help-0

[alpine sable]

frrr lmao

[vagrant meteor]

why wud i need help

[alpine sable]

some kid showing his desmos picture lmao

so its 84 + 21= 105 m^2

[young finch]

i think that trapezoid on the top right of that one pic is impossible too

hypotenuse 11 one side is 10 and the other is 4

[alpine sable]

yeah it is hahah

its not, u literally split it into a triangle and square

[young finch]

wait prolly not let me check

[alpine sable]

like i just explained

[young finch]

but i mean the triangle part might be impossible

[alpine sable]

@trim hull you should email/contact your teacher lmao, atleast 2 of the questions are impossible.

[alpine sable]

Bruh no its impossible due to triangle inequality

with a special case here since its a right angle, the hypotenuse cant be smaller than the other sides but in that example it is.

[young finch]

i guess you can still get a value with the right equation thats all the teacher wants

[alpine sable]

its not drawn to scale obviously

[young finch]

huh

[alpine sable]

the shapes in the problems are degenerate. You'd basically be guessing how the teacher wants you to solve it (which i assume is using 1/2(a+b)h)

[young finch]

how its drawn doesnt matter

the values of the sides dont add up

[alpine sable]

what? drawing to scale has nothing to do with shapes being possible/impossible lmao.

try drawing a right angled triangle with 5 as the base, 4 as the height and 1 as the hypotenuse @alpine sable lmao

oml just coz hypotenuse isn’t the longest value who cares, they just want the answer to the questions

[young finch]

thats like saying bob bought 20 apples from a store that only had 10 and saying its because the drawing didnt have all the apples he bought

[alpine sable]

🤔 if its not mathematically possible then there is no answer to the question.

nice idc

[young finch]

[lethal ore]

@pure olive Got the solution?

[young finch]

i dont like geometry it makes my head hurt

[alpine sable]

look up circle theorems

[young finch]

i went to homework help and it told me to look at math notes that said something about inscribed angles

wait am i dumb

40+63=103

180-103=77

so measure QSO is 77?

[alpine sable]

where did you get 40 from?

[young finch]

inscribed angle

80/2=40

[trim hull]

can u tell me when u guys are done

[knotty oxide]

Is this correct?

[young finch]

👍

[knotty oxide]

Thanks

[trim hull]

need help with non red

[alpine sable]

bruh we just had a whole convo about it earlier

[young finch]

the same one?

[alpine sable]

scroll up

its an impossible question. same with the one top right. I would email your teacher.

[young finch]

its just the top right one but different values

[trim hull]

i understand that

but i can't find the base

ik the height

[young finch]

no its just the area dont bother with emailing your teacher being like "tWo QueStiOnS aRe TecHniCaLlY nOt PosSiBle sO i DiDnT dO thEm"

base is 9

b1+b2/2 *h

[trim hull]

height is 12.5

[young finch]

wait no

height is 14

average of the two bases find that then multiply with height

[trim hull]

still wrong

no im 12

not 11

[young finch]

huh

[trim hull]

im on the non red one

im on the one that is next to the red one

[young finch]

oh

7+12.5/2*9.7

the red one should be 105 btw

[trim hull]

ik

wrong

its aprrellogram

parrellogram

[young finch]

shouldnt parallelograms have two sets of parallel sides

[trim hull]

12.5 and 7

[young finch]

thats one set

wheres the other

[trim hull]

9.7 and 10.3

but the 10.3 is wrong

so idk

[wicked parcel]

Classify the function f(x)=7(0.5)ˣ

pls

[young finch]

those arent parallel

[trim hull]

ik

[young finch]

channel already in use

[trim hull]

she did this on purpose

[wicked parcel]

🥲

[vagrant jetty]

is this taken ?

[young finch]

ok then just find the area of the triangle and area of the rectangle separately and add if that didnt work

[trim hull]

yup

[knotty oxide]

Need some help on this one

[young finch]

use arcsin

sin(B)=8/17

B=arcsin(8/17)

@knotty oxide@trim hull

you guys still need help?

[trim hull]

yup

[tight locust]

,calc arcsin(8/17)

[ocean seal]

The following error occured while calculating:
Error: Undefined function arcsin

[tight locust]

,calc sin^-1(8/17)

[ocean seal]

The following error occured while calculating:
Error: Unexpected type of argument in function pow (expected: number or Complex or BigNumber or Fraction or Unit or Array or Matrix or string or boolean, actual: function, index: 0)

[tight locust]

wow

,calc asin(8/17)

[ocean seal]

Result:

0.48995732625373

[young finch]

what do you need help with? I said either divide the shape into a triangle and rectangle, find the area of the individual shapes, then add them together or use the formula b1+b2/2*h

[tight locust]

,calc 0.48995732625373*180/pi

[ocean seal]

Result:

28.072486935853

[willow bluff]

Can someone help me ?

[young finch]

divide into two triangular prisms and the trapezoidal prism or whatever its called

i meant rectangular prism not trapezoidal prism

or you can just find the area of the trapezoid then multiply it by its depth

[willow bluff]

How would I do that?

[young finch]

b1+b2/2*h then multiply by depth

[willow bluff]

How would I set that up?

