help-0

[nimble elk]

thanks

[pale basin]

@feral crag post the question

[feral crag]

@pale basin

[pale basin]

i dunno

[feral crag]

Oof

[pale basin]

if you look up some hyberbola equation

perhaps it will have its equation defined in terms of asymptotes

[distant bay]

I’m confused

[pale basin]

@distant bay what x do you need to plug in f(x) to get the result 0, -12 etc etc?

you calculate that

[distant bay]

Ok solve for x

Basically

[pale basin]

@distant bay just plug in the inputs, and write your equation

[distant bay]

Okk

[pale basin]

for 17 too

just plug it in for both f and g, write the equation

[distant bay]

I got -15 for a) 16?

[pale basin]

no, you dont plug in 0

you plug in x

@distant bay

[distant bay]

Ohhh

[nimble elk]

do I set this up as 8x+7x+90=180?

nvm it mega wrong

[muted raft]

why do you think that is wrong?

[lime valve]

can someone help me?

[uncut cosmos]

what have you tried

[viral owl]

i dont understand it

too

he goes at my class

we're spanish

and we don't understand it

because the homework is in english

[uncut cosmos]

alright

you are have trouble understanding the question or trouble solving it?

[viral owl]

both

[lime valve]

yeah

[alpine sable]

? help

[uncut cosmos]

ok so you've been given that the gray part has area 10 and that the line x is parallel

[lime valve]

in my class we haven't gave this

no geometry

and im 15 years old

[uncut cosmos]

The only thing required for solving this is area of triangles

[lime valve]

i know whats an area but no more

[uncut cosmos]

You know that right?

[lime valve]

no

[uncut cosmos]

you don't know area of triangle?

[lime valve]

no, sorry

is it a x b

like

altura x base

[uncut cosmos]

it's 1/2 multiplied by base and hight

height

[lime valve]

base is base and height is altura

so yes

[uncut cosmos]

1/2 ab

[lime valve]

but what 1/2 means

[uncut cosmos]

Half of a multiplied by b

I can send you solution but I think you should learn basic geometry first

[alpine sable]

help me please

[uncut cosmos]

Ask in unoccupied channels please

[uncut cosmos]

write two equations and solve them

[lime valve]

i know "basic" but not at an expert level

like i know whats a perimeter, a polygon, a side, etc

the problem is we haven't gave how to do this

and i have to give my homework in 30 minutes

[uncut cosmos]

that's maths

wait lemme help

[lime valve]

if you can give me solutions and then explain @viral owl and me how to do it

we would apreciate

appreciate*

[lime valve]

explain

[uncut cosmos]

Here b1=b2, so what will be the area of the rectangle?

[lime valve]

idk

20?

[ashen wave]

Can anyone tell me everything I need to know about quadratic equations?

[lime valve]

IDK 😫

[uncut cosmos]

It will be b1 multiplied by (h1+h2)

[ashen wave]

im really struggling with the quadratic unit

[lime valve]

is the answer 22

[ashen wave]

especially the word problems

[uncut cosmos]

the answer is 20 yes

[lime valve]

knew it

ty

[uncut cosmos]

Area of gray part with be 1/2(h1+h2)*b1 = 10 so area will be 20

C'mon dude lol you're just guessing

[lime valve]

yes

but with luck

[uncut cosmos]

Don't you wanna know the process

[lime valve]

i know 10 + 10 is 20

so yeah 20cm

[uncut cosmos]

cm²

[lime valve]

i dont know how to type that number

[uncut cosmos]

What're you struggling with?

[lime valve]

but i know if we talk 'bout cm i think its with that 2

the perimeter is the sum of all the numbers

[alpine sable]

what is x^2 = -9

[lime valve]

but there's no image

theres no solution

[alpine sable]

-3 right?

[lime valve]

no

[uncut cosmos]

so this one yourself you don't need image

[lime valve]

so hars

hard

can't do it

is it 1846

?

[uncut cosmos]

I can help you but not with the answer

[lime valve]

this one is actually easier

can u help me at dm?

[lime valve]

theres no solution

[uncut cosmos]

no

[alpine sable]

Ok

[lime valve]

yeah

[lime valve]

ok explain here

[uncut cosmos]

aight take the sides of the rectangles as a and b so the options for choosing three different sides with diffrent sums becomes a+2b and 2a+b

[lime valve]

what

can u do images

or paint

[uncut cosmos]

There's nothing to show in the image

[lime valve]

my english is not that good

[uncut cosmos]

length is a and breadth is b

[lime valve]

oh

ok

is it 56 or 42? i think i understand it(im not sure)

[uncut cosmos]

2a+b=40
2b+a=44

Find perimeter

figure out yourself

[lime valve]

84

but why 2a+b is 40?

i want to know

[uncut cosmos]

cause you choose 3 sides right
two of them were breadths and one length

[lime valve]

eva did

i didn't

[uncut cosmos]

Yea ok

[lime valve]

ok

another question

i finished my homework, can u tell if something is wrong?(DONT SAY THE ANSWER, just say: 1 is wrong, and ill try to fix

@uncut cosmos

[uncut cosmos]

Alright

[uncut cosmos]

Dude this many questions 😐

[lime valve]

10

[uncut cosmos]

I've got stuff to do too y'know

[lime valve]

😦

[uncut cosmos]

Tell me the one you're most doubtful of

[lime valve]

there are 2

[uncut cosmos]

Which ones

[lime valve]

and this one

hi?

