help-0

[alpine sable]

DOODLEBOB

tiggle like im real spongebob u could be like patrick

but like im spongebob

[vast ether]

Nah I've been spongebob my whole life. I'll let you be squidard tho

[alpine sable]

https://tenor.com/view/spongebob-gif-10166169

LULULULULUULULULULULULU

TIME TO GET CATCH JELLYFISH

LULLULULUUL

[vast ether]

1. Give each side of the triangle a label

2. Use that label to decide which trigonometric identity to use

ULULULULULULULULULUL

[alpine sable]

ULULULULULULULULULUL

[vast ether]

Those jellyfish dont stand a chance

[alpine sable]

fax

[vast ether]

@halcyon cloud ^

[alpine sable]

https://tenor.com/view/spongebob-squarepants-dance-happy-dance-歡快-gif-5084836

I LIKE SHAKING MY SQUARE BOOTY

LEFT TO RIGHT

[vast ether]

Damn look at him go

[alpine sable]

https://tenor.com/view/plankton-evil-laugh-evil-laugh-spongebob-gif-7256015

I HATE THIS GUY

[vast ether]

Me & the bois all hate plankton

[alpine sable]

yk whos cute though

[vast ether]

Everyone's secret crush

[ashen wave]

that dump truck tho 😩

[sly mantle]

@alpine sable @vast ether keep offtopic posts away from the help channels

[halcyon cloud]

thanks @vast ether

can u help with something else?

[alpine sable]

sorry

[ashen wave]

is anyone here good with quadratic functions?

[vast ether]

Hit me

[ashen wave]

A rectangular pen is to be built along a wall from 72 yards of fencing. Find the maximum area that can be enclosed and the dimensions of the pen.

[vast ether]

Understood

[vast ether]

Yes

[halcyon cloud]

this practice is due in 10 minutes

[ashen wave]

@vast ether

I think he might have went afk

[frank cave]

is this channel occupied?

[ashen wave]

no one is rlly on here :/

[frank cave]

i know 1, 4, and 25 are squares but idk how I get a recursive sequence from that

[gray isle]

consider (-2 +1)^2 = 1
etc

[stable dune]

is this 15^2+12^2=c^2?

[frank cave]

wdym?

[gray isle]

consider (1 + 1)^2 = 4

etc

[hybrid pike]

Ping me if you have time to help me. Sorry, I don't know how this server works

[glass lichen]

#❓how-to-get-help

[frank cave]

wait so its like a_n = (a_n-1 + 1)^2 ?

[gray isle]

use appropriate parentheses pls

[ashen wave]

Hi moshill!

[gray isle]

a_n = (a_(n-1) + 1)^2

[ashen wave]

oh moshil do you mind helping me out xD?

I know ur good at quadratic functions

[frank cave]

?

[ashen wave]

And i need help with word problems rip

[gray isle]

fk discord formatting

[ashen wave]

A rectangular pen is to be built along a wall from 72 yards of fencing. Find the maximum area that can be enclosed and the dimensions of the pen.

[frank cave]

$a_n = (a_{n-1} + 1)^@$

[ocean seal]

oof

[frank cave]

replace @ with 2

lol

[gray isle]

yes

[frank cave]

aight thanks

[glass lichen]

then also you need to write a_1

[gray isle]

that too

[wild shard]

How would I solve for ray torus intersections

[frank cave]

yea a_1 is just -2 right

[ashen wave]

could you help me T-T

A rectangular pen is to be built along a wall from 72 yards of fencing. Find the maximum area that can be enclosed and the dimensions of the pen.

[glass lichen]

yes

so $a_n=(a_{n-1}+1)^2\a_1=-2$

[ocean seal]

moshill1

[frank cave]

let length be x width be y

2x+2y = 72 so x+y=36

so x=36-y

[ashen wave]

how do you know which is which?

[frank cave]

it doesnt matter

i just chose those variables

[ashen wave]

oh

wait did you use ax^2+bx+c?

[frank cave]

and the area is x*y correct?

[frank cave]

no

[ashen wave]

A=L*W?

[frank cave]

wait i might use that

later

[ashen wave]

then yeah

[gray isle]

setup is wrong

[frank cave]

its been a while since i've done this lmaoo

[gray isle]

built along a wall implies that only 3 sides need fencing

[ashen wave]

right

[frank cave]

o yea

listen to ramonov

[gray isle]

drawing a diagram also helps

[ashen wave]

okk so like a square with a wall instead of the 4th side

[gray isle]

not a square, rectangle

[ashen wave]

oh right!

oh wait there is no wall in this question

[gray isle]

A rectangular pen is to be built along a wall

[ashen wave]

oh oops i misread it

alright now what?

[gray isle]

have you drawn your diagram

[ashen wave]

yep

[gray isle]

can you show what you've drawn

[stable dune]

isnt it a^2+b^2=c^2

[ashen wave]

hold on let me go get my phone

[stable dune]

but 20^2+b^2=29^2?

[gaunt sparrow]

Is the answer 21?

[stable dune]

im not sure

[gray isle]

but 20^2+b^2=29^2?
hopefully this will be very short.
yes continue

[stable dune]

okok

so 20^2 is 400

and 29^2 is 841

400+b^2=841

[next lynx]

de(mod x)=1 is there a way i can find d given the values for e and x ?

[stable dune]

841 minus 400\

thats 441

square root of 441 is 21

[frank cave]

is there another way to do part b without using the graph as justification?

[gray isle]

evaluate the limit algebraically

[frank cave]

what limit would i evaluate?

[gray isle]

limit as n→inf of the nth term of your sequnece

$\lim_{n \to \infty} b_n$

[ocean seal]

ℝamonov

[frank cave]

ah ok how would i do part c?

[alpine sable]

boys i have a question

what do i do

?

[gray isle]

well since you're dealing with a sequence, n will be an integer
cos(pi * n) will alternate between -1 and 1

[alpine sable]

do you know how to use a notpad

like a whiteboard that is online

just draw it out and send it pls

[frank cave]

but how would that change if n >= 4?

[gray isle]

doesn't change much

[frank cave]

so how would i write the explicit formula?

