help-36

[magic sparrow]

my apologies matt, I got distracted in a different channel

[quartz spade]

No problem, I'm just really confused now

[magic sparrow]

g(x), by definition is a function of x

it is an arbitrary function, so it can be whatever you want it to be (*to make the two sides equal), but it is a function of x, not y

so g(x) = y does not make any sense

likewise neither does g(x)=x^2 *y

or any variation including a y

[quartz spade]

It;s supposed to be g(y) apparently, but yeah.

I don't actually know if my math is correct because the teacher for this class has given me zero resources to figure out what I'm doing at all.

[magic sparrow]

Yes, Matt I think you are closer to figuring this out than you think

the point of this is

when you do your integrations and stuff

you will find common terms on both sides of the equation

[quartz spade]

Right

I only found one common term though

[magic sparrow]

and you will find the one, or both sides, contains an arbitrary function of either x or y

[quartz spade]

Unless a positive and negative is still common

[magic sparrow]

and then you as the solver, can decide what those functions are

[quartz spade]

They didn't tell me if it was or not

[magic sparrow]

to show that the sides are equivalent

[quartz spade]

Is -y^2/(x+y) common to y^2/(x+y)?

[magic sparrow]

just moving this down real quick

[quartz spade]

That's what's really tripping me up hard

[magic sparrow]

okay so see if you can follow this with me

multiply that negative on the left through the top of your fraction

you will now see the two sides are equivalent * except for the negative sign on the other side

you can now add the term on the right side (the negative one) to the both sides of the equation

this will end up doubling it on the left side and getting rid of it on the right

as you have it written, they are not common terms

[quartz spade]

I'm supposed to add them?

[magic sparrow]

I do feel like there might be a small error somewhere in your process along the way

[quartz spade]

The teacher just vaguely said if it's not a match on the left, ignore it

[magic sparrow]

no, I was just demonstrating that they are not common terms

[quartz spade]

There definitely could be, I'm just so tired from this that idk what it is

I've been up since 6 AM doing this nonstop because I have so many assignments due at midnight

[magic sparrow]

Let us both go through the problem from start to beginning again more carefully, up until the point you are at right now

and see if we can figure it out from there

Tag me once you have redone the steps you currently have done

I'll definitely try to help you out with this then

you are closer than you think

[quartz spade]

I'll try, but I'm lowkey falling asleep really hard

I have 9 more assignments due in 41 minutes

[magic sparrow]

ah, I know the feeling, it sucks. Good luck though! if you want help with this problem still , let me know and we can do it. Or if you want to do it sometime in the future you can feel free to DM me

[quartz spade]

(x^2+2xy-y^2)/(x+y)^2 dx + (y^2+2xy-x^2)/(x+y)^2 dy = 0
M(x,y) = (x^2+2xy-y^2)/(x+y)^2
N(x,y) = (y^2+2xy-x^2)/(x+y)^2
integral of M(x,y) in respect to x = -(x^2+2xy-y^2)/(x+y ) + 2x
integral of N(x,y) in respect to y = -(y^2+2xy-x^2)/(x+y) + 2y
int M(x,y)+g(y)=int N(x,y)

@magic sparrow

[magic sparrow]

Okay

One second

okay Matt sending an image now

[quartz spade]

Ok

[quartz spade]

How did you get the 2y^2/(x+y)

[magic sparrow]

that is the antiderivative of the function, is it not?

[quartz spade]

I got -(x^2+2xy-y^2)/(x+y) + 2x using integration by parts

[magic sparrow]

i used u=x+y

du=dx

rewrite as (u^2-2y^2)/u^2

[quartz spade]

I used u=y^2+2xy-x^2

[magic sparrow]

but I did not do by parts, just normal sub

I am unsure about your integration, but taking the derivative of mine does produce an equivalence to the original function

[quartz spade]

Mine didn't, I tried rederiving it like 10 times

[magic sparrow]

okay, well... 2 things about that

[quartz spade]

I'm so tired I'm not really processing anything at this point

[magic sparrow]

1. atleast we know that your issues are coming from your integration

but 2

[quartz spade]

I'm just getting increasingly more stressed

[magic sparrow]

I apologize if this adds to your stress lol, but using my integrations there is not constant functions g(y) and g(x) that make the two sides equivalent

unless x=y

[quartz spade]

I understand kind of

The workload for this week from the teacher was just extremely hyperunrealistic.

[magic sparrow]

what does it mean when it says C=?

what is it asking for you to find

[quartz spade]

17 assignments in 3 days, when one of the days was a required school event that lasted 10 hours

C= is just the final answer, for the purposes of the software's syntax

[magic sparrow]

dang. is this diff eq or calc?

[quartz spade]

Diffeq

[magic sparrow]

do you get more than one guess for the answer?

I have a few ideas

[quartz spade]

I get 5

For this specific question, I have 4 more tries

[magic sparrow]

okay give me a few more minute

I do not understand

I feel as if your question has to be incorrrect

but obviously that can't be the case

....

I got very close

but ended up with 2xy=xy

2=1....

