help-10

[topaz walrus]

what was the question anyway

[lone dirge]

🤯

[gritty path]

2(sin30°) + cos60° + tan60°
lol

[topaz walrus]

hmmm

huge decimal

[gritty path]

2 1/2 + 1/2 + √3

there

[topaz walrus]

yea

[gritty path]

so 3+√3 is the final?

[topaz walrus]

convert the first fraction to an improper

wait

yep

3 + sqrt(3) is correct

hold up

how did u type the root

anyways

i gtg

[gritty path]

thank youuu

.close

[obtuse pebble]

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[next ravine]

Can someone tell me which in maths those questions are related to

I would like to practise them as I find them very difficult

[obtuse pebble]

@next ravine Has your question been resolved?

[timber island]

Work and time for this one

[timber island]

And the first 3 r algebra

[next ravine]

@timber island thanks ❤️

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[obtuse pebble]

@mighty surge Has your question been resolved?

[narrow jackal]

Do you know what Taylor series is?

Because without it, for now I don't really see how this can be solved

Are you sure you wrote it down correctly?

[mighty surge]

Yeap answer is pi/2

[narrow jackal]

oh

💀

[obtuse pebble]

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[odd mountain]

$|x^2 + x - 20| = x^2 + x - 20$

[warm shale]

Meatball.

[spice citrus]

Try solving |x| = x

[odd mountain]

i am getting the solution as x belongs to [4, infinity)

[spice citrus]

Yes

[odd mountain]

alright gimme a sec

[odd mountain]

but thats not the correct answer apparently lol

[ruby elm]

I think it should be x belongs [ -infinity, -5] U [4, infinity].

[spice citrus]

Oh yes of course

[odd mountain]

ya thats the answer in the solution

[high lily]

show your work

[ruby elm]

Just see, a mod always gives positive value right?

[odd mountain]

|x| = x gives me one case correct

[spice citrus]

Yes

[odd mountain]

yepp

[ruby elm]

So, lhs being mod is defined for all x real.

[spice citrus]

which case? btw

[ruby elm]

Now, rhs must also be positive or equal to zero.

[odd mountain]

x >= 0

[spice citrus]

Yes

[high lily]

i am getting the solution as x belongs to [4, infinity)
can you show how you're getting that

[spice citrus]

The same holds for this problem, x^2 + x - 20 >= 0

[ruby elm]

So x^2 + x -20 > = 0.

[odd mountain]

i dont have my mobile phone with me to click a pic so thats kind of the problem

[high lily]

draw on paint

[odd mountain]

ohh right

so, (x+5)(x-4) >= 0 and then solve the inequality?

[odd mountain]

ill do that wait

this is for case 1, which is the only case that had something to return

excuse my brilliant handwriting using the mouse

for case 2: -5 <= x < 4
it gave me x = 4 which i couldnt count in

for case 3: x < -5
it gave me x = 5 which again didnt satisfy the condition of the case

@high lily

[high lily]

not quite sure waht you're actually doing in your casework

for case 2: -5 <= x < 4
it gave me x = 4 which i couldnt count in

for case 3: x < -5
it gave me x = 5 which again didnt satisfy the condition of the case
i don't know what you're actually doing there

what exactly gave you x=4, what gave you x=5

[odd mountain]

drawing it on jamboard is painful 😫

[odd mountain]

here you go case 2

[odd mountain]

and case 3:

[high lily]

you messed up your expansion in case 3

[odd mountain]

damn i realised it just now too

yupp i got the answer, thanks!!

.close

[obtuse pebble]

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[obtuse pebble]

What step are you on?
1. I don't know where to begin
2. I have begun but got stuck midway
3. I got an answer but I'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above

[distant flame]

I tried to unify the scales and then multiply what comes after the equal sign

but ıt didnt work

[timid silo]

first show that b/c must be an integer

[distant flame]

i cant i solve it on pdf know

[timid silo]

?

[distant flame]

but can u give a hint so i start

[timid silo]

I just did

[distant flame]

yup i didnt read it

[distant flame]

okay so b/c its a number

[timid silo]

now convince yourself what the best value of b/c is

keep in mind that b < a

[distant flame]

okay i need more help

cuz this type of question new for me

<@&286206848099549185>

[brazen nacelle]

؟

[distant flame]

i need help with the question

[brazen nacelle]

which?

[brazen nacelle]

alr lemme see

which grade is this?

[distant flame]

i live in turkey right now and we have kind of exam to enter university

[brazen nacelle]

uhm sorry i only solve 10-12

but lemme try

[distant flame]

thats okay

[distant flame]

okay

[brazen nacelle]

nvm it seems complicated

sorry for wasting time

I will try to focus more on the university registration exams

[distant flame]

no thats okay nice to meet u btw

[brazen nacelle]

nice to meet u🙏

[distant flame]

<@&286206848099549185>

[leaden ginkgo]

@distant flame

[distant flame]

thank u it literally was disappeared

.close

[obtuse pebble]

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[lunar hedge]

I said we could just use intermediate value theorem

f is continuous on the compact set and this means there is some m in [0,1] such that we get any value between inf and sup f

Since 1-x is always in [0,1]

