help-28

[drowsy wyvern]

ok let’s take vector (56,73)

(56,73) = a(1,1) + b (2,1)

a+2b = 56

a+ b = 73

solve for a and b

is that right @nova basin

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[maiden zodiac]

Sorry for the stupid question but what do I need to calculate the a values ​​since I only use x and b? (RSA algorithm, variation of the Euler function)

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[maiden zodiac]

<@&286206848099549185>

[maiden zodiac]

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[torn jolt]

2x^3-7x^2+10x-2

[torn jolt]

how many terms are there

[elfin compass]

terms?

[torn jolt]

yea

in the polnomial

polynomial

one sec

there

[elfin compass]

4?

[torn jolt]

are u sure?

[elfin compass]

Yea just count the terms in equation
1 is 2X^3 , 2nd 7x^2 , 3rd 10x and 4th constant thats 2

[torn jolt]

yea

so 4 it is

ty

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[runic spruce]

For this

[runic spruce]

I’m trying to fill in the hessian matrix and don’t know what f31,32,33 would be ?

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[fluid coral]

3/1 x 4 + 5/4 x 9 + 7/9 x 16 +..... + 19/81 x 100

[fluid coral]

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[atomic dagger]

Pls help.

10 testers can complete 50 test cases in 40 days. All testers are equally productive. A project team has 40 testers available for 10 days.

How many test cases can they complete?

[left bone]

compute how much one tester does in one day

then extrapolate from that for the second part

[atomic dagger]

I found 1 tester did 1.125 in one day. Is it correct?

[atomic dagger]

Can't find second part

[left bone]

no

if this were true 10 testers would do 10+ in a Day, and 50 in less than 5 days

[atomic dagger]

1 tester did 5 tests in 4 days. Then in one day it's 5/4 = 1.25

I confused

[left bone]

4 days?

[atomic dagger]

Actually i divide all numbers to ten. But i don't know it's right or not and get 4

[left bone]

well its not correct, as you can see from my message explaining why its not right

think about a simpler version:
2 testers, 2 test cases, 2 days

each tester did one test cases in 2 days, think about why

[sacred crystal]

or think about it like this you have a total of 10 people that can complete 50 tests in a total of 40 days, now you have a restriction of only 10 days but you also have 40 testers how many tests can 40 testers complete in the restriction of 10 days based on the original idea of 10 people that can complete 50 tests in a total of 40 days

basically the idea here is to find how many tests one tester can do in a single day and then go from there

[atomic dagger]

Did you mean to divide tests by people?

To find 1 day

[sacred crystal]

its more like (50/40) tests per day / 10 per person

[atomic dagger]

In this case in 1 day 0.125

[sacred crystal]

sorry thats the wrong math

lol

i made a mistake

[atomic dagger]

Oh(

[sacred crystal]

tests / days * people

i think

beacuse its the amount of tests solved / how many people * days alotted

[atomic dagger]

Yeah actually it can be

But then i need again for second part

[sacred crystal]

nope

that solves for how many test on person can do per day

so u just then plug in and multiply for end resuly

[atomic dagger]

Answer is 50?

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[mystic latch]

hey so im confused as to

will the 7 replace all X shown on the picture

as in

[left bone]

$f(7) = -7^2+9(7)$

[mystic latch]

so

do i solve without the f

as in

7=(-7^2)+9(7)

or

-7^2+9(7)

[left bone]

its asking what is equal to f(7)

[lilac pagoda]

your missing the negative sign

[left bone]

which means you want whats on the other side of the equals sign

yes you are also missing the negative sign

[mystic latch]

so that will be the answer

Thank you

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[lilac pagoda]

do the 7^2 first btw

then multiply by -1

[mystic latch]

thx

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[sullen jacinth]

Hello, just started studying and can't seem to understand where the answer i came across comes from

[sullen jacinth]

Can't figure out how

x = -1 or x = 7 comes from

[lilac pagoda]

you just solved the quadratic

[buoyant pewter]

use delta method

[lilac pagoda]

theres a lot of ways to solve it

factorize, complete the square, quadratic formula etc

[sullen jacinth]

ahhh, makes way more sense, thank you! Might just be too tired for this

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[unreal hull]

What went wrong

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[unreal hull]

<@&286206848099549185> would like some assistance

[uncut pelican]

Take -32 feet per second ×5 seconds. Equals -160 from 500. Equals 340

[unreal hull]

no 💀

[unreal hull]

that's just respectfully wrong, + i already put in 340 as a desperate attempt

i wish all i had to do was plug in 5 😭

[uncut pelican]

Oh, sorry

[unreal hull]

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[unreal hull]

sigh

wasted 40 mintues on that problem

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[fickle gale]

i'm pretty lost on this question, would someone be able to help me?

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<@&286206848099549185>

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@fickle gale Has your question been resolved?

[brittle steeple]

Maybe draw a big circle and a small circle

and a chord of the same length in each one

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[desert musk]

Are you supposed to do it like so

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[ivory moon]

Can anyone explain the underline?