[young finch]

b1 and b2 are the two bases of the trapezoid

so 5+3/2

4

then multiply 4 by the height

then by depth

the height is 4

[willow bluff]

What’s the depth. I’m at 16

[young finch]

9

$$(5+3/2*4)9$$ is probably the best representation for this

[ocean seal]

Arctic

[young finch]

oh

i dont know how to make it look like a fraction

just imagine the 2 is under 5+3

$$5frac2$$

idk

$$5frac/2$$

[ionic jewel]

$\left(\frac{5+3}{2\cdot4}\right)\cdot9$

[ocean seal]

bunny

[young finch]

that would be 9

[willow bluff]

I have been hit with confusion

[ionic jewel]

do you want me to add = 9

[young finch]

dont worry its just formatting with this bot

derivatives are not okie dokie for me

[ionic jewel]

whats the question

if you want to integrate the second one, split it into 3 integrals, then you can do each one itself easily

,w integral from 1/2 to 3 of -2x/3+7/3-1/x dx

perhaps some wrong arithmetic something but the idea looks rigjt

or perhaps i misread your handwriting somewhere

[ocean seal]

Results provided by WolframAlpha

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

Requested by 兔子#6562

[ionic jewel]

you got it right @alpine sable

all of your work is correct

so hopefully you understand that?

if you just copied it from Wolfram i can explain it

[alpine sable]

Me too

Spam here

Hi5 bunny

[ionic jewel]

that emote is in my frequently used now lmao

[alpine sable]

Show what you have done so far

[ionic jewel]

,rotate

[ionic jewel]

The last integral is from the +7/3 in your original integral

[alpine sable]

Last one is from the 7/3

1 times 7/3 is 7/3

[ionic jewel]

it's $\int_{0.5}^3 \frac73 , dx$ but they pulled the 7/3 out

[ocean seal]

bunny

[alpine sable]

The 1 is redunant

[ionic jewel]

you should write it how I just did

here let me put it in order too]

[alpine sable]

$\frac73 \int_{0.5}^3 dx$

[ionic jewel]

$$\int_{\frac12}^{3} -\frac{2}{3}x , dx + \int_{\frac12}^{3} \frac{7}{3} , dx + \int_{\frac12}^{3} -\frac{1}{x} , dx$$

[ocean seal]

bunny

[ionic jewel]

this is what its actually splitting into ^

[ocean seal]

Em

[ionic jewel]

then wolfram is doing extra work to put it into a different form

[alpine sable]

First one polska

Yes

First, put all constants in front of integrals so you can see better

For example, you have integral -1/x dx Write it as minus integral of 1/x dx

Then you can try and find the exact integral in the table

Do the same for others too

2/3 is a constant as well

So is 7/3

Do that too

Then we can look at the table

Looks good

Now look for the first integral in your table

Yes

No, the integral is gone

You will add them

After you write it out, $-\frac23 \frac12 x^2 |$

No

@ionic jewel how do I do line

[ocean seal]

Em

[alpine sable]

Almost

Let me grab some paper and a pen, one moment

[ionic jewel]

$\biggr\rvert_a^b$

[ocean seal]

bunny

[alpine sable]

The integral is gone, but you leave the limits like that

[ionic jewel]

might just be able to do $\frac12\left|_a^b$

[alpine sable]

You dont need c for each, they all are a constant and constants add up to one constant

[ocean seal]

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

[ionic jewel]

nah thats pretty ugly

[alpine sable]

I wont remember that, but thank you

[ionic jewel]

$\left. \frac12 \right\rvert_a^b$ should automatically scale

[ocean seal]

bunny

[alpine sable]

@alpine sable yes

Even better, cancel out the 2's then multiply

Yes

Yep

Now, the way you deal with bounds is you sub in the top bound and subtract the subbed in lower bound

Waiting

$-\frac13 [(3)^2-\big(\frac12\big)^2]$

This

[ocean seal]

Em

[alpine sable]

Your first was x^2

So you sub in 3^2 minus (1/2)^2

Instead of x

Top instead of x minus bottom instead of x

Yes

And subtract top from bottom

Yep

Yes, and 7/3 in front

One problem, should be minus ln

Second problem, -(ln3 - ln(1/2))

[hybrid radish]

is anyone able to help with this?

[alpine sable]

have you learned about sin?

Is that power of 3 or just 3

Ln(x) is a function as a whole. It's not ln times x

That's fine then

Work out the mixed numbers and fractions

Yep

So you can multiply -1/3 and 35/4

Same foe the second one

For ln you have the rule: ln(a)-ln(b)=ln(a/b)

Yes

That's the same solution as wolfram

End result

Nope, the c stays

[ionic jewel]

there shouldn't be a C

[alpine sable]

Oh yeah, its a definite integral

[ionic jewel]

this is a definite integral

no C

[alpine sable]

The c goes away

need help with these 2 if thats ok

[ionic jewel]

there should be no C in the entire problem, although technically there is but it cancels out halfway

[alpine sable]

You didnt need it at all with a definite integral

[ionic jewel]

first one is dividing by two, second one is multiplying by 1/3

[alpine sable]

Dont blaspheme, you're welcome hi5

[young finch]

An unused channel

[alpine sable]

what do i put as common difference (f) im confused

[ionic jewel]

unused channel is a good idea

unless this one is now open

also I do not see an f in your problem

it's a geometric sequence

and I gave the common whatever u wanna call it

i gave the common ratio

i think only arithmetic sequences have a common difference

[alpine sable]

ah

im stuck on what the ratio is

[dense snow]

Ratio is literally like devision

so if i said something like Apples to Orange is 1:2, than I could also say Apples/Oranges=1/2

[near pendant]

okay so

am i able to ask the thing for 4th time if i still havent got answer

[dense snow]

but if I said

Apples:oranges:pineapple = 1:2:3, this isn't 1/2/3

[wild hedge]

hi can anyone help me with this question, i tried using ASTC but i cant get the second answer.

