

Reading from either side has same digits

[opaque inlet]

Yeah ok

Can we do 10b?

[alpine sable]

Hmm lemme see

[opaque inlet]

I’ll give it a try too

[alpine sable]

Here’s a way I think will be intuitive

Or do u want to try it first

[opaque inlet]

(A,G,B),G,G,G

Try first

[alpine sable]

Sure

[opaque inlet]

4! * 2!

Is that it?

[alpine sable]

Yes

[opaque inlet]

Les gooo

How do we do 11?

Wait let me try

[alpine sable]

Hmm

[opaque inlet]

Actually nvm

Idk know how to do this

[alpine sable]

Ok so imagine it this way

U first make the the three boys sit

So that’s 3! Ways

[opaque inlet]

Yep

[alpine sable]

Then imagine them like this

0101010

[opaque inlet]

Yep

[alpine sable]

1 -> is a boy

0 -> empty seat

[opaque inlet]

Yeah ok

[alpine sable]

We need to make the girls sit in empty seats so that no two girls are together

Hence at most 1 empty seat between two boys

[opaque inlet]

Yep

[alpine sable]

Then we choose 3 out of 4 seats using the combinations formula

And once u have done that , permute the girls in 3! Ways

[opaque inlet]

But why is it 4 empty seats and not 3 empty seats?

[alpine sable]

Cause since there are 3 boys , there will be one gaps between each of the boys and then two end gaps

So 2 + 2 = 4 gaps

[opaque inlet]

Wait nvm

[alpine sable]

We count the end gaps as we can still place girls there

[opaque inlet]

Ok

4C3 * 3!

How do we do question 16?

[alpine sable]

For (a) we just choose 3 out of 25 points

[opaque inlet]

Yeah ok

[alpine sable]

For (b) , we just do 3 choose 5

I think

I might be wrong

[opaque inlet]

Why

[alpine sable]

Lemme think

[opaque inlet]

Ok

[alpine sable]

I’m getting confused whether the slanted lines count

Lol

Like the 5 points on the diagonal count or not

<@&286206848099549185>

[opaque inlet]

Yeah

Idk

[alpine sable]

I don’t wanna give a wrong answer

I guess I’ll wait for someone who knows this to help

[opaque inlet]

It’s fine lol

It’s not like my teachers checking it or anything

Let’s skip 16b. For now

[alpine sable]

No wait if slanted lines count then it’s still simple

If I’m not wrong it should be something like this

[opaque inlet]

All sorts of lines will count

[alpine sable]

Wait lemme write it down

[opaque inlet]

As long as it’s straight

[alpine sable]

I think I got it

[opaque inlet]

Ok

Let moi see

[alpine sable]

Here is how I did it

I did 2 times 5 choose 1 multiplied by 5 choose 3

For choosing the horizontal and vertical lines

Since there’s 5 of them in each I chose 3 points from it

Next I did 4 choose 1 multiplied by 4 choose 3 for the slant lines of length 4 points

Similarity for 3 point length lines

And finally 2 choose 1 for the two diagonals of the grid

[opaque inlet]

I don’t understand any of it tbh

[alpine sable]

Oof

Lemme write again

[opaque inlet]

Sorry

[swift shore]

@alpine sable if diagonals didn’t count, wouldn’t it just be 5C3 * 10

[alpine sable]

Yeh

[opaque inlet]

Wait I’ll have a look at the answer in my textbook and compare it to 5C3 * 10

[alpine sable]

Sure

[swift shore]

I have a feeling diagonals might count, because (c) talks about the vertices of a triangle, which have lines on diagonal dots

[opaque inlet]

But why is it 5C3 * 10?

[alpine sable]

Choose 3 points from 5 , but there is 10 such lines

Counting 5 vertical and 5 horizontal

[opaque inlet]

Ahh ok

Thanks for the clear up

[hearty stirrup]

If you want to form a triangle, can't you just pick three points that don't lie on a single line

you computed picking points on a straight line in part b

[alpine sable]

Ik but for that we need to first find all points that do

And subtract from a

[opaque inlet]

16c. Answer is 2148

[alpine sable]

To get c

[hearty stirrup]

Oh I thought we were doing c)

[opaque inlet]

The answer for 16b is 152

[alpine sable]

What’s the answer of 16b

Yup

Diagonals count I guess

[opaque inlet]

I barely understand this

[alpine sable]

One sec

[opaque inlet]

Can u give a more in depth explanation of ur workings pls

[alpine sable]

Lemme write it with diagrams

[swift shore]

5C3*10 + 2(5C3 + 2 * 4C3 + 2)
@alpine sable I thought this would work but It didn’t

2() because the diagonals go up-right and up-left, 5C3 for center diagonal, 2*4C3 for the four dot diagonals on either side, and 2 for the three-dot diagonals

[hearty stirrup]

