help-17

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[gaunt panther]

i dont really get what theyve done for iii

[jolly shadow]

ru doing a level now lol

[gaunt panther]

im bored

so i doing a level papers

i miss further maths

plus i wanna see how well i do a year on from exams

[jolly shadow]

well one oscillation occurs in 2pi/3 time, and the damping constant is k

so in one oscillation the amplitude should decay by e^-2pik/3

but youre also told it decays by 0.98

So those are equal and you solve by logs etc

[gaunt panther]

what about the Acos3t and Bsin3t?

[jolly shadow]

yes its the (trig)3t that tells you the oscillation takes 2pi/3

but else A and B are constant

the only reason the oscillation would get smaller is because the exp(-kt) outside is smaller

[gaunt panther]

so here did u sub in 2pi/3 into this ?

[jolly shadow]

just into the e^-kt

because i dont care about the actual value if the oscillation just the amplitude

[gaunt panther]

ok makes sense

thank u

.close

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[dull lynx]

if the Xs cancel to get 8a = 1 shouldn't the 1 be a zero?

[strange crater]

what do you mean?

[paper depot]

$8\alpha x = x = 1x$ not $0x$

[twin meteor]

Ann

[dull lynx]

yes so here didn't the Xs cancel on both sides?

@ancient panther

how do you solve this differential equation?

[vocal sleet]

@dull lynx Has your question been resolved?

[dull lynx]

no

[vocal sleet]

@dull lynx Has your question been resolved?

[vocal sleet]

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[zenith bay]

for how many integers x do we have:

[dapper meteor]

solve for x this equation : quotient = k with k in Z

$\frac{x+202300000000}{x+102300000000} = k$

[twin meteor]

ByShaDowZ

[dapper meteor]

solve for x and keep only the integer solutions

[zenith bay]

i tried this: 1 + (10^11/1.023*10^11+x) = the equation

10^11 = 2^11 * 5^11

12*12 = 144 dividers positives

so, 288 = k?

its correct?

[dapper meteor]

where does it comes from

[zenith bay]

let me take a pic

a sec

.=, i'am brazilian and here we use , instead .

[dapper meteor]

ok that's good

but you have to make this = k with k in Z

and solve for x

not for k

[zenith bay]

a sec

[dapper meteor]

what don't u understand ?

[zenith bay]

let me try

what i did is wrong?

[dapper meteor]

no

[dapper meteor]

but it's just the beginning

[dapper meteor]

you don't search k

you search x

[zenith bay]

288 is the x*

i said wrong

[dapper meteor]

you should find an expression of x with a k

[zenith bay]

but i wont find an answer

[dapper meteor]

the answer will be a set

{}

the answer will be many values of x

[zenith bay]

1 + 10^11 = 1.023*10^11k+kx

[dapper meteor]

that is wrong

not 1

1,023 * 10^11 + x + 10^11 = 1.023 * 10^11k+kx

[zenith bay]

what?

[dapper meteor]

you didn't multiply the 1 by the denominator

[zenith bay]

how?

[dapper meteor]

$1+\frac{10^{11}}{1.023*10^{11} + x} = k$

[twin meteor]

ByShaDowZ

[dapper meteor]

$1.023*10^{11} + x + 10^{11} = (1.023\times 10^{11} + x)k$

[twin meteor]

ByShaDowZ

[dapper meteor]

I just multiply by $1.023*10^{11} + x$

[twin meteor]

ByShaDowZ

[zenith bay]

why we can do it?

[dapper meteor]

because you always can multiply an entire equation by what you want

[zenith bay]

but how do you transformed 1 + 10 ^11 in 1.023 * 10^11 + x + 10^11?

[dapper meteor]

I have $1+\frac{a}{b}$ and i multiply by b so i get $b+a$

[twin meteor]

ByShaDowZ

[dapper meteor]

like it's normal multiplication

[zenith bay]

oh

I understand what you did now

[dapper meteor]

nice !

[zenith bay]

but in the same way, we will not arrive at an integer

[dapper meteor]

how do you know ?

[zenith bay]

beucase we have 2 unknown

[dapper meteor]

No

k is an integer

x is an unknown

we want to find an expression of x with some k inside

and we'll apply some values to k

and see if there is any value of k that makes x an integer

[zenith bay]

but we would have endless possibilities, wouldn't we?

[dapper meteor]

maybe yes

but that's what we want

[dapper meteor]

^

You said it yourself

"For how many integers" means that x can be many different integers

[zenith bay]

ok i got it

thanks for your help man : )

[dapper meteor]

Hope you understood all of it

[zenith bay]

.close

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[indigo solar]

Can someone do the stuff on the right?

