help-38

[wraith hinge]

How can I solve this limit ?

[trim jolt]

@wraith hinge Has your question been resolved?

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@wraith hinge Has your question been resolved?

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[astral sleet]

hello

[trim jolt]

Please don't occupy multiple help channels.

[astral sleet]

hello

can you solve thus

I only get to thus step

[fair bison]

what happened to your previous channel?

[trim lichen]

#help-12

it's still there

!onechannel

[trim jolt]

Please stick to your channel.

[astral sleet]

you can close it

[fair bison]

this is the same question, no?

.close

[trim jolt]

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[fair bison]

I'll help you in the other channel

[astral sleet]

yes but he is not responding

[astral sleet]

okay thnx

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[sleek delta]

hi, can i get some guidence and confirmation wether my solution is right?

[sleek delta]

i got this as my solution

[zinc ginkgo]

,rotate

[zinc ginkgo]

probably right

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[sour fox]

.reopen

An equilateral triangle ABC with side 3 is inside in a circle point D lies on the arc AB doesnt have the too find BD and CD

[sour fox]

.close

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[weak yoke]

Hii

[weak yoke]

Help with 4th pls

[unique minnow]

,rotate

[unique minnow]

Is that calculus? What have you tried so far?

[weak yoke]

hm i need to know how do i do it?

4t one?

[unique minnow]

No I know that but what have you tried? Any ideas?

[weak yoke]

i tried changing x in terms of y and then find the area with respect to y axes

with the coordinate axes

[unique minnow]

With the coordinate axes likely means in the first quadrant

[weak yoke]

idk in which quadrant it would make the graph

i need help with that

[unique minnow]

Or actually, if you graph the function, you will see that it encloses the axes a bit before 0

[weak yoke]

yes ik

i need intercept

[unique minnow]

,w y=ln(x+e)

[weak yoke]

can u help me with that

[unique minnow]

Thought it would graph mb

Ok so you need the intercept with y = 0

So set y=0 and solve for x

[weak yoke]

ok

got it

[unique minnow]

This will give you the bounds of you integrals, since we see that the enclosed area starts at that intercept and finishes at x = 0

[weak yoke]

thx buddy

i just got mad ,i need rest lmao

i cant think this simple thing lmao

anyways thx bro

[unique minnow]

It's ok

Have a good day

[weak yoke]

i must do it tmrw

bye

.close

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[hearty sparrow]

I've been trying to do this for over a day

[hearty sparrow]

I get stuck

<@&286206848099549185>

Gtg to eat*

Can still read

[swift anchor]

wouldn't dn/dx work?

[hearty sparrow]

Pls type at me

[hearty sparrow]

Pls explain

[swift anchor]

I could be mentally stupid

nvm I saw the v in the equation

if n=0 then -n is just -0

[hearty sparrow]

Show that...... n>0

Oh I didn't write it but yh n had to be above 0

[swift anchor]

oh

so is 2n>20 or 2n= or < 20

[hearty sparrow]

We don't need to know the value of n

We need the integral with -n+1 in terms of integral with -n

[swift anchor]

so -n+1 has to be around the value of the integral of -n

[hearty sparrow]

Nope

Have u studied reduction formula

[swift anchor]

what the f**k is that

[hearty sparrow]

Oh

Nvm then

I'll just ping <@&286206848099549185>

[swift anchor]

that's the best option

[hearty sparrow]

This question is actually stressing me the fuck out

I hate when I just can't do maths

I can't explain it

<@&286206848099549185>

[radiant quartz]

@hearty sparrow try using dv/dx=1 instead

[wraith hinge]

Don't you need non-elemntary functions to solve this?

[hearty sparrow]

Okay ty ty

Will try

[hearty sparrow]

I'm trying now

It won't work

Jt rlly rlly won't work

Please

<@&286206848099549185>

[trim jolt]

@hearty sparrow Has your question been resolved?

[hearty sparrow]

<@&286206848099549185>

<@&286206848099549185> please man I've tried so many fucking times

[pearl cape]

heyo

[pearl cape]

alright whats the problem

[pearl cape]

this?

[hearty sparrow]

Its this:

Yh

[pearl cape]

alright lemme try it out rq

this is the original integral?

[hearty sparrow]

Yh

[pearl cape]

and we want to show thos?

j making sure im reading it write

[hearty sparrow]

Yh

[pearl cape]

kk

[hearty sparrow]

I hate this shit

I've been trying for a day

I gave so SO SO MUCH SHIT

To get done

And I cant

Because i need this done

I'm so behind

[pearl cape]

what class is this for btw bc keep in mind this shit is HARD

[hearty sparrow]

It isn't im just being stupid

[pearl cape]

and also is it I_n * the integral or I_n = the integral

[hearty sparrow]

I can do these normally

[pearl cape]

what class is this

[hearty sparrow]

?

