help-0

[celest anvil]

ok i will try setting that up

so set the system of equations equal to 0 and 0?

[hushed pasture]

yep

[paper canopy]

A true-false quiz contains 6 questions. In how many ways can a student answer the questions if the student answers two of the questions with “false” and the other four with “true”?

[placid zinc]

Choose which four are true. The rest are false.
6C4

[static parcel]

I have this basic function y = 15x^2+50x+100 and I need a function to represent the same function, but with each prior value added. Here is a table of the current function:

1 | 165
2 | 260
3 | 385```

I need a function to yield me these results

```0 | 0
1 | 100
2 | 265
3 | 525```

How would I go about doing this?

[placid zinc]

It's going to be a cubic

So fit
y = ax³ + bx² + cx to your data

[leaden star]

is this the correct answer?

or would it be different?

i know that is the final answer, but im not sure if thats how i am supposed to be rewritting it

[static parcel]

How would I go about doing that? Is there no better solution than brute forcing it? I feel like that would take forever

[haughty falcon]

One message removed from a suspended account.

[placid zinc]

,w row reduce {{1,1,1,100},{8,4,2,265},{27,9,3,525}]

[ocean seal]

Results provided by WolframAlpha

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

Requested by Kaynex#7520

[placid zinc]

@static parcel
Last column is the coefficients

[haughty falcon]

One message removed from a suspended account.

[static parcel]

thank you so much

[alpine sable]

ceiling fan and a potato tied to that fan

[haughty falcon]

One message removed from a suspended account.

[alpine sable]

prob not

[placid zinc]

@leaden star
See a video on "function composition" if you're unsure.

[alpine sable]

stupid question lol @haughty falcon what class is this

literally a chandelier and a ceiling fan

[haughty falcon]

One message removed from a suspended account.

[alpine sable]

both of those are suspended from the ceiling

[haughty falcon]

One message removed from a suspended account.

One message removed from a suspended account.

[alpine sable]

yea

unless it means the type of material to use to suspend objects from the ceiling

[haughty falcon]

One message removed from a suspended account.

One message removed from a suspended account.

[alpine sable]

lol that would be my guess though

[haughty falcon]

One message removed from a suspended account.

[alpine sable]

anyways, this is the solution for this question and can anyone tell me why the solution has four a's when it says use 2

then this one says use 3 a's at least and has 4 a's so that makes sense

but for b, how can there be four lol

[paper canopy]

Ma C. Pag withdrew some cash from his savings account. He spent P18 500 to buy a new phone. He also paid his tuition fee which amounts to P21 000. Half of what’s left, he spent in the repair of their washing machine. Now, he only has P7 500 with him. If his remaining balance in his savings account after withdrawing some cash is P64 800, how much was the original amount in his savings account?

[celest anvil]

how do?

[warm brook]

You need to know {u,v,w}, but you’re finding a k such that that set S has a vector that can be written as a linear combination of the other vectors

[misty plover]

@everyone “I have just heard some incredibly Bad news, there is a possible chance tomorrow there will be a cyber-attack event where on all social networks including Discord there will be people trying to send you gore, racist insults, unholy pictures and there will also be IP thieves, Hackers and Doxxers. I advise you not to accept any friend requests from people you do not know, stay safe. Please broadcast on all servers where you have admin permissions or are owners and can ping to broadcast the warning. Hope everyone is safe. Also, make sure you are offline tomorrow, as that will be less likely to happen to you. If possible, send this to your friends as well to spread the message more quickly, I repeat, stay safe. It does not matter if it is real or not, the important thing is that everyone is to be careful with this delicate subject

Please be sure to send this in all servers you are in, moderator or not.
Stay safe everyone”

[alpine sable]

@bitter juniper this dude is wilding out

[pearl rover]

if I have log(x) > log(y) can I just assume that x > y?

[misty plover]

@everyone I have just heard some incredibly Bad news, there is a possible chance tomorrow there will be a cyber-attack event where on all social networks including Discord there will be people trying to send you gore, racist insults, unholy pictures and there will also be IP thieves, Hackers and Doxxers. I advise you not to accept any friend requests from people you do not know, stay safe. Please broadcast on all servers where you have admin permissions or are owners and can ping to broadcast the warning. Hope everyone is safe. Also, make sure you are offline tomorrow, as that will be less likely to happen to you. If possible, send this to your friends as well to spread the message more quickly, I repeat, stay safe. It does not matter if it is real or not, the important thing is that everyone is to be careful with this delicate subject

Please be sure to send this in all servers you are in, moderator or not.