[frank cave]

since it cant be recursive right

[gray isle]

it isn't really clear what they actually want

[frank cave]

i thought like explicit formula works for every b_n term

[ashen wave]

shoot I forgot about discord

[gray isle]

well you're already given an explicit formula

[ashen wave]

I got my phone ;-; lmao

and had lunch rip

[gray isle]

by rewrite, the best i can infer is rewrite the cos(pi * n) as a power of (-1)

[frank cave]

yea i dont think it would change much for N >= 4.

[frank cave]

wdym. how would i rewrite it?

[ashen wave]

sorry I took so long but could you still help me?

[gray isle]

label your length and width

[hollow grove]

hi guys

can anyone help me ?

please

[gray isle]

cos(pi * n) will alternate between -1 and 1
specifically cos(pi * n) will be 1 for even n
and -1 for odd n

ok using those dimensions set up an equation for the amount of fencing

[hollow grove]

guys?

[ashen wave]

wait what?

how would I do that

what equation format

[hollow grove]

can y'all help me how to draw this thing

[ashen wave]

A=L*W?

[gray isle]

that's the equation for area which will be useful later

[frank cave]

but for N>= 4 theres both odd and even n right?

[gray isle]

according to your diagram, how much fencing will there be?

use something like (-1)^(n)

[frank cave]

o wait so it would be like (-1)^n / (n+1)

since for even's

[gray isle]

that's my guess at what the question wants

[frank cave]

aight thanks

[ashen wave]

im confused :/

[gray isle]

according to your diagram, how much fencing will there be?

(in terms of L and W)

don't overthink this

it's not supposed to be a trick question

[ashen wave]

wait give me a sec

[ashen wave]

idk W+W+L

idk

oh wait

aren't we supposed to be talking about perimeter?

72 yards of fencing

[gray isle]

yes

i'm leading up to that

according to your diagram the amount of fencing will be
W+W+L

and you are told that the numerical value will be 72 (yards)

hence the equation you would set up is
W + W + L = 72

[ashen wave]

oh ok but when it talks about 72 yeards of fencing is that referring to the area orr?

[gray isle]

72 yards of fencing refers to the amount of fencing

says nothing about area

Area is what you're trying to optimise

yards is a measurement for distance not area

[ashen wave]

wait so 72 is the width and the length added up?

[gray isle]

72 is the sum of the lengths of your 3 fences

[ashen wave]

ohh ok

[gray isle]

W + W + L = 72

[ashen wave]

oh ok

[gray isle]

now

A=L*W

ideally you want to get the area in terms of 1 variable

so you could isolate W or L from W + W + L = 72
and then sub that into your equation for area

here it seems isolating/substituting L would be less tedious

[ashen wave]

is there a difference from using L or W

isolating*

[gray isle]

the end result will be the same

[ashen wave]

oh ok

[gray isle]

calculations using 1 may be less tedious than the other

[ashen wave]

oh so isolating L is easiest?

also how would you sub it into A=L*W

[gray isle]

replace L with whatever L is

[ashen wave]

but what is L?

A rectangular pen is to be built along a wall from 72 yards of fencing. Find the maximum area that can be enclosed and the dimensions of the pen.

it doesn't give it to you

[gray isle]

W + W + L = 72
is one of your equations

[ashen wave]

right

[gray isle]

what happens when you isolate L

[ashen wave]

erm

i dont really know T-T

[gaunt sparrow]

Um........whats the question again?

[ashen wave]

A rectangular pen is to be built along a wall from 72 yards of fencing. Find the maximum area that can be enclosed and the dimensions of the pen.

[gray isle]

you're doing optimisation and quadratics now

you should definitely be capable of isolating a certain variable

are you able to solve something like
x + 4 = 5

(for x)

[ashen wave]

yeah

x=1

[gaunt sparrow]

Wdym by 72 yards of fencing? Is that the perimeter?

[ashen wave]

yeah I assume

[gray isle]

and what's stopping you from applying the exact same principles for
isolating L for
W + W + L = 72

[ashen wave]

L=72-2W

?

[gray isle]

yes

exactly

[ashen wave]

oh

ok

[gray isle]

now sub that into your equation for area

[ashen wave]

alright

for width do I put x or w

[gray isle]

well you defined your width to be W...

so why would you use anything else

[ashen wave]

my teacher used X tho

that's the answer key

She usually defines the variables to the side as well

[gray isle]

use whatever variables you initially chose,

be consistent

it's all personal preference

very similar to the other one you had earlier

yes, +2 then square

[frank cave]

aight thanks man

[ashen wave]

alright now what should I do?

[gray isle]

what do you have atm

[ashen wave]

is that right?

[gray isle]

use whatever variables you initially chose,
be consistent

[ashen wave]

oh alright so is it ok if I erase the L and W in the beginning and keep X and Y

[gray isle]

your labels on your diagram should match everything else you're writing down

[ashen wave]

oh ok ill change that too

[gray isle]

don't feel the need to follow your teacher's use of variables

use whatever feels natural and are most comfortable with

[ashen wave]

but what if she takes points off

alright

now what should I do?

[gray isle]

identify the location of your vertex of your quadratic

[ashen wave]

X=-b/(2a)???

[gray isle]

parentheses in the wrong location

and also use lowercase a and b

parentheses still in the wrong location

x = -b/(2a)

[ashen wave]

oh

there xD

[gray isle]

alternatively you could also identify the roots from the factored form and take the average

[ashen wave]

So I factor it out then use the vertex thing

can I use this form tho?

[gray isle]

for the purposes of this question you don't need that

[ashen wave]

oh ok

oh yeah you dont xD

the width is 18

[dusk panther]

Can someone explain how to do this?
I’m supposed to use inverse trig but I’m confused

[ashen wave]

is the width 18

[gray isle]

yards, yes

[sly mantle]

$\trig$

[ocean seal]

RokabeJintaro

[gray isle]

@dusk panther do you know your sohcahtoa?

[dusk panther]

Yes

[gray isle]

first, use the appropriate trig function to relate your given sides and angle

[marble panther]

is that wiley plus?

freaking hate the website

[muted raft]

because thats not in vertex form.

[gray isle]

well firstly you didn't do anything for the vertex form

[alpine sable]

do u guys know how to solve trig equations

[cerulean slate]

I thought it was already in vertex form

[alpine sable]

kinda, change the question channel to unoccupied one, i'll try to help you

[dusk panther]

I was given a new formula to use but it’s not working so I think I did it wrong

[gray isle]

start with the basics

gettin so crowded here

everyone except for jasmine should move

[gaunt sparrow]

Where

[sly mantle]

jasmine was here 1st?

