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#❓how-to-get-help

move to a vacant one

delete your message

and

just choose under the Math Help (Available)

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[rustic gyro]

Hello eveyboady my lenguage is spanish im sorry,I have a test

[rustic gyro]

Of Log and pitagoras teorema

and Cos Tan Sin exercises of search the angle

[weak bison]

Do you have any specific questions you need help with?

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@rustic gyro Has your question been resolved?

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[steady basin]

could someone mark my question 5 plz

[frank wren]

Hi whos in set 1 im there classes or grade 9 or the best dm me

[lone heart]

@steady basin Has your question been resolved?

[steady basin]

channel being used

<@&286206848099549185>

[frank wren]

How do i

Make my self

This

[steady basin]

what

[steady basin]

https://discord.com/channels/268882317391429632/488120190538743810

[pseudo ice]

The final answers and the method looks fine to me, if that's what you're asking?

[steady basin]

ye

[pseudo ice]

Though personally I'm not sure how much explaining is(/n't) needed for your course

Wait let me try something

[steady basin]

ok

[pseudo ice]

,w solve y''-2y'+17y=0

[steady basin]

bruh

yh i tried this

and it didnt work

for diff equations

[ocean seal]

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[steady basin]

thats why i neded someone else to check

[pseudo ice]

Nice xD

Always wanted to try the bot out haha

[steady basin]

how do u use it

[pseudo ice]

just type ",w solve [equation]" I think

Still somewhat new to here(!)

[steady basin]

,w solve [y'' + 4y' + 3y = 0]

[ocean seal]

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[steady basin]

SUIIIIIIIIIIIIIIIIIIIIII

[pseudo ice]

Oh you don't have to put the actual equation into brackets, I did that as a placeholder lol

[steady basin]

oh lol

[pseudo ice]

Ah either way it works out 😂

[steady basin]

thanks for that

also

would it be okay if u could have a look at a proof i did

and lmk if its valid

its a proof on complex conjugates

[pseudo ice]

Sure sure, I'll try my best

All the steps look valid to me!

[steady basin]

noice

thnx

[pseudo ice]

Some steps could be simplified, but at the end of the day, as long as it's valid, that's all that should matter

[steady basin]

cool thanks mate

appreciate it

[pseudo ice]

No problem! I actually saw this question posted earlier, but I'm shy at answering questions here 😂

Scared I'm gonna end up making some silly mistake and embarrassing myself lol

[steady basin]

haha nw mate

👍

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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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[open marten]

Is there a way to solve the unset condition of the figure : +inf -inf
using l'hospital's rule or something like that

[alpine sable]

in some problem can solve with different way like limit deferential but some problem hasn't answers

[open marten]

Exactly because there are some cases in which the solution cannot be found, or it takes time, so I am looking for a faster way

[alpine sable]

all problem han't same way

in 0/0 problem some time should try a lot of way and end know it hasn't answer 😂

[open marten]

I recently discovered that I can solve it using l'hospital's rule You helped me a lot , but In the exam there are cases that put us in a state of indeterminacy of the form +inf -inf , which I can't solve with this rule 😢

[alpine sable]

i don't know what is your grad and knowledge but i know hospital isn't work in all question so in this question you should be creative and smart try solve different example

you can send some example for me to solve it and find best way🙂

[open marten]

Minute

[open marten]

Here when i Calculate the limit at +inf It will be a non-set state (Regardless of the compensation in the largest extent)

[alpine sable]

🙂

ln x^2 / ln x

2 ln x / ln x

f(x) = 2

understand?

[open marten]

Yeah , so if we have just exp like[ (e^x)-x]

[open marten]

Limit in +inf

[alpine sable]

what??

[alpine sable]

example

[open marten]

Limit x->+inf

[open marten]

.

[alpine sable]

it's not 0/0

[open marten]

It +inf -inf

How i can solve it

[alpine sable]

ok

e^ inf - inf not have answer

[alpine sable]

see if x = +inf its inf but if x = -inf its's -inf this question not come in your exams , usually inf / inf come

[open marten]

Oh ok , so how i can Apply it in the current example 😅

[alpine sable]

really in this question just can give it number for x and plot it to understand what is it shape and were it go up or down

[open marten]

Oh , e^10 - 10 then e^11 - 11

[alpine sable]

no x - 2 -1 0 1 2 not 10

ok

[open marten]

Ok , just i use 10 to konw if is go up or down in +inf

Anyway, thank you

[alpine sable]

😁

[alpine sable]

😊

don't have any example?

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[carmine flint]

Prove that for every n∈N, 2^(5n+3) + 5^n * 3^(n+2) is divisible by 17

[alpine sable]

$n\in \mathbb{N},17\mid( 2^{5n+3} + 5^n 3^{n+2})$

[carmine flint]

hold on typo

redo

[alpine sable]

where?

