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[prime sluice]

i will leave the channel open,i would like to attempt another question myself, is it fine i confirm the answer here in a few minutes?

[ocean hawk]

sure, I might not be here but someone should answer

[prime sluice]

ok thanks

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[narrow knoll]

Let f(x) = ax^2 + bx + a, where a and b are constants and a , 0. If one of the roots of the
equation f(x) = 0 is x = 4, what is the other root?

[ocean hawk]

what does "and a, 0" mean?

[narrow knoll]

a not equal to 0

[livid sage]

presumably a > 0

valid

[narrow knoll]

i got some crazy equation when i tried to solve

i got 17a = 4b and i assume it went downhill from there

[ocean hawk]

should it be 17a = -4b

[narrow knoll]

yeah

soryr

but when i plugged in

b = -17/4a

to the equation

it became a really not nice equation

[ocean hawk]

b does not equal -17 / a

[narrow knoll]

sorry another typo

[narrow knoll]

do you have any idea sfor this problem?

[ocean hawk]

yes

what is the quotient that you get from the division

i gotta go, but just take the quotient, set it equal to 0, and substitute for b. then solve for x

[narrow knoll]

what quotient?

[ocean hawk]

From dividing. I assume that's how you got to 17a =-4b

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[lone heart]

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[cunning bloom]

yo

[cunning bloom]

which formula would i use for this

like the disc or washer

[hollow wren]

i would say disc/washer

its just u have a diff rotational axis

[cunning bloom]

wait i lowk forgot the difference in formula

[hollow wren]

oh

holdon

[cunning bloom]

would it be like

oh ty

oh wait nvm

pi(R(x)-r(x))^2?

[hollow wren]

mhmhm

outer radius minus inner radius

well

ig yeah its technically washer

cuz outer radius is 2 + 2x^2

and inner is 2

[cunning bloom]

but i thought washer would look like this tho

[hollow wren]

holdon

in this case washer would be

[buoyant saddle]

why washer method?

it isn’t just the region bounded to the x axis

the radius is 2x^2+2

[hollow wren]

$\pi \int_{0}^{2} ({(2+2x^2)}^2 - {(2)}^2 ) \mathrm{d}x$

[ocean seal]

Potatomonke

[cunning bloom]

that wat i thought at first but wasnt too sure

[buoyant saddle]

if there were a hole

[hollow wren]

its revolved around the line y=-2

[buoyant saddle]

it would be washer

[hollow wren]

theres a hole

[buoyant saddle]

there’s no hole

it’s the entire region

[hollow wren]

oop im blind

i thought the line in the image was the x-axis

[buoyant saddle]

if it were just the region bounded by the x axis and the function then yes

[hollow wren]

yeah so its just

[buoyant saddle]

that would be right

you only use washer method when the region bounded isn’t touching the axis of rotation

[cunning bloom]

so this is the final answer correct?

[buoyant saddle]

looks good

[hollow wren]

mhm

[cunning bloom]

thanks my brutha

WAIT

one quiock questiopn

how would i know if it should be negastive or positive

[hollow wren]

its volume

its always gonna be positive

in this case at least

[cunning bloom]

oh wait nvm i see lol

[hollow wren]

area can be negative with integrals, but volume is always positive

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[simple wyvern]

hey there, I am minimizing the regularized least squares $f(x)=\frac{1}{2}\norm{Ax-b}{L^2(\Omega)}^2+\frac{\alpha}{2}\norm{x}{L^2(\Omega)}^2$. That I did just fine by doing basic steps (see the attached photo). Where I used the classic result from matrix calculus $\frac{\partial x^TBx}{\partial x}=2Bx$, where $B$ is a symmetric matrix, solving for $\hat{x}=(A^TA+\alpha I)^{-1}A^Tb$.

What I am struggling with is how would I go about solving the same problem is the regularized term is in the $H^1$-norm so $f(x)=\frac{1}{2}\norm{Ax-b}2^2+\frac{ \alpha}{2}\norm{\nabla x}^2{H^1(\Omega)}$ (last picture) I tried to to the same calculations but my matrix differentiation needs a little bit of brushing, any resources maybe? thanks

[ocean seal]

nani?

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[lofty owl]

how do I find a percentage of a number?

[fiery merlin]

Are you talking about how to find the percentage of how much a number is compared to another number? like what percent of 5 is 3?

you just take the smaller number and divide it by the bigger number

3 is 60% of 5 because 3/5 is 0.6

[hot hatch]

@lofty owl

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[stone imp]

Can anyone explain this question to me

[lone heart]

@stone imp Has your question been resolved?

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[stone imp]

.reopen

[lone heart]

✅

[stone imp]

Please anyone answer it

.close

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[delicate flower]

simplified this to root (that quartic crap) / root (quartic crap) - 1

[alpine sable]

What form of limit is this ?

@delicate flower

[delicate flower]

0/0?

