help-19

[feral glacier]

Ok so what are the units for concentration

[maiden crow]

g/ml

[feral glacier]

Close

Well

Have you studied molarity?

[maiden crow]

not yet actually

later on they said

[feral glacier]

Ok so molarity is concentration

The units are moles per liter

You can convert grams to moles and milliliters to liters

But in this case do you have the volume of coke used?

[maiden crow]

50.0 ml

[feral glacier]

[maiden crow]

so conver that to liters

[feral glacier]

What about grams of sugar

[maiden crow]

i know its 12.3% sugar

lol

[feral glacier]

Ah

You shouldn’t need to convert to liters

If coke has 12.3% sugar in it

How much sugar would be in 50.00 ml of coke

[maiden crow]

50.00 * 12.3 *100?

[feral glacier]

Close

[maiden crow]

so 50.00 * 12.3

[feral glacier]

50.00 * 0.123

[maiden crow]

ohhhhh

shit

lol

50.00 * 0.123

[feral glacier]

Well 50.0 cuz that’s what your paper says

[maiden crow]

6.15

since 3 sigfigs

[feral glacier]

Yes

6.15 what

[maiden crow]

gram/ml

[feral glacier]

Just grams

[maiden crow]

so for part 3

i just do that with the nutrition facts again

[feral glacier]

You are solving for percent now

[maiden crow]

ah

so take grams

and the volume

[feral glacier]

m/v

[maiden crow]

43g / 355ml

[feral glacier]

Yup

[maiden crow]

so these are all 1

sig fig

and i got 0.12112

and i know this is percentage

so just 12%

[feral glacier]

Woah

Only 1 sf?

[maiden crow]

43 and 355

no wait 2

[feral glacier]

Numbers that are not 0 are automatically significant

40 = 1 sf 43 = 2 sf

[maiden crow]

makes sense

so two sig figs would be 12%

[feral glacier]

Yes

[maiden crow]

because not counting 0

then 12 cutoff the 1112

112*

[feral glacier]

Yes

You round then cut off

You seem to round fine

[maiden crow]

ive lowkey taken calc

just been awhile

lol

and sigfigs are annoying

[feral glacier]

Yea luckily in calc you don’t have to worry about sf

There are plenty of other things to worry about

[maiden crow]

yeah chemistry woulda been daunting if i hadnt taken upper level math of any kind

[feral glacier]

You a chem major?

[maiden crow]

nah engineering

[feral glacier]

Ah ok

I’m a chem major

[maiden crow]

damn yeah youre wild with it

im over here with flashcards and an periodic table

lol

i got the first four rows down

[feral glacier]

You have to memorize?

[maiden crow]

yeah

[feral glacier]

Oof

[maiden crow]

i hate it

lol

[feral glacier]

That’s rough

[maiden crow]

not just periodic table either

my physics class was open book open note

chillin

id just look online my sigfigs

and calculate the velocity of a planet

but now ive fallen from grace

and back to the stone age

[feral glacier]

Lmao

[maiden crow]

i didnt even need this class

since physics counted as my lab science

I though this would be fun

😂

[feral glacier]

Haha

[maiden crow]

then when he said nah no open book or notes

😮

[feral glacier]

Well classes are almost done

Won’t have to take it for too much longer

[maiden crow]

facts end of the season thankfully

first exam in morning

[feral glacier]

Dang good luck

I’ve got a chem test tomorrow and finals next week

[maiden crow]

which is why i wanted quizzing on sig figs

thats my weakest link

[maiden crow]

good luck aswell what year are you?

[feral glacier]

Freshman

[maiden crow]

oh wild

im fourth year I can program a network and automation facility with python

but this stuff kills me

[feral glacier]

Dang lol

[maiden crow]

i did a program to plot xy of a robots end effector

which is its hand

based on the angle of the motors

[feral glacier]

I uhh mixed some different colored liquids lol

[maiden crow]

and it turned oil

into cotton candy

lol

[feral glacier]

Yup I’ve turned lead into gold

[maiden crow]

wtf thats sick af

thats why i started chem

its fascinating field

[feral glacier]

Yea if only turning lead into gold was possible

[maiden crow]

i wanna know what nilered be saying

[feral glacier]

Nile is the goat

[maiden crow]

ong

my chem teacher intimidated by him

lol

[feral glacier]

I think anyone would after the amount of hot dogs he’s disintegrated

[maiden crow]

😂

yeah nilered big influence for me checking chem out

[feral glacier]

You know there is always chemical engineering

[maiden crow]

thats facts and this could help me get into that

I do plan on trying to get a second bachelors or a masters after this so its an option

[feral glacier]

I started as a chemical engineering major than swapped to chem

[maiden crow]

rough?

[feral glacier]

Dayum

[maiden crow]

chem engineering?

[feral glacier]

I liked chem way more so I swapped

[maiden crow]

I dont blame you

[feral glacier]

And the program I was in initially only offered chem engineering

[maiden crow]

yeah honestly chem is the class that includes alot of answers to questions ive had about life

kinda like physics answered alot of my questions

you taken physics?

