help-42

[hushed tartan]

<@&286206848099549185>

[white atlas]

looks good to me

[hushed tartan]

how can i find the coordinates of B

[white atlas]

hmm you can use heron's formula on the BCA triangle to get its area

then use A = 1/2 bh to get the height

[hushed tartan]

idk heron's formula

isnt there a way using laws of sines and cosines

[white atlas]

i mean yeah? I guess you can use A = 1/2 ab sin(C)

but for that you'd need to find another angle

using law of cosines

[hushed tartan]

how did you get that

[hushed tartan]

idk if my question is stupid but i suck at geometry how will it help to get the height

[hushed tartan]

oh wait if we have the height issued from B to AC then we add that to the height issued from O to AC?

this will give us the ordinate of B

or is this wrong

[white atlas]

yes that was the plan

[white atlas]

you can find green angle from law of cosines, right?

now that you have that angle, you are able to use the 1/2ab sin(C) thing to get the area of the triangle ABC

finally, Area = 1/2 base * height and since you have everything aside from the height

you can algebraically isolate for the height

[hushed tartan]

how will the height be of any use to me

[hushed tartan]

cant i get sinC by getting C using law of cosines then finding sine of that

[white atlas]

either way works

[hushed tartan]

but will that pose a problem bc idk the quadrant that the angle lies in

[white atlas]

blue + green is the y coordinate of b

[hushed tartan]

yes we will still need the x coordinate

[white atlas]

the red is the "height" of the triangle

the purple is AB

you can find the distance OA

[hushed tartan]

OA is given

[hushed tartan]

7.3 from the figure

[white atlas]

sorry not OA

i'm talking about this pink segment

you can find that using OA

you can also find AB from the height

so you can find OB right using those two in conjunction?

it's just purple (AB) - pink

[hushed tartan]

yes it is just the green part of AC

[white atlas]

yeah so we have both the x and y coordinate of B

[hushed tartan]

this is a solution to a similar problem

why did he use 90-A

[white atlas]

where am i looking? lol

[hushed tartan]

like this for example

[white atlas]

it's exactly what you did

cos(90 - x) = sin(x)

obviously x is in degrees

[hushed tartan]

ik

but this will be different

bc what i did was getting the angles using cosine rules

then rcosa

where r is the length of the side joining O and the corresponding point

[white atlas]

I'm talking about these parts

you didn't use cosine rule here, did you?

[hushed tartan]

me too

yes i did to get the values of OAC and OCA to get their cosines and sines

[white atlas]

idk what you mean lol

the red part is just 7.28 cos(76.06 degrees) and the other leg is 7.28 cos(90 - 76.06 degrees)

7.28 cos(90 - 76.06 degrees) can be equivalentally written as 7.28 sin( 76.06 degrees) so that was just his matter of choice

[hushed tartan]

i will tell you what i mean in triangle OAC, $5.1^2=6.1^2+7.3^2-2(7.3)(6.1)cos(OAC)$

[hushed tartan]

so that $OAC=arccos(\frac{6.1^2+7.3^2-5.1^2}{2(7.3)(6.1)})$

[white atlas]

yes and i did mention that it looked okay to do so

ofc i'm assuming you put the numbers in right

[hushed tartan]

thats why i was asking about whether doing this will pose problems bc of the quadrant

[white atlas]

but the idea of using law of cosines to find the blue angle is correct

[white atlas]

no, you'd use the reference angle

arccos conveniently would return that for you

your x-y plane here is a slightly tilted version of the actual x-y plane

it's just like a physics ramp problem where your x-y plane is rotated

[hushed tartan]

yes but no problem

i mean that wont change anything

[hushed tartan]

but from here he has sin(x) i did cos(x)

the angle that he named A' is the angle OAC

i used cos(OAC) for the x-coordinate he used sin(OAC) for the x-coordinate

[white atlas]

yes because he's using a different coordinate system compared to you

his "horizontal" thing is y

yours is x

it all checks out

your coordinate pairs are just switched

[hushed tartan]

oh wait i am stupid i didnt pay attention to this

[hushed tartan]

i am too stupid i wasted time for this

[hushed tartan]

the x coordinate of B will be <0 right

[white atlas]

if you've defined rightwards to be positive then yes

[hushed tartan]

yes i did

[white atlas]

then yes

[hushed tartan]

how should i formally say that the green part here is the x-coordinate of B

[white atlas]

idk what you mean by "formally" but it should be evident by construction

all the letter' have the same x coordinate as letter itself

so A' = A, B' = B, and O' = O in terms of their x coordinate

x coordinate of B' or B = - (A'B - O'A)

[white atlas]

this is cuz we have a rectangle by construction

[hushed tartan]

now i need to find the coordinates of A,B and C after placing A at the origin

ill call them A',B',C'

A'(0,0)

now the angle between A'B' and the x-axis is 180-C'A'B'=180-(20+C'A'C+CA'A)=180-(20+C'OC+COA) i have C'OC and COA from the calculations before when i got coordinates for A and C

so i can get the angle between A'B' and x-axis and use rcos and rsin to get the rectangular coordinates of B

what remains is C

now i have C'A'B' and A'B'C' so B'C'A'=180-(C'A'B'+A'B'C') and i am done

[hushed tartan]

is this work correct or is it flawed somewhere

[hushed tartan]

<@&286206848099549185>

[calm coral]

@hushed tartan Has your question been resolved?