[vocal sleet]

Show your work, and if possible, explain where you are stuck.

[vast shale]

we cant do anything for you, we can only try to assist you in doing it yourself

[indigo solar]

ok

can you assist?

[vast shale]

sure but you need to say what's troubling you

with the question

[indigo solar]

idk what its asking

like its confusing me

the questions

because it could be asking this or that

[soft walrus]

for statement 1 and 2

it's saying that after the rotation the sides and angles are the same on the shape after the rotation

is that true or false?

[indigo solar]

the sides and everything havent changedso yes

[soft walrus]

so are the statements true or false?

[indigo solar]

true

or false the second one

[soft walrus]

try to justify to yourself what happens to the angles when they are rotated?

[indigo solar]

they are changed

as in which angle thats what I dont get

this

or the angles on the object

if its the angles on the object it hasnt moved

[soft walrus]

the angles inside the parallelogram

[indigo solar]

yeah it hasnt changed

so true

then?

[soft walrus]

🎉

[indigo solar]

🫡

are the other two correct?

Mrfancy

I submitteded idk what I got thanks

.close

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[wind sequoia]

I’m in pre calc can I get some help with subtracting these functions

[wind sequoia]

So I heard to subtract fractions you multiply each by the other’s denominator. So I did that and I get -x - 5 but that doesn’t line up with other things I see

[toxic junco]

It is wdym

You mean for the numerator ?

[silver finch]

@wind sequoia

multiply by one to both fra tions

they will have the same denominator

The domain will be all the x values you can plug in
but the domain will have a restriction since x+2 and x - 1 are on the bottom
so if u plug in -2 or if you plug in 1, you will get a 0 in the denominator

[wind sequoia]

That looks like what I did

google says the answer is (-x -5) / x^2 + x - 2 but im not getting that

\

ik how to get domain im just trying to figure out how to subtract these

[wind sequoia]

no for whole thing

[vocal sleet]

@wind sequoia Has your question been resolved?

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[sharp pendant]

would like to ask why use t distribution instead of z score

and can you explain part d pls? wt i understand is the degree of freedome is 50-1= 49 and idk where the 0.025 come from (alpha =0.01) but not 0.05/2

[lavish aurora]

t table is used when you do not have the population standard deviation

[sharp pendant]

oh got it thanks

then where the 0.025 come from?

in part d

[lavish aurora]

I guess whatever the t value came out to on the table

[sharp pendant]

weird I checked t table .01 is 2.405

.close

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[hollow wasp]

<@&286206848099549185>

[hollow wasp]

<@&286206848099549185>

[lunar lagoon]

cylinder is pi x r^2 x h right?

[hollow wasp]

yes

@lunar lagoon

[lunar lagoon]

so r = diameter/2 = 0.75 feet

[hollow wasp]

which question are you looking at?

[lunar lagoon]

so we can find the volume of the cylinder

1st one

[hollow wasp]

ok

[vocal sleet]

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.

[karmic imp]

And please do not open a channel, pinging helpers as your first message. Just post your question next time

[hollow wasp]

ok

sorry

[lunar lagoon]

so pi x 0.75^2 x 1.6 = volume in ft^3 right

[hollow wasp]

Yes

2.826 ft^3

or 2.8 ft^3 if rounded

oh so 3 if rounded to the whole number

[lunar lagoon]

ok so now convert that into gal

dont round yet

only ever round at the end

[hollow wasp]

21.139948

[lunar lagoon]

so 2.826 x 7.5 in gallons

ok so 21 gallons to the nearest gallon

[hollow wasp]

yes

so thats the answer?

hello?

[lunar lagoon]

yep

[hollow wasp]

Ok

So

hwo would I write it

[lunar lagoon]

they want it in terms of pi actually

[hollow wasp]

oh

yea Idk how to like write in terms of pi

[lunar lagoon]

well they want both so we did need that 21

oh right

if you treat the pi just like an x in algebra

and rearrange

[hollow wasp]

can you give me an example?

