help-0

[orchid perch]

i.e. given a tree that starts with event A and branches out to event B

i get that one of the arms that branch out of the event B are P(B|A)

i mean

im not sure how to explain this

does a path represent P(A cap B) or P(A)* P(B)?

[tacit arch]

this?

[prime badge]

a path is an outcome

[tacit arch]

https://www.mathsisfun.com/data/probability-events-conditional.html

[prime badge]

it represents A and ~B for example

[orchid perch]

yes thats whaht i mean

a path can be A and ~B

or A and B

or ~A and B

or ~A and ~B

[prime badge]

exactly

[orchid perch]

yes but

what is thhe probbability here

like for example

or ~A and ~B

the fourth one

is that $P(\overline{A} \cap \overline{B})$

[ocean seal]

metnal

[orchid perch]

or P(~A) multiplied by P(~B)

[prime badge]

yes

not conditional

the first one

[orchid perch]

alright thanks thats what i needed to know

wait but

so if a path has 0.1 and 0.4 probbabbilities for example

the path ~A and ~B

does that mean $P(\overline{A} \cap \overline{B})=0.1 \cdot 0.4$

[ocean seal]

metnal

[prime badge]

a path is an endpoint

you mean like a branch

[orchid perch]

i mean a path of 2 branches each with a given probability

[prime badge]

i don't know, you stopped making sense

ima go

[orchid perch]

oh k 😦

i meant like a route

like from an event to the next

if ~A is 0.4

and then we jump onto ~B or B

and B is 0.1

that means P(~A and B) is 0.1 * 0.4?

[prime badge]

it means P(~A) × P(B | ~A) and also P(~A and B)

[orchid perch]

ohhh righttt

because we cant know if theyre independenbt or not

hmmmmm

righht thanks 😄

.close

[lone heart]

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[obtuse bronze]

let |x|=y (y+5)(y-1)=0 y>=0 since |x|>0 so y=1 |x|=1 which yields x=-1,1

If you wanna do math do aops.com

[vapid steppe]

Can I use Quadratic Formula

[obtuse bronze]

I guess you could, but factoring would be a lot easier

[vapid steppe]

so (|x|+5)(|x|-1)=0
|x|=-5
|x|=1

[obtuse bronze]

ya but |x|=-5 is absurd so |x| only equals 1

9-T/6=5

[vapid steppe]

9- T/6 = 5

[obtuse bronze]

https://www.geogebra.org/geometry/tmdp9nba

Moving the points is so satifying

I made this yesterday

[fallen verge]

Please move this discussion somewhere else

This is a help channel

[pseudo ice]

...you don't have access to Google, but you do to Discord?

[wind cloak]

Dude I was wondering the same thing

[obtuse bronze]

3n-2=x+5

[fallen verge]

Please read #❓how-to-get-help @jolly sluice

[vapid steppe]

bro what happened to my help channel

[wind cloak]

And the kid is using Discord to learn math how nice of him

[fallen verge]

I suggest reopen one

Open another one not reopen lol

[obtuse bronze]

x^2/4-9=9

where x is the diMeter

[lone heart]

@vapid steppe Has your question been resolved?

[lone heart]

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[torn dagger]

I understand that y = 6 part however where it says 6 = -6/-1

im confused how it got that this is Graphing piecewise functions btw

[solid gust]

My guess is that: since you know the slope is +6, which means when x-coordinate decreases with 1, so does the y-coordinate with 6.

And the opposite, when x increases with 1, y increases with 6.

[lone heart]

@torn dagger Has your question been resolved?

[lone heart]

@torn dagger Has your question been resolved?

[lone heart]

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[sand creek]

Need help with question 3

[lone heart]

@sand creek Has your question been resolved?

[rocky grove]

Could you post a more high-res image please?

Nvm

I suggest rewriting the expression as fractions

[tacit arch]

factor out (x-2)^(-5) and (5x+3)^(-7)

[lone heart]

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[alpine sable]

I'm new to trigonometry

[sullen meteor]

What’s the question

[alpine sable]

And need some help understanding what I'm actually doing

[sullen meteor]

Ok

Do you know soh cah toa

[alpine sable]

Yeah we learned those last class ( I have class Tuesday and Thursday )

[sullen meteor]

What question is hard for you?

Could you give an example

[alpine sable]

So the first question is sin 11pi/3

[sullen meteor]

To find the answer of this plug it into a calculator

[alpine sable]

Sorry

[sullen meteor]

But make sure the calculator is in radians

[sullen meteor]

Nah it’s all good

[alpine sable]

We have to find it with no calculator

[limpid turret]

gotta know your unit circle here

[sullen meteor]

Oh then know the unit circle

First simplify it into the first quadrant form

Actually first subtract 2 pi from it

Cause it’s one rotation

[alpine sable]

The professor said to do it using the reference angel

[sullen meteor]

So it’ll be 5pi/3

The first quadrant would be sin pi/3 however since it’s in the fourth quadrant it’ll be -sin pi/3

Do you know the 30 60 90 triangle

[alpine sable]

No we have not leaned that yet

[sullen meteor]

Oh then maybe it’s called the pi/3 pi/6 triangle?

