help-10

[pastel lichen]

that are really nasty looking lol

[astral ivy]

Now we can multiply both sides by x^2

30x^4 - 6 = 0

Right?

[pastel lichen]

yee

i end up with

x=4square root 125 over 5

positive and negative

i dont know what this question wants lmao

<@&286206848099549185>

[astral ivy]

You should get $$x = \pm \frac 1{\sqrt[4]5}$$

[warm shale]

abs_0

[astral ivy]

So those x-values, together with x = 0, are the critical values of f

@pastel lichen

[limpid roost]

Are you sure this is right?

Wasn't your initial function (10x^3 +6)/x?

[pastel lichen]

my initital was f(x) = 10x^3 + 6/x

[limpid roost]

Oh, oops.
Never mind. Ignore what I just said.

[pastel lichen]

im not sure

how you get that

[limpid roost]

Well, the initial problem said x cannot equal 0, so not x = 0.

[astral ivy]

Oh you’re right yeah

[pastel lichen]

i get the square root on top

as 4squareroot 125

and 5 on bottom

[astral ivy]

(30x^4 - 6)/x^2 = 0
30x^4 - 6 = 0
30x^4 = 6
x^4 = 1/5
hence what I got

[pastel lichen]

yea on my last step x^4=1/5 goes to 4^squareroot 125/5

not 1/4^squareroot5

[astral ivy]

How do you figure 125/5?

[pastel lichen]

\root(4)(125)

ugh thisi s annoying not knowing how to write this crap XD

[astral ivy]

But where did 125 come from

$$\sqrt[4]{125}$$

[warm shale]

abs_0

[astral ivy]

Try to mimic this

[pastel lichen]

not sure i put it into my calulator and thats what i get

im taking the root of both sides of the equation which leaves x=or-$$\sqrt[4]{125}$$

[warm shale]

pancake

[pastel lichen]

well its x^4 so im doing square root the square root of 1/5

[astral ivy]

You have $$x^4 = \frac{1}{5}$$ right? So if you take the fourth root of both sides you get $$x = \sqrt[4]{\frac{1}{5}} = \frac{\sqrt[4]1}{\sqrt[4]5} = \boxed{\frac 1{\sqrt[4]5}}$$

[warm shale]

abs_0

[astral ivy]

@pastel lichen

[pastel lichen]

hmm

[astral ivy]

Well, plus or minus that

[pastel lichen]

i was just doing a square inside a square lol

[astral ivy]

Oh

[pastel lichen]

so is that my critical point ?

or do i use that to find it ?

[astral ivy]

Well our candidates for critical points are $$x = 0,\quad x = -\frac1{\sqrt[4]5},\quad x = \frac1{\sqrt[4]5}$$

[warm shale]

abs_0

[astral ivy]

There can be multiple critical points, the question is asking for all of them

From the definition, it says a critical point must be a number in the function’s domain

They say the domain is “all real numbers except 0”

So x = 0 cannot be a critical point because it’s not in the function’s domain!

Are you following so far?

@pastel lichen

[pastel lichen]

sorry i was trying to do the tutorial to explain it and its dumb

and yes that makes sense

[astral ivy]

Ah

[pastel lichen]

0 isnt in the domain so its not a option

and im trying to see which of the others is in the domain ?

[astral ivy]

Ok cool and since the other two numbers are definitely in the domain, those are our two critical points

Yeah they’re both in the domain

[pastel lichen]

also so like im doing this on a caluclator but it keeps giving me weird answers when i do something x^4=1/5 how do i get it to do the 1/4sqrt5 ?

[astral ivy]

Your calculator can solve equations?

[pastel lichen]

yea sometimes lol

[astral ivy]

Oh

[pastel lichen]

but i gues not for these

kept screwing me over giving me weird stuff XD

[astral ivy]

Wait so u put in x^4 = 1/5 and it gave you that weird 125 thing?

[pastel lichen]

yes

[astral ivy]

That’s super odd

[pastel lichen]

yeaa it was lol

[astral ivy]

What calculator is it

[pastel lichen]

photomath on my phone lol

so my next one is f(x)=20x/25x^2+1 do i do that the same way ?

0=-500x^2+20/(25x^2+1)^2

-20=-500x^2

1/25=x^2

1/5=x

that look right ?

i didnt plug it into the calculator this time so it looks very simple haha

[pastel lichen]

or ?

[astral ivy]

Wait this is unclear

Is it 20x/(25x^2 + 1)?

[pastel lichen]

20x is the only thing on top yes

i got it right lol

i keep putting zeros even for some reason

i thought zero would be included if the domain is - infinty to positive infinity

[astral ivy]

Oh

Yeah the domain is all real numbers (make sure you understand why)

[pastel lichen]

Find the maximum and minimum values of the function y=6squarerootx^2+1 then -x at [0,3]?

what would i do here ?

i tried getting the derrivative then setting it equal to zero

and i got x= -1/6

[pastel lichen]

idk how to do this haha

[astral ivy]

Well the denominator can never be zero, that’s why. No matter what you put in for x, x^2 will always be at least 0, so certainly 25x^2 + 1 will always be bigger than 0

[pastel lichen]

well i meant the next problem lol

like i got 2 problems on this homework left but idk how to do them XD

<@&286206848099549185> can any1 help i have only 20 min left to finish this homework

[obtuse pebble]

@pastel lichen Has your question been resolved?