[carmine flint]

meant * 3

not +

[alpine sable]

ah

[ocean seal]

Toby

[alpine sable]

ig mod 17

[carmine flint]

i tried but it never comes out right

[alpine sable]

and split 3^(n+2) into 3^n*9

[vale wigeon]

2^(5n+3) = 32^n * 8, and 5^n * 3^(n+2) = 15^n * 9

@carmine flint are you allowed to use modular arithmetic or is there an explicit instruction to do it via induction or something

[carmine flint]

yep modular

arithmetic

is the chapter

i got 32^n * 8 + 8^n * 9

did something wrong somewhere

[alpine sable]

5*3=15, not 8

[carmine flint]

yep i!

thanks it checks out now haa

-2^n * 17 right?

[alpine sable]

yeah

[carmine flint]

alr thanks man

appreciate it

.close

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[barren portal]

I was trying to understand the conditions for finding arclength of a parametric curve

it's mentioned that if the curve intersects itself the formula doesn't hold true

Let's say, if I have this curve parametrized in the interval 0<t<10, so it's not possible to find the arclength simply integrating from 0 to 10 ?

Is this constrain of non-intersecting curve added due to inability to uniquely identify the Kth length during in the Reimann sum setup ?

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[barren portal]

🤞

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[frosty wigeon]

Anyone know the answer

[alpine sable]

i cant see the exponents in the answers its too small

even on a big monitor

sorry

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[deep fable]

hello

[deep fable]

this is a problem using washers (solids of revolution)

set up an integral using washers to find the volume of the solid formed when the region, bounded by the graphs of y = sqrt(x), y=0, and x=9, is revolved around x=9

my integral was

is this correct?

this is what the graph looks like

please ping me, i don't have notifications turned on

thanks

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@deep fable Has your question been resolved?

[deep fable]

<@&286206848099549185>

[deep fable]

yellow?

[deep fable]

hello

anyone?

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[rose ledge]

The distance between every point on the parabola y = 8 x 2 and the y-axis is doubled

[rose ledge]

wait ill send a picture

i dont understand how the answer is 2x^2

any help is appreciated

[outer lark]

ok

say I have like x^2

if I put a leading coefficent of (1/2) infront, that means every x value that I used to plug in , produces a value half of the original function, so it would stretch is horizontally, (1/2) isnt the answer here but just as an example,

,w plot x^2 and (1/2)x^2 for 0<x<3

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[rose ledge]

thanks for the response, but wouldnt that make the answer 4x^2?

[outer lark]

yes, its not the answer here

this doesnt double the distance if you look at the graph 😄

you can play around with some numbers and test to see if the distance is doubled, what you are looking for is say the original function at x=a produces a y value of 1, then you want the modified function to produce a value of 1 at 2a

that is doubling the distance between the y axis

so in our example

if we had 1=x^2 , x = 1, and 1 = (1/2)x^2 , x = sqrt(2)

and since sqrt(2) is NOT 2*1

1/2 x^2 doesnt double the distance between the y axis when our original function is x^2

[rose ledge]

thank you i understand it now

[outer lark]

so what would your leading coefficent be?

to double the distance

[rose ledge]

for my question?

[outer lark]

ye

[rose ledge]

2x^2

[outer lark]

yes

but do you understand how it got there

run it through the test

[rose ledge]

,w plot 2x^2 and 8x^2 for 0>3

[ocean seal]

Wolfram Alpha doesn't understand your query!
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Requested by xla#6137

[abstract fractal]

You can also see that doubling the distance is a horizontal stretch by a factor of 2, which means replacing x with x/2

[outer lark]

if we pick our y value to be say 2, then 2=8x^2 , x = 1/2

then our modified function 2=1/4(8x^2) x = 1, and since 1 = 1/2 * 2 having a leading coefficent of 1/4

doubles the distance horizontally from the y-axis

:DD

thats the reason

8 * 1/4 = 2

[rose ledge]

is that since 1/2 is squared it becomes 1/4?

[outer lark]

sure

so for a cubic it would be 1/8

etc

[rose ledge]

yeah yeah

thank you guys ❤️

[outer lark]

,w plot x^3 and (1/8)x^3 for 0<x<3

[ocean seal]

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[rose ledge]

.close

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[worn fox]

?

[timber eagle]

ive been trying to find active poeple

[plain flame]

pfft abrams

leopard gang

[timber eagle]

people*

for over a week

[worn fox]

what?

[royal plank]

enough memery

you have a math question?

[last ether]

.close

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[outer lark]

Chally gang 😎

[visual depot]

For addition and subtraction rational expressions, do we remove the giant ones or do we not ? I can show you examples of what I mean if you want

[worn fox]

#❓how-to-get-help

[visual depot]

i sent my question

it is supposed to make automatic channel

sry im confuse

[abstract fractal]

This is not yet an open channel

[visual depot]

where to go to open channel ?

nvm

i got it

[lone heart]

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[formal ocean]

I’m confused on how to start this?