[idle kelp]

You are just replacing n with x

when x >= 1 log(1) >= 0 so you can drop that term, similarly x^2 > =1 when x>= 1 so you can drop that term too

[ivory moon]

Sorry I don’t get it

if log(x)>=0

If we take away logx isn’t that gonna decrease the values

[idle kelp]

There is a negative sign infront of the log(x)

You have a positive number (1-alpha)x^2. Suppose it is 7 for the sake of illustration, and you have log(x) >= 0, suppose it is 3, also just for illustration

[ivory moon]

Yeah I would understand if it’s (1-a)x^2 - logx <= (1-a)x^2

[ivory moon]

Yeah then u have 7 - 3 >= 7?

[idle kelp]

Yeah okay, there might be something wrong there

[ivory moon]

Hm also how does that show this one the first place

if (1-alpha)n^2 - logn >0

isn’t that supposed to be a less than

[idle kelp]

I suspect the problem is that the series you were supposed to be studying is supposed to be n^2 + log(n), not -log(n)

I don't see an obvious way to recover this strategy with that error

[ivory moon]

I checked on wolframalpja and apparently because alpha is less than 1

The inequality holds

Otherwise it fails but I don’t see why that is the case

[idle kelp]

Well, for starters, (1-alpha)n^2 is positive

so you at least have that alphan^2 + (1-alpha)n^2 > alpha n^2

You are really then interested in whether or not (1-alpha)n^2 > log(n)

Usually in the context of this kind of problem, you don't really care what happens for small values of n, and you know that n^2/log(n) tends to infinity, so that inequality is "good enough"

But I don't see that inequality as immediately obvious from the little bit that was written down

[ivory moon]

I’m so confused rn

Why is for example 1.5x^2 - log(x) not greater than 1.5x^2 when x>1

But likes like 0.5x^2 - log(x) > 0.5x^2

[ivory moon]

No wait this makes sense

[ivory moon]

But this doesn’t t

[idle kelp]

Just to be clear, you are aware that this is supposed to be true for some alpha between 0 and 1

You don't need this to be true for every single alpha

[ivory moon]

Yeah but I don’t understand why it’s true

My logic is that because logx is positive

So taking away logx will decrease the value

so how does something positive - something else positive end up being more than the original thing

[idle kelp]

One way to look at it is that you only really need to establish (1-alpha)n^2 > log(n)

Note that n^2 is always larger than log(n) for n>0

and the gap gets larger as n increases

So you can always choose alpha closer to 0 to make the gap between (1-alpha)n^2 and log(n) larger

[ivory moon]

Why is alpha being close to 0 making the gap larger?

Oh yeah

Makes sense

I still don’t get the inequality y

[idle kelp]

Honestly, that argument is really more thinking than I usually do for this kind of problem

You have an infinite series, whether you start at n = 1 or n = 100000 it doesn't really matter. A finite sum of finite numbers is finite

So you have that (1-alpha)n^2 > log(n) in a way that is "good enough" to test the convergence, because if that inequality isn't true, just start your index at an even larger number until it is true

and you know that such a number exists because the limit of n^2/log(n) goes to infinity as n gets large

Worrying about the specifics of an alpha that satisfies this is really irrelevant

[ivory moon]

Hm okay yeah that makes sense

Okay

But hold on I think I might see a way to show it

That inequality is the same as showing

x^2 - (1-a)logx> 1

Right

Oh no it’s not

damn it

it’s x^2 - logx /(1-a) > 1

Which is not really obv

[idle kelp]

I really do insist that this problem makes a lot more sense if it was just a +log and not a -log

You can see that with the - sign, you have a lot more to worry about than what is written, and if it were a +, no further details are required anywhere

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@ivory moon Has your question been resolved?

[ivory moon]

Yeah Hm

Thanks I’ll try opening another channel just to see if someone can make sense of the inequality

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[ivory moon]

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✅

[ivory moon]

Can someone make sense of this inequality

[smoky wing]

@peak drift

[glossy valve]

$Pure$

[peak drift]

faq

[smoky wing]

lol that’s weird

[peak drift]

it's comparison test

@smoky wing

[glossy valve]

$Pure2$

[smoky wing]

Yeah the inequality is weird

Would’ve made a lot of sense if it was a +

[peak drift]

are u p series...

[smoky wing]

Bro what

[peak drift]

ok

[ivory moon]

Can u help

@peak drift @smoky wing

[glossy valve]

Faq

[smoky wing]

No I don’t see it

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[peak drift]

lol

[smoky wing]

Do you see it my student

[glossy valve]

$Pure$

[peak drift]

i do

[smoky wing]

Go on then

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[vocal gorge]

Just to preface, this is not a test. It’s an open book assignment that is meant for practice, cooperation and asking people is 100% allowed.

Is that correct or am i doing something stupid

I feel like there shouldnt be a variable on the bottom

Grade 12 calc btw

[worn matrix]

,rccw

[near iron]

No, that's right

[vocal gorge]

Wonderful, thank you

[near iron]

you should take a look at how you expanded the denominator though

[vocal gorge]

O what did i do wrong

[near iron]

do you know about the FOIL method?