Oh so like

[lunar lagoon]

(pi x 0.75^2 x 1.6) x 7.5

[hollow wasp]

right

2.826

[lunar lagoon]

but keep pi in there dont replace it with 3.1415

[hollow wasp]

well my teacher said we replace the pi with 3.14

[lunar lagoon]

the answer they want is 0.75^2 x 1.6 x 7.5

[hollow wasp]

oh

ok

[lunar lagoon]

they have two answer boxes

[hollow wasp]

so 6.75

ohhh

ok

[lunar lagoon]

first is 6.75, second would be the 21

or 6.75 x pi

[hollow wasp]

allright

Umm let me just recap what you said

ok so

how did you get 0.75

oh nvm ok

you got it from the

1.5

ok

so

(pi x 0.75^2 x 1.6) x 7.5

But we keep the pi

so it will be

(o.75^2 x 1.6) x 7,5

giving us

6.75

[lunar lagoon]

yes

so first box is 6.75

and then all you gotta do is times by pi

and round

[hollow wasp]

oh wow that was suprsingly simple

ok can you hang on here for a second

I just need to write this down

[lunar lagoon]

yeah sure

[hollow wasp]

Ok got it

and the next question

my answer is very much wrong

I just don't know how to do this one

[rose raft]

surface area

[lunar lagoon]

ok i dont remember the surface area equation

[hollow wasp]

I got you

[lunar lagoon]

its like 4/3 pi r^2 or something

[hollow wasp]

A=2πrh+2πr^2

[lunar lagoon]

oh yeah ofc

so substitute a and r into that to get h

[hollow wasp]

ok

hol on

im going to write it

done

it will give us

1850=2 x 3.14 x 9 x h + 2 x 3.14 x 9^2

1850=6.28 x 9 x h + 6.28 x 81

1850 = 56.52 x h + 508.68

am I right?

[lunar lagoon]

i think so

i dont have a calculator with me so im trusting your abilities to type it in

ok i now have a calculator

[hollow wasp]

ok good

I have this open right now

[lunar lagoon]

yeah it all looks good

[hollow wasp]

Ok

[lunar lagoon]

so you gotta find h from that

[hollow wasp]

Do we add 56.32 and 508.68

[lunar lagoon]

508.68 doesnt have an h so we cant just add them

[hollow wasp]

oh right

[lunar lagoon]

1850 also doesnt have an h tho...

[hollow wasp]

Ok

So

56.32h + 508.68 = 1850

56.32h = 1850 - 508.68

56.32h=1341.32

h=1341.32/56.32

h=23.81...

[lunar lagoon]

i think so yes

[hollow wasp]

h≈24

am I right?

[lunar lagoon]

again we only round at the end but yes

cause they didnt ask for h

[hollow wasp]

Ok so we keep 23.81?

[lunar lagoon]

never round until youre actually writing down the answer

[hollow wasp]

I got this

[hollow wasp]

I will keep that in mind

[lunar lagoon]

just use the ans button

so the question wanted volume

[hollow wasp]

yes

so

v=pi x r^2 x h

v=3.14 x 9^2 x 23.81

??

[lunar lagoon]

im with you yep

so now just calculate that

and round to a whole number

[hollow wasp]

6056

that is the rounded

[lunar lagoon]

did you use the ans button

[hollow wasp]

where is that

the equal??

[lunar lagoon]

if you just start typing it will like continue

so when you had the long number if you just press x 3.14 x 9^2

[hollow wasp]

this?

[lunar lagoon]

yep

[hollow wasp]

ok

so

[lunar lagoon]

so 6057

[hollow wasp]

Yes

[lunar lagoon]

which is why you dont round

[hollow wasp]

thats the answers?

[lunar lagoon]

pretty sure

[hollow wasp]

huh.

it marked me wrong'

when I checked it

[lunar lagoon]

hmm

ok ill get some paper gimme like 5 mins

[hollow wasp]

ok

[lunar lagoon]

the first q was right tho?

[hollow wasp]

yes

wait

q?

[lunar lagoon]

question mb

[hollow wasp]

Idk

I was out of checks

[lunar lagoon]

oh nvm then

ok i just did it and got 6036 lemme try and spot where we went wrong

[hollow wasp]

I got 671

rounded

how did yu get 6036

i got 6033

@lunar lagoon

yo

[lunar lagoon]

ok the answer is 100% 6035.94

[hollow wasp]

100% sure?

6036?

[lunar lagoon]

i did it without substituting anything and only substituted at the end the equation was (Ar/2)-pi x r^3

[hollow wasp]

ok im check it

bruh

im out of checks

💀 \

[lunar lagoon]

wow

ill go through my steps

[hollow wasp]

ok

[lunar lagoon]

$A = 2\pi r h + 2\pi r^2$

[twin meteor]

Poelymole

[lunar lagoon]

divide both sides by 2 pi r

[hollow wasp]

both sides meaning

[lunar lagoon]

$\frac{A}{2\pi r} = h + r$

[twin meteor]

Poelymole

[hollow wasp]

ok

[lunar lagoon]

lmk if i lose you

[hollow wasp]

wait

[lunar lagoon]

$h = \frac{A}{2\pi r} - r$

[hollow wasp]

what about the

[twin meteor]

Poelymole

[hollow wasp]

what about the r^2

[lunar lagoon]

$\frac{2\pi r^2}{2\pi r} = r$

[twin meteor]

Poelymole

[hollow wasp]

oh ok

makes sense

[lunar lagoon]

we just divided everythin there by 2pi r

[lunar lagoon]

so youre with me here?