[feral glacier]

In high school yea I’ve taken physics and astronomy

I’ll be taking more physics and astronomy next year

[maiden crow]

yeah man that stuff is also really interesting

id love to take astronomy

[feral glacier]

I wanna be an astrochemist ideally

[maiden crow]

im not the quickest learner so its rough and hard for me sometimes, but when i get a grasp on it , its fun

so would you study the chemical reactions in space

or the chemicals in space?

[feral glacier]

Yea a lot of spectroscopy from what I’ve heard

Relating light to different elements

[maiden crow]

thats sick so how the light interacts with the object will give you data to determine what the composition of it is

[feral glacier]

Pretty much yea

[maiden crow]

now once you categorize that data

couldnt you just write a program that pulls that data and categorizes it based on like data?

[feral glacier]

Definitely

[maiden crow]

sick thats where youll want a python guy!

😄

unless yall write your own codes

I wouldnt see yall wasting your time though

just throw a coding maniac in there lol

CS master

[feral glacier]

Yup I don’t want any part in coding

[maiden crow]

meh its not too bad

the sun = 20,000,000 kg

if the sun = True:

print("the sun")

lol

[feral glacier]

lol

What about in Cow

[maiden crow]

methane = (200,205,202)

if methane == 205:
print("The cow nearby")

see the easy power that has

if methane == 200:
print("septic tank")

if methane == 202:
print("Automobile")

[feral glacier]

Seems like a lot of typing

[maiden crow]

true,but sometimes type once to save from typing 10000times

[feral glacier]

True true

[maiden crow]

so youre looking for planets in space

you dont wanna type them all

you just wanna collect that data as variable

my_planet_data = (200.1x 300.1z 7000.1 y)

if my_planet_data == (200.1x 100.1z 700.1y):

print("Mars")

[feral glacier]

Low key that’s kinda cool and interesting

[maiden crow]

no doubt just saying creating a program as a tool for you industry is always pro move

[feral glacier]

Makes sense

[maiden crow]

thats all my thing with that robot arm hand was for

was so i could ask it if im at 45 degrees and 85 degrees whats the xy coordinate of that

and no matter what itll give me the answer even if i do it 1000 times

only typed it once

[feral glacier]

That’s dope

[maiden crow]

just an idea

yooo

i skipped over this

would this just be g/ml

[feral glacier]

I assumed you used the same volume for each sample of soda?

[maiden crow]

yeah they were all pre-measured for the lab

[feral glacier]

Ok so mass of the sugar I guess would be what the increased concentration can be attributed to

[maiden crow]

so because of the %

because it says cite my data

so the sugar percentage is seen as a mass in grams of sugar

[feral glacier]

Yea

[maiden crow]

because yeah

the sugar percentage rises and so does the height

[feral glacier]

Yea

Sugar percentage = mass

Not = but related

[maiden crow]

so they are basically scaling together

[feral glacier]

Yea

They are proportional

As % increases mass increases

Only if volume is constant

Because % is also proportional to volume

Inversely so

As % increases volume decreases

[maiden crow]

percent error is one mine the other right?

minus*

[feral glacier]

(Measured - real)/real

• 100

[maiden crow]

(12.3 - 12) / 12 * 100

[feral glacier]

Yea

[maiden crow]

so 12.3- 12 = 0.3

cause 1 fig

[feral glacier]

1 sf?

[maiden crow]

shit

2

lol

[feral glacier]

Yup

[maiden crow]

0.30

12.3 -12 = 0.30

0.30 / 12

so 2fig / 2fig

0.03

[feral glacier]

Times 100

[maiden crow]

0.03 * 100 = 3

[feral glacier]

3% error

Pretty good

[maiden crow]

getting closer lol

those get me

atleast i did parenthesis first!

[feral glacier]

Yea lol

[maiden crow]

would carbonation make the sugar percentage more or less?

id say it would decrease it because it inflates the volume right

because the parts per substance of air is higher

[feral glacier]

Carbonation as in adding CO2?

[maiden crow]

yeah

my bad

the parts per substance of co2 is higher

[feral glacier]

Hmm I don’t think so

Because the sugar does not dissolve in the gas

It dissolves in the water

The CO2 might have an effect on the solubility of the water im not sure

[maiden crow]

yeah it just says does the carbonation of soda artifically increase or decrease the concentration? Explain by using how carbonation increases or decreases the solution volume.

[feral glacier]

Could you send the pic of the problem

[feral glacier]

Ok yea so more CO2 = more volume which decreases concentration

[maiden crow]

do any of these involve specific gravity too?

[feral glacier]

Gravity?

[maiden crow]

Density of sample / density of water

or nah

?

[feral glacier]

Density of water is 1

[maiden crow]

yeah nah then i dont think so

so for that question

this one

its just mass lol

[feral glacier]

Yea

[maiden crow]

not volume or anything else

[feral glacier]

Nope you had constant volume

[maiden crow]

that makes sense

so it could only have been how much sugar was inside

how does the hydrometer work?