[uncut cosmos]

Should be 4

[uncut cosmos]

You only need to fact that sum of all angles is 180 here figure rest on your own

[lime valve]

then<??

oh

mmm

let me guess

please dont say it

[uncut cosmos]

this is wrong

don't guess my man, solve em

[lime valve]

like

im solving it

[uncut cosmos]

Cool

[lime valve]

i get 97

and theres no 93 option

97*

[deep trellis]

can someone help me with this?

[lime valve]

@uncut cosmos please help

i have to give it

[uncut cosmos]

Its correct

11

[lime valve]

oh

the problem is the circle one

[uncut cosmos]

The circle one is 4

[lime valve]

i said 4.5 but no 4.5 option

so 9/2

[uncut cosmos]

although I don't completely understand the wording of that

[lime valve]

and this one?

[lime valve]

when i give the homework i can tell you how i did

[uncut cosmos]

Ok

[lime valve]

this is 32 i bet

NO LYERIFF

WHY U LEAVE

@uncut cosmos :(ç

[uncut cosmos]

bro do I do all your homework

[lime valve]

no

[uncut cosmos]

Do these on your own

[lime valve]

just say if its right or wrong, and ill fix

without you

[uncut cosmos]

Ask your teacher after this

[lime valve]

😦

[lime valve]

is 8

[subtle seal]

Can anyone help with this please? I tried evaluating it but to no avail

channel taken?

[real briar]

is that sc or what?

and what goes to infinity?

[azure idol]

how would i multiply 810 * 8/9?

[lime valve]

3

[subtle seal]

x

[subtle seal]

what do you mean?

[real briar]

simplifty 810 by 9 so you get in total 90*8=720

[azure idol]

it says the answer is 720

[real briar]

he is trolling i think

[lime valve]

oh

sorry my bad

[real briar]

the letters is sC?

are*

[lime valve]

not, i wanted to reply myself

with another thing

[real briar]

oh okay, sorry

[lime valve]

no problem

[subtle seal]

that's x, just in cursive xD mb

[subtle seal]

this is it with the normal x

[azure idol]

so how would i

?

[real briar]

i just explained you mate

you can write it as (810*8)/9

simplify 810 by 9

you get 90

90*8 equals 720

[azure idol]

oh sorry thanks

[fallow laurel]

Can you remember me the name of that rule?

[uncut cosmos]

idt that has a name it's just basic equality

[fallow laurel]

so basicly, if I can do the same thing to both sides?

[uncut cosmos]

Yes

[fallow laurel]

Is this going to be sqrt?

I think we're busy here

in this channel lol

[real briar]

i think you can rewrite this as (e^2/x-e^2/x+1)/1/x^2 which leds you to 0/0 so you can apply l'hopital

like this

you get an 0/0 case so you can apply l'hopital

[ashen wave]

Is anyone here good at factoring?

[mystic vigil]

can i get help on a pls

[alpine sable]

depends, what are we factoring?

[alpine sable]

you should investigte a bit about scale factors and trig in order to solve this

[deep trellis]

Can someone help me with this?

[ionic jewel]

two right triangles

14,21, center
10,2x-3, center

[ionic jewel]

use Pythagorean to solve for the line in the center then solve for x

[deep trellis]

ok ty

[wanton plinth]

I need assistance

Im currently doing sine rule but have no idea what I am suppose to fine for these 2 questions

[glass lichen]

nowhere does it say they're right

[ionic jewel]

is there another way to do it?

don't see how it's possible without that assumption

[glass lichen]

similar triangles if they're similar

but i only see SA

[ionic jewel]

they aren't similar

SA?

[glass lichen]

side angle

for similarity

[ionic jewel]

you literally know two sides on both of them they can't be similar

they share the same center line, but have different sides on the "24" part

[glass lichen]

the 2x-3 and 21 could be similar. . .?

or am i smooth braining

[ionic jewel]

nope

it doesn't end up working out

pretty sure

one triangle ends up 14,14,21, and the other one is 14,10,2x-3

[wanton plinth]

so no?

[ionic jewel]

it tells you what to find

with the words

[rugged lynx]

i need help on how to solve for x

[glass lichen]

if they're opposite angles, what does that say about their size?

[rugged lynx]

180 degrees?

[glass lichen]

84 clearly isnt 180

[rugged lynx]

i thought u said what do adjacent angles add up to

[glass lichen]

No, I asked what you knew about the sizes of 84 and x-3, given they're opposite angles

I never said add or sum

[rugged lynx]

uh idk

84 and x-3

[glass lichen]

look in your notes then

[rugged lynx]

i have no notes about it

if i had notes i wouldnt be asking about it right now

[glass lichen]

Ok well opposite angles are equal.

[rugged lynx]

oh

ok

thanks

[narrow vector]

can someone explain how to solve this

log(-x)=2

[glass lichen]

base 10?

[narrow vector]

if base is missing it’s always 10?

[glass lichen]

Im just making sure

some notations have log meaning ln

anyways -x=10^2

[narrow vector]

so -x=-100

as final answer

to find x

[glass lichen]

yes, x=-100

[narrow vector]

thank you

[pearl vortex]

having trouble writing a power series as a 'regular function
such as representing the series from 0 to infinity of x^n being written as 1/(1-x)^2

i have to find the power series of 1 to infinity of (n)(n-1)x^n

[alpine sable]

Can you be a bit more precise ?