[astral ivy]

If there are maximum and minimum values, they must be critical values

So look for critical values of f, and then check which ones are maximums or minimums

[pastel lichen]

i did and i got it wrong a few times lol

[obtuse pebble]

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[fringe sorrel]

How do I do: Find dy/dx in terms of y when x=sin^2 y?

[fringe sorrel]

idk like 2cos2y?

or is it 2sinycosx?

okay cool thx

oh?

so what is it?

oh is it y not x oops

👍

[obtuse pebble]

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[timid silo]

can someone explain this to me

im reaply confused

<@&286206848099549185>

[obtuse pebble]

@timid silo Has your question been resolved?

[halcyon tulip]

What are you not getting

[timid silo]

its clear now i ask smn else

[obtuse pebble]

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[obtuse pebble]

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[errant shale]

How do i solve for b?

[obtuse pebble]

@errant shale Has your question been resolved?

[wary vigil]

you know the x coordinate of the point you want to find

you gotta find the y coordinate

you also have the equation

[obtuse pebble]

@errant shale Has your question been resolved?

[errant shale]

sorry for the late reply!

how do i start it off?

[wary vigil]

well you have the equation for the ellipse

and the x value

you can find the y

[errant shale]

wait i think i get it, lemme write it down

ill send a pic here

[errant shale]

Would it be like this? or

This was an example i found online but didn't quite get it but it looks like i can apply it

[wary vigil]

yes this is the way to go about it

[errant shale]

Ohh alright, but why did they suddenly switch places?

Wasnt the 2500 the x and not the y?

[wary vigil]

they multiplied everything with 2500

which gives 2500 y^2 + x^2

and also multiplied by 900

giving

900 x^2 + y^2

[errant shale]

Oh i thought they just cross multiplied

Ill try to do it on my question one second

[errant shale]

I got it ty

.close

[obtuse pebble]

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[twin forge]

I don’t know where to start

[fallen mantle]

hope it helps

[twin forge]

Ohh thanks, i was using the wrong formula

.close

[obtuse pebble]

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[fallen mantle]

you are welcome

[obtuse pebble]

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[stable heron]

Guys I need some help: How can I, if I have this task, solve it without calculator?

[balmy mortar]

whats 2^10 / 2^8

[obtuse pebble]

@stable heron Has your question been resolved?

[obtuse pebble]

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[long jolt]

i need help again but with my trig hw 💀

[long jolt]

idk how to do this

[wary vigil]

well what's the range of sin

[long jolt]

0 to 1?

[wary vigil]

not quite

[long jolt]

oof

hm..

ohh -1 to 1?

[wary vigil]

yes

if you put those into the equation for r what do you get?

[long jolt]

8 and 0

[wary vigil]

yes

[long jolt]

so i put it in as [0,8] ?

[untold forge]

Yes

[long jolt]

oh okk so then how can i find the symmetry for sin?

it gives me options

[wary vigil]

well sine is symmetrical around when it is max and when it is min

[untold forge]

So first is sine symmetrical about the x axis?

[long jolt]

oh so i just have to find the middle of the maximum and minimum value(?)

[wary vigil]

well the thing is that r is symmetrical at the same points as sine

this using polar coordinates translates into a symmetry axis

blue is r

orange is sine

[long jolt]

oh

[untold forge]

Now we need to test those 3 things

[wary vigil]

see how it's symmetrical around those max and mins

because they go on forever

towards either side

[long jolt]

ohh

sin is symmetrical over x axis?

[untold forge]

does the top reflect the bottom?

[wary vigil]

do you know what the r means?

[long jolt]

i think so (?)

[long jolt]

no i dont 💀

[wary vigil]

r means the distance from the origin

in polar coordinates

[long jolt]

ohhh

[wary vigil]

in this case they gave r a function

and the idea is to find the symmetry of the shape

that is given with that specific r

[long jolt]

ohh icic

so r would be symmetric over the y axis since r's the distance from the origin (?)

[wary vigil]

i can show you the graph with that r

[long jolt]

ooooo

[wary vigil]

r itself doesn't have any symmetry in the possible options unlike sine because it has been moved up by 4

[long jolt]

o

[obtuse pebble]

@long jolt Has your question been resolved?

[long jolt]

i think ive figured it out tysm again!

[obtuse pebble]

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[real garden]

Hello, all. I have a question in discrete mathematics about formal languages. I have tried to solve it, but I am not really sure if this is the correct way to do it or if my answer is right. Here is my question, and I will post my solution shortly. My concern is only part b

[balmy mortar]

#proofs-and-logic might be better

#foundations or this idk which

[real garden]

Okay. Thank you for the heads up!

.close

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[stoic stump]

help

Idk how 2 bisectors can divide a side into three parts

[obtuse pebble]

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[obtuse pebble]

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[slow sonnet]

$\int \frac{1+\sin(x)}{1+\cos(x)}dx$

[warm shale]

Mohad

[slow sonnet]

any ideas how to integrate this?

[drowsy girder]

Product rule?