Stay safe everyone”

[glass lichen]

dont spam

[gaunt mulch]

Guys what is 2+2? I heard it was 5

[glass lichen]

yes, log is injective

[misty plover]

sorry just trying to get it to @ everyone but it didn’t work

[glass lichen]

yeah... no shit it doesnt work

[misty plover]

oh shoot this is a big server i’m dumb lol

[glass lichen]

also use a General channel for non-question related things

[pearl rover]

What about this example then:
log(0.5^3) > log(0.5^2)
0.5^3 > 0.5^2
0.125 > 0.25

We started with a correct statement and ended with a false one, where did I go wrong exactly?

nvm

I misread the question lol tysm tho

[glass lichen]

yeah you have -3x>-2x

for positive x

which isnt true

(x being log(2))

[sick torrent]

On the 3rd step why is (cos(h)-1) there?

[dusty quiver]

hey guys i have been stuck on this for quite some time. i decided that since the limit is negative infinity that there cant be a minimum, but how can i use the EVT to determine theres a max? the sets A and A \{a} are entirely different

[sour dove]

you can factor out sin(x).
So **sin(x)**cos(h) + cos(x)sin(h) - sin(x) becomes
sin(x)(cos(h) - 1) + cos(x)sin(h)

[sick torrent]

I don’t understand

[sour dove]

sin(x) is a factor.
Similar to : a*b - a becomes a(b-1)

you can factor out a common term

[sick torrent]

Oh

[sour dove]

does that make sense?

[tall bluff]

can someone help about investment percentage

[tropic dagger]

a^2+2ab+b^2

[tight locust]

let me just walk you through the proof i don't now how else to explain it

you start with some $ax^2 + bx + c$

[ocean seal]

EndTimes

[tight locust]

then factor out a: $a(x^2 + bx/a + c/a) = a(x^2 + Bx + C)$

[ocean seal]

EndTimes

[tropic dagger]

Yep

[tight locust]

then you use the expansion of $(x+k)^2 = x^2 + 2kx + k^2$

[ocean seal]

EndTimes

[tropic dagger]

Yep completing the square right

[tight locust]

then we can clearly see that 2k = B

[tropic dagger]

Mhm

[tight locust]

and now we let $C' = C - k^2$

[ocean seal]

EndTimes

[tight locust]

so now we have:

$a((x+B/2)^2 + C')$

[tropic dagger]

Wait whats c prime coming from im confused

[ocean seal]

EndTimes

[tight locust]

C' = C - k^2. it's because of the constant term k^2 in the expansion of the square

[tropic dagger]

Can we like solve it without subsitution

[tight locust]

and then you get this formula once you substitute everything back in:

[tropic dagger]

Idk i dont think my tracher wants me to solve w subsitution

[tight locust]

ok let's start over.

[tropic dagger]

I get the subsitution makes it a lil more neat but idk its kinda confusing me

[tight locust]

$ax^2 + bx + c \newline= a(x^2 + \frac{bx}{a} + \frac{c}{a}) \newline= a((x+\frac{b}{2a})^2 + (\frac{c}{a} - (\frac{b}{2a})^2) \newline= a(x+\frac{b}{2a})^2 + (c - \frac{b^2}{4a})$

[swift hamlet]

How do I find the equation of the straight line through (0,1) and (3,7)?
It's one of the questions for my homework and I'm too tired to remember how to do this

[ocean seal]

EndTimes

[sour dove]

You can use point slope formula, which is y - y1 = m(x-x1). Your x1 and y1 are one of the two point's (x,y) value that you have.

[pliant charm]

if the rate of change is derivative of the formula for the area, and the length and width are both constants, should it be 0?

[alpine nacelle]

A = lw the area, dA/dt = dl/dt * w + dw/dt * l

[alpine sable]

What would be the cartesian form of this vector?

[swift hamlet]

So would the equation be 2x-y+1=0?