We can say that there is such a point

[kind hawk]

well then we get an m with f(m)=1-x after we picked an x

but we want that m and x are the same

[lunar hedge]

m is from the set [0,1]

[lunar hedge]

wait can you explain that a bit more

I think I get it'

[kind hawk]

IVT works by first picking some output value, in our case 1-x and then obtaining an input value m with f(m)=1-x

[lunar hedge]

yes

[kind hawk]

but you want that m=x. you want to pick them "at the same time"

[lunar hedge]

i see

[kind hawk]

like if f(x)=x, then sure I can pick 1-x=0.8 and obtain m=0.8. but then m=0.8 and x=0.2 so they are not equal

[lunar hedge]

so would i have to say f(x)-(1-x) needs to have some point where evaluated at m you get 0

[kind hawk]

for example, yes

so you define g(x)=f(x)-(1-x) and want to find an m with g(m)=0

from where to where is g

is g continuous?

[lunar hedge]

it has to be right

f and 1-x are

so g must be cont

[kind hawk]

yes

[lunar hedge]

from 0 to 1 right

[kind hawk]

domain is [0,1], yes

what is the codomain

[lunar hedge]

greater then 0

[kind hawk]

or better question, what can g(0) and g(1) be

[lunar hedge]

greater then 0

or less then as well

g0<0

g1>0

[kind hawk]

well <= and >=

[lunar hedge]

yeah

[kind hawk]

can you now finish it?

[lunar hedge]

g(c)=0

=f(c)-(1-c)

fc=1-c

x=c

we're choosing c where g is 0

[timid silo]

Good luck getting into the university though.

[lunar hedge]

is everything right

[kind hawk]

yes

although I hope that you give more details when you write it down

[lunar hedge]

yeah I'll be more clear

probably start with f(0)<1 f(1)>0

[kind hawk]

<= and >=

[lunar hedge]

yeah

and then ill explain g

[kind hawk]

(in case of = you are immediately done)

[lunar hedge]

yeah

and then eplain g0<0

g1>0

and then say gc=0

then I'll probably say out everything i did earlier

is that right

=

g0<=0 g1>=0

[kind hawk]

yes

[lunar hedge]

thank you big man

much appreciated

.close

[obtuse pebble]

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[cedar ferry]

Help

[tardy epoch]

the answer is given?

or just plug into wolfram alpha

[cedar ferry]

No

[slender pulsar]

"Expert Answer"

[cedar ferry]

Lmao

[civic zealot]

holy hell the formatting on that question is abysmal.

[tardy epoch]

true

[obtuse pebble]

@cedar ferry Has your question been resolved?

[obtuse pebble]

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[queen fractal]

I have found the stiffness of $980N$, but I am trying to calculate the compression by $EPE = KE \rightarrow 490x^2 = 0.09 $ But I am completely off, I get 0.01355m, but the answer says 1.36m. What am I doing wrong?

[warm shale]

totalminer

[obtuse pebble]

@queen fractal Has your question been resolved?

[obtuse pebble]

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[timid silo]

could anyone help me with this please? (c)

[clever spoke]

Could you provide the problem, in the correct orientation?

[trim portal]

not required

,rcw

[trim portal]

you can use ,rcw to rotate in clockwise dir and ,rccw to rotate in counter clockwise

[clever spoke]

damn, didnt know thanks

!status

[obtuse pebble]

What step are you on?
1. I don't know where to begin
2. I have begun but got stuck midway
3. I got an answer but I'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above

@timid silo Has your question been resolved?

[timid silo]

if you can solve it haha

[clever spoke]

I suppose the question is about providing the proof?

[timid silo]

yes

[obtuse pebble]

@timid silo Has your question been resolved?

[obtuse pebble]

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[sinful ivy]

I don't know how to use the linear interspersion principle to solve

[ruby path]

No idea what that is, but I can help with a combinatorics approach

[sinful ivy]

Yes please that will help

[ruby path]

If an integer $n$ is even, then $n = 2m$, where m is also an integer

[warm shale]

NEONPerseus

[ruby path]

Knowing this we can say $2a_1 + 2a_2 \cdots 2a_{12} = 100$

[warm shale]

NEONPerseus

[ruby path]

With me so far?

[sinful ivy]

Yep

[ruby path]

We can now divide by 2 throughout

$a_1 + a_2 + a_3 \cdots a_{12} = 50$

[warm shale]

NEONPerseus

[ruby path]

Are you aware of the stars and bars formula?

[sinful ivy]

No I don’t think so

[ruby path]

It's used to distribute n identical objects into r identical containers

It's given by $\binom{n - r - 1}{r - 1}$

[warm shale]

NEONPerseus

[ruby path]

Can you think of how this would be applied here

[sinful ivy]

N is 50, r is 12

[ruby path]

Yes good

So your answer would be $\binom{37}{11}$

[warm shale]

NEONPerseus

[sinful ivy]

Thank you so much

[ruby path]

No worries

You can close the channel if you're done

[sinful ivy]

.close

[obtuse pebble]

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[obtuse pebble]

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[mortal thunder]

Answer then explanation thanks

[robust sleet]

No

[mortal thunder]

Meanie

[robust sleet]

Yes

[tardy epoch]

against the rules to give answers

if you want help ask questions

[mortal thunder]

Ohh

.close

[obtuse pebble]

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[glossy ermine]

this one please

.clos

.close

[obtuse pebble]

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[obtuse pebble]

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[unique remnant]

need help with graphs

[tardy epoch]

[unique remnant]

y= -x squared - 2x + 8 -5 equal to x equal to 3

[clear condor]

y= -x^2-2x+8 -5=x=3

hm

[unique remnant]

yesss

[clear condor]

-5=x=3

?

