help-0

[naive valley]

in the picture, how long is the line SR?

[wheat isle]

Well we don’t know that length right?

[whole shell]

You do

[naive valley]

well what are you calling the endpoints?

[whole shell]

Well interms of other things

[wheat isle]

SR = s + r I’m not sure

[naive valley]

if we call the upper right corner of the rectangle (x,y)

[whole shell]

@wheat isle SR means

The line from

[naive valley]

then what are the other three coordinates?

[whole shell]

Point S to Point R

[wheat isle]

I’m not sure I follow

[whole shell]

You see your rectangle

The bottom line

[wheat isle]

Yes

[whole shell]

Is the line SR

[wheat isle]

Right

[whole shell]

How long is it

I'm not asking for a number

[wheat isle]

But there aren’t any measurements given

o

[whole shell]

But interms of x or y

[naive valley]

but you got "2x + 2y" from somewhere

you must be making some assumptions about how x and y relate to the rectangle, right?

[wheat isle]

Well I labelled the four sides x and y and when added gives perimeter

[naive valley]

unfortunately that's not gonna be compatible with the formula y=6-x^2

[wheat isle]

are we looking at the bottom rectangle line as two parts separated by the y axis or one whole line

[whole shell]

Well your getting close

[wheat isle]

SY+RY?

[whole shell]

Sure

How long

Do you think

Each of them are

Interms of x or y

[wheat isle]

uh

[wheat isle]

Oh

so we are looking at the rectangle divided by the y axis

Oh I see

4x+2y

[whole shell]

Yh

Now

Get that quadratic again

[wheat isle]

Alright

[naive valley]

ha, doctor99268 beat me to it, that's what i was getting at when i asked you to consider the coordinates of the four vertices, like this:

[whole shell]

I had this for quite some time

But wanted him to understand

[naive valley]

apologies for the ghastly typesetting haha

[whole shell]

Before i showed

[wheat isle]

Ahhh

Yeah that makes more sense now

[whole shell]

This is the part you are stuck at right?

You have the formula for the perimeter. And you need for find the maximum.

[wheat isle]

Yeah I’m not sure what to do now

[whole shell]

Do you know how to find the maximum of a quadratic

Do you know how to complete the square

[wheat isle]

yeah

couldn’t we also use power rule too

[whole shell]

Power rule?

Never heard of it

What is it

[wheat isle]

Power rule calc?

[whole shell]

Still never heard of it

[whole shell]

Wait

If you do

Then what are you stuck at

You just didn't know that the maximum of the perimeter is the maximum of that quadratic?

[wheat isle]

yeah I guess so

I was having severe trouble on what to do beforehand to get to this step

Thanks though for the help and you too bungo

[lone heart]

@wheat isle Has your question been resolved?

[unkempt token]

.close

[chrome salmon]

pretty loose bounds

[lone heart]

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[raw citrus]

For area under the curve using integration, when i add together A and B, would i get 9/4 or 37/12 where the equation is 4x² - x³ - 3x

[alpine sable]

,w integrate |4x² - x³ - 3x| from 0 to 3

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[alpine sable]

,w integrate 4x² - x³ - 3x from 0 to 3

[ocean seal]

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[raw citrus]

so which is the best?

[alpine sable]

if you want the area and not the signed area, then you should the first one

[raw citrus]

i saw a video that said that its a common mistake for the second one

[raw citrus]

so this one is best? with the absolute values?

[alpine sable]

yep

i used the abs val cuz i didnt want to write 2 expressions :p

but what you should do is find the intersections first

[raw citrus]

understandable

[alpine sable]

👍

[raw citrus]

so find it for A and then B

and add their values instead of subtracting?

because B is negative

like the integral for it is

[alpine sable]

if you integrate over B, you will get a negative value so you should subtract it from A

well see

in the end we want

|A| + |B|

[raw citrus]

oh i see

thank you very much

[alpine sable]

anytime

[raw citrus]

.close

[lone heart]

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[cosmic roost]

hello

[cosmic roost]

how would you integrate this?

[alpine sable]

aver gudari

el seno

is es que no se en que iidioma

watch idiom

what lenguage

friend

eeee friend eeee jjajaja

[cosmic roost]

english

[alpine sable]

aaah okey

look

a seno coseno gasogeno and you have to rest the sin with cos and mulltiplicate by 7

4 dissappear

inbisibol

you understand? my little txoriburu?

[cosmic roost]

.....I don't 😕

[alpine sable]

AVER FRIEND

listen

dont worry

be happy

its easy look

wait a minute im going to do it

and i will send you a photo

okey txoriburu?

[cosmic roost]

umm okay?

[alpine sable]

okey??