[tight locust]

find the 0s of the function in that interval

[golden arch]

Is x ln(x) = x?

[tight locust]

not in general

there is a value which should make that statement true

it is a conditional equation, not an identity

[golden arch]

But isn't it equal to the ln x**x?

or does that only work for log?

[tight locust]

xln(x) = ln(x^x)

that is true

but xln(x) does not equal x

[golden arch]

But if it was a log it would be right?

[tight locust]

wdym

ln is a log

[golden arch]

or am i just mixing up different rules 😅

[tight locust]

this is called power to product rule of logarithms

[golden arch]

yes i am oops

[tight locust]

ln(a^b) = b * ln(a)

[golden arch]

i forgot that it had to be e

Instead of x

[tight locust]

it doesn't even have to be ln, it works with any base

[golden arch]

my bad

Thanks!

[tight locust]

eln(e) = e yes

good job

[alpine sable]

Can someone solve these for me real quick?

153

107

Could you please explain b?

wait its not 107

108

[oak chasm]

@alpine sable @alpine sable Please read the rules in #❓how-to-get-help. Just giving answers is not allowed here.

[alpine sable]

💀😭

sorry

My bad...

I’m just trying to understand how to solve b

[alpine sable]

ok so they tell u that Un is 45 right?

Yes

so then you can substitute in 45 instead of Un right, since you know what it is now?

Right...

So now you have the equation $2n^2-5n+3=45$

[ocean seal]

sxkura

[alpine sable]

Any thoughts on what to do next?

Ugh

Subtract 3 from 45

I get what ur thinking but then you would have $2n^2-5n=42$ and you can’t really solve that can you

[ocean seal]

sxkura

[subtle mantle]

yes, yes you can, just subtract 42 from both sides

[alpine sable]

Have you learnt about quadratic equations?

Honestly I don’t know shit and I’m in high school

Instead of taking away 3, take away 45 so the equation is equal to 0, this way you get a quadratic equation which you can then solve

tell me what u get now from doing what i just said

4n - 8n

no

take away 45 from $2n^2-5n+3=45$

[ocean seal]

sxkura

[alpine sable]

Umm

lets break it down

2n^2 - 5n + 3

what would happen to the right side when you do 45-45

0

what is 5+6

correct

and whatever you do to one side of an equation you do to the other

so now what’s 3-45

honestly I’m totally confused

This is not the way I got told to do it

-42

[alpine sable]

yep

so now we’re left with $2n^2-5n-42=0$

[ocean seal]

sxkura

[alpine sable]

We have a quadratic equation now and we have it equal to 0 which is what you need to solve it

Have u learnt how to solve quadratic equations

Nope

What you would do next is you solve that equation that we have for n, to find out what n is

https://youtu.be/YtN9_tCaRQc

watch that, it’s easier than explaining

[subtle mantle]

or just use the quadratic formula

[alpine sable]

yeah I have too much to learn for this exam

I understood so far

Hopefully my scientific calculator can do the rest

Is this right sorry

[alpine sable]

good luck, youtube videos r really good plus this discord always has ppl who explain rlly good, sorry i couldn’t help more

nah I appreciate your help. My bad I haven’t studied for years to regret it now.

Prob will be back for more

[unreal depot]

anyone down to help?

[alpine sable]

what are you struggling with to begin with?

[wild talon]

Uh heres the translation : a,b,c,p,q,s forms an arithmetic series where the difference between the integers is a constant not equal to 0.
Show that the system only has one unique solution.

I know the answers are there but i'd like to know how to do the problem

[drifting jacinth]

Comme a,b,c,p,q,s forme une suite arithmétique, de raison k par exemple, tu peux remplacer a par nk, b par (n+1)k, c par (n+2)k ...

[wild talon]

I did that but couldnt figure out where to go from there

[drifting jacinth]

I guess you just have to solve the system

[wild talon]

also, wouldnt a stay as a and b be replaced by a + k then a + 2k so on

[drifting jacinth]

ah, true

[alpine sable]

can someone find me the answer

[wild talon]

1 percent

pre sure

[drifting jacinth]

the channel is taken right now

[alpine sable]

ok

[wild talon]

wait no

i dont remember how to do those acc my b

ok wait

i had

it simplfied

to

yd = a + 2d
3dx + 4dy = a + 5d

where d is the difference

then put them together and just got 3dy + 3dx = 3d

so y + x = 1

which is on the right track i guess

[drifting jacinth]

i have y + x = 1 too

[wild talon]

since -1 and 2

but idk where to go from there

[drifting jacinth]

have you tried to replace x by 1 - y in the previous equation ?

