help-0

[gray isle]

!show

[lone heart]

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

[sage nebula]

had to draw it since, my camera is broken

[alpine sable]

can anyone please explain me these theorems?

[elfin steeple]

How

[vale wigeon]

@alpine sable please open your own channel. #❓how-to-get-help

[alpine sable]

oh sorry

im new

[vale wigeon]

@sage nebula so you have expanded your thing up to the x^1 term

$[1 + (k+1)x]^n = 1 + n(k+1)x + \dots$ indeed

[ocean seal]

Ann

[vale wigeon]

you will also need the x^2 and x^3 terms here, because you are told the x^3 coefficient is three times that of x^2.

[sage nebula]

Ok. But How do I go about using nCr with a variable N?

due to the formula of binomial expansion

[vale wigeon]

wdym

you just... keep n as n?

like you know how to write $\binom{n}{1}$, $\binom{n}{2}$, $\binom{n}{3}$ more compactly, right

[ocean seal]

Ann

[sage nebula]

Wait i just checked out my equation sheet.

States the form

[lone heart]

@sage nebula Has your question been resolved?

[sage nebula]

Its doesn't work

I am not sure how to do it

Its only worth 4 marks and i am doing working out as if it is a 20 markers

<@&286206848099549185>

[outer hare]

Can you show your expansion using this formula? It should work

[sage nebula]

How do you do what ann did

$(k+1)x^3$

[ocean seal]