Horizontal and vertical lines aren't too hard to understand. For horizontal lines, start by picking any horizontal line. Then choose three points out of five to be the "vertices" of the triangle. The same works with vertical lines

There are five horizontal lines and you choose 1 of them. You also have five vertical lines and you choose 1 of them. This gives you 10 total straight lines. In each of these straight lines, you choose 3 out of the five possible points which gives you that 5C3 * 10 component

[opaque inlet]

I understand the 5C3 * 10 part

[hearty stirrup]

Notice a symmetry in the diagonals. This means that we only need to count half of it

[alpine sable]

Oh

[hearty stirrup]

There are multiple main diagonals

[opaque inlet]

I’m struggling with understanding the diagonals

Sorry autocorrect

[opaque inlet]

Ohhhhh

[hearty stirrup]

count the number of ways you pick your diagonal this way

[opaque inlet]

So we count half and then multiply by 2

[hearty stirrup]

then the same works when you consider this way

[alpine sable]

Here

I drew it

Similarly for diagonal of length 3

[opaque inlet]

Ahh ok

[hearty stirrup]

yeah, so count all the ways of picking straight lines in the direction of the yellow line. Then multiply by 2 to count all the ways of picking straight lines in the direction of the pink line

[alpine sable]

Exactly what I did in red

[hearty stirrup]

that should be all of the ways of picking three points along a diagonal as far as I can see

[alpine sable]

I’m getting answer 140

Where did the remaining 12 come from lol

From my method

[opaque inlet]

There are 7 diagonals in the same direction as yellow

[alpine sable]

Wut

[opaque inlet]

7*2 = 14

[alpine sable]

I think this has to do with something like multiplying 4 x 4 on the 3 diagonal part

Then we get 100 + 16 + 16 + 20 = 152

But why do we need to do that

[opaque inlet]

I don’t understand 😭

[alpine sable]

Me neither

[opaque inlet]

Skip question?

[alpine sable]

@hearty stirrup lol please help

Bruhhhhh

[swift shore]

Me too

Oh I got it

[swift shore]

Guys

[alpine sable]

There is one more type of 3 dot diagonal

[swift shore]

So this was right

[opaque inlet]

Can we do question 10

[swift shore]

Yeah there’s 12 more 3 dot diagonals

And they’re in really weird orientations

[alpine sable]

Yup

Saw one of them

It’s like in weird positions

[swift shore]

But yeah if you count them all, they total 12

[swift shore]

Isn’t it 26*25*5*4?

[hearty stirrup]

Oop sorry, I’m eating dinner rn lol

[alpine sable]

Np

@swift shore yeh I saw it

[hearty stirrup]

Willl be back to do more combinatorics in about 15 mins if y’all still stuck on new problems

[opaque inlet]

Wouldn’t you need to multiply 4! Onto that?

Bcuz we don’t know the position of the vowels

[swift shore]

You’re totally right, yes

[opaque inlet]

Ok

[alpine sable]

@swift shore got it

[swift shore]

Yeah this only works assuming it’s C-C-V-V, so we have to multiply by 4! to account for all rearrangement of such words

[alpine sable]

There is 12 more 3 point diagonals with the distances like this

[opaque inlet]

Yea

Can we do question 14?

[alpine sable]

Like 2 vertical and 1 horizontal point comprise distance between two points

Sure

[swift shore]

Yeah, over 1 down 2 over 1 down 2

[alpine sable]

It’s really tricky to see that

[opaque inlet]

I did 6C2 * 5C2

[alpine sable]

Anyway I gtg now

Cya guys

[opaque inlet]

<@&286206848099549185>

[opaque inlet]

Can anyone help me on 16?

[hearty stirrup]

What about cases like AARR

Oh wait I misread the problem statement

[lone heart]

@opaque inlet Has your question been resolved?

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[quick zealot]

Hi, I have a question about my homework

[quick zealot]

its about question 8, I have already seen the answers but my question is why option b is not a continuous function

I figured that statement 8b represents a straight line, because for all x there exists a y, so a straight line, right? And a straight line is a continuous function, so.. what am I doing wrong here

This is from the book 'Analysis with an introduction to proof by Steven R. Lay btw

[swift shore]

No no, that’s just a function

Like consider f(x) = x

That is not constant

But certainly, for all x in R, there exists a y in R such that f(x) = y

[haughty wren]

hwllo

[swift shore]

@quick zealot

[haughty wren]

oh sorry

[swift shore]

np

[quick zealot]

f(x)=x is not contstant?

I think it is, right?