[hushed tartan]

<@&286206848099549185>

[calm coral]

@hushed tartan Has your question been resolved?

[hushed tartan]

<@&286206848099549185>

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@hushed tartan Has your question been resolved?

[hushed tartan]

.close

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[astral magnet]

can someone check that i have the right idea on how to solve this by proof by induction

[runic nova]

yes it s correct

[astral magnet]

thank god

i spent the last 6 hours trying to figure this out

just to make sure i have the idea down for the induction step, we are basically trying to make the RHS to equal the RHS of an equation that we replace all the k for k+1?

i feel thats poorly worded

[runic nova]

yeah kind of, you want to show that if it works for k, it still works for k+1

[astral magnet]

ya, i get that

its just how you show that is weird

and tedious

ill work on another problem after dinner to see if I understand the induction step

thank you for checking my work

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[leaden sandal]

How do we get rid of abs on 1-y?

[leaden thunder]

,rotate

[leaden thunder]

Without more information I guess you can't

[leaden sandal]

Would this be correct?

Wolframalpha says it’s 1+e^cos(x)*C not 1-

[leaden thunder]

C is just a constant

So is -C

[leaden sandal]

So would this make my answer wrong? Or is it still right? Since C could be anything

.close

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[dire depot]

Help

[dire depot]

Is this possible

[karmic quail]

what test do i do

[karmic quail]

.?

[dire depot]

I’m not sure

[honest quiver]

Open a new channel if you have a question

[dire depot]

But

Ive tried to solve for a b c d

That’s supposed to be a new 2x2 matrix

[honest quiver]

Have you learned how to find matrix inverses

[dire depot]

But it’s kind of difficult to get everything equal to zero

Yeah

[honest quiver]

Wait this isn’t a inverse problem is it

Let me see

[dire depot]

Yeah so I take matrix a and moltioly by B to get the zero matrix

I’m pretty sure it’s possible for B=0

[honest quiver]

Well take a look at that matrix

[dire depot]

When AB=0

[honest quiver]

Do you notice anything about the columns

[dire depot]

There’s a negative in each one

[honest quiver]

What about the ratio between the top and bottom entry

[dire depot]

If multiplied by -2

[honest quiver]

You know basic vector math right (just checking)

?

Shoot I have to go, <@&286206848099549185> could someone else help this fellow

[karmic quail]

um try
4 2
2 1

[dire depot]

Thanks

[dire depot]

Did not work

[untold drum]

B has 4 elemetns, name them a,b,c,d -> AB =0 would give you 4 equations in 4 unknowns -> solve.

[dire depot]

Right I tried solving

So

Matrix A X ab|cd

3a-4c=0

3b-4d=0

-6a+8c=0

-6b+8d=0

Do I just solve for 1 variable

Plug it in

[untold drum]

as in your equations -6 does not appear they must be wrong.

[dire depot]

I mixed that up with something

[untold drum]

so the first and the third are jst the same equation. same for secondand fourth. true?

[dire depot]

Are they not

[untold drum]

multply the fitst be -2.

[dire depot]

Got -6 8;-6 8

[untold drum]

if I multiply 3a-4c=0 by -2 i get -6a+8c=0 whih is te third equation.

[dire depot]

Got that

[untold drum]

so you have only 2 equations in 4 unknowns whic means you can choose two of the unknowns (e.g. c and d) as you want and determine the other two unknowns.

[dire depot]

Can the unknowns be a and c

[untold drum]

you can choose c and d or a and b.

[dire depot]

Ah alright so

I’ll do c and d

C = 6/4A

8^

D = 6/8b

[untold drum]

as i said, you can choose c and d or a and b. so you can choose a = 4 (or any value you want) and then determine c. then do the same with b. choosa a value for b you like and determine d.

[dire depot]

Would this same concept work with a 3x3

[untold drum]

YES

[dire depot]

Thanks @untold drum

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[remote mural]

how am i getting this wrong?