[alpine sable]

I cannot figure it out since I have to basically do z/0

https://tenor.com/view/spongebob-squarepants-sad-lonely-alone-gif-5247861

[sour dove]

Yep that looks correct! Although it's better to be in the form y = mx + b, since y is your dependent variable. So the answer is y = 2x + 1. Nicely done 🙂

[swift hamlet]

how would i know the slope of the line y=7-2x?

[wispy olive]

Do you have to do it algebraically?

Or you can graph it too?

[sour dove]

If that's the same problem using (3, 7) then that's incorrect.
But to answer your question, m is always the slope. So in your case, the slope would be -2

[viscid night]

the slope is characterized by how fast y changes as x goes 1 unit in positive direction

follow bohemian jack advice

[swift hamlet]

ok so if its displayed like that then the slope is always the coefficient to x

[wispy olive]

First, a more graphic solution.

You see, it is -2 because for any equation in the form y = mx + b, the m is the slope of the line.

[swift hamlet]

the lines y = 2x + 1 and y = 7 - 2x are not perpendicular

thats why i needed the slopes of both of them

[wispy olive]

Here you can see that is changing by -2 y(going down by 2 in the y axis) when x changes by + 1.

They meet each other, yes.

[sour dove]

basically yes. The point slope formula is y - y1 = m(x - x1). Distributed out that becomes y = y1 + mx - mx1. Here, m*x1 is a number. Same goes for y1, so those terms can be combined. This value (b in y=mx + b) is your y-intercept when x = 0. So the slope is m * an x value and then it's "shifited" up or down depending on your b

[sour dove]

Are you supposed to have perpendicular lines?

[wispy olive]

We explained how the equation is. In the form y = mx + b and m is the slope.

So tell the slope of y = 2x + 1.

First, what is the m here?

[swift hamlet]

no im supposed to explain how the 2 lines are perpendicular or not

[wispy olive]

@swift hamlet .

[swift hamlet]

2

[sour dove]

so y = 7 - 2x iwas given to you?

[wispy olive]

Yes exactly. This is the slope.

So now you know why the 2 lines meet each other?

[swift hamlet]

yeah

[swift hamlet]

yeah

[wispy olive]

That is basically because their slope is different. If the slope is exactly same, then the lines are generally always perpendicular.

[alpine sable]

can someone help me

[wispy olive]

Your current system of equations.

And if they would be perpendicular, i.e.- this slope will be the same.

[sour dove]

oh, okay. Sorry that context was needed for the problem lol

A good protip is that your perpendicular line is that it's always -1/m. Linear lines are just that: linear so they're just straight lines.
Perpendicular lines are formed at 90 degrees from one another, so in your case it would be perpendicular at -1/(2) or -1/2

[tight locust]

find -2.

[wispy olive]

Sure.

See.

[tight locust]

then go to the left by 3/4

🤣

[wispy olive]

First tell me, where is -2?

[swift hamlet]

if the slope is the same that means they are parallel to each other

[wispy olive]

I mean it is clearly visible.

[sour dove]

So -2 and 3/4 is the same thing as -2.75 That basically means that the point on the number line will be somewhere between -3 and -2, and closer towards -3. How much closer? By 3/4 away from -2

[wispy olive]

@alpine sable come to #help-2 I will show that there.

[wispy olive]

Yup. Exactly.

[swift hamlet]

thanks guys i finally finished my maths homework

[wispy olive]

Cool!

[ruby sluice]

I have a quad with 2 pairs of equal sides
if one of the corners are 90 degrees then does that mean the rest are also 90?
and how bout vice versa
if one of the corners aren't 90 are the rest not 90 aswell making it a trapazoid?

[wispy olive]

Weird when people ask questions and suddenly leave.

[ruby sluice]

wha

[wispy olive]

Not to you.

[quaint pecan]

Anyone can solve this?

[wispy olive]

No, if one is 90 then the rest are not necessarily neeeded.

[wispy olive]

Channel busy, you can move to #help-2 .

[wispy olive]

Because see.

[ruby sluice]

I have two sets of equal sides doe

[wispy olive]

Sum of angle of a quadrilateral is?

[wispy olive]

Ohhh.

[ruby sluice]

360

[alpine sable]

I would need to ask bunch of questions after 2 hours 30 mins anyone up for that time?

[wispy olive]

Still, it does not need to be 90 degrees.