[alpine sable]

Yes

[delicate flower]

please don't tell me to L hopital this

i hate it

[alpine sable]

It is

But

[delicate flower]

there must be other ways

[alpine sable]

Take x from numerator to denominator

What do you observer

Observe

[delicate flower]

is this right?

first step

using e^x -1 / x standard limit

[alpine sable]

Yes

Assume that sqrt (.....)/x as a

Now it should be simple

[delicate flower]

a/(a-1)

[alpine sable]

❌

[delicate flower]

sqrt/x

oh

ax/(ax-1)

[alpine sable]

Or you can just write the direct answer if you know the answer for the standard form

[delicate flower]

huh when did quadratic get its own standard form

[alpine sable]

Did you do this?

[delicate flower]

i got

root(1+x^2 + x^4)

root (1+x^2 +x^4) - 1

i multiplied and divided it by x

to get
a/x

a/x - 1/x

[alpine sable]

???

[delicate flower]

my first step was to multiply and divide the numerator by the power in e

so that e goes

[alpine sable]

No

[delicate flower]

oh

then what do i do

[alpine sable]

[delicate flower]

uh

how do i do that

💀

[livid sage]

they are telling you to divide the numerator and denominator by x

[delicate flower]

that makes a 1/x in denominator which is x in numerator 😭

[livid sage]

yes that's the point

[delicate flower]

OH SHTI

aewioupe80rwupoidfu[pog

BRUHHHHHHHHHHHHHHHHHHHHHHHHH

[alpine sable]

Do ou know how to solve it @livid sage

[delicate flower]

i should kill myself

[alpine sable]

If yes , I will leave

[delicate flower]

this is literally the limit

💀

it makes the standard limit

right

[alpine sable]

Nvm ig

[delicate flower]

wait im trying

[alpine sable]

its 1

[delicate flower]

i know that

[alpine sable]

lol jee cringe memorize standard limits

ok

[delicate flower]

how will i memorize this

e^x - 1 / x = 1 is all i know

[alpine sable]

e^m-1/m where m tends to 0 is always 1

you can realize this by taylor expansion of e^x

[alpine sable]

thats you need to know

[delicate flower]

im not able to manipulate this into the standard limit man

[alpine sable]

and the question itself is a standard form

[alpine sable]

multiply divide denominator by x

[delicate flower]

did

i get
e^ (a/x) - 1

(a-1)/x

[alpine sable]

then where are you stuck

no standard limit won't work here

you will have to use taylor expansion

because its e^0/0

[delicate flower]

1+x+x^2/2!

and so on

[alpine sable]

yes

[delicate flower]

this one right

e^x

[alpine sable]

yes

yes

[delicate flower]

a/x + a^2/2x^2

a-1/x

[alpine sable]

whats a

[delicate flower]

sqrt and the thing

quartic

[alpine sable]

is ans 0

[delicate flower]

no its 1

😭

[alpine sable]

yes its 1

right

[hot hatch]

Is this done?

[alpine sable]

so just expand it

i am calling the sqrt (crap) - 1 = m

okay ?

[delicate flower]

m

[alpine sable]

yes

[delicate flower]

ok lemme write it

that way

[alpine sable]

so this is basically after expanding it x(( e^m/x)-1)/m

right ?

[delicate flower]

e^(m)/x - 1

m/x

[alpine sable]

no

[delicate flower]

wait you are calling sqrt (thing) -1 = m

[alpine sable]

yes

[delicate flower]

now

[hot hatch]

Hey, just use binomial theorem

Everything will get easily cancelled

[alpine sable]

no e^m/x

yes

[delicate flower]

am i drunk

[alpine sable]

it will nulify to 1

[delicate flower]

this is the standard

limit

what was i doing

[alpine sable]

yes

[delicate flower]

till now

😭

[alpine sable]

yes

[delicate flower]

idiot

[alpine sable]

no its not legal

[delicate flower]

real

thank you so much @alpine sable

[alpine sable]

yw

[delicate flower]

.close

[lone heart]

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[alpine sable]

You don't have to

[alpine sable]

yes if you know its expansion or we may just use Lh

Lh would be easier

Just saying

[elder forge]

u dont need to remember expansion also
u can derive from taylor series??

[alpine sable]

Topper

[alpine sable]

High school

No Taylor series

time consuming for examination but ys one can always generate a good polynomial approximation

[elder forge]

we were taught about taylor series bruhh

[alpine sable]

for that you would have to memorize generalized form of taylor polynomial or

[elder forge]

thts better than remembering the whol expansions list

[alpine sable]

go through tedious task of assuming a n degree polynomial

then equate derivatives of function

at a point

to get coefficients

so there are lots of ways i was suggesting something i find convinient

[elder forge]

mhm

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[zenith pilot]

im having issues to solve this any help? im really struggling understanding

[zenith pilot]

so i tried doing
2sin(x)^2= 1
sin(x)^2= 1/2 but then idk how to continue

but then i tried doing
-(1-2sin(x)^2)=0
and then a solver told me to transform it into - cos (2x) = 0 but WHY
so idk how to continue

[zenith pilot]

is that the double angle formula?