[hearty sparrow]

Idk I'm not American we don't name classes

"Advanced level further mathematics"

Its pretty uni

Pre* uni

[pearl cape]

after the I_n is there a miltiplication symbol or an equal symbol

i cant tell

[hearty sparrow]

=

[pearl cape]

ok

[hearty sparrow]

@pearl cape

Did u do it?

[pearl cape]

working on it

[pearl cape]

@hearty sparrow so i gtg

but

i found a method that will work, you gotta take it from here tho

thej plug in

n+1

also @hearty sparrow im not sure how familiar ur with feynmans integration method but if ur good with it itd highly reccomend just doing f(x) =1/(x²+a²)^n, differentiating under the integral sogn and plugging in n+1 and evaluating at F(1)

but if ur not then this should suffice

[trim jolt]

@hearty sparrow Has your question been resolved?

[hearty sparrow]

Idk

[hearty sparrow]

Idk how you got the dx on the top bit of the fraction

[pearl cape]

wym

integral of 1/x dx = integral dx/x

its just notation

[radiant quartz]

sorry boa i had another thing to do

Ill show you my working

gimem a minute

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[covert oxide]

I already did 12

[hearty sparrow]

Ty

[covert oxide]

I mean

I already did 11

I need help on 12

[radiant quartz]

check #latex-testing cz i didnt know where else to put it bc this channel "timed out"

[covert oxide]

<@&286206848099549185>

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[covert oxide]

Everybody ignores me

.close

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Please don't occupy multiple help channels.

[covert oxide]

Hi

I made a new ticket

[night zodiac]

#help-18

.close

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[finite basalt]

I have a simple question about proportions. In my textbook it states Ohm's law as I = k * V and then it shows it as V/I = K. I am confused as if to isolate K you will need to divide both sides By V and then get K = I/V

[wraith hinge]

what is it that you're asking?

[reef plaza]

if I = K * V than it wouldnt be right than V/I = K

but isnt ohms law V = I*R

[finite basalt]

I don't get how the book rearanges it to become K=V/I

[reef plaza]

Well

[dusty sleet]

Well, they're calling K the quantity 1/R

As far as I know K is usually called G (conductance)

[reef plaza]

does big k and small K mean 2 diff things in the book

or you just wrote like that

[finite basalt]

I suspected that K would be 1/R but I can't find that mentioned in the book or any other that I have available

its just wrote like that

lowercase k

my apologies for putting in uppercase

[reef plaza]

all g

Either your missing something or the books a bit funky

you got the name and authur?

[finite basalt]

Adrian Waygood - An Introduction to Electrical Science-Routledge (2018)

and

Basic Engineering Mathematics John Bird (2005)

[reef plaza]

page no

?

[finite basalt]

pg 71

[reef plaza]

https://gyazo.com/89430d4cc2fd20888420b3452d27403c

My guess woudl be

Tha since k isnt defined here and is just a constant

I = K * E

I/E = K

so like

Its still a constant

1/k is still a constant

E / I = 1/k

[dusty sleet]

Yeah, I would have changed the name of the constant, at least for clarity

[reef plaza]

Yea

[dusty sleet]

Now I get your point, and I agree that it makes quite a lot confusion

[finite basalt]

I am trying to think how to prove that Resistance is k but for that to be true and then becoming the classic V=IR(where R is the constant of proportionality) it can only be that if expressed as I= 1/k *E

[dusty sleet]

Their E is your (and the usual) V

So you have I = kV, and let k = 1/R. So that you now have I = V/R (which can be rearranged into V = RI)

[finite basalt]

I am trying to find a way to explain that k = 1/R

and 1/R is conductance if I remember well

[dusty sleet]

You define it

[dusty sleet]

Yep

[finite basalt]

I am going to put more thought in this. Thanks for the help, helped me to clarify a lot.

.close

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[lyric kiln]

hi

[exotic pike]

[lyric kiln]

I am a little confused hahah

I plugged the vertex into the f(x)= a(x-h)+k

then I foiled it and opened the bracket

but I am a little confused on why this is wrong

Oh I GOT IT

[lyric kiln]

also do u know what I did wrong here haha

hello

<@&286206848099549185>

It has been 15 minutes

[hot forge]

Set up an inequality equation like this

Ignore the back side of the paper it is just other stuff

@lyric kiln

You can solve this the same way you solve an equation. Just pretend the greater than sign is an equals.

Another thing is when you divide by a negative in an inequality, the sign flips.

This is the work

[trim jolt]

@lyric kiln Has your question been resolved?

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[lyric kiln]

isnt that what I did

[lyric kiln]

thank u though appreciate it!