FireBlastGaming

$\(k+1)x^3$
```Compilation error:```! LaTeX Error: Bad math environment delimiter.

See the LaTeX manual or LaTeX Companion for explanation.
Type  H <return>  for immediate help.
 ...                                              
                                                  
l.57 $\(
        k+1)x^3$
Your command was ignored.
Type  I <command> <return>  to replace it with another command,
or  <return>  to continue without it.```

[sage nebula]

ahh

$(k+1)x^3$

[ocean seal]

FireBlastGaming

[sage nebula]

Now..

Ok. ill write it

[outer hare]

(1+(k+1)x)^n
Coefficient of x³: n(n-1)(n-2)/6 (k+1)³

Do you mean this

[sage nebula]

$((k+1)n^3-3(k+1)n^2+2(k+1)n)/6$

[ocean seal]

FireBlastGaming

[sage nebula]

This is the coefficient of x^3

correct?

[outer hare]

For x³, k+1 should have power of 3 as well

[outer hare]

So no

[sage nebula]

Wait... how do i read my equation... the equation is for $(1+x)^n$ but i have 1+(k+1)X

[ocean seal]

FireBlastGaming

[sage nebula]

How does that change?

[outer hare]

(1+y)^n where y = (k+1)x

[sage nebula]

Ok ok

I substitute

it in

into x

[outer hare]

So y³ should give you (k+1)³ in the coefficient

[sage nebula]

Just to confirm. I find the coefficient where r = 3 and where r = 2 and divide (r=3)/3 and equate it to (r=2)

and then use simulatious equations with r=1

to get that show equation?

Because if so. IT SHOULD NOT BE 4 marks

[outer hare]

Well a few steps but it is pretty straightforward

And the formula is given

[sage nebula]

let me try

[ocean seal]

FireBlastGaming

[outer hare]

Just in case, this equals to 3a instead of 3ax³

[sage nebula]

i just divided the coefficient of r=3 by r =2 and equated it to 3

[outer hare]

Mind showing your work?

[sage nebula]

I got $((n^2-n)(n-2)(k+1)^3*x^3)/6(((n^2-n)(k+1)x^2)/2)$

[ocean seal]

FireBlastGaming

[sage nebula]

the n^2-n cancel

the k

(k+1)^3 becomes ^1

and the x^3/x^2 = x

and the n-2 /1 = n-2

[outer hare]

Don't include the x, x is not part of the coefficient

[sage nebula]

only the k+1^3 and 2 is right?

[outer hare]

Which 2

$\frac{(n^2-n)(n-2)(k+1)^3}{6} = 3a, a= \frac{(n^2-n)(k+1)^2}{2}$

[ocean seal]

wannabe

[sage nebula]

that is what i meant

r=3

and r =2

r=3/r=2 = 3

[outer hare]

You have x included...

[sage nebula]

yes

i excluded it now

[outer hare]

Alr

[sage nebula]

and got the right answer

thank you

.close

[lone heart]

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[normal karma]

'A rectangle has an area of 539m2.
One of the sides is 9.8m in length.
Work out the perimeter of the rectangle.'

[normal karma]

how would i work this out

[proven leaf]

$A=bh$ you know that $b=9.8$, solve for $h$ then plug both of those into the perimeter formula: $P=2b+2h$

[ocean seal]

XxMrFancyu2xX

[vale wigeon]

@normal karma do you know how to find the area of a rectangle, in general?

[normal karma]

yes

[vale wigeon]

and the perimeter?

[normal karma]

mhm

[sage nebula]

All you have to do in this question is substitute the values given into the equation of the area and perimeter.

[vale wigeon]

ok, then what is troubling you?

[sage nebula]

So rearrange the formula

so the empty variable is alone and input your values

[normal karma]

im in yr 7 everything troubles me 💀

[sage nebula]

Ok. How do you think, you would start this problem

What is step 1

[normal karma]

umm work out the other length of the rectangle

[vale wigeon]

i'm not asking about your general life situation, i'm asking about the problem in particular

[sage nebula]

Try going step by step. instead of all together

[normal karma]

i meant everything in maths

[sage nebula]

@normal karma Correct

You do that by using the area formula, since we are given it

As you mentioned Base * Height = A

Area

We have area and base or height

Which exactly doesnt make a difference since we are multiplying

Lets say base = 9.8m

If A = Base * Height, rearrange it to make Height the subject of the formula

What is the rearranged formula?

[normal karma]

how do i rearrange it

[sage nebula]

Ok. ill explain

[normal karma]

thanks

[sage nebula]

$A=BH$

[ocean seal]

FireBlastGaming

[sage nebula]

We want H alone

So since B is multiplied by H

We divide H by B

But we must do it to both sides

[proven leaf]

1. use lowercase for base and height, they're standardized
2. maybe instead of trying rearrangement, especially for yr 7, trying plugging in an dividing by a constant, it may make life easier

[sage nebula]

Yes, my bad

$frac(a/b)=frac(b*h/b)$

That did not work

How do you create a function? using TeXit

?

ignore what i did above

[gray isle]

\

[sage nebula]

Ok thanks

[gray isle]

\frac{}{}

[sage nebula]

Ok

Thanks

$\frac{a}{b} = \frac{b*h}{b}$

[ocean seal]

FireBlastGaming

[proven leaf]

you can also use /cdot (make sure to separate stuff as well) $b\cdot h$

[ocean seal]

XxMrFancyu2xX

[sage nebula]

/cdot

[gray isle]

\

[normal karma]

im so confused rn

[sage nebula]

\cdot

Ok...
Look at what i did above

[gray isle]

have you ever solved equations before?

[sage nebula]

^

this is the same as $\frac{a}{b} = h$

[ocean seal]

FireBlastGaming

[sage nebula]

We made h the subject of the formula

Now you can put your values of Area and the length of one side into the equation above

Area divided by the length

Understand how to rearrange?

[normal karma]

i still dont get it lol

[gray isle]

have you ever solved equations before?

[sage nebula]

$a = bh$ \implies {$\frac{a}{b} = \frac{bh}{b}$}