[remote hazel]

yup

[zenith pilot]

ok so wait

im stuck again

this is the solution

someone told me to add the last 2 together but idk how

[lone heart]

@zenith pilot Has your question been resolved?

[zenith pilot]

<@&286206848099549185>

[sullen pivot]

What was the original problem?

[sullen pivot]

I think that could be wrong

[hot crescent]

Right?

[sullen pivot]

You have many solutions

[zenith pilot]

ah

cuz thats the solution the book gave me 😭

[sullen pivot]

One of them is x=pi/4+2pik

[zenith pilot]

ye

[zenith pilot]

so is this wrong? i tried doing it from the cos 2x identity

[sullen pivot]

Also, you can replace and verify this

[sullen pivot]

Try to do by difference of perfect squares

[zenith pilot]

how would i do that? (a+b)(a-b)
(2sinx-1)(2sinx+1) ?

im trippin

[hot crescent]

how about just moving the 1 to the RHS and dividing by 2 to get sin^2 x = 1/2,
from there just solve for x

Didnt mean to reply to ur message

[sullen pivot]

Yes, but with the "sqrt" on the 2

[sullen pivot]

It looks nice

Im just saying that bcse you can find more solutions if You use other methods

[zenith pilot]

ahh

right

alr ty everyone i think i got it

.close

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[simple wyvern]

.reopen

[hybrid ravine]

how do you prove this

[sullen pivot]

You can use the "limit" definition of derivate

[hybrid ravine]

??

What's that

[elder forge]

Lt h is 0

[hybrid ravine]

ye i got that part

[hollow wren]

$f’(x) = \lim_{h \to 0} \frac{f(x+h) - f(x)}{h}$

[elder forge]

Yes

[hollow wren]

i’m typing this on my phone

[upbeat gorge]

It’s -f(x)

believe it’s x+h too

[ocean seal]

Potatomonke

[hollow wren]

i don’t like typing latex on my phone 😭

[sullen pivot]

Thiis @hybrid ravine

[left wharf]

yup, -h multiplies the derivative by -1

[hybrid ravine]

i dont get what to do after u plug in x+h into the f(x)

[upbeat gorge]

Show your work

[hybrid ravine]

uh hm idk how to type this

[upbeat gorge]

Screenshot of paper is fine

[hybrid ravine]

g(x+h)k(x+h)-g(x)k(x)/h

[hybrid ravine]

i dont hv phone on me rn

[upbeat gorge]

Ok

[sullen pivot]

Or search on YouTube

You can find nice proves

[upbeat gorge]

The idea is to add and subtract the same thing, and the plan is that you can factor out stuff and use the definition of the derivative again

[hybrid ravine]

Alright

I'll try it and see what happens

thanks

.close

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[violet pasture]

i don’t understand why i had to add 180 degrees to question 2

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@violet pasture Has your question been resolved?

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[hoary summit]

hey, a question that i couldn't find the answer by googling. Is there a technical name for a number that splits a set of numbers to have x% numbers higher than this number?

Like similar to how a median splits a set of numbers to have 50% of the numbers higher than said number.
In a way i'm looking for a technical name for a "variable" median

[olive yarrow]

percentile

[olive yarrow]

you can say the 5th percentile 92nd percentile and so on

[hoary summit]

yeah!
That's what i'm looking for

thanks!

.close

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[wet harness]

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[haughty swan]

if i do divergence test and the limit equals 0 do i consider it convergent or do another test?

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@haughty swan Has your question been resolved?

[subtle light]

the divergence test is inconclusive when the limit equals 0

divergence test can only prove divergence and not convergence, so yeah, do another test

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[alpine pivot]

Kinda need help with a lot of topics, got exams in 4 days, undergrad maths. Would super benefit from like a couple hours 1 to 1 going through questions. Willing to pay

[alpine sable]

I believe payment isn't allowed in this server.

[alpine pivot]

daym

[alpine sable]

<@&268886789983436800>

[hollow warren]

based pfp

[next brook]

Paid tutoring is allowed, as long as it doesn't mean paying to actually do homework.

[alpine pivot]

nah

i just wanna go through an aexam paper or 2 with someone

[next brook]

With the caveat that the server moderators will have absolutely nothing to do with disputes about whether the help provided was worth the price asked or not.

If someone takes your money and spews GPT nonsense at you, you're on your own.

[alpine sable]

What exam is your math

[alpine pivot]

topics are

• complex numbers
• Curvilinear coordinates
• differential equations
• Fourier series
• and some stats

[real gazelle]

you'd likely get better help if you just posted a question here that you want help on instead of asking for a tutor

[lone heart]

@alpine pivot Has your question been resolved?