[wild talon]

yeah

in the 3dy + 3dx = 3d one it wouldnt work cuz thats just where we came from

and if i took the

yd = a + 2d
3dx + 4dy = a + 5d

ones

i would also have to solve for a

which we dont know either

ok wait im just going to try anyways

i dont think it works

[drifting jacinth]

it does

you replace it in which one?

[wild talon]

both

then shifted them over so they both = 0

and put them together that way

[drifting jacinth]

well, give me a minute to look at your equations

[trim hull]

Can someone help with this last question

It's a trapezoid

[drifting jacinth]

no, this channel is taken for now

[wild talon]

3dx + 4d - 4dx - a - 5d = d - dx - a - 2d

i just end up with x = all values

[drifting jacinth]

do you agree that ax + (a+d)y = a + 2d ?

[wild talon]

yep

and xa + 3dx + ya + 4dy = a + 5d

[drifting jacinth]

if you replace x in this equation, you'll get y

[wild talon]

replace x?

[drifting jacinth]

x = 1-y

[wild talon]

with x = 1-y

ok

a(1-y) + ay + dy = a + 2d

a -ay + ay + dy = a + 2d

dy = d2

[drifting jacinth]

x = 1-y, not y-1

[wild talon]

oh crap

bet

thanks so much

🙏

[drifting jacinth]

you're welcome

[alpine sable]

min at x = 1.53 & y = 3.07

but why is my answer wrong?

can someone help with this

[trim hull]

Hole server is thrash noone responds

Trash

[ionic jewel]

Arithmatic sequence, which part do you not understand?

[trim hull]

Welp

[ionic jewel]

the equation is going to be something like a_n = initial_value + common difference * n

[tight locust]

Arithmetic

[ionic jewel]

oops

[dim epoch]

is there any way to make a function from a vaalue table? I know you can do it with excel etc. but i need to know if there is a manual way

[pallid void]

A ball is thrown upward at an initial speed of 14.7 m/s. The height h in meters that the ball reaches t seconds after being thrown is given by the equation h=14.7t-4.9t^2. When will the ball be 9.8 meters high. how many seconds will the ball be in the air

[dim epoch]

barlow move to next channel

[ionic jewel]

Given any finite number of points (or countably infinite), there are infinite possible functions that go through every point

if I had to guess I would think you may be looking for a least squares approximation

[pallid void]

@ionic jewel can you help me in #help-1 when you get a chance

[idle trench]

https://tenor.com/view/frog-chill-gif-18325010

[shrewd elbow]

I need help with this I think I have everything right up to there but don’t understand how to continue

<@&286206848099549185>

[glass lichen]

just isolate for x

$2(x-5)^2=18$

[ocean seal]

Mosh

[shrewd elbow]

would i square root everything first to take the 2x^2 and take away the ^2

[glass lichen]

you cant take sqrt of both sides yet..

unless you want to deal with unneeded radicals

[shrewd elbow]

so what would i do to get rid of that ^2

[glass lichen]

square root

but you havent isolated for just the a^2 yet

[shrewd elbow]

oh so i need to take away the 2 first

[glass lichen]

yes, you need to isolate the a^2 still

[shrewd elbow]

so now i have x^2 - 20x + 32 = -2

is that right?

[glass lichen]

no

cause you completely disregarded everything I said

if you want to expand everything then sure, go ahead. Im trying to show you the quicker way given it's in vertex form..

[shrewd elbow]

wait would i take the 2x^2 to the other side and then divide by 2

so now it would be 10x - 16 = x^2

[glass lichen]

Ok you're still heartset on expanding everything

[shrewd elbow]

idk what im supposed to do then

[glass lichen]

$2x^2-20x+32=0$ if you're insistent on doing it the long way

[ocean seal]

Mosh

[glass lichen]

$\implies x^2-10x+16=0$ which is factorable

[ocean seal]

Mosh

[ionic jewel]

why not just move the 2 and sqrt

oh

i see the conversation

[glass lichen]

they want to do it this way 🙃

[shrewd elbow]

idk its just the way my teacher taught it

[ionic jewel]

i guess they get some bonus factoring practice

[shrewd elbow]

well atleast i know how to finish it now

ty

[ionic jewel]

Solving it like this is sorta like using the quadratic formula when you can easily factor it in your head

it also works but its extra work for no reason

[shrewd elbow]

how can i do that tho

[glass lichen]

$2(x-5)^2=18 \ (x-5)^2=9 \ x-5=\pm 3 \ x=5\pm 3$

[ocean seal]

Mosh

[shrewd elbow]

oh i get it

[ionic jewel]

$$2(x-5)^2 = 18$$
Divide by 2
$$(x-5)^2 = 9$$
sqrt
$$x-5 = \pm 3$$
solve for x
$$x = 5 \pm 3$$

[ocean seal]

bunny

[shrewd elbow]

my teacher never taught that

[ionic jewel]

oh mosh is faster

but do you not understand it?

[shrewd elbow]

i understand it now

thank you thats so much easier

she never taught that

[ionic jewel]

$\frac2x = 5 \ 5x=2 \ x = \frac25$

oh

[ocean seal]

bunny

[shrewd elbow]

i have another question

[ionic jewel]

@glass lichen do u know how to do thicker newlines

[shrewd elbow]

whats the "completing the square" method

[ionic jewel]

that little trick doesnt work with fractions well

[glass lichen]

Nope

[shrewd elbow]

its the same thing as the last question but completing the square

[ionic jewel]

I could explain this, but frankly its probably better to just look it up and watch a video

[shrewd elbow]

ok

[glass lichen]

converting a quadratic from standard to vertex form

[ionic jewel]

^

[glass lichen]

$y=ax^2+bx+c\to y=a(x-h)^2+k$

[ocean seal]

Mosh

[alpine sable]

is it possible to express these in exact form without the i?

