help-10

[obtuse pebble]

@sour lantern Has your question been resolved?

[sour lantern]

<@&286206848099549185>

[sour lantern]

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[proud wolf]

2.) Selecting 5 basketball players out of 10 team members for the different positions 8.

[proud wolf]

Why is it permutation?

[obtuse pebble]

@proud wolf Has your question been resolved?

[obtuse pebble]

@proud wolf Has your question been resolved?

[zenith spade]

Different positions

[proud wolf]

But why does it matter what positions they play they are still the same team

[zenith spade]

For example, think of a student council

A president, a vice president, and a secretary

All of them are members of the council, but they have different roles

Similarly in basketball, there are people who are point guards, centers, power forwards, etc.

[proud wolf]

So by making the members play distinct roles the order becomes relavent?

[zenith spade]

yes

[proud wolf]

I see thanks

.close

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[lime moon]

Im using complementary slackness for this question

But as x1 and x3, are zero, for the dual of the program can I only use the second constraint?

to calculate y1 and y3

[obtuse pebble]

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[timid silo]

just want to make sure

[timid silo]

#16 is invalid right?

no answers in the back and i want to make sure i understand this correctly

i can't see any way we can deduce r from all those propositions

[night solstice]

It's because of q

There's no way to settle on a truth value for q

[timid silo]

right

[night solstice]

From there, we can't settle on s

[timid silo]

can i ask one more logic related question

[night solstice]

Lemme finish with this thing just in case I missed it

[timid silo]

oh ok

[night solstice]

We don't need to care about q it turns out

We assume that at least one of p and s is true

That's from the third line

From the first, (r V s) -> p means that if p is false, (r V s) is false

So we know that (r V s) cannot be true if p is false

[timid silo]

yeah

that was a detailed and good explanation

[night solstice]

If p is true and s is false, r must be true

...but if p is true and s is true, then we don't know what r is

So yeah, no way to settle on r

It depends on the truth value of s

[timid silo]

does it only depend on r?

oh wait

it is

i see why now

[night solstice]

Remember, we assume that each line above that horizontal line is true

[timid silo]

s*

yeah, i get it now

that makes total sense

[night solstice]

Wait, (r V s) -> p can still be true if r, v and s are all zero, so r's value doesn't just depend on s

[timid silo]

In addition, I am doing 21 for practice, if I evaluated this correctly it reads negation (for all values of x, x>=x^2 is true) so all values of x, x >= x^2 is false, so negate that and its true?

[night solstice]

But there's still just no way to settle on it.

[night solstice]

I like this first-order logic notation since it makes domains and quantification very explicit.

Haven't seen it in so long. What the fuck am I doing with my life...

Anyway...

The statement's true.

You can find numbers for which x<x^2 (e.g. assuming x is real, x>1)

But then you're told to negate the claim that x>=x^2 for all x

That results in negating a falsehood.

[timid silo]

haha

thank you very much

helped me a lot

.close

[obtuse pebble]

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[hushed cairn]

A line with slope m passes through the origin and is tangent to y = ln(x/3) what is the value of m

[hushed cairn]

I have the derivative of ln x/3 as 1/x

But idk where to go fro. There

From*

[high lily]

consider a point P(p, ln(p/3))
on the curve

determine the slope at that point (using the derivative)
and the slope between that point and the origin

[hushed cairn]

Ok

Let me try that

Like this?

[high lily]

,rotate

[high lily]

i would've introduced another variable for the arbitrary point

[hushed cairn]

Another var?

Ok

[high lily]

like

consider a point P(p, ln(p/3))

[hushed cairn]

I did

Now what

[high lily]

solve for your variable

and hence determine m

[obtuse pebble]

@hushed cairn Has your question been resolved?

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[rotund geyser]

Im not really sure how to solve this :
Find the components of 2 vectors of length 1 that form a 90-degree angle with the vector v [1 -3]

[swift marsh]

Do you know about the scalar product?

[rotund geyser]

yes if it equals 0

it is a 90 degree angle

[swift marsh]

Alright

So let the desired vector be (a b)

And (a b).(1 -3) = 0

See what you can do from there

[rotund geyser]

So if my vector ''Z'' is (a,b) and my vector V is (1 -3)
I should do something (a 1) * (b -3)

Not sure about it tho

[muted gale]

Just figure out the product

[rotund geyser]

Well, am i right to say (a 1) * (b -3) ?

[muted gale]

a-3b=0

a=3b

[muted gale]

I thought the * is supposed to be a +

[swift marsh]

Idk if he’s done the cross product

[swift marsh]

Have you?