[vocal gorge]

Sure

I just skipped it

[near iron]

ah

so the thing is that you can't just square the first term and the last term

here's an example

[vocal gorge]

Oh i missed the middle term lol

[near iron]

yeah

[vocal gorge]

So its wrong

[near iron]

in your case it would be (2x+5)(2x+5)

[near iron]

just the denominator

you applied the quotient rule correctly, just didn't expand (2x+5)^2 properly

[vocal gorge]

So its 4x^2 +20x + 25

[near iron]

yes!

[vocal gorge]

So deriv is 17/that

[near iron]

yup

[vocal gorge]

Thank you

[near iron]

you could also just keep it as (2x+5)^2

unless your teacher says otherwise idk

[vocal gorge]

I just asked she said it doesnt matter

[near iron]

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[rare haven]

Can someone explain why he doesn’t do +2pi n

[lilac pagoda]

functions bounded from 0 to 2pi

[rare haven]

But for number two he does do that

[lilac pagoda]

wdym where does he put +2 * pi * n in q2?

[rare haven]

Before he divides by 2

In the first part 2x= 7pi/6 + 2 pi n

[lilac pagoda]

oh do u mean why he puts pi n in q1 and 2 pi n in q2?

[rare haven]

Yea

[lilac pagoda]

or like why the answer doesnt actually have either?

[rare haven]

The first one why he put 2 pi in question two and pi in q1

[lilac pagoda]

whats q1?

can u send both questions not the actual working out

[rare haven]

This was the first question

[lilac pagoda]

for each of the following, find what?

critical points?

[rare haven]

Basically the teacher told us to solve for increasing and decreasing for both of them

And not just find the critical values

[lilac pagoda]

did u delete the message with the other one that was + 2 pi n?

[lilac pagoda]

the reason its + pi n here is because its sin(2x) and cos(2x). the period of sin and cos is pi, so the solutions recur every pi/2 instead of pi

[rare haven]

Ok but in the other one it’s cos(2x) also

But there isn’t a sin(2x)

And the question is in the picture the one with 2 pi n

@lilac pagoda

[lilac pagoda]

wait where

can u reply to the message

I dont see the image anymore

[rare haven]

Right here

It’s sin(2x) but he does + 2 pi n

Is it because there’s no cos(2x)

[lilac pagoda]

because its not sin(2x) = 0

its a specific point

which aren't at regular intervals of pi

[rare haven]

Can you explain that a little more

[lilac pagoda]

see 0 occurs every pi

but for non-zero values they occur every 2pi

[rare haven]

Ohh

But what if it was sin(x)=0

[lilac pagoda]

then + pi n

but it was sin(2x) = 0

[rare haven]

Ok

[lilac pagoda]

so he did + pi/2 n

[rare haven]

Ok thanks

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[exotic dew]

,tex \int \frac{3}{1 + x²} dx

[glossy valve]

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

[exotic dew]

is the answer

[red blade]

Take out the 3

And it’s a common trig integration

[exotic dew]

I have a doubt

Can I use log

[red blade]

It’s arctan

You should know this

[exotic dew]

,tex 3 log |1+ x²|

[glossy valve]

Nalla Manithan

[exotic dew]

I know

[red blade]

,w compute d/dx(arctan(x))

[glossy valve]

Results provided by WolframAlpha

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

Requested by nosqldb

[exotic dew]

Okay

[red blade]

That’s completely wrong

Very wrong

,w d/dx( 3 log( abs(1 + x^2)))

[glossy valve]

Results provided by WolframAlpha

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

Requested by nosqldb

[exotic dew]

Thanks for your help

Is it because of the constant 3

. close

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[spark vapor]

whats the difference in doing svd for full matrix and the rank format

[fast peak]

could you elaborate on what you mean?

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[naive gulch]

help please

[smoky wing]

https://youtu.be/Y6M89-6106I?si=6PuCHHfNrnFjO7g8

[naive gulch]

hello

[smoky wing]

[restive kelp]

https://www.youtube.com/watch?v=iX7uU3YNOKk

[naive gulch]

Ty for vid I forgot what to do when the top number is bigger

so i go 8-5 = 4

I cant do 5-9

So I take away 1 from the 6 and its 15-9?

[smoky wing]

Right but 8-5 = 3

[naive gulch]

LMAO

right

okay

I got that one now

i have these next

[restive kelp]

how old are you?

[naive gulch]

24

[restive kelp]

https://www.cuemath.com/numbers/multiplying-decimals/

[naive gulch]

ty

i know its like 5th grade math I just forget the steps/order, just need to do a few to refresh my memory

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[lost jackal]

Can anyone help differentiate this:

[sharp vine]

$\QuotientRule$

[glossy valve]

Modus

[lost jackal]

uhhh

i still dont understand

[lost jackal]

help

[sharp vine]

just use the formula

what is the problem

[lost jackal]

hmm okay

I need to differentiate

[sharp vine]

I know I'm aksing what you're struggling with

I mean, you don't understand the formula or you can't differentiate x^2 + 2x - 1 or x + 3?

[lost jackal]

I was wondering how to differentiate but i think i understand now, Ill get back to you when i finish

[lost jackal]

I forgot

Lol

[sharp vine]

$\PowerRule$

[glossy valve]

Modus

[lost jackal]

I seem to recall this now

Ty

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[twin wolf]

How do I do D?