[ruby sluice]

i have to idenify types quads

[wispy olive]

[alpine sable]

Ohkk!!

[ruby sluice]

like this

[wispy olive]

What do you mean?

[ruby sluice]

let me draw a better pictures

30 sec

[wispy olive]

Aha 2 pairs of equal sides.

Then yes.

If one is 90, then the others must be 90 degrees I believe.

[wispy olive]

Since in a Rectangle it is like and all angles of a rectangle are 90 degrees.

[wispy olive]

Is this your test?

[ruby sluice]

no

hw pratice

practive

i have to find the lengths for each one

then the slope

[wispy olive]

I will eat breakfast and come.

[ruby sluice]

i'm just so done with finding all the slopes

[wispy olive]

Begin by marking those in desmos I guess.

[wispy olive]

IKR .

[ruby sluice]

so that's why i asked if i could just find two, idenify if they're parallel or not and just get the answer from there

cs im lazy

LMAO

ty @wispy olive

mwah

[oak chasm]

@ruby sluice If two of the sides are parallel, you have a parallelogram. If those two sides are equal length, you have a rectangle. If a third side is the same length as those two, you have a square.

That's not quite right.

[ruby sluice]

i think i just ahve to find what type of quaderlatial it is

[oak chasm]

If those two sides are equal length and their slopes are perpendicular to the slope of a third line, then you have a rectangle.

If those two sides are also equal in length to that third side, you have a square.

Oh, two parallel sides is a trapezoid.

[paper warren]

I tried doing it by creating triple simultaneous equations

First i did angle SBN = angle NBR

using the equation for cos theta being the same for both (since the angles are the same)

actually first step was letting d = (a, b, c)

put it into the first equation

[wispy olive]

Aight I am back.

@ruby sluice did you finish plotting the points on Desmos or something?

[paper warren]

oops sorry didnt realise there was a questions already here mb

[wispy olive]

You do the tedious and easy part I will do the understanding part .

[spark reef]

chain rule within chain rule? 😳

[paper canopy]

@spark reef

[mortal cedar]

I wrote this a month ago but don’t remember how I got 16

[alpine sable]

can ssomeone help me witht shis

[tight locust]

if x = +-8 then 8 = +-x

[mortal cedar]

-1.75 ? @alpine sable

[tight locust]

it says improper fraction

[mortal cedar]

Oh my bad

[ruby sluice]

I good now

i got the answer

tysm

[wispy olive]

Cool.

[mortal cedar]

@tight locust oh shit I’m an Idiot, I didn’t even need to ask that question I legit just blanked that 16 was already in the existing equation. I was out here trying to figure out how I got 16 from x^4/3

[tough swift]

ABCD is rectangle oriented anticlockwise with BC = 2AB. CDEF is rhombus ori-
ented clockwise with m∠DEF = 120o. A(2+i),B(5−i), If complex numbers corresponding
to F is a + bi + cω + dωi, find a,b,c,d. ω is cube root of unity.

Can somebody please help me with this
i can explain whatever i have done

[tropic dagger]

can u elaborate on how u want from a(x^2+bx/a+c/a) to the step after it? I think you left out the actual making of the perfect square trinomial

sorry to bother

[sick torrent]

What does this mean?

Like with the !

[cunning kayak]

factorial

[wary stream]

Most likely factorial

[sick torrent]

What does that mean

[wary stream]

But never seen it with cos(x)

[sick torrent]

Uh

[wary stream]

So 3! = 3 * 2 * 1

[sick torrent]

So

What does cos(x)! Equal?

[tough swift]

<@&286206848099549185>

[cunning kayak]

idk the graph is really wierd, lots of asympototes

[surreal meadow]

can you show us the whole question?

[surreal meadow]

it's just exclaiming that it's cos(x)

it's like "wow! look at this it's cos(x)!"

[cunning kayak]

oh lmao

[placid zinc]

That's really dumb lol. I've never seen ! be used accidentally in the middle of an equation

[surreal meadow]

related

[placid zinc]

That I believe

[eternal crown]

What must be the third digit of 86__ to make it divisible by 9? Note: Please encode only the digit or the number as your final answer to make it valid. Example: 7 *
1 point

[wary stream]

1 point? Is this an exam question?