[rotund geyser]

No 😅

i've just started with the vectors

[muted gale]

Also, it says their lengths must be 1

[rotund geyser]

I know what a cross product is

[swift marsh]

Yeah okay

[muted gale]

Use the Pythagorean theorem

[swift marsh]

So word out the scalar product of (a b).(1 -3)

[muted gale]

a^2 + b^2 = 1

Uhhh

[swift marsh]

There’s an easier way tbh

Just unit vectkr

vector*

[rotund geyser]

I can show you how my teacher did it if it can help

[swift marsh]

I mean I’m telling you what to do

[royal solar]

bro, this has to be a joke

[swift marsh]

But sure of you qant

want*

[royal solar]

just (3,1)

3i + j

[royal solar]

inverse and flip sign

[muted gale]

Yeah

[rotund geyser]

so -1 3

[royal solar]

then divide by unit vector

[swift marsh]

Oh yeah tbh I was doing the 3d way

[rotund geyser]

To divide by the unit vector i have to find my length which would be square root (1^2 + 3^2

[swift marsh]

Or ‘a’ 3d way

[royal solar]

brooo😭

[muted gale]

💀

[muted gale]

Square root of 10

[swift marsh]

I’m so used to it in 3d

I’ve never really bothered with 2d before

[rotund geyser]

square root of 10 is 3.1622

[royal solar]

bro, I swear that’s high school stuff

[rotund geyser]

it is !!

[muted gale]

Just use the square root of 10

It’s exact

[leaden ibex]

approximately*

[royal solar]

just keep it as sqrt of 10

[royal solar]

ye

[muted gale]

And you just divide it by the horizontal and vertical components

[royal solar]

your vector is divided by a scalar

so

[swift marsh]

Yea but I skipped that

[royal solar]

you skipped hs?

[swift marsh]

No I just went on to a level whilst I was still in gcse

[rotund geyser]

Lets break this down alright
My vecotr V is (1 -3)
then i just flip the sign so i have a new vector that it (-1 3)
Then i do the square root thing to find what ? 1 unit ?

[swift marsh]

Think about perpendicular lines

[rotund geyser]

ye

[swift marsh]

Uh

[royal solar]

dw, I finished my Gcse in y 10

[swift marsh]

Likes perpendicular lines on graphs

[royal solar]

my school didn’t let me do my maths a level in y11

I would have if they let me

[swift marsh]

My teacher basically let me self-learn it her maths classes

[swift marsh]

Rather than the gcse stuff because they ended up just doing the same things again and again

[royal solar]

basically that

[leaden ibex]

you invert the vector and negate one component of it

Nice shortcut to get perpendicular vectors in 2d

[royal solar]

ye

in 2d

very specifically

[royal solar]

indeed

[swift marsh]

It’s not too bad in 3d even before you learn the cross product*

[royal solar]

3d and your dot product = 0

[leaden ibex]

You have a whole plane of vectors perpendicular to a single 3d vector

[royal solar]

it’s scalar product unless we’re tryna find the perpendicular vector of 2 distinct non parallel lines

[rotund geyser]

I just dont understand the 1/ square root 10

[royal solar]

ok, i’ll try explain this

so that initial vector there

it travels 1 and 3

[leaden ibex]

This is called "normalizing" a vector. Basically, you divide a vector by its length to get a unit vector in the same direction.

[rotund geyser]

Yes

[royal solar]

right

so, the total displacement is sqrt(10)

yes?

[rotund geyser]

Yes because its the result of my product

[royal solar]

yep

but we want our vector to only travel 1

[rotund geyser]

Yep which is 1 unit

[royal solar]

yep

so we divide the whole vector by sqrt(10)

[swift marsh]

Yea that’s what I was talking about, I see this problem as more ‘like’ that than just finding the plane

[royal solar]

how were you planning to do vector product with two, let me try it

[swift marsh]

Wdym?

[royal solar]

|i j
1 -3|

yeah it works i think

[swift marsh]

Oh 2d not 2 vectors

Was gonna say

[royal solar]

it still works

so it’s gucci

[royal solar]

-3i - j

[swift marsh]

Yep

And just adjust for unit vector obv

[royal solar]

oh ye

[rotund geyser]

I flip my sign now i have a new vector which would be (-1 3)
Then i do the product thing of my initial vector which will be Square root 10
And to find my unit i divide my ''x'' and ''y'' by the square root
x : -1 / sqr 10 = -.31
y : 3 / sqr 10 = .94

That would be one unit right ?

[leaden ibex]

$\approx$

[warm shale]

Remavas

[rotund geyser]

Ah, yes

[swift marsh]

Yeah but it’s better to leave in exact form

Unless the exact form looks outrageous

[leaden ibex]

,w continued fraction of sqrt(10)

[warm shale]

Results provided by WolframAlpha

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

Requested by Remavas#3737

[rotund geyser]

like that

[leaden ibex]

yes

[rotund geyser]

Its not that complicated

[swift marsh]

Yeah

If you think about the gradient of each vector from the origin it makes sense

Like how the normal gradient is the negative reciprocal

It works off that logic, it’s also obvious looking at a circle with the desired length as the radius (unit circle here)

[rotund geyser]

Not sure what would be gradient in French but i guess i figured the big picture of this problem

[swift marsh]

Um

[rotund geyser]

At first i just didnt knew how to find perpendicular vectors, but if i just have to flip the signs and stuff im fine with that

[swift marsh]

pente?

[rotund geyser]

YES

y2-y1/x2-x1

eeh

[swift marsh]

Yeah

[rotund geyser]

well something like that

okay alright thanks for helping me with that i really appreciate !