[shrewd elbow]

ty i looked up a khan academy video and got the work done

only 7 more

[oak chasm]

@alpine sable Remove the i and put a negative sign inside the radical that i is next to.

[charred flint]

What is the millionth decimal digit of the 10^10^10^10th prime?

[alpine sable]

inside???

[ocean seal]

Chai T. Rex

[noble stone]

here's what i did

[opal hull]

someone help me

pls

<@&681260374879633482>

[trail stirrup]

v

[opal hull]

i need serious help

[trail stirrup]

yes you do

not in algebra

but in reading comprehension

[opal hull]

do you know what is

[trail stirrup]

read the rules

[shrewd elbow]

I have no clue how to do this ngl

I know how on a calculator but not algebraically

[tepid flame]

use discriminant i think

D < 0

[vital relic]

^^

[shrewd elbow]

Isn’t discriminant formula -b/2a

[vital relic]

im mentally broken

[tepid flame]

no

no

[vital relic]

b^2 - 4ac

[tepid flame]

b^2 - 4ac

yeah

[shrewd elbow]

Oh ok ty

[tepid flame]

that is sum of roots

-b/2a

no problem sir 🙏

[vital relic]

its a problem sir 🙏

[silver echo]

-b/2a is x coord of vertex of a parabola

[edgy owl]

Um does anybody know how to find parallel lines in the slope by the equation?

[silver echo]

just same slope

[vital relic]

just if the slopes are the ame

y=2x + 1 is parallel to y = 2x

[silver echo]

^

[shrewd elbow]

Yesss only 5 more

[edgy owl]

How bout a negative

One with a negative and one without

[vital relic]

not negative

has to be the same

[edgy owl]

Ok

[edgy owl]

How bout Y=2x +4 and Y= 4x +2

[vital relic]

just look at the coefficient of x

if its the same then parallel

in this case, the first coefficient is 2 and the second one is 4

so its not parallel

[silver echo]

try using desmos

[vital relic]

just play around on https://www.desmos.com/calculator

[silver echo]

you can input functions

should be very helpful

o.0

[vital relic]

good

[edgy owl]

How bout fractions? In the equation

[alpine sable]

ofc

[silver echo]

slope ?

[vital relic]

dont respond to him, hes mentally damaged

good

[alpine sable]

0 = 0

[alpine sable]

gotcha

[vital relic]

[alpine sable]

[vital relic]

[sly mantle]

@vital relic stop trolling @plucky gate stop shitposting

[vital relic]

okay

[dim epoch]

but no actual manual method right? i gotta do a presentation and if theres a manual method id have to know

[ionic jewel]

Can you specify your problem more

are you trying to create a line that gets as close to all the points as possible

or are you trying to make a function that goes through some arbitrary amount of points

[shrewd elbow]

I have no clue what to do next

[glass lichen]

you didn't do anything, so there's no next step

[shrewd elbow]

Yea

[glass lichen]

when it hits the ground, what's the height of the projectile?

[shrewd elbow]

0

[glass lichen]

so solve for t given that...

[shrewd elbow]

So 0 = to whatever

Or h = 0

[glass lichen]

I mean given we just established the height was 0

clearly h=0

[edgy owl]

What does it mean what is the equation of the line though the points?

[vital relic]

u have the points given and u just sub it into y = mx + b

so like say a line goes through (2, 3) x = 2 and y=3

so u get 3=m2 + b

[edgy owl]

2,3 and 4, 5 is y=x+1?

[silver echo]

if you alrdy have slope, input the coords of the points to find the 'b' from y = mx + b

@edgy owl

[vital relic]

^

[edgy owl]

Ok

[patent tinsel]

Hello please help wih this two >~<

[alpine sable]

remember the properties of a square, if TS=TR how would you write the equation if you have the whole of PR

[patent tinsel]

Uuum well like ST=PR? @_@

[alpine sable]

no because PR is the whole thing and ST is a little part you’re going have to multiply by 2 to equal it out

$$2(x+8) = 4x + 6$$

[ocean seal]

karskaa

[alpine sable]

this wouldn’t make sense however PR=QS would though

but given ST then it’s the equation i gave

[patent tinsel]

OoO then it's gonna be 2x+8=4x+6?

[alpine sable]

carry the 2 to the 8 as well

2x+16

[patent tinsel]

OoO oh yes

If i need to find QT too can i use their x?

[alpine sable]

why does this mean we assume x = y?

[alpine sable]

yes

[patent tinsel]

OOOOO thank u!!!

[tight locust]

if there are no solutions where x does not equal y

then you must assume that x = y

2x^2 = -1/2

x^2 = -1

hmm how do you solve that?

you have a negative number you have to take the square root of

i'm not sure that's possible

is it?

[alpine sable]

so we assume x = y, because there are still no solutions which doesnt change the problem?

but it makes the problem easier?