[gray isle]

start with the basic trig function to relate your angle and given sides

[sly mantle]

ram are you handling axelle too?

[gray isle]

can't multitask atm

[dusk panther]

Ok so I’m supposed to use one of the three either sin/cos/tan for the triangle depending on the sides

[gaunt sparrow]

Can I help?

[sly mantle]

ax is in q3 if you can help

[gray isle]

yes. you said you knew your sohcahtoa so you should know which would be the most appropriate function to use here

[dusk panther]

Yeah that bit I can understand but when it comes to actually putting in the new stuff that’s where I start to mess up

[gray isle]

like I said. start with the basic first

start with what you know

the basic trig function to relate your angle and given sides

can't really move on if you don't do that first

[ashen wave]

i need help

[dusk panther]

Yeah ok I’m gonna send the picture again

[ashen wave]

the sum of a number and its square is 72. What is the number?

[alpine sable]

@dusk panther check trigonometry rules for triangles

[dusk panther]

So I labeled the sides on paper the opposite/adjacent/hypotenuse

[alpine sable]

@ashen wave set up an equation to solve

[gaunt sparrow]

x + x^2 = 72

x + x^2 -72 = 0
Solve fornx

[gray isle]

what's the position of the 15 (relative to theta)?

[ashen wave]

how did you get x^2 tho

[gray isle]

what's the position of the 19

[gaunt sparrow]

It's in the question. The sum of a number and it's square. Let the number be x. It's square will be x^2

[dusk panther]

19 is the hypotenuse

[alpine sable]

What about the 15

[rough spear]

adjposite

[dusk panther]

Isn’t 15 the opposite

[ashen wave]

is there going to be more than one answer then?

[gray isle]

no. the side with length 15 is NOT opposite theta

[dusk panther]

So it’s the adjacent which would mean that you would use cos for the triangle?

[gray isle]

yes

[dusk panther]

I don’t know what I’m supposed to do after that. I know that I have cos^-1 (15/19)

[alpine sable]

<@&268886789983436800>

[chilly hatch]

thank you

[alpine sable]

👍

[crimson summit]

does someone know how to find a derivation of the formula ¬¬P ∧ ¬Q in natural deduction so that ¬Q ∧ P is the only open assumption in the derivation?

[fast vigil]

holy

what kinda math is dat

[heavy otter]

@fast vigil get a better nickname

[fast vigil]

yes

aight

im off

[crimson summit]

someone who may know how to do it and can explain me?

[shrewd oracle]

logic

[alpine sable]

take square roots of both sides

[mellow anchor]

ok then?

x+9=6

do i add the plus or minus sign?

[alpine sable]

yes

x+9=+-6

split it up into two cases

[mellow anchor]

mhm

[alpine sable]

x+9=6 or x+9=-6

solve each one

[mellow anchor]

x=3 and x=-3

[alpine sable]

no

[mellow anchor]

wait

[alpine sable]

x+9=6
what is the solution for this case?

[mellow anchor]

x=-3 x=-15

[alpine sable]

correct

[mellow anchor]

thank you

[mellow anchor]

[alpine sable]

can someone help

[ionic jewel]

what have you done so far?

[alpine sable]

found derivative of both

and then i put them equal so e^x + e = 2e

[glass tide]

is this simplification I did illegal?

or is it V = Q / (E * A * d)

[ionic jewel]

i think yours is right

[ionic jewel]

is there a reason solving this for x doesn't work?

[glass tide]

thanks bunny

[oak chasm]

No, but $d \ne 0$ is now required.

[glass tide]

I don't understand

[ocean seal]

Chai T. Rex

[oak chasm]

It was in the denominator of a fraction before, right?

And denominators can't be zero, even if they're later not denominators.

[glass tide]

ohh

that is true

good catch

[alpine sable]

@vivid comet number 1 isn't correct.

assuming you're looking for... domains of these functions?

in math i don't recommend you memorising methods like a robot.

nor this server supports it.

so let's step back first, do you know what the domain of a function is?

can you try to define it for me with your words? just to be sure.

i'm interpeting this as you have the right idea of it but you don't know how to word it.

the domain is pretty much the set of all x allowable values in this context.

instead of running around through these without a proper grasp of what a domain is, let's have an example. do you know what we can't have in the denominator of a fraction?

right. bc we don't want to be dividing by 0.

and in an example, f(x)=1/x, what would you do to find the domain?

i mean, what did you do to solve it. what was your thinking process to arrive to that?

no. on this example i just gave you

ok. if you had a function like g(x)=1/(x-3), i'm guessing you'd probably solve for x-3=0, right?

yeah.

do you know and understand why do we do this?

if you don't, please tell me, i want to build a base before moving onto the problems.

ok that's fine.

by equating the denominator to 0 on a fraction, like you just did on x-3!=0, you are solving for the values of x that make the denominator to be 0.

[rapid pecan]

how do you find x?

[somber stone]

With ease

[alpine sable]

@rapid pecan please read #❓how-to-get-help , this channel is occupied.

you don't just randomly find a fraction and think oh you equate it to 0, you want to think why you do it, once you understand the reason of methods, not doing this it's pretty much what's causing you all the issues.

what is this?

no, read what i say carefully. we want to know which values of x make the denominator to be 0. hence solving the equation of denominator=0. if you solve the eqn you will get all the x values that make the denominator to be 0 and hence, the values of x that are excluded from the domain.

$$\overbrace{{\color{green}{x-3}}}^{\text{we want to know which values of}\ x \text{ make the {\color{green}{denominator}}}}\overbrace{=0}^{\text{to be 0}}$$

[ocean seal]

Al𝟛dium

[alpine sable]

no, x is a variable, take a few minutes to try to understand what and why we are doing this.

by solving $x-3=0$, we are solving for the values of x that will make the denominator to be 0. $x-3=0 \implies x=3$. and you can check by yourself that by inputting $x=3$ into the function will make the denominator to be 0. $$g(3)=\frac{1}{3-3}=\frac10$$

[ocean seal]

Al𝟛dium

[alpine sable]

we are almost there, but i can't do much about the time.

is this a test?

[flat estuary]

I have no clue what that means.

Its algebra right?

[alpine sable]

okay. we don't give away answers here, so i can't do much about the time except for you to try to grasp a good concept of this.