[swift marsh]

Np man

[rotund geyser]

.close

[obtuse pebble]

@rotund geyser Has your question been resolved?

[tall arrow]

Using the PEMDAS rules, and one parathethes, how can you make the following equation

So far, I haven't found the answer, and all I am doing so far is literally guessing by placing the parantheses somewhere.
Is there a better way of doing this without having to guess?

[wicked holly]

Is the : a division sign?

[obtuse pebble]

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[native sentinel]

hello, just need quick help with this one question :D

[restive ridge]

what have you done so far

[native sentinel]

well i started plugging in -1 for the n but then what do i do with the -2 for a1

[restive ridge]

why -1 for n?

[native sentinel]

bc its a -1 for a0

idk what to do with it

[high lily]

look at what you're being asked to find

what is the first box asking for?

[native sentinel]

a2 !

[high lily]

a_2 yes

and you're given that
$$a_n = na_{n-2} - a_{n-1} - 1$$
without overthinking this, which value of $n$ will most likely get you what you want?

[warm shale]

ℝamonov

[native sentinel]

wouldnt you just plug in 2 for the n values

[high lily]

yes, exactly

[native sentinel]

oh see i thought so! but the values it was giving me for a0 and a1 were throwing me off i thought i had to use those

thanks a lot!

[high lily]

well you will

[native sentinel]

oh? okay but when

[high lily]

what do you have after plugging in n=2

[native sentinel]

ooo okay wait i think. i got it thx

.close

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[granite thorn]

I gave myself a physics problem, that included a moving object ( P→(t) ). after some time I got those equations and I have no clue what to do with them, in the internet I only got results for first order differential equations. can someone please point me to a good direction?

[granite thorn]

<@&286206848099549185>

I know this might be more advanced then the usual questions here (although I saw some incredible things too), so maybe I should ask this on another channel?

[obtuse pebble]

@granite thorn Has your question been resolved?

[tardy epoch]

what problem are you even solving for

looks like circular motion
https://phys.libretexts.org/Bookshelves/Classical_Mechanics/Classical_Mechanics_(Dourmashkin)/06%3A_Circular_Motion/6.03%3A_Circular_Motion-_Tangential_and_Radial_Acceleration

[obtuse pebble]

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[granite thorn]

and I am taking into account the fact that the further away you are from the planet the less gravity you would have

.reopen

[obtuse pebble]

✅

[tardy epoch]

what do you mean "less gravity you would have"

[granite thorn]

$a=G\frac{M}{r^2}$

[warm shale]

Shainy_oreng

[tardy epoch]

So just basic newtonian mechanics?

[granite thorn]

yes

so the change in speed in any moment is $\frac{K}{\mid \vec{P}(t) \mid^2}$ in the direction of $-\vec{P}(t)$

when K is some constent

[fallow rose]

are you trying to get the differential eq. of motion?

or the analytic solution to said differential eq.?

[granite thorn]

this

[fallow rose]

ok

[obtuse pebble]

@granite thorn Has your question been resolved?

[granite thorn]

.close

[obtuse pebble]

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[obtuse pebble]

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[toxic elm]

how to find the lower quartile in this group data?

[obtuse pebble]

@toxic elm Has your question been resolved?

[obtuse pebble]

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[timid silo]

Can you help me on line plots.

[timid silo]

im very confused on line plots

and we started learning it

[nocturne minnow]

Maybe Khan Academy would help

[obtuse pebble]

@summer raven Has your question been resolved?

[obtuse pebble]

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[lost drift]

The Differential Equation is

[warm shale]

iooosef

[lost drift]

Is it correct that the general solution for this is

[warm shale]

iooosef

[worthy comet]

@lost drift yes

[lost drift]

thank you, looks like the choices in the quiz I got are all incorrect

.close

[obtuse pebble]

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[ionic crystal]

Find the equation of the line that is orthogonal to both u = 2i + 5j - 3k and the z-axis.

[obtuse pebble]

Please don't occupy multiple help channels.

[junior patrol]

@ionic crystal

[ionic crystal]

Oh thanks!

.close

[obtuse pebble]

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[wind spade]

I don’t remember how to solve #2

[wind spade]

Do I find the radians first using (-5.2,-4.4) and (0,0)?

Radius*

[nocturne minnow]

Pythagorean theorem

[wind spade]

but I don't have the length of any side of the triangle?

[nocturne minnow]

You do

[wind spade]

I only have the arc length and that point

do I use distance formula to find r?

[nocturne minnow]

The coordinates tells you the distance from the origin

[wind spade]

WAIT

OMG

you're smart

to find the angle I just use s=r/θ right?

s=rθ*

thank you I finished the problem

.close

[obtuse pebble]

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[obtuse pebble]

@lavish crow Has your question been resolved?

[lavish crow]

<@&286206848099549185>

[obtuse pebble]

@lavish crow Has your question been resolved?

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[swift marsh]

What have you tried? Show your work? What are you thinking?

[delicate bay]

@vagrant obsidian

[vagrant obsidian]

Hi

[vagrant obsidian]

So for this one I did
x+0.26=3x+0.14

And then I don’t know what to do after

[sage iron]

solve for x?