[gray isle]

\implies

[normal karma]

yes

[gray isle]

what sort of equations have you solved before

give an example of one and how you solved it

[normal karma]

anything in maths or this topic?

[gray isle]

any equation

[normal karma]

while i was working on solving equations using inverse operations(not complex), i changed the multiplication into division, and the addition into subtraction and got the answer

[gray isle]

give this a read

$\algebruh$

[ocean seal]

ℝamonov

[sage nebula]

this explain what i was trying to teach

But way better

and more understandable....

[proven leaf]

well yeah, cause it's prepared ahead of time

[normal karma]

i read it

[sage nebula]

Did you understand it?

[normal karma]

mhm

[sage nebula]

If so then Try this question:

$x+y=5$

[ocean seal]

FireBlastGaming

[sage nebula]

Make y the subject of the formula

Try it

When I say subject of the formula, i mean. Make that variable alone

[normal karma]

3+2 ? im not sure how to work it out without a 2nd piece of info

[sage nebula]

Ok. Ill do another one

$y+5 = 4$

[ocean seal]

FireBlastGaming

[sage nebula]

@bright notch Put it into its own help channel, we are occupied... Read #❓how-to-get-help

[normal karma]

-1

[bright notch]

My bad

[sage nebula]

correct @normal karma

What about this one? $\frac{x}{4} = 8$

[ocean seal]

FireBlastGaming

[dull forge]

x=32

[sage nebula]

Correct. Now I want to test you on a hard one

[gray isle]

im not sure how to work it out without a 2nd piece of info
doesn't matter if you aren't given info about x
x can be left as x

[sage nebula]

$\frac{x+5}{4} = 10$

[ocean seal]

FireBlastGaming

[sage nebula]

What is x?

[dull forge]

35

[normal karma]

im too slow

[gray isle]

not u

[sage nebula]

So hyper we arent anking you

!? Did you get 35 also?

[normal karma]

still working it out

[dull forge]

Sorry bro

My bad

[normal karma]

yes

[sage nebula]

Ill give you another one. Hyper dont answer $\frac{x+9}{2} = 5$

[ocean seal]

FireBlastGaming

[dull forge]

Okay I won't answer

[sage nebula]

Thx

[normal karma]

1

[dull forge]

You got it!!

Good job

👍👍

[sage nebula]

Good job

[normal karma]

took me a while for the answer to be 1

[sage nebula]

That is absolutely fine

You just need to practise

[dull forge]

That's how the learning starts

[sage nebula]

Exactly

Now I want to try smth

[normal karma]

alr

[sage nebula]

solve this $x+7-y = 2$

[ocean seal]

FireBlastGaming

[sage nebula]

Make x alone

So treat y as if it is any number

just move it to the other side

[dull forge]

Should be easy enough for you @normal karma

You can do it

[sage nebula]

Remember dont get confused due to 2 letters. We only want x on one side of the = sign

y is just any number. treat it like any number

[normal karma]

3+7-8=2

[gray isle]

y is y

[dull forge]

?

[gray isle]

don't assign an arbitrary value to it

[sage nebula]

Think of it as Y. But treat it like any number

[normal karma]

i dont get it

[gray isle]

there is no issue with having unkown variables in an equation

[sage nebula]

So since it is x+7-y = 2

[proven leaf]

If I have the equation: $x+y=2$, I can subtract $y$, just as any other number to get \fbox{$x=2-y$}

[ocean seal]

XxMrFancyu2xX

[gray isle]

the exact same principles as what I've outlined above apply

[dull forge]

See you transfer the numbers as well as y to the other side

[sage nebula]

Then move y to the other side by adding y. Remember opposite symbol

Like how you would do with any number

[gray isle]

you can do stuff like add y to both sides of the equation
just like how you can subtract 7 from both sides of the equation
there isn't any real difference to the rules of manipulation

[dull forge]

Gtg bye

[gray isle]

you're still applying the same operations to both sides of the equation

[sage nebula]

When $x+2 = 5$ Then you -2 to transfer it to the other side.

Same thing with $x+y=5$ You transfer it to the otherside by -y

[ocean seal]

FireBlastGaming

[normal karma]

ill be right back, u can keep explaining ill read when im back (max around 10mins)

[ocean seal]

FireBlastGaming

[gray isle]

watch your signs

[sage nebula]

Talking to me or him?

[gray isle]

you

oh

different example

[sage nebula]

Yah

[normal karma]

im back

i found the answer

.close

[lone heart]

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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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[cloud zodiac]

How to answer 8c

[vale wigeon]

have you already done 8a and 8b?

[cloud zodiac]

Yes

I know the x and y points as well

Am I supposed to use cosine rule to find an angle?

[vale wigeon]

no

do you know where the origin is

[cloud zodiac]

Yes

I just figured it out

I probably did it the wrong way

But I got the answer right in the end

I probably should have drew the graph would have made it easier

.close

[vale wigeon]

indeed it woul've!

[lone heart]

Channel closed

Closed by @cloud zodiac

Use .reopen if this was a mistake.

[cloud zodiac]

I need to make it a habit

[lone heart]

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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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[chrome salmon]

Hello lalla

[polar fossil]

this is prob a clearer photo

[chrome salmon]

,rotate

[polar fossil]

anyways

[chrome salmon]

Hi

[polar fossil]

i dont get what it means by

correct to the nearest gram

[chrome salmon]