[viral jasper]

When do your criticial points occur?

[twin wolf]

at x=pi

Well is when it’s at a minimum no?

Critical points are like

[twin wolf]

0, pi/2, pi, 3pi/2 and 2pi tho

[viral jasper]

and how can you determine which are mins or maxes?

[twin wolf]

Well in this case there’s no phase shift so it doesn’t matter at what height the min max occurs because it still happens at the same time as regular y = cosx does

[twin wolf]

You can just look at it graphically

can I get help with part D tho

like

idk I’m not making any progress lol

[raven quail]

They are asking for the times at which h is minimum

[twin wolf]

yes but how do I do that

I don’t know how to do that..

[raven quail]

f(t)= 12cost +15

Find t at which function is minimum

-1<=cos t<=1

You'll get minimum value of f(t) when cos t = -1 yea?

[twin wolf]

yes

[raven quail]

So the all the t where cost=-1

Is your times where h is min

[twin wolf]

How would I write this as an answer tho

Am I solving for cos(t) = -1?

[raven quail]

Yes

You know where cos (t) = -1?

[twin wolf]

Yeah

[raven quail]

Nice

[twin wolf]

But I’m not given a domain restriction so

I guess I’ll just write the first few solutions

Since there’s multiple

[raven quail]

Or you can write it as (2n+1)π

Ie odd multiples of π

[twin wolf]

ohh I see

Why not like

npi

• 1 Or something

What does the 2n do there

[raven quail]

Because cos = -1 only at odd multiples

Thats why 2n+1

And not n

Cuz n would give both even and odd

[twin wolf]

oh okay

Thanks for the help

By the way

For part a) is this the same thing basically?

[raven quail]

Yes

[twin wolf]

Would I still use 1 and -1?

or not

[twin wolf]

if so do I use like -1<=cos(2pi•t/3) <=1

[raven quail]

Mhm

Yes

[twin wolf]

so cos(2pi•t/3) = 1 and -1

And solve for t

trig equations

[raven quail]

Yes

[twin wolf]

Okay thanks now I know how to do these problems

Hold on

[somber sonnet]

!!!

Do not forget to drink water

Stay Hydrated

[raven quail]

Yea they are basically asking when the function is max or min so you just have to get where the function is max and where it's min

[raven quail]

Crocodile bro this your home in the pic?

[somber sonnet]

nah

[twin wolf]

Part a is the same type of problem right

but in the solution they don’t solve the trig equation

They let cos(4pi•t/25) = 1 or -1

And then plug that into 1.3-0.6(1) or 1.3-0.6(-1)

[raven quail]

You dont "let" that, it's just a fact that cos lies -1 to 1

[twin wolf]

So you don’t solve an equation?

[raven quail]

If they are not asking at what times

And just the values of function

[twin wolf]

Ohh

So if it asks when the max or something occurs then you solve the equation but if it just asks the height at max and min you can plug it in

[raven quail]

Yep

[twin wolf]

-1 and 1

hm okay

so say I had

f(x) = 1 + 3cos(pi/3•x) + 9

And I wanted to find the max and minimum

I can do

1 + 3(1) + 9 = max

1 + 3(-1) + 9 = min?

[raven quail]

Yes

Now do for 5- 3cosx

[twin wolf]

Okay

Well since it’s reflected across x axis then

5 -3(-1) is a max

And 5 -3(1) is a min

[raven quail]

Nice

I have something to say tho

Don't try to "learn" the way to do that question

Remember the basic idea i told you

Value of cos can be anything form -1 to +1 so you use basic logic what value from -1 to +1 do you need to put. To make the function maximum or minimum

[twin wolf]

Okay thanks I think I get it now

I have a test today so this would help 👍

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[graceful peak]

AB is 8, AC is 12 and ST is 5. if SB is twice the length of AT, how will i get:
a. length of AT
b. length of BC

[graceful peak]

i know similarity theorems but i dont know how to apply it

[short bridge]

How do you even know that triangles are similar?

[torn jolt]

Guys

Is there any French?

[short bridge]

I don't think this is the place to ask this. Try #chill #discussion.

[torn jolt]

I need help on something

[short bridge]

!occupied

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[graceful peak]

oops sorry forgot to mention that its given that st is parallel to bc

[short bridge]

Ah. well, then just close your eyes and apply similarity stuff.

[graceful peak]

uhm

as/ab = at/ac so as/at = 2/3

i apply same logic with sb/tc = 2/3

i dont know how to go from there

[short bridge]

Here you found as = 2/3 at. Pretty sure you can use that somewhere.

You have some implicit equations as well. Just look at the figure closely.

[graceful peak]

ohhhhh

im so dum

since as = 2/3 at and sb = 2at, as/sb = 1/3 right?

which gives as = 2 and sb = 6, so at = 3

so ratio as/ab = 1/4

which makes ab = 4ST = 20

am i right

[short bridge]

Yes

[graceful peak]

thank you!

