help-26

[sullen river]

and x + y = 12

can i manipulate the bottom equation to be 3x + 3y = 36

and eliminate the y variable to solve for x

[deep forum]

that works

[meager glacier]

Yes

[sullen river]

are there like many many ways to do this?

[deep forum]

or just y=12-x

[sullen river]

ok thanks

[meager glacier]

Yes

[deep forum]

and you plug that in

here

[sullen river]

and

whatever value you get for x or y

whichever one you did first

can you just plug that valuje into either equation

cause in systems of equatiosn your gonna have two equations

it doesnt matter right

[deep forum]

yeah

great problem btw

[sullen river]

ahh

thanks

i figured it out

help

i need help with making the two equations

you have 15r + 20v = ?

do you just combine the two numbers

2r + 4 = 3r + 1

like that?

[topaz sinew]

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[sullen river]

no

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[sullen lake]

how would i integrate y" = 2yy' ?

[loud oasis]

you don't have to solve it yourself, you have to demonstrate that if you let y = tan x then both sides of the equation are true, and the values for y and y' at x = pi/4 are accurate

[sullen lake]

got it, thank you

.close

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[burnt summit]

How can we approach this

[pastel oracle]

what do parts a and b say?

[honest jungle]

can we call a and b complementary or is that incorrect?

[topaz sinew]

@burnt summit Has your question been resolved?

[pastel oracle]

try using the result from part b

letting x = a + b

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[onyx lance]

hi

[onyx lance]

(-2w-1) + (w+1)i = 0

does that mean -2w - 1 = 0 so w = -1/2 and w + 1 = 0 so w = -1

otherwise why did they equate 3a+b-4 to 0 and -8-4a to 0

[teal gust]

uh

w cant take two different values

[teal gust]

that is right

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[onyx lance]

.reopen

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✅

[onyx lance]

ok one sec

I’ll be eight back

right

[onyx lance]

oh

so I can’t equate it if one of the bracket includes a variable that’s included in both brackets?

if that make sense

[teal gust]

you can equate it

its just that your example doesnt make sense

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[hearty tundra]

uh sorry

[vale fulcrum]

na -- crazy timing

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[vale fulcrum]

In a game of chance, six cards numbered 1 to 6 are lying face down on a table. Two cards are selected without replacement and the sum of both numbers is noted. State the total number of outcomes.

.close

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[grave hedge]

Can someone help me with this question? I am doing it wrong and idk how to work it out

[pastel oracle]

where did "2a - b = 2" come from?

[topaz sinew]

@grave hedge Has your question been resolved?

[grave hedge]

this

i thought that was meant to equal 2 from the zero of 2

and anyways i did it wrong so im looking for help on how to do it

[neon iron]

what does "monic" mean?

[grave hedge]

1

[pastel oracle]

no it means that f(2) = 0

[grave hedge]

ooh so then its 2a-b=0?

[pastel oracle]

no...

the whole function evaluated at x=2 equals 0

[neon iron]

the step "2a - b=2" is wrong

[neon iron]

[pastel oracle]

we've covered that

[neon iron]

oh

[grave hedge]

so i make the whole equation equal 0 after subbing a=1-2b?

and find b first?

[pastel oracle]

yes, try that

[grave hedge]

This?

What do I equal it to

[pastel oracle]

you didn't use the fact that 2 is a zero of the function

and the second term should be x^2, not x^3

[grave hedge]

so i sub 2 into x

[pastel oracle]

yes

[grave hedge]

This? Did it do something wrong in this

[pastel oracle]

that's right

[grave hedge]

so i sub b into a=1-2b?

[pastel oracle]

yes

[grave hedge]

and it equals -1/2?

[pastel oracle]

you have enough to finish the rest

[grave hedge]

thank you

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[neon iron]

hey! I have a math question about permutations and combinations can anyone help?

[neon iron]

4. A staff car park at a school has 10 parking spaces in a row. There are 7 cars to be parked.
   • How many different arrangements are there for parking the 7 cars and leaving 3 empty spaces?

Is it supposed to be 10P7 or 10P3? and why so? Thanks!

---

Find the number of ways that the letter in “NATIONALITY” may be arranged if the two N’s and two I’s must be together.

and is this correct? thanks!

[dense crescent]

see u are selecting 7 from 10 in 10C7 and then shuffling them in 7!
so it will be 10C7*7!
which is 10P7

[dense crescent]

it is 9!/2!2! so im getting 90720
is that right?

[cursive patrol]

it is 90720

[dense crescent]

yep

[neon iron]

oh wait what? hahaha do you mind giving me the working way? I'm confused

[dense crescent]

consider NN to be 1 unit

II to be 1 unit

and other letters, each to be 1 unit

u have 9 things

u shuffle them in 9! ways

but since there are 2 T and 2 O u divide by 2!2!