[nimble blaze]

try using a trig identity for sin

[true rain]

Substitution?

[nimble blaze]

one where you can convert sin into something with cosines

[true rain]

I don’t think that will work

[nimble blaze]

oh actually

use this form of substitution

[slow sonnet]

I reached $1/2(1+t)^2$

[warm shale]

Mohad

[slow sonnet]

integral of it

is that right?

[obtuse pebble]

@slow sonnet Has your question been resolved?

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[random hatch]

So I'm supposed to find the m for which this equation has exactly one solution, I know how to solve it, more or less, but it's hard to check the answers for stuff like this online so could someone tell me if the m values are supposed to be 5/7, 3 and 1?

[sour lantern]

what equation?

[random hatch]

Oh wait, I was supposed to send a screenshot, one second.

[timid silo]

ok so I got dis

so you are generally supposed to be confident enough to not "check stuff online"

so do let us know what type of equation this is

[random hatch]

Quadratic with a parameter.

[timid silo]

great

do you know which quantity determines whether the eq of this type has a solution?

[random hatch]

Yeah delta.

[timid silo]

determinant

ok

[random hatch]

If delta = 0 it has 1 solution, if the thing before x^2 is equal to 0 it also has 1 solution.

[timid silo]

we generally assume that coefficient at X^2 is not 0, so good point

so what you need to find is when delta = 0 or m-1=0

which gives you m=1

and ?

you say 5/7 and 3

if you have a working out you can show it

and we are done

bruh

handwriting

ok

I will try to read

[random hatch]

I mean, you can just tell me what the soution is, that's why I didn't send it right away. :'3

[timid silo]

b^2 - 4ac

b= 3m-1
a=(m-1)^2
c=4

writing for myself

this is quicker

one sec

9m^2 - 6m +1 - 16( m^2 -2m +1 )

-7m^2 +26m-15

-7m^2 +26m-15=0

checking with Wolfram, it's 5/7 and 3

so well done @random hatch

you had absolutely no problem

[random hatch]

Thanks for your help either way. ^w^

.close

[obtuse pebble]

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[timid silo]

4𝑥³-7𝑥-3=0

[timid silo]

How would you solve this if you never learned the cubic formula?

[nocturne minnow]

Have you done polynomial long division?

[timid silo]

Yes

I have a given linear factor

Do I divide by it and find other factors?

[nocturne minnow]

If you're given a factor, then yes divide it

Because then you'll end up with a quadratic and you can factor that

[timid silo]

Okay that clears it up, thank you so much!

.close

[obtuse pebble]

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[timid silo]

what does the second part of question b mean "determine the concavity..."

[short spruce]

do you know what concavity is?

[timid silo]

yeah

is second derivative positive or negative

concave up concave down

[short spruce]

so what issue are you having exactly

[timid silo]

of all solution curves

dont know what that means

[idle thunder]

in the 2nd quadrant

[timid silo]

what does that mean

[idle thunder]

recall what the 2nd quadrant in a graph is

[timid silo]

yeah i know the top left

but

i still dont know what im looking for

wdym solution curves in second quadrant

solution curves in general

[short spruce]

it's just a curve that can be a solution lol

very literal term

[timid silo]

i really dont get it

[short spruce]

what exactly is the equation

[timid silo]

dy/dx = 2x - y

[short spruce]

alright

so determine the 2nd derivative

[timid silo]

i did

[short spruce]

and what is that?

[timid silo]

2 - 2x + y

[short spruce]

alright

so you want to know when that is positive and when that is negative

that'll determine concavity, yeah?

[timid silo]

oh so i just need the ranges?

[short spruce]

well think about Q2 for a second

what do you know about x and y values in Q2

[timid silo]

like positive from - 2 to -1 or whatever?

[timid silo]

idk

[short spruce]

well yes, but your function is a lil different

you don't know anything about x and y in q2?

look at a graph maybe?

pick a point in q2?

[timid silo]

thats a slope field

[short spruce]

i understand that

i'm talking about any graph

[timid silo]

function always decreasing in quad 2

[short spruce]

not the function

ignore the slope field

just picture a graph

what is true about x and y in Q2

[timid silo]

they exist

[short spruce]

that they do

pick a point in Q2

[timid silo]

(-1, -1

[short spruce]

that's in Q2?

[timid silo]

fuck

(-1 1

[short spruce]

mk

pick another point

[timid silo]

(-1, 2

[short spruce]

what's similar

about x

and what's similar about y

[timid silo]

ones negative and ones positive

[short spruce]

right

so x is always negative in Q2 and y is always positive

so... looking back at your 2nd derivative

[short spruce]

.

plugging in negative x and positive y, what will the 2nd derivative always be?

[timid silo]

negative

no

[short spruce]

if no then what

[timid silo]

it cant always be negative

[short spruce]

indeed

try plugging in a point

a negative x, positive y

[timid silo]

(-1, 1)

[short spruce]

plug 'er in

[timid silo]

positive

[short spruce]

right

[timid silo]

oh

always positive

[short spruce]

yep

which means concavity is always...?