[quartz spade]

I'm just going to skip it at this point

It's taken up a full 2 hours of my day, which I didn't really have to spare

It's not worth it at this point when I have 10 minutes left

I still have 7 other assignments due

[magic sparrow]

goodluck with those, I'll keep tinkering around with this for a bit and tag you if I end up getting it

[quartz spade]

I have 5 reading assignments due as well which bodes extremely badly for me because my vision is extremely at this point in the day.

blurry

[magic sparrow]

dang, you got it! grind out what you can and don't worry about what you can't do. At the end of the day you can only do what you can do, and if you end up missing some stuff it is just an opportunity for you to realize you'll have to work a bit harder next week to stay on top of it. No need to put yourself down though because once the deadlines come around, what is done is already done.

@quartz spade my apologies for messing up some algebra earlier, but I actually did find the solution

[quartz spade]

Wait there's a g(x) and y?

The lecture and book said nothing about that

[magic sparrow]

well

so you are doing two integrals right?

one dx and one dy

both produce an arbitrary constant

the constant for the integral with respect to x, could be any function of y (because it is treated as constant)

[quartz spade]

Yeah

[magic sparrow]

and the opposite is true for the integral with respect to y

[quartz spade]

It seemed to have worked

[magic sparrow]

so you end up with a g(y) and a g(x)

[quartz spade]

I'm just trying to get through these reading assignments now, but the questions are referencing equations that simply do not exist in the book at all

[magic sparrow]

refer back to this image, do you see where they come from in this

[quartz spade]

I've been staring at this for 5 straight minutes

[magic sparrow]

well I'd say that method is using an integrating factor

idk what the real name is

[quartz spade]

This book is so wildly unhelpful for this so called reading assignment, that I'm not entirely sure where he's drawing these questions from

[magic sparrow]

yah that is a horrible question for introducing the topic

diff eq, taught poorly, is a terribly difficult course

here is the idea behind that question

[quartz spade]

I'm already struggling as it is since I haven't taken a math course in 5 years

[magic sparrow]

,, y'+y*g(x)=h(x)

[soft zealot]

AustinU

[magic sparrow]

this is a first order linear differential equation

you understand the notion correct?

[quartz spade]

Yes

[magic sparrow]

As is, the equation is not seperable

[quartz spade]

I am aware what integrating factors are, the notation he used is just nowhere similar to the book's.

[magic sparrow]

well do you not think it is the correct answer?

[quartz spade]

It sounds correct, but I went to the next question, and that was the answer to that one

[magic sparrow]

could it perhaps be the method of undetermined coefficients?

[quartz spade]

The way these assignments are set up, you can't find out what's wrong until you finish the whole thign

[magic sparrow]

I strongly believe the answer is integrating factor method

[quartz spade]

I'm still trying to get to the end to see what was right

[final saddle]

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[harsh elk]

how does this work?

the options for each answer is a, b, c, d

[final tangle]

consider whether 13 and/or 19 are included/excluded for each statement

[harsh elk]

so higher than would be included?

and then ended at 19 hours would be excluded?

[final tangle]

no

e.g. 2 isn't higher than 2

2 wouldn't be part of the values higher/greater than 2

try starting with b) or d)
those are clearer

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@harsh elk Has your question been resolved?

[harsh elk]

.close

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[hard ridge]

Uranium-238 (U-238) has a​ half-life of 4.5 billion years. Geologists find a rock containing a mixture of​ U-238 and​ lead, and determine that ​76% of the original​ U-238 remains; the other ​24% has decayed into lead. How old is the​ rock?

[hard ridge]

Ok so, from what I understand, I have to do log2/4.5billion

I think

so I think how I would set this up is: .76 = N(sub 0)e^(log2/4.5billion)*t

but I dont know if thats correct

[tired walrus]

no, you've kinda made your life difficult

the equation you are looking for is 0.76 = (1/2)^(t/L)

where L is the half life and t is the unknown i.e. the age of the rock

[hard ridge]

So L would equal: 2/4500000000

[tired walrus]

no

[hard ridge]

Oh

I see

[tired walrus]

L is the halflife

[hard ridge]

Ok

That makes thing look a little better

I got .79185

[tired walrus]

you got what?

how did that number come to be?

[hard ridge]

t= .79185735

Wist

[tired walrus]

show your work

[hard ridge]

Oh my

I see 🤦

I put 2 for the half-life

[tired walrus]

you overthought it.

[hard ridge]

t=1781679043.49013

[tired walrus]

[hard ridge]

So 1.782 billion years

[tired walrus]

this would have been so much better if you had chosen to show your work and not throw numbers at me

[hard ridge]

Well thank you nonetheless?

.close

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[solar cape]

how do i solve this

[chrome heart]

move all terms to one side

so

[chrome heart]

$m^2-15m+50=0$

[soft zealot]

FusedMeme

[chrome heart]

then factorise

$(m-5)(m-10)=0$

[soft zealot]

FusedMeme

[chrome heart]

$therefore, m=5 , m=10, by null factor law$

[soft zealot]

FusedMeme

[chrome heart]

@solar cape u understand ???

[solar cape]

yea so you move the -1 and m to the other side and then find two numbers that multiply to 50 and add up to -15

right

[chrome heart]

yes

[solar cape]

ok thanks

[sonic hazel]

can someone help me with the law of sines and cosines please

[wraith solar]

dont paste your question into other help tabs

if 15 minutes passes you may call the helpers on your own tab

and bruh I was helping you lmao

[final saddle]

@solar cape Has your question been resolved?