[cosmic roost]

okay

[alpine sable]

lets go baby

https://tenor.com/view/rio-hello-bird-wave-waving-gif-8894877

are you AATHLETIC CLUB FAN

https://tenor.com/view/sport-deporte-athletic-club-de-bilbao-gif-11804344

[cosmic roost]

.close

[lone heart]

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[alpine sable]

nooo

.close

imbecil

stupid

AUPA ATHLLETIC

TXORIBURU

https://tenor.com/view/athletic-club-athletic-bilbao-athletic-club-bilbao-bilbao-iñaki-williams-gif-22223885

ASI AASI TE VOY A HACER

[lone heart]

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[main cedar]

how do I solve this

not given

[copper delta]

no

as in

all radii are equal

@main cedar

[main cedar]

well yes

[copper delta]

and what is a triangle when only two of its sides have the same length

@main cedar

[main cedar]

isosceles

[copper delta]

and…

[main cedar]

The angle in the middle should be 104

180-104 = 76

Theta is 76

or am i wrong?

[copper delta]

you got it

[main cedar]

thanks a lot

.close

[lone heart]

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[real cipher]

i tried
$$ 25000 = -0.012x^2 + 0.828x + 15.750 $$

[ocean seal]

JXHN

[real cipher]

it gave imaginary/complex number which were not in taught in course so, I am guessing the process i did was wrong

[vapid shuttle]

^ I'd assume the same thing since it wouldn't make sense for the amount of years to be imaginary

[real cipher]

@vapid shuttle the question say nearest to 25,000 not exactly 25000 what should i do about that?

[vapid shuttle]

I'm assuming that is because your answer will be x= (some number containing a decimal)

and you wouldn't really say like, 3.8291 years for example

you would just say 4 years

yknow

[real cipher]

oh, oh

then what should i do?

[vapid shuttle]

d is in 1000's of dollars

so if you want to know when d is 25,000 dollars, you don't write 25000=.....

you write 25=.....

Which represents 25 (in thousands) of dollars (which is 25000 dollars)

[vapid shuttle]

so replace 25000 with 25

[real cipher]

oh okay but

can u state what's meaning of the pharse "the difference, d, in median earnings, in $1000s"

[vapid shuttle]

the same thing can be said like this (which might make more sense)

Call the difference in median earnings, d. d is in thousands of dollars

[real cipher]

okay

[vapid shuttle]

So, d is the difference in median earnings. But, if we said d=1, we need to know if that means the difference is $1 or $10 or $100..... So, d is in thousands of dollars tells us what we need to know (that d=1 represents a difference in median earnings of 1,000 dollars)

[real cipher]

so if d =1 then, it can represt any $1, $10, $100 or $1000?

[vapid shuttle]

well, if we didn't specify that d was in thousands, yes

but the problem did specify

[real cipher]

so if d =91, then it represtent 91000, we are essentially dividing by 1000 then?

[vapid shuttle]

to get from 91000 to 91, you divide by 1000

but the reason that they say d is in thousands of dollars, is just to simplify the problem for you

It is because d will usually be pretty big

so instead of dealing with numbers like

91000, 25000, 70000

you can deal with 91, 25, and 70

just remembering that in dollars, these represent thousands of dollars, instead of what you might assume, which is that they represent 1 dollar

[real cipher]

okay thanks i think i understand now

.close

[lone heart]

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[sage dew]

can anyone help me about this questio“Find a special solution to a differential equation y''+y=e^x+cosx

[sage dew]

Anyway thanks a lot

[vapid shuttle]

Don't interrupt other channels

@sage dew what language do you speak?

I'd like to help, but I'm not sure if you will be able to understand my help good enough

[sage dew]

that's ok

[vapid shuttle]

What language?

[sage dew]

english is fine

[vapid shuttle]

$y''+y=e^x+cos(x)$

[ocean seal]

AustinU

[vapid shuttle]

have you found the complementary solution?

the solution to $y''+y=0$ is the complementary solution

[ocean seal]

AustinU

[sage dew]

i know this complementary solution

[vapid shuttle]

then use variation of parameters to find the particular solution

[sage dew]

is the complementary solution y=c1cosx+c2sinx?

[vapid shuttle]

yes

[sage dew]

and the special solution is y=c1cosx+c2sinx+（1/2）(e^x+xsinx)

is this right?

[vapid shuttle]

,w y''+y=e^x +cos(x)

[ocean seal]

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[vapid shuttle]

yes, it is

[sage dew]

full of respect

thanks a lot bro

[vapid shuttle]

no problem!

[sage dew]

I just joined here and I don't know exactly what to do

[vapid shuttle]

Read #❓how-to-get-help and #rules for some background on what to do. You can also scroll through the channels to see what others are doing

if you want the channel to close because your question is done, type ".close"

[sage dew]

.close

[lone heart]

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[forest scroll]

How would I approach this problem? integration by parts and should i select secˆ2(x) as my u value for u sub?

