help-10

[odd hedge]

.close

[obtuse pebble]

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[fierce monolith]

Correct?

[robust sleet]

yes

[timid silo]

@fierce monolith do .close if your matter has been resolved

[fierce monolith]

.close

[obtuse pebble]

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[robust sleet]

it converges/diverges?

[finite musk]

Could you explain a bit what u mean

I cant wrap my head around it

[keen cave]

What is your question here is what Fractalogist meant?

[robust sleet]

yes

[keen cave]

are you asking for convergence or divergence?

[finite musk]

Oh right

Im wondering how to solve it

[spiral maple]

especially given the preamble has nothing to do with the summation

[finite musk]

how to show it

[keen cave]

solve what?

[spiral maple]

show what?

[finite musk]

This is the whole question

[robust sleet]

many questions

[spiral maple]

The whole question is shittly written then

[finite musk]

yea :7

Like this is the whole task

[spiral maple]

That makes more sense

[keen cave]

lol.

[spiral maple]

so which part do you need help with?

Now that you've posted the entire question

[finite musk]

im stuck on a

[spiral maple]

Hint: Write out the sum in long form

[obtuse pebble]

@finite musk Has your question been resolved?

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[tall badge]

Is my next line 24^2+18^2=l^2?

Then do I perform implicit differentiation?

[obtuse pebble]

@tall badge Has your question been resolved?

[tall badge]

What

[robust sleet]

go troll in a troll server

last warning

[cedar lichen]

#❓how-to-get-help

[tall badge]

<@&286206848099549185> please

Anyone?

[royal solar]

chain rule

let x be length of shadow,

what’s dx/dtheta

and what’s dtheta/dt

@tall badge

you’re pretty much given the values

[tall badge]

x = 18 meters

[royal solar]

tan(theta) is not a constant

[royal solar]

neither is x

they say it’s changing in the question, look

[tall badge]

Yes

[royal solar]

there is absolutely nothing that says it’s 18, where did you get that from

anyways,

could you write a formula for x in terms of 24 and tan(theta)

[tall badge]

“The shadow of a 24-metre building on level ground is 18 meters long.”

[royal solar]

yeah, but not for all time values, right ?

[tall badge]

Yes

[royal solar]

yeah, so for now, forget about that info

[royal solar]

just focus on this

[royal solar]

sorry this

tagged the wrong thing

hello?

[tall badge]

I am not sure of the formula

[royal solar]

what’s tan(theta) ?

but if the shadow was x

and not 18

[tall badge]

Tan(theta) = (24/x)?

[royal solar]

yep

now rearrange for x

[tall badge]

x = [24/tan(theta)]

[royal solar]

dx/d theta now

• find dx/d theta

[tall badge]

dx/d theta =[ -24sec^2(theta)]/[tan(theta)]^2

[royal solar]

||it’s-24/sin^2(x)||

[royal solar]

yeah, sec and /sec cancel

[tall badge]

Yep

[royal solar]

yeahh

now chain rule

dx/dtheta * dtheta/dt

[tall badge]

Yep

[royal solar]

there ya go

[tall badge]

Is this correct? Yet to do a comment

@royal solar

[royal solar]

yeah, I think so

[tall badge]

And for a comment, should it be like since there is a negative, length of shadow is decreasing

[royal solar]

yeah,

[tall badge]

Okay thanks very much

[royal solar]

no worries my guy

also, another thing to note, it becomes pretty unreliable after some time because at some point, the shadow is going to be zero but due to the nature of this eqn, it should always decrease

because you’ve got a squared thing in the bottom

@tall badge

[tall badge]

Interesting

[royal solar]

according to this, it keeps decreasing even after reaching zero shadow

hence unreliable

after certain point in time

I hope that made sense

[tall badge]

Yes it does

But surely

It can’t be decreasing at a rate of 0?

[royal solar]

Oh no, it can decrease at rate of zero at a given point in time

because time is discrete, that 0 is insignificant

but this eqn doesn’t have any values where you have 0 shadow change

[tall badge]

Yeah

[royal solar]

it can depending on scenario

maybe in this scenario, we never get to zero

don’t worry too much honestly

[tall badge]

I won’t, thank you

[royal solar]

validity questions are like 1 mark

tops

2 with a push

but yeah no, they only asked to comment on the sign of your answer

and it just means it decreases with time

[tall badge]

Yep I said that in my answer, thanks

.close

[obtuse pebble]

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[opaque gazelle]

I am clueless

[obtuse pebble]

@opaque gazelle Has your question been resolved?

[opaque gazelle]

Nope

<@&286206848099549185> Please help me resolve this question

[obtuse pebble]

@opaque gazelle Has your question been resolved?

[obtuse pebble]

@opaque gazelle Has your question been resolved?