[feral glacier]

Not sure never used one before

Ah I see

They measure density

If a soda has more sugar the density would be greater because there is more mass because of the sugar

Because density = m/v

[maiden crow]

so its the density making it rise?

[feral glacier]

Basically the only thing you are trying to quantify is the amount of sugar and you do that based on the density value

[feral glacier]

Yea

Basically

[maiden crow]

more accurate than just the mass?

[feral glacier]

Well to get the mass you need to know the density

[maiden crow]

makes sense

so i got 1.38/ 0.958

[feral glacier]

What are those numbers

[maiden crow]

should i be getting 14.4 as a percentage

finishing of the y= mx+b

6.65 cm = 0.0958(x) + 5.275

[feral glacier]

Ah ok

[maiden crow]

i believe thats the right percentage

[feral glacier]

Yea looks right

Should be a little higher than the coke one

[maiden crow]

apple juice

lol

[feral glacier]

Yup

That’s real sugar tho

[maiden crow]

5.65

5.275

0.375

because all 3 sigfigs

[feral glacier]

What’s that calculation for

[maiden crow]

5.65 cm = 0.0958(x) + 5.275

[feral glacier]

Oh i see

Only do sf last

Don’t do it in between calculations

Only do it for your final answer

[maiden crow]

just use my least used?

sorry just alil confused now

[feral glacier]

Do the equation normally ignoring sig figs

Solve for x

[maiden crow]

k i got 3.91440501

so

[feral glacier]

For your final calculation when solving for x is when you account for sig figs

[maiden crow]

3.91

[feral glacier]

Yea

[maiden crow]

i see okay

[maiden crow]

what would a qualitative observation be in this case?

the colors of the liquids?

[feral glacier]

Yea

[maiden crow]

lol thats basically it right?

[maiden crow]

I greatly appreciate your help

could i add you for more chemistry questions in the future?

[odd edge]

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[ashen juniper]

how is this c?

[ashen juniper]

negative two works cause itll be 1/-2 > -1/4 no?

and negative two isnt included in c?

[cloud sun]

-1/2 > -1/4?

look again

[ashen juniper]

damn

im tripping

[cloud sun]

lmao

[ashen juniper]

ty for the help

[cloud sun]

np

[ashen juniper]

.close

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[fair bridge]

Help me with this

[wooden pasture]

,rotate

[regal cargo]

You use the tan

[wooden pasture]

use trigonometry

[regal cargo]

Yes

[fair bridge]

Can u show me steps

?

I am a beginner

[wooden pasture]

the definition of cosine

[fair bridge]

Now what do I do?

[wooden pasture]

are you allowed calculators?

[fair bridge]

I guess

We are

[wooden pasture]

so basically

to find the angle, you use the inverse cosine function

it gives the measure of an angle if you know the cosine of the angle

there should be a way to type it into your calculator

it should kinda like $\cos^{-1}$

[clever fjord]

math X meth ✓

[wooden pasture]

or it can also be written as arccos

[regal cargo]

First, use the cos for the angle.

It's the adjacent side outta the hypothenuse

[wooden pasture]

approximately 43 degrees

[regal cargo]

Then, you use your calculator to find the arccos of the result.

The arccos will be the measure of the angle

Do you understand ?

[regal cargo]

Okay, I didn't follow the steps but it should be the correct answer

[odd edge]

@fair bridge Has your question been resolved?

[odd edge]

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[deft flicker]

sorry if this is a dumb question

but are we allowed to multiply the denominator out

with something like this?

so that 15-b^2=0

[sick fossil]

yea

[open crown]

Yes

[deft flicker]

is there any case where it's not okay?

or we might lose solutions

[open crown]

Probably no

[gusty moat]

You're not going to lose solutions, the only problem point might be b = 5i

But that's not really relevant here it's not a solution

[deft flicker]

okay tysm

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[blazing portal]

how do i find the value of n if

[blazing portal]

n root 27

like

[clever fjord]

uoǝu

[long tinsel]

you mean this?

[blazing portal]

yes

that = 3

how do i find the value of n

[onyx cloak]

27^(1/n) = 3

make the bases same

and compare powers

[onyx cloak]

this means nth root of 27

[blazing portal]

can you elaborate

[onyx cloak]

you can denote sqrt(27) as 27^(1/2) right?

[blazing portal]

yeah

[onyx cloak]

so second root of 27 = 27^(1/2)

now how would you write it if I said nth root instead of second root?

[blazing portal]

27^(1/n)

[onyx cloak]

exactly

[swift rock]

u can use log base 3 as well if you are familiar

[onyx cloak]

now that is equals to 3 as it is given

[blazing portal]

hm

[swift rock]

Both ways give same answer

[blazing portal]

how do you do the log method

[swift rock]

log 3 both sides

$$log_3 \sqrt[n] {27} = log_3 3$$

[clever fjord]

JustToPro

[swift rock]

u can rewrite the nroot 27 into

$$log_3 3^{\frac{3}{n}}= log_3 3$$

[clever fjord]

JustToPro

[swift rock]

using log rules

$$\frac {3}{n} = 1$$

[clever fjord]

JustToPro

[swift rock]

if u dont understand anything u can ask

[blazing portal]

oh

i undersyand noe

thank you so much

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[grizzled trail]

Hello how do we establish if there is a maximum on the boundary before proceding to use the lagrangian?