[tight locust]

yeah pretty much

[rapid horizon]

hey can someone help me with this i have a few questions btw

[woeful stag]

Think of each sector as part of a circle as AC and BC being radii of circles of different sizes

All you need to do is find the difference between the circle sector with radius BC and the circle sector with radius AC

and that's the shaded area

[rapid horizon]

yeah

so what is the formula that i need to use for everything

or formulas

[woeful stag]

well, what is the circle area formula, and how would you find the area of a 30 degree sector in a 360 degree circle?

[rapid horizon]

circle area formula is Area = pi(radius^2)

[woeful stag]

right, and how would you find a 30 degree sector of that circle

hint: use ratios

[rapid horizon]

sorry im confused by would it be pi on top of 180?

this channel is in use

[woeful stag]

ok, lets simplify things

what would the area of a semicircle be

what is a semicircle ?

[rapid horizon]

a semi circle is a part of a circle

like a circle cut off

but the area formula is

area = pir^2 /2 = pid^2/8

[woeful stag]

Just pi*r^2/2

A semicircle is actually a circle cut in half; by definition it is half of a circle

So if its half a circle, the area would be pi * r^2 / 2 (since it would have half the area)

which you seem to understand

But where does that 1/2 really come from?

Let's think

[rapid horizon]

yeah ik what a semi circle is

[woeful stag]

What is the angle of a semicircle at the centre?

[rapid horizon]

90 degrees

180 degrees

[woeful stag]

if this is our semicircle, what angle would it have

[rapid horizon]

ohhh 180

[woeful stag]

mods do ya thing

yeah, 180

So we know that a full circle have an angle value of....

[rapid horizon]

360

[woeful stag]

and so since a semicircle has an angle of 180 degrees, we see that the area will change based on how much its changed from the original circle right?

[rapid horizon]

yes

[woeful stag]

lets say 180 degrees = a, how can we use a in our formula pi*r^2 to find the area of the semi circle

[rapid horizon]

but we are trying to find this

[woeful stag]

we'll make a generalization before we get to the solution

[rapid horizon]

ok

[woeful stag]

so that you can understand it better

[rapid horizon]

yeah alrighty

[woeful stag]

Think carefully, semi circles have 1/2 the area, and their angle value is 180 degrees, while the angle of a full circle is 360 degrees

[rapid horizon]

am i modifying that formula?

[woeful stag]

yep

you want to get something*pi*r^2

[rapid horizon]

180

[woeful stag]

to get the sector area

we saw before that the semi circle area = pi * r^2 / 2

[rapid horizon]

what formula is this?

[woeful stag]

semi circle

[rapid horizon]

area?

[woeful stag]

yeah

since its just 1/2 * Area of circle

[rapid horizon]

yes so do i have to add something to that

sorry just confused

[woeful stag]

let me say half circle from now on haha

[rapid horizon]

yeah ahaha

[woeful stag]

half circle will have half the area because its angle value over a full circles angle value will be 1/2

That is:
angle of half circle: 180 degrees
angle of full circle: 360 degrees

area = 180 / 360 * pi * r^2

[rapid horizon]

yes

[woeful stag]

which is also equal to?

[rapid horizon]

the area of a semicircle?

[small hatch]

How would this be solved? It's a review for my final in 5 days!

[woeful stag]

yeah! because 180/360 = 1/2

[rapid horizon]

mhm

[woeful stag]

So we can generalize this to any angle

since it will just be a ratio to a full circles angle value

which is 360 degrees

[rapid horizon]

yes, so then how would it be used in this context?

ohhhh

i get you

so for this im guessing

it will be

30 / 360 * pi * r^2

in this context

[woeful stag]

yes, exactly

A = angle/360 * pi * r^2

and there we've done it, we've described the circle sector area

[rapid horizon]

so then what else will be used in this context to find the "shaded area"

[woeful stag]

now we have two different radii right

[rapid horizon]

well what should i plug into the equation we came up with

here is the question again

[woeful stag]

since there's two different radius values

we see that one is larger than the other, and since the smaller circle sector is inside the larger circle sector, what can we do to find the area in between the two circles?

if I have a square with area 5 m^2 inside a square with area 10 m^2, how would I find the remaining area?

[rapid horizon]

we can see the distance between them from what it says in the question

[supple socket]

This problem requires strong induction

They assumed P(k) for all k that is less than n

[rapid horizon]

i actually wouldnt know im very confused

[supple socket]

I solved the problem the same way for all k that is less than or equal to n

[rapid horizon]

this channel is full

[supple socket]

sorry

[woeful stag]

how about this?

the red square has area 10

the blue square has area 5

how would i find the green area?

[rapid horizon]

multiplying the five again

or like

the inside peice

[woeful stag]

You would actually subtract

[rapid horizon]

oh the five

that area

[woeful stag]

Because the smaller square is part of the larger squares area right?

[rapid horizon]

yes

[woeful stag]

we know the difference would be the shaded area

the same idea applies to that circle question

[rapid horizon]

so what should i do now with the problem

[woeful stag]

the circle section with the smaller radius - lets call r1 - is inside the circle section with the larger radius, r1.

So A1 = area of smaller circle sector

= 30 / 360 * pi * (r1)^2

A2 = area of larger circle sector

= 30 / 360 * pi * (r2)^2

so the shaded area, as you may have guessed, would be the difference between which values?