[eternal crown]

no

its a worksheet

homework like

[wary stream]

A number is divisible by 9 if you sum up the digits of that number and that sum is divisible by 9

[hoary quiver]

can someone help me with my 5 page math homework

9th grade btw

i dont get anything on it

[buoyant edge]

Post if you have a specific question

[wary stream]

So like 936 is divisible by 9 because 9 + 3 + 6 = 18 and 18 is divisible by 9

[hoary quiver]

These type of questions

[wary stream]

Do you know what slope intercept form is?

[hoary quiver]

nope 💀

[wary stream]

$$y = mx + b$$

[hoary quiver]

i used to but that was back in 7th grade when i did advanced

[ocean seal]

dldh06

[hoary quiver]

oh yeah ive heard of that

[wary stream]

All you do is set those equations equal to y

[hoary quiver]

can i get an example on one?

[wary stream]

Made up one that's not on your sheet
30x - 7y = 32
-7y = -30x + 32
y = (-30/-7)x + (32/-7)
y = (30/7)x - (32/7)

[hoary quiver]

ok

[foggy onyx]

can someone help me rn

can someone identify the terms of this problem

👉🏻👈🏼

[buoyant edge]

From 9 to 10 AM, it's PhP 30.00

Then every hour after that until 7PM, it's PhP 5.00

Add it up.

[hoary quiver]

bro im confused

[foggy onyx]

so from 9-10: 30 PhP.
after that time its 5 PhP until 7pm.

so the terms are 30,5?

[wary stream]

https://www.youtube.com/watch?v=MfkMsY7I6qw&ab_channel=StepbyStepScience

[buoyant edge]

The terms? What do you mean?

[foggy onyx]

im gonna solve the problem using arithmetic or geometric.

im finding the set of sequence

[buoyant edge]

If you wanted to express the situation in variables you'd write C(t) = 30 + 5t, where t is the number of additional hours parked.

[latent zephyr]

Yeah like chris said, there is a constant

which is 30

whether you park for 1 hour or 20 hours, you have to pay 30

then every hour after that is 5

so if t is total number of hours parked, the equation is Total cost = 30+5(t-1)

because 30 dollars is always paid and that pays for 1 hour

then 5 x the remaining hours parked which is total hours minus the 1 you already paid 30 for

[hoary quiver]

@wary stream mine on where he divides -8x and 4 mine is -7 and 10 would I have to put the whole answer which is −1.428571428571429

[wary stream]

Keep it in fraction form

[latent zephyr]

is it 20 on the other side?

oh right yeah fraction is the way to go there

[austere fossil]

can i ask a calculus question?

[latent zephyr]

Go hard bro

[austere fossil]

i straight up dont know how to do b)

😅

[latent zephyr]

Have you already drawn out the two?

[hoary quiver]

yo this is easy

im so dumb 😂

i appreciate the help

[austere fossil]

i've done it on desmos

[latent zephyr]

Thats the way

and Im assuming you know what continuous means

[austere fossil]

somewhat xD

i literally have no idea how to do this question and i have 9 mins to do it

[latent zephyr]

Actually

it is contunuous?

[hoary quiver]

Can someone confirm my answer

[wary stream]

Where's the 20 from?

[hoary quiver]

bro

where did i get that

wtf

[wary stream]

That's a really good question

[hoary quiver]

-8

replace 20 with -8 is it right

[wary stream]

Yeah

[hoary quiver]

ok ty

[tough swift]

can anyone of you help with a complex numbers problem?

[latent zephyr]

Both are continuous as far as I can see???

Unless Im missing something

OHHH

IM DUMB

-1.634

a = -1.634

or a = 0.596

Because then the line is continuous

[hoary quiver]

Am I in the right track so far wanna make sure I’m doing doing it all wrong

[wary stream]

You have fractions wrong

[hoary quiver]

oh yeah

[wary stream]

Process is correct but when you did fractions, you got them wrong

[hoary quiver]

i see what ur talking about

[wary stream]

Like -2/6 doesn't equal -3

It's equal to -1/3

[wary stream]

Also, 7 is wrong, because you still have the 8 with the y even though you divided

[hoary quiver]

oh thanks i didnt notice that

[stark grail]

anyone knows how to solve this?