[alpine sable]

Only memorized 30°,45°,60°

[sullen meteor]

Ok that’s good

Cause pi/3 is 60 degrees

And 60 degrees is root3/2 for sin

[alpine sable]

So the first quadrant of the graph

[sullen meteor]

So your answer is -root3/2

[alpine sable]

The answer is the book says -1

[sullen meteor]

Yeah basically first step: subtract 2 pi cause it’s the same rotation. Step 2 is: convert to first quadrant: step 3 is to evaluate

[sullen meteor]

That’s impossible

What

@limpid turret no way is this -1 right?

[limpid turret]

for sin(11pi/3)?

Impossible

books tell lies all the time

[alpine sable]

I'm sorry!!

[sullen meteor]

Yeah it’s -root3/2

[alpine sable]

It's over 2

[limpid turret]

-1/2?

[sullen meteor]

I thought it’ll be -root3/2 but I might be wrong

[limpid turret]

-1/2 sounds right in my head

[sullen meteor]

Cause sin pi/3 is root3/2

[alpine sable]

Let me start over its sin 11pi/2

[sullen meteor]

…..

[sullen meteor]

First step is always to subtract two pi

Subtract 2 pi until it’s impossible to

@limpid turret could you help @alpine sable I gtg to class rn

[limpid turret]

sure

[alpine sable]

So in sa sense reversing the rotation

[limpid turret]

I'm at work so I'll have slow replies

But I am indeed around

Like a ghost

[alpine sable]

All good

[limpid turret]

👻

okay so, we are looking for sin(11pi/2), correct?

[alpine sable]

Ok so I minus 2 pi from it. And correct

[limpid turret]

Yes. But do you know why you subtract 2pi?

[alpine sable]

Because 2pi is a full 360 rotation

[limpid turret]

yes perfect answer

[alpine sable]

So when we subtract we get...

[limpid turret]

Okay so what is 11pi/2-2pi?

[alpine sable]

9pi/2 ??

[limpid turret]

Not quite. You did 11-2 to get 9

[alpine sable]

Yes lol

[limpid turret]

Do you remember how to add and subtract fractions?

[alpine sable]

Yes

[limpid turret]

$\frac{11\pi}{2}-2\pi=\frac{11}{2}\pi-2\pi=(\frac{11}{2}-2)\pi=?$

[ocean seal]

SWR

[alpine sable]

Ok I'm confused how u got that

[limpid turret]

which part?

[alpine sable]

How to subtract the fractions

[limpid turret]

this part?

Are you not sure what to do next from here?

[alpine sable]

Yes

From there

[limpid turret]

You need to have the same denominator for both numbers

[alpine sable]

So 2

[limpid turret]

you have 11 halves and 2 wholes

1 whole is two halves, so 2 wholes is 4 halves

So now you are subtracting 11 halves and 4 halves

[alpine sable]

So 7pi/2

[limpid turret]

huzzah

exactly right

Now

Tell me you if you notice something with 7pi/2

Something important, perhaps something you should consider

(that's a little vague, so sorry if you don't get it)

[alpine sable]

Equals 630 degress???

[limpid turret]

Probably (I didn't check)

Okay lemme say this, we want the angle to be between 0 and 2pi

Is 7pi/2 between 0 and 2pi?

[alpine sable]

No it's not

[limpid turret]

correct

So we must subtract 2pi once more.

[alpine sable]

So keep unwinding let me do the math

So 3pi/2

So still keep unwinding??

No that would make it negative and we would over shoot right?

So what's next

[limpid turret]

Now we have our angle

We need to know where it points to on the unit circle, and then measure the coordinates of that point

x coordinate is cosine, y is sine

[alpine sable]

So sine falls right down the middle so -1

[limpid turret]

https://tenor.com/view/perfection-michael-fassbender-perfectionist-perfect-gif-7910211

[alpine sable]

Awesome!!

The next one is cos (7pi)

We can bring it down to just pi that Is half a rotation

So 180

So cos equals 0?

Cos is x right

[alpine sable]

The terminal side is along the x axis going to 180

[limpid turret]

what?

[alpine sable]

Wait

It negative

It's to the left so it's negative

[limpid turret]

negative what, exactly

[alpine sable]

-1

[limpid turret]

bingo

[alpine sable]

Next is tan (6pi)

So tan is y/x

But since it's 6

We will rotate back to the origin so it's zero

Next is cot (7pi/2)

So also zero??

[limpid turret]

You're getting faster

[lone heart]

@alpine sable Has your question been resolved?

[alpine sable]

Ok this one is tricky. Cos (-3pi/2)

So we are adding now to go the other way

So we would add 4/2 that would give us pi/2

So zero?

Great! Takes me a little bit to think about lol

So next ones are sin 45°+ cos 60°

Do I convert them to radiant?

[limpid turret]

If you don't know the value in degrees, then yea

[alpine sable]

So sin pi/4 + cos pi/3

Hmm

Not sure

[limpid turret]

two ways:

1. review your unit circle

2. Geometry

I recommend 1

2 only if you want to to know why the answers in the unit circle are what they are

[alpine sable]

So I'm guessing

Sqrt 2/2 +1/2

Hmm

So you have to remember that whole circle ???