[rapid horizon]

but which ones in the problem have a larger radius

uhh

the angle

[woeful stag]

Look at the diagram

BC is the large radius

[rapid horizon]

oh is it a and b

[woeful stag]

BC is the biggest radius, see the line between B and C?

[rapid horizon]

yes

[woeful stag]

and which would be the small radius? remember, the radius must touch the centre

[rapid horizon]

a and c

[woeful stag]

right, exactly

what values are given in the question for side lengths?

[rapid horizon]

well we obviously have the 30 degree angle

and then the distance of the shaded area is

3 inches

and the other part is 8 inches

[woeful stag]

right, so how can we describe that line

[rapid horizon]

the non shaded region

[woeful stag]

which line would be 3 inches? BC, AB, or AC?

[rapid horizon]

AB

[woeful stag]

right, and which line would be 8 inches?

[rapid horizon]

a and c

[woeful stag]

Okay, so we want BC first

since we said that it is the largest radius

But wait, it doesn't say what its equal to, how can we calculate BC?

[rapid horizon]

^

[woeful stag]

we need to find r2 first!

[rapid horizon]

so how we do that

[woeful stag]

how would we calculate the distance between b and c?

[rapid horizon]

add both the formulas

of AB and AC

[woeful stag]

Right, so BC = AB + AC

we said that AB = 3 inches

ac = 8 inches

so BC = ?

[rapid horizon]

is 11inches

[woeful stag]

right, exactly

and there we go, we have both the values we need

r1 = radius of small circle sector = AC = 8 inches

r2 = radius of large circle sector = AB = 11 inches

now we find the difference in the larger sector's area and the smaller sectors area and we get the ?

So A1 = area of smaller circle sector
= 30 / 360 * pi * (r1)^2

A2 = area of larger circle sector
= 30 / 360 * pi * (r2)^2

A2 - A1 = ?

[rapid horizon]

3?

wait now

no

sorry lemme do that

[woeful stag]

What would A2-A1 calculate?

[rapid horizon]

the shaded area in the whole model

or just in one

[woeful stag]

since its just 30 degrees we would only be calculating one right?

But in the question, it says that all four are the same!

[rapid horizon]

times it by 4

[woeful stag]

exactly

and there you go, that should do it!

[rapid horizon]

yeah let me calculate this

this was the hardest problem on the sheet i have a few more questions if you dont mind answering

[woeful stag]

sure! I'm going to leave in a bit though, so I'll try to help you out as simply as possible

[rapid horizon]

they are not as difficult as this one

did i set this up right?

[woeful stag]

yep! make sure to explain what A1 and A2 are!

[rapid horizon]

do i divide 30 by 360?

[woeful stag]

here's the area formula if you need

[rapid horizon]

also this is how you would describe A1 and A2 right

[woeful stag]

well, A2 would be A1 + the shaded area, the whole thing

which is why we use the long radius BC

[rapid horizon]

ok let me just do the other questions i only have like a few let me ask you these if you have to leave soon

this is one of them

[woeful stag]

just to make this clear:

[rapid horizon]

yeah i did that

[woeful stag]

awesome

this one is quite simple haha

[rapid horizon]

yeah i just gotta get it started lol

and i have a few that are very simple (2) and then one i gotta finish but i did the majority of work on

[woeful stag]

let s represent the arc length, and r represent the radius

then s = r*theta, where theta is the angle of the circle sector

just rearrange and solve for theta, not too much to include here 🙂

[rapid horizon]

wait so what

s=r*the angle but we dont have the angle

[woeful stag]

right, but we have s and r right?

ignore my ugly circle

i hope this gets the point across

[rapid horizon]

yes

we have the numbers on the graph

the radious of the rotation is 25

and the arc for ab is 58

[woeful stag]

right, so lets rearrange the formula

s = r*theta
theta = ?

(hint: its shown in the question)

[rapid horizon]

the arc?

[woeful stag]

if c = a*b , then c/b = a

if we divide b on both sides

similarly

s /r = r * angle / r
angle = s/r

r*angle/r = (r/r) * angle = 1 * angle = angle

[rapid horizon]

btw this is what i got for the last problem

[rapid horizon]

so what would i out for this situation tho

[woeful stag]

if s = r * angle, then dividing r on both sides, we can isolate the angle

[rapid horizon]

cause we dont have the radius

[woeful stag]

because we want to solve for the angle

[rapid horizon]

oh so divide by 25

[woeful stag]

right, or in other words: angle = s/r

[woeful stag]

I haven't solved the question btw, that was all you 🙂

I just gave you the proper steps, I have no clue what the solution is

[rapid horizon]

alright thanks tho

so this is what the formula for this would be right

[woeful stag]

right

so how do we solve for x

x = ..?

[rapid horizon]

divide 25

[chrome patio]

(2x+1)≡6 mod 5

hello how can i get this

[rapid horizon]

@woeful stag

this is what i got for x

[woeful stag]

thats probably it

[rapid horizon]

so is that the solution

because that is a answer on the multiple choice]

[woeful stag]

just a linear congruence, just solve using common factor or euclids algorithm

[woeful stag]

looks good

[chrome patio]

in layman's terms?