[chrome heart]

Use the fact that a/sinA = b/sinB

to find the pronumeral x

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[west citrus]

I did not understand as well as I thought first thing I need help with is "the number of bacteria present at 8am was 1500, by midday the number had increased by 400. assuming exponential growth how many bacteria would be expected by 6pm'

[west citrus]

so it would be like 1500e^(k(240))=1900??
e^(k(240))=1900/1500 and then do I do the log or ln i can't remember ☹️ either way that's either k=0.0004 or k=0.0009 but if I put either of those in it doesn't give me a right answer so I'm once again lost

?? I put in 1500e((ln19/15)/240)(600)=x and i got 2708.6 so 2709 which is an actual answer but I dont . understand how 😭

ok whatever I got the answer idc I'll let that one go, the next one is "the number of ants in a nest is increasing by about 5% per day, how many days will it take for the number of ants to double" how tf do i figure that out

<@&286206848099549185> so sorry ☹️

[verbal furnace]

isnt it a 100% increase?

so u just have to figure out that how many days it will take to get to 100 %

ig

[west citrus]

it would be increased by 200% wouldn't it bc if you have something at 100% that's just the initial number

I thought

I don't understand percentages I won't act like I do

[final saddle]

@west citrus Has your question been resolved?

[west citrus]

ok I did random stuff until I got the right answers and got 93% 🙏 good enough for me

.close

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[brittle tulip]

no idea where to start

[verbal furnace]

thats wrong mate

[west citrus]

what

I mean

if I got 93%

its good enough 💀 the one I got wrong was one of the first ones I did earlier anyways

[worldly vale]

This isn't your channel anymore don't interrupt

@brittle tulip figure out what the inside approaches

[verbal furnace]

but his answer is wrong and we are suppose to help

[west citrus]

I closed the channel because I was satisfied with my score

[worldly vale]

Do it in a new channel

[west citrus]

thats all there is

[verbal furnace]

well fair enough ...sorry for disturbing but thats wrong and according to someone i cant help u here anymore

[west citrus]

I got all the questions I asked about right shrimple as that, have a great day

I wish you luck keisuke

[verbal furnace]

lol good luck and read the question mate it is asking for days not percentage !

[brittle tulip]

so

find the limit of the inside

then outside

[worldly vale]

Give it a try

[brittle tulip]

ok

[brittle tulip]

got negative infinity

[worldly vale]

Agree

[brittle tulip]

now i do arctan(-infinity)?

as Lim approach 2 from left

but im not sure how to do that

[willow eagle]

<@&286206848099549185> is This correkt

[brittle tulip]

Uh

[worldly vale]

Youre not assertively doing lim as y tends to -infinity of tan(y)

[brittle tulip]

hm

[brittle tulip]

would it be an asymptote of Tan

pi/2 etc

[worldly vale]

It will be, but just think of the graph of arctan

[brittle tulip]

arctan

has no va or ha tho

nvm

it has ha of -pi/2 and pi/2

o

cuz tan -1(-infinity)

-infinity is basically the horizontal asymptote

right?

[final saddle]

@brittle tulip Has your question been resolved?

[final saddle]

@brittle tulip Has your question been resolved?

[brittle tulip]

<@&286206848099549185>

[final saddle]

@brittle tulip Has your question been resolved?

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[forest mesa]

I feel dumb as hell but I 100% forgot how adding and subtracting fractions with unlike denominators work and none of the online explanations make any sense

[forest mesa]

The problem is 1/8 + 7/12 but I can't come to any coherent answer

[distant wraith]

LCM

[forest mesa]

Yeah which is 96 but like 7 isn't divisible into 96 without turning into a decimal

I thought it was multiply denominators together

Jfc none of these explanations have given me a straight answer

[distant wraith]

or you can take 24 common

[forest mesa]

That's right!

Holy shit

[distant wraith]

since 24 comes in the 8 times table as well as 24

[forest mesa]

Cuz 24 multiplies into 95

96*

So now what do we do to come to a coherent answer?

Welp just flunked it because I multiplied 1 by 12 which game me 12/24 or 1/2

[forest mesa]

Now I need to try a different one

[distant wraith]

hope this helps

thats how you would add fractions

[forest mesa]

Now its 3/8 1/12

Alright

So a common number in all factors

[distant wraith]

did u undertand it?

yes

since 24 comes in the 8 times table as well as 12

12 x 2 = 24
8 x 3 = 24

multiply each fraction by the same number

[forest mesa]

Got to 11/24 and it was right!

[distant wraith]

look in image

[forest mesa]

I'm lookin

Because 3 is common in the first one and 2 in the second

[distant wraith]

mines is 17/24

which is correct

[forest mesa]

No

I'm doing another problem now

Because I flunked the other

[distant wraith]

ah alright

[forest mesa]

It gives you three tries so I did 3/8 + 1/12

I realized that 8 goes into 24 3 times and 12 goes into 24 2 times

[distant wraith]

yes

[forest mesa]

So badabing badaboom can't be reduced

[distant wraith]

11/24 is right

[distant wraith]

?

[forest mesa]

Now there's subtraction but I'll figured it out
11/24 can't be reduced any further

[distant wraith]

well think abt it, can it?

are there any number that multipled give u 11 OR 24?

try 2, 3, 4, 5,6,7,8,9 .... times table

[forest mesa]

No, there isn't. I typed in my answer and it said 11/24 was correct

[distant wraith]

👍

as long u understand it

substraction is also the same

[forest mesa]

Cool! Gonna crack at this problem

.close

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[tranquil pine]

I already did 3 I just need 4

I don’t understand it

<@&286206848099549185>

[hushed plover]

do u know how to use those to solve for the individual values>

?