I have another question if u dont mind this one I cant seem to understand what to do here

.reopen

[hot forge]

Okay

For the first one, you typed x greater than 10,000 I believe

[lyric kiln]

oh that was a error

I did 100,000 after

still it was wrong for some reason

[hot forge]

Hmm ok

[lyric kiln]

but can we try the next question at least

[hot forge]

Ok

[unborn path]

try thinking about parabolas

[lyric kiln]

that one I dont seem to understand it

[lyric kiln]

thanks guys

[lyric kiln]

I know what 2x^2 is and looks like

but how is that relevant

[unborn path]

yeah

[lyric kiln]

dont we need a vertex point

and another 2 points

[hot forge]

What types of forms of equations are there

Have you learned this form??

Try using this

[lyric kiln]

Ohh okkk

but then u will solve for x or y first right

[hot forge]

y = a(x-p)^2 + q

[lyric kiln]

does it matter?

thanks so much brother

[hot forge]

No just plug x and y

Into the equation

[lyric kiln]

ohh right okk but then what will we solve

[hot forge]

Because x and y is on the graph

You solve for q

[lyric kiln]

OHH

OKk

thanks so much my friend

[hot forge]

Not at all

[lyric kiln]

sometimes the variables being different confuses me a little bit I really appreciate ur help!

[hot forge]

Anything else?

[lyric kiln]

wait so if the function on the left acts as the Y and the p acts as X what does the q represent o a graph

just the vertex point?

[hot forge]

q is the vertical translation

You've learned this form before, yes?

[lyric kiln]

yes just not entirely used to it yet

[hot forge]

Ok

a is stretch factor

[lyric kiln]

Yeah we did the transformations just recently

[hot forge]

p is the units moved

[lyric kiln]

oh yeah that part I understand

[hot forge]

Oh ok

[lyric kiln]

thanks by the wat

way

[hot forge]

Q is how many units moved vertically

pq is vertex

Vertex is at V(p,q)

[lyric kiln]

ohh yeah brother

[hot forge]

p and q just represent the movements made from the original graph y = x^2

[lyric kiln]

I have one last question my friend, how do I find p?

I found the Q

do I plug it in again or am I confused

[hot forge]

One sec

[lyric kiln]

ok

np

oh wait

the vertex is on the y axis

so that means x=o

[hot forge]

?

[lyric kiln]

so I can plug in x=0

[hot forge]

wait

I do not think this is right, sorry

Are you given a second point in the question?

[lyric kiln]

no

[hot forge]

Then it cannot be solved that way

[lyric kiln]

oh ok

what would could we do then

[hot forge]

One sec

Vertex on y axis means x = 0

That means p = 0

[lyric kiln]

p=o

[lyric kiln]

p acts sort of like the x axis right

[hot forge]

On y axis just means that the x = 0, otherwise it isn't on y axis

p is a point on the y axis

It acts as a horizontal translation

[lyric kiln]

oh yeah I know about the horizontal stuff

translations and alll that

but I get confused why are tehre two x's in the equation

then

generally its written as f(x)= a(x-h)+k

but when x can also be written as h

[hot forge]

Yes

h is 0 in this case

[lyric kiln]

wait then what will I solve for?

[hot forge]

Now try subbing in all the points

[lyric kiln]

we really dont need f(x)

or X

[hot forge]

You still solve for q

[lyric kiln]

weird question

but how will we ever find the h point

we need that!

[hot forge]

h is on y axis, which means that it is 0

[lyric kiln]

oh thats what that means

thats how u solve for q

[hot forge]

Is this your equation

?

[lyric kiln]

yes

[hot forge]

Okay that should work

Anything else?

[lyric kiln]

wait I got -1 for q

[hot forge]

That's for q

[lyric kiln]

2(1-0)^2 = 2(1)^2 = 2x1=2

isnt that how it works^

[hot forge]

Oh shoot I am tripping

Yes -1 is correct

[lyric kiln]

oh ok haha

sorry for taking up ur time

ur so helpful

[hot forge]

Np

That's all?

[lyric kiln]

yup that should be it for now lol

[hot forge]

Have a nice day!

[lyric kiln]

you too!

[trim jolt]

@lyric kiln Has your question been resolved?

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[maiden zinc]

This one seems to easy

Am I right ?

Tan x times 1/tan x is just one 1 right ?

[nimble stone]

seems logically sound

[maiden zinc]

Alright ye just making sure

.close

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[wraith hinge]

Hi, can someone help me with basic stats… I’m not too familiar with concepts, so I’m trying to make sure that I’m getting stuff right

[wraith hinge]

Also, don’t know how to answer the final question

Thank you so much

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@wraith hinge Has your question been resolved?

[wispy sparrow]

$\sigma^2=Var(X)=E(X^2)-E^2(X)$

[solid kiln]

chlamydia

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@wraith hinge Has your question been resolved?