[mortal trellis]

by parts and u-sub are different

[forest scroll]

every problem i've seen using integration by parts uses u sub at some point i'm pretty sure

[mortal trellis]

doesnt have to

[forest scroll]

or at least the example problems i've seen do

[mortal trellis]

are you maybe confusing notation

[forest scroll]

possibly

yes

[mortal trellis]

ibp also uses u, du and v,dv as part of their notation

[forest scroll]

that's probably the case then

[mortal trellis]

$\int u dv = uv - \int v du$

[ocean seal]

Denascite

[forest scroll]

yes

[mortal trellis]

where u is the function you choose to differentiate and dv is the function you integrate

[forest scroll]

using integration by parts

would secˆ2(x) be my u value then?

[mortal trellis]

well maybe

that means you would have to differentiate sec^2(x) and integrate x

[forest scroll]

i'm having trouble choosing the best value for integration by parts. i know we want to make the problem easier to integrate and that usually implies that one value is better than another to use for u

integrating x would be easier in this case?

how would you approach it?

[mortal trellis]

it will come with experience

there is also a rule of thumb, LIATE for what to choose

while x is easy to integrate, you end up with x^2/2, which looks "harder"

meanwhile if you differentiate it, you end up with 1

which is easy

so in most cases you want to differentiate polynomials

[forest scroll]

ok

[mortal trellis]

because eventually you will get a constant

[vapid shuttle]

looking at $4x \cdot \sec^{2}(x)$ I'd choose $u=x$ because I can see that $du=dx$ will make it go away. Additionally, I can see that $\sec^{2}{(x)}$ has a nice antiderivative, being $\tan{(x)}$ So this further solidifies the choosing of x as u and $sec^2$ as dv

[ocean seal]

AustinU

[forest scroll]

ok

does LIATE always work in selecting the best value?

[vapid shuttle]

not always, but in general it does

[forest scroll]

ok. i'll try to work this out and come back to the help channel.

thanks guys

.close

[lone heart]

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[shrewd ermine]

hey can someone help me?

[lone heart]

@shrewd ermine Has your question been resolved?

[lone heart]

@shrewd ermine Has your question been resolved?

[lone heart]

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[paper sage]

I have problem with finding the bounds for phi. I know that r is between 0 and 1. But what is the bounds for phi?

[echo sundial]

this is an equation of a circle so i'm guessing it should be 2pi

zero and 2pi

[lone heart]

@paper sage Has your question been resolved?

[paper sage]

No that’s wrong

It should be between -pi/4 and pi/4 for some reason I don’t know why either. I also thought like you first between zero and 2pi

@echo sundial

[echo sundial]

oh really?

[paper sage]

yeah i think so

[echo sundial]

hmm i thought it was just dat

atleast thats the only way ik :<

[paper sage]

but i don't understand why it's that

[paper sage]

do you have any idea

[echo sundial]

did u solve by using zero and 2pi?

like do u have the answer?

[paper sage]

no

[paper sage]

yes

[echo sundial]

oh what is it

[echo sundial]

ohh im not sure then

[paper sage]

Thanks anyway

[echo sundial]

maybe u can ping helpers, its been more than 15 mins since u posted so

[paper sage]

Yeah I will thanks for ur time

@crisp iron

@mortal trellis do you have any idea why the bound for phi is between -pi/4 and pi/4. Why is it not between 0 and 2Pi since we are working with a circle?.

.close

[lone heart]

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[simple parrot]

Hey, can someone help me with this 3d vectors q

[simple parrot]

for c i got an ugly 3 simul eqs witb 3 unknowns thing

so im pretty sure im not seeing something

c) simul eqs: the first 2 come from b, bc $$1 + \lambda = a, 4 + s\lambda = b$$

[ocean seal]

epsilon

[simple parrot]

the third one is because (a, b, 0) and (1, s, t) i think must be perpendicular so they multiply to 0

since were finding the shortest length

<@&286206848099549185>

[lone heart]

@simple parrot Has your question been resolved?

[lone heart]

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[languid bolt]

Aight im actually curious rn

[languid bolt]

It’s not my assignment but I don’t know how to prove it, so it’s okay if you don’t help me because you think that this is a graded assignment.

[brittle forum]

and yes im only stuck w the diagram

[languid bolt]

Channel is taken btw

[brittle forum]

AHHH OKAY TY

[languid bolt]

Ping me if someone’s here btw

I need help on how to do it and if the answers are correct

And why it is correct

It’s not my work

[lone heart]

@languid bolt Has your question been resolved?

[languid bolt]

I don’t understand the statistics of 42% part

<@&286206848099549185>

[worthy tiger]

can you tell me how can i do this

[lone heart]

@languid bolt Has your question been resolved?

[grand sable]

Can you reword your question?

Are you saying that you don't understand the relevance of the 42% in the question statement?

[languid bolt]

What does "for a statistic of 42%" mean?

I don't understand what it is

[grand sable]

I believe it's just the center of the confidence interval

[languid bolt]

so the mean?

wait no median?

[deep garden]

42% is the same thing as 42/100 if that helps

[grand sable]

lol

[languid bolt]

i fr don't understand, i might try to go to khanacademy tbh, but idk which unit

[grand sable]

It's would likely be something like the sample proportion

Did you submit any of these answers?

