help-27

[still pulsar]

my bad, I meant solve for x, using the fact that the radius = 6

ignore the 6

for now, what would

$x^2 + x^2$ be using pythag

[woven radish]

Rαιη

[inner oyster]

2x^2

[still pulsar]

square root that

to get hyp

[inner oyster]

2x?

[still pulsar]

root(2) x

[inner oyster]

radicals arent my specialty

[still pulsar]

root(2)x = 6

now we want "2x"

rearrange to get "x = 6/root(2)"

[inner oyster]

why wasnt da 6 rooted

[still pulsar]

6 was the radius

and also the hyp

[inner oyster]

but if u root one side dont u root da other

[still pulsar]

the "rooting" has already been done

[inner oyster]

xroot2?

[still pulsar]

we're now equating what we have rooted with values we know

[inner oyster]

ok

[still pulsar]

but you'd still need to solve for x

actually, no

ignore what I just proposed

you have to solve for hyp before equating the hyp with 6

$\sqrt(2)x = 6 => x = \frac{6}{\sqrt{2}} => \frac{6 \sqrt{2}}{2}$

[woven radish]

Rαιη

[still pulsar]

we want 2x

so

$\therefore 2x= 6 \sqrt{2}$

[woven radish]

Rαιη

[inner oyster]

im confused

6root 2 is da hypothenuse

it equals 2 legs?

[still pulsar]

x = 6/root(2), 6 is the hyp, you can simplify it

so you get (6 root(2))/2

*multiply by root(2)/root(2) = 1

so so hyp = 6, but it is also root(2) x

basically you need an expression that can get you what "x" alone is

and then you find 2x

then add 2x to the arc length

[inner oyster]

2x=6root 2

right?

i really don't get it should i move on from this problem

would problems like these show up on the shsat

[devout snow]

@inner oyster Has your question been resolved?

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[carmine swallow]

How do I factor out x^2-5x-6

[loud root]

https://youtu.be/9MUDAr1PnlE

[devout snow]

@carmine swallow Has your question been resolved?

[carmine swallow]

anything shorter

35 minutes is hella long

[supple knot]

Just watch on 2x until you get enough knowledge to solve it

[storm crater]

disagree

[inner oyster]

write it as (x__)(x__)

_=2 negetive/positive values dat adds up to 5 and multiply to get 6

[carmine swallow]

what

how do I write that

[devout snow]

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[loud root]

I don't want to be annoying, but the video might help. It's harder to explain a whole topic via messages, and where there are such great resources online is also a waste of time tbh

[devout snow]

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[empty flame]

Hi

[empty flame]

I was asking if this answer is correct, is it ?

[devout snow]

@empty flame Has your question been resolved?

[empty flame]

<@&286206848099549185>

[devout snow]

@empty flame Has your question been resolved?

[devout snow]

@empty flame Has your question been resolved?

[still pulsar]

sorry, I had a 3 hrs prac sesh, dm me if you still need help on that question

[devout snow]

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[mental dew]

Guys i really need someone to help me with understand what are
Rational numbers
Irration no
Whole no
Integers

[grand smelt]

rational means a number that can be represented as a fraction

a fraction with whole numbers at the denominator and numerator

irrational is numbers that can’t be represented in such way, for exampless √2, π, e, etc

[loud root]

integers=whole numbers: 0, -1, 1, -2, 2 etc...

[grand smelt]

whole numbers are numbers with no decimal point^

and integers are the same thing,

there’s also natural numbers, which are the integers (whole numbers) that aren’t negative

whether or not you consider 0 to be a natural number is up to debate, idk if it is but it’s not that deep

i hope that helps

[mental dew]

So for example -2.7 , is this a while number or integer?

[grand smelt]

it’s neither

whole numbers and integers are the same thing

this is not whole as it contains a .7

[mental dew]

Ah ok

[grand smelt]

integers do not have decimals

[mental dew]

Thank you so much

[grand smelt]

no worries, feel free to .close :)

[mental dew]

.close

[devout snow]

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[upper mortar]

yo how would I get sqrt(368) == 4*sqrt(23)

[upper mortar]

like how does that simplification process work, i just have no clue

[supple knot]

https://www.wikihow.com/Factor-a-Number

[loud pebble]

@upper mortar you need to split the number, 368, into two factors

[upper mortar]

right ik that, its just how would u pick those numbers?

[loud pebble]

Personally, I like to split it into a square and a non-square. E.g., 16 and 23, because I then know that sqrt(16) is 4

[supple knot]

you can just use the primes

[upper mortar]

idk primes

can i do it another way?

[upper mortar]

but how did u get 16 and 23

did u just know off the top of ur head that it makes 368

[loud pebble]

not at all. i divided by 2, then by 2 again, then by 2 again, then again

[upper mortar]

why 2? and how does that get to 23 and 16, youd only have 1 num

[supple knot]

learn prime numbers

there are 7 of them in that image

[upper mortar]

are they important?

[loud pebble]

very

[upper mortar]

how so?