[outer lark]

kinks

[formal ocean]

I’m sorry I don’t understand?

[outer lark]

https://i.stack.imgur.com/BKgrA.gif

see the 'sudden jump' between tangent lines

[lone heart]

@formal ocean Has your question been resolved?

[formal ocean]

Yeah?

[outer lark]

pretty much

by the definition of derivative, the limit from the left, doesnt agree from the limit on the right, and therefor the limit at a doesnt exist

so its not differentiable

this is for |x|

but for any kink really

the tangent will randomly go

PEW PEW BANG SMOOSH

and wont agree from left and right

it will still be continuous though

because the limit of f(x) from the left and the right agree at a

[formal ocean]

So would the answer be B?

[outer lark]

no thats not continuous

[formal ocean]

The only point I see that's continuous is A

[outer lark]

why is 2,3 not continuous?

the limits agree at all points from the left and right

[formal ocean]

I'm a little confused but I thought it was continuous but it was still differentiable

[outer lark]

its continuous because the limits agree from left and right , its not differentiable because the limits of f'(x) from the definition of derivative dont agree from left and right

[formal ocean]

What's the difference between B and C?

[outer lark]

B has a dot in the middle of nowhere

disrupting the continuity and therefor differentiability

[formal ocean]

Oh okay I get it

Is it possible I could go over another question?

[outer lark]

sure

[formal ocean]

.close

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[mint estuary]

I need help with this simmilarity question

[mint estuary]

Would the the setup be 5/20 = 8/x or 5/20= 5+8/x

<@&286206848099549185>

[ebon otter]

Second one

Wait no

x/20 = (5+8)/5

*it's a triangle isn't it?

[mint estuary]

I assume so

[merry depot]

5/20 = (5+8)/x
you need the whole side length corresponding to x

[mint estuary]

Ok

Setup for this

I made the big triangle into 2 smaller triangles

Now how do i set it up

<@&286206848099549185>

<@&286206848099549185>

[merry depot]

what are you trying to do here?

[mint estuary]

Solve for x

I need a setup

I separated the triangle so it would be easier to see proportions

[merry depot]

don't separate it, use the large triangle and the medium triangle

well... i guess you could use the two smaller ones too

[mint estuary]

How

Draw larger and medium

[merry depot]

the large triangle with side lengths 12, 16, 20
and the medium triangle with sides 16 and x

[mint estuary]

Draw

[mint estuary]

Draw 2 separate triangle

Like i did

I know what your talking about, but what would the setup be

Bd/?

BD/?

[merry depot]

here you have the hypotenuse and the short side (the side opposite of angle C)
so which sides should use from the large triangle?

[mint estuary]

Idk what you r saying

I thought u said large and medium

U use abc i know

What are the proportions bruh

[merry depot]

what sides do you have on the red triangle in this picture?

[mint estuary]

Can you vc

Or draw picture

This will take too long

[merry depot]

i did. The red triangle. what sides are labeled?

[mint estuary]

Vc

Pickup plz

Yo

Bruh

How is abc proportional to anything

<@&286206848099549185>

<@&286206848099549185>

@merry depot

Where did u go

[merry depot]

Vc isn't a side

(I assume this means angle C)

[mint estuary]

😂

Voice call

[merry depot]

oh, no

[mint estuary]

Draw 2 triangles

[merry depot]

i did

[mint estuary]

No you didnt

Draw 2 seperate triangles

Like draw

[merry depot]

you do it.

[mint estuary]

Bro i dont know💀💀💀😂😂😂😂

I wonder why im asking you????

[merry depot]

look at the red triangles I drew, redraw them with the sides labeled

[mint estuary]

bro which side corresponds to what

[merry depot]

triangles ABC and BDC

[mint estuary]

ok but that doesnt work??

There what do u do with them??

[merry depot]

mark the right angles

[mint estuary]

Only bdc has right angle

[merry depot]

?

[mint estuary]

He said adb was right💀

Leme rewatch vid

Abd isnt right

Adb is

He drew the red

Not me

[merry depot]

so do you have a solution to this already?

[mint estuary]

Yes

But i didnt understand wtf he did

[merry depot]

what triangles does he use?

[mint estuary]

That doesnt matter there are different methods same solution

But here

[merry depot]

is triangle ABC right?

[mint estuary]

No abc is not right

Angle d is right

For both

[merry depot]

then what is the marking on angle B?