[ebon ibex]

how do i study for verifying trigonometric identities im like confused

[languid bolt]

nope

my friend did

[grand sable]

you'll have to go to an empty room

[ebon ibex]

its so difficult

[grand sable]

Were they correct?

[languid bolt]

I- don't know

Can I maybe get a recommendation on where to learn this

[grand sable]

What is your mathematical background?

[languid bolt]

Highschool

Year 10

[grand sable]

I typically recommend textbooks, are you willing to read?

[languid bolt]

I prefer videos

I have very low attention span for books

sorry

But I can try

[real cipher]

[languid bolt]

Ok maybe just recommend a textbook, I'll read it tomorrow if there is a free e-book version of it

[real cipher]

yup I have 100+ math e-book

which category u want?

[languid bolt]

Something related to the question

[grand sable]

Perhaps try
Statistics, by Freedman, Pisani and Purves,

[real cipher]

@grand sable u mean david freedman one?

i have that

[languid bolt]

Btw can you maybe try to explain a) for me too?

I just want to see how to do one of em

[grand sable]

Yeah

It's probably something like "statistics 4th edition..."

help

@languid bolt the idea is pretty simple

The center of your interval is 42

[languid bolt]

just +- the margin of error?

[grand sable]

The radius of the interval is the given margin of error

assuming i'm interpreting the question correctly, yes

[languid bolt]

ohhh

wait what does 95% confidence level imply?

i mean what does it do

[grand sable]

I think that's more or less nonsense

It has meaning when you attempt to interpret this window

It means that

when you read the statement; e.g. number 1

you say

"I am 95% confident that the proportion is between 38 and 46 percent"

I.e. "i think it's in this window, but there is a 5% chance that I'm wrong"

but without more data than just the question provides, it has little quantitative meanin

does that make sense?

[languid bolt]

yeahhh

so it's just how confident you are with the range of the .... center of interval?

wait no

aaaaaa

is the center of interval the mean of the interval??

wait

median is center

so... it is just how confident you are

got it

thanks alot!

.close

[lone heart]

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[real cipher]

not me why?

in past though i did

u need relationalship advice or something ?

any question i mean to say

[languid bolt]

are you in grade 7?

[lone heart]

@alpine sable Has your question been resolved?

[lone heart]

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[pale haven]

A random variable X represents the number of hours of use until an electronic component needs to be
replaced. X is normally distributed with a mean of 27500 hours and a standard deviation of 4000 hours. 99% of the components do not need to be replaced until they have been used for k hours.
Find the value of k.

[pale haven]

What am I doing wrong please?

[tacit arch]

The probability you're starting with is wrong. Should be P(X>k)=0.01

[pale haven]

OMG I was stuck in this question for 3 days. Thanks man!

.close

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[rotund crater]

help

[rotund crater]

why is -8

[cyan seal]

Can you show your work?

[cyan seal]

You are doing it right

[lone heart]

@rotund crater Has your question been resolved?

[lone heart]

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[finite marsh]

hey, could someone help me?

[finite marsh]

I did not understand this question:

31. Let s be a string of length 2 with characters from {0, 1, 2}, and define statements a, b, c, and d as follows:
    a = “the first character of s is 0”
    b = “the first character of s is 1”
    c = “the second character of s is 1”
    d = “the second character of s is 2”.
    Describe the set of all strings for which each of the following is true.
    a. (a v b) ^ (c v d)
    b. (~(a v b)) ^ (c v d)
    c. ((~a) v b) ^ (c v (~d))

could someone show me an example of how to solve this by solving a?

[frigid stream]

What are these 5s in front of each statements?

[finite marsh]

5?

v = or operator
^ = and operator

~ = not operator

[finite marsh]

ah

ignore this

[frigid stream]

Ok!

First of all, do you know what is a string of length 2 with charcters from {0,1,2}? If so, can you write me out two or three examples of them?

[finite marsh]

[1, 2], [0, 1]

in programming would be something like "12", "11", "01"

[frigid stream]

Ok, I trust you on the notation you use

So, for (a)

Could you try to describe in words what does $(a \lor b) \land (c \lor d)$ mean?

[ocean seal]

all matrices are invertible

[finite marsh]

Yes, I can

the first character of s is 0 or the first character of s is 1 and the second character of s is 1 or the second character of s is 2

(the first character of s is 0 or the first character of s is 1) and (the second character of s is 1 or the second character of s is 2)

[frigid stream]

Ok, well, then can you write to me all the examples?

That would satisfy this condition?

[finite marsh]

well, no. But I saw the answer, it is 00 01 11 12

[frigid stream]

The first character can be either 0 or 1

And the second character can be either 1 or 2

so 01 works, as the first character is 0, and the second character is 1

[finite marsh]

Why the first item in the set is 00?