[timid silo]

must have an iq of 70

[timid silo]

up

[short spruce]

concavity must have an iq of 70, yes

[short spruce]

👍

[timid silo]

does all solution curves mean all possible graphs with the derivative given

[short spruce]

yes

[timid silo]

im bad at math in the stupidest ways

how do u find the general solution

im having trouble isolating the y variable

[obtuse pebble]

@timid silo Has your question been resolved?

[obtuse pebble]

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[winter geyser]

How can I solve arccos(1/8) without a calculator

[balmy mortar]

so if you know a cos that makes 1/2

can you figure out a cos that makes half of that 🤔

to be more precise

cos x = 1/2

cos ? = 1/4

hmmmmmm

[winter geyser]

hold on

lemme think

[balmy mortar]

I have some doubts you can get there.

Uhhh you could try some geometry

or maybe some trig identity that involves 4cos

I think the triple angle for cos does?

[winter geyser]

[balmy mortar]

yh that sounds like the way

ah no not quite

🤷‍♂️

maybe double angle is good enough if u play around with it . ..

[winter geyser]

how will that work though

[balmy mortar]

idk - u play around with some algebra

plug in cos x = 1/2

or 1/8

no, i dont see this immediately working

,w arccos(1/8)

[warm shale]

Results provided by WolframAlpha

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Upgrade to WolframAlpha Pro!

Requested by Shuri2060#9525

[balmy mortar]

doesnt appear to be exact.

so its unlikely you could, then.

[winter geyser]

OH nevermind

I am dumb

I didn't have to do this

thanks a lot for your help @balmy mortar

.close

[obtuse pebble]

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[pastel forum]

why is this incorrect

[obtuse pebble]

@pastel forum Has your question been resolved?

[sterile wyvern]

Why do you say it is wrong?

[sand quest]

How can i interpret a graph with percentiles on the x axis?

[pastel forum]

cuz someone told me its wrong

[sterile wyvern]

It seems correct to me

Ask them a value of x that doesn't line up with your answer maybe

So we'll know

[pastel forum]

its supposed to be -pi/2 < x < -pi/3 or pi/3 < x < pi/2

<@&286206848099549185>

[sterile wyvern]

,w sum k=0 to inf (2cos(1/2(pi/2+pi/3)))^k

It converges also for a value that is not in those intervals though

,w sum k=0 to inf (2cos(1/2(pi/2+2pi/3)))^k

[warm shale]

Results provided by WolframAlpha

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Requested by Mat#9616

[pastel forum]

im so confused

mark scheme says this

[sterile wyvern]

They are taking only positive values of cos(x), would you know why?
What is A1A1?

[pastel forum]

a1a1 is just marks awarded dw about it

but ye idk why they taking only positive values

should go till -1/2

[sterile wyvern]

Maybe it is because of part a) of the question?

[pastel forum]

bruhhh it is because of that

i didn't see the domain

@sterile wyvern thanks for ur help

[sterile wyvern]

Np!

[pastel forum]

.close

[obtuse pebble]

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[lunar abyss]

I need help for ex3 and 4.

I’m really bad with series/differential/integrals, but I don’t have choice this time and I had to finish this work

For q1 ex3 I supposed limit series inversion must be used, but idk how

[obtuse pebble]

@lunar abyss Has your question been resolved?

[obtuse pebble]

@lunar abyss Has your question been resolved?

[obtuse pebble]

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[obtuse pebble]

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[timid silo]

how does this make any sense?

oh wait wrong ss

this

the first one is a partial sum as the index approaches infinity

and the second one is only evaluating the expression as the variable n approaches infinity

they are not the same

what is it am i getting wrong?

[tardy epoch]

Partial sums and single expressions are two different things

[timid silo]

yea i know as far as i understood the whole thing partial sums are the sequences value at an specific index

series*

[tardy epoch]

Then what's your question

[timid silo]

why are they treating it as an equation

they are not equal

[astral ivy]

I think they’re saying a_n equals that fraction, and this text writes that lim s_n equals lim a_n

Which is not the case

[tardy epoch]

Show the whole problem

[timid silo]

sure

its this

https://tutorial.math.lamar.edu/Solutions/CalcII/ConvergenceOfSeries/Prob3.aspx

[astral ivy]

Oh that’s fine

That fraction is the nth partial sum

[timid silo]

how? to me that actually looks like the nth sequence term

[tardy epoch]

They tell you it is

You're not tasked to find out what a_n is

[astral ivy]

They don’t tell you what a_n actually is

They do tell you its nth partial sum though

Which is that fraction thing

[timid silo]

oh wait is that only the formula to get the sum at a certain index

[astral ivy]

Yes, that’s the nth partial sum

[timid silo]

AHHHHH

[astral ivy]

Lolll

[timid silo]

thanks

thanks a lot of both of you

[astral ivy]

No problem lol

[timid silo]

.close

[obtuse pebble]

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[crystal wind]

I need more guidance here. Why is this not 1^inf?. Why is it not just 1? And because of this, how do I best get this into a form where I can apply L'h?

[gloomy valve]

1 + 6/x = (x + 6)/x. you could let the limit be equal to L and take the log of that.

or wait you could actually just use the exponential limit (if you know that)

$e^x = \lim_{n\to\infty} \qty(1 + \frac{x}{n})^n$

[warm shale]

Navix

[thick fog]

It is an indeterminant form of the form 1^inf, the problem is that it isn't the number 1, it is a number getting closer to 1. If it were actually the number 1, this would not arise.