[hollow wasp]

yea

wait

yes yes

I am

[lunar lagoon]

cool

now we get v involved

[hollow wasp]

aight

[lunar lagoon]

$V = \pi r^2 (\frac{A}{2\pi r} -r)$

[twin meteor]

Poelymole

[hollow wasp]

uhh

[lunar lagoon]

substituting for h

[hollow wasp]

ok

[lunar lagoon]

please lmk if ur not following

[hollow wasp]

not following here

[lunar lagoon]

i realise im skipping some steps so

earlier we got

[lunar lagoon]

this

[hollow wasp]

yes

[lunar lagoon]

and we know $V = \pi r^2 \times h$

[twin meteor]

Poelymole

[hollow wasp]

yes

Oh

Ok

Yes

I follow

[lunar lagoon]

so substitute $V = \pi r^2 \times (\frac{A}{2\pi r} -r)$

[twin meteor]

Poelymole

[hollow wasp]

Yes

continue

[lunar lagoon]

now expand brackets

$V = \frac{A\pi r^2}{2 \pi r} - \pi r^3$

[twin meteor]

Poelymole

[hollow wasp]

umm

[lunar lagoon]

ok middle step

[hollow wasp]

not following

[lunar lagoon]

$V = \pi r^2 \times (\frac{A}{2\pi r}) - \pi r^2 \times r$

[hollow wasp]

here

ok

So

ok

yes I see

You add the exponet 2 and 1

[twin meteor]

Poelymole

[hollow wasp]

ok

[lunar lagoon]

yeah the r^2 and the r make the r^3

[hollow wasp]

yes

[lunar lagoon]

and the r^2 and the 1/r combine to make r

[hollow wasp]

it gives us Aπr^2/2πr x πr^3

[lunar lagoon]

yes

[hollow wasp]

Now do we subsitute in the numbers

[lunar lagoon]

we can do 1 more step

[hollow wasp]

ok

[lunar lagoon]

$V = \frac{Ar}{2} - \pi r^3$

[twin meteor]

Poelymole

[lunar lagoon]

cancel the r and the pi

[hollow wasp]

ok

[lunar lagoon]

then substitute

[hollow wasp]

A=1850?

[lunar lagoon]

$V = \frac{1850\times9}{2} - 3.14\times9^3$

[twin meteor]

Poelymole

[lunar lagoon]

$\therefore V = 6035.94 \approx 6036$

[hollow wasp]

and we get 6035.94

[twin meteor]

Poelymole

[hollow wasp]

ok

yea that makes sense

I have two questions

i forgot to mention

[lunar lagoon]

i realised they did not want all that algebra but i find it easier idk why so sorry about that

[hollow wasp]

This one we have 2 checks

[hollow wasp]

no no your fine

Thank you for taking your time to help me

[lunar lagoon]

all good

i like latex anyway so its cool

[hollow wasp]

if you could help me with this last one

[lunar lagoon]

yeah ofc

[hollow wasp]

then I have one more you just have to check the explaintion

[lunar lagoon]

so really similar to the first one we did

[hollow wasp]

yes

[lunar lagoon]

$V = \pi r^2 h$

[twin meteor]

Poelymole

[hollow wasp]

So we can put in the formula

yes

[lunar lagoon]

but remember to find it in terms of pi

[hollow wasp]

yes

[lunar lagoon]

sshould be 2^2 x 6

so 24?

[hollow wasp]

Yes

[lunar lagoon]

then convert to £

[hollow wasp]

oh I think we are looking at lb

[lunar lagoon]

yeah lmao im just really funny

[hollow wasp]

oh

Sorry I didn't get it, I was just really focusing on the question

[lunar lagoon]

ig im not really funny😔

[hollow wasp]

No no no

Don't take it like that

[lunar lagoon]

yeah lmao ik

[hollow wasp]

😔 Bro made me feel bad

[lunar lagoon]

man im laughing at my own shitty joke its all fine

[hollow wasp]

you laught at your own jokes too?

[lunar lagoon]

ofc

anyway it should be 62.5x24 right

[hollow wasp]

idk

the conversion not working

put probably it

1500

[lunar lagoon]

1ft = 62.5 pounds so 24ft = x pounds

[hollow wasp]

yes

[lunar lagoon]

ratios

[hollow wasp]

one sec I need to do something

gimme a seocnd

[lunar lagoon]

it better be laughing at my joke 😤

[hollow wasp]

laughs

[lunar lagoon]

good

[hollow wasp]

lol

ok

anyway

[lunar lagoon]

yes

[hollow wasp]

1500

can we need to multiply that by 3.14

right?