Are just the first part

Quadrant

[limpid turret]

first quadrant is fine

Really, all you need is 0, 30 and 45, then trig identities

sin(30)=cos(90-30)

sin(x)=-sin(-x)

cos(-x)=cos(x)

cos(x)=-cos(180-x)

[severe ice]

What is the sample skewness formula? Here are the two things i get
$\tilde{\mu}{3}=\frac{\sum{ }^{ }\left(C_{i}-\overline{x}\right)^{3}}{n\cdot S_{C}^{3}}$,
$\tilde{\mu}{3}=\frac{\sum{ }^{ }\left(C_{i}-\overline{x}\right)^{3}}{\left(n-1\right)\cdot S_{C}^{3}}$

[ocean seal]

Sonni

[limpid turret]

!help

[lone heart]

Please read #❓how-to-get-help

[severe ice]

;-;

[spiral bronze]

Find the unit rates. If necessary, round your answers to the nearest hundredth.

6 ounces for
$7.89

can someone help please

[limpid turret]

!help

[lone heart]

Please read #❓how-to-get-help

@alpine sable Has your question been resolved?

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[lone heart]

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[plucky monolith]

so

i just need help with all the statements

the question below doesn't matter

<@&286206848099549185>

[wind cloak]

What angles do you know 13 is equal to

[plucky monolith]

15 3 1 5 7 11 9

right?

[wind cloak]

If you know 13 is equal to 3

What do you need help with

I assume you have the rationale behind it

[plucky monolith]

okay ill try to do it

like this???

what would the reasons be😭

mb

[wind cloak]

I'd say 3 = 11 and then 11 = 13 thus 3 = 13

[plucky monolith]

i thought u were offline

[wind cloak]

You should try figuring out why

Have you learnt properties of transversal lines

Corresponding angles and what not

[plucky monolith]

yeaish

i dont really know them well

alr

yea

itll work

ty

.close

[lone heart]

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[restive chasm]

Question from conic section ellipse.

[wind cloak]

Screenshots

[restive chasm]

I tried to first get parametric points and get the intersection of tangents at those points. Then, I made them lie on the director circle of ellipse. After that, I tried to get the normals at those points and tried to get their intersection. Now, the question was to get the locus of intersection of normals. I tried substituting but could not get anywhere after that. Sending my attempt.

Handwriting is a little messy. Sorry for that.

[lone heart]

@restive chasm Has your question been resolved?

[restive chasm]

Anyone got something?

<@&286206848099549185>

[wind cloak]

Screenshot the question

[restive chasm]

OK

Question no 10

Got something?

Coming back in around 20 minutes.

[lone heart]

@restive chasm Has your question been resolved?

[restive chasm]

Someone got something?

[limpid turret]

I'd start by finding the equations of the tangent lines

[peak cipher]

man this was a really lengthy sum, had to take some help to finish it

did you get it though?

@restive chasm ?

[restive chasm]

Nope.

At the end, I was unable to completely eliminate the parametric coordinates in theta

[peak cipher]

ah

well this isn't my idea but you can consider the quadrilateral formed by the (x1,y1), the parametric coordinates and (x,y) to be a rectangle

[restive chasm]

Ah yes.

[peak cipher]

yeah so by doing that

you'll get two coordinates for the mid point

[restive chasm]

Let me try. 1 min

[peak cipher]

yep

[restive chasm]

Hello, I am done.

Thank you. That little observation of rectangle makes the question a lot easier.

Help me again sometime.

[peak cipher]

haha surely

[restive chasm]

Bye for now.

[peak cipher]

bye bye

[restive chasm]

.close

[lone heart]

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[alpine sable]

Uhh help

[agile raptor]

is it subtraction property equality in the first two ? in 1.

damnit

[alpine sable]

What is arc length if BC

Diameter is 7

[autumn condor]

first calculate the angle BC

[alpine sable]

100 degrees ?

[autumn condor]

then you can determine the arc lenght by using the formula 2pi r (angle/360)

yes

[alpine sable]

So the answers non of the above

[lone heart]

@alpine sable Has your question been resolved?

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[alpine sable]

.close

[lone heart]

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[tough flame]

For this question, is there anything that hints what the lower of integration going to be? I'm guessing its "0", but where is it mentioned in the question, is it just assumed?

[tough flame]

$\int_a^{1} \bqty{\pqty{ 3 - \arctan x}^2} :dx$

[ocean seal]

LP

[wind cloak]

$\bqty{A}$

[ocean seal]

NEONPerseus

[wind cloak]

😲

[lone heart]

@tough flame Has your question been resolved?

[lone heart]

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[broken falcon]

Help with the limit pls

[crimson totem]

translate

[broken falcon]

the limit of the succession

[pliant cedar]

well it just asks to evaluate the limit ig

[broken falcon]

yes

in this case becuase is +infinite taylor can't be used right?

.close

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[cyan drum]

[wind cloak]

Keep plugging in

[cyan drum]

Do I have to calculate x -> 1 from the left and right

Or just plug in x=1

[wind cloak]

Just x = 1

[cyan drum]

So is the answer 1/2?