If you want to use L'Hopital's rule, you would rewrite the limit as $e^{\lim_{x\rightarrow \infty} \frac{\ln(1 + \frac{6}{x} )}{\frac{16}{x}}}$

[warm shale]

Hexicle

[crystal wind]

Thanks all. Gonna try to figure this out with these pointers. Im a bit out of my bounds here.

Got the answer, not confident I could replicate a similar problem without guidance yet. But very thankful.

[gloomy valve]

Mind telling us which approach you used @crystal wind

Good job, nevertheless! :3

[crystal wind]

I ended up using the L'H because this lesson was focused on taht, so I was assuming thats what they were expecting me to use. 🙂 I also dont think ive explicitly been taught exponential limit.

Appreciate the options regardless

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[timid silo]

Does the tabular/DI method work on integrals where neither function can be differentiated to 0?

[high lily]

if used appropriately yes

[spiral maple]

Yes, however you need to know when to stop it yourself, Tabular is just a quick way of doing IBP repeatedly

[high lily]

(and depends on the integral)

[timid silo]

You’d stop after it gives you the original function then just use algebra to move it to the other side so it no longer repeats right?

Also, I saw someone use the tabular method for ln(x) but they did something weird where by the end instead of multiplying diagonally they multiplied across and I saw any example online of some different integral where they did that at the end as well.

I thought you were always supposed to go diagonally

[spiral maple]

yes

Though I'd frankly not use Tabular for stuff like ln(x), or e^xsin(x) or cos(x)

[timid silo]

Why not?

Just go the long way for those?

[spiral maple]

Yeah

[timid silo]

Even though I shouldn’t use it for those, I’m still curious as to why he went across at the end

[spiral maple]

ask them

[timid silo]

I can’t

It was a video

But I did see someone else do the same thing online

I’m very confused as to why didn’t generate the next u and dv so they could go diagonally

[high lily]

that's how you stop when you want in tabular

and they stopped there because x * 1/x = 1 which is trivially integratable

[timid silo]

So if you don’t feel like continuing you just go across?

Thanks for the help!

.close

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[brazen smelt]

Yo

[brazen smelt]

So it says a limit may fail to exist when the function increases or decreases without a bound. What does this mean? An asymptote?

[forest sinew]

this is an example, yea

you can also consider just like, limits at infinity

so $\lim _{x \to 0^-} \frac 1 x$

[warm shale]

jan Niku (Shuri for Honorable)

[forest sinew]

this fails to exist because its an asymptote

whereas something like $\lim _{x \to \infty} x$

[warm shale]

jan Niku (Shuri for Honorable)

[forest sinew]

doesnt exist, just because, you know

obvious reasons

[brazen smelt]

Hmm

Alright then what about

'The function oscillates between 2 fixed values'

Thats just like a jump discontinuity right

[forest sinew]

nah

[brazen smelt]

Huh

Whats that mean then

[forest sinew]

this is probably limits at infinity right

[brazen smelt]

Nope

Just reasons why a limit may not exist

[forest sinew]

well i mean, the oscillations

yea

so it doesnt make sense for a function to oscillate endlessly between two values at a point

well there are some esoteric examples of this

but probably more like

$\lim _{ \theta \to \infty} \sin \theta$

whats it equal?

[warm shale]

jan Niku (Shuri for Honorable)

[forest sinew]

this is more oscillation in generally, this could be made to oscillate between points

say by like

[brazen smelt]

Thats considered undefined right

[forest sinew]

well, regardless, you could create a continuous function

think of a sawtooth wave

[forest sinew]

yea, can you tell why?

whats it approach as theta gets big

[brazen smelt]

Cuz it approaches an undefined point, that shit keeps goin

[forest sinew]

yea shit keeps goin

[brazen smelt]

https://tenor.com/view/speed-wheelchair-me-running-late-gif-14178485

[forest sinew]

its just oscillating forever

no limit

[brazen smelt]

This be the limit

[forest sinew]

lol

push it to the limit

[brazen smelt]

Accurate representation

[forest sinew]

https://tenor.com/view/stalin-no-limit-weird-wtf-cmon-gif-5483812

[brazen smelt]

Kek

Thx man

.close

[obtuse pebble]

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[small tinsel]

This is part of a questions I’m doing. Is this true or false

[slow skiff]

What do you think?

Use the definition of absolute value on |x|<=3 and you'll find out for sure

[obtuse pebble]

@small tinsel Has your question been resolved?

[obtuse pebble]

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[woven parcel]

This is hypothesis testing, confidence level, is this always true, regardless of what significance level may take?

[woven parcel]

And I also realized that we need to have k to be multiplied here, what is k? wouldnt [p -/+ sqr root()] be enough to find the tails at the end?

[obtuse pebble]

@woven parcel Has your question been resolved?

[obtuse pebble]

@woven parcel Has your question been resolved?

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[shadow wave]

PQ and RS are two equal chords of length 24 cm each which intersect each other at A. AR > AS. If AQ :AP =1 :3, then show that AP+AR = 36 cm.