[frigid stream]

The order doesn't matter, it's just a list of the four possible strings that satisfy the condition given in (a)

[finite marsh]

the second character is 1 or 2, if not both then it is false

[frigid stream]

Ohhh, yes, 00 is not right.

Your answer should be: 01 02 11 12

[finite marsh]

yes, I mistook

I think I understood it

[frigid stream]

Great 🙂

Do you think you can do the last two ones?

[finite marsh]

Trying what I understood by answering b:

in words, it translates to: it is not the case that the first character of s is 0 or the first character is 1 and the second character of s is 1 or the second character is 2

(By the de morgan's law, the first statement could be wroten as: the first character of s is not 0 and the first character of s is not 1.)...

if the first character is nor 0 neither 1, then must be 2 considering the set of all possible characters. Then, the answer is:

21, 22

did I got it?

the book just show the answers for a, not for the others

idk why ;-;

[frigid stream]

Yes, this is good

[finite marsh]

The c one is… (writing…)

translating it into words:

The first character of s is not 0 or the first character of s is 1 and the second character of s is 1 or the second character of s is not 2

[tacit arch]

#old-network for physics server

[finite marsh]

If the first character is not 0, then it could be either 1 or 2

If the second character is not 2, then it could be 1 or 0.

The set is: 10, 20, 21, 11

Is it right?

@frigid stream

Or the set is: 11, as the first cant be 0 and the second cant be 2

[frigid stream]

Yes, this is right

[finite marsh]

What one is right?

[frigid stream]

The first one, as it means, for example (for the first string)
it can't be 0 or it can start with 1

so starting with 2 is fine too

[finite marsh]

Thank you

How could I kiss you?

[real cipher]

uh

i could drive to your house

type .close

[finite marsh]

.close

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[heady plank]

finding a polynomial function with given zeros, there are multiple answers.

2, 2+sqrt(5), 2-sqrt(5)

1. What is most convinent way to find given zeros instead of doing (x-2) (x-2+sqrt(5)) (x-2-sqrt(5)) ?
2. What other answers can achived? (corrected, sorry)

[whole shell]

(x-2)²(x-2+√5)⁴(x-2-√5)³

[heady plank]

could you explain a bit, as i dont understand it...

[whole shell]

@heady plank you asked for other answers

[vale wigeon]

if you want convenience, 2 ± sqrt(5) can be covered by one integer-coefficient quadratic.

[heady plank]

yes, but i dont understand how that can be other answer. that's what im curious about, not just answer only

[whole shell]

Because

When you put 2 in

You get 0

When you put 2+√5

You get 0

When you put 2-√5

Guess what you get

[heady plank]

you are right. so any power values can be applied to that then.

[whole shell]

Well any power value that is bigger than 1 and integer

[heady plank]

oh, yes

[heady plank]

not sure what you mean by integer-coefficient quadratic, sorry. i was thinking about this for some mins but didnt come up with any ideas 😦 could you explain more?

[vale wigeon]

a quadratic with integer coefficients.

these are in some sense "simple" to write down.

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[alpine sable]

weird question but does anyone know a formal notation(without words) of indicating that a function f has positive/negative values on some intervals

[tacit arch]

$\sgn(f(x)) = 1$ ?

so sgn(f) = 1 if f is positive

[alpine sable]

not really like typing with intervals so suppose a function f has positive values on the interval (0;3) my question is how can i note that without words i ve seen some notation with quantifieres but i dont know if its correct

[modern sedge]

$\forall{\left(x \in (0, 3)\right)} \left(f(x)>0 \right)$

[ocean seal]

MathIsAlwaysRight

[modern sedge]

this should be what you're looking for

for every x in that interval, f(x)>0

[alpine sable]

ye well that makes sense what if i had 3 intervals do i write the $\cup$ or $\wedge$

[ocean seal]

MrTrim

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[brittle slate]

in how many ways can we choose 4 employees out of 7 to fill 4 jobs (without one of them being able to take more than one job)

[brittle slate]

is it 7c4 or 7p4

[prime badge]

either one makes sense

can't be certain

[brittle slate]

how

[prime badge]

i dont know what you mean when you ask how

[brittle slate]

uhhh

idk either

[prime badge]

if the jobs are "different" you do 7p4, if it's the same job 4 times, you get 7c4

there's no way to convincingly argue that they must mean different jobs

oe the same job

[brittle slate]

i thoughht its 7c4 cuz the question didnt specify the jobs

like it didnt say one of them should be a manager and the other.....

[prime badge]

it didn't "specify the employees" maybe the answer is 1

[brittle slate]

i-

[prime badge]

my intuition says 7p4, i would trust your own inttuition over mine

if you solved problems from this source before you can better guess what they want

[brittle slate]

th thing is its an exam sample

so idk and my exam is tomorrow lol

ill just guess

[prime badge]

if they wanted 7c4, they could phrase like it's one job, that requires 4 people

4 jobs makes me think of different tasks idk

[ocean seal]

trixx

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[abstract badge]

$A\in\mathbb R^{n\times n}:$A\cdot A^T=identity\Rightarrow invertible$

[ocean seal]

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

[abstract badge]

what is a good way to prove or visualise this?