[loud pebble]

in this case, i kept dividing by 2, so 368, 186, 92, 46, 23, and i can't go any further

[upper mortar]

cant u get 23/2

x.5

[loud pebble]

well prime factorisations are important in their own right, but by knowing once i get to 23 i can go no further I know I can say 16*23

[upper mortar]

howd u get 16

and why cant u go further

or are u just going into the nearest int

[supple knot]

https://www.mathsisfun.com/numbers/fundamental-theorem-arithmetic.html

[upper mortar]

so a prime num is any num that cant be made by multiplying ints together

[loud pebble]

I am trying to find a square. by finding the prime factorisation, which is 2^4 * 23, I know I have sqrt(2^4)*sqrt(23)

[upper mortar]

did u intentionally chose 2? why not just pick 16 at the start

once u know 23

[loud pebble]

I highly recommend you look up how to do prime factorisations. a useful method is the prime factorisation tree

i chose 2 because of intuition, and because it's easy with the tree. if i knew 16 and 23 made 368 i could have just said that off the bat -- my mental maths skills aren't that great

[upper mortar]

ok but equally u couldve tried 2^1,2^2,2^3,2^4 and then u have ur number

once u got 16 did u multiply it goether to check?

[supple knot]

if a number isn't divisible by 2, it's not divisible by 4

[upper mortar]

huh?

[supple knot]

oh nevermind i misread

[upper mortar]

all nums are divisable by 2

[supple knot]

yes it doesn't matter the order how you get 16 and 23

there are many ways to do this

[upper mortar]

so should i just look up how to prime ig?

[loud pebble]

here's an example of finding the prime factors of 120. The answer in this case is 2 * 2 * 3 * 5 * 2, or 2^3 * 3 * 5, which I could say is sqrt(2^2) * 2 * sqrt(15) = 2*sqrt(30)

[supple knot]

just read this

[upper mortar]

i dont know why ur chosing these nums

[loud pebble]

Read that article first. if you're still stuck open a new Q and I can go through an example

[upper mortar]

i have read

it said a num cant be divided by another num

[loud pebble]

you can pick any factor. just pick whatever jumps out at you

[upper mortar]

but that doesnt make sense

[loud pebble]

take 368, what's the first most obvious factors you can think of?

[upper mortar]

2

[loud pebble]

yea

you see it's even, so you divide by 2

so your tree would have 368 at the top, then 184 and 2 as the children

[supple knot]

they give a systematic list in the image

[loud pebble]

2 is a prime, it can't be decomposed any more. 184 however isn't -- so you continue. You expand every branch until you can't (it's prime)

[upper mortar]

does exactly devided by mean like it wont give a decimal result?

[loud pebble]

yes

[upper mortar]

ooo ok

[loud pebble]

remember this: it doesn't matter what factors you choose since in the tree they all end up as primes -- i.e., every number has a UNIQUE prime factorisation

[upper mortar]

so 2 is prime?

[loud pebble]

yea, it can only be divided by 1 and itself

so i could divide 368 by 2, which is easy, or jump to 8. it doesn't matter, because i'd end up expanding 8 to be 4*2, then 4 to be 2*2

have a go at drawing out the tree diagram for 368 for me @upper mortar

[upper mortar]

alr

huh

[loud pebble]

why did u start at 512?

[upper mortar]

i started at 2

[loud pebble]

you started at the bottom?

[upper mortar]

ye

[loud pebble]

ah no, you start at the top. whatever number you are trying to find the prime factorisation of, you start there

then decompose it however you wish -- it doesn't matter how you divide it up, just keep expanding until you are left with only primes. every number has a unique prime factorisation so you'll always get the same answer, however you divide it up

(The easy cheat way if you spot an even number is to just divide by 2 which is why that happened with 368.)

[upper mortar]

so i hit 23

[loud pebble]

yea, you expanded down by dividing by 2 multiple times until you got 23

[upper mortar]

now i count how many times i stepped down and do 2^steps_down

[loud pebble]

so you know that 368's unique prime factorisation is 23 * (2 * 2 * 2 * 2 )

[upper mortar]

ye

[loud pebble]

which is 23 * 16

[upper mortar]

will that always work?>

[loud pebble]

so sqrt(368) = sqrt(23)*sqrt(16)

yes, always

if you get nowhere, i.e., you start with an odd number but there are no factors (not jsut that you can't think of any) you started with a prime, and you can go no further

[upper mortar]

then what do u do

u just cant do it

[loud pebble]

nothing. if someone said that i needed to simplify sqrt(23) I would say I can't. it's a prime. 23 has no other factorisation

[upper mortar]

and why do we not just convert it into decimal

why stop at 23 when u could do 23/2

11.5

[loud pebble]

it serves no purpose. saying sqrt(23/2) is not precise

we are looking for factors, integer factors

[upper mortar]

but cant u still count step down

so youd have 11.5 *2

[loud pebble]

11.5*32 = 368

[upper mortar]

huh?