[shadow wave]

How to solve this question?

I just need to know how to prove it.

<@&286206848099549185>

uhhh what is the usual wait time here?

[full relic]

Have you tried to draw out the problem?

[full relic]

Visualising and referring to a diagram youve drawn would make it much clearer

[shadow wave]

ok

i will see if i get it after i draw

[full relic]

lmk once youve drawn your diagram!

[shadow wave]

alright

i wil leave this channel open

if i get it i will close it

[shadow wave]

hello, i drew the diagram but i could not find the correct value of AR. the value of AP is 18cm for sure but how do I know AR is also 18cm? They only gave the ratio for AP and AQ.

I also have a diagram which i drew...should i send it?

[full relic]

There's this theorem called the Intersecting Chord Theorem. Have you learnt that?

[full relic]

Sure!

[shadow wave]

huh could u tell me?

[shadow wave]

so does this mean segment B = C?

[full relic]

B=C only if A=D

[shadow wave]

so in my question it says both cords are equal

ohhh i get it

[full relic]

Both chords are equal, yes. But we can only be sure that the product of the sections AP.PQ=AR.AS

It may not necessarily mean that B=C

[shadow wave]

ok so does that mean AS = AP*AR/AQ

[full relic]

Using this theorem, you'd have to eventually solve a quad formula

[full relic]

or a better way to define it would be AS=24-AR

[shadow wave]

yeah i was going by the formula

[full relic]

Yup. And then you can sub it into the Intersecting Chord Thm

[shadow wave]

thanks for your help i think i got the answer!

imma close this channel now

.close

[obtuse pebble]

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[bleak steppe]

A river flows at 3 km/h. At what rate should a boat sail in still water so that its actual speed upstream is 18 km/h?

[obtuse pebble]

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[bleak steppe]

When Jorrel was born his father was 25 years old. Now, his father is 3 years more than twice his age. How old is Jorrel now?

Let Jorrel be x

Is the equation "2x+3-x=25" correct for this problem?

[royal basin]

when you say "Let Jorrel be x" do you mean "Let Jorrel's present age be x"?

if so, then yes, your equation is correct.

[bleak steppe]

yes :))

Thank you!

.close

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[slender flax]

Haiya so doing this questions and ik that the square would be 4x but idk how to find what y would be

[slender flax]

https://cdn.discordapp.com/attachments/409596215697866773/954713049321857034/674332158973706261.png

[astral ivy]

@slender flax did you do part a

[slender flax]

not ahts what I am trying to do

I got 4x

but idk what y is

[astral ivy]

Ah

Do you understand the premise of the question?

[slender flax]

kinda

[astral ivy]

Ok I’ll rewrite it here so I don’t have to look at that image

[slender flax]

if the length is 4 times as long I thought that would wake width just 1y

make*

[astral ivy]

There’s a piece of wire 80 cm long, and it’s cut into two pieces. One of the pieces is bent into a square, and the other piece is bent into a rectangle four times as long as it is wide.

Would you agree that the square’s perimeter plus the rectangle’s perimeter would give you 80?

[slender flax]

yes

so 4x+?y = 80

[obtuse pebble]

@slender flax Has your question been resolved?

[obtuse pebble]

@slender flax Has your question been resolved?

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[timid silo]

yo how would i explain this sequence in an equation? 2, 4, 7, 11, 16 you basically do 2+n 4+n 7+n and n increases every single number, so its 2+2, 4+3, 7+4
idk how to write it down as an equation and no, this isnt any kind of assignment, im just curious for myself. (not even sure if this is possible haha)

[timid silo]

i know this is really wack question

[unborn valley]

do you know what first difference and second difference is?

it is basically this

[unborn valley]

you bascially want general term right?

[obtuse pebble]

@timid silo Has your question been resolved?

[timid silo]

i guess but how would you write this down as a one liner

i mean

an algo or equation

idk how its called my bad

[unborn valley]

yes like a sequence, where you put values of n and you get the series

[timid silo]

yeah

[timid silo]

we havent learned this yet lol

im 14

[unborn valley]

yes yes

but you got what it is tryna say right?

[timid silo]

yup

[unborn valley]

it is similar to your sequence, where the second common difference is 1

[timid silo]

ye

but is it possible

to describe the differences and its parameters

in a oneliner

[unborn valley]

its general form is quadratic

wait

https://owlcation.com/stem/How-to-Find-the-General-Term-of-Arithmetic-and-Geometric-Sequences#:~:text=This process applies only to,table and form two equations.

check problem number 2 from this website

[timid silo]

alright ill look into this

thank you

.close

[obtuse pebble]

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[devout hatch]

trying to understand these notes, i dont know where the y^2 or the y' came from

[haughty coyote]

you differentiate xy² as a product of (x)(y²) since they're both functions of x

[devout hatch]

idk what that means exactly sorry

[haughty coyote]

use the product rule

with f(x)=x, g(x)=y(x)²

[devout hatch]

ahhh, and how do they get the y'?

[haughty coyote]

when differentiating y², use the chain rule

[devout hatch]

idk how you get y' from using chain rule though... can you run through the steps? y^(2x) differentiated becomes 2xy^(2x-1) i think?