[alpine pivot]

yeah but i want help on like 50 questions and want to know the details of working them out ygm

[real gazelle]

Yeah you might as well just post the first one you want help on and see if anyone wants to help you with it

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[alpine sable]

Is someone available to help me ?

[gray isle]

[alpine sable]

Well there are some problems that I have to complete in the math olimpics, that I have a really hard time solving. And as I dont know what category or type of problems they are I cant find videos nor forums explaining. I think there in some way solved by descrbing them in formula, but nevertheless I dont have that much experience in that subject in particular.

For example:

The sum of the digits of the number N is three times the sum of the digits of the number N+1. What is the smallest possible sum of the digits of N?

I write down a 4-digit number N = pqrs. When I place a decimal point between the q and the r, I find that the resulting number pq.rs is the average of the two-digit numbers pq and rs. What is the sum of the digits of N?

A student started with the number 1 and multiplied it by either 6 or 10. He then multiplied the result by either 6 or 10, and continued this procedure many times. Represent this problem in a formula.

[gray isle]

basic number theory i suppose

did you make any attempts for any of these?

[alpine sable]

Yes

But I cant find a solution that involves a fix formula based a make up by myself. I want to go prepared for the next exam with a more wide knowledge of how to visualize this problems in a formula based solution and not trial and error.

[gray isle]

show what you did

[alpine sable]

I dont have it on me, but I can show you how I would try to do it

I'll send it in shortly

[ocean hawk]

I don't have a principled way to do that one. but you should know what the last digit will be in order for it to work

[alpine sable]

Could you elaborate?

[ocean hawk]

for almost all numbers N, when you add 1, the sum of the digits of N + 1 will be greater than the sum of the digits of N. right?

for example if N = 7. or N = 93. or N = 853742. etc.

so what's the only way the sum of the digits of N can be greater than the sum of the digits of N + 1

[alpine sable]

There's no way right ?

[ocean hawk]

there is a way

[alpine sable]

Let check, a negative number wouldn't work

[alpine sable]

I actually don't know, what is it ?

[ocean hawk]

take just single digit numbers. see when the sum of the digits of N exceeds that of N + 1

1 won't work, because 1 < 2. same with 2, 3, ...

[alpine sable]

So they will never be the truly equal

[ocean hawk]

just think of when the sum of N exceeds the sum of N + 1

before trying to solve it

hint: N = 1, 2, 3, 4, 5, 6, 7, 8 does not work

[alpine sable]

Okay, let me see if I understand

N = (11 + 12)3

[ocean hawk]

I don't know what you are doing there

[alpine sable]

Im confused, because I dont understand what you mean with exceeds. How can a Value exceeds its one's self when it will always have one more unit above it ?

[ocean hawk]

because you are working with the digits of the numbers. not the numbers themselves. obviously, N < N + 1

but the sum of the digits of N can exceed the sum of the digits of N + 1

what if N = 8? what is the sum of the digits of N?

[alpine sable]

1 because there is only one digit being represented ?

[ocean hawk]

no

ok. how about N = 18

what is the sum of those digits

[alpine sable]

When you say sum of the digits, its saying 1+8 ?

[ocean hawk]

yes

[alpine sable]

So, 8

[ocean hawk]

ok and N + 1 = 9. the sum of the digits is 9, which is more than 8

what if N = 9. what is the sum of the digits of N

[alpine sable]

9 + 1 = 9

[ocean hawk]

no

[alpine sable]

wait

[ocean hawk]

N = 9. the sum of the digits of that number (there is only one digit)

[alpine sable]

So we ignore the 1 for now ?

[ocean hawk]

what 1? the number is just 9

I am asking one question. what is the sum of the digits when N = 9

[alpine sable]

N +1 = 9

9

[ocean hawk]

yes

then what is the sum of the digits of N + 1, when N = 9

[alpine sable]

10

[ocean hawk]

no. that is what N+1 equals

what is the sum of the digits

[alpine sable]

1

[ocean hawk]

yes

so when N = 9, the sum of the digits of N > sum of the digits of N + 1

now what if N = 19? what is the sum of the digits?

[alpine sable]

10

[ocean hawk]

yes

and the sum of the digits of N + 1, when N = 19

[alpine sable]

1

[ocean hawk]

no

if N = 19, what is N + 1

[alpine sable]

19 + 1 ????

[ocean hawk]

yes, which is?

[alpine sable]

20

[ocean hawk]

and what is the sum of the digits?

[alpine sable]

of 20 ?

[ocean hawk]

yes

[alpine sable]

2

[ocean hawk]

right

so when N = 19, the sum of the digits of N > sum of the digits of N + 1

do you see a pattern?

[alpine sable]

Yes

[ocean hawk]

what is it?

[alpine sable]

Ratio ?

[ocean hawk]

ratio of what?