[flat estuary]

Is algebra important???

[alpine sable]

..yeah. if you don't have any math question but you want to discuss about math, please move to #math-discussion

as i said, i can't do much about the time.

are you willing to continue this?

think of it. is there anything that you want to avoid when there's polynomials like 1?

oh no worries, an example of a polynomial is number 1, another examples could be: x²+1, x³-7x+4, 8x+2, etc.

involves not having fractional exponents, ie not having fractions or roots.

can you really think of any restriction that we want to avoid in polynomials like 1?

tell me what you think, don't worry of being wrong.

you are here to learn.

well, i have to go in 10 minutes precisely to go sleep. if you are interested, we can proceed tomorrow if you tag me to ask any doubts or anything, or you can as well ask away here.

yeah.

[limpid spade]

No

[alpine sable]

you may want to errase the black ink parts though.

[limpid spade]

Nvm

[alpine sable]

yeah no, there's a mistake at 2.

[limpid spade]

, yes

Not greater than 4x5

4,5

[alpine sable]

when dividing both sides by a negative number, you want to flip the inequality sign.

and you can take an example to understand why, let's say 5>4, this is totally correct, now let's multiply both sides by a negative number like -1, -5>-4, would you say this is correct? no, you want to flip it, -5<-4.

[limpid spade]

, <, etc

[alpine sable]

no worries, i'll just leave a wall of text before heading to sleep.

whenever you read this, read it carefully, it will help build intuition you are missing of right now.

what do we want to avoid ranges with examples like:

• dividing by 0
• having a negative number inside a square root or an even-th root.
• having a non-positive number inside a logarithm.
  these are the basic ones, and you want to remember them whenever you're finding domains of functions, but most importantly why. take h(x)=sqrt(x-3), now think, what do we want to avoid? having negative numbers inside square roots, hence we want to find the values of x that are allowed, the non-negative numbers. and we are going to find this precisely by solving x-3≥0. finding where the inside (x-3) is a non-negative (≥0) number, hence x-3≥0. you can apply this logic for each, just be sure you think why you are doing each thing.

[north hemlock]

How exactly does one solve b?

[shell widget]

differenciate both sides with respect to x

actually no need for chain rule here mb

[north hemlock]

ahhh

of course

6y-3x-1

[shell widget]

No

[north hemlock]

I'm not sure what else it'd be

$$\frac{d^2y}{dx^2}=\frac{d}{dx}[3y-x]=\frac{d}{dx}[3y]-\frac{d}{dx}[x]=3y'-1$$ and then just simplifying $$3\cdot (3y-x)-1=6y-3x-1$$

[ocean seal]

Jukelyn

[north hemlock]

this is correct, no?

LMFAO 3 TIME 3 = 6

[violet storm]

Hello anyone here?

[stiff vortex]

Can someone help

i cant get the right answer

i keep getting 3000

and using the exact formulas

[oak chasm]

@stiff vortex Find the surface area of the two circles (top and bottom). Find the surface area of the curved rectangle that's its side.

[stiff vortex]

curved rectangle?

dude

[oak chasm]

Yes, the side is a rectangle that's bent into a circle.

[stiff vortex]

pretty sure it's a cylinder

[oak chasm]

Right, and if you take a rectangle of steel and bend it into a circle, that's how they make cylidrical cans.

[stiff vortex]

true

let me show u what im about to do

hold on

[oak chasm]

So, the width of the rectangle is the circumference of the circle. The height is 14.

[stiff vortex]

ik

somehow i keep getting a wrong answer

[oak chasm]

OK, show your work. Let's see.

[stiff vortex]

bet

[manic quail]

,w 216^2 pi+32pi14

[ocean seal]

Results provided by WolframAlpha

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

Requested by veryhappyperson#1152

[stiff vortex]

yeah thats what i got

960 * pi

[manic quail]

I get 3000 too, what do I do wrong here?

[stiff vortex]

Samee

[violet jetty]

You used diameter instead of radius

[manic quail]

Where?

[violet jetty]

Wait no you didn’t

One sec

[ocean seal]

Chai T. Rex

[manic quail]

I did that.

[violet jetty]

Yeah, answer is like 3015, question is wrong.

[manic quail]

Ahh, okay.

@stiff vortex

[stiff vortex]

exactly

[oak chasm]

Yep, no answers fit.

,w 2 16^2 pi

[ocean seal]

Results provided by WolframAlpha

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

Requested by Chai T. Rex#7323

[oak chasm]

,w 32 pi 14

[ocean seal]

Results provided by WolframAlpha

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

Requested by Chai T. Rex#7323

[stiff vortex]

yyep

[oak chasm]

Not even leaving out a part helps.

[stiff vortex]

i got 3.29 for this question.. doesnt seem right to me

[alpine sable]

make up an equation

[stiff vortex]

let me show u how i got to 3.29 hold on

i may get a different answer in the process lol

[alpine sable]

think it's a cylinder

O=2⋅π⋅r⋅h

[oak chasm]

@stiff vortex No, it's somewhat higher.

[alpine sable]

180,64=2⋅3,14⋅2,5*h

solve

[oak chasm]

Oh, wait

[alpine sable]

@manic quail no, it's the surface area.

[manic quail]

You forgot adding the 2 circles, didn't you?

[alpine sable]

A=2⋅π⋅r⋅h+2⋅π⋅r2

yez

there

[stiff vortex]

holy shit reading the formula and not figuring it out myself is so unintuitive

[oak chasm]

@stiff vortex That can can't exist.

[stiff vortex]

wdym

[alpine sable]

[oak chasm]

,w height of cylinder surface area 180.64cm^2 diameter 5 in

[ocean seal]

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Requested by Chai T. Rex#7323

[oak chasm]

A 5 inch diameter makes the bottom and top take more area than the can's area.

,w 5 in to cm

[ocean seal]

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Requested by Chai T. Rex#7323

[stiff vortex]

wow

[oak chasm]

,w 2 (12.7/2)^2 pi

[ocean seal]

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Requested by Chai T. Rex#7323

[stiff vortex]

yeah this is some weird homework lol

even worse theres no multiple choice on the question

making it way harder

[oak chasm]

Yeah, I'd just show that the area of the top and bottom is greater than the area of the whole can and then say the can can't exist.

[stiff vortex]

@oak chasm so ur saying that it's practically impossible for me to get an answer

[oak chasm]

Yeah, the height is negative.