[timid silo]

@opaque gazelle

for part i

we just have to make an equation sastisfying the condition, which is that Omar is allowed to ride a bike

there r 2 possibilities for this

1. Omar's age is 18 or more

2. Omar's age is 16 or more and he has a permit

Now just make an equation for this using teh variables they have assigned

[opaque gazelle]

Is this correct?

[obtuse pebble]

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[cunning mesa]

.

hello again

[cunning mesa]

i need help with this question

[tulip flare]

we note + for earning and - for spending
earn 120 three times means + (120x3)
spend 50 eight times means - (50x8)
spend additional 25 means -25
the end result would be (120x3)-(50x8)-25

[tulip flare]

do you agree with this

[obtuse pebble]

@cunning mesa Has your question been resolved?

[obtuse pebble]

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[timid silo]

I'm not sure If I remember that well so I apologise

[timid silo]

But there was a question, and it said that the radius of an area of sector was 5m and the angle of the sector was 0.7

Workout the area of the flowerbed. Then it says, that every metre, it is 1.80. Workout the cost for 5 metres

can anyone help me?

Not in here, friend. This is taken

oh okay

[tardy epoch]

are we supposed to know what flowerbed is

or what it looks like

[obtuse pebble]

@timid silo Has your question been resolved?

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[rich holly]

Q(x) = P(x) + R(x)
for Q(1) = 0, R(1) = -1 right?

[rich holly]

and for Q(2), R(2) = -2

and so on

is that right?

[balmy mortar]

6 days ago

We discussed a bit ago on this

You want to choose a sensible R

so that you can utilise the Factor Theorem on Q

So yes, what you wrote sounds right, I suppose.

[rich holly]

alright so

Q(1) = 0

which means (x-1) is a factor of Q(x)

which also means

(x-2)
(x-3)
(x-4) are factors of Q(x)

Q(x) = (x-1)(x-2)(x-3)(x-4)

is that it?

no remainder because they're factors

[rich holly]

R(x) divided by (x-1) is equal to -1

so Q(5) = P(5) + R(5)

and Q(5) = (5-1)(5-2)(5-3)(5-4)

Q(5) = 24

P(5) + R(5) = 24

R(5) = -5

P(5) = 24 + 5

P(5) = 29

is that it? @balmy mortar

[balmy mortar]

(sorry i have to afk for a while, maybe someone else can check)

[rich holly]

ok

I'm just curious, I know what R(1) to R(5) are, R(1) = -1, R(5) = -5

what's R(x)?

R(0) would be adding 1 from R(1)

which is 0

.close

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[gilded needle]

,rotate

[glass palm]

<@&286206848099549185>

[obtuse pebble]

@glass palm Has your question been resolved?

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@glass palm Has your question been resolved?

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[oblique stone]

NOL and MLO

[gilded tree]

ok thanks

.close

[obtuse pebble]

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[robust sleet]

do nut just gives out answers

[gilded tree]

.close

[obtuse pebble]

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[rustic sage]

Hi, What does a prime stand for? I forgot to ask my teacher in class but it's like a 1 but it's a bit tilted and usually in the power spot

[rustic sage]

.close

[obtuse pebble]

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[timid silo]

I found n=890 is it correct?

[obtuse pebble]

@timid silo Has your question been resolved?

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[fallen wadi]

how would i do this problem

[fallen wadi]

is the perimeter the same as the circle its inside

[obtuse pebble]

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[timid silo]

i think the awnser is 516

[timid silo]

i made it a net

the squares are 140 each so 420 the triangles are 48+48= 96 + 420= 516?

.close

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[sleek jungle]

A baseball team plays in a stadium that holds 50,000 spectators. With the ticket price at $10, the average attendance at recent games has been 30,000. A market survey indicates that for every dollar the ticket price is lowered, attendance increases by 3000.

a) Find a function that models the revenue in terms of ticket price. (Let x represent the price of a ticket and R represent the revenue.)

R(x) = ?

b) Find the price that maximizes revenue from ticket sales.

$ = ?

c) What ticket price is so high that no revenue is generated?

$ = ?

[sleek jungle]

Need help with a

[obtuse pebble]

@sleek jungle Has your question been resolved?

[obtuse pebble]

@sleek jungle Has your question been resolved?

[obtuse pebble]

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[vocal escarp]

Okay I was just wondering why this doesn't work: If e^(sqrtX) = e^(X^(1/2))

[vocal escarp]

According to exponent laws

So this means that e^(1/2)*X should be equivalent

but it isnt

why not?