[vagrant obsidian]

I guess so

[delicate bay]

have u drawn a picture?

[vagrant obsidian]

Yeah I drawn down the right triangle

[delicate bay]

did u label what you could?

[vagrant obsidian]

Yeah

What do I do now

<@&286206848099549185>

@delicate bay

[obtuse pebble]

@vagrant obsidian Has your question been resolved?

[stable flume]

Do you just have to solve this equation

or did I miss the point

[timid silo]

If you apply soh cah toa it turns into that. sin and cos of complementary angles are the same thing.

[stable flume]

it was moreso a question to OP

[vagrant obsidian]

Nope I don’t

I got

0.26=2x+0.14
-2 2 -
— —
-1.86

Idk

[obtuse pebble]

@vagrant obsidian Has your question been resolved?

[nocturne minnow]

Will you please read #❓how-to-get-help before posting in every single channel?

[versed chasm]

Available channel ?

Where

[nocturne minnow]

In the section that says available

[obtuse pebble]

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[versed chasm]

İ got it all done

[obtuse pebble]

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[versed chasm]

<@&286206848099549185>

[obtuse pebble]

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[keen ingot]

does "neither" mean "not or"?

[fierce lagoon]

Under what context

[keen ingot]

logic

~(X v Y)

like that?

[fierce lagoon]

Oh then idk

[keen ingot]

ok, np

[obtuse pebble]

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[warm shale]

BASU

[obtuse pebble]

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[sacred root]

Bruh

[fierce lagoon]

Just reopen it

[sacred root]

Ok

.reopen

Huh

[fierce lagoon]

Well this seems like a fuck up lol

[sacred root]

I opened another channel

#help-11

[obtuse pebble]

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[noble kindle]

Is this on the right track?

I just want to confirm before I go through that painful computation

wait, the root test should be 1/n instead of 1/2

.close

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[timid silo]

Given 28 distinct rays with common end points, there are how many different angles that can be identified.

[obtuse pebble]

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[long belfry]

Yes it is John

[long belfry]

Root test is 1/2

Not 1/n

[obtuse pebble]

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[timid silo]

In the figure AOB is a straight line. OD bisects ∠AOC . If ∠AOC is 24° more than m∠1, what is the measure of ∠3?

Would this be right

angle 3+2 = 51x2
180 - both angles = 78
angle 1 = 78
51x2 - 78 = 24
means angle 3+2 is bigger than angle 1 by 24
51x2+78 =180
angle 3 = 51 = angle 2

Angle 3 = 51

Answer: 51

[obtuse pebble]

@timid silo Has your question been resolved?

[royal solar]

let m3 = x
4x = 180 +24
4x = 204
x = 51

looks right

[timid silo]

thank you so much!

.close

[obtuse pebble]

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[royal solar]

no worries

[obtuse pebble]

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[halcyon ruin]

What is wrong with the reduction of this?

[fierce lagoon]

Is this trying to do the limit definition of a derivative

And could you translate the text

[halcyon ruin]

To start with, we remove the brackets.

Now we can subtract some variables in the numerator

Now we can divide Δx in the denominator by Δx denominators in the numerator

Yes im trying to do the limit definition

But I got stuck

It's supposed to be 2ax+b

[fierce lagoon]

Yeah we usually use "h" instead of Δx

So this is gonna take me some time to look at

[balmy mortar]

Your last line does not follow

[fierce lagoon]

Put paranthesis around the "a • (x)^2 + b • (x) + c" part of the numerator, first fraction

[halcyon ruin]

You mean like this?

(a • (x+h)^2 + b • (x) + c)

[balmy mortar]

nvm i see why

[halcyon ruin]

why?

[balmy mortar]

you need brackets in the first line

pemdas

you've written
++-++

thats is just subtracting one term

[halcyon ruin]

But that is not part of the formula

[fierce lagoon]

Well you're subtracting f(x)

Which means f(x) in its entirety

You need to subtract f(x) in its entirety, not it's first term

[obtuse pebble]

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[sour lantern]

why while solving this inverse laplace transform we only take into account pole at s=3i and not also at s=-3i?

[obtuse pebble]

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[wanton dagger]

Actually I got it, answer key is wrong

.close

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[rotund ingot]

How can I prove $n^n \geq n \times n!$ for every $n \geq 2$.

[warm shale]

veganlatina

[obtuse pebble]

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[timid silo]

A standardized test is designed so that scores have a mean of 50 and a standard deviation of 4. What percent of scores are between 42 and 58?

[timid silo]

please help

is the correct anwer 47.7% ?

[brave bramble]

How'd you get the answer?

[timid silo]

it shows in the picutre

50-58

and in the middle its 54

and 47.7 points to it

is that right?

[novel knoll]

Sounds like you are reading whatever picture you are looking at wrong

[timid silo]

oh

[novel knoll]

If 50-58 is 47.7

You haven’t looked at 42-50 have you?

So why would 47.7 be the answer?

[timid silo]

shitt

between 42 and 58 hmm

then it woul be 95.4

since that is the majority

[novel knoll]

Wdym majority?