[mint estuary]

Idk bruh he doesnt explain

Idk how u get the answer using his 2 pictures

[merry depot]

you shouldn't be able to, without introducing a new variable. The sides aren't corresponding

[mint estuary]

Exactly bruh

I think

Abc might be right

I dont understand why he used 2 smaller ones

[merry depot]

no idea

[mint estuary]

You cant use adb if b is right

Adb is 4 sided💀

[merry depot]

BD cuts angle B

angle ABC is right, angle ABD is not

[mint estuary]

Nvm

I got it

[wanton cradle]

Yo

Anyone here???

I need this shit done

I missed something my teacher said during instructions

[gusty gorge]

since you don't really seem interested in knowing what knowledge you're missing

lemme teach you a useful thing

,w solve 5(6x+2) = -20

[ocean seal]

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[gusty gorge]

,w solve 5(16 + 4x) = -70

[ocean seal]

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[gusty gorge]

now you know how to use the resources at your disposal

[wanton cradle]

Uh

Yea

Thanks

[lone heart]

@mint estuary Has your question been resolved?

[wanton cradle]

,w solve 5(16 + 4x) = -70

[ocean seal]

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Requested by Christmas desel#7215

[wanton cradle]

I just wanted to see how to show the work

I think I get it anyway

,w solve 5(10+4x)=-70

[ocean seal]

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[wanton cradle]

Ok I'm starting to understand that

,w solve -12x+7=-57

[ocean seal]

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[wanton cradle]

Damn

Nvm

,w solve -3(4x+7)=-57

[ocean seal]

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[wanton cradle]

Dude I fucking knew it

At least Im starting to understand it

Oh yea

,w help

[ocean seal]

Wolfram Alpha doesn't understand your query!
Perhaps try rephrasing your question?
Click here to refine your query online

Requested by Christmas desel#7215

[wanton cradle]

Wanted to learn the commands but alright

#help-12

[lone heart]

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[mint estuary]

Use mathway

[lone heart]

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[solemn tinsel]

can someone help me with point c

[open dune]

ayo

can anyone help me w calc

[solemn tinsel]

Is a there a difference in the average number of hours between Neverready and Pennysonic batteries?

[solemn tinsel]

bruh

[open dune]

so yes?

[solemn tinsel]

girl u gotta get another help channel

but ig i could help

whats up

[open dune]

oh sorry i’m new here lol

[solemn tinsel]

lmao dw

[open dune]

is this stats?

[solemn tinsel]

yep

[open dune]

like w a significant difference?

[alpine sable]

Trying to understand the Spanish, I am guessing u already found the variance and everything else right?

[solemn tinsel]

wdym??

[solemn tinsel]

yeah

[open dune]

is that what you are trying to find

the significant difference

[solemn tinsel]

i mean im using the data given

[open dune]

yes

[solemn tinsel]

im trying to find if there's a difference with the means

i tried using an equation

[open dune]

is s the standard deviation

[solemn tinsel]

yeah but for a sample

[gusty gorge]

isn't it asking you

[solemn tinsel]

and we got x bar

[gusty gorge]

to test whether the variances are different

or is my spanish that bad

[solemn tinsel]

nah nah

its asking for the meam

mean

lol

[gusty gorge]

Habría alguna diferencia en las varianzas entre las pilas neveready y pennysonic

[solemn tinsel]

here

[solemn tinsel]

numero promedio

[gusty gorge]

oh you're talking about part c

[open dune]

yes you’re finding the significant difference

[solemn tinsel]

yeah part c

[open dune]

or if there is one i should say

[solemn tinsel]

l

im pretty sure i gotta use that equation

[gusty gorge]

do you know the sample sizes of each of neveready and pennysonic?

[solemn tinsel]

yep, its 25 for each

my problem is that idk the value of a

[gusty gorge]

so yeah you basically want to estimate the pooled sample variance

[solemn tinsel]

bc my null hypothesis is mux - muy = a

however idk what a is 😭

[gusty gorge]

no your null hypothesis is that mu_x = mu_y yeah?

[solemn tinsel]

oh??

why's that

[gusty gorge]

part c is asking "is there a difference in the average number of hours between the (piles???) of neveready and pennysonic?"

right?

[solemn tinsel]

is it the same reasoning for a difference in variance ??

[gusty gorge]

so your null hypothesis would literally be there's no difference

[solemn tinsel]

yeahhh

omg

okayyy

[gusty gorge]

and no difference means mu_x = mu_y

[solemn tinsel]

i was struggling with that im so silly

[gusty gorge]

difference in variance would be an F test yeah?

[solemn tinsel]

thank you??

[solemn tinsel]

yeahhh

[gusty gorge]

de nada lol

[solemn tinsel]

thank youuu!!!

si necesitas alguna ayuda con español me cuentas jajajaj

[solemn tinsel]

u still need help w calc??

[open dune]

one sec lol

[solemn tinsel]

bet bet

[lone heart]

@solemn tinsel Has your question been resolved?