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[rocky scaffold]

hi i was wondering if anyone cud give me a hint for this assignment question?

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[tawdry narwhal]

1. a,b,c

1. a,b*

[wicked frost]

plug in x values that are close to 0 into the function and fill out the table

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[strong cradle]

ik i have to use lhopitals rule but im not sure how to make it into inf/inf or 0/0

[chrome idol]

how about, set y = function. Then take log of it

[deft tulip]

try taking $e^{\ln(\cdots)}$ of the whole thing then you can use exponent law for log

[glossy valve]

Soosh

[strong cradle]

like this?

[chrome idol]

yeah

so you can take the limit into the power

also note that 10/x comes down

by log rules

[strong cradle]

what does this mean

[chrome idol]

$e^{\lim{\frac{10}{x}}\ln(e^x+2x)}$

[strong cradle]

where did the ln go

[glossy valve]

WhoTao

[strong cradle]

oh ok

[rough tundra]

whenever you have a function with the indeterminate form $1^{\infty}$ you should most of the time take $e^{\ln(x)}$ becuase that is how you get the $\frac{0}{0}$ indeterminate form which is easier to work with:\
$$1^{\infty}=e^{\infty\cdot\ln(1)}=e^{\frac{1}{0}\cdot0}=e^{\frac{0}{0}}$$

[glossy valve]

PajamaMamaLlama

[rough tundra]

note that that final part has some very cursed calculations but we're taking limits so it's fine but I just didn't bother writing them

so when we get that 0/0 finally, we can very simply apply lhopitals :)

and also don't forget because $e^{x}$ is a continuous function in $\mathbb{R}$ we can say $\lim_{x\to c}e^{f(x)}=e^{\lim_{x\to c}f(x)}$

[glossy valve]

PajamaMamaLlama

[strong cradle]

oh that makes sense

i think i screwed up

[rough tundra]

I also think so

btw you only need to take e^ln(x) of one side

because e and ln cancel

[strong cradle]

oh

[rough tundra]

so you have $y=e^{\lim_{x\to0}\frac{10\ln(e^x+2x)}{x}}$ how would you proceed?

[glossy valve]

PajamaMamaLlama

[strong cradle]

plug in 0

oh

and then its 0/0

[rough tundra]

ahh you know how to do that one, yes? :)

[strong cradle]

take the derivative of the top and bottom of fraction and then do the limit

[rough tundra]

[strong cradle]

tysm bro

ur the goat

[rough tundra]

hope I taught you something

thank you for taking the time to learn and listen much appreciated as well

[strong cradle]

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[solid wagon]

did i do this correctly

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[solid wagon]

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[stiff swan]

can someone tell me how to get the matrix multiplied to A?

[stiff swan]

I know it had something to do with the steps of the RREF process done to A

but I can't remember how exactly

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[strong pawn]

Can anyone check my proof?

I am using this fact

[devout valley]

You're kind of going backwards in a way and assuming what you need to prove

$g \circ f$ being injective implies that whenever $(g\circ f)(x_1) = (g\circ f)(x_2)$, then $x_1 = x_2$

[glossy valve]

@devout valley

[devout valley]

You're given that g compose f is injective, and you have to figure whether f must be injective

[devout valley]

i.e. for f as is, you want to show that this must be true (or otherwise provide a counterexample where it isn't!)

[strong pawn]

So my problem lies from * to **?

g(f(x)) = g(f(y)) assumed right

since injective

[devout valley]

Yep and also this isn't necessarily true (you don't know whether g is injective by itself either!)

[devout valley]

Basically if you have that anywhere, you must have x=y

[strong pawn]

since g(f(x))=g(f(y)) is injective I cannot say f(x)=f(y)? I can only say x=y?

[devout valley]

Correct

(in fact there are counterexamples where g needn't be injective in general but the composition g circ f is)

Remember: this is what you want to show to be true!

[strong pawn]

I feel like its just a definition i forgot to memorize...

i miss when math was just numbers

[devout valley]

Awww takes a while to get used to

Anyways, let's try to prove this then

We know that $g \circ f$ is injective, so whenever we see anything like $(g \circ f)(x) = (g \circ f)(y)$, we're immediately allowed to say that $x=y$

[glossy valve]

@devout valley

[devout valley]

But we want to figure out whether $f$ is injective, so let's assume we start off with $f(x) = f(y)$, do you have any ideas of what you can do with that?

[glossy valve]

@devout valley

[strong pawn]

i know f is function

A -> B

uhhh

thats it lol

also g : B -> C

also an injective function means the definition mentioned earlier

also the converse is true

[devout valley]

interesting

[devout valley]

This is the contrapositive: an implication is equivalent to its contrapositive

The contrapositive of "if A, then B" is "if not B, then not A", whereas the converse of "if A, then B" is "if B, then A"

The converse does happen to be always true, by definition of a function of course

[devout valley]

interesting...

[devout valley]

if we were able to see something like this, our job would be done, right?

[strong pawn]

am i supposed to have an epiphany

i thought we already set the gof x = gof y to x = y

since gof is injective

[devout valley]

That is a true statement, but...