[lunar lagoon]

4710 yep

so the two boxes are 1500 and 4710

[lunar lagoon]

bosh

[hollow wasp]

😤 😤 😤 💯 💯

[lunar lagoon]

you had 1 more quezzie?

[hollow wasp]

Yes yes

the multiple choice is right

i just want to know if my explaintion is

because umm

I calculated

😔

I believe im right, but idk

ahh, now I have a lot of questions

😭 😭 I feel so bad

[lunar lagoon]

cylinder:cube
pi x 4^2 x 8: 8^3
pi x 4^2: 8^2
8^2 is clearly bigger than 4^2 x ~3

[hollow wasp]

but you can't calculate

[lunar lagoon]

the cube has corners?

[hollow wasp]

Yea

[lunar lagoon]

the cylinder cannot be as big bc the cube is 8 wide at all points but the cylinder varies btwn 8 and 0 width

• same with length

question 4:

[lunar lagoon]

yeah ig

[hollow wasp]

this one

[lunar lagoon]

$10000\pi = V = \pi r^2 h$

[twin meteor]

Poelymole

[lunar lagoon]

$\frac{10000\pi}{\pi r^2} = h$

[twin meteor]

Poelymole

[hollow wasp]

do we write it in terms of pi?

[lunar lagoon]

no they would have put pi next to the box

[hollow wasp]

ok

and the pi cancels out?

[lunar lagoon]

$\frac{10000}{16^2}$

yep

[twin meteor]

Poelymole

[hollow wasp]

So 39

[lunar lagoon]

to the nearest inch yeah

[hollow wasp]

ok

terms of pi this time

[lunar lagoon]

base area is pi x r^2

$4\pi = \pi r^2$

[twin meteor]

Poelymole

[lunar lagoon]

$4 = r^2$

[twin meteor]

Poelymole

[lunar lagoon]

$r = 2 (or -2 but we dont care)$

[twin meteor]

Poelymole

[hollow wasp]

ok

[lunar lagoon]

actually screw that

we dont care

[hollow wasp]

so radius is 2

[lunar lagoon]

volume is just base times height

20pi

[hollow wasp]

Well

ok

62.8

[lunar lagoon]

or if we did use the radius is would be pi x 2^2 x 5

which is 20pi

yep

[hollow wasp]

Ok so I will put in

62.8

ok

thats all

[lunar lagoon]

its kinda 3am for me so thats good news

[hollow wasp]

Well thank you man, for taking your time with this

[hollow wasp]

lol

[lunar lagoon]

imma go to bed

[hollow wasp]

yo

would you mind

if I

friend yoiu?

[lunar lagoon]

yeah go for it

[hollow wasp]

thanks

have a good night

[lunar lagoon]

im in uk so im around like uk time obvs but yeah

see ya

[hollow wasp]

oh ok

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[woven shadow]

Hey guys in terms of multiple regression, does this residual plot seem to violate any regression assumptions that may make this model invalid?

e.g. linearity, independence of errors, normality, etc?

[strange crater]

why does the plot go from 0 --> 140 when all the values are from 80 --> 120 or so

and any more context could be helpful

but in general, linear regression is relatively robust to violations. you can also look at a QQ plot

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[hushed atlas]

i tried connecting centres, making a triangle, splitting it in half and getting the remaining length

[hushed atlas]

seems wrong

[jagged gorge]

hello bonx

[hushed atlas]

hi lmao

[jagged gorge]

icosceles triangle

[patent nymph]

Can you write out the steps of what you tried

[jagged gorge]

it is trig

[hushed atlas]

is it not equilateral when u connect the dots

connect the dots i mean literally btw

[hushed atlas]

oh

[jagged gorge]

trig

cos 30 = 6/x

x = 6/cos 30

[hushed atlas]

yh my first step was wrong

okay thanks

[patent nymph]

not a right angled triangle
edit: I see it now

[jagged gorge]

it is tho

[hushed atlas]

he split it?

[jagged gorge]

i split it in half

[hushed atlas]

its a bit hard to see

but i can see it

[jagged gorge]

my bad

[patent nymph]

oh

oops

[hushed atlas]

no no its fine its not bad😂

its more useful than what i did😭

[jagged gorge]

there you go

[hushed atlas]

thanks

[jagged gorge]

dyk what cos 30 is

root3 / 2

6/(root3/2) = 6*2root3/3 = 4root3

so its 6 + 4 root 3

[hushed atlas]

mmm nice

[jagged gorge]

QED

[hushed atlas]

yh makes sense

thanks

[jagged gorge]

how old are you fr tho

going from differentiation to simple geometry

[patent nymph]

it could be that they couldn’t see the step to get the right angled triangle

I couldn’t, until you pointed it out

[jagged gorge]

she was close tho

got the connecting the dots going

[hushed atlas]

this

[jagged gorge]

.close?