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@grizzled trail Has your question been resolved?

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@grizzled trail Has your question been resolved?

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@grizzled trail Has your question been resolved?

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[grizzled trail]

.close

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[pine drift]

Hey guys

[pine drift]

Where did I go wrong?

It says my answer is wrong :(

[lean willow]

What's the answer

,w 3/(3sqrt(2)-2sqrt(3)) simplify

[clever fjord]

Results provided by WolframAlpha

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

Requested by plopperdeploppeke

[pine drift]

This

[lean willow]

3*3=9

U wrote 6

[pine drift]

Ohhh ok

I see

Thx

Time to erase my hard work and do it again

[lean willow]

And in denom the middle term cancel each other

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[odd edge]

@mystic saffron Has your question been resolved?

[dawn viper]

what have you tried?

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[final parrot]

You can show that there only exists 5 platonic solids by considering how many regular polygons can touch the same vertex and make an angle of less than 360°. After that, "raising them" into the 3rd dimension and building a solid. That only works 5 times, which means you can only have a maximum of 5 platonic solids.
If you had (n-1) dimensional regular figures (I don't know the proper nomenclature, I'm sorry), could you make the same argument for how many "n dimensional platonic solids" exist?

As a follow-up question:
Say you can combine figures in such a way that it works 5 times in n dimensions, for some number n. Does that mean that there must be 5 "platonic solids" or merely that the maximum is 5?

I don't know if I made myself understood. Hopefully I did 😁

[wintry panther]

https://youtu.be/2s4TqVAbfz4
this is a really good video

apparently they're called regular polytopes in general

[final parrot]

Oh, I think I've seen this video before. I found that sequence quite amusing. I'll rewatch it and see if it answers my question, but thanks for hastily responding 😄

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[frozen atlas]

Hello?

[frozen atlas]

Merrp

A line h with gradient 4 passing through the origin intersects the curve 2y = x² - 5x + 1 at two points then the number of possible x values is

Im stuck

[dull fossil]

whys that 4x

line would be y=4x

so 8x=

its 2y in the curve, not just y

[frozen atlas]

There's a line passing that curve?

[frozen atlas]

So it should be

Equation1=Equation2

???

[runic swift]

your equation is 2y = something

not y = something

[dull fossil]

its 2y not y

so 2(4x) =

[runic swift]

or you first divide by 2 in the first equation

then equate them

[frozen atlas]

Owh sheet

Owkeh

[runic swift]

now you equate it with 4x

[frozen atlas]

So i stuck with the

"Possible value of x"

If anyone wants to respond please ping

[runic swift]

why did the -5x become -x

[frozen atlas]

Owh sheet

-9x

[frozen atlas]

Owkeg

[runic swift]

no?

you still have that 2 on the bottom

multiply it to the other side first then subtract

[runic swift]

no

[runic swift]

go back here

you have y = (x²-5x+1)/2

and y = 4x

equate them

4x = (x²-5x+1)/2

here you move the 2

[frozen atlas]

6x

[runic swift]

-5x - 8x is 6x?

[frozen atlas]

x²-5x-6x+1

=x²-11+1

Owh my god

[runic swift]

4x multiplied by 2 is not 6x

[frozen atlas]

Mu brain

=x²-13x+1

Uhhh

Do we need uhhh

That ABC equation??

[runic swift]

yeah

[west merlin]

quadratic formula?

[odd edge]

@frozen atlas Has your question been resolved?

[frozen atlas]

Sheet

Okay then

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[jade cloud]

why r they plugging to the g’(x) in the first one and in the second one they’re plugging back to original equation

i don’t understand that

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[indigo reef]

For nonzero P^{nxn} such that P^2=P, prove that 1 is always an eigenvalue of P

[indigo reef]

??

Delete this brother

.close

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[gritty oar]

!status

[odd edge]

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

@mystic saffron Has your question been resolved?

[mystic saffron]

2

x, x+2, x+4, x+6
x mod 5 can be 0, 1, 2, 3, 4

if x mod 5 is n, then
x + 2 mod 5 = n + 2 mod 5,
x + 4 mod 5 = n + 4 mod 5,
x + 6 mod 5 = x + 1 mod 5 = n + 1 mod 5

[gritty oar]

you are slightly overcomplicating it

if you want to continue with your approach, remember it's a product

and also these numbers are odd so they have the form 2k + 1

so really what you would want to consider is the product (2k+1)(2k+3)(2k+5)(2k+7) mod 5

however there is a much simpler approach

hint: how many odd numbers are there mod 10

[mystic saffron]

gimme a min lemme share my progress im writing it on notebook

please 1 min

i dont know how to solve if x mod 5 =2

[gritty oar]

ok so if $x\equiv 2 \mod 5$

[clever fjord]

chebyshev's infinite pee norm

[gritty oar]

what are x+2, x+4, x+6?

then, what is their product

[mystic saffron]

7, 9 , 11 , 13

99 x 13 x 7 = 1287 x 7

1287 x 7 = 4 mod 5

[gritty oar]

yep

[odd edge]

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[gritty oar]

.reopen

[mystic saffron]

but how you wriiteen this ?