Send the question directly (as a screenshot) if possible

[pearl vortex]

here it is

[alpine sable]

anyone wanna help a brother out with some substitution *by parts

[pearl vortex]

@alpine sable is there a good first step I could take?

I recognize 1/(1-x) is a power series giving me x^n

[ashen wave]

Is anyone here good with quadratic equations?

[shrewd oracle]

i imagine many are

just shoot with the q

[tough tangle]

What is the value of the IRA when you turn​ 65?```

help meh i suck at these things

[ashen wave]

are you good with quadratic equations? I need help on the word problems

[shrewd oracle]

just put in the question

[ashen wave]

alr

I need help finding out when/where an object hits the ground. here is the word problem- An object is launched directly upward at 64 feet feet per second (ft/s) from a platform 80 feet high. The path of the object can be modeled by the function h(t)=-16t^2+64t+80

[shrewd oracle]

physics class?

[ashen wave]

no this is just math but its high school math but im in middle school

[shrewd oracle]

i mean i ask cause i could approach this from how a physics student would

[ashen wave]

but- you need to factor to get the x-int

[jagged imp]

It hits the ground when it’s height is...?

[shrewd oracle]

so how far the object travels in the x-direction ya?

[shrewd oracle]

zero i assume

[ashen wave]

0

yeah

[jagged imp]

I was trying to get them to answer lol

So set h(t)=0 and solve for t then

[ashen wave]

I did, isnt it 2?

[jagged imp]

Nope

[ashen wave]

uhm 5?

[jagged imp]

Ye

[ashen wave]

alright that clears things up but wait

2 is the x value for the max right?

[alpine sable]

Write the equation of an exponential function that passes through the points 2, 48 5, 750

[jagged imp]

The max height?

No.

[ashen wave]

yaya i love it when you actually know how to do math

[shrewd oracle]

its the time at which the height is a maximum

[ashen wave]

yeah the max height of the object. (2,144)

[jagged imp]

Oh that’s what they were were asking

You should have said t value lol

[ashen wave]

no I was asking for when it hits the ground

where*

actually wait it says - when/where the object hits the ground

[jagged imp]

It just hits the ground directly below where it was launched from right?

It was launched vertically upwards

So it’s not moving horizontally

[ashen wave]

uhm i think theres a bit of a slope after the vertex

because these are parabola questions

[shrewd oracle]

not if its being shot vertically with no air resistance

[ashen wave]

yeahhh but this isnt physics xDD

[jagged imp]

Craby the parabola isn’t the shape of its motion

[ashen wave]

we would save that for another day xD

what??

its the height and time tho

[shrewd oracle]

its the model for the height at a certain time

[ashen wave]

yeah

[jagged imp]

It’s it’s height against its time, the shape of its motion would be its height against its displacement in the horizontal direction

[narrow vector]

can someone help me out on a question if no one is getting help already

[shrewd oracle]

yeah so it has nothing to so with how the object is moving horizontally

[ashen wave]

oh

[jagged imp]

Assuming there’s no wind, if it was launched vertically upwards there’s nothing to make it move horizontally@ right?

[ashen wave]

Conor when we are talking about any X value we are talking about the time?

or Y?

[shrewd oracle]

nt talking about x values whatsoever

[ashen wave]

y is usally height in my class

[shrewd oracle]

object is shot vertically in the +y direction

assuming you set y as up

[ashen wave]

oh no im just asking in general

[shrewd oracle]

i mean, yeah in general the time would be used to help find the x diresction if it were a projectile that wasnt shot vertically

[ashen wave]

bc when I get the coordinates or the max height its (2,144) but does that mean the X is the time and y is the height

so the 144 would be the height

[shrewd oracle]

no no theres no x here

[ashen wave]

ft

???

[shrewd oracle]

in your eq, your using t as your time

[ashen wave]

right

[shrewd oracle]

so h(t) is your height at some time

144?

height of what

[ashen wave]

the height of the object

[shrewd oracle]

what max height?

[ashen wave]

The max height of the object is (2, 144)

[shrewd oracle]

yeah

[ashen wave]

but the Y axis is identified as height so would that mean at 144 that would be the height

and 2 would be time

[shrewd oracle]

yeah

[ashen wave]

oh!

ok that helps thanks!

[shrewd oracle]

no bother

[robust flame]

Can someone help me with this?

[shrewd oracle]

okay so for this @robust flame, we will be using one of $sin(\theta) = \frac{O}{H}, cos(\theta) = \frac{A}{H}, tan(\theta) = \frac{O}{A}$

[ocean seal]

Conor Sheridan

[shrewd oracle]

so we want to find the angle F, and we know 2 sides, we know the longest side which is known as the hypotenuse (or H), and also the adjacent side to F (or A) and this side is 12

so we want to use one of the formulas that have both H and A in it, if we look above we can see that $cos(\theta) = \frac{A}{H}$ uses both A and H, so now if we can find $\theta$ then we will have our angle F

[ocean seal]

Conor Sheridan

[alpine sable]

HOW IS THIS

equal to

[shrewd oracle]

so to get the angle we then just use $\theta = cos^-1(\frac{A}{H})$

[alpine sable]

BRUH MOMENT

[shrewd oracle]

@alpine sable use other channel

please

[ocean seal]

Conor Sheridan

[robust flame]

Okay thank you so much!