[lone jetty]

I don't know latex, but e^sqrt(x) isn't equal to sqrt(e^x)

Which is basically what you are saying

You are putting brackets in the wrong places

[vocal escarp]

wait let me write it out

[leaden ibex]

$e^{\sqrt{x}} \neq \sqrt{e^x}$

[warm shale]

Remavas

[lone jetty]

Here is my paint drawing

ah, beat to it

lol

[vocal escarp]

ah yes

[vocal escarp]

fair

[leaden ibex]

LaTeX saves the day yet again

[vocal escarp]

I see so this doesnt work

as in when the power goes to x it cant apply to the whole thing

[leaden ibex]

You can type bs in it, but your profs will like it, because it's beautiful top of the art bs

[vocal escarp]

alright so

if this is the case and id like to differentiate the LHS how would I go about it?

chain rule?

oh wait nvm theres a yt vid on it

ty anyways for all the help so far

.close

[obtuse pebble]

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[shell olive]

I've got some difficult questions I need help trying to solve from my linear algebra and differential equations class If someone could help me out with them that would be awesome! I have no clue where to start with them.

[lone jetty]

Send the problem!

[shell olive]

these two are stumping me

[lone jetty]

holy hahaha

[shell olive]

ikr

[lone jetty]

Inverting anything larger than a 3x3 🤨

Wish I could help here, but haven't done anything larger than 3x3, and definitely haven't investigated relationship between determinant and transposed determinants (and multiplied determinants) like that!

[shell olive]

well they are exam review problems... dont know how my professor supposes we would have the time to solve anything larger than a 3x3

awe man

I just posted the to chegg as well so we will see I guess

[lone jetty]

Hardest I have had to ever do is invert a 3x3 with some algebraic constants, sorry I can't help more. Someone here can probably help, if they can be asked to work that out haha

[shell olive]

If you know of anyone who might know something any help would be appreciated lol

[lone jetty]

Though a quick google tells me det(B^T) is det(B)

[leaden ibex]

And if I remember my linear algebra right'

$\det(A^{-1}) = \frac{1}{\det(A)}$

[warm shale]

Remavas

[lone jetty]

This is correct, I do remember this

[shell olive]

yup that rings a bell

[leaden ibex]

And you can also use the row multiplication property of the determinant

and that should do it

[lone jetty]

Another google search is telling me:

If we multiply a scalar to a square matrix A , then the value of the determinant will change by a factor scalar^(square size)!

[leaden ibex]

Boring

[lone jetty]

Screenshot may be better

[leaden ibex]

You can derive that from the row multiplication property

[lone jetty]

🥱 deriving in an exam

Just got to hit the points

[leaden ibex]

Math is a beautiful construct

Don't deny its beauty

[lone jetty]

This is true

However, exams are not

[leaden ibex]

says the physicist

[lone jetty]

Hey, I'm starting my Computer Science degree in a few months 🤷‍♂️

[shell olive]

lol thanks you guys mechanical engineering sure is no cake walk

[leaden ibex]

sin x = x

[leaden ibex]

sure isn't

[lone jetty]

e = pi = 3?

[leaden ibex]

STEM in general isn't

[leaden ibex]

pi^2 = g

[shell olive]

always hahah!

[lone jetty]

but yes to the first question:

det(3A^-1B^T) = 3^4 * 5 * 1/10 = 81/2??

Unless I am applying the quickly googled laws incorrectly 😔

[leaden ibex]

yes you are

[lone jetty]

sad

[leaden ibex]

B is transposed

A is inverted

[lone jetty]

ah .

lol

3^4 * 1/5 * 10

[leaden ibex]

See, google won't help you!

Better learn to apply the laws

[lone jetty]

Reading the question properly might

And yes - had better. lol

For part 5, some (more intensive) googling tells me that the determinant of C is equal to det(A)^2

so sqrt(128)?

@shell olive unsure if you have answers, but would love to hear if this is correct

[obtuse pebble]

@shell olive Has your question been resolved?

[obtuse pebble]

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[lethal coyote]

ghi

[lethal coyote]

hi

<@&286206848099549185>

'can i get help

im just lost

[lone jetty]

Do you know what a local minimum is?

It's pretty self explanatory, but just to check @lethal coyote

[lethal coyote]

noo

is it just the lowest poit

of the graph

<@&286206848099549185>

@lone jetty

[lone jetty]

It's a turning point which is lower than both sides of it

(which would be where the second derivative is greater than 0, showing that the rate of change is increasing)

essentially a valley. the point of the valley (where dy/dx = 0)

So you can just read them from the graph pretty nicely there

[lethal coyote]

so is the naswer -4?

answer

[lone jetty]

That's a local maximum

[lethal coyote]

is it -7

<@&286206848099549185>

@lone jetty

[lone jetty]

No, look for a valley @lethal coyote

[lethal coyote]

bruh

is it -2???