[leaden thunder]

Try removing the units

[normal wadi]

you used degrees I believe

[remote mural]

my calculator was in degree

[normal wadi]

^

change to rads

[remote mural]

i got another problem

[halcyon rock]

oh

I think they are using the $v_f^2 = v_i^2 + 2a \triangle x$ equation

[potent lotus]

nosqldb

[halcyon rock]

with $v_f = 0$ m/s, so it becomes like $vi^2 = 2g\triangle x)$

[potent lotus]

nosqldb

[halcyon rock]

so $\triangle x = \frac{v_i^2}{2g}$

[potent lotus]

nosqldb

[remote mural]

yes

95^2 for v

[halcyon rock]

but v is not in the y direction fully

[remote mural]

but what is 5pi/11? i dont see it in the unit circle

[halcyon rock]

we need the v in the y direction

[normal wadi]

do you need to do this by hand

[halcyon rock]

okay hmm

[remote mural]

yes

[halcyon rock]

if you need to do this by hand

I'd recommend taking like 5 terms of sin(x) taylor expansion

[remote mural]

what does that mean?

[normal wadi]

bruh what

[halcyon rock]

wym prob the easiest way no?

[normal wadi]

this looks like a class that you take way before calc 2 dog chill

[tacit tulip]

hahaha

[halcyon rock]

ohh

[normal wadi]

then I'd recommend maybe applying an angle sum formula or something of the sort

[halcyon rock]

sounde really annoying to do ngl

[remote mural]

i feel like we r overthinking

[normal wadi]

yes, we are

[halcyon rock]

,w calculate sin(\frac{5\pi}{11})

[normal wadi]

wolfram can't even simplify it

[potent lotus]

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[normal wadi]

I'm pretty sure you don't have to do it by hand

[remote mural]

wym do it by hand?

[normal wadi]

finding the actual answer without using calculators at all

[tacit tulip]

hes using a calculator guys

what are u doin

hahahaha

[normal wadi]

dog

thats why I was confused

[halcyon rock]

,w calculate \frac{5\pi}{11}

[potent lotus]

Results provided by WolframAlpha

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[remote mural]

yeah we can use calculator

my bad

[normal wadi]

literally just plug in all values with your calc in radian mode and you'll get the height

[halcyon rock]

yeah that's why I suggested taylor expansion

lmao

[tacit tulip]

love how his first assignment was literally just plugging in values

[normal wadi]

yeah guess what you can't get the exact answer with taylors

not in a finite amount of terms

[remote mural]

dont we have to find the sin of 5pi/11 tho?

[tacit tulip]

then the next one he gets told to use taylor series

[remote mural]

to plug it in the formula?

[halcyon rock]

I mean neither with a calculator lol

[normal wadi]

do you know how to ask your calculator to do that?

[remote mural]

sin 5pi/11?

[normal wadi]

what calculator are you using

[halcyon rock]

what kinda calculator is that bro 💀

use google

[normal wadi]

I'd recommend using wolfram

[remote mural]

my guy its given for my hw

[normal wadi]

just overall better

[remote mural]

i cant use any other calc

[normal wadi]

ah

[remote mural]

i gotta get used to this

[halcyon rock]

goddamn rip to you

[remote mural]

LMAOO

making me feel hopeless

[normal wadi]

ok well set it to radians

[tacit tulip]

my professor really wanted us to use some old ass emulated calculator as well

[remote mural]

does this look right?

[normal wadi]

yes

[remote mural]

yeah this website is from 90s

[normal wadi]

just close the second (

dunno if the calculator gets pissy over that

[remote mural]

got it

[tacit tulip]

btw

why cant u just use the built in one in windows if u have to use one like that

[tacit tulip]

u should probably do some urself

[halcyon rock]

nah you gotta try it yourself lil bro

[remote mural]

lmaoo

got em wrong brothers we r down

[tacit tulip]

what the f

[tacit tulip]

why

oh wait its drop down menus

[remote mural]

yeah

how am i wrong?

got it

.close

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[warm arch]

why is this true

[warm arch]

I assume u take the ln but then I get stuck

like ln y = lim n ln( n+1/n )

oh wait I think I see

[pseudo wedge]

This is the definition of e

You can’t “prove” this

[pseudo wedge]

If you really want to, you can do this limit

But like, the methods you use to solve that limit are derived from this very limit

[upbeat venture]

there are various things that can be used as definitions for e, but if you just assume this limit is unknown, yeah taking logarithms works

assuming the limit exists blah blah blah

[warm arch]

sorry I saw a very old post on a website

it isn't that bad I just am tired and integrated the numerator lol

you can solve it with l'hopitals

thank you all!!

.close

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[shell kiln]

how can I approach this? it's the first problem I've had equal to 0 and ask for ∂z/∂x instead of ∂f/∂x.

[shell kiln]

.close

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[shell kiln]

.reopen

[calm coral]

✅

[pseudo wedge]

Try isolating z

As in, write z as a function of x and y only

[quaint sphinx]

you are asking them to solve a cubic

[pseudo wedge]

Ah wait I thought the z^3 was a z

My bad

[shell kiln]

i did ∂f/∂x as normal and got y + 3z^(3x) ln(z)

[pseudo wedge]

Doesn’t look right

That term is z^3 * x, not z^(3x)

[shell kiln]

ok y + 3z^2

[pseudo wedge]

No

Not quite

Would it be 3z^2 or just z^3?