[neon iron]

NATIONALITY

NNII ATOALTY = 8

NNII = 1
A = 2
T = 2
O = 1
L = 1
Y = 1

[dense crescent]

count again its 9

[cursive patrol]

NN and II are separate

[dense crescent]

yep

[neon iron]

oh so i shouldn't make them together? I thought because the question said "two N’s and two I’s must be together" hahaha. I'm really confused sorry my teacher taught this method

based on the question

[cursive patrol]

both of us interpreted that to mean “if the two Ns are adjacent and if the two Is are adjacent”

since that is more commonly how this type of problem is set up

[neon iron]

ahhh alright, I'll keep that in mind. Thanks! it was really clear

[cursive pollen]

Hey can you take a look at my help ticket? #help-16

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[ornate magnet]

a_n+1 = (a_n+1)/(a_n+2)
a_1 = 2

[ornate magnet]

How do we find a_n in terms of n?

[spring nacelle]

is that $a_{n+1}$ on the LHS of the first equation

[thorny flame]

tim

[ornate magnet]

Yes

[spring nacelle]

or $a_{n} +1$

okay

and on the right hand side

is the notation similar

or is it

[ornate magnet]

No on right side it is an + 1

[spring nacelle]

okay

[ornate magnet]

Same with denominator

[spring nacelle]

okay

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@ornate magnet Has your question been resolved?

[spring nacelle]

you may want to start by finding a formula for a2

and a3 recursively

and see changes in the behavior

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[fossil haven]

Hi

[crystal grail]

Interesting

Not quite sure, I found that sum or first row = sum of second row = 9, sum of third row = 18 so sum of 4th row might also = 18 which leads to ? = 0

[cursive patrol]

one interpretation is to look at the diagonals going from top left to bottom right

[crystal grail]

Oh that makes much more sense

Ignore what I said lmao

[topaz sinew]

@fossil haven Has your question been resolved?

[fossil haven]

The book said it was a. 0 but this was another way

but can yall help me how to get the books answer

[crystal grail]

Did the book provide it's logic

[fossil haven]

nope

[crystal grail]

This does give 0 but it's a very rough estimation

[fossil haven]

kk, can yall help wit this

[crystal grail]

Are the circle and square also numbers?

[fossil haven]

theyre binary operations

so their special operators that do a special operation

[crystal grail]

Oh

So either "+", "-", "*" or "/"? (If I am understanding correctly)

[fossil haven]

nope

if 8 circle 16 is someting

and circle is a*b+a

8 is a

16 is b

solve the operations

and u get the answer

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[neon iron]

[hollow plover]

Bro

I dont trust you

[neon iron]

lemme ss

[hollow plover]

, rotate

[hollow plover]

Which one ?

[neon iron]

both

[hollow plover]

lets do 5 first ok

[neon iron]

ok

[hollow plover]

Tan ø = opposite /adjacent

So tan 60° = O/5

Or O = 5×tan 60

Now area = 1/2 × base × height = 1/2 × O × 5

Okkk ?

[neon iron]

yes

[hollow plover]

Now do the other similarly

[neon iron]

ok lemme try

[hollow plover]

Sin60 ° = you know opposite/hypo

So use that

[neon iron]

yes

[neon iron]

what does √3

do

[hollow plover]

O =

So tan 60 = √3 useful here

[neon iron]

ok

so

(25√2)/2

?

@hollow plover

[neon iron]

yes

ok

what about q 6

@neon iron

[neon iron]

cos(60°) = 6/x
solve for x

lemme try

x=12?

bc cos 60 = 1/2

yes

thats all?

yea it's just basic trigonometry lol

ok thx

urwelcome

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[fallow heart]

What's the question?

[topaz sinew]

@neon iron Has your question been resolved?

[fallow heart]

Yeah let me think a little

[topaz sinew]

@neon iron Has your question been resolved?

[fallow heart]

I haven't come up with any idea, so far

Wait a moment, is there 2tanx before 8cosx or not?

Because you wrote two different things in the messages, I don't understand which one is the right one

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[grim sable]

ik you can simplify the logs

so

$\frac{2(\log{2} + \log{y})}{\log{x}} = \frac{2(2\log{2}+\log{z})}{\log{2} + \log{x}} = \frac{3\log{2} + \log{y} + \log{z}}{\log{2} + 4\log{x}}$

[thorny flame]

Dork9399

[grim sable]

but idk where to go from here

btw this is 2012 AIME I p9

<@&286206848099549185>

[shy sparrow]

@grim sable Could you resend the question and if there are options send them too

[grim sable]

this is the question

there are no options

it has to be an integer from 0-999

<@&286206848099549185> help?

[trim owl]

I ain't helping u...no one helps me🫵

[shy sparrow]

Gimme some time

I'll try

[shy sparrow]

Yo sad life

[grim sable]

then why are you a helper?