We want to show that f(x) = f(y) leads us to x=y somehow

[strong pawn]

aight so we got x = y

[devout valley]

There needs to be a set of valid steps that allow us to say that x=y

[strong pawn]

so we start at f(x) = f(y)?

and want to change it to x = y

[devout valley]

This is where we start, that's all we can really assume so far

[devout valley]

Yep

[strong pawn]

so lets put it in the g then ?

put both in the g?

[devout valley]

perfect!

[strong pawn]

g(f(x))=g(f(y))?

seriously

is that it

[devout valley]

It is!

[strong pawn]

So we use

?

Wait but how would that work for composite

This is just one

[devout valley]

You start off with $f(x) = f(y)$, then you can then conclude that $g(f(x)) = g(f(y))$, but as $g\circ f$ is injective, that gives $x=y$ as we need

[glossy valve]

@devout valley

[devout valley]

As per...

[devout valley]

...here

[strong pawn]

Oh so thats just a theorem I should memorize

[devout valley]

Basically if function [blank] is injective then whenever blank = blank, then x=y

Replace [blank] with whatever the function you're thinking of, whether that be g, f, g circ f, etc etc

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[dense nimbus]

Translation: m element of p exactly when m divides n

either proove or disprove that the relation, if given as a subset of the cartesian product is a function

[fast peak]

well what do you have to check for something to be a function

[dense nimbus]

i only know the german words but lefftotality and injectivity

[fast peak]

no you dont have to check injectivity

not all functions are injective

[dense nimbus]

its "rechtseindeutig" in german

[fast peak]

its not

its injektiv in german

[dense nimbus]

no no

[fast peak]

but ok

[dense nimbus]

i confused it with injective

[fast peak]

whatever

[dense nimbus]

is it univalent ?

[fast peak]

lets call it right unique

what do these properties mean

[dense nimbus]

ok

[fast peak]

and I have to go, sry

[dense nimbus]

no problem

thx nonetheless

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[dense nimbus]

<@&286206848099549185>

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[wicked aurora]

Yes this is a function I believe. It is the function that takes an integer and returns the set of its divisors.

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[thorn fjord]

To find the angle of intersection, i first have to determine the possible point(s) of intersection, but how do i do that?

[thorn fjord]

Think ive found it, just put these 2 in a system of equations and solve

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[paper lion]

hey

[paper lion]

is it legal to prove something by proving that the opposite of it is wrong?

i have to prove that thisis normed spacebtw

[gritty rose]

What axiom are you disproving exactly?

[paper lion]

i want to prove that |x+v1| + |y+v2| <=|x|+|y|+|v1|+|v2| by disproving |x+v1| + |y+v2| >|x|+|y|+|v1|+|v2|

[granite shore]

In general, yes. If you are trying to prove statement A, and you can show assumption of NOT A leads to a contradiction (ie. NOT A is false), then you know A must be truthful.

[granite shore]

If you could show assuming $|x+v1| + |y+v2| >|x|+|y|+|v1|+|v2|$ leads to a contradiction, then this should allow you to conclude $|x+v1| + |y+v2| \leq |x|+|y|+|v1|+|v2|$ is correct (I believe)

[glossy valve]

pencentre

[paper lion]

ooo right

thx

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[sullen jetty]

I know that ab=-3, but what should I do next?

[shut thorn]

write (a-b)^2 in its expanded form

you have all your vars

[rough tundra]

$(a-b)^2=a^2-2ab+b^2=\textcolor{red}{a^2+b^2}-2\textcolor{blue}{ab}$

[glossy valve]

PajamaMamaLlama

[sullen jetty]

OMG THX SO MUCH

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[warm knot]

i need help

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Please don't occupy multiple help channels.

[woven sand]

Please use your original channel #help-17

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[grizzled lion]

how can i find every combination of elements in a set X, that sum to an integer N?

For example, X = {1, 2}. N = 4.

Solution set =
{1, 1, 1, 1}
{1, 1, 2}
{1, 2, 1}
{2, 1, 1}
{2, 2}

[grizzled lion]

i think this would be a combinatorics problem

[brittle steeple]

Do you want an algorithm to enumerate every single combination?

[grizzled lion]

yeah

i guess this is more of a programming problem than a combinatorics problem then?

[brittle steeple]

Probably yeah

You can make it recursively

We'll say N=10 and X={1,2,3}

First return every set that works that starts with 1

Then return every set that works that starts with 2

Then return every set that works that starts with 3

To return every set that works that starts with 1, first return every one that starts with 1,1

Then every one that starts with 1,2

Then every one that starts with 1,3

So you'd get like

1,1,1,1,1,1,1,1,1,1
1,1,1,1,1,1,1,1,2
1,1,1,1,1,1,1,2,1
1,1,1,1,1,1,1,3
1,1,1,1,1,1,2,1,1
1,1,1,1,1,1,2,2
1,1,1,1,1,1,3,1
...

basically listing them in lexicographic order

[wild sleet]

i mean i would do it manually

like, you didn't say you need it for large Ns

For example, X = {2, 3, 4}. N = 14
manually look for sorted solutions
4 4 4 2
4 4 3 3
4 4 2 2 2
4 3 3 2 2
4 2 2 2 2 2
3 3 2 2 2 2
2 2 2 2 2 2 2

then permute each

[full forum]

@grizzled lion Has your question been resolved?