So, the can can't exist.

Don't forget to convert the 5 inches to centimeters, though.

They're being tricky.

[stiff vortex]

oh shit

[oak chasm]

The area is in square centimeters, but the diameter is in inches.

[icy wadi]

hello could someone help me with this? i'm not sure how to start

[oak chasm]

@icy wadi Do you understand how they start with a square, and then cut isosceles triangles from the corners of the square and how that makes an octagon?

[icy wadi]

yes i get that

[oak chasm]

OK, it's a regular octagon, so all its sides are the same length.

OK, so draw that on a diagram.

The top side of the octagon will be $2000 - 2 \times $ the leg length of one of the isosceles triangles, right?

[icy wadi]

yea, i got x sqrt(2) for the hypot lengths of the isoceles triangles, i used x for the leg lengths

[oak chasm]

OK, and that equals the hypotenuse of an isosceles triangle, since the hypotenuses are octagon sides too.

[ocean seal]

Chai T. Rex

[oak chasm]

So, solve for the leg length.

[ocean seal]

Chai T. Rex

[next void]

Can I get some help with parts b and c?

There are about 3 million births per year in a certain country and about 4800 hospitals. For the sake of simplicity, suppose the births over a ten-year period were evenly distributed over all the hospitals, and suppose each of those hospitals divided their births into strings of 19 consecutive births. Assume that boy and girl births are equally likely.

(a) What is the probability of 19 births in a row being boys?

(b) What is the probability, in any one of those hospitals, of having a string of all boys?

(c) Based on your answer to part (b), what is the probability that at least one of those
4800 hospitals would have a string of all boys?

I already solved part a and got 1.907x10^-6. I am not sure how to solve b or c.

[next void]

<@&286206848099549185>

[keen sluice]

Can anyone help

/just send answer and work

Lolll

[muted raft]

no

[sullen nova]

Yo

Pls halp

Halp

<@&286206848099549185>

[misty moat]

can any1 help me with Geometric probability?

[charred flint]

sure

[misty moat]

ok

[knotty garnet]

Imagine that every point has an equal chance of being selected

That means that the more area, the higher the probability

Twice the area, twice the probability

Does that give you a hint?

[misty moat]

uhh no lmao

i need to know the method

[ionic jewel]

he pretty much gave you the answer

that area of the blue over the area of the whole circle

[misty moat]

yes but how do i work that out xd

how do i find the area of the blue

[ionic jewel]

how many degrees is a full circle

how many degrees is your section

whats the ratio

[misty moat]

360

78:360

78/360

[ionic jewel]

great now whats that as a percent

[misty moat]

21.66666667%

[ionic jewel]

,calc 78/360

[ocean seal]

Result:

0.21666666666667

[ionic jewel]

yep

[misty moat]

then?

[ionic jewel]

then what?

[misty moat]

is that the area of the blue?

[ionic jewel]

no thats the percent of the circle thats blue

[sullen nova]

Lmao

That’s easy

[misty moat]

@sullen nova whats the answer then

[ionic jewel]

you already answered it

its 21.667%

[misty moat]

k

[ionic jewel]

sorry do you have a question?

read the rules

[misty moat]

how do i get the area of the whole circle?

[ionic jewel]

you dont need it

it asked what percent of the circle is blue

you solved for it

[misty moat]

yeah

[sullen nova]

Do you know the formula how to get the area of a circle?

Hello pls halp

[ionic jewel]

you literally came in here, called someone elses problem easy, then broke the rules

[misty moat]

,calc 74/360

[ocean seal]

Result:

0.20555555555556

[ionic jewel]

dont expect immediate help

[sullen nova]

you already answered it

[misty moat]

0.206

[ionic jewel]

no!

its 78 not 74

[misty moat]

i got it wrong so i have a dif question

[ionic jewel]

whats your new question

[ionic jewel]

ah yes

that one is 20.556%

0.206

i guess

[misty moat]

i need to round it dont i?

k

yeah it was correct

thanks

[ionic jewel]

👍

[sullen nova]

<@&286206848099549185>

[ionic jewel]

didnt you already ping helpers dude

inconsiderate

[low geyser]

i got a question

[ionic jewel]

[low geyser]

ok ok

what is 2+2

its fish right

[ionic jewel]

fantasic

dont you have better people to be trolling

[low geyser]

lol

ight ight

answer dis

C=
5
9
(F−32)

The equation above shows how temperature F, measured in degrees Fahrenheit, relates to a temperature C, measured in degrees Celsius. Based on the equation, which of the following must be true?

A temperature increase of 1 degree Fahrenheit is equivalent to a temperature increase of
5
9
degree Celsius.
A temperature increase of 1 degree Celsius is equivalent to a temperature increase of 1.8 degrees Fahrenheit.
A temperature increase of
5
9
degree Fahrenheit is equivalent to a temperature increase of 1 degree Celsius.
A) I only
B) II only
C) III only
D) I and II only

i need it

[sullen nova]

i need too

[low geyser]

i needs

[sullen nova]

Why are you using Fahrenheit

[low geyser]

huh

idk

i wanna see if dey can answer

[ionic jewel]

you could at least bother to format the fractions without just posting it

[sullen nova]

he doesn't give a shet

it seems like

[ionic jewel]

at least he didnt ping helpers a bunch of times

[twilit sierra]

i have maths exam on monday 💔😥

[low geyser]

lol

[twilit sierra]

xD

[low geyser]

enjoy

[twilit sierra]

thx xd

[low geyser]

i succ at math

answer da question

wait

If 3x−y=12, what is the value of 8x/2y?

A) 212
B) 44
C) 82
D) The value cannot be determined from the information given.

[charred flint]

think about this problem:
If x+1=y, what is the value of x/y?