[rapid horizon]

so thats the answer?

damn

aight here is the last two

[woeful stag]

use the same formula as mentioned above

[rapid horizon]

ok

let me plug the last question

[vale wigeon]

lmao the hint is just misinformation

[rapid horizon]

uh oh hahaha

[vale wigeon]

they forgot the half

[rapid horizon]

do yk what it is tho i wanna go to sleep lmao

[terse iron]

i did this and got 8x pi if anyone can double check please

[vale wigeon]

draw the height of this triangle, you'll find that it'll split the triangle into 2 right triangles each with an angle of 68°

[rapid horizon]

im thinking it would be number two

[vale wigeon]

incorrect

the height is not 14 sin(68°)

[rapid horizon]

?

[whole maple]

How do I find the turning point?

[vale wigeon]

no

try not to just guess randomly.

you know your basic trig, right?

[rapid horizon]

ig

[sudden tulip]

Any1 can assist me ?

[pearl marlin]

Getting 40

[terse iron]

confused

how did u do it

[pearl marlin]

I assumed d is diameter

[pearl marlin]

Hope you can try further

[past thicket]

4 = 2^2

[terse iron]

thank you i must of did sum wrong them

[pearl marlin]

X= -2 , 3

[sudden tulip]

yes i get it now

btw must i reject 1 number'

[sudden tulip]

i officialy got both -2 and 3 but shld I have only 1 ans ?

[pearl marlin]

Both are answer of this equation ,because we made a quadratic polynomial out of that and also you can see fundamental theorem of algebra .

[pearl marlin]

It depends what is asking for ( integers, natural ,real , complex ) solution

[sudden tulip]

got it thks !!!

[scarlet spire]

what are x and y

[brisk inlet]

Notation for adding an element to a set?

I have a set A and want to add x to it, how would I write that?

[umbral pulsar]

U

[pearl marlin]

Union should work here

[umbral pulsar]

Union

[remote heron]

how about just $A \cup {x}$

[ocean seal]

jan Niku

[pearl marlin]

Like Au{x}

[brisk inlet]

Is that really all you need? Was expecting something to signify that it was a permanent change

[ionic jewel]

A = A U {x}

[pearl marlin]

https://math.stackexchange.com/questions/271725/is-there-a-shorthand-notation-for-adding-an-element-to-a-set/3594755#:~:text=I know that if you,write A∪{x}.

[ionic jewel]

ah yes A; x too

[remote heron]

just name the new set yea

if you need to use it more

[distant socket]

how do you do the dijkstras shortest path for this graph

[ionic jewel]

there's no tricks on this graph, it's the same way you would do it for any other one

[distant socket]

oh i just realised

i did the wrong one

[ionic jewel]

take the shortest path u traversed at all times, then update the shortest distance table as needed

[distant socket]

this one i mean

so for the first iteration D would be 2 and B would be 7 right

and A is 0

and everything else is infinity

[ionic jewel]

well you have to define iteration better than that

but no

you would take AD first, then DB

B would never be 7

[distant socket]

you cant go for AB?

how come for this example you're allowed to take 2 paths

[ionic jewel]

dijsktras always picks the shortest available path, it's a greedy algorithm

[ionic jewel]

1 and 2 are the two shortest, so that's what it would do

although I'm not sure why they did it like that either

tou don't go two at s time unless it's modified version

[distant socket]

alright so ill just go 1 path at a time

[distant socket]

can u clarify this one @ionic jewel why is the shortest path from A to D: A,C,E,B,D I get A,C,E and D but why b

[ionic jewel]

the shortest path from A to D is A->C->B->D with length 9

ACEBD isnt even a valid path

[distant socket]

man

yea ik

[ionic jewel]

dude

it doesnt ask for the shorest path

[distant socket]

it says

attempting to solve for the shotest path??

[ionic jewel]

read what its actually asking for

[distant socket]

which order are the nodes visited

[ionic jewel]

yes

which should be ACEBD

[distant socket]

but theres not a valid path

so you dont care about the path

[ionic jewel]

it doesnt ask for the path

it asks for the order of nodes visited when you run dijkstras on the graph

and dijkstras always uses the shortest path available

[distant socket]

okok

so can i remember it like when i run dijkstras

i got ACE

B has to be fourth as D should be the last

[ionic jewel]

it doesnt have to visit them all

it does in this case though

[honest umbra]

How can I find of x and y in the geometric sequence -2, x, y, 1024

Wait is this channel busy oopp

[ionic jewel]

like I really dont know what else to say here that can help you, it wants you to run dijkstras and keep track of the order you visited nodes

[ionic jewel]

its fine

[ionic jewel]

geometric means common ratio

lets make the common ratio k

[honest umbra]

I did another one that wasn’t consecutive variables

but this one has two variables together so idk

[ionic jewel]

ok

so we have

-2, -2k, -2k^2, -2k^3

you agree thats how the sequence goes with common ratio of k?

[honest umbra]

yes

[ionic jewel]

great

so we know -2k^3 = 1024

[honest umbra]

Yes

[ionic jewel]

,w -2k^3 = 1024

[ocean seal]

Results provided by WolframAlpha

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

Requested by 兔子#6562

[ionic jewel]

now we found k, so you know how to find x and y from that?

[honest umbra]

-2k and -2k^2

[ionic jewel]

yep

[honest umbra]

wow u smart thx

[wheat prawn]

is this channel free now?

[honest umbra]

Yes