[hushed atlas]

.close

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[calm zephyr]

Can I get a second point

[calm zephyr]

Opinion

On question 3

Is this correct?

[patent nymph]

on question 3, all the restrictions you gave are right

[calm zephyr]

Thank you again

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[vast shale]

Do i need to take the 4 out?

[vast shale]

I haven't integrated in awhile

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[mint remnant]

What’s distance MP?

[merry python]

couldn't it take any value from 0 to 400

is any angle given?

[mint remnant]

The answer is 400 theta and I’m not sure how they got it

[merry python]

ohh

[mint remnant]

We need to answer it in terms of theta

[merry python]

in terms of theta I see

[mint remnant]

Yep

[merry python]

Triangle MPN is a right triangle

[mint remnant]

Yep

I figured out that NP is 400cos(theta) for the first part of the question which was easy

[merry python]

MP should be 400sin(theta) ig

[mint remnant]

That’s what I’ve been getting but the answer is apparently 400theta which I don’t get

[vocal sleet]

@mint remnant Has your question been resolved?

[mint remnant]

Sure

Yes

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[main finch]

Hey need some help with this

[main finch]

Here is the answer im provided, what im confused about is why the partial derivative with respect to xj doesnt affect Fj

But F is a function of x,y and z

[vocal sleet]

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[urban edge]

!status

[vocal sleet]

What step are you on?
1. I don't know where to begin
2. I have begun but got stuck midway
3. I got an answer but I'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above

@analog torrent Has your question been resolved?

[analog torrent]

3

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[vocal sleet]

@errant briar Has your question been resolved?

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[echo fiber]

uh i asked for help before about an equation but i need help understanding why x^2 = 16 has the answer of -4 and 4

[desert hornet]

$x^2=16\implies x^2-16=0\implies (x+4)(x-4)=0\implies x=\pm 4$

[twin meteor]

kheerii

[midnight estuary]

if you square a negative and a positive number, both will lead to the positive number

so when square rooting, you must indicate that to the other side by using plus or minus symbol

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[vast shale]

On the left there's an exponential equation.
On the right side is my attempt to solve it.
Where did I make a mistake?

[lime gorge]

u got it?

[vast shale]

yeah

[lime gorge]

Aight

[vast shale]

thanks for giving help in general 🙂

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[lime gorge]

Np

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[sterile pecan]

Alrighty, hi there.
Im doing some homework here, and im having some problems with a tangent and a circle. We know the equations of both orthogonal lines, aswell as the angle from the horizontal line and the tangent. I also know the intersection points coordinates, and the circles radius.
We can decide for ourselves the circles position and size, it just needs to be on the tangent.

We tried to use pythagoras on it with the horizontal angle, but for some reason that did not work properly.

Thanks in advance :)

[sterile pecan]

Heres our attempt:

The radius is 8 and the intersection point is -33;-6

hd is the angle from the sharp horizontal line of the tangent ofc.

[regal bane]

What's the question?

[sterile pecan]

the answer i got from the pythagoras is wrong

ya see?

eq2: 8² = (x + 37.8)² + (y + 12.4)²

<@&286206848099549185>

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@sterile pecan Has your question been resolved?

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[floral pagoda]

I need help and this is the only place I can hope to get answers

If I borrowed $500 for 6 years at an annual interest rate of 7% how much will I pay altogether

[vocal sleet]

Please don't occupy multiple help channels.

[karmic imp]

Don't open multiple channels

[floral pagoda]

I don't know how to close other ones

[karmic imp]

.close

[floral pagoda]

.close

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[weak dome]

Hi! In a question, im supposed to find the equation of a circle circumscribed about this. How would I do that

[weak dome]

Or, in general, how do I find the equation of a circle with 3 points on the circle

[rose raft]

what is "this"

[weak dome]

The triangle

Can you not see the while thing or did I mess up

Whole*

Nevermind that first question, turns out I was doing the wrong homework, but I still need help knowing how to find a circle equation qith 3 points

[rose raft]

(𝑥 − ℎ)² + (𝑦 − 𝑘)² = 𝑟²

[weak dome]

Yes I know, but how do I find the center and the radius?

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[daring saddle]

Where can I get help with my Spanish Homework?

[mystic skiff]

probably not in the mathematics discord

[daring saddle]

Are there any other servers for Spanish help?