[mint estuary]

Y tis exist

Ima just quit life tbh

💀💀

[gusty gorge]

the formula is a little convoluted but the idea behind it is decently simple lol

it's really bad when expressed in terms of standard deviations

[lone heart]

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[rare bay]

How do I solve for a.Period? I have the answer but dunno how to solve for that

[rare bay]

from a pdf test bank

I understand period is the time to complete one cycle

[lone heart]

@rare bay Has your question been resolved?

[naive valley]

the period in seconds is simply 1 / (frequency in hz)

[rare bay]

okay

1/400 Hz

[naive valley]

1/ (400 Hz)

which is 1/400 sec

since Hz = 1/sec

[rare bay]

2.5ms

[naive valley]

ye

[rare bay]

great

now here's where I get confused

I'm good for now I'll create a 2nd help ticket because I have another problem I wanted to go over

[naive valley]

sounds good, good luck

[rare bay]

thnx

[lone heart]

@rare bay Has your question been resolved?

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[vale beacon]

Hi! Just want to check if this is correct? Because no matter what I do, it's what I'm getting, but the system says otherwise...

[rose sigil]

i think it's cus you just have an approximation for the decimal

what if you use a fraction?

like -1/30 instead of -0.033

@vale beacon

[mortal trellis]

They literally explicitly say to use a decimal approximation

Maybe more digits help?

[rose sigil]

aesfiuhaef

sorry

[mortal trellis]

Answer is correct

[vale beacon]

This amount of decimal places worked for all the other questions, but I'll try. Thanks!

Yep, it worked. Thanks so much!

.close

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[golden cove]

I need help with my hw

[golden cove]

Im not able to solve any of the questions

[raven rover]

Start with 1 problem my friend

[golden cove]

I would

If I knew how to

If someone could tell me the steps I could try and do it

[vast schooner]

I forgot how to do these. I know they r simple but me stupid....

[slender remnant]

m sry to text here but i need sum help, its been like an hour-

[raven rover]

#❓how-to-get-help

[raven rover]

#❓how-to-get-help

[vast schooner]

I did

[raven rover]

Do you have one specific example,

[slender remnant]

m already in #help-8

[vast schooner]

THATS WHAT I DID

YOU FOOL

[raven rover]

Don’t type in channels that aren’t yours

[vast schooner]

I WAS IN HELP 0

[raven rover]

You’re in someone else’s channel, my friend

[vast schooner]

WELL I FOLLOWED THE STUPID HOE TO GET HELP

FOOL

[raven rover]

Unless you’re helping or participating

[vast schooner]

BE GONE

[raven rover]

I mean if you want me gone I don’t have to help, that’s up to you

[lone heart]

@golden cove Has your question been resolved?

[golden cove]

I do

Let me send it

That’s one

And that’s the other

[raven rover]

Mind rotating the images?

The pictures are a bit dark, look up cam scanner on the App Store - it can remove shadows

[golden cove]

Here u go

First example

Second example

[lone heart]

@golden cove Has your question been resolved?

[golden cove]

@raven rover

hello?

[raven rover]

Let’s just do one

I’ll have to leave soon unfortunately

Consider the first one - send a screenshot of it

[lone heart]

@golden cove Has your question been resolved?

[golden cove]

That’s rly helpful thx

[hot marsh]

🌧️

[lone heart]

@golden cove Has your question been resolved?

[golden cove]

<@&286206848099549185>

<@&286206848099549185>

[livid palm]

Claim

W8 I didn't get a channel

[lone heart]

@golden cove Has your question been resolved?

[jagged maple]

I'm really lost here

[jagged maple]

<@&286206848099549185>

[lone heart]

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[icy quartz]

Idk any of the real words for any of this, so I will try to explain it:
I have an assignment at school where we have been given the percentage of government officials who were women. So 2000, 2001 etc. all the way to 2017. All of these of course have values attributed to them. How do i plot the average of each year in a program like maple?

[tall topaz]

[icy quartz]

I am very sorry about that

It's to show the progression in female representation in government on a generalized global scale

https://tenor.com/view/crickets-chirp-chirp-gif-5280278

[lament glen]

I basically only use C, but it'd be something like the following in every language:

#define LENGTH 6

int values[LENGTH] = { 3, 1, 7, 4, 2, 6 };

int sum = 0;
for (int i = 0; i < LENGTH; i++) sum += values[i];

int average = sum / LENGTH; // Average is calculated here

[icy quartz]

Okay, thanks :)

.close

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[twin oasis]

help

wich graph solves the inequality ? Does anyone know

[alpine sable]

if a number is above the line, it's greater than the line at that point

the shaded area simply shows all the points at which the condition defined by the inequality is met

[twin oasis]

i think its B

[alpine sable]

yeah

[twin oasis]

it is 🤯🤯🤯

thanks

[lone heart]

@twin oasis Has your question been resolved?