[dim pulsar]

https://artofproblemsolving.com/wiki/index.php/2012_AIME_I_Problems/Problem_9

[grim sable]

i don't want to look at the sol

i want a hint

[shy sparrow]

There are 3 expressions as we know so they can equate to any common value (Not 0) like 2 lets say cause that way its easier

[grim sable]

ohh

i got it

thx

.close

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[shy sparrow]

Happy to help

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[fallow wharf]

?

[fallow wharf]

Guys is the zeroes of the equation correct

?

[pastel oracle]

plug in some values to the original equation, see if they are valid

[fallow wharf]

WIt

*wait

Can I show you the wavy curve of the equation

Hey?

<@&286206848099549185>

[shy sparrow]

Q please

[fallow wharf]

I want an explanation

Is the zeroes of the equation correct

@shy sparrow

[shy sparrow]

Which

[fallow wharf]

Q.b)

?

[pastel oracle]

plug in t=0 for example. does it satisfy the inequality?

[fallow wharf]

Yeah

[shy sparrow]

Yeah its correct

[fallow wharf]

And

If t=|x|

Then

Then also is it correct??

Guyz??

@shy sparrow @pastel oracle ??

Will it make any difference

[shy sparrow]

Do it and check

[fallow wharf]

.close

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[warm beacon]

WHAT IS THIS QUESTION PLEASE HELP ME HOW DO I SOLVE THIS????

[static scarab]

set up a system of equations withe the points

[warm beacon]

Wdym

[static scarab]

$ax^2 + bx + c = y$ where $x,y$ is the coordinates to your points

[thorny flame]

caspar

[warm beacon]

So I replace all the points?

[static scarab]

if you take the point $(-2,-11.5)$ the equation would be $4a -2b + c = -11.5$

[thorny flame]

caspar

[warm beacon]

How?

Like this

[static scarab]

$ax^2 + bx + c = y$ sub in $x = -2$ and $y = -11.5$

yes

[thorny flame]

caspar

[warm beacon]

so I find c?

[static scarab]

do that for all the points you have been given

[warm beacon]

then after I get all the numbers what do I do

[static scarab]

at this point you cant find anything, as you have 3 unknowns and only one equation

you will have to set up the rest aswell

[warm beacon]

wait I don’t understand

[static scarab]

$4a -2b + c = -11.5$ is the equation that you got from $(-2,-11.5)$, now you will need to do the same for $(0,-2.5)$ and $(4,-20.5)$

[thorny flame]

caspar

[warm beacon]

Wait how do I solve the equation

Using completing square or quadratic formula or what

[static scarab]

to solve for $a,b,c$ you will need 3 equations, the other 2 you get from the points given in the task

[thorny flame]

caspar

[warm beacon]

?????

I’m lost

[static scarab]

have you learned how to solve sets of equations?

[warm beacon]

ya Ik completing square and quadratic formula and factoring

[static scarab]

x+y = 2 and 2x-y = 1 for example

[warm beacon]

What?

[static scarab]

like these

[warm beacon]

No

[static scarab]

what topic are you learning in math at the moment?

[warm beacon]

Like

Solving quadratic equations

[static scarab]

probably supposed to solve it differently

[warm beacon]

This is in my final

And I think I’m gonna fail

[static scarab]

you could always just plug in the values and see if they fit

[neon iron]

actually you don not need to solve quadratic, you have 3 unknowns a,b,c and after obtaining 3 equation which will be linear hence you can solve with 3 eq. with 3 unkowns

[warm beacon]

What??????

[neon iron]

1.put values of x and y in all options and check which one is satisfying all points, that will be your answer
OR

2. use what @static scarab just said

[warm beacon]

so my answer is

This???

[neon iron]

do you need to show them steps? or they just want answer?

[warm beacon]

Yes just the answer but how do I get the answer tho

In the answer sheet it says it’s c but I don’t understand how we got c

[neon iron]

put the values of x and y in that option,if it satisfies for all x and y that will be your answer

[warm beacon]

Ohhhhhhhhh is the solving systems like eliminating or substituting???

[neon iron]

yes either you can solve it directly

[warm beacon]

No the final isn’t multiple choice

Okay how

Do I solve

Directly

Pls explain

[neon iron]

just like you did for x1,y1
there are other two points, put them in similar fashion you will get another 2 eq.

[warm beacon]

So after that

[neon iron]

okay first write all 3 eq.

[warm beacon]

Wait I will try to solve

1 min

????

Please help me I’m gonna cry

What is this

I don’t wanna fail

[static scarab]

ok, now you have 3 equations

what information can you get from the 2nd one?

[warm beacon]

That c=-2.5

[static scarab]

then plug in for c in your other equations

[warm beacon]

Okay then

[static scarab]

good, now you will need to try and find a

[warm beacon]

How

[static scarab]

like you would solve for x in an equation

[warm beacon]

So it’s 4x-2x-2.5=-11.5

??