[gray isle]

you'd do one sided limits

[cyan drum]

How exactly do I do that

[gray isle]

have you made any attempt to eval the one sided limits?

[cyan drum]

I did, but im not sure if what I did was even correct

[gray isle]

show work

[cyan drum]

As you can see, I had no idea what I was doing

You can refer to the graph but I took the value of f(1) by the left and right hand side

[gray isle]

you shouldn't be using the value of f(1)

gimme a min to double check my own math

[cyan drum]

Then what should I be using? Sorry for the questions

[cyan drum]

Alright!

[gray isle]

should should be considering stuff like
what value f(2-x) approaches as well as whether its from above/below as x→1^-

do you have any idea what i'm referring to

[cyan drum]

this part?

[gray isle]

what value f(2-x) approaches as well as whether its from above/below as x→1^-
(instead of evaluating f(1))

[cyan drum]

so I have to consider the top and bottom

when x tends to 1 from the left side, f(2-x) tends to 2

when x tends to 1 from the right side, f(2-x) tends to 1/2

is that what you mean?

[gray isle]

you have those mixed up

(and also ignored stating whether you'd be approaching above/below)

note that for

x→1^-
2 - x could be donated as 1^+

[cyan drum]

could you write a few steps for me, I cant really understand through text, maybe the x->1^- part?

sorry 😢

[gray isle]

if you subtract a number slightly less than 1 from 2,
will get a number slightly more or less than 1.
eg is 2 - 0.999 more or less than 1?

[cyan drum]

more

1.001

oh....

[gray isle]

same idea applies to

x→1^-
2 - x could be donated as 1^+

[cyan drum]

so when x tends to 1 from the left side, f(2-x) is to the right side of f(1)

since 2-x > 1 in this situation

vice versa for x tends to 1 from the right side

is that it

[gray isle]

of f(1)
you shouldn't be using f(1) here

[cyan drum]

alright

so when x tends to 1 from the left side, I should consider the value of f(2-x) to be 1/2

[gray isle]

well you'd also want to state whether you're approaching 1/2 from above/below

[cyan drum]

from above

[gray isle]

yes

[cyan drum]

right?

[gray isle]

which you could now denote as
f(3/2 - 0.5^+)

[cyan drum]

and then for when x tends to 1 from the right side, f(2-x) tends to 2 from above

[gray isle]

and then for when x tends to 1 from the right side, f(2-x) tends to 2 from above
yeh

and apply the same idea to continue from

f(3/2 - 0.5^+)

[cyan drum]

and then calculate the values of both functions, if they are different then the limit does not exist

if its the same then thats the limit

[cyan drum]

is that just f(1)

[gray isle]

no

you shouldn't be using f(1) here

[cyan drum]

3/2 - 0.5^+

wait is that not 1

[gray isle]

note that \verb|f(3/2 - 0.5^+)| might be considered a bit of notation abuse; is supposed to represent
$$\lim_{u\to 0.5^+} f\br{\frac32 - u}$$

[ocean seal]

ℝamonov

[gray isle]

its pretty much the same idea as what we just went through

[cyan drum]

ohhh

$$\lim_{u\to 0.5^-} f\br{\frac32 - u}$$

[ocean seal]

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

[cyan drum]

so the other one is like this

[gray isle]

i have custom commands

[cyan drum]

did I do that wrong

oh lol

[gray isle]

and no

note that for the right side limit, the value was different: 2^+

[cyan drum]

$$\lim_{u\to 2^+} f\br{\frac32 - u}$$

[ocean seal]

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

[cyan drum]

forgot to change that

[gray isle]

$$\lim_{u\to 2^+} f\br{\frac32 - u}$$

[ocean seal]

ℝamonov

[cyan drum]

yep that was what I was going for

so now I have these 2 limits

and I have to find out if they are equal?

[gray isle]

yeh

https://www.desmos.com/calculator/zroroxor6q
i've entered these into desmos for you to double check and help understand

[cyan drum]

Is this right

[gray isle]

seems alright

[lone heart]

@cyan drum Has your question been resolved?

[cyan drum]

I just finished dinner, whats the difference between

$$\lim_{u\to 2^+} f\br{\frac32 - u}$$

[ocean seal]

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

[cyan drum]

and

$$\lim_{u\to 2} f\br{\frac32 - u}$$

[ocean seal]

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

[cyan drum]

How do you combine 3/2 and u?

[gray isle]

same idea as before

consider what 3/2 - u
approaches and whether its from above or below

[cyan drum]

$$\lim_{u\to 0.5^+} f\br{\frac32 - u}$$

[ocean seal]

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

[cyan drum]

so for this one, f(3/2 - u) approaches 2 from above

since (3/2 - 0.5^+) < 1?

[gray isle]

yeh

[cyan drum]

$$\lim_{u\to 2^+} f\br{\frac32 - u}$$

[ocean seal]

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

[cyan drum]

so for this one, f(3/2 - u) approaches 1 from above

since 3/2 - 2^+ < -0.5

[gray isle]

yeh

[cyan drum]

and because 1^+ =/= 2^+ , limit when x-> 1^- =/= limit when x-> 1^+, so limit when x-> 1 DNE?