[unique remnant]

yes

i need to draw the graph of it

[dark stirrup]

https://xyproblem.info/

Show us the original problem

[unique remnant]

mk

wait

wait

u meant like take a pic

ok waitt

help

[clear condor]

ohh

[unique remnant]

yea

[clear condor]

do you know how to use the quadratic equation

[unique remnant]

no i dont

is it like

x= -4 -3 -2 -1 0 1 2 ?

or

x= -5 -4 -3 -2 -1 0 1 2

then the x squared is double it?

like the 5x5= 25

the 4x4

!help

[obtuse pebble]

Please read #❓how-to-get-help

[clear condor]

uh

[unique remnant]

u dont understand also?

HELPP

[tardy epoch]

take a picture/screenshot of the original problem

[unique remnant]

i dont have a phone

its destoryed

i wrote it out

[dark stirrup]

Looks like a lot of info is missing

For one, no question is being asked

[unique remnant]

thats how my teacher gave it

[tardy epoch]

then you're leaving out information your teacher told you

[dark stirrup]

I must respectfully disagree and I'm assuming you're missing information

[unique remnant]

no thats exactly what i saw

[dark stirrup]

I must respectfully disagree and I'm assuming you're missing information

What you've given us has no context

Are you trying to graph it?

[unique remnant]

yes

[dark stirrup]

Okay. I see now

You want to graph $y=-x^2-2x+8$ in the interval $-5\le x\le 3$, correct?

[warm shale]

SWR

[unique remnant]

yes

[dark stirrup]

Bet way to do this is calculate y(-5), y(-4), y(-3),...y(2), y(3) and plot those points

Then draw the curve that connects them

[unique remnant]

alr

thx

[obtuse pebble]

@unique remnant Has your question been resolved?

[hallow cradle]

w

[obtuse pebble]

@unique remnant Has your question been resolved?

[obtuse pebble]

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[obtuse pebble]

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[atomic umbra]

i dont understand what more i was supposed to do

,tex My answer: $-32i^{2} + 64ij - 24j^{2} \ $Correct answer: $-56$

[warm shale]

@atomic umbra

[latent walrus]

do you understand what the |...| are?

[atomic umbra]

tbh i dont

i was paying attention when it was taught but i forgot it cause too much notation

[latent walrus]

its the absolute value of the vector in this case, for example u=-4i+6j, and the absolute value gives the length of u, |u|=sqrt[(-4)^2+(6)^2], you can show that by drawing the vector and its components then using pythagoras

[atomic umbra]

OHHHH

so i have to add up the (positive) lengths of each vector?

[latent walrus]

not quite, |u+v| is the abs of u+v which is |-2i+5j|, similar for the u-v

oh, if you meant that, then yes

[atomic umbra]

so i first add the vectors, then absolute value, then square

[latent walrus]

yup

[atomic umbra]

ok ty

[wild swallow]

it's best not to call these "absolute values" but rather their proper name which is "norm"

[atomic umbra]

we call it magnitude

[atomic umbra]

but ive never heard of the word "norm" before

[wild swallow]

also note that writing down expressions like i^2 or ij is nonsensical

[atomic umbra]

ya i thought that too

cause in this case, i/j arent even numbers, real or not

[wild swallow]

sure, this would be fine

[atomic umbra]

is this correct

[atomic umbra]

nice im so cool

.close3

.close

[obtuse pebble]

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[golden hamlet]

how can i find queadratic function(s) which passing two points, opens upward and downward?

[golden hamlet]

(0,-4),(2,0), i seriously suffered this problem for hour

but still have no idea how to properly solve this 😦

[atomic umbra]

so theres a quadratic equation that passes through both points

ok

[golden hamlet]

yes

[tame narwhal]

opens upward and downward?

[atomic umbra]

*or, i think

[golden hamlet]

sorry.
(a) upward and (b) downward

so basically i have to find two functions

[atomic umbra]

@golden hamlet

what is x intercept

and what is y intercept

[golden hamlet]

x int is (2,0), y int is (0,-4)

[tame narwhal]

you can try just with the generic formula for a quadratic, and solve for the coefficients using the given points

[atomic umbra]

from this, can you tell me one of the roots of the function
hint: ||use the x-intercept||

[atomic umbra]

if u still dont understand, pls dont hesitate to ask

[golden hamlet]

yeah so uh, x-int itself is root of function

not sure what else can i do with them

[golden hamlet]

how can i do that? if i use x-int for generic formula, it became 0 = 4a+2b+c, what should i do then?

[atomic umbra]

when x is 2, y is 0. Therefore, (x - 2) is a root of the function (for both u-shaped and n-shaped) because (x - 2) = (2 - 2) = 0.

but since its a quadratic, we have to have an x^2 somewhere

so, we can simply multiply the function by x because we already have one of the x's in (x - 2)

someone take this over i gtg

[obtuse pebble]

@golden hamlet Has your question been resolved?