[static scarab]

more like $4x-2y-2.5 = -11.5$

[thorny flame]

caspar

[static scarab]

then move everything thats not x to the other side

[warm beacon]

so then after it

[static scarab]

you will get $4x = 2y - 9$

[thorny flame]

caspar

[warm beacon]

then

[static scarab]

$x = \frac{y}{2} - \frac{9}{4}$

[thorny flame]

caspar

[warm beacon]

why

how did this happen

[static scarab]

i divided by 4 on both sides

[warm beacon]

u divided two

[static scarab]

?

[warm beacon]

Can u hop on call I don’t understand

Also what is this

I understand the factoring part but how do I use the factored form to find the vertex

[static scarab]

have you learned a formula for finding a vertex?

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@warm beacon Has your question been resolved?

[topaz sinew]

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[upbeat minnow]

If a derivative $f'(x) > 0$ does that mean it is increasing?

[thorny flame]

dingypine

[gleaming reef]

Yes f is increasing

[upbeat minnow]

ok thank you

.close

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[old prism]

i need help with x/2 +4=2x/3 i get rater 2.25 or 4
the answer is 24

[viscid lodge]

Multiply everything by 2 to get x + 8 = 4x/3

Then multiply everything by 3 to get 3x + 24 = 4x

Then subtract 3x from both sides to get 24 = x

[old prism]

how to kow hvat to do

[viscid lodge]

I always start with the denominators

[old prism]

?

[viscid lodge]

It does not matter which order you multiply them, whether it's multiply by 3 then by 2 or vice versa, but start with denominators, be careful not to make any mistakes and remember to multiply EVERYTHING on both sides to cancel out the denominators then work through the rest as you would with basic equations

Basically cancel out the denominators first, so if there are fractions multiply by the bottom, then go through the rest of the steps

[old prism]

but multiply with 3 with 4x/3 isent tha 4x?

that

never mind

thanks for the help

[viscid lodge]

No problem

[tawdry herald]

When you see a division that is bothering you, you need to neutralize it with a multiplication

x/2+4=2x/3

The /2 and /3 are bothering us so we can multiply both sides by 2 and by 3 to get rid of them
Thats how you know what is a good move

Of course you dont need to do that, you can do anything you like

But this is a smart move

Just like when you see a minus, you neutralize it with a plus

Like y - 2 = 5

The "good move" is to +2 both sides
y - 2+2 = 5+2

So y = 7

[old prism]

what dose 2/5 of 400 mean

ok

how to solv 2/5 of 400

[craggy haven]

multiply fractions

$\f25 \times \f{400}1$

[thorny flame]

hayley

[craggy haven]

multiply the tops and the bottoms, so

$\frac{2\times400}{5\times1}$

[old prism]

?

[thorny flame]

hayley

[old prism]

?

[craggy haven]

i don't know what more there is to explain.

you're going to need to use your words.

[old prism]

how to get the anwver from that

ok i get it

but how to know to do 5*1

[craggy haven]

well 400 is 400/1

[old prism]

?

ok

so i do that to all

[craggy haven]

a very large part of math is using rules to transform problems you don't know how to do, into problems you do know how to do

[old prism]

.close

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[twin galleon]

i dont even know where to start this question

[nimble hemlock]

start by listing facts you read (provided in the question)

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[charred belfry]

Three identical spheres are in a hemisphere with radius 15 such that the spheres are tangent to each other and the hemisphere and the plane containing the centers of the spheres is parallel to the flat face of the hemisphere. A smaller sphere is placed on top of the big spheres that it is tangent to the other spheres and hemisphere. Find the radius of the big spheres and of the small sphere.

[charred belfry]

Drawing

side and front view

[topaz sinew]

@charred belfry Has your question been resolved?

[craggy haven]

good problem tbh

figure out where the 3 circles are first ofc

there's one variable which is how far away are they from the hemisphere edge on the xy plane

or how far away are they from each other, or a few other options for variables

[charred belfry]

<@&286206848099549185>

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[hoary hedge]

i dont really understand how to solve cubics like y=x^3-2x^2-x+2

[craggy haven]

factor by grouping

that doesn't always work but it will in this case

[hoary hedge]

by grouping the x value out?

[craggy haven]

y = (x^3 - 2x^2) + ( -x + 2)

GCD factor the thing on the left

[jade thunder]

When people give you a general cubic to solve it’s either doable by inspection or you just plug it into a formula

[hoary hedge]

what is inspection? i saw it in my textbook but didnt understand

[jade thunder]

You look at it

And see the answer

Like if I asked you what’s 8 + 5

You don’t count your fingers

[hoary hedge]

mhmm

[jade thunder]

You just inspect the answer to be 13

[hoary hedge]

oh i see

[wet cypress]

by inspection I think he means just subbing in values

which you can further reduce the guess and check by testing factors of the constant

[wary tulip]

you can check integer roots by looking at divisors of the last term

[jade thunder]

It’s sort of a jokish way to say that once you do enough of these problems you’ll see a trick quickly

[wet cypress]

i.e. You can test $\pm {1, 2}$ as possible solutions to the poly since they are factors of the constant term (rational root theorem)

[hoary hedge]

so 2 ?