[swift shore]

No, constant would be like

No matter what you plug in, the output is constant

Ie f(x) = 5

Or something like that

[quick zealot]

Google says a straight line is constant, or am I missing the point here

[swift shore]

Do not think of it like that

Google has vague answers a lot

A function f(x) is called a “constant function” if f(x) = c for some constant c

[quick zealot]

yes i agree

[swift shore]

When you graph it in the x-y plane with real numbers, you get a horizontal straight line

[quick zealot]

yes

[swift shore]

Ok

[quick zealot]

soooo.. then 8b is a constant function, because its a horizontal straight line

[swift shore]

Why would that be the case

Try to think of a counterexample

$\forall x \exists y$ such that $f(x) = y

[ocean seal]

abs_0
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[quick zealot]

you just said yourself theA function f(x) is called a “constant function” if f(x) = c for some constant c

[swift shore]

C is a placeholder for a fixed number

[quick zealot]

yeah, but y can be a fixed number in this case

[swift shore]

Here, I can be a little less vague because I see where you’re tripping up

Do you know what a function actually is

Like, in set theory terms

[quick zealot]

not yet i think

[swift shore]

Ok then nvm

[swift shore]

Not necessarily

I can make a function f(x) = x^2

For all x, there is definitely a y (namely x^2) such that f(x) = y

[quick zealot]

yes in this case you have a constant function

[swift shore]

X^2 is not constant though

[quick zealot]

huhhh

[swift shore]

And it fits #8b’s description

Dude the description says “for all x, there exists a y such that f(x) = y”

That’s for (b)

[quick zealot]

yes

the statement implies

a straight line

agree?

[swift shore]

No

I just gave an example

X^2

Is a function that satisfies that definition

And isn’t constant

[quick zealot]

i mean it could be anything

so it could be a straight line aswell

but also can be your example

right, just one has to fit

[swift shore]

You’re right, (b) fits a lot of functions

But that’s not what they’re asking

They’re asking which description best fits a constant function

In other words, guarantees a constant function

(B) includes a lot of junk functions that aren’t constant

So it’s not a valid answer

[quick zealot]

ohhh I think the word 'best' is the thing im tripping over

because b could be a constant function, but not always

[swift shore]

Oh yeah

[quick zealot]

so c is a much better option

[swift shore]

Exactly I get your confusion, the wording is kinda vague

Exactly

In fact (c) is the definition of a constant function

[quick zealot]

yeah its vague

alright

Big thanks man!!

[swift shore]

Yeah good luck dude!

Remember to .close

[quick zealot]

thank you sir! :)))

.close

[lone heart]

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[swift shore]

Np

[lone heart]

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[desert sand]

can anyone help me with this?

[severe sluice]

PQ is an arc with center O, right?

[desert sand]

yup

[severe sluice]

calculate the area of the sector

and the triangle (which is an isosceles right triangle)

[desert sand]

ah

i see

[lone heart]

@desert sand Has your question been resolved?

[lone heart]

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[finite parrot]

A= {x:x € N, 9<x<99 and the sum of digits of x = 7}

[finite parrot]

what is meant by
sum of digits of x=7

is it the cardinal number

[median dirge]

Um. It means.

x is such a natural number that it belongs to the interval (9,99)

And

The sum of its digits

is 7

Like

Lets say

16

It lies in the interval

And

Its sum of digits is 7

[finite parrot]

what is meant by sum of digits

@median dirge

[median dirge]

Sum of digits.

Do you know what digits are?

[finite parrot]

yes

[median dirge]

So

1283 is a number

What are its digits?

[finite parrot]

ohh

1,2,8,3

[finite parrot]

so this is a really long set then

i have to add the digits right?

like this

34 = 7
43 =7
61 = 7

only numbers which give 7 right?

@median dirge

[median dirge]

Yeah

Exactly

Not so long

The interval limits it

[finite parrot]

okay

thanks

.close

[lone heart]

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[finite parrot]

[lone heart]

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[alpine sable]

is that correct?

argument less than pi so its just top half

and smaller than 2 on the circle?

oh wait no its wrong

is it purple area?

i think its purple area actually

[lone heart]

@alpine sable Has your question been resolved?

[supple tundra]

yh purple area

[lone heart]

@alpine sable Has your question been resolved?

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[alpine sable]

thanks

[lone heart]

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[alpine sable]

need matrix terminology help

[alpine sable]

So you got 3X3 matrix M

when you find each of the 'cells' (is cells the right word?? each of the number values in a the matrix? what they called?) corresponding 2x2 matrix

(which you apply the + - + - + - + - + thing to)

then you get the matrix of minors?

wait no im confused already

terminology of matrix of minors/ matrix of co - factors/ whats the + - + matrix actually called, etc.

i think co factors is when you apply the 2x2 thing to each respective cell

but thats already got the + - + thing applied to it

so what on earth is minors

[lone heart]

@alpine sable Has your question been resolved?

[lone heart]

@alpine sable Has your question been resolved?

[lone heart]

@alpine sable Has your question been resolved?