[gray isle]

you don't need the + at the very end anymore

[cyan drum]

ah

[gray isle]

those were for the intermediate results

but yeh, 1 isn't 2, limit doesn't exist

matches the results you reached

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[dim matrix]

How can I figure out what to take common in these kind of problems? (1/3n) taken here

[wind cloak]

If it exists in every term in a parenthesis

It can be factored out

[echo socket]

If you factored with n and continued, you'd end up with n(4n^2/3 - 1/3) and then you'd (probably) factor the 1/3 out

So doesn't really matter

[dim matrix]

okay thanks

.close

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[half bone]

how do I evaluate this?

my friend gave it to me and said the answer is ln(2)

[autumn condor]

I believe this is done by approximating an integral with a sum. In the limit you then get ln(2) .

[half bone]

wdym?

[autumn condor]

Rewrite the sum starting with x and ending at 2x.

The expression after the big sigma will then be 1/n

[half bone]

ahhh, i kind of get it now

thanks

[keen plinth]

now this is a riemann sum

[half bone]

.close

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[echo vessel]

how would i integrate both sides

dA = dt

[echo vessel]

so I would get A= t

[wanton pebble]

+c

[echo vessel]

can u integraet that though?

thats what i am confused about

[wanton pebble]

yeah

[echo vessel]

is there any working out to show how you could do this

[wanton pebble]

what are A and t

[echo socket]

What's the original problem?

[echo vessel]

so like you have c = dA/dt

so dA=c dt

so how do you integrate both sides so that you get
A = ct

[mortal trellis]

just integrate this on both sides

[echo vessel]

could you draw it out or explain it please

cause im not sure how it cancels out

so that dA= cdt

becomes A = ct

[mortal trellis]

you have c = dA/dt

the left side is a constant, if you integrate that with respect to t you get ct

the right side is the derivative of A with respect to t, so if you integrate it again you get A back

(plus constant of integration)

[ornate ginkgo]

So shouldn't it actually be
$A + C_1 = ct + C_2$

[ocean seal]

ColdTee

[mortal trellis]

yes but you can just pull one of the constants to the other side and then just call the difference a new constant

A = ct+C2-C1 = ct+D with D=C2-C1

[ornate ginkgo]

Makes sense

[thorn tapir]

Yeah

If this confuses you, you can think it of like this

$\frac{d}{dt}\left(A\right) = c$

[ocean seal]

rikusp2002

[thorn tapir]

Now, antiderivative is the opposite of derivative (not exactly but here it works)

So

A = ct + k

As

$\frac{d}{dt} (A) = \frac{d}{dt}(ct) + \frac{d}{dt} (k) = c + 0 = c$

[ocean seal]

rikusp2002

[thorn tapir]

In general

$\frac{dy}{dx} = u \implies y = \int udx + c$

That's how an antiderivative is defined

[ocean seal]

rikusp2002

[thorn tapir]

This way your solution would be like this

$\frac{dA}{dt} = c \implies A = \int cdt + k = ct + k$

[ocean seal]

rikusp2002

[lone heart]

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[reef dawn]

What do I do next? So far I have u = cos^2 and du = -sin(2x)
-1/6(u)

[raven haven]

oh that's actually really good

I don't see a dx

your du is missing a dx somewhere

[reef dawn]

wdym? du/-sin(2x) = dx?

[raven haven]

as in

you have du= -sin(2x) -1/6 u

btw I'd pick u = cos^2(x) + 6

[reef dawn]

no I just have du= -sin(2x) the -1/6(u) is seperate

[reef dawn]

ok so that would just be -(u) now?

[raven haven]

one second

,w differentiate (cosx)^2

[ocean seal]

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[raven haven]

ok yup

and then your top term is uuseful

-1/6(u) is incorrect

because the derivative of a constant is 0

[reef dawn]

its just -u right? because the sin(2x) cancels?

[raven haven]

du = -sin(2x) dx

you got pretty far actually

[reef dawn]

and that would be du/-sin(2x) = dx?

[raven haven]

yep

[reef dawn]

now its sin(2x)/u * du/-sin(2x) and we cancel out sin(2x) to get -u?

[raven haven]

so far so good

[reef dawn]

answer is -(6+cos^2(x))^2/2 + C?

[raven haven]

,w integrate [(sin2x)/(6+(cosx)^2)]

[ocean seal]

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[raven haven]

you made a mistake

the integral of 1/u is not that

[reef dawn]

wdym?'

[raven haven]

do you know what the integral of 1/x is

[tacit pollen]

40y+30x=100 Help me
i know y =1 and x =2
but how

[reef dawn]

read #❓how-to-get-help

[raven haven]

do not hijack the help channel

[vale wigeon]

@tacit pollen open your own channel. see #❓how-to-get-help

[raven haven]

continuing from here

[reef dawn]

yes but where did you get 1/x from

[raven haven]

i'm using it as an example

[reef dawn]

oh wait

[reef dawn]

its -1/u? not -u?

[raven haven]

yeah

sorry

I didn't see either

[reef dawn]

so -ln(u)?