[loud pebble]

remember, we are trying to split up 368

[upper mortar]

im saying for 23

like why cant i say 23/2

[loud pebble]

oh right

[upper mortar]

11.5

and keep going

can we not do 2^steps_down

and so then we cant simpify

[loud pebble]

well you'd go forever, and that leads nowhere useful, and the whole point of the tree is to find prime INTEGER factors. if we were to then report back to someone and say 'well, sqrt(368) = 2*sqrt(11.5 * 2)' that's not simplified anything; it's uglier than before

[upper mortar]

but its still equal

so its not 'incorrect' its just not useful for a human to do

[loud pebble]

yes and no

[upper mortar]

wdym

[loud pebble]

we are dealing with surds here, i.e., things which sometimes do not have finite decimal representations

[upper mortar]

if its equal it cant be incorrect, if people dont do it why are you claiming its useful to humans

[loud pebble]

saying that sqrt(368)=4*sqrt(23) is very useful

[upper mortar]

true

oh im specifically claiming decimals

[loud pebble]

saying sqrt(368)=4*sqrt(2)*sqrt(11.5) is not

[upper mortar]

the 2sqrt(11.52)

ye ok that makes sense

[loud pebble]

it's convention to never allow decimals in surds

we express in integer form

[upper mortar]

but if somebody was trained to recognize 'surds' it could be useful to them

but no1 else

so we developed a standard

just learn the easy stuff, dont simplify further

[loud pebble]

i kind of get what you're pulling at, but no

[upper mortar]

no to which part?

[loud pebble]

surds are useful because of simplification and later use; if i gave you the expression 2/sqrt(2), i can change that to be 2*sqrt(2)/2, which may be more useful.

if i gave you sqrt(368) there is nothing to do with it. but if i said 4*sqrt(23) you now have a 4, which is divisible by 2, and could lead to further simplification in an equation later

the point being: sqrt(368) has no visible common factors with anything, until I split it up

[upper mortar]

and sqrt 369 cant be simplified with prime nums right

[loud pebble]

yea it can

it's 3*sqrt(41)

[upper mortar]

oh right

what num cant

i thought u said 1

367?

[loud pebble]

anything that's already prime can't be split further

[upper mortar]

right 23

[loud pebble]

or a square, because you could just square root it. e.g., sqrt(4) is just 2

[upper mortar]

so we are just going off the basis that its really just not worth the effort

not helpful enough

[loud pebble]

wdym?

[upper mortar]

to go past prime

[loud pebble]

no it's not possible to get an integer factor past the primes

[upper mortar]

yes

and decimals are too anoying to work with

so just stop at prime

[loud pebble]

put it this way: you are conflating two problems:

1. Given some surd, simplify it
2. Find the prime factors of a number

Finding the prime factors is a helpful and quick method to find simplified surds. Not the only method, just one of them

[upper mortar]

yeah thats understandable

[loud pebble]

Prime factors are perfect in this case because every number has one prime factorisation

(and it will contain a lot of powers of 2, so you can square root things to get integers)

[upper mortar]

yep

[loud pebble]

often times you won't draw any tree; you'll just recognise it. If I said sqrt(32), I'd know that's sqrt(16*2) and therefore 4*sqrt(2)

if i were using that in some equation, i can now simplify with that 4. previously i couldn't do anything, it was just on its own, sqrt(32)

[upper mortar]

yeah i think that all makes sense to me now

and the theory behind it

appriciate you talking about the theory behind it

a lot of people have been telling me that u do it that way 'because it works'

[loud pebble]

np, just remember that they're 2 different things. at he heart of it is the desire to make things easier to deal with. the way we do that (not the only way) is to split it up into primes.

[upper mortar]

but now i feel i have a broader knowledge of it

[loud pebble]

oh i hate that. i always like to understand

np

[upper mortar]

anyways ty, have a good day

.close

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[devout snow]

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[reef pilot]

Can anyone tell me if these row operations are correct

[reef pilot]

am i allowed to do like R1 - R2 -> R2?

[upper nova]

you can do that

because that would satisfy rule 3 which is being able to add a multiple of one row to another

which would mean R1 + (-1)R2 -> R2

[reef pilot]

Kk

[upper nova]

you could also do something like R1 - R2 -> R1 because that is equivalent to R2 - R1 -> R1 , -R1 -> R1

[devout snow]

@reef pilot Has your question been resolved?

[devout snow]

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[gilded wharf]

Hi guys, could you please check if I answered question a and b correctly?

[devout snow]

@gilded wharf Has your question been resolved?

[gilded wharf]

<@&286206848099549185>

[midnight dirge]

seems right i guess

i mean its just trivial multiplication

[gilded wharf]

Are u certain @midnight dirge ?

[midnight dirge]

...

[gilded wharf]

?

Ok, so how do I answer c?

What is the area scale factor?

[devout snow]

@gilded wharf Has your question been resolved?

[gilded wharf]

<@&286206848099549185>

[lyric imp]

Hi so your first step is to read the rules

!15min

[devout snow]

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.

[lyric imp]

Do not ping more than once

[gilded wharf]

Sorry, very sorry

.close

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[serene wren]

Help on these two

[lone ravine]

,rotate

[lone ravine]

For the first one try to write everything in terms of 3^x

[serene wren]

ok

Its right?

[lone ravine]

I can't read it

[serene wren]

Better?

[lone ravine]

Yes

Can you solve for x now?

[serene wren]

Yes, but its in this part that in stuck

[lone ravine]

If you multiply by -3/25 what do you get?

[serene wren]

-45/25

[lone ravine]

Can 3^x be negative (for real x)?

[serene wren]

no

[lone ravine]

So no solution

[serene wren]

oh ok

About the other

I already did this

[lone ravine]

,rotate

[lone ravine]

How did the 3.5^x turn into a 5^x?