[odd edge]

✅

[gritty oar]

using latex

[mystic saffron]

i know latex

i mean to say concept ?

x mod 5 = 2 is equivalent to 2 mod 5 = x

right ?

[gritty oar]

no

[mystic saffron]

is it inverse type thing ?

[gritty oar]

it's how you write the notation

[mystic saffron]

i wrote x mod 5 = 2

[gritty oar]

yeah usually when people write a mod b, it's just interpreted to be the remainder of a upon division by b

so what you wrote is basically "x has remainder 2 when x is divided by 5"

[gritty oar]

this is slightly different, but esentially means the same thing

[mystic saffron]

bro im so confused in these notation

7 = 2 mod 5

is it true ?

[gritty oar]

yes

are you familiar with any programming languages

[mystic saffron]

then x mod 5 =2 means when we divide 2 with 5 reminder would be x

[mystic saffron]

like ?

[gritty oar]

any

[mystic saffron]

R and LaTeX

thats all

[gritty oar]

ok nvm

[gritty oar]

it's not the case though

what if x = 7

2 mod 5 = 2 and not 7

[mystic saffron]

id even k whether these are programming language

[gritty oar]

but 7 mod 5 = 2

but we write $7\equiv 2\mod 5$ to mean that 7 and 2 are equivalent modulo 5

[clever fjord]

chebyshev's infinite pee norm

[mystic saffron]

here x can be 7 or 12 or 17

is it true ?

[gritty oar]

if x is 7, 12, 17 then x mod 5 = 2 yes

but if x is 7, 12, 17, etc then 2 mod 5 is not x

[mystic saffron]

yes

got it

[gritty oar]

also

back to your original question

[mystic saffron]

i need to be careful about these

[gritty oar]

the slightly nicer way was to realize

you can have the following cases

one of the consecutive 4 odd nubmers ends with a 5

and none of the consecutive 4 odd numbers ends with a 5

since you can only have 1 ,3, 5, 7, 9

[mystic saffron]

yea

[gritty oar]

so the following 4 cases, 9,1,3,5 ; 1,3,5,7 ; 3,5,7,9 ; 5,7,9,1 all contain a 5

so their product is 0 mod 5

and the final case is 7,9,1,3

which has product 4 mod 5

[mystic saffron]

ohh thats an easy one

[gritty oar]

[mystic saffron]

idk i always make things intense and tedious

maybe deficiency of practice

thanks 🙏

[gritty oar]

all good, you can't be expected to know a niche trick if you've never seen it before

npnp

[mystic saffron]

but i think of a better idea

but left it just to look smart

(2n+1)(2n+3)(2n+5)(2n+7) mod 5
(2n-4)(2n-2)(2n)(2n+2) mod 5
16(n-2)(n-1)n(n+1) mod 5
(n-2)(n-1)n(n+1) mod 5

if one of n-2, n-1, n, n+1 were divisible by 5, then its 0
if one of them wasnt then we can reduce to 1 * 2 * 3 * 4 mod 5 which is 24 mod 5 or 4 mod 5

so {0,4}

idk why i left it midway but now i solved and get the easy , but still not easier than yours , thanks again

[gritty oar]

very nice as well

[mystic saffron]

.close

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[trim mica]

what happened here?

[nimble blaze]

property of even function

[trim mica]

could i have just kept it the same and i'd get the same answer?

[nimble blaze]

yes

[trim mica]

ah

thank you

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[hushed island]

Can someone pls check if i got part b right? i dont have the ms and couldnt find this exact question online anywhere

[hushed island]

i got 10/11

[odd edge]

@hushed island Has your question been resolved?

[hushed island]

<@&286206848099549185>

u subbed in t into h. you have to find h first. you could do this by working out the volume and then using the formula they provided to get a quadratic in terms of h to work out h.

remeber h has to be posive

ohhhh thank you

np

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@magic shale Has your question been resolved?

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[timber geode]

give the equation of a function that is increasing in the intervals $\left(-\infty, -1\right)$ and $\left(2, +\infty\right)$, which maximum value is $4$ at $x = -1$, and which minimum value is $-3$ at $x = 2$

[clever fjord]

milanesa de pollo

[timber geode]

.close}

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[fickle rapids]

I am having trouble understanding cube root of unity concept

[fickle rapids]

Can anyone please explain it??