[alpine sable]

Forget it, i dont know the pattern but I see what you were saying

[alpine sable]

Taking what you said

N = ab

N = a + b

3(a+b) > ab + 1

3(a+b) > a + b +1 = 3:1

[ocean hawk]

it's easier if you notice the pattern I was trying to show you

[alpine sable]

Give me another practice question to see if I can find it

[ocean hawk]

so we already saw that if N = 9, or N = 19, then the sum of the digits of N exceeds the sum of the digits of N + 1

try another

[alpine sable]

Lets check with N=29

N = 2 + 9

N= 11

ab + 1

11 +1

1+1+1 = 3

[ocean hawk]

no

[alpine sable]

why not ?

[ocean hawk]

N = 29, so the sum is 11. that is correct

but N + 1 = 30

[alpine sable]

Oh, because I just sum and then sum the digits

[ocean hawk]

yes

so N = 9, N = 19, N = 29 work. what does that tell you for this particular problem?

[alpine sable]

A number that contains 9 as its ones, always has its sum of the digits of N greater than N+1

[ocean hawk]

well, not just 9 in any digit. N = 90 doesn't work for example

9 has to be the last digit

[alpine sable]

the unit in other words

[ocean hawk]

ok, I don't know the term

[alpine sable]

My bad ones

I confused myself there

[ocean hawk]

so you want a number "a9" (or "ab9") such that a + 9 = 3(a + 1)

because when you add 1 to "a9" you get "(a + 1)0" as the next digit

[alpine sable]

Okay

So, 3(a+b) > a + b +1 = 3:1, has to contain a number that has as its last digit 9

N = 39

N = 12

1 + 2 +1

12:4

3:1

Finally I understand this problem

Thanks a lot @ocean hawk, I really needed the help

Would you let me send you a friend request incase I have any other doubts?

[lone heart]

@alpine sable Has your question been resolved?

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[bold sedge]

hello

[bold sedge]

could I please have some help with this question

I understand I am going to have to rearange absinC/2

to calculate d

which I believe is 34.03

so now I need to use sin rule

but Im not sure what im doing

<@&286206848099549185>

please

<@&286206848099549185>

[half epoch]

Do you know the area formula with sin?

[bold sedge]

is it not this

[half epoch]

Yes, but write it using the sides of the triangle acd, and the one angle we know in that triangle

[bold sedge]

yes so it would be 25 times sin39 times d / 2

[half epoch]

26

[bold sedge]

yes sorry

[half epoch]

But yes

[bold sedge]

so if i rearange

[half epoch]

Now set that equal to the known area and you will find d

[bold sedge]

yes

34.03

but I dont know what to do from here

[half epoch]

Now we use law of sines to find the length of |AB|

[bold sedge]

a/sinA = b/sinB

[half epoch]

We know the side that faces the angle B and we know the angle that faces the side |AB|. So write it in terms of that

[bold sedge]

34/sin95 = c/sin47

[half epoch]

Exactly. All that remains is to rearrange to get c

[bold sedge]

and then multiply

ok

23.71

so now I have two edges and two angles

do I just pick three and find area

[half epoch]

Many ways to do it. I would calculate the remaining angle and then calculate area with sin again

[bold sedge]

38

and then I just put that into the area formula

[half epoch]

Yep

[bold sedge]

but im missing

a

[half epoch]

At the very end you need to sum up the area of the two triangles and you'll have your answer

[bold sedge]

acc nvm im stu[od

idk

that seems wrong

but maybe not

im getting

248.15

plus 250-

[lone heart]

@bold sedge Has your question been resolved?

[lone heart]

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[lone heart]

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[alpine sable]

Heelo,I'm back again

[alpine sable]

Could a kind soul assist with this question of numericals??

<@&286206848099549185>

🍃

[exotic belfry]

!15min

[lone heart]

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.

[exotic belfry]

write the number as ab (a and b are the digits). then use the gien information two write formulas in a and b.

[slow parrot]

The original two digit number can be written as 10x + y where x is the tens digit and y is the ones digit

[alpine sable]

Hmm...ok lemme see if I understand

So basically ab are is the rep for the 2 digit number?

[exotic belfry]

yes

[alpine sable]

Oh ok ok

[alpine sable]

Huh?

[exotic belfry]

its the same using x and y instead of a und b

21 = 2 times 10 + 1

[alpine sable]

Oh but why multiply by 10 ?

[exotic belfry]

for example 21 = 2 times 10 + 1

[prisma cosmos]

because its place value is 10

like number 213
2 is 200
1 is 10
3 is 3
so 2(100)+1(10)+3(1)=213

[alpine sable]

Hmm...okay...

[prisma cosmos]

so this

[alpine sable]

Why add one tho?

[prisma cosmos]

now based on the questions, the ones digit exceeds twice the tens digit by 2

[alpine sable]

Yeah?

[prisma cosmos]

so form an equation

[exotic belfry]

21=2 times 10 + 1

[prisma cosmos]

he meant 2(10)+1=21

[alpine sable]

By they said by 2 not 1

[exotic belfry]

21 was an example for the notation of 10a+b

[alpine sable]

...