[shrewd oracle]

does any of it confuse you

[robust flame]

So I got 36.9

I would round that to 37 right?

[glass lichen]

,w calculate arccos(12/15) in degrees

[shrewd oracle]

depends on whether or not your asked to round it

[ocean seal]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by moshill1#9771

[robust flame]

Yeah round to the nearest degree

[glass lichen]

so yes, 37 deg

[shrewd oracle]

yeah then you round up

[robust flame]

Ok thank you!!

[deft scroll]

https://www.youtube.com/watch?v=Ds8ijPsg26g

isnt this video bullshit

i tried it on some other numbers but it didnt add up

tried it on 50,802

didnt work

tried it on 120,467

didnt work

[glass lichen]

cause 50802 isnt a cube number...

it's clearly not going to work on an abritrary number

[deft scroll]

0_0

mhm

yes i knew that

for sure for sure

was just testing you clearly

[shrewd oracle]

lol

[glass lichen]

sure you were. . .

[blazing rose]

ok i got a which is the right choice

but idk how i got it really

like i did an educated guess

i knew that there was one rel max and 1 rel min because f'(x) goes from + to -, which means rel max at the point where it switches signs, and f'(x) goes from - to positive, which means rel min

but why is there 3 points of inflection

[dusky moat]

can someone help with part b

[tight locust]

no thank you

[dusky moat]

my initial attempt was f(x) = {1 if x is in Q and O, 0 if x is in I and O, and 0 if x is not in O}

but i'm pretty sure that would lead to discontinuities at any limit points of O

this is 4.3.12 function it was mentioning

[thorn kindle]

1 if x in O, 0 otherwise?

don't see why you have to bother with Q and I

[dusky moat]

don't want it to be continuous on O

[thorn kindle]

it wouldn't

[dusky moat]

??

[thorn kindle]

it's 0 everywhere except O

[dusky moat]

yes but it would be continuous on all of O then..

O is an open set

[spark ibex]

Anybody good at elasticity of demand that could help me

[shrewd oracle]

just post the question regarding it

[flat gust]

How

[alpine sable]

first find the length of a diagonal of the box, then you can make a second right triangle

[flat gust]

I don’t get it

[alpine sable]

can i have help on this pls

[flat gust]

Hm I see

So find the hypotenuse of with 80 and length 70

Triangle

[alpine sable]

yeah

then to find the diagonal you look at the other right triangle

[flat gust]

Ya I see I just didn’t understand what the question was really asking because there are many lines from one corner to the other corner of the box

So which hypotenuse is it asking

[alpine sable]

yeah but they would all have the same length

[flat gust]

Oh really

[alpine sable]

if you go from one corner to the other

yeah

[flat gust]

So I just find one hypotenuse and that’s it

[alpine sable]

just find the length of one diagonal across the cube

[flat gust]

Ok

[alpine sable]

Pythagorean theorem

kinda like dat lol

[tight locust]

it can help if you think about it as using pythag twice

first use it to find the diagonal of the base of the box

then use the diagonal and the height to find the diagonal of the 3d shape

[slender marten]

You could also imagine one corner of the box is the origin in a three dimensional space then the other corner of interest just has the dimensions as coordinates then use the three dimensional Pythagorean theorem.

[tight locust]

sqrt(a^2+b^2+c^2) = sqrt(sqrt(a^2+b^2)+c^2) ?

huh?

[slender marten]

$d = \sqrt{x^2 + y^2 + z^2}$.

[ocean seal]

stabulo

[tight locust]

oh nvm it checks out

i just forgot to square the base diagonal

so it should be

sqrt(a^2+b^2+c^2) = sqrt(sqrt(a^2+b^2)^2+c^2)

[slender marten]

Something like this.

[echo haven]

Hi so I tried finding out what the hole was and I got an undefined number for the y

so what do I do if the y of the hole is undefined?

[thorn kindle]

holes are limits of the form 0/0

that means the numerator and the denominator have a common factor

factor the polynomials

[echo haven]

I did

[slender marten]

This question screams factorisation.

[echo haven]

I got 5(x-5) over (x-5)(x-5)

cancel x-5 out

You get 5 as the x of the hole

and when I plug it in I get 5/0

[slender marten]

Yeah, it appears there will be a vertical asymptote at x = 5.

[echo haven]

alr

ig I’ll just put no hole

[thorn kindle]

yeah that's right

there can't be a hole because there is no finite limit

[echo haven]

got it

ty

[keen wasp]

Does anybody understand the difference between finding volume by cross sections when the shape is perpendicular to x axis versus y axis

[worthy verge]

Sry channel taken ill delete

[charred flint]

@keen wasp you'd prefer it be perpendicular to the x-axis, otherwise you should convert it to x=... as a function of y, and integrate between y values

[keen wasp]

okay thanks

[olive pewter]

i’m really poor when it comes to square roots and derivatives qwq

how would i go about solving 5 sqrt x^3 ?