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[hearty elbow]

Hallo; I have a dumb question that is half math, half excel spreadsheet. I need to put the Stefan-Boltzman constant into an equation I have, but I don't know how to do that. Is there anyone who does? (I understand if not)

[hearty elbow]

If wanted, I can provide said equation

[nimble stone]

(5.67*10^(-8)) may work

if its just part of an equation

[hearty elbow]

Let me check really quickly

ohmygoditworked

[nimble stone]

nice

[hearty elbow]

thank you i've been stuck on this for 4 hours

[nimble stone]

no worries

[hearty elbow]

.close

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[strong remnant]

it should be so obvious but i tried it like 3 time sand it didnt't work

some1 please help me i will be forever grateful

[inland orbit]

you might be overthinking this

you're not trying to simplify it completely

only making sure that the left side is equal to the right side

notice that both sides have cos(a) in common

since that part is already the same on both sides, you can pretty much ignore it.

does that makesit a bit more clear?

[strong remnant]

yeah that makes sense

would you be able to help on one more

i got the 1st part

but the 2nd part I tried like 3 different things and it didn't work even tho I thought it was the answer

[inland orbit]

well what did you do to simplify $\frac{\sin^2 \theta + \cos^2 \theta}{\cos \theta \ \sin \theta}$

[solid kiln]

tatpoj

[strong remnant]

I just don't think cos0 and sin0 can simplify any further

like I knew that sin^20 cos^20 is 1

but I am just confused

@inland orbit

[inland orbit]

you mean $\sin^2 \theta + \cos^2 \theta = 1$

[solid kiln]

tatpoj

[strong remnant]

yes

are you able to just say what the bottom part is

[inland orbit]

well look at what the top part is

it was sin^2 + cos^2

and you just agreed that's equal to 1

[strong remnant]

it’s because I had like a trig identity sheet

and it said that it was 1

[inland orbit]

yes that's true

look, you had

$\frac{\sin^2 \theta + \cos^2 \theta}{\cos \theta \ \sin \theta}$

[solid kiln]

tatpoj

[inland orbit]

if sin^2 + cos^2 = 1, then this is equal to

$\frac{1}{\cos \theta \ \sin \theta}$

[solid kiln]

tatpoj

[inland orbit]

isn't it?

[strong remnant]

I thought it couldn’t simplify…

I guess I should of just put it

Thanks

You helped a bunch

[inland orbit]

awesome, no problem 👍

[strong remnant]

.close

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[wraith hinge]

Hello can any body help me with this equation I have no idea what it is about

[wraith hinge]

It is on graphing

[wispy sparrow]

Graph the line with the equation $y=\frac25x-2$.

[solid kiln]

chlamydia

[wispy sparrow]

what don't you understand about this

[wraith hinge]

i do not understand the steps on how to graph it

[wispy sparrow]

find x and y intercepts

[wraith hinge]

idk how to

[wispy sparrow]

x intercept: let y=0 and solve for x
y intercept: let x=0 and solve for y

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[pale patrol]

i don’t even know how to start 🙁

[idle cloud]

in the g(x+2) function substitute x by -8 and then look at the graph of g(x) finally don't forget to do -1

[trim jolt]

@pale patrol Has your question been resolved?

[pale patrol]

whe only learned how to do a h k in class so i don’t know what to do when i get x🙁 sorry

do i like evaluate it

[idle cloud]

when you replace $x$ by $-8$ in $g(x+2)-1$ you get $g(-6)-1$ then evaluate $g(-6)$

[solid kiln]

deus ex machina

[idle cloud]

and don't forget to do -1

[little condor]

To evaluate g(-6), look at the graph of g(x) you were given, look at -6 on the x axis, then see what y value corresponds to that -6. In this case, its ||2||

[idle cloud]

!nosol

[pale patrol]

thank you so much

did i do this correct

[little condor]

I don't understand the question unfortunately. It would make sense to me if it asked g(x) = f(x + square), but it seems to say g(x) - f(x + square) when I look at the screenshot instead. Hopefully someone else understands what they are asking.

[pale patrol]

okay don’t worry thanks for trying💯

[idle cloud]

is it = or - ?

[pale patrol]

the square is wher the answer should be

i think

which is weird

[idle cloud]

don't you have it in front of you ?

[pale patrol]

no i don’t 🙁 but let me look for a clearer pic

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@pale patrol Has your question been resolved?