[reef dawn]

answer is -ln(6+cos^2(x)) + C?

[raven haven]

yup

well

yes

wolfie expanded it so

[reef dawn]

thanks for the help

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[steep widget]

Hi, I am trying to calculate the symmetry of a function to find if it's even, odd or neither. Organic chem teacher has an easy trick for this

[steep widget]

if all the powers of x are even then it's even, odd then it's odd and both then it's neither

so this even right?

since it's basically x^2 + 1 / x*2 - 1

( I know I am better off learning the actual way to solve this but I don't have much time left before my exam )

[dim oasis]

If all the powers of x being even means it's even, then I guess it's even? That's not really what defines even functions though

[alpine sable]

$\frac{x²+1}{x²-2x+1}$

[ocean seal]

rbit ✨

[steep widget]

Symmetry ( even, odd or neither)

• even = if all the powers * of X are even ( 2, 4 , 6 , 8 ) x*2
• odd = if all the powers * of X are odd ( 1, 3 , 5 , 7 ) x*3
• neither = if all the powers * of X are both odd and even ( 1 , 2 , 3 , 4 , 5 , 6 ) x*2 + x *3

here's what I wrote in my notepad

[dim oasis]

Even functions are symmetric about the y axis

[alpine sable]

this is what we get when we expand the denominator

[dim oasis]

Yeah you could consider the +1's to be raised to an odd power

Namely 1

[steep widget]

I always forgot that a + b ^ 2 doens't equal a^2 + b^2

so it's neither

[alpine sable]

no the +1s are x^0, so an even power

[steep widget]

but -2x^1

1 is odd

so doesn't it make it neither?

[alpine sable]

yeah

[steep widget]

nice nice nice

I appreciate the help

.close

[lone heart]

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[dim oasis]

Oh durr sorry lol I blanked

[steep widget]

np <3

[lone heart]

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[brisk parrot]

How would i find the perimeter of this if the angle was something other than 90 lets say 60

[pliant cedar]

(300/360) * circumference = curved length, if the angle there was 60 instead of 90

[last ether]

Arc length + 2(radius)

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[warped topaz]

https://gyazo.com/3420712fa64c5f9c9edbf37ebe44de79.png

[warped topaz]

So I dont really understand the question

I translated the bullet points as:

• No circles are blue
• There exists a circle and there exists something blue
• a is right of b
• a is left of b OR c is a square

I think the answer to the first question is 'yes it can exist with these properties' since none of the properties contradict eachother, but not sure if thats the right answer

And I dont understand the 2nd question at all

[lone heart]

@warped topaz Has your question been resolved?

[pliant cedar]

i guess write a list of at most 5 things that satisfy these

[warped topaz]

Sorry I still dont really understand, can you give 1 example please?

[pliant cedar]

im not sure how to interpret "right of"

so maybe a list of things like a red circle, a blue square, blue triangle etc

[pliant cedar]

ig is what they are asking for

so u must include circles in the list and none of the circles must be blue

[pliant cedar]

so if forall a,b rightOf(a, b), then forall a,b ! leftOf(a,b), so everything must be a square

💀

[pliant cedar]

and "there exists a circle" will have to be false

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[alpine sable]

Yall

Help 😭

[near dove]

which

[alpine sable]

Farmer joe need to calm down fr fr

14

Number 14

[near dove]

they ask you to find perimeter

so open the roots

like root45 equals 3root5

[alpine sable]

Okur

[near dove]

do it for all of them

[alpine sable]

Ok slay ty

[near dove]

👍

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@alpine sable Has your question been resolved?

[alpine sable]

Yas

[lone heart]

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[sharp bloom]

can anyone pls provide the soln to this qs

[lone heart]

Please read #❓how-to-get-help

[lone heart]

@sharp bloom Has your question been resolved?

[sharp bloom]

<@&286206848099549185>

[sharp bloom]

.close

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[willow herald]

Could someone help me understand if this relation is a total or a partial function or neither?

[raven haven]

recall definition of a function

||this is not well defined lmao||

[willow herald]

For each element of the domain set, there is exactly one corresponding element in the codomain set.

[raven haven]

okay

now

[willow herald]

It's descrete math

[raven haven]

yes, I am aware

[willow herald]

I don't understand the whole multiplication of sets idea

[raven haven]

cartesian product?

[willow herald]

yeah, Like I get it when I watch youtube videos visualizing it but I don't see what the x's and y's are

like is x all integers and y all positive integers?

So for this would it be the opposite?

[raven haven]

yep

actually this one is a function (can you see why?)

[willow herald]

hold on 😄 I wanna figure out the first one first

So (posInt) = (int) - 1

[raven haven]

also totally forgot to ask you to recall the definition of partial function

[willow herald]

Um hold on I had it a sec ago xD

[raven haven]

no worries

[willow herald]

It only works for some specific inputs whereas total function works for all

[raven haven]

ok

now can you proceed?

[willow herald]

yea so (posInt) = (int) - 1
got distracted

-4 - 1 is not a pos int so its a partial function

because 4 - 1 is a posInt

does that make sense?