But yes its approx 95.4

[timid silo]

ight thanks

[obtuse pebble]

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[obtuse pebble]

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[languid vapor]

hey

[languid vapor]

guys can someone explain something to me

Q. In how many ways can we arrange the letters of the word MOON?

the answer is $\frac{4!}{2!}$ but i don't get why

[warm shale]

PixelWolf

[languid vapor]

my teacher just spoonfed this to me

[leaden ibex]

Well, think of it this way

Is MOON any different from MOON

[languid vapor]

no

and I know that since the letter is repeated twice i divide by 2!

but hang on a moment

[leaden ibex]

Brainfart (on my side), but yes, you can't tell the difference whether it's the first or second O

[languid vapor]

can you please tell me which one of these "general" formula did we use

that's what bugging me

[leaden ibex]

twice

4! - how many ways can I arrange 4 letters

[languid vapor]

yes

[leaden ibex]

2! - how many ways can I arrange the two Os

[languid vapor]

okay i agree

[leaden ibex]

We divide 4! by 2! because we actually don't care whether it's the first or second O

OOMN is the same as OOMN

[languid vapor]

okay I see

but which one is it out of the four main formulae ^^

[leaden ibex]

@restive ridge stop deleting messages 😢

[languid vapor]

or is there a different one for this question

[leaden ibex]

permutation without repetition

[languid vapor]

so this?

[leaden ibex]

but I would suggest not trying to blindly apply it to every situation

[restive ridge]

I always think that what I'm saying is correct, then that it's incorrect, and then that it's correct again lol

[leaden ibex]

😄

[languid vapor]

yeah so basically this doesn't always work?

[leaden ibex]

you just have to know what you're calculating

[languid vapor]

and there's no general form for the question I got asked

yeah I know

[leaden ibex]

If all you had to ever do was plug in numbers into formulas

math would be pretty boring

don't you think

[restive ridge]

if all you had to ever do was apply logic, math would be pretty boring

[leaden ibex]

no misquotes please

[restive ridge]

didn't mean to put that in quotes

my bad

[leaden ibex]

And I mean you can generalize it

[languid vapor]

but my point was that if I want to later revise for my midterm and don't have time to redo every exercise, and if i forget this exists (oh boy did we account for too many possibilities) then I'll be screwed because I don't have a general form to remember

[leaden ibex]

Very easy. Know what you are calculating. If you do 4!, you account for all possible combinations of the four letters, considering that each combination is unique.

In your case, that is clearly not true.

[languid vapor]

how

I know how but like I would want a neat generalization to use for later

[leaden ibex]

https://www.ck12.org/book/ck-12-basic-probability-and-statistics-concepts/section/2.4/

[languid vapor]

ily

@leaden ibex thanks a lot

i'm closing this and will ask again if anything stumbles me, thanks

.close

[obtuse pebble]

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[valid phoenix]

how can i find a 95% confidence interval for the true mean?

[obtuse pebble]

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[radiant isle]

can anyone help me with this problem? Normal simplification is not feasible. Is there any nice way to solve it?

[obtuse pebble]

@radiant isle Has your question been resolved?

[obtuse pebble]

@radiant isle Has your question been resolved?

[timid silo]

I think you should isolate the common part

[obtuse pebble]

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[somber inlet]

Hi, I'm having a lot of trouble with this question, I don't really know what to do at all

[robust sleet]

you can find out r

by dividing volume by h

and solving for r

80pi=pir²*h

16pi=pir² what will r be?

[somber inlet]

4?

[robust sleet]

yes

[somber inlet]

Do you then apply that to the surface area?

[robust sleet]

now u ccan solve surface area

[somber inlet]

Oh I see

Thank you!

[robust sleet]

np

[somber inlet]

.close

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[grand plaza]

Hello does anyone know how to get the second half of the question?

[grand plaza]

I am not sure because then there's only one angle and one side inside the triangle in ii

Unless the two sides on the right of the triangle = 185km?

[civic zealot]

If that angle is 20, then you know it's complimentary angle on the same line?

and you can find 2 of the sides since you know the speed of the boat and the time traveled.

[obtuse pebble]

@grand plaza Has your question been resolved?

[grand plaza]

I have that the inside angle is 160 but i only have 1 side since for part 1 it asked for 1 hour after it turned

[obtuse pebble]

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[fallow glen]

What is the variance when the sample of n = 5 scores produces SS=20?

[fallow glen]

From what I understand, I divided SS by the sample.

which is 20 / 5

So doesnt the variance equal to 4?

[brave bramble]

Produces SS = 20?

[fallow glen]

yes

[ionic cedar]

I believe your variance is 20/(5-1) = 5

[fallow glen]

Do not have to square or square root at the end?

[ionic cedar]

no

the square root is the standard deviation and the square is variance which is what you said you are looking for

[obsidian isle]

what is SS

[fallow glen]

Ohhh I see

Thank you very much!

[fallow glen]

sum of squared deviations

.close

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[vernal saffron]

how would I simplify this?

[river python]

well

what do you know about properties of exponents

[vernal saffron]

i know it involves -4^n * 4^-n

but that doesnt simplify right

[river python]

uhhh

not exactly

$(-1)^n4^n = (-4)^n$

[warm shale]

levio

[vernal saffron]

so then I get (-1)^2n+1/n?