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[random citrus]

!status

[trim jolt]

What step are you on?
1. I don't know where to begin
2. I have begun but got stuck midway
3. I got an answer but I'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above

[wicked hollow]

1

[random citrus]

well just use the implicit function theorem

ur solving for y and u in terms of x,z,v

show that the derivative of F wrt y and u is invertible at that point

[winged hinge]

To find Dg u can use chain rule on appropriate functions

[wicked hollow]

i just dont think i learend this well enough in class

is there anything i can find on this

cant find any youtube vids of examples

[winged hinge]

idk usually class textbook works for me

this might help? https://youtu.be/bk9IKHS5KbY?si=tfTE-qSzxgNb47wG

[trim jolt]

@wicked hollow Has your question been resolved?

[wicked hollow]

i still hardly understand

idek

why i cant figure this out

[wicked hollow]

.close

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[ripe knot]

is there an easier way to caclulate E(X^2) with this ?

the pmf is P(x) = (1/2)^x where x is = 1 , 2 , 3, 4,.....etc

I am trying to use derivatives here but my answer does not match the solutions

the "solution" which I pulled from chegg

so it could be wrong

but idk

I got 5 - 4 not 6-4

[trim jolt]

@ripe knot Has your question been resolved?

[zinc ginkgo]

where's the definition of the distribution of X

[ripe knot]

its a pmf

I dont know what you mean by distribution though

like its a discrete random variabl e

[zinc ginkgo]

what's the definition of the pmf then

or the random variable

[ripe knot]

is that what you mean by distribution thought>

though*

[zinc ginkgo]

no

if you don't know what i mean just ignore it

[ripe knot]

can you explain distribution? i see that word come up alot tbh

[zinc ginkgo]

...

[ripe knot]

im on part b

ah nevermind

I see what I did wrong

I didnt use the right formula for M(t)

.close

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[knotty locust]

I'm wondering if my proof here works. I am doubtful because it doesn't use the fact that A is a finite set with odd amount of elements

but I can't see where it is wrong either

[zinc ginkgo]

your contradiction has to contradict something else besides what you're set out to prove.

[knotty locust]

Why is that?

if I want to prove that there is one element that satisfies f(a)=a

can't I say "assume that there is NO elements that satisfy f(a)=a"

and then derive a false statement

so it must be atleast one element that has f(a)=a?

[zinc ginkgo]

your false statement must be something different otherwise your argument is circular

[knotty locust]

so the issue if the f(b)=a being the contradiction? I'm a little confused how it is circular

[zinc ginkgo]

oh

that's what you're saying

how do you know there's a b such that f(b) = a

[knotty locust]

because f(a) is equal to some b in A

because f: A->A

and b is not equal to a

by the contradiction assumption

so f(f(a))

evaluates to

f(b)

where b not equal to a, and it is in A

and f(b) has to evaluate to a

by the definition of the function

but then since b in A, this is a contradiction

I thought atleast

[versed sand]

ur b is actually f(a)

[knotty locust]

yeah

so f(b) has to equal a and that can't be? because we said no f( anything ) = a

[zinc ginkgo]

where's the contradiction? you just assumed f(a) != a for all a.

[knotty locust]

well we showed that f(b) = a

so that is the contradiction

[zinc ginkgo]

why is that a contradiction ?

[knotty locust]

because f(a) can't equal a

but we just showed it does

with b

if f(x) can't evaluate to a

and we show it does evaluate to a

for b

then thats the contradiction

[zinc ginkgo]

what statement in your assumptions is being contradicted?

[zinc ginkgo]

you showed f(b) = a, not f(a) = a

[knotty locust]

I thought that f could never be a

[versed sand]

no. $f(a)=a$ means f doesnt have a fixpoint. not if i plug in anything into f it shouldnt evaluate to a

[knotty locust]

not that f evaluated at a point could never be the point

[solid kiln]

Gigrise

[knotty locust]

I see okay

I thought it was saying

f can never be a

not f(something) can never be something

[versed sand]

no no

[knotty locust]

I would've had to show f(b)=b

for contradiction?

is that the point

[versed sand]

yes

[knotty locust]

ah okay

I'll retry

thank you riemann and gigrise

.close

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[runic axle]

Would i use the combination formula for question a)?

[runic axle]

Or would part a) only be equal to 2 since theres 8 balls and you can only get 2 sets of 3 before theres only 2 balls left?

[trim jolt]

@runic axle Has your question been resolved?

[potent bone]

i suspect the question is asking how many possible results there are if you just do this procedure once, not how many times you could repeat it

i'm not entirely sure which formula "the combination formula" is but there's definitely some formula that it makes sense to use here

keep in mind that it says "ordered", so the implication is that if you draw balls 2, 4, 5, that's considered different from drawing balls 5, 2, 4
if draws of the same balls in a different order were considered the same then you'd get a different answer

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[dense hornet]

not really sure how to do this problem, im completely lost; heres where i got stuck (im not sure if my steps are even right)

[wispy sparrow]

-18 for dV/dt, it's decreasing

[dense hornet]

ooo ty i forgot about that

[wispy sparrow]

can you explain the second line

[dense hornet]

i tried product rule

idk if that was the right way to go though

im confused 😭

[wispy sparrow]

notice that r is constant

[dense hornet]

is dr/dt just 0?