[golden hamlet]

well guess im giving up then 😦 cwatson gave some glympse but i have no idea how to continue after that mentioned above...

through still thanks for helping

.close

[obtuse pebble]

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[obtuse pebble]

What step are you on?
1. I don't know where to begin
2. I have begun but got stuck midway
3. I got an answer but I'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above

[forest sinew]

yea where are you stuck

[obtuse pebble]

@oak flume Has your question been resolved?

[oak flume]

i uh

everything

test

[forest sinew]

test?

[oak flume]

i need the answer for a test

dont shame me

lmaooo

[forest sinew]

we dont give answers to tests its unethical

[oak flume]

ah

[forest sinew]

but good luck

[obtuse pebble]

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[gritty kettle]

how do u find periods froma graph

[gritty kettle]

@slender pulsar so it'd just be pi?

the width of the repeating?

what abt the top

[slender pulsar]

what top?

[slender pulsar]

period is the width of the repeating

[slender pulsar]

still pi

[gritty kettle]

@slender pulsar

ty

so would the period for this be 2?

[slender pulsar]

yes

[gritty kettle]

ty

.close

[obtuse pebble]

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[boreal spade]

pretty lost on this part of my unit

(the answer is given above, this is the answer key version)

im not sure how to solve to get that

no clue how to get sq root 3 for example

[wanton hull]

you can always ignore a whole rotation for any trig function

[boreal spade]

uhm

not sure what to do though

to actually solve

[boreal spade]

cool

[wanton hull]

both of these angle give the same results when used in trig functions

[boreal spade]

alright

[wanton hull]

so take the first angle

[wanton hull]

960 degrees

[boreal spade]

basically just becomes into uh

[wanton hull]

how many 2pi do you see?

1 whole rotation = 2pi

[boreal spade]

2 full rotations

so 720*

[wanton hull]

yes

[boreal spade]

so 240

[wanton hull]

now we can ignore 720 degrees from it

yes right 240

[boreal spade]

ye

[wanton hull]

now cot theta

is cot +ve or -ve in 3rd quad

[boreal spade]

+ve or -ve?

what are those

[wanton hull]

like will the value be in positive or negative

[boreal spade]

its in the third quadrant so

(-1,-1)

negatives

[wanton hull]

i dont think so

[boreal spade]

oh

[boreal spade]

ASTC

i remember my teacher mentioning ASTC

but im not sure waht it truly means

[wanton hull]

ASTC refers to 1,2,3,4 quadrants respectively

A stands for all, ( all are positive)

S stands for silver (sin and csc are +ve)

T stands for tea( tan and cot are +ve)

C stands for cups (cos and sec are +ve)

it doest actually stand for all silver teacups but its easy to remember taht way

[boreal spade]

our teachers version was 'all students take calculus'

okay that makes sense

A S T C represents what equals positive in that quadrant

and their counterparts

so in our example its positive

cause cot

[wanton hull]

yes exactly

now

we want to basically find cot 240

we know that $\cot (\pi + \theta) = \cot \theta$

[warm shale]

bettim

[wanton hull]

can you find any use for this formula in our question?

[boreal spade]

hm

to be honest ive

never used that formula

[wanton hull]

well they are all there but you dont to mug this up you can visually understand them

nevertheless we can use this

so can we write 240 in pi + theta form?

[boreal spade]

uhhhh

[wanton hull]

pi = 180 degrees

[boreal spade]

so would theta just be

60 degrees

[wanton hull]

yes

[boreal spade]

180 and 60 = 240 cot 240

[wanton hull]

yes

thats it

now what is cot theta

[boreal spade]

60

or well

wouldnt it still be cot 240

[wanton hull]

now its just cot 60

[boreal spade]

oh alright

okay so cot 60

[wanton hull]

yes

what is it

[boreal spade]

okay heres a problem

we have a calculator on the test

which is all ive used to find sin cos tan etc etc, the few times that weve had to use it

but it gives a decimal answer

im not sure how to solve to get the answer like how the answer key has them

[wanton hull]

you use the table

[boreal spade]

okay

we have never used that before

everrr

[wanton hull]

thats so weird

[boreal spade]

i can recall a small

example of what weve done before

i think

for these kind of problems which was

we use the terminal angle and make a triangle

and solve

Kinda hard to see it but it looked more or less like that above

[wanton hull]

that works but its too basic

and time consuming ig

[boreal spade]

wdym too basic

[wanton hull]

that is not effiecient

[boreal spade]

do you know how to use it

i think it might be better to try that out considering she might mark me off if i use other methods

[obtuse pebble]

@boreal spade Has your question been resolved?

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[grizzled shore]

if i want to write that im summing a_i b_j but i and j start and different values how can i do that

[grizzled shore]

does $\sum_{i=1, j=2}^n$

work?

[warm shale]

Frosst

[tardy epoch]

Nah that's not common at all

Just use two summations

[grizzled shore]

it doesn't mean the same thing

i want like a_1 b_2 + a_2 b_3 + a_3 b_4 + ....