[bronze helm]

By definition

[molten pivot]

So you're saying if AAt is the identity matrix then A is invertible

[abstract badge]

yes

[bronze helm]

AA^T=I is a special type of matrix

[molten pivot]

Have you considered that A might not even be square?

[bronze helm]

Orthogonal matrices

[abstract badge]

did you read A in Rnxn

[molten pivot]

Yeah mb

Just show that the column space of A is an orthonormal basis for R^n

[abstract badge]

it is not a definition that this relationship leads to the invertibility of the the matrix

there is a proof here that i didnt understand

let me translate it to english

[bronze helm]

Yes it’s not literally by definition but one of the standard facts of orthogonal matrices is that their columns form an orthonormal basis

[molten pivot]

If the column space of A is orthonormal, then all dot products become 0 outside the main diagonal

Then just show it must be normal because the magnitudes are unit

(The dot product of a vector with itself yields its squared magnitude)

[limpid turret]

A square matrix A is invertible if there exists a matrix B such that AB=BA=I

If AA^T=I, then you must show that A^T*A=I

[abstract badge]

The proof used on my sheet goes as follows:
an invertible matrix is equivalent to one with a full rank. From AA^T=I we draw that the image of I (All of R^n) is a subset of the image of A. rank(A) is minimum rank(I)=n, so it is maximum.

what i dont understand is first. how did we draw out from the equation that the image of I is a subset?

I am aware of that definition. But i have to reach the property of invertibility from the transponent relation

i should have started of by translating the proof. since my endgoal was to understand it anyways. bad question phrasing on my part

[limpid turret]

just take transpose of both sides of initial equation

[abstract badge]

oh wow

thanks
that was simple enough

[limpid turret]

linalg is deceptively simple (in hindsight)

[abstract badge]

out of curiosity wtf does the answer sheet mean here?

[limpid turret]

no clue

[abstract badge]

hmm

[limpid turret]

I only deal with matrices in computer graphics, so I forget stuff like that

[abstract badge]

I know it is related to the graphical representation of matrices

ill think about it again
thanks for the help

.clsoe

.close

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[vague coral]

factor x^3 + 1

[molten sky]

can u explain more

[torn elk]

use that

[molten sky]

haa okay let me try

[brisk bay]

Yea you might want to factor something such that you can potentially eliminate (x+1)² to isolate A

[molten sky]

then what?

[brisk bay]

there are many ways to do this and you don't even have to factor

[vague coral]

Then factor by (x+1)

[molten sky]

can u tell me best way

[brisk bay]

there is a different way but it's slower

[vague coral]

$(x^3 +1) = (x+1)(x^2 -x + 1)$

[ocean seal]

Herels

[brisk bay]

let x be a certain number--- find the value of A by dividing both sides by (x+1)²

substitute value of a to the options

if equal to a, that's the answer

but it's slow

[torn elk]

Don't confuse him please, the way is factoring out

[brisk bay]

not trying to confuse him Lord Archimonde

[vague coral]

$$(x^3 +1)- 3(x+1)^2 = (x+1)(x^2 -x +1) - 3(x+1)² = (x+1)(x²-x+1 - 3(x+1))$$

[brisk bay]

he asked I delivered

[ocean seal]

Herels

[torn elk]

Just let him do it, the hint of factor is enough to solve it

[brisk bay]

ok

[torn elk]

This is wrong btw

[unkempt vector]

ily lord archimonde

[torn elk]

you copied wrong the exercise.

[vague coral]

yes

$(x+1)(x²-x+1)-3(x+1) = (x+1)(x²-x+1-3)$

[ocean seal]

Herels

[molten sky]

are u sure thats right?

[molten sky]

cuz this didint work

[vague coral]

this one is wrong

[torn elk]

ameer, do you know how to factor?

[molten sky]

i do let me solve it

[molten sky]

so this is right i keep going on it right?

[torn elk]

you should know the answer to that... you have x^3 + 1^3, and you know that can be factored out the way Heles said

after that, you must keep factoring until you get what you need

[lone heart]

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[vital forum]

How would you do this question?

[deep moon]

Ok

What's the problem

!status

[lone heart]

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

[vital forum]

3

I know my answer is wrong

I made an attempt to get marks but I knew it was wrong

[deep moon]

Ok show me your work

What answer did you get

[vital forum]

All I did was say that it divides by two every two terms so I divided it by four to get term 0

I was supposed to get term 1

So I know it’s wrong

[deep moon]

Ok

So as the series progresses

You know it gets divided

[vital forum]

Yes

[deep moon]

Then shouldn't the series multiply as the series goes backwards?

[vital forum]

Yes

Ohhh

Yes that’s a mistake

But I’m still working out term zero and not 1

[deep moon]

Let's get this in a mathematical approach shall we?