[tranquil pine]

No I do not

[hushed plover]

so b = 105, now plug 105 into b for a = 3b - 9 to find a

so it would be:

a = 3(105) - 9

a = 306

b = 105

we know that:

a + b + c = 522

so we have:

306 + 105 + c = 522

411 + c = 522

subtract 411 from both sides

c = 111

[tranquil pine]

306 + 105 + 111 = 522

[hushed plover]

yep

[tranquil pine]

Is that all?

Or is there more

[hushed plover]

?

that is all

[tranquil pine]

Oh

[hushed plover]

the first plane (a) has 306 seats, the second plane (b) has 105 and the third plane (c) has 111

[tranquil pine]

Thank you

[hushed plover]

to be clear im not like an official helper or anything but i would be really surprised if i got that wrong

[tranquil pine]

As long as you helped is all that matters

I wouldn’t have been able to write anything down

I’m horrible at math

[hushed plover]

im not too great at it myself to be honest thats why im here asking questions of my own🤣

[tranquil pine]

Lol well thank you though

I still need a couple more questions

[hushed plover]

send them i dont think that they r gonna get to my question for awhile

its not a fun one to solve

[tranquil pine]

I’m pretty sure this is really easy math but In my eyes I feel lost when i see it

[hushed plover]

what year are you in school if you dont mind me asking?

[tranquil pine]

A senior

Ive never been good at math

[hushed plover]

okay that makes sense

that ur a senior

it was sort of an odd mixture of topics

[tranquil pine]

It’s the only class I don’t understand

The other I’m doing good in

It’s just math

[hushed plover]

for 6

[tranquil pine]

Okay

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@tranquil pine Has your question been resolved?

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[minor oracle]

how do u do thishttps://cdn.discordapp.com/attachments/1046992915882328186/1072338377275351151/IMG_1993.png

[vast stump]

hi

so cos^2x

what do we know about this trig ratio

[minor oracle]

what do we need know?

[vast stump]

refer back to the given question at hand

given cot^2x = 0.04

What comes to mind?

[final saddle]

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[tranquil pine]

Don’t understand

[grim badger]

Find the circumference of the circle and the area of the square

[tranquil pine]

C=pi r

[grim badger]

Find the circumference

You know the formula

[frail flax]

i literally helped you in another channel…

[fathom walrus]

Number 13 is beautifully written

[muted prairie]

these are all treats

[fossil geyser]

Omg you're right. Who wrote these problems?

[tranquil pine]

My teacher

.close

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[jaunty vessel]

can someone help me figure out problem i?

[ocean stratus]

the limit can only exist if the limit from the left side is equal to the limit from the right side

[jaunty vessel]

is the limit just a point on either side of the line

?

[ocean stratus]

those are the left sided and right sided limits

[jaunty vessel]

is there a formula i use

[ocean stratus]

there is a definition but it won't be useful in this case

it's better to solve graphically when given a graph

[jaunty vessel]

what does that mean

[frail flax]

look at the left and right side of x=0

from the left of x=0 what is it approaching

[jaunty vessel]

left and right side of x = 0 seem to be approaching infinity

and increasing

like

[frail flax]

no it stops somewhere

[jaunty vessel]

the line is going up

o

wait

[frail flax]

yea?

[jaunty vessel]

i = 0
ii = -1
iii = -2?

becus

[frail flax]

nope

[jaunty vessel]

o

[frail flax]

from the left this is what

[jaunty vessel]

close to 1

[frail flax]

yeah you say it approaches 1

what about the right side

[jaunty vessel]

approaching -1?

[frail flax]

is it?

[jaunty vessel]

looks like it

[frail flax]

does that look like negative one?

[jaunty vessel]

o

0?

[frail flax]

yeah

so the limits from the left and right aren’t equal so this limit does not exist

[jaunty vessel]

oh

so left limit is going towards the right approaching 1 and the one at the right is approaching 0 by going to the left?

[frail flax]

yeah

[jaunty vessel]

o

oki

ii would be -1 right?

[frail flax]

ye

[jaunty vessel]

it seems like for iii theyre not approaching anything because of the circle that isnt filled in

and then the floating dot

could that be limit does not exist?

[cursive delta]

You can show a limit exists rigorously by using the defn: For all epsilon > 0, there exists a delta > 0 such that the if 0 < abs(x - a) < delta) then abs(f(x) - L) < epsilon)

[jaunty vessel]

when x is approaching 3

its the limit doeswnt exist?

i think im good

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[haughty moth]

he have 20 balls in an urn, 5 are red, the rest is white; we take 3 balls without replacement. A="At least 2 balls are red". What is P(A)?

[haughty moth]

If #o is the number of all possibilities, #o = 20x19x...x3

to find P(A)=#A/#o where #A is its cardinality

how do i find #A ?

[fair ledge]

Okay take 2 situations

1st situation is all 3 balls r red

2nd situation is 2 balls r red

We gotta add these

[fair ledge]

Probability of 1st ball red is 5/20. After this, there r 4 red ball out if 19, so probability that 2nd ball is red is 4/19. Similarly, 3rd ball red is 3/18

[fair ledge]

Thus probability that all 3 are red is their product (543)/(201918)

[haughty moth]

ok and then i add the other situations

how many of them remaining?