And for the second one (int) = (posInt) - 1
so total function because every posInt - 1 is inside the Z set

[raven haven]

very good

[willow herald]

idk how to even read this 😄

[raven haven]

err

let R be that set

exists a z in the natural numbers such that y = xz

[willow herald]

@raven haven What does it mean when it says "on Z"?

[raven haven]

a relation is defined on a set

[lone heart]

@willow herald Has your question been resolved?

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[pliant estuary]

Are my calculations incorrect?

Apparently it should be this

[hollow sparrow]

yours is correct if the matrix equal to $\matr{2&1&1\0&2&2\0&0&2}$

[ocean seal]

Mehdi_Moulati

[hollow sparrow]

the original matrix

[mortal trellis]

you know, instead of equal signs you should really write down what steps you are doing

[pliant estuary]

yeah, i know that, i was doing it fast, cause im doing some problems for my exams recapitulation, so i dodnt write down the steps when im doing this

[pliant estuary]

well, that is not the starting matrix so i went wrong somewhere

[hollow sparrow]

what is the starting matrix ?

[pliant estuary]

wait, im dumb, there was one more step that is not included in the picture, well then yes, the one that you wrote was my beggining matrix

so the one that should be the answer is wrong?

[hollow sparrow]

since the starting matrix is the same as i wrote then your works is correct

,w invert [[2,1,1],[0,2,2],[0,0,2]]

[ocean seal]

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[hollow sparrow]

-1/8 in the corner is wrong , it should be 0

[pliant estuary]

great, thanks for your help, cya

.close

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[severe timber]

Hello math enthusiasts! I have a question regarding roots: Why does an even root produce a positive and negative number (numerical value), while odd roots (e.g. cube roots) give only the positive number? Is it because an odd root written as factors will always produce a negative number — which is not possible within real numbers?
Thanks 🤓

[mortal trellis]

sqrt(9) is not equal to both 3 and -3

it is only equal to 3

by definition

in your example, (-3)^3=-27 and not 27

so really why should it be a possible value for the third root of 27 at all

it doesn't even equal 27 when you cube it

it's not an even function. it isn't even defined for x<0. (lets leave complex numbers out here)

[severe timber]

Can you elaborate?

[severe timber]

Is not (-3)(-3)=9?

[mortal trellis]

yes it is

so -3 is also a solution to x^2=9

but by definition, sqrt(9) is only equal to 3

a function always can only have one output

[severe timber]

I see. Playing around in GeoGebra revealed the answer, visually. I think.
I mean, the odd function allows negative outputs, while the even ones don’t

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[young spear]

minus to minus is plus

[lone heart]

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[tacit bridge]

how do i find the other term when i only have the sum = 44 and second term =-3

[vale wigeon]

wdym "other term"...?

can you show the problem in full

[tacit bridge]

geometric series

its only text

[vale wigeon]

yes, show the full text of the problem.

[tacit bridge]

In a convergent geometric series with sum equal to 44, the second term is equal to −3. Determine the first term in
this row

[vale wigeon]

... you translated this from another language, didn't you?

anyway

[tacit bridge]

yes

[vale wigeon]

are you able to write out the sum and 2nd term of a general geometric progression in terms of its first term a and common ratio r?

[tacit bridge]

yes

[vale wigeon]

ok, then do it here.

[tacit bridge]

s = a_2/1-r

$s = \frac {a_2}{1-r}$

[ocean seal]

Sas

[tacit bridge]

$44 = \frac {-3}{1-r}$

[ocean seal]

Sas

[tacit bridge]

am i on the right path? @vale wigeon

[vale wigeon]

you are on the right path but you misstepped and didnt do what i asked for.

i was expecting you to write $ar = -3$ and $\frac{a}{1-r} = 44$.

[tacit bridge]

i did not fully understnad

[ocean seal]

Ann

[tacit bridge]

ok

$a_2= -3$

[ocean seal]

Sas

[tacit bridge]

okei so what now? @vale wigeon

got $r = \frac {41}{44}$

[ocean seal]

Sas

[vale wigeon]

i have a feeling you went wrong somewhere.

[tacit bridge]

is r sapose to be r^2

[vale wigeon]

no...?

i am using the letter a (without a subscript) to mean the 1st term, so the 2nd term is a*r

[tacit bridge]

ok

[lone heart]

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[tacit bridge]

.close

[lone heart]

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[civic spindle]

I've tried solving it but got a wrong answer

wait I found the mistake

[last ether]

Shouldn't this just be 2 lol

[civic spindle]

yeah

how did you do that?!

[last ether]

The -n^2 end behavior ain't gonna do jackshit against 2^n

So it's just the nth root of 2^n

Which is just 2

The limit of 2 as x approaches infinity is ... 2

[civic spindle]

I get that

[civic spindle]

not that

[last ether]

End behavior allows you literally erase low-end terms

So you don't care about the -n^2

[civic spindle]

?

I think Ive messed up

[lone heart]

@civic spindle Has your question been resolved?

[tacit arch]

mistake here

you used power rule to differentiate 2^x

[civic spindle]

what should have I done?

[tacit arch]

https://www.cuemath.com/calculus/derivative-of-2-to-the-x/

[civic spindle]

so the derivative of a^n is a^n * ln a?

ok thanks 🙂

.close

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[scenic crescent]

where's the yellow stuff come from

[scenic crescent]

i know sinB = cosA but then ?