[wary tulip]

1,2,-1,-2

[jade thunder]

Ok that’s a much better way to say it 😭

[hoary hedge]

i kind of still dont get it😭

[thorny flame]

poudel

[wet cypress]

its a theorem u'll learn later on

[hoary hedge]

oh i see

[wet cypress]

hayley's method is what I think they want you to see though

$y=x^3-2x^2-x+2$
\ $\Rightarrow y = x^2(x - 2) - (x-2)$
\ $\Rightarrow y = (x-2)(x^2 - 1)$
\ $\Rightarrow y = (x-2)(x+1)(x-1)$

@hoary hedge

[hoary hedge]

ohh i see

[thorny flame]

poudel

[wet cypress]

yeah but like u'll notice that the roots are just factors of the constant term

but dw abt that

[wet cypress]

this was defo the intended sol

[hoary hedge]

i think ill just have to practice more then

yeah

thank you that makes sense

[wet cypress]

yeah gl

you'll get w practice

[hoary hedge]

yeah

ty

.close

[wet cypress]

nws

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[grave hedge]

Can someone check this question for me, my answer is not right and I’m confused which part I did wrong because when I retried it still got to where I am

[topaz sinew]

@grave hedge Has your question been resolved?

[wet cypress]

i see your mistake

its cause you incorrectly equated $\frac{p^3 - q^3}{p-q}$ as being equivalent to $p^2 - q^2$ when solving for $a$

[thorny flame]

poudel

[wet cypress]

the correct solution would be:
$$a = \frac{p^3 - q^3}{p-q} = \frac{(p-q)(p^2 + pq + q^2)}{p-q} = p^2 + pq + q^2$$
$\fullwidth$

@grave hedge

[thorny flame]

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

[wet cypress]

oh wait you've also made a mistake when solving for b asw

let me see what you did

give me a sec

[grave hedge]

i think i made a mistake on b from the value of a

[wet cypress]

this is du hw asw right 💀💀

oh yeah right

yeah alr

u should be good now

[grave hedge]

how did you know

[grave hedge]

probably,

thank you

[wet cypress]

i legit did polys in 3u like a few wks ago

but i hvnt done the hw

[grave hedge]

💀

[wet cypress]

lowk if ur a2 3u can u send thru w the hw

😭😭

i cba to do it

but i dont wanna get demoted

[grave hedge]

im not in a2 lol

[wet cypress]

what class

most of the questions should be the same if ur in a3

[grave hedge]

3

[wet cypress]

nah im not even trolling i deadass need the hw sol

ahahah

[grave hedge]

do you not have the homework?

wait no you need the working out?

[wet cypress]

like I have the hw and could do it

but I have exams coming up

so I'm prepping those instead rn

[grave hedge]

ooh good luck with your exams

[wet cypress]

yeah ty

nah u dont have to send but would be lifesaver

cause I'm pretty sure I'm good w polys alr

but dus so strict abt hw submissions

[grave hedge]

you'll be able to speedrun it under 20 minutes then

[grave hedge]

fr

[wet cypress]

grr

nah im joking

allg

gtg now

[grave hedge]

alright thank you and bye

[wet cypress]

oh btw

close the channel

".close"

[grave hedge]

.close

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[golden blade]

I came to my own conclusion that I need to treat the constant as a function of z in order for this to make work (calculating the antiderivative of the gradient field v)

But I wonder how integrating 0 gives us a function of z

C'(z) would be 0 after differentiating z again

so we would have actually 0 = z instead of C'(z) = z

[jade thunder]

I don’t even know what I’m looking at

[thorny flame]

𝔸dωn𝓲²s

[golden blade]

I am trying to find f

[thorny flame]

𝔸dωn𝓲²s

[golden blade]

Integrate that wrt x

Then I get f with some constant function of y and z which I need to determine so I differentiate that again but wrt y and equate it to the 2nd component of the vector field and so on

Since it's 5 am I am going off anyway so this seems hopeless

[jade thunder]

But how do you know $\partial_xf = v_1$

[thorny flame]

Frosst

[jade thunder]

Tbh I dont know what you’re trying to solve here

[topaz sinew]

@golden blade Has your question been resolved?

[golden blade]

Because of the assumption

grad f = v_2

So they partials of f must be equal to the components v_2

I am just trying to find the antiderivative of f lol

[jade thunder]

Oh that’s right

[golden blade]

If only snowseph was here ;-;

[jade thunder]

I’m at work I’m only looking at this in pieces 😭

[quartz adder]

With ∂xf=v2x∂x​f=v2x​, ∂yf=v2y∂y​f=v2y​, and ∂zf=v2z∂z​f=v2z​, you can integrate each partial derivative with respect to its respective variable to find the antiderivative of f in each direction.