[lone heart]

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[nocturne iris]

Hello

[nocturne iris]

Is there someone here familiar with Farey’s sequence?

Anyway it’s this

If we take a F_n big enough can we find all the irreductible fractions between 0 and 1?

So farey sequence would be something like this, till F_n

[worn fox]

Well there are infinitely many irreducible fractions between 0 and 1

So no matter how big n is, F_n will not capture all of them

[nocturne iris]

Oh so it’s a no?

Do u have a concrete proof

[worn fox]

I mean the proof is literally what I said

[nocturne iris]

Mmh ok yes so it’s quite intuitive

Thanks 🙏

[nocturne iris]

Do u know things about farey’s sequence ?

[worn fox]

Not a clue

[nocturne iris]

Oh ok

Thanks again

.close

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

I'm not really sure what to do, I plugged in v+w for u but I didn't get what I was expecting

[muted tinsel]

it feels like the A will always be a coefficient, so I'm not sure how you get rid of that. And I don't really know what to do with the symmetric fact

[mortal trellis]

have you multiplied out <A(v+w), A(v+w)> ?

[muted tinsel]

yea

I got like
A(A(<v,v>+<v,w>))

if I did it correctly

[mortal trellis]

that can't be correct

<v,v> and <v,w> are numbers

A(number) makes no sense

[muted tinsel]

is A a matrix or a scalar

in this case

[mortal trellis]

and in particular it's not equal to <A(v+w), A(v+w)> which is again a number

well they don't say. unless you are not giving all context

but probably a linear transformation

V isn't necessarily finite dimensional so not necessarily a matrix

[muted tinsel]

so how do I multiply that out then?

i thought I was supposed to use the bilinear property

but I guess if it's not a scalar then it deosn't make ksense

[mortal trellis]

you are

you can still use bilinearity

on the vectors Av and Aw

[muted tinsel]

so

<A(v+w), A(v+w)> = <Av + Aw, Av + Aw> right?

<Av + Aw, Av + Aw> = A<v, Av+Aw> + A<w, Av+Aw>
?

[alpine sable]

What is y < - 15x + 3000
y < 5x

[mortal trellis]

do not pull the A out of the bilinear form

[muted tinsel]

oh

so

[mortal trellis]

it is not a scalar

(probably)

[muted tinsel]

<Av, Av+Aw> + <Aw, Av+Aw>

right?

<Av, Av+Aw> + <Aw, Av+Aw> = <Av, Av> + <Av, Aw> + <Aw, Av> + <Aw, Aw>
?

[mortal trellis]

yes

[muted tinsel]

how do I simplfy that?

[mortal trellis]

first also multiply out <v+w, v+w>

and then you can go about proving the statement

[muted tinsel]

use a separate help channel for individual help

<v+w, v+w> = <v,v>+<v,w>+<w,v>+<w,w>
?

oh

and it's symmetic so

<v+w, v+w> = <v,v>+2<w,v>+<w,w>
<A(v+w), A(v+w)> = <Av, Av> + 2 <Aw, Av> + <Aw, Aw>
?

but if you set them equal, it's not necessarily the case that it cancels out to what we need right?

[mortal trellis]

so what do you have to prove

[muted tinsel]

that <Av, Aw> = <v,w>

and we have

<v,v>+2<v,w>+<w,w> = <Av, Av> + 2 <Av, Aw> + <Aw, Aw>

like the easy way would be if we could cancel the <v,v>, <Av,Av> and the w's

#help-10

any of the empty ones work

[mortal trellis]

what are we given

[muted tinsel]

OH

OH

HAHAHAH

thank you man

[mortal trellis]

also don't forgt about the other direction

[muted tinsel]

wdym

[mortal trellis]

(although that one is trivial)

[muted tinsel]

oh

so we also need to show that given <v,w> = <Av,Aw> that implies <u,u> =. <Au, Au>

just set w = v?

and then it's done?

[mortal trellis]

yes

[muted tinsel]

cool

thank you so much!

[mortal trellis]

youre welcome

[muted tinsel]

,close

.close

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[dense fiber]

!help

[lone heart]

Please read #❓how-to-get-help

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• 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.

[dense fiber]

i need help im stuck on a problem if anyone could help me that would be nice

[dense fiber]

bro 22 and 24

[mortal trellis]

,rotate

[dense fiber]

its number 22 and 24 I'm struggled with btw

[wicked seal]

don't ping them till after 15 minutes of waiting.