[wild sleet]

if it's not a long story, why you need that

[grizzled lion]

i was trying to solve this programming problem, i rewrote the problem into what i posted here, and i figured it could be solved with pure maths.

[wild sleet]

i don't think so

[full forum]

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[grizzled lion]

ty guys

[wild sleet]

i think the wizard describes the same i algorithm i would use, it was hard to recognize

[full forum]

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[civic beacon]

im very confused by how this triangle is described

[wild sleet]

same

[civic beacon]

so it's an equilateral triangle, so all side lengths will be some same number, and then the diagonal length is 2 feet which i think is the thickness?

[wild sleet]

i get diameter of a triangle, but diagonal?

[civic beacon]

yea

let me send a picture of what i think it is

like this

and the 2 is the length between the triangle faces

idk though

thats a weird window

[wild sleet]

i need more context to guess

if it's 2 dimensional, the total force is 0

it just gets pushed equally from both sides

[civic beacon]

its the window of a ship

hold on let me send the whole thing

[wild sleet]

i get what you say, just why would that be called diagonal length

[civic beacon]

here's my understanding of the first part:

[wild sleet]

right, water is on one side

i went crazy there

it's 2 dimensional

like this is not about buoyant force

it's just a question of what they mean by diagonal, is ithe side or the height

the side makes more sense, vertices on both ends

[civic beacon]

how can it be about a 2d shape

there would be no volume

[wild sleet]

there is no volume needed

it's not about buoyancy

[civic beacon]

then how do u find force

its about the force on the window

[wild sleet]

which comes from the water being X deep at point Y

[civic beacon]

force is mass times acceleration

mass is volume times density

so how do i figure it out without a volume

and windows have volume

[wild sleet]

"3×2 square"

what

[civic beacon]

im confused by that as well

[wild sleet]

solution from google

[civic beacon]

hm okay, so i guess diagonal length would be the sides then

for the triangle

if it's just a 2d shape

im still just confused by the question asking for a slice

ive never heard of that outside of the context of a 3d shape

and finding volume

[wild sleet]

yeah it's being weird

[civic beacon]

so the triangle would be the same idea but i need to use proportions to account for the changing slice size

[wild sleet]

what's 62.4

what even is the unit

[civic beacon]

its an average density of water

[wild sleet]

pound per cubic foot

amazing

[civic beacon]

kg/m^3 is the typical units

yea

[full forum]

@civic beacon Has your question been resolved?

[civic beacon]

u wouldnt happen to have found the answer to the second one

[wild sleet]

no it has the question but not the solution

[civic beacon]

how does this look

478 pounds is the answer

[wild sleet]

i don't get why it becomes − h

they also did −y in the solution i sent

[civic beacon]

the 5-h?

thats represents the distance the item is submerged

[wild sleet]

but depth of 5 is the lowest force, and it grows from there

[civic beacon]

we're accumulating the force at different distances and different cross section lengths

that's why there is a variable in both those parts of the integral

[wild sleet]

yeah, and the depth is at least 5, and more than 5 at every other point

[civic beacon]

how more than 5?

so im actually confused because i thought it should be the entire distance from the surface of the water

but your answer only does the length of the shape minus h

[wild sleet]

what it looks like on your picture is also what i picture

i don;t know why they did 4 − y

[civic beacon]

in my mind it should be 5sqrt3 - h

so im not sure

but if thats the answer to 1 ill just follow what it did

[wild sleet]

sorry i don;t know this well

[civic beacon]

no worries

maybe someone else will see this and know

<@&286206848099549185>

[full forum]

@civic beacon Has your question been resolved?

[full forum]

@civic beacon Has your question been resolved?

[full forum]

@civic beacon Has your question been resolved?

Channel closed

The owner is missing!

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[mighty tiger]

i am not sure how to approach this

[sharp thorn]

Find y in terms of x then diff

[strange basalt]

you are given a striaht line equation in parametric form
you can just use parametric differentiation or find straight line equation in general form
and then perform implicit differentiation

[mighty tiger]

k

[strange basalt]

i would suggest the latter

[mighty tiger]

ok

.close

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Remember:
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[shy root]

.opem

.open

$square root(1849)=43?$

[glossy valve]

3x3 cuber \learnt CFOP

[shy root]

@

[smoky wing]

Yes

[shy root]

<@&268886789983436800>

[smoky wing]

It is

[shy root]

Coool

[smoky wing]

Omd

Don’t ping mods for help

[shy root]

I was meant to do helpers /:

[primal stag]

@shy root why ur even asking this when u can calculate that using calculator

[smoky wing]

Well also don’t ping helpers immediately

!15m

[full forum]

Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.

[shy root]

I forgot a lot of my math skills

Do you think you could help?

[smoky wing]

Sure

[shy root]

Why not start with geometry?

Send a question and explain it

[worn matrix]

what r u even talking about bro

[shy root]

Geometry?

[worn matrix]

do u have any question?