For example, integrating ∂xf=v2x∂x​f=v2x​ with respect to x would yield:

f(x,y,z)=∫v2x dx+g(y,z)f(x,y,z)=∫v2x​dx+g(y,z)

Similarly, integrating ∂yf=v2y∂y​f=v2y​ with respect to y would give:

f(x,y,z)=∫v2y dy+h(x,z)f(x,y,z)=∫v2y​dy+h(x,z)

And integrating ∂zf=v2z∂z​f=v2z​ with respect to z would result in:

f(x,y,z)=∫v2z dz+k(x,y)f(x,y,z)=∫v2z​dz+k(x,y)

Where g(y,z)g(y,z), h(x,z)h(x,z), and k(x,y)k(x,y) are functions of the remaining variables. Combining these results, you can find the antiderivative of f with respect to the given assumptions about its gradient vector.

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[solid hornet]

I understand that the dot products if parallel should be the product of their magnitudes

[solid hornet]

I kind of forgot how you can find a second equation to find both the x and y of this parallel vector

[topaz sinew]

@solid hornet Has your question been resolved?

[modern rock]

yo

[modern rock]

what are u after?

[solid hornet]

I'm stuck at b

I got |L| sqrt(116) = L • (unknown vector)

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[modern rock]

yo sorry i didnt see ur msg

[modern rock]

a vector is parallel to L if it has some scalar of 'b'

so if we wanted to find a vector, say 'v', which is parallel to L and has a magnitute of sqrt(116)

$v=\sqrt{116}\cdot\hat{b}$

[thorny flame]

Galaxy

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[frail cave]

can anyone teach me how to do completing square

[frail cave]

take this for example

[meager dawn]

https://youtu.be/pYSYL_vy6YQ?si=TsIgclkRAfWDIk_g
https://tutorial.math.lamar.edu/classes/alg/solvequadraticeqnsii.aspx
these two are friendly introductions, specific problems aside

second link has example problems

[frail cave]

alright thanks sigma

which is easier, quadratic or completing square

[meager dawn]

what do you mean specifically by "quadratic"

you mean like the formula? it depends on the kind of question you're solving

[frail cave]

the formula

[frail cave]

yeah

[meager dawn]

by doing a billion examples you'll come to understand which is better for what kinds of questions

but for now you should end up being good at both of them

becuase they're both tools that you'll use later

[frail cave]

ok sigma

we can factorise by quadratic formula right

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@frail cave Has your question been resolved?

[meager dawn]

yeah but you don't want to

[frail cave]

I did this way is it correct?

[sweet wedge]

yep

the answer is correct, but you may want to avoid one line answers if there's more marks

[frail cave]

but I already showed my working tho

[sweet wedge]

idk about your teachers but usually most would want to see the "middle term" part of the working

if they accept this its cool though as the answer isn't wrong

[frail cave]

what would you show as your middle term working?

[sweet wedge]

$3x^2 +2x-1 \newline 3x^2 + 3x -x -1 \newline 3x(x+1) -1 (x+1) \newline (3x-1)(x+1)$

[thorny flame]

r

[sweet wedge]

the second and third line are called the "middle term working" among other names

your method isn't incorrect though so it should do

[frail cave]

you basically did reversed expansion right?

[frail cave]

ok thanks sigma

[sweet wedge]

nope, you start off by thinking about which numbers product makes 3 and sum makes 2

which is probably what you also did in your tic tac toe box

so its all good

[frail cave]

okie

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[timber sundial]

B2 please

[timber sundial]

I’m not understanding what to do

[prisma mesa]

hint: note that the value at t = 0 is -5

try plugging t = 0 in the equation

wait 2, sorry

do the same, just plug in t = 1, t = 2 and t = 3

[timber sundial]

ohh thatmakes sense

thanks both ofu

[prisma mesa]

S = -5 when t = 3

[timber sundial]

illtryit

[prisma mesa]

so it would actually be -5 = a(3)³+b(3)²+c(3)-5

[timber sundial]

.rotate

-rotate

Rotate

,rotate

[timber sundial]

like this? @prisma mesa

[prisma mesa]

Yes, but the first equation was already used to find d

so it now simplifies to -5 = -5

and it doesnt give any useful info

so you need to add the last equation

with t = 3

[timber sundial]

okayy

wait

[prisma mesa]

this is correct

the first equation is redundant, so you dont need to include it in the answer

[timber sundial]

i. just realized my c is incorrect

[prisma mesa]

oh yeah

[timber sundial]

i fixed it

[prisma mesa]

it should be c(0), c(1), c(2), c(3)

[timber sundial]

i did that

isthat all they are asking

can i leave it likethat

or do. i have to. do another stepp

[prisma mesa]

For b yes, they are asking jsut for the last 3 equations

[prisma mesa]

you could probably expand it and write it like -1 = 8a + 4b + 2c - 5 etc.