[shell kiln]

just z^3

so y+ z^3

[pseudo wedge]

Yep

Now you can just input your point (1,1,1) in this derivative

[shell kiln]

i just did ∂f/∂x

isn't ∂z/∂x something else?

[calm coral]

@shell kiln Has your question been resolved?

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[median cloak]

a

[calm coral]

Please don't occupy multiple help channels.

[winter elbow]

Zzz

[warm warren]

.close

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[buoyant quiver]

First two highlighted

Need to check my answers

[signal harbor]

the vector diagram for question (f)

[still gate]

: Since xy is less than 0, x and y must have opposite signs. Because you know one of them is
negative, when you simplify the second expression (by multiplying through by xy), you must flip the
inequality sign, yielding:
Therefore, Quantity B is greater.
5. (C) and (F): Setting the value of f (x) = 14 in the original function gives the quadratic equation x
2 –
5x = 14. Subtract 14 from both sides to get x

xy< 0 and
Quantity A Quantity B
ay bx solve

[brittle crow]

asd

why cant i claim channel

[blazing coyote]

How do I regain the roles I lost by leaving the server temporairily ?

.close

[tender vessel]

<@&286206848099549185> @mossy gulch

pls help me find the limit

[blazing coyote]

notice that ((2n)!)^1/n increases way faster than (n^n)^1/n

[past zinc]

you need to use Stolz - Cesaro theorem or stirling formula

[past zinc]

hint to use stirling limit version:

[past zinc]

and stolz theorem:

[calm coral]

@tender vessel Has your question been resolved?

[tender vessel]

.close

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[tender vessel]

Wtf? Never heard that and they don't teach that. I asked someone else and they got infinity too

[tender vessel]

We did with the lim X/X-1

[past zinc]

yes thsi one converges to 1/e

that is known formula

[tender vessel]

I used this for this one

And we got to infinity

[past zinc]

i was not calculating it now, let me do that then i wil be able to confirm, mooment

[past zinc]

using stirling you get the same result too

[tender vessel]

Ok thx haha

We confirmed then

[past zinc]

yes 🙂

[tender vessel]

.close

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[dapper moon]

Wolfram says there is no two-sided limit? Why is that? Where is my mistake

[modern peak]

is that sqrt (1 - sin x) in the numerator

?

[dapper moon]

yes

[modern peak]

,w plot (sqrt (1 - sin x)/(2x - pi))

[potent lotus]

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[modern peak]

^

that is why

[dapper moon]

I still do not really know how to see that from the function without seeing the graph since there is no 1/0 or so, where I would check left and right limit seperate

[finite maple]

I had a similar problem on my previous calc test. I had no idea if I had to check left and right limit seperate, so +1

[calm coral]

@dapper moon Has your question been resolved?

[dapper moon]

I do not understand where I see that there is no two-sided limit for this function

Would love if someone could explain this to me. <@&286206848099549185>

[calm coral]

@dapper moon Has your question been resolved?

[past zinc]

the second liimt, compute in an analogous way

please also, write it in an exercise book, to not lose it

[calm coral]

@dapper moon Has your question been resolved?

[calm coral]

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[autumn finch]

Hi

I'm having a doubt

Pls explain if you can!!

Article are marked at a price which gives a profit of 25%. After allowing a certain discount,the profit reduces to 12½%. Find the discount percent.

[calm coral]

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[spiral panther]

Let p = the original price of the article. The article is being sold at a profit (I'm assuming to the seller), so you'll pay 1.25 × p.

[spiral panther]

The profit itself is 0.25, so you're finding a perecent of that original profit. The rule of thumb is that "of" usually means to multiply. So you'll multuply 0.25 × 0.125 (which is 12½%). That wil, give you the answer.

[autumn finch]

The answer is 10%

[remote mural]

please please dont post answers

!nosols

[calm coral]

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.

[remote mural]

oh wait

you are the one in needing of help

[spiral panther]

Is that the textbook answer?

[remote mural]

im dumb

[autumn finch]

Yep

[spiral panther]

Ok. I looked at the question again. I misunderstood. So you're looking for the discount, or what you subtracted from the profit. I'm on the same page now.

[calm coral]

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[spiral panther]

But then again, they're asking the discount PERCENT, which means the ratio of 0.25 to 0.125

[sacred valley]

use .close

the bot thinks you asked a question

[autumn finch]

Hmm 🤔🤔

[spiral panther]

Thx

[autumn finch]

I think we have to take the CP as a constant like 100

And if I'm correct then
CP=100
Profit=25%
Marked Price=125

And there will be 2 cases

CP=100
Profit=12.5% (after reducing)
Marked Price=112.5

We have To find discount percent

[spiral panther]

Gotcha. 9% (1.125/1.25), but it rounds to 10%

[autumn finch]

How are we planning to do this?