[wide raven]

@alpine sable

a minor is the determinant of the 2X2 matrix

a cofactor is when you apply the +- sign accordingly

[alpine sable]

but i thought the minors had the co factor applied already???

because i always have

and ive always gotten it right so far?

am i misunderstanding or have i always gotten lucky or something?

e.g for matrix
a1 b1 c1
a2 b2 c2
a3 b3 c3

where A1 is the corresponding co factor of a1

for matrix
A1 B1 C1
A2 B2 C2
A3 B3 C3

i have always put the minors into this

so as soon as i work out A2 for example, i do -[b1c3 - b3c1]

and then when i work out the determinant e.g for the A's

i just do a1[A1] + b2[B2] + c2[C2]

are you telling me this is wrong and the minors should not be involved in the determinant?

[wide raven]

lemme read

wait

[wide raven]

this is cofactor

[alpine sable]

its got the - there tho?

[wide raven]

yeah cofactor is with sign

[alpine sable]

if a minor is a cofactor with the + - + applied, isn;t that a minor?

[wide raven]

minor is without sign

[alpine sable]

oh its minor first

oh so basically

do u ever actually use a minor then?

[wide raven]

not actually

[alpine sable]

because ive always just went straight to co factor then i guess

which is where my slight confusion was

[wide raven]

yes

done then?

[alpine sable]

uh 2 minor other questions

so the + - + thing

does it have a name?

like if you wanna say 'apply the [+ - + thing]'

[wide raven]

not actually

idts

[alpine sable]

would you just say turn the matrix of minors into matrix of co factors then i guess?

[wide raven]

yes

[alpine sable]

and secondly, whats a value in the matrix called, like a singular number?

i called them 'cells' earlier

but thats me guessing

[wide raven]

yea i think it would work

[alpine sable]

oh alright, just wanted to make sure all my terminology was alright if i ever need to explain to someone. Thanks.

[wide raven]

we used to call it just "values"

no problem

[alpine sable]

.close

[lone heart]

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[rigid ravine]

There are 60 spots for the job called economics education. The number of applicants is 170% of the number of spots . How many people applyed for the education?

[orchid sparrow]

170% of 60 is what?

[rigid ravine]

102

So 102 people applyed for the job?

[orchid sparrow]

yes

[rigid ravine]

Ok thx

[orchid sparrow]

np

[rigid ravine]

The population in Europe was 730 million in 2010. In Sweden, the population was 9,400,000. What percentage of Europe's population lived in Sweden?

[hearty frost]

how do you take out percentages ?

(9.4 million/730 million)*100

[rigid ravine]

12.8

1.28

So 1.28%

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[lone heart]

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[rocky spindle]

does arctan(i) exist? if so what is it?

[severe sluice]

behold my googling skills

https://math.stackexchange.com/questions/3330016/what-is-the-solution-to-arctani

[rocky spindle]

thanks

.close

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[karmic rapids]

I'm trying to understand u sub right now, but I don't quite get what was done here:

[urban pine]

think of u as u(x)

[karmic rapids]

but then du=6x^2dx

[severe sluice]

yeah

so...?

[karmic rapids]

shouldn't it be du=6x^2

[severe sluice]

excuse me, where did the dx in the RHS go

[karmic rapids]

but the derivative of 2x^3+1 is 6x^2?

[urban pine]

so you're saying the derivative of u wrt x is 6x^2
aka du/dx = 6x^2

[urban pine]

this is sort of an implicit diff way (that's ok, but don't lost that dx)

[karmic rapids]

du/dx = u'(x)?

[urban pine]

yes

[karmic rapids]

OH

thank you

I get it now

[urban pine]

yay 😄

[karmic rapids]

.close

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[eager shale]

How to solve BCD

[severe sluice]

when you have an isosceles triangle, the 2 angles opposite to the equal sides are equal.

use this with the fact that the sum of the interior angles of a triangle is 180deg

[urban pine]

haven't worked this out, but angle sums of ∆ACD and ∆BCD seem promising

i think you can express it in terms of angle A = x and angle D = 26

[lone heart]

@eager shale Has your question been resolved?

[eager shale]

I get that stuff, but I can't comprehend how I'm supposed to come up with the values tho

[alpine sable]

Here u go

Don’t mind the hair on the notebook Lel

[ashen raptor]

Hello

[eager shale]

Why do you divide ACD?

[alpine sable]

Divide ?

Sorry I don’t get it

[eager shale]

It's first 2ACD=180 and then ACD=90

[alpine sable]

Oh I divide both sides by 2

So I can get value for ACD

[eager shale]

.CLOSE

.close

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[rigid ravine]

how much promilles is 6g of 1g

[gray isle]

promilles?

[rigid ravine]

per thousand

[gray isle]

start with something like
6 = x/1000 * 1

[rigid ravine]

i dont understand this one

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[lone heart]

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[lone heart]

@alpine sable Has your question been resolved?

[lone heart]

@alpine sable Has your question been resolved?