[serene wren]

Wait, where?

[lone ravine]

Like what did you do to get to step 2?

[serene wren]

Only separated them

[lone ravine]

Is 3.5 3*5 where you live?

[serene wren]

3.5

[lone ravine]

Like 5^2.5^x= 5^[x+2] ????

[serene wren]

yes

[lone ravine]

https://tenor.com/view/wtf-blink-bruh-show-man-wtf-going-on-gif-21848921

I've never seen such a notation

[serene wren]

The point is the multiplication

[lone ravine]

And how do you write 3+1/2

[serene wren]

the same way

[lone ravine]

https://tenor.com/view/my-god-what-did-i-just-saw-hitting-computer-im-mad-right-now-gif-16617551

OK, makes sense now

[serene wren]

srry, im making exchange in other country

[lone ravine]

I think it is correct. You should probably doublecheck with calculator

[serene wren]

k

thanks for the help

[lone ravine]

Did you solve for x with log ?

[serene wren]

no

didnt learn log yeat

[lone ravine]

So devide by 508/25

[serene wren]

ok

[lone ravine]

What do you get then?

[serene wren]

20,32

[lone ravine]

Try again 1256/508*25

[serene wren]

61,8110

[lone ravine]

Yes

So 5^x = 61.8110

If you want to know x you type in log base 5(61.8110)

log is the reverse of the exponential function

Like arctan to tan

So x=2.562

[serene wren]

Oh ok

Makes sense now

.close

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[pale solar]

Need help on this one i need to solve for X

[restive river]

you would combine like terms which would be 5x and -4x since they both have x in them

soo

5 - 4

1

y=1x

[pale solar]

Thanks i wasnt too sure cause it a moving around equations question

Wait

I dont think thats how it works

[restive river]

o-

[pale solar]

Cause how would i put a 1x

[restive river]

is this algebra

[pale solar]

Yea

[restive river]

I WOULD ASSUME but dont trust me

ping helpers

[pale solar]

Ok

Do i say @ helpers cause i feel rude if i do cause i ping multiple people at a time

[scarlet peak]

Don't @ for 15 minutes

if y=X then x=y

It's like 6=3x2 and 3x2=6

[pale solar]

Oh yeah cause 1=x

[scarlet peak]

Yeh

[pale solar]

.close

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[hardy trail]

Hello everyone, I am a programmer and I am trying to implement a system in which a random price between $5000 and $50,000 is calculated from a scale of 0 to 100

[hardy trail]

I would like to use a graph like this

[whole otter]

what

[hardy trail]

And I'm wondering if someone could help me with coming up with a formula to map a graph like that

For example given the scale (t) = 50 it will output $15000

t = 10 will equal approx $7800

and t = 100 will equal $50,000

I'm really not familiar with this sort of maths so any help would be greatly appreciated

I will pay

[devout snow]

@hardy trail Has your question been resolved?

[hardy trail]

.close

[devout snow]

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[hasty marten]

review hw. How do I find the inverse of this function? I can show that it's odd. but I do not know about the inverse part.

[hasty marten]

.close

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[olive mango]

Is this histogram skewed left or right in your opinon?

[autumn blaze]

i would say right

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[warped pawn]

yo

can u help me

[devout snow]

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[olive mango]

i think it would be left

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[timber pebble]

skew describes how the mean is moved from the median

you could think about it skew as a shift of the center of mass

if it helps

so like

if you have a bunch of people in a room

well, maybe this isnt helpful

but, youre right either way

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[mortal berry]

does a negative squared equal positive or negative

[pastel pasture]

Positive

[main gull]

Depends on how it's written

[main gull]

Not always

[mortal berry]

oh

[pliant vine]

neonn hii

[mortal berry]

so what would it depend on

[main gull]

If you have parentheses

[pastel pasture]

Oh you're on HWH

[main gull]

Because $-2^2 \neq (-2)^2$

[woven radish]

dldh06

[pliant vine]

lol

[pastel pasture]

This ain't squaring a negative number

Which is what they asked for

[mortal berry]

so like, if it doesn't have the parenthesis, would it equal positive or negatvie

[main gull]

They asked "does a negative squared equal positive or negative"
Both ways I wrote is squaring a negative number

It depends on if it has parentheses

[main gull]

Neg

[mortal berry]

oh alr

thanks

how do i close

[pliant vine]

.close

[mortal berry]

.close

[devout snow]

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[pastel pasture]

No it's not

In the first case, in essence you squared a positive number and multiplied it with -1

The second case was actually squaring a negative number

[main gull]

But reading it into words, negative 2 squared can mean -2^2

Or (-2)^2

Depends on what the how it's read

[pastel pasture]

💀

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[restive river]

I need help with number 2 and 4 I can’t come up with any linear equations that relates to the problem.

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[restive river]

<@&286206848099549185>

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[grave glen]

shut up nerd

shut up nerd

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[undone cape]

For the differential equation y'''+6y''+12y'+8y=0 you can get the soln y=e^{-2x} by trialling y=e^{cx}. Wolfram Alpha gives two other solutions of the form x e^{-2x} and x^2 e^{-2x}, what theory provides these solutions?