[autumn finch]

How

?

[spiral panther]

Well, as I'm playing with the numbers, I'm starting to understand the question better. The information is in terms of profit, but the question is in terms of discount

[autumn finch]

Hmm

[spiral panther]

Oh here we go. Take the original price, p, and multiply by 1.25 to get the new price. The price fell to 1.125p, so all we need to do is calculate by what percent the price fell. The price fell by 0.125, (1.25-1.125), so that's how much it fell. Now as a percent of the total price, that's 0.1 (0.125/1.25), which is 10%.

[autumn finch]

Oooooo

K

[spiral panther]

It's been a while since I did this lol.

[autumn finch]

Thankzzz

[autumn finch]

Oo

[spiral panther]

Ur welcome. Hope it helped.

[autumn finch]

Btw what's your name @spiral panther

[spiral panther]

Ian. TrenchGoat's a fun username I like to use.

[autumn finch]

Noice

Good name

[spiral panther]

Thx. Is Zion your actual name?

[autumn finch]

Nope

Prateek is my real name

I am from India it's an Indian name

[spiral panther]

Oh cool!

[autumn finch]

Ya

[spiral panther]

I saw on your bio that you like to play chess. My little brother is really into that too. How'd you get into chess?

[autumn finch]

No I Don't like to play chess

Where is this written

I like to do coding

I'm not into chess

[spiral panther]

When I tapped on your profile picture, it showed the all the info tags. Chess was one of them. Maybe that's just a discord thing.

[autumn finch]

Hmm probably

It's possible

[spiral panther]

What language do you code in? (I do mostly Javascript/Typescript and other web languages, although I've messed around with C# and java)

[autumn finch]

I'm beginner and I started coding few months ago

And I'm currently learning HTML,CSS and I want to learn JavaScript

[spiral panther]

That's what I started with, too. They're great languages.

[autumn finch]

Hmm

I don't know anything about js I want to master CSS

JS is hard ig

It is very complicated

[spiral panther]

Knowing CSS is a great skill. It's hard to do well, but when you can master it you can do some awesome stuff.

[autumn finch]

I know

[spiral panther]

That's true. Especially when you get into all the different ways you can write the same line of code. But if once you get an idea of variables and functions, all the rest comes easier.

[autumn finch]

I think it's very hard to create or code a function

[spiral panther]

Yea It is.

[autumn finch]

Well I'm a beginner so

According to me it's complicated

[spiral panther]

May I show you a short piece of code?

[autumn finch]

Ya sure

[autumn finch]

I believe that with time, everything will become okay and easy to understand.

[spiral panther]

This is a line of code in css:
#paragraph {
background-color: red;
}

CSS is designed to make styling things easier. But js has more capability:

Here's the same thing in js:
document.getElementById("paragraph").style.color = "red";

It was definitely more complicated, but watch this:
Loop () {
document.getElementById("paragraph").style.color = HueRotate();
}

[spiral panther]

What the last bit of code does is make the paragraph change color infinitely.

[autumn finch]

What does loop mean in end of the code

[autumn finch]

Ooo

[spiral panther]

So that was a function. Functions look like this: randomFunction(). You can make whatever kind of function you like--you could have a makeALottaNoise() function, an extraCheesePlease() function, or a
wreckTheConsole() function.

[spiral panther]

What you name it doesn't really matter.

[spiral panther]

A function is shorthand for a bunch of code. Say you write some code, but you end up needing to use pretty much the same thing later. You could write all that code again, or you could just make turn it into a function that you use multiple times.

[autumn finch]

Woa

I learned a lot

Thankzz

Do you make webpages or a website and earn money

?

[spiral panther]

I do make webpages, but I don't earn money lol.

[spiral panther]

My uncle does make money for it though.

[autumn finch]

Means you practice to make webpages

[autumn finch]

Oo

[spiral panther]

Although with AI that can write code, people are wondering how that will change. I don't think people that write code will lose their jobs, but I do think that they will work more with AI than ever. My recommendation is that if you are wanting to write code professionally, learn to work with AI (like ChatGPT) as well.

[autumn finch]

Hmm we can learn with AI

A lot

Do you want to get a banner or logo designed?

Me and my friend also do that

If you want anything like that so you can tell

And also video edits

[spiral panther]

What have you done before?

[autumn finch]

You wanna see

?

[spiral panther]

Yea

[autumn finch]

What do you wanna see video edits or banner

Actually I can't show you coz I sold that

So if you save that I am gonna be in trouble

Hope you understand

[spiral panther]

Lol

[autumn finch]

Still wanna see?

So

I have to ask my friend

Wait a minute

[calm coral]

@spiral panther Has your question been resolved?

[spiral panther]

Oh woops I think the bot thinks I have a question

Idk what will happen if I close it.

@autumn finch I'm going to close it, but idk what will happen

[calm coral]

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[calm coral]

@remote mural Has your question been resolved?