[alpine sable]

Lol

Ur prayers will be answered holdup

@alpine sable

What math is this?

@alpine sable Post the entire question please

[lone heart]

@alpine sable Has your question been resolved?

[charred flint]

.close

[lone heart]

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[alpine sable]

<@&286206848099549185>

[remote heron]

im bad at math but 37.5N is a nonstandard way to write bearings, right

unless you want to just drop the N

and call it 37.5 in nondirectional bearing notation

[lone heart]

@alpine sable Has your question been resolved?

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[supple tundra]

,,

[supple tundra]

The question is

For the first circle, shouldn't it be $\int \frac{\sec(t)\tan(t)}{\sec(t) \sqrt{\sec^2(t)-1}} \iff \int \frac{\tan(t)}{|\tan(t)|} = \pm \arcsec(x+2) + c$

[ocean seal]

azeem321

[supple tundra]

Why have they assumed that $\sqrt{\sec^2(t) - 1} = + \tan(t)$ is my question

[ocean seal]

azeem321

[lone heart]

@supple tundra Has your question been resolved?

[woeful heart]

can u post the whole question

im assuming it is maybe defined in a certain range

[supple tundra]

I think I've figured it out. So if $x+2 = \sec(t)$ then $\tan(t) = \sqrt{(x+3)(x+1)}$. The natural domain for the function in the first integrand is $x>-1$ and $x<-3$. Hence, for these x values, $\tan(t) > 0$

[ocean seal]

azeem321

[supple tundra]

.close

[lone heart]

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[woeful heart]

just another thing

about these inverse trig functions

[lone heart]

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[woeful heart]

@supple tundra if you wanted to define an inverse function on this

[woeful heart]

it isnt clear which way around you are defining it

and the ways you can define it are negative to each other

.close

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[supple tundra]

ahh, i see thanks!

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[surreal abyss]

Hi everyone, sorry for bothering, I have a question about solving logarithmic problems, I don’t really understand what the rules are to solve these…

[surreal abyss]

I have tried a few before, but didn’t get the right answer

[lone heart]

@surreal abyss Has your question been resolved?

[marsh rapids]

What is that power on the left notation ?

[pale kestrel]

pretty sure its the log base

[surreal abyss]

Indeed

Sorry if isn’t the notation you used to

[pale kestrel]

i would advise trying to write everything inside the log

as a power of the log base

or at least, something related to the log base

for example 27 = 3^3

$$27 = \sqrt{3}^6$$

[ocean seal]

Shuri2060

[pale kestrel]

Also the roots arent helpful

writing them as powers would be more helpful

$$\sqrt{3} = 3^{\frac{1}{2}}$$

[ocean seal]

Shuri2060

[surreal abyss]

Okay Thankyou

[tawdry sphinx]

are you solved? @surreal abyss

[lone heart]

@surreal abyss Has your question been resolved?

[lone heart]

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[brave aurora]

Can anyone help me with this problem?

[gray isle]

why have you tried?

[brave aurora]

why?

I have tried

[gray isle]

whoops

what

sry

[brave aurora]

i tried subtracting 18 from 24

cuz it would become 3t, and then 3(6)=18

[gray isle]

what's your issue with the result

[lone heart]

@brave aurora Has your question been resolved?

[brave aurora]

it isnt right

[pale kestrel]

it isnt 6? 🤔

issue with the answers, not your working.

[lone heart]

@brave aurora Has your question been resolved?

[brave aurora]

oh 😦

[lone heart]

@brave aurora Has your question been resolved?

[lone heart]

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[alpine sable]

Hello

I need help in determining the function equation for ? and ?2

?2 is parallel to Boulevard veilleux

[pale kestrel]

no more info???

?2 is arbritrary no?

is it halfway?

[alpine sable]

Its quite a weird question in french

?2 is halfway through Boulevard Morin

[pale kestrel]

ok i think i get it maybe

you should find the 3 coordinates

for the 3 vertices of the triangle

[alpine sable]

Oh

[pale kestrel]

this will get you the midpoint coordinates

and you can go from there

[alpine sable]

Ok thanks alot

.close

[lone heart]

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[minor crypt]

Can someone ETLI5 the difference between infimum, lower bounds, minimum and minimal elements.

[minor crypt]

In the context of posets.

[severe sluice]

alright

let's say we have a poset $(M, \leq)$

[ocean seal]

Mobius Earth Gang COO Sam.

[severe sluice]

and a subset $N \subset M$

[ocean seal]

Mobius Earth Gang COO Sam.

[severe sluice]

the definitions for lower bounds and infimums are similar to the definitions with real numbers

k is a lower bound of the subset N if k <= all elements in N

k is the infimum of N if k is a lower bound of N and (all other lower bounds) <= k

wait a sec @minor crypt?

you there?

(ping me when you're back)

[minor crypt]

I am @severe sluice

[severe sluice]

right

so do you understand what i said there?