If omega cube = 1

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[mystic saffron]

can someone explain how he differentiated it? I thought product rule but I'm confused why he is subtracting it and why he divided by (x+1)^4

[mystic saffron]

referring to the second thing he done in q3a

[gusty tundra]

He's using the quotient rule

[mystic saffron]

yeah ur right

[gusty tundra]

If you have a function $f(x) = \frac{u(x)}{v(x)}$ then $f'(x) = \frac{ u'(x)v(x) - u(x)v'(x) }{v(x)^{2}}$

[clever fjord]

TomB

[mystic saffron]

preciate

close

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[warped phoenix]

can someone tell me how we got x+1

this is the question

how did we get the bounds too 😭

[sturdy trail]

Looks like it's using the shell method

So x + 1 is distance from the vertical line x = -1 and the bounds 0 to 3 are where the parabola is positive (so where the region actually is)

[warped phoenix]

it is a shelll methd thing

but i dont understand how they got them

got the x+1 and the bounds

[copper quarry]

i think x+1 is the radius

[sturdy trail]

x + 1 is the distance from a point x to the line x=-1

Because it's x - (-1)

[warped phoenix]

so to find radius i do x-( vertical line)?

@sturdy trail please tell me how do i find the radius

[sturdy trail]

Yeah the radius is just the distance from a point to the axis of rotation

So if you have the a point at 2 for example, the distance to the line x = -1 is ofc 2 + 1 = 3

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[copper quarry]

so i tried doing this with weistrass sub and got the correct indefinite integral but i keep messing up my bounds. i tried directly plugging in pi/2 and -pi/2 after into the indefinite but it doesnt evaluate to pi/4 which is the correct answer.

Im not sure where i am making a mistake in the bound change

[frigid canopy]

waterbeam , you're a booster now? Nice!

the sub looks right

[copper quarry]

ya since like a week ago and a bit

[frigid canopy]

$\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}}\frac{du}{3+2\cos\left(u\right)+\sin\left(u\right)}$

right

[clever fjord]

ƒ(Why am. I here)=misery

[copper quarry]

im either going crazy and putting wrong numbers into the calculator cuz when i tried this last time i got it wrong with 0 and 1 as my bounds

[open crown]

Not really related but I want this @copper quarry 😭

[frigid canopy]

15 minute cities

[long tinsel]

I mean if you have $\int_0^1 \f{\dd{v}}{1 + v^2}$ why are you going all the way back to $\theta$

[copper quarry]

lol

[clever fjord]

uoǝu

[open crown]

Can u paste it here

[copper quarry]

oh wait

[long tinsel]

Is pi/4 not the right answer

[copper quarry]

its not?

[long tinsel]

That integral evaluates to pi/4

[copper quarry]

let ne check again

[long tinsel]

,w integrate 1/(3 + 2cos x + sin x) from -pi/2 to pi/2

[clever fjord]

Results provided by WolframAlpha

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

Requested by neonperseus

[long tinsel]

yeah

you're good

[copper quarry]

wait

so did i do something wrong or

[long tinsel]

Nope

I just don't know why you went all the way from v back to theta

Just keep integrating

[copper quarry]

o

$\arctan\left(1\right)-\arctan0$

[clever fjord]

شعاع الماء

[frigid canopy]

that's right

[copper quarry]

o ok

thanks guys

.close

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[mystic saffron]

waterbeam

[copper quarry]

hello

[open crown]

Dude, can u share ur abt me section

I want it

[copper quarry]

u have to do it manually with blood sweat and tears

cant u copy and pasre it

[open crown]

Bruh i can

I have to click from the outside region

Thanks

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[dawn geode]

how would this be solved? isn't P(X=0.5) equal to 0 since this is a continuous distribution?

[sturdy trail]

No you'd find the marginal distribution for x

To calculate P(x=0.5)

[dawn geode]

so would this be correct

oh i was supposed to go from 0.25 to 0.5 not from 0 to 0.25

[dawn geode]

but would it be correct aside from that ?

[odd edge]

@dawn geode Has your question been resolved?

[dawn geode]

<@&286206848099549185>

[dawn geode]

<@&286206848099549185>

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@dawn geode Has your question been resolved?

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[glass bolt]

I do not understand why they are talking about product rule

[forest sky]

the utility of the integrating factor is to turn the entire left side into a single derivative

by using the product rule in reverse

[glass bolt]

That would mean partial integration though? (Which yes, I know how to do)

I can't really see what is going on unfortunently

like, the steps are being jumped over here

[forest sky]

so we want to turn the left side into a single derivative. if we have
[ y' + p(t)y ] then you can see that this looks a bit close to the product rule formula:
[ (y(t) \mu(t))' = y' \mu(t) + \mu'(t) y ] so we just need to multiply the entire equation by the right function $\mu(t)$ to make that happen, because we can then collapse the entire thing into a single derivative (which can then be undone with an integral)

[clever fjord]

pnoןɔ

[forest sky]

otherwise, we'd have integrals involving both $y'$ and $y$, which would leave us without a solution for $y$ only in terms of $t$ and not as a function of itself

[clever fjord]

pnoןɔ

[glass bolt]

u(t) * y' + p(t) * u(t) * y

u(t) * y' + u'(t) * y

y' * u(t) + u'(t)* y = (u(t)*p(t))'

Right, I see

(u(t) * p(t))' = u(t) * g(t)

Alright, I see why this equality exists now.