[alpine sable]

square roots are just fractional exponents

use power rule

to find the derivative

[olive pewter]

ONE SEC

aaAaaa

oki i’m a bit lost, n sqrt a power m becomes a power m/n

so i got to x ^ 3/5 and then 3/5x ^2/5

i’m not sure whether the 2/5 is negative or not

and then following that is ?

[alpine sable]

how to solve for missing side

yea

[bold star]

u can use

a^2+b^2=c^2

[olive pewter]

oh yee

there’s no angle lmao

[alpine sable]

so it would be

14.42

rounded 2 decimal places

[bold star]

not quite.

can you tell me what value is your a , b , and c?

if they are unknown say its unkonwn

[alpine sable]

2 legs

and hypo

would it be

[bold star]

yes

what would the values of a b c be

[alpine sable]

a is 8^2

b is unknown

c is 12^2

[rocky sorrel]

listen

use pythagorean

[bold star]

a is 8 and then a^2 is 8^2

@rocky sorrel yes but they mis identifing the legs and hypo when using pythagorean is not gonna help

@alpine sable yes so if you solve the the equation now, what do you get?

[rocky sorrel]

you know c is 12, b is undefined and a is 8. plug that into pythagorean, (a^2 + b^2 = c^2). so then you would get 8^2 + b^2 = 12^2. solve for b.

[alpine sable]

solving now

ok

80

so

4 5

[celest void]

Could someone help me with 4 and 5?

[bold star]

oh so what is b equal to? @alpine sable

[celest void]

I model it as a sinusoidal function right but i guess i need the phase shift?

$x=A\cos(\omega t + \phi)$

[ocean seal]

Serena!

[celest void]

How am i getting the phi here which i guess is the phase shift?

[alpine sable]

@bold star 4 5

[bold star]

ur getting 45 for b? or 4.5

[alpine sable]

b is 80

but im squaring

idk the sign

but 4 5

[bold star]

u are squaring or square rooting?

[alpine sable]

root

[bold star]

i got 8.94 when i square root 80

[rocky sorrel]

@alpine sable

[dire wren]

does it ask for decimal? because usually i leave it as a simplified radical

[slender marten]

Oh no. Not decimals...

[woeful pulsar]

oh no

[slender marten]

$\sqrt{80} = \sqrt{(4)(20)} = \sqrt{(4)(4)(5)} = 4\sqrt{5}$.

[ocean seal]

stabulo

[slender marten]

Please no decimals though.

[rocky sorrel]

thats if it asks for exact form

[dire wren]

90% it asks for that

[rocky sorrel]

true

[dire wren]

lol

[slender marten]

Unless it says otherwise, it's always exact form.

[lament rock]

i expanded the equation but i have no idea how to make the equation into a form including cos2ø

[vale wigeon]

i mean, you could factor cos^8(θ) - sin^8(θ)

into $(\cos^4(\theta) + \sin^4(\theta))(\cos^2(\theta) + \sin^2(\theta))(\cos^2(\theta) - \sin^2(\theta))$

[ocean seal]

Ann

[vale wigeon]

and then observe that $$\cos^4(\theta) + \sin^4(\theta) = (\cos^2(\theta) + \sin^2(\theta))^2 - 2\cos^2(\theta)\sin^2(\theta) = 1 - \frac12 \sin^2(2\theta)$$

[ocean seal]

Ann

[vale wigeon]

@lament rock

[lament rock]

i did that

[lament rock]

didnt know this formula tho

[slim wolf]

does anyone know discrete math

[lament rock]

nvm im just an idiot i needed to change ip cos2ø=-1/√3

[wintry trench]

need some help please

[alpine sable]

i have a question about physics, why does Fnet = Fg - Fk(the kinetic friction)?

Evaluate would be to find a decimal equivalent

I would personally show the intermediate log step as ur boxed answer

And than just write 2 under it or something

[split fulcrum]

Really not sure what I'm doing wrong here. Worked the problem out like 10 times and gotten the same answer every time.

[jagged imp]

you took the derivative of dy/dx wrt t, you need its derivative wrt x

so unfortunately its another application of chain rule

[vale wigeon]

a^2 + b^2 = (a+b)^2 - 2ab

[split fulcrum]

okay thanks

[slender marten]

@split fulcrum This might help you.

To understand why imagine dy/dx = u(t) and x = x(t) then you're just doing the process again. Hence du/dx = (du/dt)/(dx/dt). Instead dy/dx = u. Giving you the formula in the screenshot.

Maybe you miss typed the power as 2 instead of 3?

[craggy trellis]

is it possible to get the slope with only x1 and y1?

[slender marten]

You mean with only one coordinate? If so, only if you have the equation of the curve.

[chilly walrus]

could someone help me with this?

and this

[small stag]

$$\begin{align*} \sin(\alpha) &= b \newline a &= \arcsin(b), a &= \pi - \arcsin(b) \end{align*}$$

[hollow atlas]

this is a unit circle problem

[chilly walrus]

I dont understand sorryu

ok

[hollow atlas]

i would advise remembering the unit circle

1 second

[chilly walrus]

yep ok

[ocean seal]

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

[chilly walrus]

with the 4 quads

[small stag]

Bruh that doesn’t work???

But yeah par is right

[hollow atlas]

one thing u need to know before hand is

that x value is cosx

and y value is sinx

correct me if im wrong

[chilly walrus]

wait for what?

@hollow atlas

oh I see

ya

[hollow atlas]

1 / root(2)

can be written as ?