[minor crypt]

I dont understand the definition of infimum, no.

[severe sluice]

so.... which part do you not understand?

[minor crypt]

and (all other lower bounds) <= k

so an infinimum is a lower bound where all other lower bounds <= infimum

I guess you could say it's the maximum of the lower bounds then 🤔

[severe sluice]

consider the set S, which contains all the lower bounds of N (that's in M)
then the infimum of N will be the greatest element in that set

[minor crypt]

gotcha

[severe sluice]

now for the definitions of minimum and minimal (tbh those should mean the same thing, but apparently they dont)

[minor crypt]

If I understand it properly:

• minimum: a unique element that is $\leq$ all other elements
• minimal element: element that has no other element $\leq$ to it (other than itself)

[ocean seal]

Axhraf

[severe sluice]

argh i hate my internet yes, you're right

[minor crypt]

alrighty

Now lets try this on an example.

Struggling to come up with a poset relation lmao

just got a random google image of a Hasse-diagram

[severe sluice]

like
1<=2
1<=3
2<=4
2<=5
3<=4
and so on?

[minor crypt]

minimal elements: 8, 9, 10, 11, 12
minimum: /
lower bounds: ...

hmm I feel like we gave minimal elements and lower bounds the same definition

[severe sluice]

hmm
you must specify a set to take the lower bound of?

[severe sluice]

umm... that's the opposite of the relation i gave, but, well, that's fine.

[minor crypt]

I'm doing it for this Hasse diagram (reading it from bottom to top)

[minor crypt]

so lower bounds are minimal elements of a subset of the poset?

[severe sluice]

no

it should <= all elements in that subset

[minor crypt]

so if we say X={5,7,8,9} $\subset P$

[ocean seal]

Axhraf

[minor crypt]

Then there would be no lower bound of X?

[severe sluice]

the element 1 is one

[minor crypt]

1 is a maximum here, right?

[severe sluice]

i think you're right

[lone heart]

@minor crypt Has your question been resolved?

[minor crypt]

hmm

[lone heart]

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[median osprey]

so i did the following

but thats not the answer

am i missing something?

[open linden]

yes because x/2 + 1 is not equal to (x+1)/2

(x+1)/2 would be x/2 + 1/2

you want x/2 + 1

[median osprey]

how did the 2+1 go down ?

[open linden]

wdym

[median osprey]

i dont understand what you said

[open linden]

so g(x)

is adding 1 to x

So g(x/2)

is adding 1 to x/2

[raw shard]

lol your answer is right

wait

no i didn’t read right

was talking about the answer selected on the first image

[median osprey]

yes i get that? so you get

[raw shard]

ok so f(g(h(x))) = f(g(x/2)) = f(0.5x+1) = 2(0.5x+1)

no

you did it in the wrong order

[open linden]

Like for eqample let x = 1

[raw shard]

h is on the very inside

[open linden]

x/2 = 1/2

And 1/2 + 1 is 3/2

[raw shard]

the way you did it it would be the second most inner

[open linden]

but if you did (x+1)/2 that would be (1+1)/2

=1

[open linden]

yeah

[median osprey]

i see

wait im still getting it wrong

im getting x+1

[pale kestrel]

what

[raw shard]

you

[pale kestrel]

where does the equals sign go

after the 1st line

[raw shard]

how did you even come to that conclusion

[median osprey]

idk i followed what you said

[pale kestrel]

how does the 2nd line follow from the 1st

[raw shard]

are you aware you didn’t multiply the whole thing by 2

it doesn’t

[pale kestrel]

lol

[raw shard]

they’re doing function composition

[median osprey]

yeah

im lost here

[raw shard]

ok so f(g(h(x))) = f(g(x/2)) = f(0.5x+1) = 2(0.5x+1) = x+2

do you follow this

[pale kestrel]

latex it

[raw shard]

not sure how that would help really

but ok

[pale kestrel]

just looks ugly xd

$$f(g(h(x))) = f\left(g\left(\frac{x}{2}\right)\right) = f(0.5x+1) = 2(0.5x+1) = x+2$$

[ocean seal]

Shuri2060

[median osprey]

ok i get it

so we times the 2 by the whole thing

[raw shard]

are you sure you get it

[open linden]

yay

[median osprey]

i was missing the 2

thanks guys

.close

[lone heart]

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[celest bison]

Hey guys

[celest bison]

Can someone help me with this question

Can someone please lay out the steps to solving one of these?

[open linden]

ok

denominator is the same so you add numerators

(6x+12)/(x+2)

sorry idk how to do latex

And then factorise numerator

6(x+2)/(x+2)

Cancel x+2

answer is 6

[buoyant kayak]

don't do people's work for them

[celest bison]

@buoyant kayak this is a question from a failed practice quiz. It’s not for marks

[open linden]

they said lay out the steps

[celest bison]

Thank you so much @open linden I will get practicing on them now

[celest bison]

I just couldn’t remember to save my life

Thanks guys

Your awesome

[buoyant kayak]

if it was an actual quiz, that's bannable...