[split shoal]

Hm, not sure if it has a specific name, but when your characteristic equation (in this case r³ + 6r² + 12r + 8 = (r + 2)³) has repeated roots, the solutions generated of the form e^rx are not linearly independent, so to get around the issue we multiply by x until we get sufficient linearly independent solutions.

[keen wren]

(the phase to look up for this is "solving homogenous linear differential equations")

[undone cape]

It's easier to show that for 2nd order odes just by expanding (when the soln is C1xe^rx + C2e^rx), but why do we expect the product rule and power rule coefficients to cancel at higher order

[split shoal]

Stole this proof from lecture slides.

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[restive river]

Using logarithmic differentiation here.. I feel like I messed up the log rules in regards to the ln(xtan(x))

[keen wren]

looks valid to me

[restive river]

why are u using logarithimic differentiation when power rule is doing the literall same thing I think ?

oh I see why u did that now

yeah

do you vouch for Sam as the problem looking valid? 😁

yes

the steps are valid

okay thank you! yeah i did ln(ab) = lna+lnb for that

now i think i take the derivative

however be carefull u could have a counter example if (xtan(x)) /(x^2+3x) < 0

ignoring those cases it's correct

okay okay one moment here

Looks weird to me

i’m usually used to just like one set of addition not 3 signs like that

[keen wren]

should be d/dx ln(y) on the left

[devout snow]

@restive river Has your question been resolved?

[restive river]

right

[restive river]

but the bottom is fine? so far? before taking d/dx

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[main saffron]

I'm struggling with how to write an epsilon-delta limit proof. My textbook doesn't include any fully written examples, so here's my best go at it. Does this make sense?

[wooden wraith]

looks good to me

[main saffron]

Great, thanks!

In general, is the strategy to make the epsilon inequality look similar to the delta inequality? And then relate delta to epsilon?

[supple knot]

https://www.milefoot.com/math/calculus/limits/DeltaEpsilonProofs03.htm

[main saffron]

The steps listed are precisely what I need. Appreciate it!

.close

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[fast helm]

someone please explain

i dont really get what they did on the third line

i know its with product rule

but dk how they got that

[lunar harbor]

they used a product to sum identity
you can verify it by expanding out the right side if you want

[fast helm]

yes i get that

how does this turn into that

would i use product and sum

on 4sin7x and cos5x first

[wicked turtle]

they're just moving factors around

no trig identities applied

[lunar harbor]

^

i thought you were talking about the cos(7x-x) stuff lol

[fast helm]

i dont even get them moving the factors around

[lunar harbor]

yk how $a \times b \times c=b \times a \times c=c \times a \times b$

[woven radish]

messy circle creation

[lunar harbor]

it's basically that logic just with trig stuff

[fast helm]

yes

i get that

but i dont get why they put 2cos5x and 2sin7x

[lunar harbor]

so like the intuition?

because here, there's a factor of 1/2

so they multiplied the product of the 2 trig functions by 2

so that when multiplied with said 1/2, it gives 1

[fast helm]

yes

[lunar harbor]

👍

[fast helm]

yk

from 2nd to 3rd line

what happens to the 2

in 2sin7x

[lunar harbor]

they rewrote $4=2 \times 2$ then rearranged the factors

[woven radish]

messy circle creation

[fast helm]

yes ik

i mean 3rd to 4th

[lunar harbor]

what I said here

the 2 'cancels' with the 1/2 in the identity

[fast helm]

o

could you do the whole equation as 4cos5x(sin7xsinx)

or would it not work

[lunar harbor]

yeah it would work

[fast helm]

.close

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[fast helm]

how do you do this

[long kettle]

There's clearly missing info

f'(x) is a function

And it's not a constant function

Yet all the answer choices are specific numerical values

[fast helm]

nope

thats the whole question?

is is even possible

[long kettle]

So it seems like it wants you to sub in a point, but it doesn't give you the point to sub in

[fast helm]

ig its a error

[long kettle]

Is that a test

[fast helm]

ye

[long kettle]

We don't help with tests here

[fast helm]

past papers

[long kettle]

Homework, sure, but tests, no

Past test?

Is this a test you are currently taking for a grade

[fast helm]

no

its tests from year before

[long kettle]

Okay then

Looks like an error

[fast helm]

ye

.close

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[round current]

Hi, I have two questions. Im going over ACT math problems from a test right now.

1: A package of candy contains pieces each of which is 1 of 6 possible colors: brown, red, green, yellow, orange, and blue. In each package, 1/3 of the pieces are brown and the remaining pieces have an even distribution of the other 5 colors. What is the probability that a piece drawn random from the package is red?
options:
1/15
2/15
1/6
1/5
2/3

For this one, I don't quite understand why the answer wouldn't be 1/6. the answer is 2/15, but I don't quite know how to get there.

2: In the complex plane, consider the segment whose endpoints are the points corresponding to -6+3i and 2-7i. The midpoints of this segment corresponds to which of the following complex numbers?
-4 -4i
-4+5i
-2-2i
-2+2i
4+5i

I got B, -4+5i, but the answer is -2-2i. I don't quite understand how they got there either.