[fierce lagoon]

First, simplify $(-1)^{n+1}$

[warm shale]

Umbraleviathan

[fierce lagoon]

We will dissect this

[vernal saffron]

-1^n*-1

[fierce lagoon]

Ye

So in the numerator, you'll get $-1 \cdot (-1)^n \cdot (-4)^n$

[warm shale]

Umbraleviathan

[fierce lagoon]

Simplify that

[vernal saffron]

the (-4)^n goes to (-1^n)*4^n

so then -1^2n+1 * 4^n

[fierce lagoon]

No quite

Use this property:

$a^n \cdot b^n = (ab)^n$ where n is any exponent

[warm shale]

Umbraleviathan

[vernal saffron]

so then -4^n

[fierce lagoon]

No. What is -1 • -4?

Well

So did you mean (-4)^n or -(4)^n?

[vernal saffron]

-1*(4)^n

[fierce lagoon]

Then yeah you're correct

Nice

So that's the numerator

From there, I think you know how to simplify the rest

[vernal saffron]

so I just get -1/n?

[fierce lagoon]

Why did it reopen?

[fierce lagoon]

Ye

[vernal saffron]

the bot is kinda wack

[fierce lagoon]

Bot kinda

Kinda did a funny

[vernal saffron]

do you know what I did wrong with my answer?

[vernal saffron]

this

[fierce lagoon]

Which one

Yeah you did a^n^b^n

which is like

Dear god uh

[nocturne minnow]

Bot is breaking

[fierce lagoon]

You made this mistake:

$a^n \cdot b^n \to a^{n^{b^n}}$

[warm shale]

Umbraleviathan

[fierce lagoon]

Which is false

Now idk about you but I wouldn't wanna work with

Whatever fuckery that is a^n^b^n

[vernal saffron]

uh wait let me redo it

oh wait yeah I see

ty for the help

[fierce lagoon]

Np

[vernal saffron]

.close

[obtuse pebble]

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[pastel dune]

Solve for Δθ
https://media.discordapp.net/attachments/343089687902027777/960059522607640586/qwe.png
This is my progress so far and I'm kinda stuck at this point. Am I going in the right direction even?

[pastel dune]

<@&286206848099549185>

[obtuse pebble]

@pastel dune Has your question been resolved?

[obtuse pebble]

@pastel dune Has your question been resolved?

[obtuse pebble]

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[chrome plover]

Hello
I am currently trying to programm a head tracking system. I used a magnetometer who gives values from -180 to 180. This value varies on the direction in which i'm looking. Now I have a problem at the switch from 180 to -180 because I want it to continue it's linearity after the switch. How can I calculate this?

[chrome plover]

Here is a picture how i thought it would look like

On the left is the value and on the right how it should looks like

If I'm lacking in infos just let me know

<@&286206848099549185>

[timid silo]

,rotate

[timid silo]

could you explain a bit more? @chrome plover

[chrome plover]

So for example i look in this direction

Ant than the value changes from like 160 to 180 and than skipps to -180 to -160

And I would like that it would be translated to a linear value

[timid silo]

convert it to 360 degrees?

[chrome plover]

Than I have a skip from 360 to 0

[timid silo]

oh

okay i still dont really understand what you need lol

if it doesnt matter if its 90 or -90 just take absolute value

then it would go 0 to 180 and 180 to 0

[chrome plover]

I'm gonna explain it further in about 30mins... Because of breakfast

:D

[obtuse pebble]

@chrome plover Has your question been resolved?

[chrome plover]

Basicaly it should make something like this:

[timid silo]

why to 100 when between 160 and -160 there are 40 degrees?

[chrome plover]

Oh yes forgot to mention but i have to be within 0 and 100... So I would basically multiply the value with 1.25

[timid silo]

could you also specify the input?

like you give that you move from -160 to 160?

[chrome plover]

I get this values from a gyro (electrical project)

So if i made a 180° spin the Area would change to -40° to 40°

But it have to work from all angles

[obtuse pebble]

@chrome plover Has your question been resolved?

[chrome plover]

Simplyfied it looks like this

That it ignores the blue line and only use the red and pink one

[obtuse pebble]

@chrome plover Has your question been resolved?

[obtuse pebble]

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[drifting sluice]

Hello, how to inverse f(x) = x^3+x^2-1

[high lily]

there's no nice way to do it

other than heavy algebra bashing

[drifting sluice]

I tried to to factorize it as (x-3)*(x^2+1/3)-x/3 but it only produced more x elements instead of reducing to one

[high lily]

what's the original problem?