[timber sundial]

hm, my equations sseemsto be wrongcompare. to the answer

[prisma mesa]

this is the third equation

[timber sundial]

oh wait hwat

[prisma mesa]

what are the equations in answer

[timber sundial]

8 = a +b+c

4=8a+4b+2c

[prisma mesa]

That's expanded version of
-1 = a(2)^3 + b(2)^2 + c(2) - 5

[timber sundial]

0=27a+9b+3c

[timber sundial]

oh right

[prisma mesa]

add 5 to both sides and you get 4 = a(2)^3 + b(2)^2 + c(2)

then just calculate the coefficients and it's 4 = 8a + 4b + 2c

do the same with other equations and it will look like the answer

[timber sundial]

i got it

okayy

,rotate

[timber sundial]

I’m lost abt the 8 =a+b+c

[prisma mesa]

lemme check

this is incorrect

there is -5 on the RHS

so you should add 5 to both sides

and that will get you 3+5 = a + b + c

which is 8 = a + b + c

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[uneven orbit]

how have these two equations been used to form the dVx/dy equation?

[soft bluff]

a) find the velocity vector s'(t)✅
b) find the t-value, where the velocity vector is perpendicular on the vector a=<6,1>❌

i have trouble with b. Its really bugging me. i cant find an elegant solution. I am a math teacher myself, so im kinda embarrased XD. im doing an examset for my students.

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@uneven orbit Has your question been resolved?

[tranquil verge]

actually we only use the first eq. by thaking the derivative w.r.t. y

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[rough vapor]

I am not sure how to do this or what the logic is behind it

[pastel oracle]

so for f(x) = 4^x

it's asking what happens as x gets more and more negative

so what is 4^(-1)

[rough vapor]

-4

or 1/1/4

[pastel oracle]

no

[rough vapor]

wait 1/4

[pastel oracle]

yes

how about 4^(-2)

[rough vapor]

1/1/16

[pastel oracle]

no

[rough vapor]

1/16

my b

I keep thinking of fractions

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[rough vapor]

.close

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[glossy marsh]

Hei, can someone help me with this exercise?

[glossy marsh]

I have to make a system of some sorts

A differential characteristic system

<@&286206848099549185>

[neon iron]

.close

do it yourself

!done

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[neon iron]

!15m

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[glossy marsh]

im sorry

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[oak cairn]

Whats the difference of a) and b)

isnt it the same question..

[primal patrol]

no it's not

let's take a simple example of 2 years

you put $100 at the beginning

[oak cairn]

because for a) i was trying to solve it and i wasnt getting the number but i realized i answered it for b

[primal patrol]

so after 1st year you have 4 interest

but then in the second year you get 4% interest on $104

[oak cairn]

right

oh

OM

WAIT

[primal patrol]

v/s putting say $50 in first year you get $2 interest only

[oak cairn]

ok wait im stil confused ok

continue

[primal patrol]

like should we just go through the q

[oak cairn]

so what formula do i use

[primal patrol]

it might be easier

so for part a)

his nephew is newborn

and at 16th birthday needs to have $1000

[oak cairn]

yes

[primal patrol]

because its 4% compounding

let's assume he puts in $p dollars

so $p (1+r/100)^{16} = 1000$ is what we need to solve where r =4

does this formula look familiar?

[thorny flame]

tyler

[oak cairn]

oh

yeah

[primal patrol]

ok good

so 1+4/100 = 1.04

1.04^16 = 1.873

so p should be at 1000/1.873 = 533.9

[oak cairn]

omg

yep

thats what it says on my answer key too

[primal patrol]

ok now for part b? unless you have a q about a

[oak cairn]

nope i did b but

thats what i also wanted to ask

[primal patrol]

ok

[oak cairn]

how do i know what formula to use

because i thought we had to use the big formula

[primal patrol]

I mean in general it's compounding interest formula

[oak cairn]

but for a you used the simple one

right

[primal patrol]

for part b you are using the compounding interest formula along with a geometric series

[oak cairn]

ya

ok tysm

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[primal patrol]

yw!

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[amber iris]

hello
does anyone know a way to calculate the modinv of 3^n under 2^m efficiently without brute forcing
a mathematical function perhaps

[amber iris]

<@&286206848099549185>

[solemn void]

Yes

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[amber iris]

@solemn void

pls elaborate

[solemn void]

Yes

[amber iris]

do you know such a method

[solemn void]

No

[amber iris]

wow

@solemn void can you help me with my question ?

<@&286206848099549185>

[neon iron]

!15mins

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[topaz sinew]

Please don't occupy multiple help channels.

[uneven otter]

How do I do question 4 and 5 and 4 and 7

[craggy haven]

you're going to need the formulas for surface area of a sphere and for volume of a sphere

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[hoary hedge]

hi i dont understand the soluton to part b would anyone explain?

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[hoary hedge]

<@&286206848099549185>

[honest jungle]

connect the point O and C

this line OC has to bisect and alpha which is 50 degrees

lets call the point where circle intersect OB M

since OB is clearly tanglent to circle, the angle OMC is 90 degrees

now we have a right angle triangle OMC

[hoary hedge]

ohh i see thank you sm!