[surreal radish]

hi can anyone help me solve this, pls?

[wary stream]

Set the first equation equal to A, plug it into the other, solve for B

[dry hare]

Mrs. Santos wants to tile her rectangular floor by choosing between two tiles, one
of which is 3 dm larger than the other. Mrs. Santos hired your services to help
her decide which tile to use
What is the area that will be covered by the small tile?
pls help

[icy geode]

Ms. Yoon wants to determine the break-even point of his business. It is the point where the total revenue is equal to the total cost. Given that x represents the number of products sold, the equation that represents his total revenue is y =120x and the equation that represents his total cost is y = 60x + 1,200. Determine the break-even point of the business.

[stark grail]

[crystal crag]

@stark grail 2?

[stark grail]

may I know how to solve it 😮 O

[crystal crag]

use this

and use the pythagoras theorem to get a relation between x, y, z

@stark grail

[stark grail]

wait ya im tryin xD

[crystal crag]

sure

[stark grail]

make them become log y (x-z) + logy (x+z) ?

[crystal crag]

yes yes

then use the product rule, log(ab)= loga + logb

[alpine sable]

Product rule haha.

The true product rule is (fg)' = fg' + gf'.

[crystal crag]

ikr, I didn;t remember the name of this log rule atm

[alpine sable]

That's also called product rule or probably addition rule of logs.

[crystal crag]

ohh thanks

[stark grail]

logy x^2 -2xz+z^2 ? xD

[crystal crag]

it will be x^2-z^2

[stark grail]

oops xD

[crystal crag]

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

[stark grail]

i didnt notice that sign xD

[crystal crag]

dw

[stark grail]

and what should i do next xD

[crystal crag]

from the pythagoras theorem, u have x^2+y^2= z^2
so, x^2-z^2= -y^2

[stark grail]

oic 😮

THANK YOU SO MUCH

💗

[alpine sable]

pls help hehehehe

[sour dove]

wait sorry I've been following this as I'm heading to bed.
That would leave log_y ( -y^2) which then is 2*log_y(-y), but you can't have a negative value in the log. So how do you get rid of it?

[crystal crag]

now thats what confuses me as well

ideally, the ques should have been smth with the second base as (z-x) and not (x-z)

[stark grail]

woww

[sour dove]

yeah for sure

[crystal crag]

and it can be possible if y is complex, but Im not exactly sure if its the right thing to do, taking logarithm of a complex

[sour dove]

true. @stark grail are you going through complex values right now?
Is "Does not exist" an option?

[crystal crag]

u pinged the wrong guy dude

[sour dove]

whoops haha

thank you lmao

[stark grail]

xD im here

whats that 🤣

[raw shard]

maybe they just didn’t think they question through completely

who knows

[sour dove]

it's a fun question, but yeah I think you're right

[stark grail]

do u mean z^2-x^2 ?

[alpine sable]

Pair of integers who’s deference is negative
77 and 19
(-62) and 37
(14) and (50)
48 and (-25)

[sour dove]

@stark grail I think you need to tell your teacher that there's not a real number answer for that

no it's x^2 - z^2. It's the same thing as (x+z)(x-z)

[stark grail]

but it is given that ‘z’ is the hypotenuse

[sour dove]

right

so think about this

[stark grail]

oic

woww

[crystal crag]

so this becomes a ques of complex analysis
rudin go brr ;)

[stark grail]

thanks a lot for helping

[alpine sable]

Any answers??

[raw shard]

@alpine sable not really sure what you’re asking

[alpine sable]

Oof

[raw shard]

1 and 2 have a negative difference

you have to specify

[sour dove]

the hypotenuse will be the larger of the 3 numbers given Pythagorean theorem.
So if you have x - z, you get a negative value for that.
A concret example would be a 3-4-5 triangle.
It would be log_y(3 + 5) + log_y(5-3) or log_y(8*-2)

[crystal crag]

yup exactly, and it violates the basic definition of a logarithm

[stark grail]

owhhh

[raw shard]

imaginary side length lol

[wary stream]

Substract

The two values

[broken belfry]

11

[wary stream]

Yes

[copper pond]

help pls

The product of 3 consecutive
positive odd numbers, where (x-2) is the smallest number, is 119 times their sum

[celest anvil]

how to do?