[low geyser]

huh

im to slow

when dey leave you alone n dont answer yo question

Pain 😦

[acoustic shadow]

You can’t find the value of an equestion with 2 variable with only 1 equation

[low geyser]

hehe

y

[acoustic shadow]

Ping me if you’re asking me lol

[low geyser]

ohhh

my bad

i forgot how to work discord

;-;

[low geyser]

i jus wanted to get a problem off da web idk wat to ask

;-;

[acoustic shadow]

The value be determined

Because you need ATLEAST 2 equations to find the values of x and y

You can solve equations by either substitution or elimination of the variable

[low geyser]

ohhhhh

well

idk wat to ask

[acoustic shadow]

Ok 😂

[low geyser]

lol

im jus bored low key

Points A and B lie on a circle with radius 1, and arc AB has a length of π/3
. What fraction of the circumference of the circle is the length of arc AB?

can you answer dat

[teal frigate]

hey is this channel busy

[low geyser]

yes

me n my friend make n cake

u want sum

[low geyser]

hey hey

[sullen nova]

Yo halp

[low geyser]

dats to hard

u trip n

[fickle dock]

Hey, so I ended up with an undefined answer but the answer is -infinity -you can tell by looking at the graph), but I was wondering if there's a way to find it purely algebraically?

[charred flint]

you got rid of the limit too early

limit of tan(x) as x approaches pi/2 from the right is -infinity

[fickle dock]

Right, but is there no way to algebraically determine that instead of having to look at the graph?

Like sometimes I get an answer that’s 1/infinity, that way I know the limit is 0, but with this I don’t have much to work with other than plugging in small values and evaluating them with a calculator or graphing

[upbeat shadow]

I’m reviewing for the ap exam, could someone help me with this question?

I put b

[charred flint]

b would be right if it was asking where the velocity is positive

[upbeat shadow]

How do you tell when the velocity is increasing?

[charred flint]

that's related to if the graph is curving upward or downward

and the inflection point tells you when it switches between the two

[upbeat shadow]

Ok so E?

[upbeat shadow]

E, no? I just want to make sure

[charred flint]

A

the green part of my pic

[upbeat shadow]

So the orange would represent decreasing

[charred flint]

right

[upbeat shadow]

Ok thanks

[hot osprey]

hello

What's the fastest way to find the real zero? since it's both plus & minus values, I don't want to go through the hassle of trying every possible zero.....
for example if i get a possible zero question with 36 as a constant.... yeah no, i'm skipping.
Also is there a way to determine whether it would be pos or neg for sure?

if i have a question where f(x)= x^3+x^2-5x-5, where none of the possible zeros give me a linear factor, what do i do?

[low geyser]

can we bake a cake

🙂

[hot osprey]

Really could use some helping hand....

[worthy kelp]

I have a question. If I am asked how many ways I can get 25 cents with pennies nickels and dimes, is there any way to solve that without writing out all the possibilities?

[charred flint]

not really, but you'll see a pattern when you count them

you want to go case by case on the biggest denomination, so like 0 dimes 1 dime 2 dimes

[cold roost]

Can you elaborate? Trying to find a zero through rational zero theorem it sounds like

[hot osprey]

oh i solved it now, i was able to factor it into x^2(x+1) -5(x+1) then solved it

but now i am stuck again lol

x^3+4x^2-5x-14. same thing, gotta find real zeros and linear factors

[meager cedar]

Can someone give me the answer i got 56 i wanna confirm it

[wicked drum]

Omg even though I live half the earth away from india, this question is exactly the same as the one I got in my final last year. You can do it in your head once you know the shortcut. Log (final balance/starting balance)/log (the % p.a in decimal)

So it's.. log (10000/1250)/ log (1.125)

[hot osprey]

<@&286206848099549185>

[wicked drum]

@meager cedar it's 17.65 years

[muted raft]

Yeah, i think its 56.

[wicked drum]

56 years my dam broke ass

[meager cedar]

Thank u

[wicked drum]

Np

[cinder sundial]

ayyyyy

what the sign is between those number

(10 * 2/5) or (10 + 2/5)

[ionic jewel]

plus

although you really should write the plus sign

[cinder sundial]

this is the original from my teacher

but how'd you know that without lookin at the right side

i mean it could be 10*2/5 or 10+2/5 or mixed number which gives you 52/5

if the result (108+4/25) of the question didnt being written on the paper, ppl might get mixed up

i wanna know how to distinguish them

[wicked drum]

@cinder sundial don't worry about getting them mixed up. There's no way your teacher would want you to think that it is 10x2/5 instead of 10+2/5, otherwise, it would instead be (10x2)/5. The same can be applied to all number, is that 21 really 21 or just 2x1

[gray isle]

when given positive integers, a mixed fraction is implied

[ionic jewel]

ngl I'd generally interpret it as

$10\frac{2}{5} = 4$

[ocean seal]

bunny

[gray isle]

the point is mixed fractions are stupid

[ionic jewel]

i agree

[gray isle]

and you won't have to deal with them after this

but for the purposes of what you're doing,
$$10 \frac 25 = 10 + \frac 25$$

[ocean seal]

ℝamonov

[gray isle]

when you have stuff like variables then multiplication is implied
$$2\frac k5 = \frac{2k}{5}$$
though ideally they'd still include a multiplication dot
$$2\cdot \frac k5$$

[ocean seal]

ℝamonov

[lunar relic]

How do I solve this differential equation for y? A video or article showing the steps would be much appreciated since I'm trying to understand where some of the equations in my course are coming from.

[sullen nova]

yoooooo

help meh

[hollow atlas]

whats your question ? @sullen nova

[sullen nova]

this

Why do you let yp in that form?

[vale wigeon]

there is a general method for guessing the form of y_p when the RHS of your equation is made of polynomials, exponentials and trig

in general, assuming no resonance:
RHS = polynomial => y_p = polynomial of the same degree
RHS = exponential (e^{kx}) => y_p = Ae^{kx}
RHS = trig (sin(kx) or cos(kx) ) => y_p = A sin(kx) + B cos(kx)

there are a lot of caveats that i didn't cover here

you may want to look up the method of undetermined coefficients @sullen nova

[sullen nova]

how do you come up with those?

[vale wigeon]

i'm not sure what kind of answer you're looking for

if you want some intuition on why it's like this, you might consider how polynomials, exponentials and trig behave when you plug them into the LHS (which im assuming is the LHS of a linear constant-coefficient equation)

[spring harbor]

Given two figures with equal area, calculate the sum of the diagonals of the rhombus. Cos alpha = 0.6

I thought area = 24
so we can say that D+d / 2 = 24 or D + d = 48

but that's not between the options

[novel crag]

How to do this ?

[spring harbor]

channel taken

[vale wigeon]

D+d / 2 = 24
missing parentheses here...

[spring harbor]

sorry
i know

[vale wigeon]

also what does the sum of the diagonals have to do w/ anything here?