[round current]

And for clarification, I'm not taking the test right now. I did a practice one yesterday and I am reviewing the ones I got wrong.

for the second one, I just simplified 3i to -i, and -7i to i. I dont think that got me anywhere though

[topaz axle]

it just asks the average of two numebrs

-6 ... -2 ... 2

[round current]

ohh wait so

-6+2/2

[topaz axle]

yes

[round current]

-2

and then 5i is the same as 2i

so -2-2i

[topaz axle]

no, for the imaginey part

[round current]

Ah, I was trying to find the midpoint by finding the distance between them. So i got 8/2 and 10/2.

[topaz axle]

you do the avergae of two numbers

[round current]

Thank you!

[topaz axle]

for the first problem, you divide 2/3 by 5

you divided 1 by 6 instead

[round current]

I understand where you got 2/3 from and I understand where you got the five from, but why would you divide 2/3 by 5?

[topaz axle]

that's what division means

[round current]

is it because 2/3 is the odds of a non brown one and 5 are the amount of colors?

i think i understand

[topaz axle]

there are equal amouints of each of 5 colors, and they add up to 2/3

[round current]

thank you! sometimes I just need to talk through it to get a solid understanding of it.

.close

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[bitter granite]

im looking to find the inverse of $F(n)=\int_0^n{\frac{e^t}{t}dt}$

[woven radish]

Ars Gratiae

[bitter granite]

is there a well known answer to this question?

if so, I would like the steps that lead to the answer

correction: the lower bound should be 1 $F(n)=\int_1^n{\frac{e^t}{t}dt}$

$F(n)=\int_1^n{\frac{e^t}{t}dt}$

[woven radish]

Ars Gratiae

[half minnow]

i dont think so but i can provide you with the differential equation

[half minnow]

with the appropriate boundary conditions

[bitter granite]

i meant inverse as in inverse function, not $F^{-1}$ which one does your solution satisfy?

[woven radish]

Ars Gratiae

[bitter granite]

^

[half minnow]

F^-1 is the inverse

[bitter granite]

i meant inverse as in e^x is the inverse of the natural logarithm

[half minnow]

yes

i defined F^-1 as the inverse

did you think i meant reciprocal?

i would have simply written 1/F if i meant reciprocal

[bitter granite]

it seemed like it

[bitter granite]

i looked quickly through your answers and didn't take the time to understand them at first

wait

so $f^{-1}(x) \neq \frac{1}{f(x)}$ ?

[woven radish]

Ars Gratiae

[half minnow]

usually no

it would be obvious from context which one was being referring to tho

if i write

,w tan^-1

[woven radish]

Results provided by WolframAlpha

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

Requested by S̨̥̫#8871

[half minnow]

thats the definition of arctan

aka inverse tan

[bitter granite]

ahh

[bitter granite]

in most of my education, ^-1 in a function referred to its reciprocal

[half minnow]

its unfortunate notation

but there's no other way to refer to inverses

you can always represent reciprocals as 1/f

but you cant do that with inverses

[bitter granite]

true

Thats why I prefer the inverse of a function to be $\mathrm{inv}(f(n))$

[woven radish]

Ars Gratiae

[bitter granite]

to be written as*

[devout snow]

@bitter granite Has your question been resolved?

[bitter granite]

umm

[bitter granite]

i still have to read through this, im multitaskin rn

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[frigid tusk]

anyone in this channel

[devout snow]

Please don't occupy multiple help channels.

[wooden veldt]

you dont need to ask this everytime you open a channel

[wooden veldt]

read this

[devout snow]

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[wooden veldt]

.close

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[upper mortar]

ignore what the question in screenshot is asking for, i included it just because it provide given information
is this circles largest angle 288 meaning this triangles angle is 72?
according angle/360 = sector area/circle area
aka x/360 = 20pi/ 25pi
the outcome is 288 making the triangles O angle 72 right?

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[upper mortar]

.close

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[pulsar ginkgo]

Fourth time's the charm. Any clues on how to solve this?

[wooden wraith]

I saw you post this last night

I spent some time looking at it but never found a pattern that works for both of the first two

[stuck field]

I found one for first two, but it doesn't work for the third, cause the options...

[woven radish]

Result:

27

[earnest lodge]

same but mine sort of disregards the bottom right corner--

,calc 9*4-2^2

[woven radish]

Result:

32

[earnest lodge]

,calc 8*2-1^1

[woven radish]

Result:

15

[earnest lodge]

,calc 15*4-2^2

[woven radish]

Result:

56

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[astral finch]

Guys when I'm using Rolle's Theorem how am i supposed to check if the function is differentiable at a closed interval [a,b]

[pseudo basin]

you're supposed to check that it is differentiable at every point in said interval

[astral finch]

lets say a function $y=x^2/3 + 1$

[woven radish]

tren-setter go-getter

[astral finch]

Do i need to learn how to graph each function?

[pseudo basin]

no

but also, rolle's only requires your function to be differentiable in the open interval (a,b). differentiability at a and at b is actually irrelevant for rolle's.

[astral finch]

owh

[pseudo basin]

anyway, the function $\frac{1}{3}x^2 + 1$ is actually differentiable everywhere

[astral finch]

mb

[woven radish]

Ann

[restive river]

well you know that polynomials are always differentiable

[astral finch]

no i meant $x^\frac{2}{3} + 1$

[woven radish]

tren-setter go-getter

[pseudo basin]

if you meant $x^{2/3}$ then type $x^{2/3}$

[woven radish]

Ann

[pseudo basin]

anyway

[astral finch]

Alright thanks

[pseudo basin]

what is your interval

[astral finch]

(-4,4)

[pseudo basin]

ok

[astral finch]

is this a polynomial?