[drifting sluice]

Actually I need to calculate derivative of inverse of that for x=-1

[high lily]

i suspected that finding the inverse isn't the original problem

https://xyproblem.info

consider looking up stuff on the derivative of inverses

and you should be able to find
f^-1(1) by inspection without having to explicitly find f^-1(x)

[drifting sluice]

Yea, and as I have been teached I ought to find it through
(f^-1(x))' = 1/f'(f^-1(x))

[high lily]

poor placement of the ' on the lhs

$(f^{-1})'(x) = \frac{1}{f'(f^{-1}(x))}$

[warm shale]

ℝamonov

[high lily]

and you want
$$(f^{-1})'(-1) = \frac{1}{f'(f^{-1}(-1))}$$

[drifting sluice]

For x=-1

Not 1

[warm shale]

ℝamonov

[high lily]

typo, but same idea

[drifting sluice]

That's right

[high lily]

explicitly finding f^-1(x) is unecessary

what you really want is to find f^-1(-1)

[drifting sluice]

I see

[drifting sluice]

Ok, I got it, thanks for your help Ramonov

.close

[obtuse pebble]

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[brave night]

Anyone know how they threw all that stuff in there?

[brave night]

<@&286206848099549185>

.close

[obtuse pebble]

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[ancient wedge]

If the word APRILFOOLS was arranged alphabetically, Then APSFOLOILR is in the nth arrangement, What is N?

[timid silo]

um

you mean you go through all permutations of APRILFOOLS in alphabetical order and you need the one which gives you APSFOLOILR?

[ancient wedge]

Yes it is, I want to know the method to find the arrangement.

[ancient wedge]

It can be arranged 907200 ways

Now with A being steady, It can be arranged in 90720 ways?

<@&286206848099549185>

[obtuse pebble]

@ancient wedge Has your question been resolved?

[ancient wedge]

Does having a double letter change the way of solving?

[obtuse pebble]

@ancient wedge Has your question been resolved?

[obtuse pebble]

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[minor valley]

How can I find angle z, I have found all other angles

[fierce lagoon]

Wel you know that ST and AB are parallel correct

[minor valley]

Yeah

[fierce lagoon]

That means that CA is a transversal of some sort

What does that say about angle CST and CAB

[minor valley]

It's says they're parralel?

[fierce lagoon]

Well

You have a transversal, CA

And you have two parallel lines that intersect at CA

So what just be true about angle CST and angle CAB?

[minor valley]

I still don't get what you're saying, they didn't teach that in school

Maybe I'm dumb

[high lily]

look up parallel line thoerems

if you're doing this type of question, they've should've taught you about them by this point

[minor valley]

.close

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[karmic vapor]

anyone know how to do this?

[fierce lagoon]

Is this a test

Or a quiz

Or some assessment

[karmic vapor]

homework

[fierce lagoon]

Aight

[nocturne minnow]

Trig ratios

[fierce lagoon]

Use arctan

In what relation are the sides to angle x?

[karmic vapor]

i am in secondary school i have not been taught that

all i know is

[fierce lagoon]

well

arctan is inverse tangent

[nocturne minnow]

You did it right

[karmic vapor]

it is also non calc

[nocturne minnow]

Work is a mess, but that's the way to do it

[fierce lagoon]

Yeah

But uh

That's a nightmare

[karmic vapor]

i am still confused

bc

thats not the final answer

and since its non calc

i am lost

[nocturne minnow]

,w (12-5sqrt(3))/(4sqrt(3)-5)

[warm shale]

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[nocturne minnow]

,w 23sqrt(3)/43

[warm shale]

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[nocturne minnow]

Looks like you made some algebra mistakes, not sure where

[karmic vapor]

i rationalised the denominator

[karmic vapor]

.

[karmic vapor]

this is the same as what u shown ...

[karmic vapor]

here

[nocturne minnow]

What happened to (-5)(5)?

[karmic vapor]

o mb

[nocturne minnow]

You didn't FOIL properly

That might be the mistake

[karmic vapor]

ok i will check it now

i got this now

[nocturne minnow]

Also, if you did 48sqrt(3) - 25sqrt(3) as the numerator, don't think you did that right either

Wait, things canceled out

You just didn't write that down

[nocturne minnow]

You didn't write the 60 - 20 * 3 part

,w sqrt(3)

[warm shale]

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[nocturne minnow]

Matches with this

[karmic vapor]

but

[nocturne minnow]

So you're good now

Use the unit circle

[karmic vapor]

i still have to do tan^-1(root3)

without a calc

[nocturne minnow]

To find the angle

[karmic vapor]

and i do not know how to do that

[fierce lagoon]

Well what kind of special right triangle contains a side of sqrt(3)

[nocturne minnow]

What's another way to write tangent?

[karmic vapor]

tan?

not sure

[nocturne minnow]

What's another way to write tangent in terms of sin and cos?

[timid silo]

Tan

[karmic vapor]

opp/adj ?

[karmic vapor]

i dont think i have been taught that

oh wait

no

[nocturne minnow]

I'm pretty sure you have

[karmic vapor]

sin/cos

right?

[nocturne minnow]

Okay, good

Using the unit circle, you know that cos relates to the x coordinate and sin relates to the y coordinate, right?

[karmic vapor]

i do not know anything about a unit circle

[nocturne minnow]

That's what you have to apply, if you're doing this by hand

[karmic vapor]

i have not been taught that 100%

i am a gcse student

[nocturne minnow]

I mean, you can draw triangles, but it's based on the unit circle

Pretty much, apply the unit circle, determine the angle(s) where sin/cos = sqrt(3), where as I stated cos is the x coordinate and sin is the y coordinate

[karmic vapor]

this is the way i know it

except i do not know radians

[nocturne minnow]

That's the unit circle in table form

Question still stands, what angle do you get when sin/cos = sqrt(3)?