[vital forum]

Yes

[deep moon]

What's a zero term? Lol

You mean it starts from zero then 1 then 2 and so on?

[vital forum]

No I mean like if it divides by two every two terms, and I’m on term four, then multiplying by four will give me the zeroth term because 4-4=0

Idk what zeroth term means

But I’m just using it to describe my dilemma

Basically I can’t just x by four right)

?

[deep moon]

Ok chill

[vital forum]

Lol

[deep moon]

Let's sort it out

Let a1 be the first term

Cool?

[vital forum]

Yh

[deep moon]

Let a1=x

[vital forum]

Ok

[wary stream]

My suggestion, if you know the equation for geometric sequence, you can form two equations with two unknowns. And the common ratio would be the "slope" of the two given terms

[deep moon]

Then a2=x×r

R is for some ratio multipled to it

[vital forum]

Yh

[deep moon]

What's a3?

[vital forum]

We don’t have equation

[vital forum]

2x

[wary stream]

you can form two equations with two unknowns
You can form them, using the equation for geometric sequence

[deep moon]

Nope it's x×r×r

[vital forum]

But also 2x

[deep moon]

Because the same ratio is being multiplied

Why the 2 x

[vital forum]

Because it x2 each time no?

Every two terms

[deep moon]

?

[vital forum]

So 2 x = xr^2

[deep moon]

Don't jump to it already

[vital forum]

Remember when u wanna get from term 6 to term 4 u Times by two

[deep moon]

Assume you don't know it

[vital forum]

Ok

Sorry it’s not 2x

It’s x/2

[deep moon]

So a4 is

Let it be

You don't know it yet

[vital forum]

X r^3

[deep moon]

Good

Now we need to find the r

We could do it as a5÷a4

What could that be?

[vital forum]

R?

[deep moon]

Yes

You should get the value as 1/2

It should be obvious

Now that we know r

[vital forum]

Wait

Why is that 1/2

R

[deep moon]

We know a5÷a4 is r

And we know what a5 and a4 is

[vital forum]

?

[wary stream]

No

They are given a6

And a4

[vital forum]

Thx dldh06

Can u help me

Aswell

[deep moon]

Oh nvm

[vital forum]

It’s 6th term

[deep moon]

It's a6

Ok

[wary stream]

I did

if you know the equation for geometric sequence, you can form two equations with two unknowns. And the common ratio would be the "slope" of the two given terms

[deep moon]

We know the 6th term

A6/a4 is r² right?

[vital forum]

Yes

[deep moon]

R² is 1/2

Then r is?

R²=1/2

[vital forum]

1/4

[deep moon]

No

[vital forum]

Oh yeah

1/root2

‘Y bad

[deep moon]

Great

Now we know what r is

[vital forum]

Oh yes

I get it now

THank u

Tysm

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[valid warren]

isn't the period 10?

[valid warren]

wait nvm I am stupid

10*0.2

.close

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[sour dove]

be nicer to yourself 🙂

[valid warren]

I am operating on 4 hours of sleep and got an essay due at midnight

my brain is at like 0%

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[eternal citrus]

someone explain this pun please

[deep moon]

So basically

[wary stream]

Not really a math question but it's just a play on words, using secant (because of the plot) instead of second

[eternal citrus]

yeahhh but I don't get why there are no secant lines on that plot

[wary stream]

Secant is a trig function

[wary stream]

You're thinking of secant, as part of a circle, which that secant is not

[eternal citrus]

hmmm okay

[wary stream]

,w plot secant(x)

[ocean seal]

Results provided by WolframAlpha

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

Requested by dldh06#2659

[wary stream]

See

[eternal citrus]

OHH so they just graphed the secant function?

and simply played on words for that phrase?

[wary stream]

Yes

[eternal citrus]

I thought there was something deeper 😳

thanks so much lol

.close

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[alpine sable]

OK

[grizzled aspen]

.close

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[mellow ore]

this is the solution of a problem but I don't understand why that highlighted part is worth 3π/2, can someone please explain it to me

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@mellow ore Has your question been resolved?

[mellow ore]

pls helpmeeeeee

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@mellow ore Has your question been resolved?

[alpine sable]

Hi

Need help

[lone heart]

@mellow ore Has your question been resolved?

[mellow ore]

yes

[gleaming granite]

It's just from the unit circle, as you go 90 degrees 3 times you get 3pi/2 radians

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[unkempt token]

heyyyyyyyyyyyyyyy

[unkempt token]

wssp

how do this? 😭

<@&286206848099549185>

[dense lake]

hm

[unique trout]

Fraction form and then evaluate for x

[dense lake]

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

[unkempt token]

So uhh,

i did divide 42 by 7

so its 6

times by 9

is 54

somehow it says 96

[dense lake]

my suggestion is

you can assume gum trees are 9x

while wattles are 7x

then, you are feel free to form a equation

https://tenor.com/view/emma-myers-wednesday-netflix-gif-27367089

[unkempt token]

GOT a new one

very confusing

[dense lake]

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

[unkempt token]

2

[dense lake]

my suggestion is, you should try it on your own first, using the experience of the last question

it's same

[unkempt token]

soooooooooooooooooooooooooooooooooooooooooooooooooo

um

uh

[dense lake]

try it

[unkempt token]

idk

im not asian

[dense lake]

assume what is x?