@chilly walrus

[chilly walrus]

root2/2

?

sorry

[hollow atlas]

correct!

[chilly walrus]

ya nah thats right

lol doubted

[hollow atlas]

so now u ask urself

where is the y value root2/2 ?

[chilly walrus]

pi 4

[hollow atlas]

from the range 0 to 2pi

bingo

where else?

[chilly walrus]

7pi 4

so its quad 1 and 4

?

[hollow atlas]

wrong

[chilly walrus]

oh 2

[hollow atlas]

i believe its 7pi/4 is -root2/2

[chilly walrus]

ah ok

1 and 2

[hollow atlas]

your second choice would be 3pi/4

[chilly walrus]

yep

[hollow atlas]

when it says 2pi

it basically means

the full circle

when it says pi its half of the circle

[chilly walrus]

ok

[hollow atlas]

do you understand how i got the solution or do you need further explanation?

there are many ways to rememebr the unit circle if your remember the [0, pi/2]

[chilly walrus]

wait so the answers are pi/4 and 3pi/4

i get that if so

[hollow atlas]

yes

all u have to rememebr is that x value is cos

and y value is sin

[chilly walrus]

what about 2nd question

What is the length of the arc on a circle with radius 6m, subtended by the angle π2 ?

yea I get that thanks!

could you give me a hand with the next? @hollow atlas

[hollow atlas]

yes i will try

give me one second been a WHILE since ive done calc

i promise this problem is very easy as well

[chilly walrus]

cool

just fyi

[hollow atlas]

its a simple formula memorization one if i believe

[chilly walrus]

i have 7 and a half minutes

yikes

mb

no worries if you cant figure it out by then, mainly want to understand

[hollow atlas]

i will get it no worries

[chilly walrus]

😎

[hollow atlas]

answer is 3pim

3 * pi * M

[chilly walrus]

?

this one?

i assume

yep

could you explain?

[hollow atlas]

formula is very simple arc length = radius * (angle in radians)

that is correct choice

i dont remember why the formula is that way off the type of my head, but make sure that when u do these problems

a common trick used by professors is that they give u degrees instead of radians

you will have to convert ur degrees in the radians

or remember the degrees version of this formula

[chilly walrus]

could you show your working?

ill understand it better I believe

[hollow atlas]

sure @chilly walrus

work for the example u did?

Ignore the banana

[chilly walrus]

ah i see

cheers for the help par ❤️ @hollow atlas

i like the nana

[hollow atlas]

thanks haha

anymore questions ? @chilly walrus

[versed osprey]

Could someone please check my question in #help-1

[undone copper]

how to show two functions are orthogonal?

[vale wigeon]

in what context?

i could say "calculate their inner product and show that it's zero" but somehow i have big doubts that this would line up with the sense in which you are using the word "orthogonal".

[undone copper]

this is it

ty

[undone copper]

this?

[vale wigeon]

well if thats the formula for your inner product then yeah

[undone copper]

i dont really have a specified w from what i can tell

[vale wigeon]

.....

ok can you show the problem in its entirety

[undone copper]

its quite long

[vale wigeon]

okay

i've braced myself

[undone copper]

wiat

oh

[vale wigeon]

your weight function's right there lul

[undone copper]

oof

im a dumbass

tyvm

[vale wigeon]

use properties of the dot product

[jagged imp]

Yes, also a.a=||a||^2

[vale wigeon]

yup those

[alpine sable]

The mean age of male and female were 28.86 ± 11.27 years and 25.31 ± 7.70 years respectively
i thought mean gives us only one result
so why is there this plus minus part?

[vivid kayak]

What would a graph look like if it was growing exponentially at a fixed rate?

[tardy timber]

not sure what you mean

like a^x

?

[vivid kayak]

i)

Because I know that it should pass through (0,1)

but im not so sure if its changed to (0,100000)

what do you think?

[tardy timber]

oh okay, so notice on the log scale network F is fairly linear

which indicates exponential growth with fixed rate

[vagrant rover]

Can someone check if this question is written wrong? I don't think there is an actual answer here. I don't really want to know the answer, I just want to know if the question is written incorrectly or not. I had a problem with questions being written wrong last year and my math teacher isn't responding to my emails.

[quaint trout]

The answers are fine

[tardy timber]

yeah

they seem fine

[quaint trout]

What they mean is not that the expressions are written as a^2 - b^2, but that the expressions are of the factorized form of a difference of squares

So what does a^2 - b^2 looks like factorized? And which one doesn't look like that

[vagrant rover]

🤔

Interesting

[vivid kayak]

and for ii) like what proportion? per day or overall?

[vagrant rover]

Alright, I'll look over it again. Thanks guys.

[vivid kayak]

nvm network w is growing constantly every 5 days at the same rate

so its slower

[tardy timber]

yeah F is exponential whereas W is linear

so F grows faster

[vivid kayak]

ty

ok jesus

iii) lol

I just need to clarify that the W is indeed the decimals

cause then it makes this alot easier

[tardy timber]

huh?

I dont see iii

[vivid kayak]

oof wait

theres like 3 of these

and they all follow the same thing

[tardy timber]

okay plug in t and F into the equation

ln(F) = number -> F = e^(number) right?