[karmic vapor]

root3/2 and 1/2

where

sin is root3/2

and cos is 1/2

so 60

[nocturne minnow]

Or even better, your table tells where tan theta = sqrt(3)

[nocturne minnow]

Yes

[karmic vapor]

but

isnt it tan-1(root3)

so

is that just tan-1(60)

[nocturne minnow]

No, tan(60) = sqrt(3)

$tan^{-1}(\sqrt{3}) = 60$

[warm shale]

dldh06

[nocturne minnow]

The inverse functions are used to determine the angle

[karmic vapor]

so x is just 60

[nocturne minnow]

Yes

[karmic vapor]

oh

ok

thank you

.close

[obtuse pebble]

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[toxic elm]

Can someone check my calculation please?

[paper quest]

this is correct

continue

[toxic elm]

my final answer

[obtuse pebble]

@toxic elm Has your question been resolved?

[tardy epoch]

Plug it into your system of equations to see if it works

[obtuse pebble]

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[obtuse pebble]

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[haughty wharf]

Hi, Stupid question.
What are the odds of picking one outcome out of three, if you have two attempts and the one you pick is removed from the pool? First time should be 1 of 3, or 33% second is 1 of 2, 50%. How is the total calculated?

[fierce lagoon]

Multiplying the chances

Chance AB = Chance A • Chance B

1/3 * 1/2 = 1/6

[haughty wharf]

so 1/3*1/2= 1/6 ?

[fierce lagoon]

Yeah

[haughty wharf]

That would be 16.6%?

Why is it lower than the 33.3% odds in the first attempt? Shouldn't it be higher? Sorry, I am just really confused.

[fierce lagoon]

Well lemme think

Well I suck at probability so affirm my math with someone else

But I'm pretty sure it's 1/6

Because it's Chance B dependent Chance A

[haughty wharf]

That's what got me confused. It seems odd to have lower odds when you get another attempt with even better odds.

[obtuse pebble]

@haughty wharf Has your question been resolved?

[distant edge]

@haughty wharf there are 2 cases, getting the number first try and getting it on the second

Chance of first try is 1/3

Chance of 2nd try is the chance of the desired number x still being there (2/3) times the chance of getting the number x out of the 2 remaining ones (1/2).
This is ⅔•½=⅓

Total chance is case 1 plus case 2, i.e ⅓ + ⅓=⅔

@haughty wharf

[haughty wharf]

I see!

That makes sense!

So the second event is dependent on the first one failing

@distant edge Thank you

[distant edge]

No problem

[haughty wharf]

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[obtuse pebble]

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[timid silo]

how do i change x²/(x²+1)

[timid silo]

i have ∫x²/(x²+1)dx

[haughty coyote]

trick: x² = (x²+1) - 1

see how it helps ?

[timid silo]

damn

so it’s 1-1/(x² +1)?

[haughty coyote]

yep

[timid silo]

ooo

[haughty coyote]

turn 1 hard integral into 2 very easy integrals

[timid silo]

yessss

[leaden ibex]

This works fairly often, so I would recommend learning to apply this yourself.

[haughty coyote]

this is a common trick with fractions that have similar numerator and denominator

[timid silo]

so that’s just x + arctan(x) +c?

[haughty coyote]

,w integral of x²/(x²+1)

[warm shale]

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[leaden ibex]

you forgot you were subtracting the second integral

[timid silo]

ohh i’m stupid

thank u thank u

.close

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[ionic cedar]

Can someone please outline the steps to get between the two parts of the problem outlined in the picture

[robust sleet]

whats function z?

[ionic cedar]

That's a fantastic question...

[robust sleet]

ehhh i havent done surface integrals yet maybe solve for z in first equation

[vapid hamlet]

z should be the height of the lamina as a function of x and y

[ionic cedar]

I just can't see how to progress the problem from the part marked 'from here'

I solved the lamina equation for z and differentiated as appropriate

[vapid hamlet]

Have you solved for z in the paraboloid equation?

[robust sleet]

,w derivative of (1-x²-y²)/3 with respect to x

[warm shale]

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[robust sleet]

,w derivative of (1-x²-y²)/3 with respect to y

[warm shale]

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[robust sleet]

,w sqrt((1+(2x/3)^2+(2y/3)^2))

[vapid hamlet]

Ok, good, now pay attention to the factor $\frac{2}{3}$ in the right-hand side

[warm shale]

Zanarcane

[ionic cedar]

Okay looking

[vapid hamlet]

What do you get if you factor out $\frac{2}{3}$ ?

[warm shale]

Zanarcane

[vapid hamlet]

In the expression you derived

[ionic cedar]

I can't draw square roots to save my life

[vapid hamlet]

Yeah, now write it as $\frac{2}{3}\sqrt{\dots}$

[warm shale]

Zanarcane

[ionic cedar]

I am not following

[vapid hamlet]

Factor 2/3 out of the square root