[tardy epoch]

Just use i+1

[grizzled shore]

but not 1 and 2, in my case im trying to convert i,j into k

[jolly ginkgo]

whats the original question?

[grizzled shore]

i have a_{i,j} b_k + ...

[tardy epoch]

What

[jolly ginkgo]

what is k?.

[tardy epoch]

Can you write out a few terms of this

[grizzled shore]

just some other enumerator

[royal basin]

$\sum_{i=1}^n a_i b_{i+1}$?

[warm shale]

Ann

[royal basin]

http://xyproblem.info/ tbh

[grizzled shore]

$a_{1,1}b_1 + a_{1,2}b_2 + a_{1,3}b_3 + a_{2,2}b_4 + a_{2,3}b_5 + a_{3,3}b_6$

[warm shale]

Frosst

[tardy epoch]

Pattern is unclear

[grizzled shore]

like this but i want alpha_i to iterate from 1 to 6

there's 6 different d's here

[wild swallow]

i literally read lecture notes using that notation the other day

[tardy epoch]

Can you still see or did that blind you

[wild swallow]

[wild swallow]

change the 3 to a 6?

[jolly ginkgo]

so how do you want to write this?

[grizzled shore]

but that iterates the d incorrectly

this was my idea but idk if it means what i want it to mean

[tardy epoch]

It looks like i*j=k or i+j=k

[grizzled shore]

fik

it should say 6

[wild swallow]

are there relations on k, i, j that you need

[grizzled shore]

i need 1,1 to map to 1

1,2 to map to 2

1, 3 to map to 3

2,2 to map to 4

[jolly ginkgo]

but why do you want to introduce k?

[grizzled shore]

2,3 to map to 5

3,3 to map to 6

[wild swallow]

so i+j = k

[jolly ginkgo]

plus i leq j

[grizzled shore]

but 1+1 ≠ 1

1 - 1 ≠ 1

[wild swallow]

just write out the full sum at this point

[jolly ginkgo]

first off, why do you want to add some k in this?

[wild swallow]

how many terms are there

[grizzled shore]

[royal basin]

whats this all for

are you doing the thing with explicit verification that a particular map is linear

[grizzled shore]

i could do this if i have no other choice

[grizzled shore]

well i want to show T is an isomorphism so yes

[royal basin]

are you forced to do it this way without just saying its clear that T is linear

whats the formula for T

[grizzled shore]

this

[jolly ginkgo]

oh

[royal basin]

frosst can we have the original problem statement PLEASE

[grizzled shore]

and secondly this is part 2

where i want to include rank nullity theorem

which we haven't proved in class works for different kinds of vector spaces

we've shown that it works from R^m to R^n but not from things like M_{2x2}(R) to R^4

[royal basin]

uhhh hold up

so you just want the dimension of $U_{3 \times 3}$?

[warm shale]

Ann

[royal basin]

is that it?

[grizzled shore]

no we want the null space of the trace of an element of U_3x3

[jolly ginkgo]

there's something more above second part

[royal basin]

oh, so it's dim(ker(tr))

[grizzled shore]

yes

[jolly ginkgo]

that's for the first part

[royal basin]

tr : U_{3×3} -> R

[grizzled shore]

yes

[royal basin]

do you already know that dim(U_{3×3}) = 6

[jolly ginkgo]

that is 5 ig

[grizzled shore]

yes

[royal basin]

a basis for ker(tr) is not hard to exhibit at all

no need for any of this long-ass pointless indexology that nobody in their right mind would ever want to read.

[grizzled shore]

but from what was shown in class we havne't showed rank-nullity works for other vector spaces

i mean it does, but we havne't showed that it does

[jolly ginkgo]

let's go with it

[grizzled shore]

anyway that's not even the point, i was just wondering if there was a way to notate that

[wild swallow]

isn't that the point of giving a basis for ker(tr)

[grizzled shore]

because whatever i've thought of has all looked very ugly

[wild swallow]

so that you know its dimension without invoking rank nullity

[royal basin]

i didn't say rank nullity

[grizzled shore]

then we need to find a basis for ker(tr)

[royal basin]

yes

and i said it is not hard to do that

[grizzled shore]

and we havne't covered basis at all

[royal basin]

you WHAT

how the FUCK

[grizzled shore]

LOL

HAHA

[wild swallow]

[grizzled shore]

[royal basin]

THEN WHATS YOUR DEFN OF DIMENSION????

[grizzled shore]

good quesiton huh

🙂

[jolly ginkgo]

are you sure

[royal basin]

URGENT question.

[wild swallow]

[royal basin]

go through your fucking textbook.

or lecutre notes or slides or whatever

[grizzled shore]

yeah it's in next semester's unit

[royal basin]

and bring me back the definition of dimension

[jolly ginkgo]

that can't be

[wild swallow]

next semester??

[grizzled shore]

we currently dont have one

[jolly ginkgo]

basis is too basic to be in next sem

[grizzled shore]

well i go to next semester's unit as well for fun

and they covered basis there

and not in my unit

[jolly ginkgo]

who structured that syllabus?