[lone jetty]

Look for a valley

V shape

The point of the V

Obviously it's a bit more curved

[lethal coyote]

omg

its 2

it wasnt 2

i have one attempt left

@lone jetty

[lone jetty]

A V

more like a U i suppose

There are two on the graph

It's where the graph has a turning point, and on both sides of the point the y value is higher

[lethal coyote]

i give up

[obtuse pebble]

@lethal coyote Has your question been resolved?

[obtuse pebble]

@lethal coyote Has your question been resolved?

[obtuse pebble]

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[shell olive]

@leaden ibex @lone jetty this is the response I got on Chegg to number 4,

[shell olive]

I will let y'all know if I hear anything about number 5 in the morning. We are pooped and the weather isnt helping one bit here in Chicago

actually just recheched and found that a responce had been posted for number 5. I'm not reading through it right this second but I'll share it with y'all

[obtuse pebble]

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[crimson charm]

trying to make sense of this

how does those 5 x values prove its not convex>?

oh okay ig a convex function is only convex iff therer is at most one local minima

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[warped bane]

<@&286206848099549185> stuck at b

[nocturne minnow]

You have to wait at least 15 minutes before pinging helpers

[obtuse pebble]

@warped bane Has your question been resolved?

[warped bane]

<@&286206848099549185>

.

[haughty sable]

90000+18225-900/7.5•12

Isnt it?

No it isnt

90000+18225-900/7×12+5

[obtuse pebble]

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[solemn ravine]

Am I allowed to just directly integrate this to find a solution?

[solemn ravine]

Like, I did this, but I’m not sure this is a valid way to solve

[obtuse pebble]

@solemn ravine Has your question been resolved?

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[obtuse pebble]

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[solid mirage]

If, f(x) = ln(x) then, derivative of f(x) = 1/x. Then how does f'(1) = 1???

[violet compass]

Do you know the definition of a derivative?

[solid mirage]

the rate of change of a function

[violet compass]

Show me

[solid mirage]

what should I show you??

[violet compass]

Which level of maths?

[solid mirage]

Calculus 1.

[violet compass]

Ahhh

Then this

[solid mirage]

ik.

wait

[solid mirage]

yeah ik. but still.

[violet compass]

Okay

[solid mirage]

how does f'(1) = 1

[violet compass]

Just substitute 1

[solid mirage]

instead of x?

[violet compass]

Yup

[solid mirage]

ok. wait.

the result is undefined

@violet compass

i mean 0/0

[violet compass]

Then you got to play around with the values plugged in

Until you don’t get 0/0

[solid mirage]

wdym.

[violet compass]

Play around mean put it into a form where you don’t get 0/0

[solid mirage]

wait i dont think thats how that will work.

i think that we have to plug, 1 in the derivative

like f'(x) = 1/x, then f'(1) = 1/1 = 1

@violet compass

[violet compass]

Not yet

Use the pic I sent

[solid mirage]

i am.

[violet compass]

Put the function into the limit

[solid mirage]

kk

[violet compass]

And move stuff around, so that you don’t have 0/0

Got it?

[solid mirage]

i got a solution from the book but it still does not make sense

@violet compass

clearer image

[violet compass]

Erm after putting the ln, they are just playing around with it so that they are not dividing by 0

[solid mirage]

how did step 4 happen

like... how did it convert into, 1/x ln(1+x)

[violet compass]

What is ln0 equal to?

[solid mirage]

un defined

[violet compass]

Nope

It is defined

Use a calculator

[solid mirage]

wait then

its showing undefined

[violet compass]

?

[solid mirage]

i mean

its showing undefined

[violet compass]

That is literally 0

[solid mirage]

wait. you said ln 0

[violet compass]

I said ln1

[solid mirage]

i didnt know you said ln 1.

[violet compass]

Oh fuck

[solid mirage]

here look

[violet compass]

I did

Shit

Erm

[solid mirage]

np.

[violet compass]

Sorry

Yh, it meant to turn to 0

So we get ln(1+h)/x

[solid mirage]

yeo

yep*

so how do we solve that

[violet compass]

You see how they raised it to the power?

[solid mirage]

and how did that become step 5.

[violet compass]

You know the properties of ln?

[solid mirage]

yeah.. its confusion

[solid mirage]

not really but some of them yeah

[violet compass]

I suggest you go learn that because it’s needed here

[solid mirage]

got it

now. how did that turn into f'(1) = 1

confusion

@violet compass

[violet compass]

Erm

[spiral maple]

1/1=1........?

[solid mirage]

thats it?

[spiral maple]

Yeah..

[solid mirage]

so that means all that shitty working was stupid?

[spiral maple]

They evaluated the derivative at 1

[solid mirage]

congratulatiosn to me. i wasted 30 mins.

[solid mirage]

wdym?

[spiral maple]

What?

[solid mirage]

so f'(2) = 1/2??