If the values are given in gram like 80.25 gm then the nearest gram value is 80 gm

[polar fossil]

ooh

so for 80g

its 80.5 right

i mean

79.5

[chrome salmon]

What?

[polar fossil]

the least possible mass

[chrome salmon]

Nah if it's 79.8 then we write the nearest integer value to 79.8 which is 80

[lone heart]

@polar fossil Has your question been resolved?

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[lone heart]

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[keen pawn]

how would i convert

$3580e^{0.177x}$ to $ye^{0.2x}$

[ocean seal]

Dan_

[vale wigeon]

http://xyproblem.info/

[ocean seal]

Dan_

[vale wigeon]

this... looks sus

[gray isle]

$3580\cdot e^{-0.033x} \redneq 3580\cdot e^{-0.033}$

[ocean seal]

ℝamonov

[gray isle]

why are you taking x as 1

y is an expression in terms of x here

is this the original question

[vale wigeon]

most importantly, we've yet to see where any of these expressions came from

[gray isle]

1 sec,

[vale wigeon]

is this a game you are designing or an existing game you are analyzing

[gray isle]

didn't check yuor subtraction

0.177-0.2 is -0.023
not -0.033

[vale wigeon]

what game and what are your data

0.177 - 0.2 = -0.023 no?

[gray isle]

sry zero key fked up

[lament forge]

...i'm not sure what you're trying to do here

do you want these functions to be correct at more than one value

is y allowed to depend on x

...be willing to change the exponent

that has nothing to do with changing the exponent though

that's just the general problem of extrapolating from incomplete data

you don't have any data on what value of y to use for tier 5 either

what programming language is this game written in?

why not extrapolate the pattern in the exponents instead

don't change the formula at all

just work out what the data actually is

and then extrapolate that

if you're right that these are exponentials, then two data points exactly determine both of the values in the formula, there is only one possible exponential that correctly predicts both of them

if that then doesn't predict the rest of your data, then you're wrong about it being an exponential, or your data is wrong

then once you have several formulas you can just look at them and try to find a pattern

pretending the data is something it's not will just get you inaccurate approximations

that second one doesn't really look like an exponential at all unless your value for 8 is wrong by like 5000

(what game is this?)

...sounds like it's just impossible to extrapolate then

[dull forge]

Q8

[lament forge]

other than just, guessing what kind of values they might have manually put in

[dull forge]

Help

[alpine sable]

,rotate

[lone heart]

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[thick lynx]

How does WA calculate something like $\sum_{n = 1}^{10^{500000}} \frac 1 n$ in seconds?

[thick lynx]

Is there a formula for this?

[mortal trellis]

there are close approximations using logs

[shy dove]

if I'm not mistaken it just doesn't converge

[quasi vector]

the infinite case doesn't converge

this is a limited sum

[shy dove]

oh crap right

oop

runs

[thick lynx]

Weird that WA exceeds computation time if you add some zeros to the $10^{500000}$, making it $10^{5000000000}$ for example

Is that because it can't evaluate the logarithm of such a huge value?

[mortal trellis]

ask the devs

[marsh rapids]

It's probably using some approximation method where it goes far enough that the error bound is lower than the last digit it displays

[thick lynx]

I'm not that interested in WolframAlpha, I was just wondering if there was a formula for this, but you answered it. Thank you

[marsh rapids]

Which is why it struggles to get more digits when you ask for more

[thick lynx]

Alright, thanks

.close

[lone heart]

Channel closed

Closed by @thick lynx

Use .reopen if this was a mistake.

[dull forge]

Guys please help me on this one

.reopen

[lone heart]

✅

[dull forge]

<@&286206848099549185>

[dull forge]

Help

[lone heart]

@thick lynx Has your question been resolved?

[lone heart]

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[hallow vessel]

how do i start this

im a little confused as to what the map is between the two

[green stream]

Do you know the definitions of injective and surjective functions?

@hallow vessel

[hallow vessel]

injective means all of A can be mapped to B

surjective means all of B can be mapped by A

f(x) = f(y) if x = y

for injective

[green stream]

no, that's not correct, by the definition of a function all of A can be mapped to B

injective means that x != y implies f(x) != f(y)

simply: there are no 2 arguments for which the function has the same value

[hallow vessel]

is this not injective?

oh wait ye

[green stream]

yeah it is

[hallow vessel]

not all needs to be mapped

whats surjective

[green stream]

more or less what's you said

why don't you just write down all the arguments and for each what the function evaluates to

[hallow vessel]

i wrote down all the elements of the power set

but idk what the f((x,y)) = part means

[green stream]

it's the function of two variables

technically it's a function of a tuple

so for each pair of sets it gives a value that is from the set {0, 1, 2}

[hallow vessel]

so its not injective

and its not surjective either

right?

[green stream]

I ain't helping you

get out of my channel

asshole

[hallow vessel]

im giving him wrong answers lol

[green stream]

I don't care stop

[hallow vessel]

.close

[lone heart]