[wild swallow]

how have you done rank nullity without defining dimension

[grizzled shore]

you're asking me questions i dont know the answer to

[jolly ginkgo]

alright

[grizzled shore]

but if u asked me i'd say the dimension of a space is equal to the minimum number of vectors required to span the entire space

but we've not touched that at all

[royal basin]

but frosst

for real

[jolly ginkgo]

what have we touched then?

[royal basin]

if your course mentions the word "dimension"

then SURELY

SURELY

it was defined SOMEHOW, SOMEWHERE

do you have the syllabus on hand?

[grizzled shore]

lol im 100% sure we didn't cover it

i literally sit front and centre every lecture and i never miss lectures

[royal basin]

so you're saying

that you never covered the concept of "dimension" at any point

and yet your assignments have you working with it?

is that what you're saying @grizzled shore

[grizzled shore]

this is about as close as it gets

"the minimum number of vectors needed to represent every vector in its column space"

but we're talking rank here

[royal basin]

is that the first occurrence

[grizzled shore]

u wanna have a look yo urself?

[jolly ginkgo]

never share notes

[grizzled shore]

why not

[royal basin]

so it appears that this is mentioned in passing

but it is unacceptable imo that "dimension" is never given a proper definition

and it is likewise unacceptable that the concept of a basis is swept under the rug

[grizzled shore]

"fit"

uh huh

yep

that also only is talking about R^m

not about any other kind of vector space either

(PS. they really dont have much time to teach all this content so it's not fair to blame them)

[royal basin]

oh no it is fair to blame them. if they dont have time to teach about bases and dimension then they shouldnt expect you to do problems that directly involve bases and dimension

[grizzled shore]

they expect a half-assed answer that kinda hand-waves a lot of things

im just writing a bunch of stuff for the fun and exploration

[royal basin]

half-assed answer?

ok

$\ker(\tr{}) = \curly{\bmqty{x_1 - x_2 & x_3 & x_4 \ 0 & x_2 & x_5 \ 0 & 0 & -x_1} : x_i \in \bR }$

[warm shale]

Ann

[grizzled shore]

yes that's the simple answer

but then how do you describe that the dimension of this is 5

[wild swallow]

the x_is describe how you could construct a basis for the kernel

the dimension is the size of the basis

[royal basin]

each element of the kernel has a unique expression in the form i gave here.

[grizzled shore]

anyway

not even the point of the question

[royal basin]

[grizzled shore]

thsi was the question

but we've somehow veered so far off topic

this was a question about notation

[wild swallow]

there's not really a good way to write your sum

[grizzled shore]

not how to do my assignment

[wild swallow]

you can probably find a horrible expression to make it work but at that point it would be clearer to just write out the entire sum or use different notation

[grizzled shore]

yeah i thought so

.close

[obtuse pebble]

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[dark stirrup]

Depends.

Does order matter in this event space?

Are HT and TH two distinct outcomes or the same outcome of "one head and one tail"

[jolly ginkgo]

then you aren't doing it this way

SWR will tell you the right method

but you said the arrangement doesn't matter

this includes different arrangements

well tell me what you wrote for a

ok then your b is right

see if order doesn't matter then the outcomes are 0H 10T , 1H 9T, 2H 8T, ... ,10H 0T which are 11 outcomes

idk you gotta search

with arrangements the total outcomes are 2^n

like when HTH , HHT , THH are considered different outcomes

[dark stirrup]

I won't. I don't know stats

[jolly ginkgo]

I don't know Stats and Maths

you are my inspiration

[obtuse pebble]

@timid silo Has your question been resolved?

[obtuse pebble]

@timid silo Has your question been resolved?

[obtuse pebble]

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[ruby elm]

To find range of the given function.

[ruby elm]

f(x) = 3 | sin x | - 4 | cos x |

[ruby path]

Take cases for when x lies in the 4 quadrants

[ruby elm]

Ok.

[split pecan]

answer would be (-5,5)

[trail musk]

yea this is gonna be a pain in the ass ngl

[ruby path]

!nosols

[obtuse pebble]

As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.

[trail musk]

i don't even think that's right haha

[ruby elm]

But the answer given is [-4 , +3]

[ruby path]

Maybe you should try to plot the graph of the function yourself

[ruby elm]

Yes, I think that too.

[split pecan]

ok ok I see

[trail musk]

lol

[ruby elm]

Since both mod sin x and mod cos x are periodic with period π , then f x must also be periodic with π right?

[median dome]

yes

[ruby elm]

I just want to know why does the graph go up and down linearly, should it not go sinusoidally?

[winged pecan]

Sorry, I don't think I've ever seen this notation. What do you mean by "mod sin x"?

[ruby elm]

| sin x|

Modulus

[winged pecan]

Ah, thanks.

[ruby elm]

Now tell me. Why it go linearly.

[winged pecan]

Well... It actually seems pretty simple when you think about it.

When we have sin(x) and x is -pi/2, y is -1. Would you agree?

[ruby elm]

Yes.

[winged pecan]

|sin(-pi/2)| is what?

[ruby elm]

+1

[median dome]

,w graph y=|sinx|, y=|cosx|

[warm shale]

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[winged pecan]

That's right. And that's why it cannot weave up and down through positives and negatives. When the curve swoops down below the x-axis, it's kinda like it's being reflected instead.

And because of this, it's impossible for the graph to be sinusoidal.