[prisma cosmos]

.

what u dont understand abt

[alpine sable]

So 2 (10)?

[prisma cosmos]

yes

thats an example

[alpine sable]

But why they say twice and by 2?

[prisma cosmos]

thats an example, different from questions

nothing related

just let u know how the 10x+y comes

like

53=5(10)+3
88=8(10)+8
75=7(10)+5

[exotic belfry]

Too many cooks spoil the broth, so i am leaving. if interested in my help dm me.

[alpine sable]

Oh ?

[alpine sable]

Okay,bye...thxs for the help so far

[alpine sable]

Oh this is like before any other calculations are added just the basic?

So y = 20x +2?

Huh?

So everyone dipped?

[prisma cosmos]

hi

thought u ran away

lets repeat again uh

[alpine sable]

Nope still here,it was the wifi

[prisma cosmos]

so this
The original two digit number can be written as 10x + y where x is the tens digit and y is the ones digit

u understand?

[alpine sable]

Yeah

[prisma cosmos]

ok

second instructions of the question

the ones digit exceeds twice the tens digit by 2

so what equation u could formed here

where x is the tens digit and y is the ones digit based on above

[alpine sable]

20x + 2 = y?

[prisma cosmos]

no

why u got 20

[alpine sable]

Twice?

[prisma cosmos]

yess

its simple
the ones digit exceeds twice the tens digit by 2
means
y exceeds twice x by 2

so what would u formed

[alpine sable]

2x+2=y?

[prisma cosmos]

yessss

gud

now lets go through

the third instructions

when digits are reversed

so our original 2 digit was 10x+y

now its reversed

so what u have now if ones digit and tens digit reversed

[alpine sable]

b+10a?

[prisma cosmos]

no

[alpine sable]

y+10x

[prisma cosmos]

10x+y is same as y+10x

u changed nothing

now the position of x and y changed right

so what changes u got from 10x+y

[alpine sable]

Oh so 10y +x

[prisma cosmos]

yess

now lets go through

when digit reversed the number formed exceeds twice the original number by 7

so

the number that digit reversed from is 10y+x

and original number is 10x+y

[alpine sable]

10y+x +7

[prisma cosmos]

so what equation here u can formed

[prisma cosmos]

yes

twice

the original number

so?

[alpine sable]

Hmm?

[prisma cosmos]

this is half correct

bcz the question mentioned exceed twice

by 7

so?

[alpine sable]

So multiply by 2?

[prisma cosmos]

hi

[alpine sable]

As in 2(10y+x)+ 7...?

[prisma cosmos]

yes

yes

yes

[alpine sable]

Sorry by the way

Lost connection again ☁️

So then what next?

[prisma cosmos]

yes

make it complete

what equal to 2(10y+x)+ 7.

[alpine sable]

So I equate it to the og one?

[prisma cosmos]

yes

what u got

[alpine sable]

20y +2x +7 =10x+y?

[prisma cosmos]

yes

[alpine sable]

Then I substitute the 2x+2=y in it right?

[prisma cosmos]

now this

yes

and solve for x and y

now the two digit number is xy

[alpine sable]

That was all?

[prisma cosmos]

yes

[alpine sable]

Thank you for helping me again 🌼🌼🌼

[prisma cosmos]

alr

[alpine sable]

.close

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[dire gale]

Question C:

will the solution be like this:

x = 2
f^-1(x) = x/2

then f^-1(g(x)) = (x^2 + 2) / 2?

[ocean hawk]

looks right

[dire gale]

.close

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as this action is irreversible, and this channel may abruptly lock.

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[hollow bay]

Question b

I said DNE becuase g(x) has 2 different values as X approaches 0

[buoyant saddle]

yes the left and right hand limits aren’t the same

[hollow bay]

only for g though

[buoyant saddle]

mhm

but

for f-g

it’s the same

f-g from the left of 0 is -1

f-g from the right of 0 is 1

-1≠1

so the lim doesn’t not exist

[hollow bay]

wait how did u get this

[buoyant saddle]

2-3

and 2-1

[hollow bay]

f-g from left of 0 is -1?

[buoyant saddle]

yes

[hollow bay]

oh i see

i was doing it completely wrong

[buoyant saddle]

did you use the actual values

where the filled in holes are

[hollow bay]

no i was just saying that there is no limit for g(x) because it ends up at 2 different y values as it approaches 0

i thought that meant there is no limit for g(0)

[buoyant saddle]

well it was for f-g

and yes because the left and right hand limits don’t exist for g the lim doesn’t exist for f-g

[hollow bay]

ok so either way is acceptable

[buoyant saddle]

you have to be careful though

[hollow bay]

y

[buoyant saddle]

always look at the function itself rather than just one of them

because that’s what it’s asking

it’s more serious if you’re trying to prove continuity

where there’s an another condition that lim x->a (f(x)) exists and f(a)=L

where L is the limit

[hollow bay]

im not familiar with all the laws or theorems

ill be doing continuity in like 15 minutes though

i have to ask though because im still uncertain... since g(0) is not the same coming from left and right sides that means there is no limit at g(0), correct? @buoyant saddle

and since the entire equation is asking f(x)-g(x) that means you cannot have 1 - DNE

or ARE you sayuing that i need to actually show the work for f(0) - g(0) for both of the g values to show that it they are not the same values...

or does it automaitcally imply that since g(0) DNE then the entire thing DNE?