[unkempt token]

strength

[dense lake]

well done

then, how can endurance be expressed

[unkempt token]

UMMMMMM

uh

[dense lake]

WELP it's complicated

[unkempt token]

didididi

vide

[dense lake]

why dont you assume strength is 5x?

while endurance can be what?

[unkempt token]

expressed

expressed what 😭 this is due in 21 hours

[dense lake]

read the info

it said, ratio is 5:3

[unkempt token]

okay'

then

2.4?

pls help me,

instead of others

[dense lake]

no

it's 3x

[unkempt token]

400 minutes!

Onto my next question

<@&286206848099549185> !

[dense lake]

try it yourself first

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

[subtle birch]

assume number of gum trees to be 9x and number of wattle trees to be 7x

[unkempt token]

i dont get it 😭

[subtle birch]

Since the trees are in a given ratio
Number of each kind of tree must be a multiple

so 9x and 7x

[unkempt token]

whats the "x" for

got it its 12

[dense lake]

WELP

we can assume wattle tree is x

can you express gum tree?

[subtle birch]

no

we'll find x later

[subtle birch]

The trees are in ratio 9:7 which means if there are 9x trees of one kind then there are 7x trees of other kind

where x can take any value

[dense lake]

just assume one kinda tree is x

[unkempt token]

next question

[dense lake]

WELPP

[subtle birch]

You don't even want to understand

[dense lake]

dont keep doing

[unkempt token]

divide the 42 by 7

then its 6

[dense lake]

you need to focus on one

learn how to solve

[unkempt token]

multiply the 9 by 6

[subtle birch]

Now find 9x

[unkempt token]

its 54

then minus it to 42

ez

so its 12

[subtle birch]

same for this question too

[unkempt token]

nah this one confusing me bru

[subtle birch]

First of all find x here

5x boys and 7x girls and 21 girls

[unkempt token]

umm, the boys?

[subtle birch]

find x then find no of boys as well

[unkempt token]

15

then plus by 28?

[unkempt token]

^

[subtle birch]

no

15 is number of boys

now find number of boys when number of girls is 28

using same 5x and 7x thing

[unkempt token]

um 4

?

[subtle birch]

what

[unkempt token]

uh uh

[subtle birch]

15 is the correct number of boys

[subtle birch]

now do this

[unkempt token]

what number

[subtle birch]

5x boys 7x girls and 28 girls

find boys

[unkempt token]

15

[subtle birch]

this time girls is 28 not 21

[unkempt token]

20!

@subtle birch

[subtle birch]

yes

[unkempt token]

then what now4

[subtle birch]

now find the difference

20-15

[unkempt token]

69

jk

5

[subtle birch]

yes

[unkempt token]

this is confusing me

you called me a boomer

!

help me now

[subtle birch]

its the same thing as question 1

[unkempt token]

wheres question 1

[subtle birch]

.

[unkempt token]

so the 3x is the height

and two appartment is 7x

[unkempt token]

am i righy?

right

175

help me with these

<@&286206848099549185>

[barren solstice]

45 mins

You can divide each hour into 4 quarters totalling to 8 quarters

8 is the number we get by adding the ratios

So

3 x 15 is 45 and 5 x 15 is 75

Strength for 75 mins and cardio for 45 mins

[unkempt token]

how abt this one

[barren solstice]

You do it this timee

Using the same logic

[unkempt token]

no i cant

[barren solstice]

Add the ratios

[unkempt token]

to where

[barren solstice]

Add the ratios to themselves ???

2 and 5

[unkempt token]

4:10

[barren solstice]

What the

2+5

[queen river]

lol

[queen river]

what the

2+5 wasnt the answer tf

[unkempt token]

just bc im not asian

[barren solstice]

Of course itts not

[unkempt token]

14+17

is

31

then

what

stop arguing and helped me

[barren solstice]

Divide the sum by 31 to get tthe value of a single unit of the ratio

Multiply that unit by the larger ratio to get the answer

[unkempt token]

fuck

[alpine nacelle]

x+y = 775
x/y = 14/17
x = 14y/17
775 = 31y/17
y = 425

[barren solstice]

Ya needed to multiply

[lone heart]

@unkempt token Has your question been resolved?

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[alpine sable]

I am begging you someone get me through this practice paper I got 5 days too revise on maths till my exams, I need a savour too get me through it

[last ether]

The question is heavily rigged

You're raising something by 0

What is any number (except 0) to the 0th power?

[alpine sable]

1