Whenever the value of y WOULD be negative, it would really be positive instead.

[median dome]

i dont think that answers their question

you can think of it like the two wavy curves "cancelling out" the wavey behaviour

[winged pecan]

I don't think that I understood their question.

[median dome]

,w graph y=|sinx|, y=-|cosx|

[warm shale]

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[ruby elm]

Oh, so due to opposite signs, the wavy nature cancels out and we get linear property.

[median dome]

i actually dont think it will be exactly linear

[ruby elm]

Would this have also worked if same sign?

[median dome]

hmm

i dont think so

,w graph y=3|sinx|+4|cosx|

[warm shale]

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Requested by kheerii#8421

[median dome]

yea it wont be linear at all anymore

[ruby elm]

Ahh yes. It is clear.

[median dome]

note that the graph of 3|sinx|-4|cosx| is also not exactly linear

there will be sinusoidal properties too

[obtuse pebble]

@ruby elm Has your question been resolved?

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[obtuse pebble]

Please don't occupy multiple help channels.

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[spring halo]

How do you approach solving infinite continued fractions containing one unknown variable analytically, if possible?

[spring halo]

.close

[obtuse pebble]

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[cloud jungle]

is this the intergral of a(ax+b)^n ??

--> a/n+1 * 1/a (ax+b)^n+1 + c ??

[cloud jungle]

like how does the chainrule work in this senario?

.close

[obtuse pebble]

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[obtuse pebble]

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[royal basin]

so what's your question/doubt/issue?

yes that's the problem

but what issue are YOU having with it?

!status

[obtuse pebble]

What step are you on?
1. I don't know where to begin
2. I have begun but got stuck midway
3. I got an answer but I'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above

[royal basin]

do you know in general how percentages work?

do you know in general how to find the answer to a question like "by what percentage is x greater/smaller than y?"

let's try this:

by what percentage is 32 greater than 25?

can you calculate this?

okay then let's dig a bit deeper

how about this:

Dave has $90 in his wallet. Mary has 25% more cash than Dave. How much cash does Mary have?

can you do this problem?

........

[heavy frost]

I would say enough to buy me lunch

But that mf broke

[royal basin]

mary has 25% more cash than dave.

mary has 90 + 0.25 * 90

or to put it another way, mary has 1.25 * 90

a 25% increase means multiplying the number by 1.25

does this make sense to you?

mary has 90 + 0.25 * 90
does this make sense to you?

or to put it another way, mary has 1.25 * 90
and this?

first you say it doesnt make sense then you turn around and say you "get it"

[heavy frost]

Look: 90+0.25×90=1×90+0.25×90=90×(1+0.25)=1.25×90

[royal basin]

do you now understand this?

a 25% increase means multiplying the number by 1.25

and generally, an increase by p% means multiplication by (1 + 0.01p)

then perhaps you should review percentages

given that you are struggling with recalling information about them correctly

[heavy frost]

If ya understand what ann said than it's simplyfing

[obtuse pebble]

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[unreal whale]

how do you find the radius of points (1,6)(5,0)

[unreal whale]

i plotted the points but

[mellow summit]

You mean distance?

[unreal whale]

ye

oh wait

i got it

bruh

.close

[obtuse pebble]

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[chilly crest]

google forms homework.... pls help

[chilly crest]

<@&286206848099549185> so i found out that The trapoziod midpoint formula states that if one were add the line on top and the line on the bottom then divide by 2, you'll get the length of the line on the middle.

soo PQ is 15-6 = 9cm

im now stuck dont know what to do

[wind isle]

try to use similar triangles(maybe)

[chilly crest]

wdym?

[wind isle]

rb/qr=cb/dc

[chilly crest]

oh uhh

[wind isle]

BRQ and BCD are similar triangles

similarly DPQ and DAB are similar triangles

[chilly crest]

the problem is i dont know the length for one of the diagonals

[wind isle]

i think maybe BQR and DPQ are related with some congruency

angle pqd and angle bqr are same

[chilly crest]

wait how do you know that?

[obtuse pebble]

@chilly crest Has your question been resolved?

[wind isle]

at the intersection of any 2 lines the opposite angles are same

[obtuse pebble]

@chilly crest Has your question been resolved?

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[chilly crest]

.close

[obtuse pebble]

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[unreal nexus]

Explain me please, if a^2 <= 1

a [-1; 1] ?

I mean

[royal basin]

что это за буква

Q?

[unreal nexus]

Это буква а

[royal basin]

по-докторски написана, видимо.

[unreal nexus]

Не мой почерк )

[royal basin]

требует объяснения переход от a^2 ≤ 1 к a ∈ [-1, 1], да?

[unreal nexus]

Да

[royal basin]

a^2 - 1 ≤ 0
<=> (a-1)(a+1) ≤ 0

[royal basin]

дальше либо нарисовать числовую прямую, либо таблицу и исследовать знак

[unreal nexus]

Так стоп

[royal basin]

the question was how to get from a^2 ≤ 1 to a ∈ [-1,1], not just the meaning of the latter

[unreal nexus]

a^2 <= 1, это a <= 1; a <= -1 ?

[royal basin]

не-а

[unreal nexus]

А как?