[shy root]

Id like to relearn it

Since I forgot all abt it

.close

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[spice orchid]

Yeah please try not to do this again

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[tranquil rivet]

https://gyazo.com/4c0ac64a9ba5c52835a0da0f613631af

[tranquil rivet]

!status

[full forum]

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 was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

[tranquil rivet]

2

i pointed out simple definitions of a function and surjective/injective but i keep on getting contradicted by saying if f is not injective then it must be many to one meaning its inverse is not a function as it will be one to many but it states f's inverse is a function

am i allowed to set rules with my function such as x cannot be equal to 0

or any other rule that will make the functions inverse many to one/one to one

[viral jasper]

That is an interesting problem. So if f is not injective, then the minimum example is f(0)=f(1)=0. But then how can f-1(0) be surjective and map to both 0 and 1?

@tranquil rivet, give me your class's definition of f-1.

[tranquil rivet]

$f^{-1}(y) = {x \in X : f(x) = y}$

[glossy valve]

luke1

[viral jasper]

Are you sure that's all your book says on it? I have one idea, but not sure if it's allowed given your current definition

[tranquil rivet]

$f^{-1} : Y \rightarrow \mathcal{P}(S)$ there also this one but idk if it even holds

[glossy valve]

luke1

[tranquil rivet]

since i used latex to note down the definition and it was said in a lecture

and the lecture board wasnt that cisible for me in that lecture

visible*

[viral jasper]

My only guess is A=B={0,1}, f(0)=f(1)=0. f-1(0)=0.

You just need to think of what to do with f-1(1) now.

[tranquil rivet]

Idk

the question says "A, B and f" does that mean I can add constraints on f? since we were just changing A, B but nothing on f

[viral jasper]

Only constraint on f is that it is not injective, so anything else is whatever you want it to be

See here's where I have concern with your definitions. A function is invertible if an only if it is bijective. So I'm feeling like you're using some non standard definition here.

[tranquil rivet]

we also use the term pre-images

if that helps

and we also proved in a lecture that a functions inverse will be a function if the function is bijective

<@&286206848099549185> Anyone else have an idea?

[granite shore]

um what. if f is a function, then f^-1 only exists if f is one to one?

im confused about the original question

[tranquil rivet]

Ye but this question says otherwise

idk how

[granite shore]

f^-1 cannot be well defined if f is not injective

ie. how do we choose what elements in A to "map back to"

its the f(x) = x^2 problem

f is many to one (ie. f(1)=f(-1))

so how do we define f^-1?

[tranquil rivet]

f−1:B→A

i found this definition

[granite shore]

I think theres an error in the original question is what im hinting at

[tranquil rivet]

related to a forum post in this module

[granite shore]

right. suppose that f(a1) = b1 and f(a2) = b1

so that f is not one to one

how do we define f-1(b1) ?

do we define it as a1? a2?

its unclear

[tranquil rivet]

oh wait

[granite shore]

f-1 cannot map to both (otherwise it's not a function)

[tranquil rivet]

when it says "and f" we can use stuff like f(x) = 3

a constraint

[granite shore]

you can use whatever function f you'd like as long as it's not one to one

Let's say we take $f:\mathbb{R} \rightarrow \left{3\right}$ to be $f(x)=3$. We note that $f$ is not one to one since $f(1)=f(2)$ for example. How do you define $f^{-1}$?

[glossy valve]

pencentre

[granite shore]

We can certainly create some function $g:\left{3\right} \rightarrow \mathbb{R}$ such that $g(3)=1$ for instance. But now this function is not surjective.

[glossy valve]

pencentre

[granite shore]

So I feel like you always run into a contradiction with this

[tranquil rivet]

Ye

[granite shore]

ya i agree with you its a funky problem that may not have an answer with the definitions that i use for my classes

(in fact, i prove to my students that in order for f^-1 to exist, f must be injective)

[tranquil rivet]

my lecturer is aware of this question and seems to have no problems with it

its a problem sheet so ill get the answers later

[granite shore]

id be curious to know how he/she is thinking about the problem

[tranquil rivet]

one post about this question says

Would the following answer be correct?

Let A = {1, 2} , B = {3}, and f(x) = 3?

f(x) is NOT injective as f(1) = f(2). And we can make the inverse of f(x) surjective by constraining the range.

[granite shore]

Ah, now you're thinking about the question in a way that makes sense to me. YES you can often create an inverse function by restricting the domain of A (we do this for inverse trig, for example). However, once we do this restriction, then you necessarily make f one to one so it still contradicts the original problem that was posed.

Basically, you restrict the domain of f in order to create f^-1, you cannot restrict the range of f^-1 (if that makes sense)

At least, this is not a technique I'm familiar with

[tranquil rivet]

.close

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[charred escarp]

Hi

[charred escarp]

I've got a logic question about estimations

I had a question were it asked me to estimate the number of errors that will present themselves after a run time of 8 hours on a computer if a specific virus was active. I answered the question and got a decimal answer, should I truncate it because it has a remainder of 0.25?

[deft tulip]

that completely depends on the expected accuracy of the method used for the estimation, expectations of the context you are answering this question in, etc.