[spring harbor]

The question is asking to calculate it

[vale wigeon]

no i mean why are you just claiming it to be twice the area

[spring harbor]

the areas of the two figures are equal

[vale wigeon]

the area is 24 here as far as i can tell

yeah but the area of a rhombus is not equal to 2 times the sum of its diagonals

even the units don't check out

[spring harbor]

yeah but isn't the area of the rhombus (D+d)/2 = A?

[vale wigeon]

no it's not. it doesn't even make sense when you consider the units.

(D+d)/2 is in meters while A is in square meters

[spring harbor]

Ohhh wait it's D * d

[vale wigeon]

yes, the area of a rhombus is half the product of its diagonals

[spring harbor]

So D.d = 48 or D= 48/d

now we use pythagoras

ok i think i have it thanks

dont we get like 4 solutions for d? @vale wigeon

-8, -6, 6, 8

so either 6 or 8

[vale wigeon]

how can a length be negative

6 and 8 are the values of your diagonal

d is one, D is the other

[spring harbor]

o

thanks

[hexed glacier]

before anyone accuses me of asking for help to solve hw questions, my question proper is as below:

why is the question correct? As in, why can't i draw a straight line, m>0, with an open point(?) on the line where x=c.
in drawing, it would be a straight line with a circle at a point.

as far as i know, the conditions of continuity is as follows:

1. limit of f(x) exist for all relevant points
2. f(x) exist for all relevant x
3. limit of f(x) = f(x) for each corresponding x

if i "teleport" a point, it wouldn't be continuous right?

oh...is it because it is monotone

if i teleport it above(where it should be), the next point is below, therefore, it isn't monotone increasing?

but what if i just delete that point then

[rugged peak]

Anyone have some idea to prove this problem

[alpine sable]

#competition-math @rugged peak maybe?

I would multiply whole equasion with x^2*y^2(x+y)^2

and then maybe you can quadratic equation

@rugged peak is it working?

[rugged peak]

I'm stuck
after I multiply with x^2*y^2(x+y)^2
will get
(x^2+y^2)(x+y)^2 + x^2y^2 = 2021 x^2y^2 (x+y)^2
I have no idea to reduce as quardaric equation

@alpine sable

[alpine sable]

yes

now simple that

short it

[spring harbor]

Given sin(x) = 1/3 and pi/2 < x < pi, what is sin 2x?

sin 2x = 2sinx cosx
cos x should be sqrt(8)/2
so is my answer 1/3 * 2 * sqrt(8)/2?

[alpine sable]

yes

[spring harbor]

I feel like it's wrong because of the pi/2 < x < pi

[alpine sable]

well cos(x)=sqrt(1-sin²x) holds for every x

so i dont see a problem

[spring harbor]

but I got 2sqrt2 / 3

@alpine sable

[alpine sable]

your calculation was off @spring harbor

it would be the last option

[spring harbor]

Ohh wait I used cosx = sqrt8 / 2

must've been because of that

nvm thank you

[alpine sable]

np np

d=[v²sin(2x)]/g

g = fall acceleration
v = 60m/s
x = initial horizontal angle

^=Hight

=time

Im using meters and second and am trying to create a function out of this.

Could someone please help me?

[alpine sable]

<@&286206848099549185>

Please excuse me if Im unclear.

I will try to add any information you may need.

[errant robin]

Please help me at this
a, b, c, d E R prove that (ab+cd)^2 ≤ (a^2+c^2)(b^2+d^2) (sorry I have poor grammar)

[rigid smelt]

bạn đã thử gì rồi?

[alpine sable]

???

[rigid smelt]

translation: what have you tried? (in his native language)

seems like it would be easier for them to use their own language

and also, try not to cross-post next time euroking

[steel scaffold]

How can I know the difference
between the graphs of C and D? https://i.imgur.com/vViJAqr.png

what difference does the sign of 13x^2 make

[vale wigeon]

close to the y-axis (x=0) the graph will look like an upward or a downward parabola, accordingly

[hot osprey]

I don’t understand how to find a real zero from these polynomials in order to do the division process to find the answer. And the linear factoring thing confuses me as well. As for 8, I just need help with 8a

[jagged imp]

Where's 8

[hot osprey]

Sorry lol upload is slow

[glass lichen]

remainder theorem

[hot osprey]

For 8? Or the one above

[jagged imp]

remainder theorem is for 8.

[hot osprey]

What about 4 & 5?

Tbh I’m bad at math so a little explanation would be very much helpful and appreciated

[jagged imp]

So as for the process for factoring a polynomial like in the earlier questions, you'll want to find a zero(there are ways to help you guess a zero, but i doubt that's within your curriculum), generally just by guessing small integers until you find a zero. For 4 for instance, -1 was the second number i tried and it ended up being a zero. Then, since we know -1 is a zero, factor theorem tells us that (x+1) is a factor. Then you can divide out (x+1) using synthetic division to express your polynomial as (x+1)*some lower degree polynomial and repeat this process until you get to something like a quadratic that you know how to factor, and then factor that and you're done. In the case of 4 and 5 just being cubic polynomials, you'll only have to go through that process once

that explanation could be worded poorly or whatever but i can reference you to a source that'll explain it better than me

[hot osprey]

so i had (x+1)(x^2-5)

[jagged imp]

thats correct so far

[hot osprey]

but isn't x^2-5 non linear?

and if i write it as sqrt of 5 then it's also wrong

[jagged imp]

sure, but its a quadratic, which you can factor by completing the square

or even easier, difference of squares(although this wont always work)

[hot osprey]

so what would it become?

sorry, i am braindead lol

[jagged imp]

using a^2-b^2=(a-b)(a+b) with a=x and b=5, we can write x^2-5=(x-sqrt(5))(x+sqrt(5))

[hot osprey]

oh, so it's ok to have a sq rt?

when it ask me linear factor

i was so lost in how i could write it w/o radicals

[jagged imp]

if you had something like sqrt(x)-5 that would'nt be linear (edit)

but x-sqrt(5) is perfectly linear

linear just means you have something that looks like mx+c for constants m and c

[hot osprey]

ah, i see

so for 5, i got -2 as a real zero

and got x^2+6x+7

...i am guessing quadratic formula

[jagged imp]

sorry, im back

[hot osprey]

all good, much thanks for your help brother

[jagged imp]

should have been +2 as a zero but ik thats a typo because you have the right quadratic

yeah, quadratic formula or complete the square

[hot osprey]

there's no square

QwQ

[jagged imp]

wym

[hot osprey]

x^2+6x+7

only quadratic formula works

[jagged imp]

I promise you completing the square here works, you might not know what it means

you dont have to, you can use quadratic formula

for completing the square, x^2+6x+7=x^2+6x+9-2=(x+3)^2-2

thats "where the square is"

but again if you havent learnt completing the square you dont have to understand that

[hot osprey]

so i got

-3 (+-) sqrt of 2

how do i write the equation into the linear factor as asked? (x-2)(?)(?)