@buoyant saddle are you there?

[buoyant saddle]

yea my fault

[buoyant saddle]

yes

in order for the lim x->a to exist the limit x->a^- = lim x->a^+

in other words it must approach the same value from both sides

[buoyant saddle]

you should show this yes

[buoyant saddle]

so long as the lim exists for f

[hollow bay]

so is f exists i stilll need to prove entire thing even if g DNE

[buoyant saddle]

you should just evaluate the whole function

[hollow bay]

ok

[buoyant saddle]

whether it’s f-g

f+g

g

f

doesnt matter

[hollow bay]

ya

[buoyant saddle]

because that’s what it’s asking for

[hollow bay]

that makes sense

so in words how can i explain that

.close

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[carmine rapids]

when solving with a quadractic formula

do I keep simplifying?

or do I stop at 12 in this example?

oh wait the 108 is wrong

.close

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[mild fractal]

firstly i have no idea how to solve it

secondly i didnt get the solution at all either

where did the a^x go, and what doe sthe r^x represent and well where did that come from-

and they divided by a^2 without multiplying by a^2???

[rose void]

You can approach it quantitatively

The approximation for sinz when z is really small is simply z. And since z= b/a^x then the a^x cancel. Thus, leaving us with b as the final answer

The reason why sinz = z when z is really small is due to the Taylor expansion of sinz

[mild fractal]

ohhh

bruh

this is literally the first time am using that physics tidbit here

[rose void]

Lol

[mild fractal]

and it's incredibly annoying how obvious of a trial and error approach it was

[rose void]

Yeah

[mild fractal]

anyways, thankyou :D

[rose void]

Np :)!

[mild fractal]

.close

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[upbeat anvil]

im using spherical coordinates and i am trying to rotate the whole sphere by a given theta and phi. at first i assumed i would just have to add the theta and phi to every coordinate however this doesn't work. does anyone know how i could rotate the sphere?

[upbeat anvil]

or any good sources that could point me to a formula? so far i haven't found anything

[lone heart]

@upbeat anvil Has your question been resolved?

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@upbeat anvil Has your question been resolved?

[tender shell]

.open

.open

When I did it I found x= 0 and y = -4 but it’s false can you help me pls

I have like 1h left

[vast ether]

Its french i cant understand it

[tender shell]

Ok imma try to translate

We know that A(-2;4) B(1;-4) and C(-2;-1) we ask you to find coordonner of (x,y) of point M that AM=BC

Solution has to be wrote like x=…. And y=….

[vast ether]

BC is a line right?

So is AM

If these 2 lines are equal then they have the same equation.

Find slope of BC since both B and C are given

-2-1 divided by -1-(-4)

= -3/3 = -1

Slope of BC is -1 , use ((y-y1 = m(x-x1)) to find equation,

You can use either point B or C but you must input x and y value respectively

Im gonna use C

y-(-1)= -1(x-(-2))

=> y+1=-1(x+2)

=> y+1=-x+2

Both sides minus one,

y=-x+1

[tender shell]

Ok ty I’m learning this cuse I did this before and that was wrong

[vast ether]

so now we have BC and it equals AM, so that both x and y values for them are equal,

We also have A

y=-x+1 , equal a line we dont know that passes through (-2,4)

You can input basically any point that passadans the linear equation

Since if two lines are equal, the distinction "two lines" is meaningless, it is the same line, we are referring to one thing

[tender shell]

Wow ok I try to understand and I text you back

Bro I don’t understand sorry

Hooo I understood

I found x=-5

Y =7

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[fleet spire]

I am having trouble doing review for calc 2

[remote hazel]

what have you done so far

[fleet spire]

I understand how to graph the region and many principals but I beleive I am messing up on the small stuff

is there any way someoone could watch me do a problem to see what I am doing wrong

[remote hazel]

you could send you work here

[fleet spire]

Yes i can but is it possible for me to call u so i can share my screen

it would be a lot quicker

[remote hazel]

sure

[fleet spire]

just sent u a friend request

thank you so much!

[clever cloud]

Help number 141

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[rapid basin]

hey

[rapid basin]

i dont understand this

[tepid dock]

what is a value for theta that suffice the equation?

just looking at the question, what would work?

[rapid basin]

80

[void nymph]

lmao yes

another one?