[civic spindle]

I don't want to mislead you but maybe this could help

its a trigonometric identity

[scenic crescent]

thank u

[lone heart]

@scenic crescent Has your question been resolved?

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[plucky blade]

How many integers in the range 1000 to 9999 (inclusive) have at least one repeated digit?

[plucky blade]

Having trouble applying the product rule to this

[mortal trellis]

count how many have no repeated digits

[plucky blade]

how would i do that with this big of a range

in the context of the product rule there are four different events(digits) right

[alpine sable]

if you count how many there are with no repeated digits, how many ways are there to choose the first digit? then how many are there to choose the second digit? and the third? fourth?

[plucky blade]

9

for the first

is the second 9 as well?

[alpine sable]

yeah

[plucky blade]

Ok

so 8 and then 7

so 9x9x8x7?

[alpine sable]

yeah

[plucky blade]

ah ok

[alpine sable]

then how to get the final solution from that?

[plucky blade]

not sure

is it just

9000- 4536

[alpine sable]

how many possible numbers are there in total?

yeah

,calc 998*7

[ocean seal]

Result:

4536

[plucky blade]

ohh

ok

thanks

.close

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[weary rose]

How do I do this

Is the first one 2/3?

[worn fox]

are you asking if $\theta = \frac23$?

[ocean seal]

ΣAC

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[lethal badger]

Need help with this problem, The probability that an uptake rate from the sample dataset is <19 or >34 umol/m^2 sec. Round your answer to 3 decimal places.

[lethal badger]

since its asking probability of a number thats anything but 20-33 can i just get the probability of getting 20-33 and subtract 1 with it to get the probability of <19 or >34

[gusty gorge]

1 - P(20 <= X <= 33) = P(X < 19) + P(X > 34) if that's what you're asking

[lethal badger]

yeah do you think that will work

[gusty gorge]

well it's mathematically true

[lethal badger]

cause during offic hour i asked the assitant teacher and they werent sure

[gusty gorge]

whether it works for your particular problem

not sure

[lethal badger]

thanks

@gusty gorge

.clsoe

.close

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[ocean seal]

birdy

[tacit arch]

define college math

if you mean calculus, no

[inland crystal]

depends on curriculums, but usually its seen before calculus i think

[tacit arch]

if you mean complex analysis, yes

[inland crystal]

wait you mean i, right?

[ocean seal]

birdy

[tacit arch]

well shit

time to catch up then
https://www.youtube.com/watch?v=5PcpBw5Hbwo
https://www.youtube.com/watch?v=OQz1ydBcQSA
https://www.youtube.com/watch?v=bZSYcIJBMqE&list=PLBh2i93oe2qtbygdXz4u6Mkh7c_hMLBA8&index=28

[limpid turret]

This isn't right

C/R should be a=0 also

Oh wait nvm

That's pure imaginary, not C/R

I am telling you lies

You seem to know more than me by this point. :p

I think you're just stressed and maybe feel a little out of place.

[raven haven]

hold on C/R - are you sure you're not taking abstract algebra?

[limpid turret]

I just think of complex numbers in a naive way. Let i^2=-1 and treat the rest like algebra

You should be taking calculus separate from complex analysis

Taking both together at the same time, and for the first time, can be difficult

Limits of real or complex functions?

Then I'm assuming reals. Maybe you should talk to your professor. It would help to actually know what will be taught to you

Do you have a syllabus?

I speak Spanish casually

Mexican Spanish

Looks like just calculus of a single, real, variable

You don't need to worry about complex analysis

I see no mention in the syllabus either

Looks like at most, you will touch on them a bit when discussing quadratic equations

Looks like you'll just start with some algebra review, and only mention of complex numbers is how understanding algebra helps you understand complex numbers

I don't think you need to worry

Worst case, pregunta tu profesora

[lone heart]

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[waxen spruce]

Yo

[waxen spruce]

I got no clue how to solve this

I got da voltage for each bc Vt=V1=v2

But since im only given quantity for one resistor i can only calculate value for one current

[naive valley]

is it intentional that they do not give a value for R1?

[waxen spruce]

I assumed that it was an unknown quantity,

But idk

[naive valley]

obviously the current through R1 will depend on that

i don't think it's something you can solve for

[waxen spruce]

I thinkwe have to solve for it

[naive valley]

you can build such a circuit with any R1 you like

[waxen spruce]

Yeah meneither

[naive valley]

and you'll get different currents

[waxen spruce]

Yeah so shouldI assume its 8 like the second resisteor

[naive valley]

maybe they want the answer as a function of R1

i.e. treat it as an unknown constant

and express I1 and IT as a function of R1

[waxen spruce]

Thank you!

[naive valley]

192 can't be right for I2

isn't it V = IR

[waxen spruce]

Yeah I mean to do 24

/8

so 3

[naive valley]

yea

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@waxen spruce Has your question been resolved?

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[empty forge]

Any assistance to get started would be appreciated

[empty forge]

I am completely lost.

[rocky grove]

Hmm