[mystic skiff]

probably try searching

[lime gorge]

whats the topic

@daring saddle

[daring saddle]

Im on Mobile lol

[daring saddle]

“Present tense or subjunctive”

Impersonal expressions

[mystic skiff]

ew subjunctive

[daring saddle]

That’s what the assignment saids

[daring saddle]

Ikr

It’s so weird

[lime gorge]

ik "homework help" server has a spanish section, tho idk how active it is

[mystic skiff]

i dmed you a server

[daring saddle]

Thanks !

[daring saddle]

Oh

,close

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[river kettle]

How do we get vdu from y = u x v? How do you differentiate that term if there’s nothing there to differentiate

[mystic skiff]

wdym nothing to differentiate

oh i see

$\frac{d}{du}y=\frac{d}{du}vu$

[twin meteor]

baro | awake

[mystic skiff]

sorry

[river kettle]

but I don’t understand the operation they do to get v•du

[mystic skiff]

one sec

$\frac{dy}{du}=v\cdot\frac{d}{du}u$

[twin meteor]

baro | awake

[mystic skiff]

$\frac{dy}{du}=v\cdot1$

[twin meteor]

baro | awake

[mystic skiff]

$dy=vdu$

[twin meteor]

baro | awake

[mystic skiff]

lowkey you can treat the differentials like fractions and just multiply over the du

[vocal sleet]

@river kettle Has your question been resolved?

[paper depot]

have to say once again that this reasoning is extremely dodgy, and it would really take some multivariable calculus to give it any kind of solid footing, but

u and v are perhaps supposed to both be functions of another variable x

so there is not "nothing to differentiate"

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[craggy helm]

I'm having problems understanding the english system. Is this correct? I think I know how to solve this using the metric system, you find the equation of the force and plug it in the integral, but in the english system I have no idea.

[craggy helm]

I think w is the weight density, but I'm not sure if I have to use that in the integral or the total weight.

I have an example of a similar exercise, but that's an one I copied when my teacher was explaining it. I think he put the weight density multiplied by y(distance) inside the integral, but I'm just confused. Please help

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[clear sundial]

i need help with this image proof

i think the range is (-inf, inf)

but im not sure where to go from here

[paper depot]

can you prove that the equation x - 1/x = y has a solution for x no matter what y is

[clear sundial]

i mean i graphed it and saw that there is a solution

but im not sure how you can find it algebrically

oh well a solution would be at x = 1

[vocal sleet]

@clear sundial Has your question been resolved?

[paper depot]

you can reduce the equation to a quadratic in x and verify its discriminant is always nonnegative

[clear sundial]

heres what i have so far

and i want to show it using mutual subset inclusion

[paper depot]

well f(R) ⊆ (-∞, +∞) is already obvious

unless you deem the statement "if x is a positive real number then x - 1/x is a real number" as nonobvious enough to require proof

it was the other inclusion i was talkign about.

(∀y ∈ R)(∃x ∈ (0,+∞))[x - 1/x = y]

[clear sundial]

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[vocal sequoia]

hi, im new here and my younger brother is asking how to get the answer. And I don't know also how to get it.

[vocal sequoia]

<@&286206848099549185>

[zinc sequoia]

!show

[vocal sleet]

Show your work, and if possible, explain where you are stuck.

@vocal sequoia Has your question been resolved?

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.close

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[craggy helm]

Is this correct? I think it's not because while the height varies (y), the force isn't changing but it should. How do I solve this?

[vocal sleet]

@craggy helm Has your question been resolved?

[craggy helm]

<@&286206848099549185>

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@craggy helm Has your question been resolved?

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@craggy helm Has your question been resolved?

[craggy helm]

No

[oblique stone]

poor guys been waiting for ages

convert the metrics into metric units and someone will probably answer the question

but it's a pulley problem

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[left narwhal]

I did this

Idk next step

[paper depot]

mark off the right angle at A

draw a line through M perpendicular to BC and mark its intersection point with AC

basically keep going with making the diagram according to the problem statement lol

[left narwhal]

So the line will be diagonal?

Like this?

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@left narwhal Has your question been resolved?

[woeful zenith]

@left narwhal your diagram should be like this

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[left narwhal]

Ohhh I thats why angle BAC is 90°

[left narwhal]

I got confused at first cuz idk hows that possible

Oh wait

A is the vertex

[rugged vortex]

Wtf 2KB why are you here lol

[left narwhal]

So i drew the triangle right and the following steps are wrong

[left narwhal]

Thankyouuu

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[torpid sequoia]

$\frac{d}{dx}\left(g\left(1\right)\right)=\frac{d}{dx}\left(f\left(\frac{1}{2}\cdot f\left(1\right)\right)\right)$

[twin meteor]

Chuti | Spanish

[vocal sleet]

Please don't occupy multiple help channels.