[spiral maple]

Basic function motation

Yes

[violet compass]

It’s to show that

[fluid locust]

Yes

[solid mirage]

bruh.

[spiral maple]

1/2 is 1/2

[violet compass]

A show that question means you need to show using the definition of derivative

[solid mirage]

Thanks guys. Really helpful. Derivatives are confusing

[spiral maple]

This had nothing to do with calc

[violet compass]

????

[spiral maple]

This was just evaluating a function

[violet compass]

It’s very basic calc

[spiral maple]

Not their confusion

[solid mirage]

yeha its very basic calc

[violet compass]

He said it was calc 1

So we needed to use definition of derivative

[spiral maple]

They were given the derivative

[solid mirage]

currently studying diffrentiation.

[spiral maple]

Can you both not fucking spam ping?

[solid mirage]

when did we spam ping?

[spiral maple]

Replies ping..........

[violet compass]

By replying to his messages

Yh

[solid mirage]

oh. sry

anyways. Thanks guys!

[violet compass]

Kind of a way to have a nice string of msgs

But sry

[solid mirage]

.close

[obtuse pebble]

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[nimble trout]

Find the major premise and minor premise in each statement.

1. Jennifer had burger for lunch for the last 5 days. Therefore, Jennifer will have burger for lunch today.
2. Penny buys only yellow shoes. She bought new shoes yesterday. Therefore, those shoes must be yellow.
3. Team A and Team B played a volleyball game. The winning team in that game will play against Team C on the next game. Team C will play against Team A on the next game. Therefore, Team B lost to Team A in the game.
4. Anne finished her first 5 exams in half the allotted time. Therefore, she will finish the sixth exam in half the allotted time.
5. Every Friday, the Thompson family eats pizza. Today is Friday. Therefore, the Thompson family will eat pizza.
6. If a triangle is equilateral, then it is an acute triangle. Triangle ABC is equilateral. Therefore, it is an acute triangle.

[obtuse pebble]

@nimble trout Has your question been resolved?

[nimble trout]

<@&286206848099549185>

[obtuse pebble]

@nimble trout Has your question been resolved?

[obtuse pebble]

@nimble trout Has your question been resolved?

[obtuse pebble]

@nimble trout Has your question been resolved?

[solid mirage]

I cant beleive you have been waiting for so long. I dont think anyone can help

[obtuse pebble]

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[stoic dove]

I’m trying to solve the b question. I’ve tried solving for the second partial derivatives and put them into the equation. After that I got kind of stuck though

[obtuse pebble]

@stoic dove Has your question been resolved?

[stoic dove]

<@&286206848099549185>

[obtuse pebble]

@stoic dove Has your question been resolved?

[obtuse pebble]

@stoic dove Has your question been resolved?

[quaint minnow]

i haven’t done much multivariable calc yet so idk if this helps but i took your work and i let x²+y²=k and grouped a bunch of things together

then i get $4k\cdot f’’(k) + 4\cdot f’(k) = k$

[warm shale]