[vivid kayak]

I just want to be sure F is the decimals

cause then it makes this alot easier

[tardy timber]

F is the decimals?

idk what you mean by that

[vivid kayak]

F=11.65...

[tardy timber]

yeah

[vivid kayak]

yea ty

[tardy timber]

well ln(F)

you need to get it into F

so e^(11.65...)

[vivid kayak]

wait what

so i can't put it simply as 11.65?

[tardy timber]

no

you are given that ln(F) = number

so to find F, you need to take base e on both sides

[vivid kayak]

So if I do e^11.65

thats essentially F

right?

[brave cairn]

is this true?

[slender marten]

Definitely not.

[brave cairn]

hmm

[vale wigeon]

$\sqrt{a+b} \neq \sqrt{a}+\sqrt{b}$

[ocean seal]

Ann

[vale wigeon]

every time you write $\sqrt{a+b}$ as $\sqrt{a}+\sqrt{b}$ a puppy dies

[ocean seal]

Ann

[brave cairn]

ooooh damn I forgot that

[slender marten]

No puppies left.

[brave cairn]

so...this term cannot get any more simplified?

[slender marten]

I'd say that is the simplification.

[vale wigeon]

this isnt a term this is an equation

and without context yeah you cant rly say much else

[vagrant rover]

So if you substitute 2 in for x then you get -48 for the given example equation. And then B also gives -48 when you substitute 2 for x. Thus, B is correct here, right?

[vivid kayak]

no

[vale wigeon]

no

[vivid kayak]

Try doing it again

but leave the neg

until the last step

[vale wigeon]

just because two expressions have the same value at x=2 does not by itself mean theyre equivalent

if they had DIFFERENT values at x=2 you could conclude they arent the same

[vivid kayak]

Wait B is correct

[vagrant rover]

K, i'm confuzelled

[vivid kayak]

B is correct

Just do the simplification

[vagrant rover]

Yeah I did

[vivid kayak]

but leave the negative symbol until the last step

[vagrant rover]

But what does this mean?

[vivid kayak]

have you subbed 2 into every other eqn?

[vagrant rover]

Yeah, they all come out wrong

[vale wigeon]

this means that the value of (B) at x=2 is -48

nothing more

honestly like

[vivid kayak]

if you have a different answer every time that isn't the same as your bracketed eqn

[vagrant rover]

Oh

[vivid kayak]

then b is correct

[vagrant rover]

Let me try with a different number

[vale wigeon]

is there anything stopping you from actually doing an honest to goodness expansion

like

[vivid kayak]

slap

[vale wigeon]

it sounds like youre trying to avoid that

fsr

why

[vivid kayak]

i mean

[vagrant rover]

What do you mean?

[vivid kayak]

its one way

but its a long way

just expand

[vagrant rover]

I don't udnerstand what's happening

[vivid kayak]

its the easiest thing

[vagrant rover]

What does expand mean

[vivid kayak]

bruh

Expand the eqn

so you end up with one of the 4 choices

[noble sinew]

Imagine if 1 equation was (2x^2) and another was (2x^5). Setting x=0 gets the same value for both 2x^2 and 2x^5 yet 2x^2 is obv not the same as 2x^5. Setting x=1 we also get the same value from both.

[vagrant rover]

Oh

So it still could not be B?

I see what you mean

[noble sinew]

If the others didn't give the same value then you can conclude by process of elimination

but otherwise just expand the equation

[undone copper]

trying to find eigenvalues/function for x(1)=0 , x(2)=0 bcs

[vale wigeon]

youre trying to find the values of lambda which make this BVP have nontrivial solutions?

do you want the long formal version or the short hacky version

[undone copper]

idm

usually bcs have like an x(0)

[vale wigeon]

your nontrivial solutions will be sinusoids that vanish at t=1 and t=2

so accordingly, you'll have $\lambda_k = -k^2 \pi^2$ i think? i might be a little off

[ocean seal]

Ann

[vagrant rover]

I'm getting 4.472135955 when solving the equation, but that is not a possible answer. Am I doing it wrong?

[gray isle]

not an equation, also how are you getting that value?

[vagrant rover]

I mean expression

[gray isle]

you're not putting your parentheses in the correct locations

also
hint: you should do this without the aid of a calculator

the square root radical is being applied the the 6s ONLY

$\sqrt{a} \pm b \neq \sqrt{a \pm b}$

[ocean seal]

ℝamonov

[vagrant rover]

That's confusing

Ohhh

Ohhhh, okay. I didn't know that.

Awesome, thanks!

-10

[fallow igloo]

How is this supposed to be done?

@vale wigeon

[vale wigeon]

$\bd{u} \cdot \bd{v} = \nrm{\bd{u} } \nrm{ \bd{v}} \cos(\theta) \ \nrm{\bd{u} \times \bd{v}} = \nrm{\bd{u} } \nrm{ \bd{v}} \sin(\theta)$ \ where $\theta$ is the angle between $\bd{u}$ and $\bd{v}$

[ocean seal]

Ann

[fallow igloo]

but i dont know the angle between those, do i?