[buoyant kayak]

again stop doing people's work

[celest bison]

No it’s a practice quiz

[alpine sable]

sorry didnt see ur message

[celest bison]

.close

[lone heart]

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[alpine sable]

For

[lone heart]

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[astral scarab]

Not sure how to get started on this one if someone could push me in the right dirrection that would be great thank you

[raw shard]

evaluate the definite integral using integration by parts first

then just input the known values

[astral scarab]

so would that be x^2/2 *f(x)

@raw shard

[raw shard]

no

$\int f(x)g(x)\dd{x}\neq\left(\int f(x)\dd{x}\right)\left(\int g(x)\dd{x}\right)$

[ocean seal]

quantum

[lone heart]

@astral scarab Has your question been resolved?

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[rain pagoda]

Back at it again, not sure how to solve

[rain pagoda]

^^

[severe sluice]

can you give the statement of the law of sines?

[rain pagoda]

i dont know it

[paper coral]

do u know what the sin law is

[severe sluice]

well...
sin A/a = sin B/b = sin C/c, right?
(where side a is opposite to angle a / same for b and c)

[pale kestrel]

if u dont know what the law of sines is... look it up 🤔

[rain pagoda]

alr

[rain pagoda]

ohh right

yeah i do

So now what tho

[severe sluice]

what does the law of sines tell about AB and angle C

[rain pagoda]

im thinking hold on

i dont know im sorry

do you mean like the sinA/a

Etc

or sum else

[lone heart]

@rain pagoda Has your question been resolved?

[lone heart]

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[solid coyote]

is this channel open

[gray isle]

yes, ask your math question

[solid coyote]

i need help defining primary trig, when its used and an equation for it, i dont understand what like any of that means

its for a cct

[orchid sparrow]

ask the question

then only we could explain something

[solid coyote]

whats primary trig

[orchid sparrow]

that doesnot seems a mathemtics question

this is definition

[solid coyote]

yes, there is no "question" i dont get what primary trig is and when its used

[orchid sparrow]

u can google it u can get a better explanation

if u have doubt in any question (real maths)

then i can help

[solid coyote]

okay

[lone heart]

@solid coyote Has your question been resolved?

[lone heart]

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[median osprey]

im i doing something wrong here?

[hollow cairn]

Yes

[median osprey]

can you please explain how to do it

[pale kestrel]

wut

how do you go from 1st to 2nd to 3rd

[rich panther]

please show the full question

[median osprey]

thats the question

[pale kestrel]

never mind full q

You need to understand what log means

[median osprey]

according to the example they gave us

it should work?

[urban pine]

this is more of a change of base question

[pale kestrel]

Ok?

And how are you using those examples to get this

for example

$$\log_2x=2^x$$

[ocean seal]

Shuri2060

[pale kestrel]

How do you get this?

[median osprey]

if i do change of base it does work

[pale kestrel]

we can explain

[pale kestrel]

but do you get how none of those are equal

[median osprey]

no i dont

[pale kestrel]

Ok, why do you think these 2 are equal

[urban pine]

these are very different functions

,w plot x and log_2 x and 2^x from -3 to 3

[ocean seal]

Results provided by WolframAlpha

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

Requested by citrusmunch#0375

[median osprey]

it seems to have same structure'?

[pale kestrel]

Bruh

[pale kestrel]

^ all 3 are completely different

its like me telling you $$x^3=x^2 = x$$

[ocean seal]

Shuri2060

[urban pine]

the only relationship is that log_2 x and 2^x are inverses so are reflected about the line y = x

but you can't equate them

[median osprey]

ok

[pale kestrel]

Alright so the approach

[median osprey]

i applied same method to this

[pale kestrel]

its not the same

lol

what you did just now is completely wrong

[pale kestrel]

How did you do this

[pale kestrel]

??????????????????

NO

you are saying

[median osprey]

thats how they explained it to us

[pale kestrel]

$$7 = 2^7$$

[ocean seal]

Shuri2060

[pale kestrel]

Then whoever explained it doesn't know what they're doing. Or you misunderstood.

[median osprey]

here is similar example

they did the same

[pale kestrel]

How is that the same.

^ ?

[median osprey]

ok so how are we meant to do it?

[pale kestrel]

$$\log_2128=\log_22^7=7$$

[ocean seal]

Shuri2060

[pale kestrel]

THIS would be the same.

[median osprey]

log change base?

[pale kestrel]

what change of base?

thats something differnt

[pale kestrel]

Do you get how these 2 are different?