[haughty coyote]

dy²/dx = dy²/dy *dy/dx, the first is 2y, second is y'

[devout hatch]

oh you ignored the x in the y^(2x)?

ive just never done product rule with a value of v where to derive it you need to derive in terms of dv/dy and dy/dx which is confusing me, what those fractions mean confuse me, especially when you just make v = y^2 not y^(2x).

dv/dy doesnt make sense to me to be 2y? i thought it would be (2x)y^(2x-1)
and dy/dx i got no clue how u get y', i dont know what steps get to that

the derivative calculator doesnt help either by giving wrong and overcomplicated results

[obtuse pebble]

@devout hatch Has your question been resolved?

[haughty coyote]

This is just called Leibniz notation. However if it is y²(x) = y(x)², then the result is what was on the board, if it was y(x)^(2x), then the derivative is indeed a giant freaking mess, here is a proof that the mess is correct (I'l let you guess whether it was y(x)² or y(x)^(2x)

I used y(x)=x² for simplicity to get a graph

and yet, and I didn't multiply by x, normally you find the derivative of xg(x) = g(x)+xg'(x), I only found g'(x)

[devout hatch]

okay thanks alot! 🙂

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[primal tangle]

.close

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[errant scarab]

Id like to ask for help on explaining how the result was achieved

[errant scarab]

according to desmos, turning point should be 3, but following the equations my lecturer has taught, i cant seem to reach what desmos suggests

[paper urchin]

okay so

the problem is already written in vertex form

meaning that the turning point is already stated in the equation

I'm just writing it down the given information for you, to try and make it easier

a = 1  [you can ignore this because it doesn't impact your turning point] 
h = 3
k = 4

As you have the (h,k), you can just input the variables and there is your answer

I hope this helps

@errant scarab

[obtuse pebble]

@errant scarab Has your question been resolved?

[errant scarab]

thanks for answer, but could you explain the thinking behind this?

as i want to learn how it works

[obtuse pebble]

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[dim breach]

I have no idea how to even plot this figure

[dim breach]

We are using maple as cad but anything else goes aswell

[gloomy valve]

you want to construct parametrisations for these 4 components

so first think about where to put your coordinate origin

then, note down the measurements for these components

(maple also has a nice function for 3d cylinder plots: https://www.maplesoft.com/support/help/Maple/view.aspx?path=plottools%2Fcylinder)

[obtuse pebble]

@dim breach Has your question been resolved?

[obtuse pebble]

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[sinful bone]

I have met with this symbol a couple of times in some functions and formulas and I have absolutely no idea what it means

[subtle hawk]

integral over some area

[sinful bone]

Doesn’t that mean that it is equal to the area under a function graph?

And what does a function graph has to do with a physics formula for example?

[leaden ibex]

An integral is much more than "just the area under a graph".

[sinful bone]

Hm ok

I know, I’m going to watch it

.close

[obtuse pebble]

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[winter sun]

Question 13

I need help plz

Lol

Yea hold on

The 10 and the 100 dont matter as long as the distance is 10x longer thsn earth to soace

X and 10x?

[leaden ibex]

Never assume things for no reason

[winter sun]

But as long as its 10x does it matter the values i put

Since its same ratios

[leaden ibex]

And also, you can show that the answer will not depend on x in that case

[winter sun]

Yeah

[leaden ibex]

So you gain more generality

[winter sun]

Should i put 10 and 100 then

Okoo

Whats the next step herep

Im completely lost

Am i trying to find angle space

Cosine and sine

When i tried everytjing with 100 and 10 tho i was completly of

Is my drawing schematically correct

Ohhh

Wait

Am i trying yo find angle at jupitor

Ohh

Ok

Now i can use random nimber for x right

Or else its impossible to sllvr

Ofc

[leaden ibex]

or you could just

use x

And not lose any generality

[winter sun]

The book gave exact answer at the back

Ok

I got 3.488 and its right

I just usdd 10 and 100

@nova marsh @leaden ibex thank you for the help

[leaden ibex]

sigh

[winter sun]

Its what the book got aswell

So they wanted us to assume a value

Since its doesnt matter

[leaden ibex]

If I were grading our hw, I'd knock off some points

for assuming x=10

[winter sun]

But if i dont assume a value i cant get a exact angle @leaden ibex

[leaden ibex]

how so

[winter sun]

Cause theres no equals

[leaden ibex]

Do the same as you did with the 100 and 10

[winter sun]

@leaden ibex could u show me how you would solve it not assuming x

[leaden ibex]

But with x and 10x instead

[winter sun]

Ok

[leaden ibex]

Now, if you can't arrive at the solution that way

your solution is wrong

And depends on your choice of initial x

[winter sun]

Yeah its impossible

Anyways i gtg eat

Ty tho

.close

[obtuse pebble]

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[leaden ibex]

....

And this is why we don't assume things for no reason

[obtuse pebble]

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[fierce vale]

What does dx mean in the integral notation??

[fierce vale]

How come we can chande it to dt or du...

[pine sail]

Basically you're calculating area where dx is the width.

Long short story.

[fierce vale]

so we always put the variable of the function?

[pine sail]

Yes, always.

[fierce vale]

I mean if we replace f(x) with f(t) then we must write dt?