[glass bolt]

And, as a consequence you can isolate y(t) after integration both sides

[forest sky]

yes

[glass bolt]

Does this integration method only work if your coefficents are functions? Such as, them being not constant functions?

[forest sky]

a constant is a type of function, it works just as well for any function (as long as they are continuous)

[glass bolt]

Okay, I understand... Why is this method used?

like, why is it useful?

[forest sky]

because it gives a formula for the solution to any first order linear ODE?

[glass bolt]

There are other ways of solving them, I know, for instance:

2y' + 1y = 2

You can set up the solution of that by finding y_p and y_h.

(Just divide 2 on both sides, and you have something like this: y' + (1/2)y = 1

But, why would this be an alternative method though? To let's say, my way of solving it.

[forest sky]

certainly any solution to a linear equation can be written as the sum of a particular solution & the general solution to the corresponding homogeneous equation

but the advantage of the integrating factor method is that it gives a formula explicitly and only in terms of the coefficients of the equation

[glass bolt]

Ah, so you can solve more complicated DE's that otherwise can't be solved with my method.

For example:

y' + 2xy = 4x

Solvable with this method, not with my method though... Am I wrong though?

y_p might as well be a constant, which does satisfy the equality.

oops, xD... not sure what examples exist where my method can't be used

[forest sky]

we can tie this together a bit. in the integrating factor formula we can find which part is which:
[ y = \underbrace{\frac{1}{\mu(t)} \int \mu(t) g(t) \odif t}{y_p} + \underbrace{\frac{C}{\mu(t)}}{y_h} ]

[clever fjord]

pnoןɔ

[glass bolt]

Holy shit, that is awfully similar

is there really a plus sign tho?

[forest sky]

if C is an arbitrary constant, then -C is also an arbitrary constant

[glass bolt]

Oh, so you simplified it

Gotcha, that's actually cool to see.

[glass bolt]

This implies, I could use this to my atvantage

for very hard ODE's where finding Y_P takes a loong time

[glass bolt]

Alright, I kinda get it now.

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[fringe wraith]

For the first part we get the limit is 1 using L'hopital
for the second part, the best I could do was setting alpha = 2 and substituting x with 1/u with x -> 0+ and u -> +infinity
then the log function behaves similarly to 1/x^2 so probably converges
however this isn't very rigorous
I think the only tools available to me are ratio, root or comparison tests and I haven't really made much progress with them so far

Thanks for any help

[forest sky]

the limit from the first part should form part of a limit comparison test

[fringe wraith]

thank you!
i searched up what that is and apparently we no longer do that in our course which is probably why I was confused

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[timber patio]

hello, how to answer this question?

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[radiant wagon]

you can substitute for n=1 and make it equal 2.75

you are given the values of the first 4 terms

so for n=1 the term value is 2.75

and for n=2 the term value is 6

so u can get a relation between A and B using this

a +b = 5/2

2a+b=2

a = -1/2

b=3

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[brisk sierra]

I need help

[lapis bronze]

um ok

[torn lotus]

do you have a specific question to ask?

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[ember oak]

You need to ask a question to receive help

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[timber patio]

thank youuu

[steady tide]

do you havw a question?

[radiant wagon]

yw i hope i was helpful

[summer cradle]

your local hot fungus

[steady tide]

hello layla

[summer cradle]

hello

m8of48…

[timber patio]

yes but it’s answered already

[steady tide]

then close this

[odd edge]

@timber patio Has your question been resolved?

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[lunar quartz]

Real Analysis student here, why are uniformly convergent sequences also uniformly bounded?

[latent scaffold]

It follows from the triangle inequality on the supremum norm I think, but I suppose you need some other property if f_n, like continuity or at least boundedness.

[lunar quartz]

.close

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[lilac wind]

can any vector in component form be written in linear combination of vectors i or j? or it's limited for only unit vectors?

[slow sphinx]

any vector (in 2d)

[merry finch]

Any ℝ² vector

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[somber breach]

Is my solution correct? Did I understood it correctly?