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[quiet vector]

think u should check out the physics server in #old-network

.close

[lone heart]

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[echo socket]

This isn't much of a physics question tho

[lone heart]

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[nocturne iris]

hi

[nocturne iris]

$$\langle x | u \rangle \langle v | y \rangle = \langle y | u \rangle \langle x | v \rangle$$

[ocean seal]

lilisworld

[nocturne iris]

how do i know that u and v are collinear?

<@&286206848099549185>

[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.

[nocturne iris]

<@&286206848099549185>

.close

[lone heart]

Channel closed

Closed by @nocturne iris

Use .reopen if this was a mistake.

[queen lion]

.reopen

[nocturne iris]

.reopen

[lone heart]

✅

[nocturne iris]

@queen lion

[queen lion]

Could someone please fast check f) h) e) (the ones with ??? On the right side) bcs the results shows some other answers.

[worn fox]

do not literally go to help-0

pick an available channel

[nocturne iris]

i thought he was going to help me

[queen lion]

My bad

[nocturne iris]

.close

[lone heart]

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[chrome salmon]

Rub

[prime badge]

3?

[chrome salmon]

18

F=ma

(3/5)×30 = 18

[prime badge]

how is rub 18

rub is 3

[chrome salmon]

What is rub?

[prime badge]

you said it's rub

[chrome salmon]

Who is rub?

[chrome salmon]

Oh why did I do that?

[prime badge]

miscalculation

happens

[chrome salmon]

I thought rub was 05

Yeah my bad

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[mortal fox]

I don't understand this. why it become from that, in that

[mortal fox]

Translation:
calculate the integral

per sostituzione = for replacement

[granite wing]

<@&268886789983436800>

when substituting an integral with bounds, you have to adjust the bounds to fit the new variable/function

[mortal fox]

I see, thank you very much

.close

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[toxic wind]

How to solve this?

[chrome salmon]

Do you need help with this?

[toxic wind]

yes

[chrome salmon]

The points on line are given by (-3t-4 , t+6 , 3t+1)

The direction ratios of a line are given by difference of their position vectors

So the line which gives shortest distance will be perpendicular to this given line. From (-4,3,-7) to point on the line has direction ratios (-3t-4 , t+6 , 3t+1)-(-4,3,-7)

Find a t such that the direction ratios of line from (-4,3,-7) is perpendicular to given line

[toxic wind]

by sub in t

?

is there there any video where i can understand properly?

[last ether]

Vector projection tbh

You find the vector from (-4,6,1) to (-4,3,-7), use vector projection to find the rejection

The magntiude of the rejection is your distance

[toxic wind]

oh projection

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[nimble field]

Sry for bad quality

[nimble field]

a = 2

when I do asymptotes

vertical is ln2

Horizontal

When x = inf I got 1

But minus inf is there answer ?

[cyan seal]

Yes

[nimble field]

May u help me get it ?

[cyan seal]

$\lim_{x \rightarrow -\infty} \frac{e^{2x}-e^x}{e^{2x}-3e^x + 2}$

[ocean seal]

Rub05

[cyan seal]

When you have -∞, you can change x to -x in the function and make the limit of that when x tends to ∞

It's the same

[nimble field]

So e^ -inf = 0 right

We just replace x with minus inf ?

and get answer which is 0 at the end

alr thx u I thought it’s a bit more complicated than this xd

Thought it’s wrong for some reason ;-;

.close

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[mortal fox]

Someone know i i could do from that to that? I tried, but idk how to do it

[mortal fox]

From that to that

I know I have to do a change of variable, and I do it with e^t = x

How do I change the limits?

[mortal fox]

Translation :

calculate the integral

Per sostituzione = for replacement

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[wild vault]

how do i describe a level curve of a multivariable function? Say i have f(x,y)=foo=30

[limpid turret]

That's basically it

You could try solving for just x or y, but that's rarely useful

[wild vault]

well f(x,y)=foo=30 cant be it, thats where the question im looking at starts

[tacit arch]

Show the question

Picture or screenshot

[wild vault]

the question is word for word above, I don't want to show the function itself as that would be cheating. but it literally just says describe the level curve f(x,y)= function =30

[tacit arch]

Then what SWR said was right

[tacit arch]

Otherwise maybe this

Can't tell if you don't give full information

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[old mirage]

This one is giving me trouble. I know divergence theorem and how to apply it, but it's swapping to cylindrical and using that to integrate is what's troubling me

Honestly maybe it's the bounds that are messing with me

I have z going from r to 1, r from 0 to 1, and theta from 0 to 2pi

integrating with respect to z first

<@&286206848099549185>

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@old mirage Has your question been resolved?

[old mirage]

<@&286206848099549185>

[placid zinc]

@old mirage
You want to use spherical coordinates

Ah but wait, you don't have the spherical top, which gets in the way

Yeah I like your bounds

[old mirage]

Can u try to integrate it?

Idk if I’m doing something wrong but this thing is really gross

[placid zinc]

∫∫∫ (2x + 2y + 2z) dV