[pseudo basin]

no

[astral finch]

It needs to be an integer?

to be raised in an integer*

[pseudo basin]

the exponents on x in a polynomial need to be nonnegative integers

[astral finch]

Thank you

so lets say

back to my function

[restive river]

thats the cube root of x², n-th roots are differentiable too, but only for positive x hmm

[pseudo basin]

$x^{2/3}$ fails to be differentiable at 0

[woven radish]

Ann

[astral finch]

how would u know that

do u need to graph it?

or is there a way to check

[pseudo basin]

you can verify this by writing out the limit definition

[astral finch]

on my limit where does x tend

to

x->xo?

Can u write an example?

[restive river]

depends on which limit you do

[astral finch]

Yeah lets say i want to check

[pseudo basin]

.

if you want to go along with what i said,

[pseudo basin]

then you want to check differentiability at 0

[astral finch]

Yeah

lets say

i didnt know

[restive river]

x_0 = 0

[astral finch]

that its not differentiable at 0

[pseudo basin]

you didn't know what

then write out the limit definition in the general case, work through it in the general case, and look for things that can go wrong

[restive river]

oh wait they are basically the same for x_0 = 0

[astral finch]

Can u give me the formula?

just to make sure its the one ik

[pseudo basin]

$\lim_{x \to c} \frac{x^{2/3} - c^{2/3}}{x - c}$

[woven radish]

Ann

[pseudo basin]

determine all values of c for which this limit fails to exist

[astral finch]

x!=0?

idk

how can x tend to c

if its x - c

[restive river]

in a limit you can assume x≠c

[astral finch]

ye but why does x tend to c

ik a different formula

[restive river]

you want to evaluate f'(c)

or at least try to see if f'(c) exists

[astral finch]

YeaH

how would i solve

that limit

x-c=0 right?

[arctic field]

but x^2/3 - c^2/3 = 0 when x=c too

so you have to evaluate the limit in other ways

[astral finch]

How can i evaluate the limit in another way

dont tell me LH

probably LH tho right?

because its in the form 0/0

?

[arctic field]

no that would be circular logic

[astral finch]

so i can do the prime of upper and lower?

[astral finch]

whats circular logic?

[arctic field]

you use this limit in the derivative of x^2/3

[grim burrow]

the more correct way would be applying your knowledge of algebra

im sure you have solved limits like these before studying derivatives

[astral finch]

well i can do (x-c)^2/3

yeah but the limit tends to c

so im a bit confused

[restive river]

can you see why it doesnt exist for c=0?

[grim burrow]

bad algebra, and that's just my hint, good luck with it

[astral finch]

Do u believe my algebra is really bad?

like should i practice algebra too?

if i cant see the solution?

idk i can break the x^2/3 and c^2/3 apart

but how does that help

[grim burrow]

no, im saying your way of manipulating x^(2/3)-c^(2/3) into (x-c)^(2/3) is bad algebra

[astral finch]

it is correct atleast?

[grim burrow]

if you are really clueless, remember how you can factor a^3-b^3

[arctic field]

uh no

[grim burrow]

no, it's pretty incorrect

[astral finch]

yeah thats what i thought

Owh

sorry guys

[restive river]

why a³-b³?

[arctic field]

denominator

[astral finch]

i can factor it as x^2/3-2/3

[arctic field]

||difference of squares on top||

[astral finch]

and that gives as x^0

[arctic field]

||difference of cubes on bottom||

[astral finch]

so 1

[arctic field]

||cancel the singularity||

[arctic field]

?

[astral finch]

is Rolles theorem supposed to be like this?

or am i missing something

[arctic field]

no

[arctic field]

somehow this became a question of showing differentiability

[astral finch]

im studying rolles theorem

Yeah

for a rolles theorem

the interval (a,b) needs to be differentiable right?

[arctic field]

yes

[astral finch]

And im curious how to check if this interval is differentiable without graphing it

[astral finch]

.

[arctic field]

well

from normal differentiation rules

you know that the derivative is 2/3 (x^-1/3)

[astral finch]

yeah

[arctic field]

so that suggests theres a problem at 0

then you check if there actually is a problem

[astral finch]

Why

[restive river]

well only problem was n-th roots arent differentiable at x=0

[astral finch]

how does it suggest theres a problem at 0

[arctic field]

well how do you evaluate x^-1/3 at 0

[astral finch]

Im really confused rn

whats the problem if my derivative is 0

[arctic field]

$x^{-1/3} = \frac 1 {x^{1/3}}$

[woven radish]

夢雪

[arctic field]

your derivative is not 0

[astral finch]

You mean x cant be 0 because if written in that way the fraction is undefined?

[arctic field]

well x^-1/3 is always undefined at 0 no matter how its written

[astral finch]

Yeah mb

So

that way

ik theres a problem at 0?

[arctic field]

yes

[astral finch]

Lets say u were to solve that problem without graphing it

u would find the derivative of f(x) and see if theres a problem?

[arctic field]

yes

[astral finch]

Okay i think i understand now!

Thanks a lot!