[jagged imp]

by factor theorem, -3-sqrt(2) being a zero means (x-(-3-sqrt(2)) is a factor, and the same for the other root

[hot osprey]

really sorry to ask dumb Qs, i recently got back from the army

koreans have mandatory service T.T

[jagged imp]

which can get a bit ugly if your poly isn't monic but it is here so w/e

i know about that from seeing my favourite league players get drafted 😢

[hot osprey]

i have no clue how to express it

[jagged imp]

yeah that'd be hard though, did you have to stop uni?

[hot osprey]

would you mind showing me?

[jagged imp]

yeah sure

[hot osprey]

no, i went to the army as soon as I turned of age 19, finished it in late 2019. Then I worked for a bit to pay for my tuition and stuff, then got back into college this sem

and i tell ya, nothing makes sense no more

[jagged imp]

so we know those factors are (x+sqrt(3)+2) and (x+sqrt(3)-2) by factor theorem

[hot osprey]

yep

[jagged imp]

so the whole thing is (x-2)(x+sqrt(3)+2) (x+sqrt(3)-2)

thats pretty much it

[jagged imp]

only thing to be careful of is if the leading coefficient of the quadratic isn't one you'll need to multiply one of those factors by that leading coefficient to make it work

[hot osprey]

Is this it?

[jagged imp]

that is it

[hot osprey]

wow

i thought when they said linear factor

it has to be like a function of a straight line

so i was frying, melting, boiling, liquifying my fkin brain

[jagged imp]

y=x+sqrt(3)+2 is a straight line

,w plot y=x+sqrt(3)+2

[ocean seal]

Results provided by WolframAlpha

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

Requested by Sneaky#0928

[jagged imp]

and so is the other one

[hot osprey]

by golly, i am a retard lmao

[jagged imp]

lmao dw its very easy to get confused what it means with all those square roots floating around

[hot osprey]

oh man, you can't fathom how much of a help you've been bro

[jagged imp]

nah dw

[hot osprey]

thank you so much brother

if you are ok, would it be ok to ask you more Questions if I have so?

like later on down the line

you explain things better than my shitty professor

[tawny lion]

can someone take me through this? i know the steps but i fuck up after i take arcsin of 1.7/4

[jagged imp]

Sure, but no guarantee I'll answer at any given time with timezone issues and my own life. Explanations by other people on this server will mostly be good if you wanna ask here again i'm sure.

[tawny lion]

2x+30 = arcsin(1.7/4) or 180-arcsin(1.7/4)

[hot osprey]

thanks man, have a great day!

[jagged imp]

u2mate

although its more of a night

,ti

[ocean seal]

The current time for Sneaky is 10:10 PM (AEST) on Sat, 24/04/2021.

[hot osprey]

Ah AU?

[jagged imp]

ya

[novel quest]

You roll 3 6-sided dice, what is the probability that at least 2 of them are sixes?
I found an online calculator for solving this but I’m wondering about how to solve it without it. I tried to find a formula but my search was unsuccessful.
Thanks in advance

[kindred helm]

do you know the correct answer?

[novel quest]

The calculator said “0.07407”

[kindred helm]

i got 1/9 as the answer

so 0.11111...

actually 0.08333

1/9 cant be right

[shell widget]

Which calculator did u use

[novel quest]

https://www.omnicalculator.com/statistics/dice

And I used these settings

[kindred helm]

ah i messed up in my calc

thats right

at least 2 sixes can mean there can be 2 or 3 sixes

odds for 3 sixes is 1/216

odds for at least 2 is 1/6 * 1/6 * 5/6 and it comes out to 5/216. now you can get 2 sixes in a 3 different way so use nCr(3,2) = 3.

then you add 1/216 + 15/216 and u get 2/27 after u simplify it

and its 0.074074

someone check if i did it right

it should be correct

[novel quest]

Thanks!

[tight basin]

how do u work this out on a calculator

i know ncd mode but what are upper/lower values

[mystic sinew]

depends on the calculator I think

[tight basin]

i got a classwiz

[alpine sable]

Hi how do you solve B??

[left frigate]

I'm trying to improve my paper by writing how each variable is calculated specifically, and I'm struggling with writing down clean and good looking mathematical interpretations of variables. How do I do this cleanly and professionally?

For instance, a simple example: I have a variable called 'familiar distance' that is calculated for each item i, by summing all participant's p estimates of the items familiar distance, divided by the number of participants. Simple, but what would be the profesionnal way to write this?

Here's my attempt

I know its kinda a trivial question, but I want to get good at writing concise and beautiful equations for more complex constructions

how about this?

[sullen nova]

YOO

<@&286206848099549185>

[indigo jetty]

@alpine sable find the coordinates of P, Q and R first, then sketch them on a graph to find out how to get your base and height of the triangle

[shell widget]

@sullen nova whats ur question

[sullen nova]

on line 3, Do we use { or [ ?

[shell widget]

for the cases?

doesnt matter

[sullen nova]

what

how come

[shell widget]

who cares what bracket is used

[sullen nova]

one means "and" and another means "or"

they have completely different meaning

[shell widget]

lol what

really?

[sullen nova]

how don't you know?

[shell widget]

not sure

[muted raft]

this is my first time hearing this as well..

[sullen nova]

bruh

[muted raft]

I always used { for every cases?

[sullen nova]

lmao

[alpine sable]

does {a,b} mean a or b

[sullen nova]

wtf

that's a set

[indigo jetty]

if you use those braces, you must have an expression on the left side

otherwise it means nothing

if you simply want to express an 'or', you might as well just use the word 'or' instead

[dawn wraith]

Oi people, just making sure, how many bisectors that intersect at the same point in a quadrilateral do we need in order to prove that the quadrilateral is tangential again?