[calm coral]

@remote mural Has your question been resolved?

[twilit lagoon]

um

are u sleeping

[calm coral]

@remote mural Has your question been resolved?

[calm coral]

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[calm coral]

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[calm coral]

@lunar sequoia Has your question been resolved?

[quaint sphinx]

which?

[calm coral]

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[remote mural]

I need help in finding the value

[winter elbow]

@remote mural

[brazen elbow]

i wonder if this can be solved with unit circle instead of solving it the equation way?

[remote mural]

what is that character above 3

[brazen elbow]

pi

[winter elbow]

pi

[hollow relic]

,rotate

[hollow relic]

,rotate

[brazen elbow]

the original question is 30deg though

[winter elbow]

…

[remote mural]

wait how is it 60 degrees

[winter elbow]

No, it’s an example

I’m just making it simpler

[remote mural]

wait how do i solve it

[remote mural]

do i subtract 30??

[winter elbow]

No

[winter elbow]

When the sum of theta and 30 equals 90, the equation stay true

[remote mural]

wait then what do ido next

[winter elbow]

Apply this phenomenon into your question

[remote mural]

i'm stumped on this one

.close

[calm coral]

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[calm coral]

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[lethal island]

How do I start?

[remote mural]

what have you tried?

[lethal island]

I divided both sides by log4

[remote mural]

you can't divide by log_4

it's $\log_4\left(\log_2(x)\right) = \frac{1}{2}$

[potent lotus]

45

[lethal island]

So multiply by 2 instead?

[remote mural]

$4^{\log_4(x)} = x$

[potent lotus]

45

[lethal island]

.close

[calm coral]

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[rocky flower]

you could also do 4^(1/2)=log_2(x) so log_2(x)=2 and clearly 2^2=x so x=4

[calm coral]

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[rich mural]

hey guys im having a brain fart on how to do operations for matrix variables, how would I expand this expression $(X^T (X^T X)^{-1} X^T n)^2$ where X is an n by d matrix

[potent lotus]

cameron

[calm coral]

@rich mural Has your question been resolved?

[upbeat venture]

note that $(AB)^{-1} = B^{-1}A^{-1}$ and $(A^T)^{-1} = (A^{-1})^T$ for any matrices A, B

[potent lotus]

doaby

[upbeat venture]

@rich mural

[rich mural]

right that makes sense but I'm not sure how I would distribute the terms when squaring the inner expression

[upbeat venture]

if you are squaring AB, do it like ABAB

then simplify

basically just copy paste it after

[rich mural]

I dont see how to simplify further from $\left( X^{T}\left( X^{-1}\right) \left( X^{T}\right) ^{-1}X^{T}\cdot n\cdot X^{T}\left( X^{-1}\right) \left( X^{T}\right) ^{-1}X^{T}\cdot n\right)$

[potent lotus]

cameron

[calm coral]

@rich mural Has your question been resolved?

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[forest palm]

hello how do i simplify this

[forest palm]

HELP!

[celest stream]

rationaliize the denominator

[forest palm]

okay

no

that will undo what i just did

[runic rune]

cant u just plug in h alr

[forest palm]

i have x

its 2

no its -1

the limit doesnt exist

[runic rune]

are you supposed to u defenition of derivative?

[forest palm]

the slope of the tangent

[runic rune]

ur doing B right?

[forest palm]

yes

the answer is wrong :(

the answer says 1/2

wait

i got 1/2

i plugged in the wrong number

LOL

[runic rune]

oh well glad u found ur mistake :)

[forest palm]

HELP!

[runic rune]

hmm

[forest palm]

oops

HELP!

question c

how do you do it

i think i made a mistake

😢

[runic rune]

ahhh its been a while that i have done definiton rule, one thing i can tell u is that you dont plug in x in the beginning

[forest palm]

but then i get stuck

HELP!

[runic rune]

uhh i got somewhere

Idk if this helps

[forest palm]

it is helping

but i dont know what to do after

[forest palm]

WOW

no

the answer is 1/-17

okay its okay

i need help with this instead

[runic rune]

do the derivative for 4-x^2 to find A

do the derivative of 2x+1 to find B

[forest palm]

oh im so silly

wait how

[runic rune]

u guys havent learned product/quotient rule?

[forest palm]

yes i think

help i am stuck

[runic rune]

Believe these should be right, where r u stuck?

[forest palm]

hmmmmmmmmm

i got -2

oh no!

[runic rune]

show ur work, maybe u made a silly eror somewhere?

[forest palm]

i made a SILLY mistake

i forgot to add the negative in

okay i understand now

[runic rune]

youll prolly learn product rule and quotient rule soon, they usually do teach it right after defenition of derivative

[forest palm]

yes

its the next unit

oh no a word problem

I DONT KNOW WHAT VELOCITY MEANS 😢💔

[runic rune]

hmm

have u taken physics before?