[fair ledge]

So the second situation is that 2 balls r red which is the same as one ball being white

Let’s say the first ball is white, the probability is 15/20. So the next 2 balls have to be red

The probability of next 2 balls red is 5/19 and 4/18 respectively

So overall probability of first ball white and rest 2 red is their product (1554)/(201918)

Try this out for the second ball being white or third ball being white… we get the same answer so add that up too

[fair ledge]

Thus the answer is thrice this

[fair ledge]

+this

[haughty moth]

mmh yes

that works and if i want the use the cardinality of A?

[fair ledge]

I’m sorry I’m not sure what cardinality is

[haughty moth]

ok nevermind it works thanks 🙂

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[outer ruin]

how i prove this

[tranquil pine]

Let x be any arbitrary element of B

And then prove that it simultaneously also exists in C

Oh wait

you can also prove it using substitution and some laws like absorption, distributivity, ...

I think I can proof it more simply without any element stuff igg

Nah, I think x one makes sense

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@outer ruin Has your question been resolved?

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[void basin]

hey

[void basin]

i need help

its a q abt percentages

[wind lark]

.

.

.

.

[void basin]

?

[fossil geyser]

[void basin]

ohh

ok here's the q: Decrease 77 by 0.25%

?

@fossil geyser

@final saddle

@final saddle

@final saddle

@tropic root

[fossil geyser]

Do you know how to express 0.25% as a pure decimal?

[void basin]

no

[fossil geyser]

without the percent?

[void basin]

do u mean 0.25

[fossil geyser]

No, % means divided by 100

0.25% is 0.25/100

[void basin]

so the question would be : 0.25/100 * 77

[fossil geyser]

Almost

To increase or decrease, you want to start with 100% (which is equal to 1), and then add or subtract your percent

So to decrease, multiply 77 by (1 - 0.25/100)

[void basin]

0.25 * 77?

[fossil geyser]

.

[void basin]

alr

ty

/.close

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[rough grove]

(2a+3)(a-1) - (3-x)(-x-4)

[rough grove]

need help on how to solve this

[rain crane]

solve for what

[rough grove]

just to write as simple as possible i think

dissolve the bracelet

backet*

[rain crane]

u can apply distributivity and things will cancel

[rough grove]

i tried and i got to 2a^2-2a+3a-3-3x-12-x^2-4x but i think its wrong

[rain crane]

simplify it further

[rough grove]

thats where im stuck

[rain crane]

there are two x terms, two constant terms

and even a terms

-2a + 3a
-3-12
-3x-4x

[rough grove]

-3-12 = -15 or 1?

[rain crane]

-15 why would it be 1

[rough grove]

9*

its saying in the answers it supposed to be 9 so i just wondered how they got there

[rain crane]

you did something wrong then, with expanding

recalculate

or show your work

maybe a sign error

[rough grove]

yeah i dont remember the rule where you make - +

think thats where im doing wrong

[rain crane]

sign change apply to multiplication only

[rough grove]

hm

[rain crane]

-2-13 is not 2+13

[rough grove]

not but when its in the bracket?

[rain crane]

-(a+b) is same as -1*(a+b)

[rough grove]

i really dont know where i did wrong in it

[rain crane]

show your work

[rough grove]

doesnt really show that much

[rain crane]

,rotate

[rain crane]

for second expression

expand them first

then change the signs

[rough grove]

what does that mean

[rain crane]

apply distributivity

-3x becomes 3x

-12 becomes +12 etc

[rough grove]

yeah so the signs do change

[rain crane]

yeah coz its -1 x (a+b) x (c+d) form

[rough grove]

because its a - infront of the brackets?

[rain crane]

infront of the term yes

[rough grove]

yeah sorry might be using the wrong words for things its not my main language

but alright thanks so when its - infront of it and - inside the - turns into a +?

[rain crane]

signs simply change

[rough grove]

didnt really understand much about that but yeah

i really need a first grade explenation on why -12 becomes + 12

and -3x becomes +3x

[rough grove]

it it because -3 x -x becomes +?

so 3x

because there are - infront of both?

<@&286206848099549185>

i really need to understand why it becomes a positive 3x and 12

scroll further up for picture

[final saddle]

@rough grove Has your question been resolved?

[rough grove]

i really need help with this i have a test tommorow

<@&286206848099549185>

[digital steeple]

$-(3-x)(-x-4)=-(-3x+x^2-12+4x)$ is this allright so far?

[soft zealot]

ThM

[rough grove]

uhm

yes

[digital steeple]

and now the "-" before the brackets change all signs.
$-(-3x+x^2-12+4x)=3x-x^2+12-4x$

[soft zealot]

ThM

[rough grove]

right gotta write it down

[rough grove]

wait why was it already +x^2

without changing the signs i get -x^2

[drifting oracle]

@rough grove
$ (-x) (-x) =x^2)$

[digital steeple]

you have a (-x) from (3-x) and a (-x) from (-x-4) -> (-x)(-x) = x^2

[rough grove]

it becomes a positive when multiplying 2 negative?

[digital steeple]

what is (-1)(-1)?

[rough grove]

-1?

[digital steeple]

no, 1.

[rough grove]

im so confused

[digital steeple]

think about 1x(-1) and (-1)x(-1), should they have the same result or not?

[rough grove]

not

[digital steeple]

so, what is 1x(-1) and what is (-1)x(-1)?