Calculate the solution quanitity for each of the two systems of linear equations below over the given field K. To generate the row step form, the Gauss algorithm should always be used

K = IR
x1 + x2 − 5x3 − 2x4 = 4
−x1 + x2 + 2x4 = 1
3x1 − 5x2 + 4x3 = 5

I did a table and used gauss:
1 1 -5 -2 | 4
-1 1 0 2 | 1
3 5 4 0 | 5

1 1 -5 -2 | 4
0 2 -5 0 | 5
0 2 19 6 | -7

1 1 -5 -2 | 4
0 2 -5 0 | 5
0 0 24 6 | -12
-> row step form not possible in this case
-> so it has no special solution xinh/it's not inhomogenous

x1 + x2 -5x3 - 2x4 = 4
2x2 - 5x3 = 5
24x3 + 6x4 = -12

... x3 = -1/2 - 1/4x4
x2 = 5/2 - 5/4x4
x4 = x4
x1 = -1 + 2x4

so the solution quantity is L = {(-1+2x4, 5/2 - 5/4x4, -1/2 -1/4x4 + x4)}

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[old whale]

How do I simplify this

[old whale]

I’ve already tried multiplying both roots by their conjugate

Didn’t really lead anywhere and now I’m stuck,

[gritty oar]

after this, the two terms share a common denominator, my guess would be to square the expression, combine the like terms, and simplify, then finally square root it at the end

[old whale]

what?

oh yea they do

4

[vagrant charm]

i think you can time (11-3sqrt13)(11+3sqrt13)

[old whale]

That’s what I did

[gritty oar]

it works

square the expression and simplify as much as you can

then square root it

[old whale]

wdym square root it

[chilly narwhal]

first i recommend calling this number, x, which we know to be an integer when this expression is simplified. like others have said, first i would recommend squaring x

[old whale]

ohhhhh

The answer is supposed to be an integer but I keep getting sqrt(156)

[chilly narwhal]

hmmm, how come, could you show me your line of working?

[chilly narwhal]

when you square both sides, everything becomes much cleaner and it does turn out to be an integer

[old whale]

Sure

Everything is supposed to be under a square root sign

Here’s a more cleaner process

taking so

aaaaa i haven’t got a single solution where it is equal to 13

help plz

[chilly narwhal]

yes, im trying to figure out where you went wrong

[old whale]

ok

it looks all correct yet

something isnt adding up

[chilly narwhal]

ahh i know where you went wrong

[old whale]

where

[chilly narwhal]

you didnt use binomial expansion correctly, you said in the fourth line practically that (a+b)^=a^2+b^2+ab instead of (a+b)^2=a^2+b^2+2ab which is incorrect

[old whale]

ohhhhhhh

dang silly mistake like that bouta cost me a whole grade 😭

ty so much

[chilly narwhal]

no problem!

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[teal marten]

Reopening a previous question cause I was occupied then it timed out

[teal marten]

I have tried doing P(A n B) = P(A) x P(B) because they’re independent but I get an unsolvable quadratic

Also other workabouts such as finding P(A u B) = P(A)+P(B)-P(AnB) and equating that to P(U) = P(A u B)’ - P( AuB)

But I then get an identical expression on both sides which doesn’t get me anywhere

[south plume]

which question number

[teal marten]

20b

[south plume]

what quadratic did you get?

[teal marten]

X^2+10x+30=0

And for reference the answer is 15

[south plume]

damn

i am not getting that yet lol

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@teal marten Has your question been resolved?

[bitter vapor]

To calculate the probability of an event, you take the number of possibilities where your event happens and divide by the total number of possibilities.

For example, the probability of A and B both happening is x / (x + 5 + 6 + 2)

The probability of A happening is (x + 6)/(x + 5 + 6 + 2)

This is why you've ended up with the wrong equation.

[teal marten]

Ohhhh lemme try it out

I misread the question slightly as in we need to find the number of events in AnB, which means we don’t need the denominators.
Regardless however, even if I represented A and B in terms of their probability, how do I find the P(AnB) as the denominators would cancel when simplifying an equation

Because the formula of P(AnB) = etc. (or n(AnB)… they function the same) doesn’t work as it provides a quadratic

[bitter vapor]

They won't cancel. Write it out.

[teal marten]

Unless I’m making a fundamental error idk

[bitter vapor]

P(A and B) = P(A)P(B)

The denominator will appear twice on the right side of the equation but only once on the left.

[teal marten]

I could just times both sides by 13+x and get rid of the denominators no?

[bitter vapor]

No. Because the denominator on the right is (13+x) squared.

We're multiplying, not adding.

[teal marten]

Ohhhh

Omg I got the answer thank you so much

Done so much adding of fractions I applied the same thing to multiplying 🤦

/close

[bitter vapor]

I think it's a dot rather than a slash.

[teal marten]

.close

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[round bluff]

In the parallelogram ABCD, point M divides side CB in the ratio CM : MB = 2 : 3. Find the area of ABCD if the area of ABMD is 21.

[modest nacelle]

It's trivial, I'm afraid.

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[earnest owl]

did i do it right

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[gleaming mason]

I am just trying to understand this answer key and what these symbols mean

[gleaming mason]

F’ is the slope, f ‘’ is the con cavity

I graphed f(4) first

I don’t understand what it made me do for the second condition f’>0

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@gleaming mason Has your question been resolved?

[open crown]

Hmm

If the second derivative act as a function of x, thats mean f(x) must be at least a third degree poly

And f"(4) = 0

Then f'(4) must be a local max/min

@gleaming mason

The function looks like this

[gleaming mason]

.close

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