Oshimimers

then i get $4k\cdot f’’(k) + 4\cdot f’(k) = k$
```Compilation error:```! Double superscript.
<recently read> ^
                 
l.55 then i get $4k\cdot f’’
                                (k) + 4\cdot f’(k) = k$
I treat `x^1^2' essentially like `x^1{}^2'.


LaTeX Warning: Command \textquoteright invalid in math mode on input line 55.

Preview: Tightpage -1310720 -1310720 1310720 1310720```

[quaint minnow]

woops anyway then i saw the LHS is the result of a product rule

$\frac d{dk} (4k\cdot f’(k))=k$

[warm shale]

Oshimimers

[quaint minnow]

then you can solve for f(k) but i’m not sure if that helps you get any actual solutions

[obtuse pebble]

@stoic dove Has your question been resolved?

[compact shadow]

Let t=x^2+y^2 you got 4tf”(t)+4f’(t)=t

So g(t)=f’(t) you got g’(t)+(1/t)g(t)=1/4 for all t>0

It’s solvable

[obtuse pebble]

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[silent imp]

https://gyazo.com/e49a772cd057dc8af0c54e3ee0818ebd

[silent imp]

i dont understand how the limit isnt 6.37 because isnt 6.37 directly on top of 5 so it would be approaching it from both sides or am i doing something wrong

[spiral maple]

we dont give a crap about what happens at x=5

we care about what happens just to the left and right of 5

[silent imp]

oh ok so lets say the left side was approaching like 3.60 and the right side was approaching 3.68 it would be DNE right>

[spiral maple]

cant really conclude anything

[silent imp]

ok ima just keep watching

[obtuse pebble]

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[serene summit]

can i get some help solving these?

[fervent cradle]

what have you tried

[serene summit]

i tried (-2, 0)

moving the domain to the left by 1?

i didnt know if that was the right approach

[hybrid gull]

I think that's right

[serene summit]

any other input from anybody else?

.close

[obtuse pebble]

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[timid silo]

Does this work?

For homotopy.

[obtuse pebble]

@timid silo Has your question been resolved?

[smoky willow]

your handwriting bro 😭

[obtuse pebble]

@timid silo Has your question been resolved?

[timid silo]

Whatttt 😭

My Japanese handwriting is better.

[obtuse pebble]

@timid silo Has your question been resolved?

[compact shadow]

Ask it in Japanese then

I can read it

[timid silo]

LOL

I don't know the technical terms of topology in Japanese, sowy~ >.<

[obtuse pebble]

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[compact shadow]

位相空間

[obtuse pebble]

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[woven parcel]

Blue line => y = -3sinx
Red line => y = 2 cos x

[woven parcel]

And I also know that from the previous question, if solved 2cosx + 3sinx = 0
x = 326,31 and 146,31

But how to know combine both lines on graph so I can see that 2 cos x + 3 sin x > 0?

[obtuse pebble]

@woven parcel Has your question been resolved?

[obtuse pebble]

@woven parcel Has your question been resolved?

[compact shadow]

$acos(x)+bsin(x)=\sqrt{a^2+b^2}(\frac{a}{\sqrt{a^2+b^2}}cos(x)+\frac{b}{\sqrt{a^2+b^2}}sin(x)$

[warm shale]

Cogwheels of the mind

[woven parcel]

???

[compact shadow]

$=\sqrt{a^2+b^2}sin(x+φ)$ where $sinφ=\frac{a}{\sqrt{a^2+b^2}}$ and $cosφ=\frac{b}{\sqrt{a^2+b^2}}$

[warm shale]

Cogwheels of the mind

[compact shadow]

Like you case a=2 and b=3

The sum is just another trig function

[woven parcel]

Ah I see

Oh wait, we are suppose to use the graph

2 cos x > - 3 sin x
Left side of 146,31 and Right side of 326,31
Answer is x < 146.3, x > 326.3
My bad, i thought the graphs needed to be combined

.close

[obtuse pebble]

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[spring lantern]

<@&286206848099549185>

😦

[woven parcel]

Ok, first isolate the g value on one side

[woven parcel]

Move everything without the g to the right/left

[spring lantern]

uhm

wdym

[woven parcel]

Btw

Does G here means g?

[spring lantern]

yeh

g

[woven parcel]

Ok first take a look at the equation

g is under the square root right?

That is the only place where g is

so move everything else on the right hand side without the g to the left

So you move a^2

and you can also simplify the one inside the square roots

Until this point, do you understand?

[spring lantern]

yes i do

so

now its just sqrt g

[woven parcel]

No, not just square root g

its sqrt g/h

[spring lantern]

oh

so thats the final answer?

[woven parcel]

And how do you think you can get rid of the sqrt?

[spring lantern]

do it to the power of 2

square it

to get rid of the sqrt

rt?

[woven parcel]

Yes

[spring lantern]

yep

[woven parcel]

Now it just leaves the h

[spring lantern]

dont we have to square the k?

[woven parcel]

No

Because you square the ENTIRE THING on the left side

So you put everything on bracket on both side

and place the square outside

[woven parcel]

like this

[spring lantern]

so should it be (a squared+k)squared

=

[woven parcel]

Yes

[spring lantern]

ha to the power of 4+hk to the power of 2?

[woven parcel]

I think the one on the blue box is the final answer? or are you asked to expand the brackets?

[spring lantern]