[royal basin]

так я ж сказала

a^2 - 1 ≤ 0
<=> (a-1)(a+1) ≤ 0
дальше либо нарисовать числовую прямую, либо таблицу, [так или иначе] исследовать знак

[unreal nexus]

А почему не так?

[royal basin]

ну во-первых непонятно, что же это за точка с запятой

это логическое "и", логическое "или" или что-то третье?

[unreal nexus]

И

[royal basin]

(a ≤ 1) & (a ≤ -1) равносильно просто a ≤ -1

но, увы и ах, при a ≤ -1 неверно, что a^2 ≤ 1.

[unreal nexus]

А, то есть |a| <= 1; |a| <= -1 ?

[royal basin]

ы!

нет, просто |a| ≤ 1.

никакого |a| ≤ -1, боже упаси

[unreal nexus]

ООООООО, спасибо )

[royal basin]

если уж брать корень от обеих частей неравенства, то будет sqrt(a^2) ≤ sqrt(1), а sqrt(1) = 1 недвусмысленно

[unreal nexus]

В плане? Я не понял

[royal basin]

что именно непонятно?

[unreal nexus]

Вот это предложение

[royal basin]

бл

[1] если уж брать корень от обеих частей неравенства,
[2] то будет sqrt(a^2) ≤ sqrt(1),
[3] sqrt(1) = 1 недвусмысленно

под каким номером непонятка

[unreal nexus]

Со мной сложно, я знаю )

[unreal nexus]

3

[royal basin]

квадратный корень из единицы -- единица

чего тут не понимать

[unreal nexus]

Слово недвусмысленно

АААААА

Кореня из -1 же нету

[royal basin]

епрст, а сразу нельзя было сказать???

[unreal nexus]

Точно

[royal basin]

не в этом дело

[unreal nexus]

Извиняюсь

[royal basin]

дело в том, что у некоторых людей иллюзия, что квадратный корень из положительного числа страдает, извините за выражение, раздвоением личности

и пишут такие люди ересь типа sqrt(9) = ±3

[unreal nexus]

То есть не a = +/- sqrt(1)

[royal basin]

для каждого x > 0 уравнение y^2 = x имеет два решения -- одно положительное, другое отрицательное. символ sqrt(x) означает ВСЕГДА только положительное решение. отрицательное равно -sqrt(x).

[unreal nexus]

Не а = +/- sqrt(1), а вместо этого а = sqrt(+/- 1)?

[royal basin]

так-то у нас не уравнение все равно

[candid sigil]

-a^2+1>=0
a^2-1<=0
a^2<=1
|a|<=1
|
v
{ a <= 1
{ a >= -1

[ancient jacinth]

ye

[unreal nexus]

Спасибо вам!

[unreal nexus]

Thank you man too!

[candid sigil]

всегда пожалуйста

[unreal nexus]

.close

[obtuse pebble]

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[cedar vigil]

noob question
if an event has a base rate of 17 months and we r already 6 months in but the event hasnt happened what should the probability based forecast be for the event happening in the next 7 months
This event becomes more likely over time

Someone told me if it was equally likely always then it wld be a Poisson distribution
(Asked this earlier but went to sleep :p)

[drifting wraith]

you don't have the data

all you can do is calculate it under pretense thatit's poisson, and say "it's more than this"

[obtuse pebble]

@cedar vigil Has your question been resolved?

[drifting wraith]

no wait, i;m not even sure you can say that part

[obtuse pebble]

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[shrewd egret]

if the angle of elevation of the sun is 55 degrees. What is the length of the shadow on the level ground of man who is 5.6 ft tall? (round off to a whole number)

[wooden cipher]

!status

[obtuse pebble]

What step are you on?
1. I don't know where to begin
2. I have begun but got stuck midway
3. I got an answer but I'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above

[shrewd egret]

I don't know where to begin

It's angle of elevation btw

[wooden cipher]

Try drawing a triangl

[shrewd egret]

Done

Wait lemme send

Idk what the hell I am doing

I'm struggling so hard in angles

Math in general

[shrewd egret]

@wooden cipher here is the triangle you asked for

[crisp cradle]

trigonometry?

[wooden cipher]

Yes, use trigonometry

[crisp cradle]

soh cah toa

basically u are looking for adjacent

and u have angle which is 55, and opposite is 5.6 ft

i think

[shrewd egret]

I still don't know what am I doing lmao

The adjacent is the top part right

Or am I wrong

[crisp cradle]

ohh

let me draw it hehe

[shrewd egret]

Thank you so much

I should be sleeping right now but I have to finish this learning assessment

1st sub in class is math so yeah no sleep this time

[crisp cradle]

since shadow is on the ground therefore u looking for adjacent

and then given angle 55 and the opposite side 5.6

so use toa which is tan x =opp/adj

cant use sin bcs you're not looking for hyp
cant use cah because there's no hyp

[shrewd egret]

Hfjdjejdksnskks I should listen more to math class

Lemme just re understand what you just said

Okay now I understand

[shrewd egret]

So whats next

[crisp cradle]

thats the ans

u solve them already?

[shrewd egret]

Ehwaykfjdjsk

[crisp cradle]

substitute the value inside

tan 55 = 5.6/adj

[shrewd egret]

I choked midway

And now I forgor