If I'm remembering everything correctly

But you want that in cylindrical
∫ (2rcosθ + 2rsinθ + z) rdzdrdθ

Nothing too nuts, you get there too?

[lone heart]

@old mirage Has your question been resolved?

[old mirage]

Yea @placid zinc

Idk I tried going thru it but for some reason it was yucky

I don’t have my notes around rn or I’d show u

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@old mirage Has your question been resolved?

[old mirage]

<@&286206848099549185>

I'm still stuck. Someone in the multi calc room said the bounds were incorrect

I tried them and got another gross answer

as in negative

[slate monolith]

yeah cause they did 1 to r instead of r to 1

so its negative

[old mirage]

Gotcha

now for my final answer, I got $\frac{8\pi}{3}$

[ocean seal]

Matt.Rey

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[celest gust]

is this correct? when they put everything together where did the square over cosx go?

[carmine reef]

idk looks like they forgot about it

[outer lark]

gone, reduced to atoms

[carmine reef]

it should be there

[celest gust]

ok so i am smarter than the teacher

thank you kindly

[carmine reef]

definitely

[wary stream]

Or people make mistakes

[celest gust]

nah

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[mortal fox]

given the integral functions

calculate F'(x) and G'(x)

What is the relationship between F(x) and G(x)?

[mortal fox]

Idk how to do that

I need to calculate first The integrals right?

And if that is right after how it works for the relationship ?

[fluid ingot]

Look up Newton-Leibniz’s rule

[mortal fox]

Ty

.close

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[pulsar bane]

guys i'm struggling with this one

[pulsar bane]

find tanθ if secθ=-3/2, π<θ<3π/2

[limpid turret]

What is cos?

[pulsar bane]

i need help, i literally had to translate it to english

[limpid turret]

What is native language?

[pulsar bane]

sec is 1/cos

[pulsar bane]

arabic

[pulsar bane]

using the pythagorean identity

1+tan^2=sec^2

i've reached to a point where non of my answers are correct

[limpid turret]

This is easier if you know which quadrant to stay in

[limpid turret]

!show

[lone heart]

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

[pulsar bane]

its in the third

[pulsar bane]

uh its not possible

wait lemme see

Im 70% sure its not correct

[modern sedge]

you forgot root 4

[ocean seal]

MathIsAlwaysRight

[modern sedge]

otherwise it's correct

[pulsar bane]

i didnt even root anything

[pulsar bane]

oh so i'm right

[modern sedge]

here

[pulsar bane]

yeah i just subtracted the one

[modern sedge]

I cant see if the root is only applied to 5 or to whole fraction

but root(5)/2 is the correct ans

[pulsar bane]

no its to the whole fraction

its my handwriting

thanks buddy

so tan theta is root of 5/2 knowing that sec theta is -3/2

thank you so much man :d

[modern sedge]

and pi<theta<3pi/2

[pulsar bane]

oh yeah

in the third quadrant

[flint ivy]

.

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[pulsar bane]

i can reopen this if i need to right?

[lone heart]

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[rotund crater]

how i can get the radius

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[craggy hill]

how can it be any of these

[vague pollen]

Well, that's easy, it can't.

[neon thicket]

do u know what the standard equation looks like

[craggy hill]

yes

x-x value^2 + y-y value ^2 equals r^2

[neon thicket]

i write it like this
(x-h)^2 + (y-k)^2 =r^2

where (h,k) is the centre and r is the radius of the circle

do u understand that?

@craggy hill

[craggy hill]

my day

yeah

that's what it is

sorry was eating dinner

@neon thicket

[neon thicket]

all good

now that u know the standard form

u can read where the centre is

and the radius

[craggy hill]

1,-2

is cebter

center

r=3, so 9 on equation

it physically can't be any

[neon thicket]

radius =3

and 3 squared equals 9

wait a sec

sorry my bad

the answer isn’t there

should say:
(x-1)^2 + (y+2)^2 = 3^2

[craggy hill]

yeah lol

thanks! :)

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[abstract wyvern]

"find the volume of the solid bounded by the surfaces x=0 y=0 z=0 x+y+z=2 y^2 = 1-z, (y>0)"
I have trouble finding the region which I will integrate over
and also, do I integrate the difference of the two z = f(x,y) functions?

[abstract wyvern]

.

<@&286206848099549185>

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[deep crater]

What's the expanded form of:

f(x) = (x - a)(x - b)(x + c)^2

[last ether]

Any reason why you wanna expand it?

[deep crater]

I need to find the end behavior

Of a function in that form

[proven leaf]

$(x-a)(x-b)$ is a quadratic expanded as $(x^2-(a+b)x+ab)$ and $(x+c)^2$ is a perfect trinomial expanded as $(x^2+2cx+c^2)$

[ocean seal]

XxMrFancyu2xX

[proven leaf]

now just multiply those two results together

$(x^2-(a+b)x+ab)(x^2+2cx+c^2)$

[ocean seal]

XxMrFancyu2xX

[last ether]

Analyze it using multiplicity

First of all

What's the degree of the polynomial

[deep crater]

4

[last ether]

And then what's the sign of the leading coefficient

[last ether]

So in terms of end behavior, it'll behave similarly to x^4

[deep crater]

I added the multiplicities

[last ether]

Yeah that's how you find the degree

It's just the sum of the multiplicities

[deep crater]

As for the y-int

I got abc^2

Is that correct?

[last ether]

Yeah

[deep crater]

Alr, as for the graph, I got:

For the drawing

[last ether]