[icy geode]

Ms. Yoon wants to determine the break-even point of his business. It is the point where the total revenue is equal to the total cost. Given that x represents the number of products sold, the equation that represents his total revenue is y =120x and the equation that represents his total cost is y = 60x + 1,200. Determine the break-even point of the business. Pls help

[raw shard]

@icy geode so you want to do something like 60x+1200 = 120x

[icy geode]

yep

[raw shard]

subtract 60x from both sides

[icy geode]

aaaaa

[icy geode]

thanks so much

[raw shard]

no problem

nope

20

[calm frost]

help do you know this problem?

[lean nacelle]

can anyone help me with this problem please. find the moment of inertia for a ball of radius a about an axis throuh its center if its density is 1/1+d where d stands for the distance from the center

i just need help on the set up of the problem / triple integral

[copper pond]

help how to solve this please

In a mathematics “squid game” competition, the contestants are asked to find the password
of a door for them to go to the next round. In the clue is stated that “The product of 3 consecutive
positive odd numbers, where (x-2) is the smallest number, is 119 times their sum”. Find the password
(smallest to the highest) before you are running out of time!

[rich basin]

@copper pond so you know that the smallest number is (x-2), and they are odd. Therefore, you add 2 for each of the consecutive odd numbers so it becomes (x), (x+2)

and then you make the equation (x-2)(x)(x+2) = 119( x - 2 + x + x + 2)

solve for x

proof by induction

so i'm stuck in trying to prove that

k^{2}-11k+2k+30 is < k^2 -11k +30

i mean the other way around

[pale merlin]

Guys is this wrong ?
If a | b and b =/= 0, then | a | < | b |

there should be equality soon too . I think

a | b mean b % a == 0

[rich basin]

@pale merlin what do you mean by "|" and "=/="

can we do this in another channel

[pale merlin]

yeah

let's discuss in channel -9

*question-9

[rich basin]

<@&286206848099549185>

[fathom field]

yes this is true

no wait its not

|a|<=|b|

because a|b means that b=a*A, A being an integer

A can be 1

so |a| is smaller OR equal to |b|

@pale merlin

oh it was answered already

[rich basin]

help my question then

[alpine sable]

is this channel already in use?

[rich basin]

yah

@fathom fieldcould you please help me, this shouldn't be that bad

[fathom field]

yeah on it

one min

[alpine sable]

How can I know if a channel is open to ask a question ?

[rich basin]

read the latest message

and depending on whether it has been solved, you can use it

So this is what i have left

but i'm stuck with trying to make the link

like how is k^2 -11k + 30 < k2-11k + 2k + 20

but then the problem here is that

for k values like 2

wouldn't work

[fathom field]

same lol

[rich basin]

since 24 < 30

so i was like what, how am i suppose to do this

[fathom field]

let me try something else

think i got it

[rich basin]

what did you do?

[fathom field]

wait no

i get that the case for n+1

is bigger than 2n-11

2n-10**

[rich basin]

can i please see full working?

[rich basin]

what did you make LHS as ?

[fathom field]

lhs i made into the n+1 case

-11n+19

=

-11(n+1)+30

[rich basin]

so you made (n+1)^2 -- 11(n+1)^2 + 30 right?

[fathom field]

yes

[rich basin]

okay

then shouldn't the righthand side be 2x - 10 instead?

[fathom field]

but to prove it you'd have to show that 2n-10<=0

[rich basin]

rather than +6

[fathom field]

yeah

[rich basin]

but here the problem is with the cases 1 and 2

which fails

[broken belfry]

any fast methods

[rich basin]

@broken belfry you just align them in a row

you multiply and then carry to the next digit to the left

for excess values

unless you want to use my method which i do in my brain

[broken belfry]

idk if its that way or the opposite

[rich basin]

in which i multiple each digit to 43 and then for each n digit that is > 1, i multiply 10^n with it as well

and then add all of it as well

then just do digits one by one and record it on paper

and then calculate the sum in your head

@fathom field but how would you prove it is >= 0 then?