[wispy sparrow]

it means you dont need dr/dt

[dense hornet]

oh

ohhhh

thank you lmao my calc teacher doesnt explain these things

so i dont need dh/dt either then because h is constant?

or

[wispy sparrow]

no height is changing as the volume drops

$\frac{dV}{dt}=\frac{dV}{dh}\frac{dh}{dt}$ yes?

[dense hornet]

o ok i see

[solid kiln]

chlamydia

[dense hornet]

the notation confuses me 😭 but that looks right?

[wispy sparrow]

so dv/dt is -18, and dv/dh is the derivative of v

and v=pi*12^2*h

[dense hornet]

so dv/dh is just 144pi?

[wispy sparrow]

yes

[dense hornet]

ohhh

so then is dh/dt -18/144pi?

[wispy sparrow]

yes

the question doesn't ask for negative so 18/144pi is fine
also simplify

[dense hornet]

thank you!!

is there a way to go about this problem using product rule?

or no because r is a constant? sry im a bit confused w things conceptually

[toxic fulcrum]

Since r is a constant, the term related to dr/dt will be 0

So the product rule is, of course, applicable, but not relevant

[dense hornet]

thank you!

i got stuck again on the next problem, i tried the same product rule approach but i couldnt figure out how to simplify it. i did the thing chlamydia showed me above in the 2nd image but idk if it works here and my answer was wrong

also i figured dr/dt is 1/2 of dh/dt since the diameter = altitude? but idk if thats right either

[toxic fulcrum]

mhmm

[dense hornet]

oh wait for the 2nd image i think its supposed to be 15=1/3pi but thats wrong too 😓

[toxic fulcrum]

so what does it mean that the base diameter is always equal to it's altitude?

[dense hornet]

r=1/2h? or h=2r?

[toxic fulcrum]

Yep

So before you take any derivatives, if that rule always holds, you can eliminate a variable

Since the question asks for dh/dt, it might be faster to eliminate r by substitution

[dense hornet]

ohhh thank you!

so v=1/3pi4h^3?

wait no oops

1/3pi(1/4)h^3?

[toxic fulcrum]

Yeah

[dense hornet]

i dont think i went about this right

do i still need dh/dt since this technically isnt implicit differentiation?

wait i just did my algebra wrong 😭

got it its 15/pi!

[toxic fulcrum]

Take the derivative of both sides at the same time

And don't substitute for the left hand side until you are done with the algebra/calculus

but you got the right idea

[dense hornet]

im still a bit confused about the dh/dt

how do i know when i need to multiply by dh/dt when i derive? is it just any time i derive h?

my teacher just told us to multiply by the derivative with respect to t whenever we derived with implicit differentiation but this just looks like normal differentiation

[toxic fulcrum]

You ALWAYS use the chain rule

And eventually you get to d/dx(x) or something like that, which is 1

In "normal differentiation"

Really internalize that the chain rule always applies, and why it applies

Because trying to memorize "when i need to multiply by dh/dt when i derive? is it just any time i derive h?" is a recipe for disaster

https://www.youtube.com/watch?v=YG15m2VwSjA

Watch the whole series if you have time...

Quick rule to help:

Ask yourself if the variable in question (h, V, anything) is a function of the independent variable?

If it is, do you know that function?

If it's an unknow function, then the derivative of an unknown function is ALSO an unknown function

we call that unknown function df/dt or f'(t)

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[wraith hinge]

How do I go about this

[versed sand]

(f+g)(2)=f(2)+g(2)

does that help?

[wraith hinge]

That?

[versed sand]

f(2) means u plug in 2 in function f

[wraith hinge]

Is it 6x^2 + 2x

[versed sand]

no

[wraith hinge]

ThatC

?

[versed sand]

(f+g)(x)=f(x)+g(x)=(3x²+1)+(3x-1)=3x²+3x

[wraith hinge]

Answer is 18

[versed sand]

(f+g)(2)=3x2²+3x2=12+6=18

[versed sand]

yes

[wraith hinge]

So answer is 18 correct?

[versed sand]

yes

[wraith hinge]

Ok thanks

One more

That?

25x-4

@versed sand

That right?

[versed sand]

perfect

[wraith hinge]

Ok thanks

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[loud wasp]

I'm getting 48

Dk what I'm doing wrong

[rugged prawn]

hollup

lemme try

[south latch]

C is right.

[rugged prawn]

C is right we know

just going thru their working out

[trim jolt]

As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.

[south latch]

175 - 28

The problem SAID C is the correct answer, so...