[forest palm]

no

this is for my calculus class

[runic rune]

ahhh these word problems usually are tricky for peple who never took physics but essentially

velocity is the derivaitve of position

[forest palm]

2-0?

do you know the first step

[runic rune]

i would try find the derivative of the position function

first

[forest palm]

but how

i am stuck 😞

on the first step

[runic rune]

for a:
try:
s(2)-s(0)
(divided by)
2-0

[forest palm]

2/2

1

now what

i need help :(

i dont know how to get started on it

[runic rune]

wait what

what do u know about velocity

[forest palm]

nothing

[runic rune]

x_x

[forest palm]

the question is supposed to use calculus

[runic rune]

you can think of velocity as speed, how can u calculate speed?

[forest palm]

hmmm

a car dashboard?

the needle thing

[runic rune]

uhmm

[forest palm]

HELP

you calculate it by time

[runic rune]

distance over time right?

[forest palm]

yes

[runic rune]

thats how u can answer number 1

distance at 2seconds minus distance at 0 sec

divided by time

[forest palm]

oooooooo

oh silly me

i get it now

I GOT -10

[runic rune]

is that right? i assume u have the answer key xd

[forest palm]

no it is not right

the answerr is -5m/s

ughhh

[runic rune]

hmm unless it was suppose to be velocity divded by time

do the derivaitve of -5t^2 + 180

[forest palm]

OMG

REREAD THE QUESTION

[calm coral]

@forest palm Has your question been resolved?

[calm coral]

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[jolly relic]

Business statistics
Q. 6 A and B

[jolly relic]

Can someone check my work?

Idk if this is right or wrong

Helloooo need help

<@&286206848099549185>

[remote mural]

can you send more cleaner image of your solution sir or maam ty.

[jolly relic]

This okay?

[jolly relic]

^

[remote mural]

yesssssssss ty sir or maam

What is the problem, and will I create my own solution and compare it to my own?

[jolly relic]

This from question 6 A and B

@remote mural

[jolly relic]

I just need someone to double check my answer

[remote mural]

it look correct for me

[calm coral]

@jolly relic Has your question been resolved?

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[leaden sandal]

Can anyone help me with this one pls? Where did I go wrong?

[leaden thunder]

,rotate

[sharp cargo]

whats the issue?

[leaden sandal]

I got the wrong answer

I checked and it’s supposed to be Ae^-x+Be^-2x+(1/10)[3sinx+cosx]

[leaden thunder]

Should be -B + 3A + 2B on the sine term

All your coefficients in the ODE are different, so should the sine term

[leaden sandal]

ohhh, and then just solve for a & b using simultaneous equations?

got it now, thanks

.close

[calm coral]

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[calm coral]

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[prime citrus]

the one i got as 1/2>=x, it's part of the answer but idk how to get the others

[lime trench]

there are fixed steps to do these type of question

at first determine the defined range

the simplify

and kinda solve the equations as much as you can

then solve inequality

for x

by making different cases

after solving cases find their intersection

and do union

that gives a final answer

then find intersection of defined range and that final anwer

you will surely get it right

@prime citrus

?

you here? @prime citrus

[prime citrus]

wait i gotta eat dinner sry ill have a look later

thank you

[lime trench]

if you wanna look at numbers and visualize it download photomath app

bye

[calm coral]

@prime citrus Has your question been resolved?

[calm coral]

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[twilit bramble]

how do u do these?

[smoky bone]

how do you find range of a function x over the square root of (x-7)

[twilit bramble]

.close

[calm coral]

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[prime citrus]

there are like so much cases tho, like it could be x-5<0 or x+4<0... do i have to solve them all?

[calm coral]

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[twilit bramble]

when trying to solve this inequality, does multiplying both sides by x and making it a quadratic not work?

[winter elbow]

You have to discuss whether x<0 or not

[twilit bramble]

it isnt, otherwise 4/x would be indeterminate

oh it is

[winter elbow]

yeah, that was a typo

only equality will works
inequality won’t

[twilit bramble]

umm what does tha mean lol

[winter elbow]

You’ll get these two inequalities after discussing the two conditions separately

If x<0
You have to change the sign in the middle

[twilit bramble]

umm im lost

[winter elbow]

Could you state the extent of this inequality?

[twilit bramble]

umm wdym extent?

[winter elbow]

The range

[twilit bramble]

oh umm x + 4/x -5 >= 0

[winter elbow]

Just times x

[twilit bramble]

and make it a quadratic??

[winter elbow]

yes

[twilit bramble]

i did that but it was wrong

this is the working out for the correct answer

and its a cubic

oh wait i think ik where i went wrong

@winter elbow if there a fraction over a function involved, are u meant to multiply both sides by the function squared

[winter elbow]

Mistake

Just make it quadratic

[twilit bramble]

thats what i though too but...