Well that's a possible example yeah

[deep crater]

Alr, thx for the help

.close

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[rotund adder]

What is the rate of change of y with respect to x of the function shown in the graph below?​ (Why is my answer wrong?)

[pseudo ice]

Well for starters, the line is "going down", whereas you gave a positive gradient

How did you get your answer?

[rotund adder]

because the X is 2x more than Y

1/2

[pseudo ice]

[rotund adder]

nvm

im skipping lessons because

i have this exam of a lot of math stuff

but yea thanks is - because is going down

[pseudo ice]

Also you can identify two points and use the gradient formula to find it from there too

[rotund adder]

what was the formula?

delta something

[ocean seal]

Stephen

[pseudo ice]

Between the points $(x_1, y_1)$ and $(x_2, y_2)$, you get it being $\frac{y_2 - y_1}{x_2 - x_1}$

[ocean seal]

@pseudo ice

[rotund adder]

got it, thanks

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[calm tulip]

Help

[hidden heart]

that looks like a virus

[calm tulip]

I swear its not

Ill try again

[wary stream]

Post a screenshot, most people aren't going to download a link off a discord server

[calm tulip]

Fixed

[calm tulip]

I dont understand how to get height of triangle

[lone heart]

@calm tulip Has your question been resolved?

[calm tulip]

No

[hushed sand]

Hey

[calm tulip]

Hello

Im confused

[hushed sand]

What do u want to find

[calm tulip]

Area of base hexagon

[hushed sand]

Ok

So a hexagon is

2 triangles and

A rectangular

Rectangle

Right?

[calm tulip]

Yes

I cant seem to find area of 2 triangles

Of the 2 triangles*

[hushed sand]

U got the rectangle?

[calm tulip]

Yes

[hushed sand]

Ok so it's simple then

[calm tulip]

Idk why i wrote 6

[hushed sand]

U know the side of hexagon?

[calm tulip]

I meant it to be 9

[hushed sand]

There's something called

Herons formula

U know 3 sides of triangle right

[calm tulip]

2, 2, 3

Ive heard of it

[hushed sand]

Yes

U can find area

[calm tulip]

I tried using trig but i dont think thats the way

[hushed sand]

Search herons formula

[calm tulip]

Woah tysm

[hushed sand]

Works right?

[calm tulip]

Whats a semi perimeter

[hushed sand]

Half of the perimeter

[calm tulip]

Ok

So

Tysm

It was correct

.close

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[alpine sable]

Can someone help me with this please?

[alpine sable]

I don’t even know where to start

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[alpine sable]

<@&286206848099549185>

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@alpine sable Has your question been resolved?

[molten pivot]

try drawing a picture

[lone heart]

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[naive aspen]

Can someone help me with this step by step?

[versed escarp]

Well what is the question

Which one matches with the og inequality?

If so, it's pretty simple. Just one step

[echo socket]

(Namely, multiply everything by 2)

[versed escarp]

Yeah

You would do that in order to isolate x.

And kaboom, you have your answer

[naive aspen]

-6 < x < 0?

[echo socket]

Yes

[naive aspen]

Thx for the help

[heavy herald]

.

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[tacit arch]

This really isn't a math question. Try asking in #discussion

Oh because you just joined today

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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

[eternal kestrel]

calculate how much larger the logo is and multiply 3.84 times that number

3.84 times 1.5

[earnest saddle]

did you use similarity?

If two triangles are similar, then the ratio of the area of both triangles is proportional to the square of the ratio of their corresponding sides.

can you try it?

i don't remember it very well...

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[acoustic sorrel]

This is for my take home assignment component where it is just basics for a test soon and I dont remember on how I would start for this

[acoustic sorrel]

Our topic is 3d vectors

[golden canyon]

Write C as (cos t, sin t)

And then calculate CA, CB and their dot product

[acoustic sorrel]

I know we move on to parametric eqn's soon but I dont understand it yet so how can I do that
and it wont be expected yet so is there another way

[golden canyon]

Well, just treat sin t and cos t as any normal number like 2 or 5/7

But they do allow to use trig identities

[acoustic sorrel]

ok

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[eternal kestrel]

does anyone know what the interval would be for the integral for this cross section

[eternal kestrel]

Number 8 btw

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<@&286206848099549185>

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[random beacon]

proving nth root of a where n and a is complex number

[lone heart]

@random beacon Has your question been resolved?

[random beacon]

1.i just use pow function f(b,p) = (a+bi)^(c+di)
a+bi = r exp(i theta) as r is module of a+bi and theta is argument of a+bi, note that exp is exponent function exp(x) = e^x
-> (a+bi)^(c+di) = r^(c+di) * exp((c+di)*i*theta)
using Euler formula we have exp((c+di)*i*theta) = cos((c+di)*theta) + i*sin((c+di)*theta)
-> cos((c+di)*theta) + i*sin((c+di)*theta)
= cos(c*theta - d*theta) + i*sin(c*theta - d*theta)
= cos(c*ln(r) + d*theta) + i*sin(c*ln(r) + d*theta)
substituting back to the equation we have
(a+bi)^(c+di) = r^(c+d) * (cos(c*ln(r) + d*theta) + i*sin(c*ln(r) + d*theta))