[dense fiber]

sorry

ill delete my ping

[dense fiber]

<@&286206848099549185>

hello

sorry if im bugging but could i please get help on the following problems above me 22, 24

[fringe sleet]

distributive property means a(b+c)=ab+ac, exponent rules are x^a x^b=x^(a+b), next you have that x^a=1/(x^-a), that is all you need for these problems

@dense fiber

$test$

[ocean seal]

Duh Hello

[fringe sleet]

ah nice bot is back, ill rewrite with latex:

Distributive property $$a(b+c)=ab+ac$$Exponent rule $$x^a\cdot x^b=x^{a+b}$$And inverse$$x^a=\frac{1}{x^{-a}}$$

[ocean seal]

Duh Hello

[fringe sleet]

using these 3 properties you will be able to change the expressions to what the questions are asking for

[dense fiber]

yes ik i just dont get the fraction with normal number part

[fringe sleet]

this one?

$3=\frac{1}{3^{-1}}$

[ocean seal]

Duh Hello

[dense fiber]

m-2 z4

distributed to the fraction

on 22

[fringe sleet]

$a(b+c)=ab+ac$

[ocean seal]

Duh Hello

[dense fiber]

yea but with a fraction

how would i do

do i distribute

to the denom aswell

[fringe sleet]

you just multiply them

no, only to the top

[dense fiber]

ik add the exponets

oh

[fringe sleet]

$a\frac{1}{b}=\frac{a}{b}$

[ocean seal]

Duh Hello

[dense fiber]

and then tk make the exponets negative you flip them right?

[fringe sleet]

yep

[dense fiber]

like flip

the fraction around?

[fringe sleet]

$$x^a=\frac{1}{x^{-a}}$$

[ocean seal]

Duh Hello

[dense fiber]

wait so the answer for 22

1- z-4/m-4z-5

?

[fringe sleet]

doesnt look quite right

[dense fiber]

it wrong?

like this

i got this

for 22

[fringe sleet]

i get $$1-\frac{1}{3^{-1}z^{-1} m^{-4}}$$

[ocean seal]

Duh Hello

[dense fiber]

wait is that the correct answer

then

[fringe sleet]

show ur steps and i can see where you went wrong

[dense fiber]

ok

[fringe sleet]

,rccw

[fringe sleet]

oh wait

you just didnt cancel the z's

[dense fiber]

wait whag

what

[fringe sleet]

ur answer is correct but you can cancel $z^{-4}$ on the top and bottom

[ocean seal]

Duh Hello

[dense fiber]

so both ways are correct

[fringe sleet]

probably not, they will want it simplified completely

[dense fiber]

oh

[fringe sleet]

but you just cancel z^-4 and you have my answer

[dense fiber]

im so confused on that cancel thing

wdym cancel it

can u explain

[fringe sleet]

$\frac{x^a}{x^b}=x^{a-b}$

[ocean seal]

Duh Hello

[fringe sleet]

in this case you have $x=z, a=-4, b=-5$ so $$\frac{z^{-4}}{z^{-5}}=z^{-4-(-5)}=z^1=\frac{1}{z^{-1}}$$

[ocean seal]

Duh Hello

[dense fiber]

is it that

[fringe sleet]

is it what?

[dense fiber]

above my text

[fringe sleet]

the z's can be cancelled

[dense fiber]

i don’t understand the cancellation rule

sorry

its confusing

[fringe sleet]

for any normal case $$\frac{ab}{ac}=\frac{b}{c}$$now you can also do it for when a is to the power of something $$\frac{a^2b}{a^2c}=\frac{b}{c}$$now if we have different powers we do $$\frac{a^db}{a^ec}=\frac{a^{d-e}b}{c}$$

[ocean seal]

Duh Hello

[fringe sleet]

and here we have z instead of a, and -4 and -5 instead of d and e

[dense fiber]

so u can cancel them since they are like terms

in a fraction?

[fringe sleet]

yep

[dense fiber]

is thatg for every fraction

with like terms'

if there is like term at bottom

and top

u can do that

[fringe sleet]

you can also just write it out $$\frac{z^{-4}}{z^{-5}}=\frac{z^{-4}}{z^{-4}z^{-1}}=\frac{1}{z^{-1}}$$

[ocean seal]

Duh Hello

[dense fiber]

alr

so ones everything is simplified

the answer is correct

[fringe sleet]

yep

[dense fiber]

alr

and for 22

how do i do it

[fringe sleet]

24 is basically the same thing

[dense fiber]

oh rlly

[fringe sleet]

except you dont need to distribute

[dense fiber]

mk

do u can cancel out

or something

[fringe sleet]

yep, and in this case they want all the exponents to be positive

[dense fiber]

ye

ok

cani try by myself

and u correct me

if i do wrong

imma work it out on paper

gimme a min

[fringe sleet]

ait

[dense fiber]

idk how bro

sorry

[fringe sleet]

start with the first one

[dense fiber]

as far as i got

[fringe sleet]

$\frac{3m^{-1}y^2}{m^{-2}}$, first see if there is anything that can be cancelled

[ocean seal]

Duh Hello

[dense fiber]

the m

[fringe sleet]

yep

[dense fiber]

3y2/3m-3

like that?