[rough grove]

i think maybe the first is -1 and like you said the second one is 1?

[digital steeple]

yes.

[rough grove]

but doesnt that just mean multiplying 2 negative numbers maning it positive

or is that just not the case

[digital steeple]

yes.

[rough grove]

right thats what i was looking for

[digital steeple]

you can say it this way: multiplication of a number a with a negative number changes the sign.

[rough grove]

multiplication with 2 negative numbers changes the sign?

[digital steeple]

as one number is negativ, it changes the sign "of the other number".

[rough grove]

can you give another example

easier to understand that way

im very sorry for being hard to teach i just really need to understand this well

[digital steeple]

lets say we have (-2)(-3). write this in the form (-1)x2x(-3), first evaluate 2x-3 so you get (-1)x(-6), now, as -1 is negative change the sign -> 6 therefore -2x-3 = 6

or you learn it this way:

positive x positive = positive

negative x negative = positive

negative x positive = negative

positive x negative = negative

[rough grove]

alright that last part explained it all to me

thank you very much

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[charred vigil]

I don't understand why the integral of pi is just Pi(x)

[charred vigil]

Isnt pi a constant?

[grand bronze]

correct

[charred vigil]

if its a constant dont we move it outside?

[grand bronze]

well you can indeed do that if you want to

$$\pi\int_1^5 dx=\pi[x]_1^5=4\pi$$ and $$\int_1^5\pi dx=[\pi x]_1^5=4\pi$$

[soft zealot]

Duh Hello

[grand bronze]

you get the same answer either way

[charred vigil]

oh, i kinda see it. I just didnt understand why the X just appeared out of nowhere.

[grand bronze]

do you know integration rules?

the integral is the anti derivative, so since $$\dv{x}\pi x=\pi$$ then $$\int \pi dx=\pi x$$

[soft zealot]

Duh Hello

[charred vigil]

i know the basics integration rules when were dealing with numbers but i never encountered a situation where i had to deal with an empty integral. i say "empty" because my first reaction when i saw a pie inside an integral was to move it outside.

[chrome cove]

$\int dx = \int 1 dx = \cdots$

[soft zealot]

Nonna

[chrome cove]

You can also see it this way

[grand bronze]

what nonna says, the 1 is just implied when its not explicitly written

since $1 dx=dx$

[soft zealot]

Duh Hello

[chrome cove]

[grand bronze]

so if you prefer that way i can write $$\pi\int_1^5 1\cdot dx=\pi[x]_1^5=4\pi$$ and $$\int_1^5\pi dx=[\pi x]_1^5=4\pi$$

[soft zealot]

Duh Hello

[charred vigil]

So basically the anti derivative of 1 is x
since dx by its own is equal to one

[grand bronze]

i would not really worry too much about the meaning of dx right now. dx is NOT equal to 1, but its there to help us with some tricks that you will learn later. but yes the antiderivative of 1 is x and that is what is being used, in fact the anti derivative of any constant is just x times that constant

[charred vigil]

Okay thank you 👍

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[violet rune]

when we're with polynomial deg 2 = 0 cause 2 = 2x^0 and deg 0 = -infinite, right?

[vital crag]

what

can you show more context

[tranquil pine]

yes

[vital crag]

problem you're working on, etc.

[tranquil pine]

constant non zero polynomials have degree 0

[violet rune]

there's no context

but that's what i've been told

to be coherent degree of 0 is -infinite the same way that factorial of 0 is 1

[vital crag]

screenshot or take a picture exactly what you're given

[vital crag]

this is nonsense

[violet rune]

that won't be in english

[tranquil pine]

deg 0 is just -inf because that fits best into most formulas

like, deg(pq) = deg(p)*deg(q)

[violet rune]

ye but degree of another constant than 0 is 0 right

[tranquil pine]

yes

[violet rune]

so this is sense lmao

[tranquil pine]

no

[vital crag]

the definition of factorial has nothing to do with polynomials. so whatever you said is nonsense

[violet rune]

it was just an example of something add to be coherent

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[gaunt hatch]

Is this occupied?

[tired walrus]

now it is, by you.

post your question here.

[gaunt hatch]

It’s just one question that I already had answered by my professor, but I’m still not understanding how

Number 3

[tired walrus]

uh huh

and what did your professor say?

[gaunt hatch]

My professor said it was c but I thought since it was a constant at 5 it would be a?

[tired walrus]

a constant?

who said f was constant...?

[gaunt hatch]

Like no matter what you plug in for x it’ll always equal 5

[tired walrus]

we only know that its limit as x->2 is 5

no

we do not know that f(x)=5 for all x

[gaunt hatch]

Yea true but going based off all the other questions ig that’s what was confusing

Maybe the wording

[tired walrus]

none of these questions establish their functions as being actual constants...

[gaunt hatch]

But I’m confused, doesn’t that question mean that the limit of f(x) at x=2 is 5…

Cant it be inferred at that point that f(2) is 5?

[tulip coyote]

Only if f is continuous

[tired walrus]

no, it cannot

[tulip coyote]

They’ve made no mention of f being continuous or not there

[tired walrus]

f may even not be defined at 2

[gaunt hatch]

I assumed cause linear functions are always continuous

But yea it’s technically not defined I guess

I kind of see now

[tulip coyote]

[remember some of the graphing exercises for limits we did some time ago]

[gaunt hatch]

So we can’t infer that this is a linear function?