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[cobalt folio]

Shouldn’t my answer also be correct? Indefinite integrals. ik the anti derivative of a number divided by x is that number times the natural log of x, but cant mine also be correct? Just use the power rule get an extra x with 5 and divided with the bottom x and have 5 alone

[elfin sparrow]

No, the power rule only applies to expressions of the form ax^n (with constant a)

For example you wouldn't say that the antiderivative of sin(x) is sin(x)•x

@cobalt folio

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[cobalt folio]

Ok thanks :D

[cobalt folio]

Yes

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[fierce sierra]

The answers say no because the zero polynomial is not in the set, I cant wrap my head around it though

[acoustic tangle]

Well, do you think that the zero polynomial satisfies the given condition?

[fierce sierra]

p'(x) = 0 for zero polynomial then what if x=-1

[acoustic tangle]

Look carefully, it says that p'(x) + x + 1 = 0 should hold for all x in R

[fierce sierra]

ohhh

ahh ok makes sense now thank u

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[autumn plaza]

how do i do this

[autumn plaza]

question C

i have 2 equations for some reason

[verbal crater]

shouldnt you add both of them

[autumn plaza]

oh u right

[autumn plaza]

why is it sometimes we equate them

[verbal crater]

when?

[autumn plaza]

when we have unknown on esch side

each vector

[verbal crater]

if you have only one vector on both sides

then you can equate them

because two vectors are equal only if they have the same components

[autumn plaza]

ohhhhh

ok

thx u

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[cobalt folio]

Is my answer correct? it gives me the answer but idk if our answers are the same just written differently or if i am just wrong. Can someone tell?

[cobalt folio]

Also sorry for the shitty handwriting i am not used to writing on ipads

[hazy pumice]

The answers are not the same

You have the same denominator as the book's answer, but you can't get x^2 + 3 in the numerator

Did you start by simplifying the given integrand?

[cobalt folio]

Yes, i can send you my steps but its very very messy, do you want it?

Nvm i thought i had it

Apparently its gone damn

ill redo the question and see

[hazy pumice]

It's pretty easy

You just need to get common denominators

At the very end

||left term had denominator of 3, right term had denominator of sqrt(x); Multiply top and bottom of left term by sqrt(x) and multiply top and bottom of right term by 3.||

[cobalt folio]

Forgot the c but ignore that

[cobalt folio]

Damn it so i did it wrong again,

Ok so it seems i simplified it right i just fucked up doin the anti derivatives i think

My eyes hurt

Ohhh yea i fucked up the anti derivatives i think i got it

@hazy pumice thanks man, appreciate it the picture of you solving it really helped

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[stone wadi]

Does the fact that sequence of functions f_n does not coverge uniformly to some function imply that the corresponding series sum_k=1^n f_k does not converge to some function uniformly as well?

[stone wadi]

does non-uniform convergence for function sequence imply non-uniform convergence for function series?

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[earnest pine]

Yes, it should.

So I’ll explain the two function case, because I dont wanna type that much on my phone, but it should be pretty easy to abstract to higher cases

So basically, u know that | f_n(x) - f(x) | < \epsilon * 0.5 and | g_n(x) - g(x) | < \epsilon *0.5

Then consider | ( f_n(x) + g_n(x) ) - ( f(x) + g(x) ) | < | f_n(x) - f(x) | + | g_n(x) - g(x) | < \epsilon * 0.5 + \epsilon * 0.5 = \epsilon

By triangle inequality

[earnest pine]

I skipped quite a few steps, but I hope that makes sense

[stone wadi]

thank you so much, I'll study this topic further

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[scarlet meteor]

help to solve pls

[noble laurel]

is fish not its own plural

[rigid nimbus]

This question is worded very weirdly

[ripe spoke]

The problem seems to have its own English issues
Regardless, start by finding the volume of water

(I'm fairly sure I know what it's saying, but the English isn't Englishing)

[rigid nimbus]

It would probably be better worded as
"If 1000 cm³ = 1 litre, 1 UK gallon = 4,5 litres, and three fish can live in 1 UK gallon of water, how many fish could live in this aquarium given below?"

[ripe spoke]

I assume the measurements are in cm?????

[rigid nimbus]

You can probably assume that

[noble laurel]

if its an aquarium probably not

smallest aquarium known to man

[ripe spoke]

A 1 m aquarium sounds reasonable

[shut belfry]

you can safely assume that nothing else is mentioned

[shut belfry]

Yes

[ripe spoke]

@scarlet meteor

[scarlet meteor]

the question is written from the exam

[ripe spoke]

Someone ban this person

[scarlet meteor]

so the question is really bad

[ripe spoke]

You have a very poorly written exam

[scarlet meteor]

no!

applicants remember them and post them on social media to help others