[fringe sleet]

not quite

[dense fiber]

jesus im stupid

[fringe sleet]

write it out like i did here

[fringe sleet]

not sure what you did there

you cant just multiply the bottom with random stuff without doing anything to the top

[dense fiber]

man i am lost

im sorry

[fringe sleet]

$$\frac{3m^{-1}y^2}{m^{-2}}=\frac{3m^{-1}y^2}{m^{-1}m^{-1}}$$

[ocean seal]

Duh Hello

[fringe sleet]

the idea is to get the same in the bottom as in the top

[dense fiber]

why did ui break it in 2

[fringe sleet]

so you can cancel them

since now you see that you have $m^{-1}$ in BOTH the denominator and numerator

[ocean seal]

Duh Hello

[fringe sleet]

and what can you do when you have the exact same thing in the top and bottom?

[honest drum]

Can someone help me with exponents in math

[fringe sleet]

#❓how-to-get-help

[dense fiber]

so is it 3m-1y2/1

now

[fringe sleet]

nope

[dense fiber]

huh

[fringe sleet]

i think you need to revisit some more basic rules

[dense fiber]

wait what is it then

after u cancel

and after breaking it in 2

[fringe sleet]

$$\frac{3m^{-1}y^2}{m^{-1}m^{-1}}\underbrace{=}_{\text{cancel out ONE $m^{-1}$}}=\frac{3y^2}{m^{-1}}$$

[ocean seal]

Duh Hello

[dense fiber]

oh

so u get the least common denominator

so u can subtract it out

and then add

[fringe sleet]

uhh

not sure what you are on about here

[dense fiber]

i mean

like common

[fringe sleet]

its the greatest common denominator and we arent subracting anything

[dense fiber]

yeha i meant that

[fringe sleet]

nor adding anything

[dense fiber]

mb

it says minues

then add

is it just subtract then

[fringe sleet]

$$\frac{3\cancel{m^{-1}}y^2}{\cancel{m^{-1}}m^{-1}}=\frac{3y^2}{m^{-1}}$$

[ocean seal]

Duh Hello

[dense fiber]

mk

then for the next one

ill try

it

[fringe sleet]

but you are supposed to get it to have all positive exponents

so we are not done yet

[dense fiber]

oh

right

flip the m to the numerator

no?

[fringe sleet]

yep

[dense fiber]

alr

so 3y2m1/1

plus the next one

[fringe sleet]

you dont need the denominator anymore but ye thats right

so next you have $$\frac{5m^2y^2}{x^2}$$again you check if anything can be cancelled

[dense fiber]

yeah u right

[ocean seal]

Duh Hello

[dense fiber]

nope

[fringe sleet]

correct

now is everything positive exponent?

[dense fiber]

yes

[fringe sleet]

so this one doesnt need anything done to it

[dense fiber]

ok

[fringe sleet]

last is $$\frac{my^2}{m^{-1}x^2}$$

[ocean seal]

Duh Hello

[fringe sleet]

im really fucking up my end brackets today

[dense fiber]

nah u g

[fringe sleet]

but again, look for cancellations

[dense fiber]

m is cancellable

[fringe sleet]

yep

[dense fiber]

then there is no longer an m there for the fractor is y2/x2

?

[fringe sleet]

nope

[dense fiber]

damnit

[fringe sleet]

remember that m alone secretly means $m^1$

[ocean seal]

Duh Hello

[fringe sleet]

so you need to get either both $m^1$ or $m^{-1}$ on the top and bottom

[dense fiber]

ye ik

[ocean seal]

Duh Hello

[dense fiber]

oh shit u right

so its nopw m2 on the top

[fringe sleet]

yep

[dense fiber]

cuz

itsbasicaly

exponet minus negative exponet]

which makes positive

at the top

no?

[fringe sleet]

exactly

[dense fiber]

THERE WE GO

[fringe sleet]

nice

so now we have the full equation

$$3my^2-\frac{5m^2y^2}{x^2}+\frac{m^2y^2}{x^2}$$

[ocean seal]

Duh Hello

[fringe sleet]

man im tilting myself with these brackets

[dense fiber]

lmao

[fringe sleet]

but now is there anything you notice here?

[dense fiber]

hm

yes

two like terms

[fringe sleet]

yep

[dense fiber]

fractions

add them

6m2y2/x2

[fringe sleet]

remember that the first one is negative

[dense fiber]

wait wha

[fringe sleet]

so -5(something)+1(something)=?

[dense fiber]

-4

[fringe sleet]

yea

[dense fiber]

thats the max it can be simplified

so u just leave as equation

no

?

[fringe sleet]

you can get them on the same fraction if you really want

but this looks cleaner to me

[dense fiber]

yes

[fringe sleet]

of course its completely subjective

[dense fiber]

how would fraction be thol

tho

just in case