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[astral finch]

I want to apply the Rolles Theorem

how to check if its differentiable

when i checked i found the derivative of f(x) and found at -4 i have a problem

the video says that f(x) its differentiable at [0,4]

[inland seal]

x is differentiable and sqrt(4 - x) is differentiable at (0, 4)

[astral finch]

owh nvm

[inland seal]

therefore x*sqrt(4-x) is also differentiable at (0, 4)

[astral finch]

u are right

My problem was that it is not differentiable at -4

[inland seal]

Why not?

It isn't at 4, not -4

[astral finch]

Yeah sorry

at 4

not -4

...

sorry

[inland seal]

all good

[astral finch]

thank u u helped me big time

cheers

[inland seal]

np

have a good day!

[astral finch]

u2!

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[short barn]

hello, im learning about newtons second law of motion, and im trying to calculate the total acceleration from the x acceleration and the y acceleration

[short barn]

i got the formula as sqrt(xAcceleration^2 + yAcceleration^2)

thats my formula

that i got using pythagorean theorem

but then that makes me question if that really works, since my xAcceleration is negative, squaring it makes it positive

would that give the right answer?

[left robin]

negative or positive is just a direction thing

so yes it does work

[short barn]

hmm, but wouldnt it be in the wrong direction then?

[left robin]

you are not calculating a vector though

you calculate a "magnitude" of a vector

[short barn]

yeah but a magnitude can still be negative or positive

doesn't squaring it make us lose that info?

[left robin]

i guess you have to lose it

[short barn]

lol

it doesnt matter i guess?

ok thanks

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[upper mortar]

hey so I solved this doing what did i do wrong?

ax^2 + axb + ab^2 = 3x^2 + 36x + c

a = 3 because ax^2 = 3x^2
b = 12 because axb aka 3xb = 36x

therefor ab^2 = 3 * (12)^2
meaning c = 432

[upper mortar]

oh... nevermind

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[round current]

hi there! I'll go through what I have with each of them + my questions.

[round current]

So for this one, what I started with is I did 40+120+50+10+5 because there were 10 votes for 4, 40 for 3, so on, and I divided that by 5 which got me 2.5. I wrote that in as the answer, however, the answer is 2 and 4/9ths. I dont quite know how they got to that answer.

[round current]

So for this one, I multiplied the 1/y on the bottom and the 1/x so they would have a common denominator, giving me x-y/xy. since it was a double fraction, I multiplied the top by that and got x^2-1/x-y. That was wrong as well, the answer is just x

and I really just dont know how to go about doing 59 and 60.

for 60 i noticed there were 4 radi per side of the triangle so i got 4r for each side, and then 2r for the base so i did a lil trig and got the height as 2r

so 4rx2r is 8r^2

divided by 2 is 4r^2

and oh shit yeah thats the answer

4r^2 root three

but how did they get the root 3?

<@&286206848099549185> so sorry for the ping! but im taking another test soon and i need to get it solidly in my brain early on

[devout snow]

@round current Has your question been resolved?

[round current]

any help would be really appreciated!

[devout snow]

@round current Has your question been resolved?

[devout snow]

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[devout snow]

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[restive river]

bro look at my drawing

[restive river]

it's so good!

@mooncake#4935

[cloud jackal]

That's pretty fire

[restive river]

IK

I'M A HUGE FAN

[cloud jackal]

I drew homer for u

[restive river]

that is so hot

[cloud jackal]

now solve the math problem

[cloud jackal]

omg

thats fucking beautiful

there are tears in my eyes

[restive river]

:^)

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[sturdy sable]

Hello I don't really have a homework to be helped with but I need to review for a short quiz about permutations

[restive river]

i've got just the thing you need

❤️

there you go

c:

[sturdy sable]

okay thanks

!

[restive river]

no problemo! 🙂

[sturdy sable]

But I do get confused in permutation of n objects taken r at a time, I need someone who would make sample problems and correct them if its wrong

I need sample problems to answer

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[slim pier]

For these kind of questions, i'm confused at where the predicates and quantifiers are supposed to be indicated. I referenced youtube videos but most of them only show simple statements like "A kid is angry"

[devout snow]

@slim pier Has your question been resolved?

[devout snow]

@slim pier Has your question been resolved?

[slim pier]

<@&286206848099549185>

[harsh wraith]

Just use the numbers?

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@slim pier Has your question been resolved?

[slim pier]

.close

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[wanton scarab]

how would i factor/solve this limit? I’m not really good at factoring, but I’m trying to figure out how to factor this limit.

[neon aspen]

tanx - tanx.cosx = tanx(1 - cosx)

[wanton scarab]

ok question

what happens to tanx(x) though?

like i just don't understand how it's factored

[neon aspen]

you can divide the numerator and denominator by tanx

then tanx cancels

[worthy magnet]

I suspect there's a misprint

why is it tan(x) everywhere else but tan x there

u get what I'm saying?

[wanton scarab]

yea i understand that, right now i'm just trying to understand how factoring with trig functions works, but i'll ask my classmates if that's a misprint.

[neon aspen]

no

[worthy magnet]

like how you do that with normal numbers

replace all tan x with n

factoring still holds

it's the identities that are different

[wanton scarab]

so why is tanx being multiplied onto cosx

is that an identity?