[vale wigeon]

you dont need theta itself

consider: $(\bd{u} \cdot \bd{v})^2 + \nrm{\bd{u} \times \bd{v}}^2 = \nrm{\bd{u}}^2 \nrm{\bd{v}}^2$

[ocean seal]

Ann

[fallow igloo]

so it has to be 6

thanks again :D

[vagrant rover]

Can someone explain this question to me? Does it want an answer that does not look like this: x^2-y^2

What does it mean by "the difference of two squares"

[shell widget]

Yes

[vagrant rover]

Ah okay

Ty

[shell widget]

It wants you to find out an expression which is not of the form x^2 - y^2

btw

x^2 - y^2 = (x-y)(x+y)

so try to look for an expression which is not of the form (x-y)(x+y)

[vagrant rover]

Interesting, interesting. Ty!

[shell widget]

np

[vagrant rover]

B, right? Just by looking at it. Both sides are being subracted.

@shell widget

Or should I dip deeper?

I'm just gonna dig deeper

[shell widget]

not sure tbh, question is kinda weird. (81 - x^2) itself is difference of two squares

[vagrant rover]

Yeah, I'm not understanding how it's supposed to be solved.

[shell widget]

im thinking it's A

because (4x^2 - 36) can be written as [(2x)^2 - (6)^2] which is the difference of two squares

But (36 + 4y^2) is not the difference of two squares

[vagrant rover]

https://tenor.com/view/understand-nothing-michael-scott-the-office-steve-carrell-gif-7915947

[shell widget]

In B, we have difference of two squares two times

xd

[vagrant rover]

xd

[shell widget]

Ok no problem, let me explain

For option B

[vagrant rover]

Right

[shell widget]

We have (81 - x^2) (81 - x^2)

[vagrant rover]

Yes

[shell widget]

Which is [(9)^2 - (x)^2] [(9)^2 - (x)^2]

Yes?

[vagrant rover]

Yup

[shell widget]

Now as you can see, we have something of the form x^2 - y^2 two times

so we do have the difference of two squares

Two times here

[vagrant rover]

Oh

Wait so x^2 - x^2 is also not what we're looking for?

Okay okay, I got unnecessarily confused.

[shell widget]

x^2 - y^2*

we are looking for an expression that can not be written as x^2 - y^2

[gray isle]

as written both A and B are valid options

[vagrant rover]

So the question is written wrong?

[shell widget]

I know ramonov, but I think they want us to see that 36 + 4y^2 isn't difference of two squares

[gray isle]

it feels like the y in A should be an x or vice versa

[shell widget]

yeah

part c and d are both difference of squares

so it's definitely A i think

[rich basin]

I need help understanding getting the tangent at a point of a function

[shell widget]

since B is also correct

try another channel

[vagrant rover]

One second, let me review what you guys just said

[gray isle]

if

it feels like the y in A should be an x or vice versa
then the answer would be B only.
B is a square

[vagrant rover]

Can't we just write (36 + 4y^2) as: (18^2+ 4y^2)

[shell widget]

but difference of two squares is being applied

no?

2 times

[vagrant rover]

And then wouldn't that be difference between two squares?

https://tenor.com/view/calculation-math-hangover-allen-zach-galifianakis-gif-6219070

[gray isle]

it seems the goal of the question is to identify the factorisation of a difference of two squares
a^2 - b^2 = (a-b)(a+b)

[shell widget]

how is 18^2 = 36?

[vagrant rover]

Oh wait nvm nvm nvm

Ignroe that

Just ignore that

[gray isle]

a^2 - b^2 = (a-b)(b+a)
would also be valid

[vagrant rover]

So then only B is correct?

[gray isle]

assuming they made a typo with A, yes

[vagrant rover]

What type would they have made?

typo

[gray isle]

the question would more sense if option A was something like:
$$(4x^2-36)(36 + 4x^2)$$
or
$$(4y^2-36)(36 + 4y^2)$$

[ocean seal]

ℝamonov

[vagrant rover]

But that still wouldn't be (a-b)(a+b)

I mean

That would still

[gray isle]

a^2 - b^2 = (a-b)(b+a)
would also be valid
since a+b = b+a

[vagrant rover]

Yeah but wouldn't the correct answer have to have either (a-b)(b-a) or (a+b)(b+a) in order to not be written as the difference of two squares?

I'm sorry if I'm confused

[gray isle]

if the suspected typo was fixed, A would be a difference of two squares

leaving B as the only correct answer

(since B isn't not a difference of two squares)

[vagrant rover]

Right, but the current answer of A is also not a difference of two squares, yeah?

[gray isle]

yes

[vagrant rover]

Because the question could be written incorrectly, it wouldn't be the first time

Alright. I'll email the principle

THanks

[gray isle]

,w expand (4x^2-36)(36+4y^2)

[ocean seal]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by ramonov#0921

[gray isle]

,w expand (4x^2-36)(36+4x^2)

[ocean seal]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by ramonov#0921

[vagrant rover]

This would be a difference of two squares???

[gray isle]

yes

[vagrant rover]

Oh right, you can rewrite 1296

Gottchu

Awesome, thank you so so so mcuh!

[gray isle]

and for B,
individually (81 - x^2) is a difference of two squares,
however (81 - x^2)(81 - x^2) is not

[vagrant rover]

I see. I'm glad I actually understand now

Ty!

❤️

[marsh wren]

is it correctly understood that if i have $QRx=y$ and $Q$ is orthogonal, then i can rewrite it as $Rx=Q^Ty$?

[ocean seal]

iBoughtWinrar

[vale wigeon]

yes, by multiplying both sides by Q^T