[tulip coyote]

No, they haven’t said that f is linear anywhere

[gaunt hatch]

Hmm

I agree with you now, i just thought that what was being referenced in this question was the function

F(x)=5

And taking the limit of that exact function

Or do I have it mixed up

[tulip coyote]

Yep, they’re talking about some general function and taking the limit of that as your input approaches 2

[gaunt hatch]

Hmm

I kind of understand more now

I agree with the answer c, mainly

[tulip coyote]

Meant 2 there sorry, they say the limit as x approaches 2 is 5

[gaunt hatch]

That’s what I mean though

Wouldn’t any value of that limit make the function equal to that?

Then again that’s me assuming the function so yea…

I guess I’m assuming too much of it? Or am i missing something else

[tulip coyote]

What do you mean here?

[gaunt hatch]

Just wanna try to understand in case something like this pops up in a future test, not trying to be a pain

[tulip coyote]

As in $\lim_{x\to 2} f(x)$ is given, and said to be equal to 5

[soft zealot]

chartbit

[gaunt hatch]

Right so

Instead of the 2

It could be a 7

F(x) would equal 5 regardless no?

[tulip coyote]

Not necessarily - it could, or it might be something else, or the limit might not exist

[gaunt hatch]

In that particular function anyway

So it wouldn’t be correct in saying that?

The way I saw it was using the graph of that actual function and realizing that it doesn’t matter if I plug in 2

Or 200

It’ll still be 6

5**

[tulip coyote]

Not without any additional information, you can't deduce anything more

E.g. you could have your function being f(x) = 5, for which that limit would be 5 for all values

[gaunt hatch]

So it’s not really a great question or?

[tulip coyote]

But instead you could have f(x) = x + 5, where the limit would differ

[gaunt hatch]

Do you think it’s purposely worded like that

[tulip coyote]

It is - it's testing you to see if you know the difference between limits existing and continuity

[gaunt hatch]

That was the thing, we haven’t gotten to continuities yet like

In the class

Even though i pretty much have a firm grasp on it now

But yea, fair play ig

Similarly for question 2 I’m not sure if you can see it there?

I had a question as well

[tulip coyote]

Yep yep - just remember that long graph exercise we did that time ago!

[tulip coyote]

Yea I can see it!

[gaunt hatch]

I’m assuming similar logic follows

Is the answer a

I had c originally

Before we went over it in class

[tulip coyote]

I can't see the option c for the second one?

[gaunt hatch]

Limit doesn’t exist

Is option c

[tulip coyote]

Ahhh fair, yea, it does exist

Approach the same thing from both the left and the right

[gaunt hatch]

Ah so technically

Wait so is the third part not referring to the previous two parts?

As in how could there be a limit at 2 but when you plug it into f(x)=5 you get 6

[soft zealot]

chartbit

[tulip coyote]

You can create examples like this fairly trivially

[gaunt hatch]

So that would create a piecewise?

I see what you did

That makes sense like that

[tulip coyote]

Yep, piecewise defined functions are the best for examples like that!

There are more complicated and larger examples, but something like that should paint a fairly good picture for you

[gaunt hatch]

I think I get it now

Appreciate it man

[tulip coyote]

No problem! Is that all good for you?

[gaunt hatch]

Let me double check

Oh, 4 was the last one sorry

But going off the other ones I think i got this one now

I used the same logic from before and chose a basically

[tulip coyote]

And do you still think it's a, or have you changed your mind?

[gaunt hatch]

I’ve kind of changed my mind to c but not entirely sure why

Would you mind explaining this one more time

Sorry

In terms of 4

I’d say just because 2 is plugged in and gives a value of 5

Doesn’t necessarily mean there’s a limit?

Am I correct in saying that

[tulip coyote]

The limit might not exist, or it might exist and be something else, you just don't know!

It might be the same thing [at which point you're continuous at x=2] but you never know unless they give you more information on it!

[gaunt hatch]

Got it

That’s good for now

Thank you sm

[tulip coyote]

No worries, have a good one!

[gaunt hatch]

You as well!

[final saddle]

@gaunt hatch Has your question been resolved?

[final saddle]

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[tranquil pine]

why would I not lhopital this

[tranquil pine]

is this not inf/inf

how did it become -1/2

bc what i did was I didsum and difference

then inf / if

lhopital

2x/2x on both sdes

= 1

1-1 = 0

[supple mantle]

Why don't you join the fractions together?

[tranquil pine]

wouldn't doing sum and difference be easier

[supple mantle]

Nope

[tranquil pine]

is there no sum a difference for limits?

[supple mantle]

Well there is but you will get 0/0 or inf/inf which will need more work

limits are linear so limit of a sum is a sum of limits

But these fractions are better off joined together.

[tranquil pine]

yeah but with inf/inf i can lhopital

right

[supple mantle]

Why L'Hopital?

[tranquil pine]

bc i have inf/inf

[supple mantle]

2 steps and you can just find the limit with no need of L'Hopital

[tranquil pine]

and taking derivative gets u 2n/2n

oh wait

no

it's just n

[supple mantle]

Also I think you're missing something really big here

You can't really use L'Hopital on these two fragmented fractions like that

[tranquil pine]

why

[supple mantle]

You need to have it as f(x)/g(x)

[tranquil pine]

but don't i split up

using sum and diff

[supple mantle]

Hmm

I think it's better if you try out joining the fractions

You'll see why you won't need L'Hopital

[tranquil pine]

why wouldn't lhopital be easier tho

ik i don't need it

[supple mantle]

It's gonna take longer

[tranquil pine]

oh

ok

sshould i just leave the unctions in parentheses

or actually distributr

[supple mantle]

Take common factor

[tranquil pine]

ok

x

[supple mantle]

What did you get so far?