[pine sail]

Affirmative.

[fierce vale]

Oh ok thnx

.close

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[leaden ibex]

except when you don't

[pine sail]

Yeah lol.

Rip.

[fierce vale]

huh?

[leaden ibex]

Don't worry about it for now

When you encounter it, worry then.

[pine sail]

Right.

[fierce vale]

but it doesn't mean anything if they're not the same

so it can be f(x).du?

[idle thunder]

i suggest finding a video explaining what dx is

it will help

[fierce vale]

i tried but i couldn't find a direct answer

[fierce vale]

I think i already encountered it

[spiral maple]

"formally" it's just a infitesimal change in the variable

[fierce vale]

kk i'll search more online

.close

[obtuse pebble]

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[gilded surge]

I only require assistance to find the answers of (b) and (c)

[obtuse pebble]

@gilded surge Has your question been resolved?

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[thorn matrix]

.help

[obtuse pebble]

Commands:
clopen: .close, .reopen
factoids: .tag
help: .help

Type .help <command name> for more info on a command.

[severe dune]

What’s A zero

Roots ?

[severe dune]

?

[thorn matrix]

a value of x for which the ans of polynomial will be 0

[scarlet gale]

@thorn matrix That polynomial looks easy to factor.

[thorn matrix]

idk how to factor polynomial

of degree 3

and that method wont come in exam

and i want to just get good marks in exam

[scarlet gale]

Well, you can see that the x³ term has a coefficient of 1 and that x term has a coefficient 5 times higher.

OK, then you can divide the polynomial by x - sqrt(5).

Then it will be degree 2 and you can solve using quadratic polynomial methods.

[thorn matrix]

when i divided

quotient was

x^2-2 root5 x - 15

then i need help in factorizing it

[scarlet gale]

@thorn matrix Do you know the quadratic formula?

[thorn matrix]

not yet

will be taught in a few months

[scarlet gale]

OK, then the easiest way is to go back to the starting point.

x³ - 3sqrt(5)x² - 5x + 15sqrt(5)

Do you see how it has four terms?

And there's a pattern, the second term in each half has sqrt(5).

Do you see that pattern?

@thorn matrix

[thorn matrix]

ok

[thorn matrix]

yup

[scarlet gale]

OK, so now we check whether the first half's coefficients are some multiple of the second half.

So, the coefficients are 1, -3sqrt(5) on the first half and -5, 15sqrt(5) on the second half.

You can multiply the first half by -5 to get the second half.

[thorn matrix]

ok

[scarlet gale]

Like 1 times -5 is -5 and -3sqrt(5) times -5 is 15sqrt(5).

[thorn matrix]

basically, (co efficient of 1st half )*-5 = co efficient of 2nd half

[scarlet gale]

Almost, -5.

But yes.

So, the exponents are two higher on the left half.

Actually, forget that.

So, we have x²(x - 3sqrt(5)) - 5(x - 3sqrt(5)).

Does it make sense how I got those?

[thorn matrix]

yup

[scarlet gale]

So, we have (x² - 5)(x - 3sqrt(5)).

[thorn matrix]

ok

root 5

[scarlet gale]

One of the factors is linear, so we're done with that one.

[thorn matrix]

is 1 zero

[scarlet gale]

Nope.

For x² - 5, use difference of squares.

a² - b² = (a + b)(a - b)

[thorn matrix]

but why

[scarlet gale]

Because we can write it as x² - sqrt(5)².

Then we get (x + sqrt(5))(x - sqrt(5)).

Does it make sense how the difference of squares factoring method works here?

Or have you covered the difference of squares factoring method?

[thorn matrix]

i understand that you used the identity

[scarlet gale]

Yes, and to use it, we need two squared things subtracted.

[thorn matrix]

and 5 = sqrt(5) ^2

[thorn matrix]

i know that much bro...

i am not that dumb

[scarlet gale]

So, we use it here to get (x + sqrt(5))(x - sqrt(5))(x - 3sqrt(5)).

[thorn matrix]

hmm

[scarlet gale]

So, then the zeroes are just whatever we subtract from x in each of the linear factors.

So, in x + sqrt(5), we subtract -sqrt(5), so that's one zero.

And the other two are sqrt(5) and 3sqrt(5).

[thorn matrix]

ty sire

you are god

[scarlet gale]

You're welcome.

[thorn matrix]

.close

[obtuse pebble]

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[cunning citrus]

How do I do this

[cunning citrus]

It’s side length is 10cm

[nocturne minnow]

The removed area is a triangle, first find the area of the entire shape then subtract the removed areas

[cunning citrus]

So 1010=100 then 11/2=0.5 and 0.54=2 and 100-2=98

?

[nocturne minnow]

Can you retype that? Add surrounding `` to the multiplication doesn't italicize it
Like this

So it looks like `Text`

[cunning citrus]

‘’10*10’’

1*1/2

5*4

[high lily]

shift ~, top left of your keyboard

writing \ before the * like \* also works

discord tends to italicise stuff between asteriska

[cunning citrus]

Nvm I got it sorry I opened this

Thanks tho

.cose

.close

[obtuse pebble]

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[lyric pawn]

solve the following matrix equation