[torpid sequoia]

how can I do the derivative of

$\frac{d}{dx}\left(f\left(\frac{1}{2}\cdot f\left(1\right)\right)\right)$

[twin meteor]

Chuti | Spanish

[torpid sequoia]

if I dont know the form of f(x)

[karmic imp]

Please don't occupy multiple help channels.
Means don't use multiple channels, so either close this one or the other one you have open

[torpid sequoia]

bruh the other channel has been opened for an hour 30 no one answered

😄

closed

[inner bloom]

hi

f(1/2 * f(1)) is a point

A(1,f(1/2 * f(1)))

you can't take deriv of a point

[torpid sequoia]

I know f(1) is 2 btw

[inner bloom]

can you send the original question?

[twin meteor]

Chuti | Spanish

[torpid sequoia]

yes, find the equation of the tangent of g on X = 1

knowing that the tangent of f in 1 has the form of

this is the complete problem

my professor did this

but idk why

I dont understand how he gets to 24 from g'(x)

[rugged vortex]

Chain rule

[torpid sequoia]

right but g'(1) is

[twin meteor]

Chuti | Spanish

[torpid sequoia]

how can I use the chain rule on a function 🤔

I'm applying the derivative on the whole thing, not only in 1/2 * f(1)

🤔

[vocal sleet]

@torpid sequoia Has your question been resolved?

[torpid sequoia]

no but ok

[vocal sleet]

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[lament flicker]

i dont get what happened here

[tacit escarp]

which line

[frozen bobcat]

2x+3 is the derivative of the denominator. So they split up the numerator to break up the whole integral. Now the last line you can see the first integral is a u-sub, and the second integral is a simpler partial fraction integral.

[lament flicker]

where did the 25/2 come from?

[frozen bobcat]

3/2(3) = 9/2
9/2 - 25/2 = -16/2 = -8

they just rewrote 3x-8

[lament flicker]

aha i get it now

thanks

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@lament flicker Has your question been resolved?

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[dusk sluice]

Can someone explain to me how the integrating factor works? My class basically just said that making this variable and multiplying it through the equation results in this and gave no explaination as to how that works or why they're making this variable.

[dusk sluice]

I've been looking at it for like 30mins and messing around with it algebraically, finding derivatives, etc. and I don't see how it works

[vocal sleet]

@dusk sluice Has your question been resolved?

[dusk sluice]

Wait I think I found it?

The red is me just messing around with things

[flat whale]

looks right

more detailed explanation here:
https://tutorial.math.lamar.edu/classes/de/Linear.aspx

your work matches up with their steps

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@dusk sluice Has your question been resolved?

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[vocal sleet]

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[blazing lintel]

I'm trying to solve this. Here is what I've done so far

[blazing lintel]

I parameterized $x = cos\theta$ and $y = sin\theta$, because the radius is 1

[twin meteor]

beanbeanjuice

[blazing lintel]

im not sure where to eve start from there though

its something like

$r(?,\theta) = <cos\theta, sin\theta, ?>$ i have no clue what to put for the question marks

[twin meteor]

beanbeanjuice

[vocal sleet]

@blazing lintel Has your question been resolved?

[vocal sleet]

@blazing lintel Has your question been resolved?

[vocal sleet]

@blazing lintel Has your question been resolved?

[timber orchid]

I’d start with a diagram

[vocal sleet]

@blazing lintel Has your question been resolved?

[weary sentinel]

let z=t/2, y+2z=2, so y+t=2, so t=2-y, so t=2-sinø

often parametricizations seem to be more complicated than they are

don't second guess yourself when you're missing just one parameter

you just have to use your last bound (the plane equation) in conjunction with your missing parameter

[vocal sleet]

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[vast shale]

I drew this

<@&286206848099549185>

[dusk python]

what was your thought process behind that drawing

[wicked sonnet]

!15m

[vocal sleet]

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.

[vast shale]

Dunno

Help@me

[vast shale]

This??

[dusk python]

that looks better

have you learned calculus

[vast shale]

Yeah

I literally don’t know this tho

I forgot

[dusk python]

since you only need an approximate slope that looks good

now pick two points on that line to compute the slope

[soft walrus]

are you doing calculus right now?

[vast shale]

Ye

[soft walrus]

have you learned implicit differentiation?

[vast shale]

Ye

[vast shale]

Rise over run?

-3/4?

[soft walrus]

if you want the slope to the tangent of the circle find y' at the point x=3?

[outer warren]

<@&268886789983436800>