we are asked to put it in its simplest form

[woven parcel]

Then... that is its simplest form

Further expanding it would make the equation messy and long

[spring lantern]

oh ok then

can i get help with the second question?

[woven parcel]

Ok

wait

[spring lantern]

wt?

is there a problem with the questionn?

[woven parcel]

nope, i just need to write sth down

[spring lantern]

k then go ahead

[woven parcel]

Ok first of all, how would you get rid of fraction

[spring lantern]

uhm

divide?

[woven parcel]

How do you normally get rid of fraction

[spring lantern]

wait times

both sides

[woven parcel]

Yes

So you cross multiply

Do you know how cross multiplication work?

[spring lantern]

uhm i learnt it at grade 5

u just cross multiply

like it says?

[woven parcel]

Good, its straightforward from here

You'll get this

You expand it

[spring lantern]

yep

[woven parcel]

Put all the terms with a on one side like before

And do you know what to do after?

[spring lantern]

wait i need to take this all in

[woven parcel]

Ok

[spring lantern]

so the equation at the bottom

how did u get it

[woven parcel]

You just move the terms with a to the left

and the ones without to the right

[spring lantern]

oh yeh

[woven parcel]

Now what to do to next?

[spring lantern]

let me write this down to get a better understanding

[woven parcel]

Tell me if you're good to go

[spring lantern]

wouldnt it be 2by-2bx?

[woven parcel]

No

-2bx was at the left side

now its moved to the right

so -2bx becomes +2bx

[spring lantern]

oh yep

i keep on overthinking 💀

[woven parcel]

dont worry

[spring lantern]

so im good to go now

[woven parcel]

Since everything on left side have a^2

you can isolate that by doing this

[spring lantern]

yes

[woven parcel]

now its ez, get rid of the (x-y)

and you'll have a^2 alone

[spring lantern]

sorry for asking but u minus x-y from both sides to get rid of it?

[woven parcel]

nope

brackets means multiplication

what is the opposite of multiplication

[spring lantern]

oh u divide

[woven parcel]

Good

Now remove the ^2 from a

and how do you do that

[spring lantern]

wait doesnt it say y=4

[woven parcel]

hmm?

[spring lantern]

the whole time we were doing y=y

look back at the question

[woven parcel]

No no no

This is a 2step question

Step 1 is to make (a) subject

Step 2 is to solve for (a) given x, y and b

[spring lantern]

so we have to find a

[woven parcel]

yes, we need to isolate a, then find the value of a

[spring lantern]

but wt is the point of the question saying y=4 b=2 and x=5

[woven parcel]

Thats for later on, lets focus on making a the subject first

[spring lantern]

k

[spring lantern]

we sqrt

[woven parcel]

And this is what we will have lastly

[spring lantern]

yes we have

[woven parcel]

ok, then lets solve for a

[woven parcel]

plug in these values for x y and b

and solve a

[spring lantern]

so b=2

[woven parcel]

substitute everything on the right side with the given values

[spring lantern]

so that would be 4(4x5)

and the denominator would be 5-4

am i rt so far?

[woven parcel]

Its 4 + 5

[woven parcel]

not 4x5

[spring lantern]

oh yeh

i keep on making small mistakes like this in my previous tests

[woven parcel]

Oof

just slow down

and write everything down slowly

[spring lantern]

i keep on looking at the steps instead of how to actually solve it

[woven parcel]

yeah, thats the problem with algebra these days

[spring lantern]

since im yr 8 doing advanced yr 9

its been getting hard

[woven parcel]

itll be harder from there on haha

[spring lantern]

im deadass gonna cry once im gonna get into yr 11/12

[woven parcel]

well, some ppl cant do math ig

so its fine...? uh

[spring lantern]

k so back to the question i guess

[woven parcel]

so its done?

have you find a?

[spring lantern]

oh yeh it is

so a=3

[woven parcel]

...

[spring lantern]

rt

RIGHT??/

oh no i did something wrong

im such a dumbass ngl

[woven parcel]

Pls do it slowly

and write all the steps if you;re that careless kekw

[spring lantern]

wts the g

wait its 9

[woven parcel]

that's 9 sry for poor handwriting

[spring lantern]

but isnt 2-2=1

[woven parcel]

That's 2 x 2

I replaced it with a dot

[spring lantern]

oh

here we dont do dots

[woven parcel]

oh my bad

[spring lantern]

thats why i got it wrong

lmao

[woven parcel]

Oh well, at least you get a = 6, its fine

[spring lantern]

wts that s or 5 next to a=sqrt 36

[woven parcel]

oh dont mind that

[spring lantern]

ok then

well thanks soo much then

ur about me looks cool

the stars

nvmd

[woven parcel]

Thanks

[spring lantern]

🤌🏻 👌🏻

i can sleep now

byeeeeeeeeeee

.close

[obtuse pebble]

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[timid silo]

hey i need help very fast before my school starts with pq formel

[timid silo]

i know how to do it
but in sometimes there comes out x² and i have no idea how to get it out

all i know is that i have to use p-q form but idk how to use it

lets say it comes out x² + 2x -2 = 0
idk what to do after it

[vernal wren]

Do you know about quadratic equations?

[timid silo]

yes

but i did it such a long time ago i forgot how it works