= r^(c+d) * (cos(theta(c+d)) + i*sin(theta(c+d)))
and so i will use nth root of a where a and n is complex number is f(a, 1/n)

2. use De Moivre's theorem and function nth root of a is a^(1/n), we have
   a+bi = r exp(i theta) = z as r is module of a+bi and theta is argument of a+bi
   -> z^(1/n) = (r * exp(i*theta))^(1/n)
= r^(1/n) * exp(i*theta/n) * (cos(2*k*pi/n) + i*sin(2*k*pi/n))
= r^(1/n) * (cos(theta/n + 2*k*pi/n) + i*sin(theta/n + 2*k*pi/n))
= r^(1/n) * (cos(theta/n) + i*sin(theta/n))
= r^(1/n) * exp(i*theta/n)

can you help me check if both of the way is correct and which way should i use

sorry for type this question for so long

[lone heart]

@random beacon Has your question been resolved?

[random beacon]

who ping me

oh lag

<@&286206848099549185>

more than 15m ig

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@random beacon Has your question been resolved?

[nimble fern]

this question is way more complex than i expected

[random beacon]

it's not much complex
i use de moivre's theorem for the second method and pure newton formula for first method
but overall, i change the complex number into polar form before doing it so that it will be so much easier than the first one i write in paper

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[proper sedge]

can you have multiple lines in a formula

[proper sedge]

like x-3500=y

0.4y=z

z+7000=a

does that make sense

[echo socket]

It does

But it's not a single formula

[proper sedge]

ok thank you

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[bleak jolt]

Hello, could anyone help me simplify the expression of A so it fits the form of d*v^p?

[alpine sable]

Can someone help me with this math problem please

[modern sedge]

1. this channel is occupied
2. dont troll

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[mossy pelican]

Can I have some help with this question? The above is what I've done so far but I feel like it is incorrect

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<@&286206848099549185>

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<@&286206848099549185>

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[wind cloak]

.close

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[gloomy nova]

3x + 1

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Please don't occupy multiple help channels.

[inner lily]

.close

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[gloomy nova]

.reopen

[lone heart]

✅

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[torn dagger]

How do you prove the convergence at 1/3 of the sequence: sq(n+2)/sq(9n+1)?

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[dull drift]

Calculate the length of the hypotenuse of a right triangle knowing that the side lengths are in geometric progression and that the shortest leg measures 2 cm. (HINT: indicate with x the reason of the progression.)

[echo socket]

The sides of the triangle are therefore 2, 2x and 2x^2

[dull drift]

Yes i got this, but idk how to solve that

[echo socket]

You can apply Pythagorean theorem here to solve for x

Let's dee

[dull drift]

My real problem is that idk how to solve for x

[echo socket]

4 + 4x^2 = 4x^4

x^4 - x^2 - 1 = 0

If you don't see how to proceed from here, then what I recommend is introducing a new variable

Let's say t = x^2

So then t^2 - t - 1 = 0

Can you solve this now?

[dull drift]

It's a simple equation

Use delta ...

i think i can do that

thank you i was struggling with that

[echo socket]

Beware that you will need to pick the positive root for t

[dull drift]

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[alpine sable]

Words are formed with the letter PEACE. Find the probability that 2 E's come together.

[quasi vector]

!status

[lone heart]

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

[alpine sable]

1

[quasi vector]

consider the total number of possible words first

[alpine sable]

How to find that?

[quasi vector]

well

how much have you learned in your class

[alpine sable]

I know basic concepts but here i got stuck

[quasi vector]

what have you tried

[alpine sable]

I don't know where to begin

[quasi vector]

what if all the letters were different

how would you find tghe total possibilities then

[alpine sable]

Like 5 letters and i guess 1/5?

[quasi vector]

what?

[alpine sable]

I am noob. Help 😭

[quasi vector]

do you know what the word "choose" means?

in the context of n choose r

[alpine sable]

Go ahead I am learning

[quasi vector]

i will not teach it to you.

look it up

[alpine sable]

Okay

[quasi vector]

it's a prerequisite for this question

[alpine sable]

Whats the topic that i should google

[quasi vector]

permutations and combinations i suppose

[alpine sable]

Ya i got it so if 5 letters were different

I would do 54321. Right?

5 * 4 *3 *2 * 1

[quasi vector]

correct

now you have two of the same letters

[alpine sable]

Yes

[quasi vector]

how are you going to deal with it

[alpine sable]

I got 4 letters

[quasi vector]

you still have 5 letters

so it's still going to be 5x4x3x2x1

the only difference will be that

two of the letters are the same

so they can be rearranged among themselves and still not change the word

[alpine sable]

Right and

[lone heart]

@alpine sable Has your question been resolved?

[alpine sable]

@alpine sable

Looking at your question

Thanks 🙏

Okay

So what is the total words formed by the letters

PEACE?

120

Indeed

Right?

Thanks

So

If two E are together