[rugged prawn]

im going through their working

[mellow tendon]

: )

[south latch]

yeah well don't ratio me, mystery person 👀

😛

[rugged prawn]

@loud wasp

punch this into the calculator properly

[night zodiac]

You messed up the calculation when finding the area of the big circ

[rugged prawn]

@loud wasp tell me what you get

probably didnt put it into the calculator properly

[loud wasp]

Oooff

That should give me 175

[rugged prawn]

yeah ur workign was right, just u not putting it into the calculator correctly

[loud wasp]

Then that subtracted by 28 is 147

Thank uuuu 🙏🙏🙏

[rugged prawn]

no worries

.close

[loud wasp]

.close

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[trim cradle]

Here the answer is 0.4 * 0.4 * 0.4 + 0.4 * 0.4 * 0.4 - (0.4 * 0.4 * 0.4 * 0.4) = 0.1024

[trim cradle]

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[wide charm]

Is there any idea/website to draw/see complex numbers circle,hyperbola?

[chilly cloak]

desmos

[wide charm]

I don't know how to use desmos for complex

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[wraith hinge]

wolframalpha?

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[wraith hinge]

The numbers x and y are two different positive integers that have a sum of 20. You know that 1/x + 1/y = 5/24. What is x*y then?

[trim jolt]

What step are you on?
1. I don't know where to begin
2. I have begun but got stuck midway
3. I got an answer but I'm told it's wrong
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5. I have a question about someone else's worked solution
6. None of the above

[wraith hinge]

I don’t know how to solve it

Where to begin

[ripe valley]

Aight

So have u combined fractions involving variables before?

[wraith hinge]

I did try some stuff but it didn’t work

[wraith hinge]

Nope

[ripe valley]

Send it

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@wraith hinge Has your question been resolved?

[old spruce]

ok so you have equation 1 is x+y = 20 thats good

second equation was given

1/x + 1/y = 5/24

i think its easier to isolate a variable in the first equation

if you can do that

then you can use substitution to solve the equations

[wraith hinge]

What does isolate imply?

[trim jolt]

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[cerulean thorn]

hello

[wraith hinge]

Huh, this channel didn't reopen yet, you shouldn't have been able to do that...

Anyways, do you need help?

I'm gonna go with "no". If you need help, check out #❓how-to-get-help. If you just want to hang out, check out #discussion or #chill

.close

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[placid valve]

can anyone here help with a circuits question?

[fluid vector]

Yeah

[placid valve]

So I need to find the voltage V (the voltage across the 18 ohm resistor)

I tried to combine the resistors then use the voltage divider equation to try and get the voltage but its incorrect somehow and im not sure why

<@&286206848099549185>

.close

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[fading pebble]

Hi

[fading pebble]

From an earlier thread that didnt get a response

[trim jolt]

@fading pebble Has your question been resolved?

[fading pebble]

@nova spire 😄

[nova spire]

ok j'arrive 😂

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[modern bough]

Hi, I am self studying combinatorics and came across this problem:

“What is the number of k-element permutations of an n-element set if k > n ?”

Is this a trick question? Since you can’t make a k-element set from an n-element set in the first place

OR

If I think of a k-element permutation as being a one-to-one function with the n-element set.

Then the number of permutations are equal to the number of unique functions there are.
Therefore my answer would be:

[modern bough]

In the second example, by “counting the number of one-to-one functions” I am allowing the k-element permutation to have empty space e.g.

A 4-element permutation of a 2-element set [1, 2] would be:

[_, _, 1, 2]

or

[_, 1, _, 2]
Etc

——————————————————
I am not sure which method of thinking is correct or if the second method makes sense at all

<@&286206848099549185>

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@modern bough Has your question been resolved?

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@modern bough Has your question been resolved?

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[nova wadi]

why is this formula correct for the distance from a point on a eclipse to mu

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[brisk ice]

Hi, sorry for the messy work. I’m wondering if I reached the end goal for this problem correctly? I don’t know how to round my final answer and I’m also not 100% on if I did everything right to get it.

[brisk ice]

Above the answer box is my final part of the problem. I ended up with 4.083

[dull temple]

hmm that answer doesn't seem right from a scale point of view

if we need $18,000 and we're getting $325/mo plus a bit of interest

it seems like it definitely should take more than 4 months

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[brisk ice]

Yeah it doesn’t sit right with me

I’m wondering where I did it wrong though according to the formula

[dull temple]

review what each variable in that formula means

[brisk ice]

I think I got my variables right

Our starting amount being deposited is 325 each month, which is P

Its being deposited monthly, so M = 12

A is the total amount we want to achieve so its gonna be 18000

We don’t know t since we dont know how long it’d take

And our rate is gonna be 5.68% or 0.0568

Might be wrong on one of these but I think I got them all correctly

[dull temple]

review the units in particular

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[wraith hinge]