[median osprey]

dude i have done pretty much the same thing except i didnt put =7 to the end

[pale kestrel]

and how 1 is wrong

NO

you wrote that thing is equal to 2^7

2^7 = 128

128 =/= 7

???

$$\sqrt{49} = 7^2$$

[ocean seal]

Shuri2060

[pale kestrel]

That's what you wrote

Important you get where you went wrong

^ cus u ended up writing this

[median osprey]

ok so for this one

[pale kestrel]

$$\sqrt{7} = 7^2 = 7$$

[ocean seal]

Shuri2060

[pale kestrel]

Anyways. Back to the question if you get why you can't do that

[pale kestrel]

ok

that is change in base formula

You need to figure out which of those expressions is equal to log_2 x

[pale kestrel]

They just want you to recognise change in base formula

thats all

[rich panther]

maybe this example will help

[pale kestrel]

Either you remember the change in base formula or you learn how to derive it (not too hard)

[median osprey]

i know the formula

[pale kestrel]

Then you should recognise 1st option is correct

[median osprey]

i just didnt know when to use it

[pale kestrel]

If you know the formula

you will recognise 1st option

Otherwise, you just go through each option

and try to simplify them

[median osprey]

alright.. thanks for the help guys!

.close

[lone heart]

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[orchid sparrow]

Q2

<@&286206848099549185>

if in day a man does x work the 40x = 1/6 similarly 60y=1/6 80z=1/6

x=1/240 , y=1/360, z=1/840

now?

is it right?

now?

[pale kestrel]

nvm

x = work/day

I don't get it

you've got to be clear what your letters represent

[orchid sparrow]

yes

[orchid sparrow]

x=work per day by men

[pale kestrel]

month?

theres no mention of day

[orchid sparrow]

then women and children respectively

sorry by month

[pale kestrel]

x = work/month, men

[orchid sparrow]

yes

[pale kestrel]

your equation doesnt make sense still

40x = 1/6

wait let me think nvm

[orchid sparrow]

x is the work done in a month

[pale kestrel]

ok yh mb

you're good

[orchid sparrow]

hmm

[pale kestrel]

x=1/240 , y=1/360, z=1/840

[orchid sparrow]

yes

1/10x+10y+10z is the answer

but either the options are incorrect or i am doing wong

[pale kestrel]

,w 1/(1/24+1/36+1/84)

[ocean seal]

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Requested by Shuri2060#9525

[pale kestrel]

ill think about it

[orchid sparrow]

yes this is the answer i am getting

https://www.competoid.com/quiz_answers/14-0-60463/Question_answers

this is answer on the site

it is quite complicated and confusing

[pale kestrel]

,w 10+(2/3)10+5

[ocean seal]

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Requested by Shuri2060#9525

[pale kestrel]

,w 6 * 40 / (65/3)

[ocean seal]

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Requested by Shuri2060#9525

[pale kestrel]

....

Well I understand their logic

and I understand your logic

I have to think which is right

[orchid sparrow]

hmm

i lil bit understood theirs too

[pale kestrel]

ah.

hahahaahaha

[orchid sparrow]

they converted all the variables into men and then made it a linear eq in one variable

[pale kestrel]

bruh

80z=1/6
z=1/840

[orchid sparrow]

and i directly put the values and solved

[pale kestrel]

Look

[pale kestrel]

.

[orchid sparrow]

ok

[pale kestrel]

,w 1/(1/24+1/36+1/48)

[ocean seal]

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Requested by Shuri2060#9525

[pale kestrel]

Yes both ways are good

[orchid sparrow]

is this wrong?

[pale kestrel]

Check your arithmetic from the start

80z=1/6
z=1/840

^ ??????

[orchid sparrow]

oh boi

480

should be there

i am so dumb still thanks for saving my day i couldnot have ever found this mistake

.close

[lone heart]

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• After 15 minutes, feel free to ping <@&286206848099549185>.
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[slender sparrow]

I've been trying to invert this matrix several times to no avail. I'm using the method of minor matrixes (?), but I always get it wrong. For example, on the top right, I'm supposed to find -1, but I find that (-1*1 - 1 * - 1 ) = 0

[wary stream]

How are you supposed to get -1? It's 0

[slender sparrow]

the correction is always -1 even when I use an online calculator so I'm very confused

[wary stream]

The top right is -1 because of the determinant of top right 4 elements

[wary stream]

That's for the bottom left element of the minor matrix

[slender sparrow]

how am I supposed to do it? I've been doing it wrong

[wary stream]

You forget to transpose it

That's why

Do what you normally do

Then transpose it

[slender sparrow]

oh i'll try to do this now then

thank you

[wary stream]

So because element (3, 1) = -1, transposing makes that element (1, 3)

[slender sparrow]

you're right, it works! thank you so much @wary stream !

.close

[lone heart]

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Remember:
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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[eternal sierra]

My math teacher keeps saying that the natural log is abbreviated as LN and some people say IN

[eternal sierra]

Which one is correct