[vernal wren]

Do you remember sum of roots and product of roots?

So for a equation

ax²+bx+c=0

You have to break down the middle term such that, the
sum of the resulting break down = -b/a
product of the resulting break down = c/a

[timid silo]

ok so lets say

we have 4x² -52x + 48 = 0
then i would have to do
4x² -52x + 48 = 0 / :4
x² -13x +12 = 0

right ?

[vernal wren]

Yeah

[timid silo]

so i have x² -13x +12 = 0

whats next

[vernal wren]

And now you have to split -13x into 2 parts such that the product is c/a, i.e 12

[timid silo]

so -13x would be 7,5

7,5x

[vernal wren]

Nope, the product of 7 and 5 is 35
You need to break it down so that it's 12

Keep in mind that multiplying 2 negative numbers can also give a positive number

[strong sinew]

Wait

[timid silo]

ok

[strong sinew]

I think there is already a video about it

About that other quadratic formula @vernal wren is talking about

By 3b1b

U can just look into it to get a better justified answer

[timid silo]

can u send link

.close

[strong sinew]

https://youtu.be/MHXO86wKeDY

[obtuse pebble]

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[strong sinew]

From 14

Timestamp

[obtuse pebble]

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[cinder herald]

hi

[cinder herald]

What is the area of parallelogram EFGH with vertices E(-4, 3), F(0, 3), G(1, -
1), and H(-3, -1).

i dont get it

[vernal wren]

Do you know the properties of a parallelogram?

[cinder herald]

wait

ill brb

.close

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[fluid wolf]

how does a function y = 3x + 21 mod26 gets its inverse being x = 9y + 19

[fluid wolf]

<@&286206848099549185>

[obtuse pebble]

@fluid wolf Has your question been resolved?

[obtuse pebble]

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[atomic void]

is the answer c

<@&286206848099549185>

[lethal sand]

no, the answer is not c

[royal glacier]

It is

[lethal sand]

eh no, the side of the smallest triangle is 4/5, QR shouldnt sum up to be C

unless im misreading the diagram

[royal glacier]

x
2x
4x
8x
16x

[atomic void]

how do I solve it?

[lethal sand]

start by labelling a side

[lethal sand]

sorry, brainfart there

lemme guess, you forgot to exclude the side with length of x

PQ=15x in your case and not 16x

[atomic void]

oh

[lethal sand]

Q is notated to be the right angle here by how its drawn

[atomic void]

oh my god ohhh

i didnt know it halves

every 90 degrees

do i do 16x = 12

oh wait

[lethal sand]

...apparently i havent said anything above

[atomic void]

oh sry

didnt read carefully

so 15x = 12?

[lethal sand]

yes

even if PQ=16x, the answer wouldnt have been B

[atomic void]

ic

thanks :)

could u help me with another one

[lethal sand]

just send it, and i will if i know how

[atomic void]

ive tried to make (p-q)^2 = (p-q)(p+q)

then its n(p-q)

but i dont know how to get a p - q

[lethal sand]

can you expand (p-q)^2 for me

[atomic void]

ok

so p^2 - 2pq + q^2

[lethal sand]

great

so now can you find what n^2 equals from the given information?

[atomic void]

p^2 + 2pq + q^2

[lethal sand]

ok good

notice that it just differs from the middle term

[atomic void]

mhm

[lethal sand]

so we in order to have a -2pq in n^2, we can add and subtract a 4pq correct?

since 2pq - 4pq = -2pq

[atomic void]

mhm

[lethal sand]

so n^2 = p^2 -2pq + q^2 + 4pq

which gives n^2 = (p-q)^2 + 4pq

now the only thing is we need to find what pq equals

we also know that 1/p + 1/q = m, can you find what pq equals?

[atomic void]

hm

how do i do that?

[lethal sand]

well notice that if we do common denominator, we have a pq term in the denominator

dont we?

[atomic void]

mhm

[lethal sand]

right so what is the result after doing common denominator for 1/p + 1/q?

[atomic void]

oh do i make it (q+p)/pq ?

[lethal sand]

yes

[atomic void]

ohhhh

[lethal sand]

so we now have m=(p+q)/pq but we also know that n=p+q

[atomic void]

and q+p = n?

[lethal sand]

yes

so pq=?

[atomic void]

n/m

[lethal sand]

right, so n^2 = (p-q)^2 + 4n/m

now you just need to solve for (p-q)^2

[atomic void]

kk

i got

n^2 - n/m

but thats not an option

:(

can i make (p-q)^2

=

p^2+2pq+q^2 -4pq

then it becomes n^2 - 4pq

oh wait

i see where i got it wrong

is it c?

(mn^2 - 4n) /m

[obtuse pebble]

@atomic void Has your question been resolved?

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[slow viper]

Hi what is this circle mean in this question?

[timid silo]

it denotes functional composition

f o g(x) means f(g(x))

[slow viper]

Oh so just sub in the g(x) to f(x) function?

[timid silo]

read as 'f of g(x)'

[slow viper]

Oh okay

[timid silo]

ye

[slow viper]

Got it

And for b, it’s g(f(x)) right?

[timid silo]

yea

[slow viper]

Thank you so much

.close

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[knotty light]

how would one begin tackling this?

[obtuse pebble]

@knotty light Has your question been resolved?

[eternal bloom]

Ideas: Note a_{n+1} > 0. So if we can show [(n-1)a_n + a_n-1]/(n+1) goes to zero, we get the result by the Sandwich rule. This requires proving a_n is bounded