[calm coral]

@twilit bramble Has your question been resolved?

[twilit lagoon]

may i help you

[calm coral]

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[fallow tusk]

Need help

[dusky flax]

multiply both sides by sqrt(2x + 15)

[fallow tusk]

I did

Its x²+2x+15=2x√2x+15

Right?

[dusky flax]

Yes

[fallow tusk]

What to do now, I can't figure it out

[dusky flax]

ah

[quaint sphinx]

big hint: ||divide both sides by x||

[fallow tusk]

Oh damn

Aight

Thankss

I found x

.close

[calm coral]

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[calm coral]

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[blazing coyote]

$y'=\frac{y}{x}+\phi\left(\frac{y}{\left(x\right)}\right)$

[potent lotus]

Why am. I here

[blazing coyote]

Bring this to quadrature

what does that even mean?

[quaint sphinx]

express the solution in terms of integrals, i suppose

[blazing coyote]

ah, ok

thanks

[quaint sphinx]

welcome

[blazing coyote]

.close

[calm coral]

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[calm coral]

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[abstract basin]

in the third line

here

why is it -2(25)

if we are adding 25 we should just subtract 25 right?

[vale pond]

because we added 50

[abstract basin]

why times -2

[vale pond]

look carefully the whole equation is multiplied by 2

[abstract basin]

oh yeah

ooh this is tricky

thanks mate

.close

[calm coral]

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[woven current]

X²+Y²=100
X-Y=6
What is the value of XY
How would I even proceed to solve this

[winter loom]

(x-y)^2 = ??

[woven current]

I don't have this value

Oh

X²-2XY+Y²=36

2XY=-64

XY=-32

Ty

Holup

[clear yacht]

square x-y on both sides

shud give u the asnwer

yee

[woven current]

Oh yeah so -32 is the answer

So how did the teacher get 32

Is there some thing with i

NVM --XY=XY

So it is Indeed 32

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[calm coral]

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[calm coral]

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[remote mural]

im trying to solve part b

[remote mural]

i got -4.44 m/min

ans key says -1.35 cm per min

I dont know where I went wrong

[celest stream]

!showwork

[calm coral]

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

[remote mural]

i literally showed work

[remote mural]

this is my work!

[celest stream]

oh shit mb

i didnt see it

[celest stream]

#bots message. ig it was only calcullation mistake

[remote mural]

@celest stream why does there need to be brackets around the 6+4sqrt3 H part

[celest stream]

dv/dt = (dv/dh)*(dh/dt)

[remote mural]

i still dont get it

[celest stream]

u have to mulltply the whholle of dv/dh whch is (6+4X0.2root3) with dh/dt coz of chaiin rule

[remote mural]

why are there no brackets for this though

[celest stream]

x and y are 2 diff variables

[remote mural]

what about this

there are also no brackets

[celest stream]

notce dh/dt is multipliid with each term

so it is basicallly (4800 + 80h/root5)dh/dt

[remote mural]

oh ok ty

.close

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[calm coral]

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[sharp night]

May someone help me on how to find the x-values

And if I’m doing question 3 right?

[calm coral]

@sharp night Has your question been resolved?

[sharp night]

<@&286206848099549185>

<@&286206848099549185>

<@&286206848099549185>

<@&286206848099549185>

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[calm coral]

@sharp night Has your question been resolved?

[whole hinge]

Please stop spamming the Helpers ping

[calm coral]

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[dapper moon]

I really struggle to check this for convergence.
In the numerator n^2 dominates in the denominator n right?

[remote mural]

not rigorous enough, also note that you have square roots in there as well

[mortal orbit]

you cannot just rely on n^2 in the num and n+1 in the denominator

yep the things inside of sqrt have their play too

[remote mural]

what convergence test do you think you can use here?

[dapper moon]

major / minor comparison. For me ratio and root test look complex for this term

[remote mural]

major / minor?

and yes ratio test will be inconclusive here

[dapper moon]

No clue how its called in english

[remote mural]

ah

well

I suggest you use the following test called the "limit comparison test"

ffs

Suppose we have two series $\sum a_n$ and $\sum b_n$ with $a_n \geq 0$ and $b_n > 0$. Define $$c = \lim_{n \to \infty} \frac{a_n}{b_n}.$$
If $c$ is positive and is finite then either both series converge or both series diverge.

[potent lotus]

45

[remote mural]

so intuitively, what do you think happens as this series goes to infinity? this will help us determine what series $\sum b_n$ we'll be using for our comparison.

[potent lotus]

45

[dapper moon]

I think it's called Comparison Test for Divergence and Comparison Test for Convergence

[remote mural]

ah yes

what we're doing right now is the limit comparison test

the comparison test is slightly different

have you studied it yet?

[dapper moon]

We only did comparison, ratio and root test. I understand all three, but I struggle for terms with too many sqrt

[remote mural]

Ok

I will teach you the limit comparison test