[rapid basin]

so i put it in a cast diagram

[void nymph]

mmmmm sure

[rapid basin]

and i got 280

but thats wrong

[void nymph]

yeah

that's not wrong lmao

[rapid basin]

it says answer is 320 so i dont understand

[void nymph]

,wolf cos(280) cos(60) in degrees

[ocean seal]

Results provided by WolframAlpha

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Upgrade to WolframAlpha Pro!

Requested by percykel

[void nymph]

oh not that.

,wolf cos(280) in degrees

[ocean seal]

Results provided by WolframAlpha

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

Requested by percykel

[void nymph]

ffs

[sly nacelle]

don't forget to subtract 20 degrees from θ

[void nymph]

OH

I didn't do that lmao

yeah right

[sly nacelle]

cos(300) = cos(60) in degrees

they add up to 360

and since you have to subtract 20 from θ to get 300, θ is 320 degrees

[void nymph]

yeahyeah

[rapid basin]

why dont we add 20 as we bring it to the other side

[sly nacelle]

add 20 to θ? what do you mean?

[rapid basin]

cosθ - 20 = cos 300

cosθ = cos 300 + 20

wai

wait

lol

thats the answer

[sly nacelle]

the 20 is inside of cos(), it can't be moved like that

[rapid basin]

oh i did something else wrong

wait

isnt the other answer cos(300)

so we can just add 20

[sly nacelle]

since both sides are in cos() in
cos(θ - 20) = cos(300)
you can remove the cos
θ - 20 = 300
θ = 320

[rapid basin]

ohhh

thank you

[sly nacelle]

but removing the cos isn't always the best thing to do

[rapid basin]

thank you so much i understand

[rapid basin]

ye

.done

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[tiny dome]

hello

[tiny dome]

how can i solve a problem like this

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@tiny dome Has your question been resolved?

[tiny dome]

no

[amber elm]

You could attempt to calculate the horizontal and vertical displacement of the plane

[tiny dome]

oh?

how can i do that

[amber elm]

You would probably need to use trigonometry

A first step would be to calculate the distance that the private plane flies in the first 2.1 hours

And also the distance it travels in the next 2.8 hours

Because the path of your plane looks something like this

Where the green line is the length the plane travels from A to B

and the purple line is the length the plane travels from B to C

Added angles

[lone heart]

@tiny dome Has your question been resolved?

[tiny dome]

hmmm

i understand it

so basically

you multiply 2 hr (110) = 220

same with 2.2 (110) = 242

now you do the pt formula

after square rooting it, you get 385

well this is for a diff answer

can someone show me how to solve this

[amber elm]

To find an angle that is coterminal with another, you can simply add or subtract 2π

This problem is essentially asking you to subtract $2\pi=\frac{20\pi}{10}$ from $\frac{49\pi}{10}$ until you get a value that satisfies $0<x<2\pi=\frac{20\pi}{10}$

[ocean seal]

otheol

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@tiny dome Has your question been resolved?

[tiny dome]

no

actually

imma ignore that question

i have a different question

how do i evaluate something like this?

@amber elm

[tiny dome]

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[prisma escarp]

LOOKING TO SOLVE F(X,Y) = 2X^2 -Y^2 +6Y WITH DOMAIN --> D: (X,Y) = X^2 + Y ^2 LESS OR EQUAL 16 . NEED TO FIND THE MINIMA AND MAXIMA OF THE CRITICAL POINTS...Hint: derivate, cos properties.

[glad reef]

How do i do this pls help

i have to write a 10 page paper on it

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[strange fractal]

Excuse@me

[strange fractal]

Did i do dis right

[wheat isle]

BUMMM CHICKEENNNN

[strange fractal]

HI

R u home for exam break

[wheat isle]

BUMMMMMMMMMMMMMMMMMMMMMMMMM CHICKEEEEEEEEEEEEEEEEEEEEN

[wheat isle]

no im just home because im sick

[empty moth]

Bummmmm chickennnn

[strange fractal]

how do i do dis

question 14b

[wheat isle]

GG

[strange fractal]

i got it.

[wheat isle]

oh ur welcome

glad i could help

[strange fractal]

u took too lon

[wheat isle]

no problem

i should be helper anytime soon now

[strange fractal]

how i do cii

[wheat isle]

gg

[strange fractal]

hELP

.close

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Please don't occupy multiple help channels.

[alpine sable]

Where did I go wrong?

[elder forge]

Which q

[alpine sable]

13

[elder forge]

It's not possible

U cannot satisfy both the 45 degree and 100N simultaneously

If u consider angle is 45 then resultant will be 60root2

If u consider resultant to be 100 then other vector will be 40 then angle is not 45

[swift musk]

I think they mean the 60 N force is at 90 degrees

and your force can be in any direction

[alpine sable]

ahhh

so like it could be west

so it would change the bearing

I got the N part correct the bearing they gave was 278.5

what did they calc for 278.5

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@alpine sable Has your question been resolved?

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