[tranquil pine]

this lol

[final saddle]

@tranquil pine Has your question been resolved?

[supple mantle]

Okay

Take common factor of x^2

And do the difference properly

[tranquil pine]

does x^2 cancel then

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[ashen umbra]

** Summation of squares as summation of product of two consecutive numbers

Sum of two nth powers expressed as a product of two consecutive integers**

I want to search a research paper similar to these topics, but whats the proper term for these kind of topics? tyia

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[wicked prism]

Consider the field F = GF(2^6) = Z mod 2[x] / (x^6 + x + 1)

[wicked prism]

how do I show that α = x is a generator of GF(2^6)*?

[desert mantle]

what possible orders can it have

[wicked prism]

I believe 1 and 63 = (2^6 - 1)

[desert mantle]

well then you would be done cause its order is obviously not 1

but no

[wicked prism]

1, 3, 7, 9, 21, 63

are the possible orders

[desert mantle]

yes

at least 1,3,7,9 are easy to eliminate by hand

not yet sure about 21

[wicked prism]

how are these generators eliminated?

[desert mantle]

just calculate x^3, x^7, x^9

and see they are not 1

I suppose x^21 = (x^7)^3 shouldn't be that bad either

[wicked prism]

so once we see that they are not 1

what is the significance of determining that the possible generator is eliminated?

I don't understand how the order is related

[desert mantle]

what is a generator

and what is the order of an element

[wicked prism]

a generator is an element of GF(2^6) of order 2^6 - 1 = 63

the order of an element is the smallest pos int t, s.t. a^t = 1

so we have candidates of orders t because it has to divide q (63)

and we check which = 1 to satisfy the defn

[desert mantle]

yes

[wicked prism]

so x^7 = x^6 * x = x(-x-1) = -x^2-x

so that's not 1, hence 7 is not a generator

[desert mantle]

no

it's not 1, so the order of x is not 7

we eventually want to show that the order of x has to be 63

[wicked prism]

I see

how do I evaluate x^3? I either go in a circle or require the inverse of (-x-1)

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[fickle blaze]

how would you work out a question like 150 000 out of 3 000 000 and how much that would be in a percentage

[fickle blaze]

i forgot

[frail flax]

cancel out zeroes and simplify

[fickle blaze]

.close

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[scarlet oriole]

Can I get help on 1 d and e

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@scarlet oriole Has your question been resolved?

[scarlet oriole]

<@&286206848099549185>

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@scarlet oriole Has your question been resolved?

[scarlet oriole]

<@&286206848099549185>, do you find total first then try to find each individual success and divide by total?

Oh shit I just saw you can only ping helpers once sorry

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[flat iris]

what

that is a lot of homework

[terse dagger]

@scarlet oriole Are you still stuck?

[scarlet oriole]

No

I figured all of it out

[terse dagger]

great 🙂

[scarlet oriole]

If it’s possible are you allowed to check if I got the right answers?

[terse dagger]

well since it is not allowed to help with tests we can always check your work

[scarlet oriole]

My work is uploading it takes a minute

[scarlet oriole]

Took me a couple hours ngl I’m slow at probability

[flat iris]

I literally failed at statistics

It was doom

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[willow edge]

How would I solve this?

If I substitute 10 in for x

Then do the calculations it would be 0.6

What would I do after?

Do I multiply 0.6 by the adult dosage 250 mg?

[storm karma]

Is it $\frac{4}{100x}$ or $\frac{4x}{100}$

[soft zealot]

Anagh

[storm karma]

?

[willow edge]

It’s like 4 over 100 then multiply x

[storm karma]

Yeah

So you have to multiply

Adult dosage by 0.6

[willow edge]

So 250 x 0.6

[storm karma]

Yep

[willow edge]

Ok thanks

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[snow anchor]

How many rectangles (using whole number lengths) have perimeters between 16 m and 20 m,
inclusive?

[snow anchor]

.cloe

.close

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[ember maple]

Prove lim n ->inf (1+2+3+..+n)/n^2=1/2

[ember maple]

normally

i would divide all the terms of the top and botton my n^2 and simply sub n for inf

but in this case i get zero if i do that

[desert mantle]

do you know a closed form for 1+2+3+...+n

[ember maple]

i dont

whats a closed form

i have dont series and sequences yet

[desert mantle]

roughly speaking, a formula consisting of the usual functions without any ... or limits etc in them

[ember maple]

so what do i do for this question

im not sure where to start

my usual method isnt working

[desert mantle]

show that 1+2+3+...+n = n(n+1)/2

eg by induction

[ember maple]

i would love to

[desert mantle]

or by pairing certain terms

[ember maple]

but i dont know how to

im prettye sure i just have to use limits to solvethis

cause this topic is about limits and then first principle

[desert mantle]

if I add 1+2+...+n in the following way: (1+n)+(2+(n-1))+(3+(n-2))+...

what do I get

how many pairs

well presumably your teacher assumes that you know this formula

[ember maple]

can u teach me the formula please

[desert mantle]

what do you think I am trying to do