Q. Write the first 3 terms of the expanded form of $(1 + x)^{-2}$. Also state the values of x for which this expression can exist

[solid kiln]

hodor776

[wraith hinge]

the first bit is pretty easy

I got my answer as
$$= 1 - 2x - 3x^2 + ...$$

[solid kiln]

hodor776

[wraith hinge]

but for the second bit,

is it that $x \neq-1$

[worldly monolith]

$x \neq -1$

[solid kiln]

Jigglyproff

hodor776

[wraith hinge]

ahh there we go thanks

[worldly monolith]

yes, you may not divide by zero

[wraith hinge]

indeed so that values of x cna be anything except of -1 right?

[worldly monolith]

yes, x is any real/complex that isnt -1

[wraith hinge]

ahh gotcha

tysm

have a great day

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[wraith hinge]

@worldly monolith hey sorry for the ping

[wraith hinge]

what about this question $(1 + x)^{\frac{1}{3}}$

[solid kiln]

hodor776

[ivory thistle]

What are you trying to find?

where it wont exist?

[wraith hinge]

yeah

the values of x for which this expression wouldn't exist

I don't think there is any real value of x for which this expression doesn't exit

*exist

isn't it?

[ivory thistle]

There are no restrictions for this

[wraith hinge]

had it been a square root, in that case, I would have made sure that x > -1 such that there is no root of negative numbers

but cube roots do output real values even when there is a negative number under them

right?

[ivory thistle]

well

yes

[wraith hinge]

so can I just say

[ivory thistle]

it would be greater or equal to 1 though

[wraith hinge]

$-\infty < x < +\infty$

[solid kiln]

hodor776

[wraith hinge]

I am not sure I understand 😅

[ivory thistle]

because you said x>-1

but it can also equal 1 and still exist

[ivory thistle]

for the 1/3 one or for the square root one

[wraith hinge]

for 1/3 one

not the square root

in that case, we would have to make sure that we aren't square rooting a negative number

right?

[ivory thistle]

no

it would be( -1,inf)

[worldly monolith]

rewrite as $\sqrt[3]{1+x}$

[solid kiln]

Jigglyproff

[wraith hinge]

yup

[worldly monolith]

now it depends if you are in complex or real space

[wraith hinge]

real space

[worldly monolith]

for real numbers there is a strict restriction to roots, their contents may not be less than zero

ah wait someone helped you already, i see

[wraith hinge]

I am really confused 😅

so can x not equal to -1 in this case?

[ivory thistle]

sorry for the original question that is correct

[worldly monolith]

right my mistake, its an uneven root

[ivory thistle]

x can can equal -1 in this case

[worldly monolith]

x can be anything for this case

[wraith hinge]

yup

[worldly monolith]

since you can hit both negative and posetive numbers

[wraith hinge]

indeed

in this example question, shouldn't the values for which this expansion is valid be $x\neq-4$?

[solid kiln]

hodor776

[wraith hinge]

I am not sure I understand why it is $|x|<4$

[solid kiln]

hodor776

[wraith hinge]

is it cause of this law?

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[daring karma]

2 vectors are parallel if their cross products are 0, right?

[daring karma]

could you also determine if they are parallel by doing something like u = < u1, u2, u3 > and v = < v1, v2, v3 >
let's just say v1 > u1. Then do v1 / u1 and then multiplying that number by u2 and u3 and seeing if they equal v2 and v3?

and if they do equal, then they are parallel

is that possible to do?

[silent sphinx]

That's correct

[west nest]

2 vectors are parallel if one is a scalar multiple of another or their cross products are 0

[silent sphinx]

The easiest way to check if two vectors are parallel is to see if their dot product is equal to the product of their magnitudes.

[west nest]

So whether u = kv, where k is a scalar or if u x v = 0

[west nest]

That too

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[pure oak]

How do I get exactly 5/36 because this problem is rigged af

[nimble stone]

what is your working?

[pure oak]

at the end i got 2/14.4

Which is same as 0.1388..

And 5/36 is that too

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[pure oak]

<@&286206848099549185>

[pure oak]

.close

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[trim jolt]

Please don't occupy multiple help channels.

[tribal kernel]

ok

.close

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[haughty solstice]

You can take help of the below concepts :

1. Sum of interior angles btwn parallel lines is always 180, ie they are supplementary angles
2. Sum of all interior angles of a triangle is 180
3. Exterior angle of a triangle is equal to sum of two opposite interior angles

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[winter tendon]

How do I find r?

[haughty solstice]

You know the slope formula ?

[winter tendon]

Yes

[haughty solstice]

Nd wht is it ?

For 2 points?

[winter tendon]

(-5,1) and (r-3) m= -2/5