when it fails in cases such as 1 and 2

[fathom field]

yeah thats where im lost

[rich basin]

same

but i went through a different way

in which i make 0 the LHS

we might need to go ask the pros

[fathom field]

so then youd have to show that your lhs is bigger than the given one

[rich basin]

@broken belfry just repeatedly do simple maths in your head, which i've done for almost the entirity of my life

yeah

[fathom field]

for questions like these you have to basically show that the inequality is either higher/lower or equal

[rich basin]

can't believe we are stuck

[fathom field]

maybe its not true (?)

[rich basin]

no

k = 1 is true

but then in this it's false

so there is an issue

unless you can think of a case

[fathom field]

no its true

the lowest this goes is 0

for 5 and 6

so it holds

[rich basin]

but it does not hold for values between 5 and 6

[topaz badge]

math

[fathom field]

but values between 5 and 6 are not integers

[rich basin]

yeah, this problem is tricky lol

[fathom field]

so for n<=1 n is an integer it does hold

[rich basin]

it doesn't matter anyways for this type of equation

[fathom field]

do you have to prove it by induction lol

[rich basin]

yeah

this entire sectionis proof by induction

[fathom field]

idk how

maybe rewrite the equation

[rich basin]

we just summon the pros and see what they think

<@&286206848099549185> we are stuck, seen in the above pictures

[fathom field]

maybe factorize it?

yeah factorize it and prove it for both cases

waiiit

idea

try this

i think that's it

@rich basin

[rich basin]

you mean n-5?

[fathom field]

yes n-5

mb

[rich basin]

but this is not proof by idncution

this is my first idea when i saw this problem

[fathom field]

fuuuck

(n-5) (n-6) btww

i think you could turn it into induction

prove by induction that for n <= 5 they are both negative or 0 making the result positive or 0

and for n>=6 they are both either 0 or positive

making the hole inequality always bigger than 0

[rich basin]

what do you mean by both negative?

[noble sinew]

I mean if you want to do induction

then you can prove it holds for all n>=5

then you need to check n=1,n=2,n=3,n=4 manually

[fathom field]

to prove the whole thing you can prove what i wrote in red byincuction

[noble sinew]

that ain't rly induction (or just forcing induction on something that doesn't require induction)

[fathom field]

yeah ig

[noble sinew]

you can show (k+1)^2-11(k+1)+30>=0 for k>=5 using your inductive hypothesis

now you just have a finite amount of base cases to check

[fathom field]

you definitely can

[rocky warren]

i have a quick question

When multiplying 2 variables which comes first? ex: q(a + y) would it be qa + qy or aq + yq

[noble sinew]

doesn't matter

[lofty pond]

1+2 and 2+1 gives same result

[dense imp]

how to solve that question?

[noble sinew]

Its asking for what value of x gives P(X>=x)=1-P(X<=x)=0.05

we can use inverse normal distribution to solve for x

[dense imp]

ppf?

[noble sinew]

?

[dense imp]

oh its used in python

programming language

[small cypress]

how do u find b?

<@&286206848099549185>

[lofty pond]

Put the coordinates of given point

(0,4) and (2,0)

[onyx sluice]

can someone help me real quick

?

[alpine sable]

never ask

just ask

[neon bramble]

can someone show me what the right answer was

[noble sinew]

is division by 0 defined?

[neon bramble]

undefined tihnk

[noble sinew]

so if denominator is 0 our expression wont be defined

so figure out when it is 0

[lofty pond]

10i

[silver current]

^

[neon bramble]

wait im confuse

[silver current]

it is defined for all real values of y

[lofty pond]

Yeah

[neon bramble]

so is my teacher wrong

[silver current]

your answer is correct

[silver current]

yep

[silver current]

that is wrong

[neon bramble]

oh ok

[silver current]

-10^2 = 100
100+100= 200

which will make it defined

[neon bramble]

yeah

[silver current]

same with y =10

[neon bramble]

ok thanks

[fathom field]

they probably meant well defined

[lofty pond]

It's roots are rational so....

[silver current]

Took me some time 🥲

[fluid inlet]

Can someone help me show me the steps for this ?

im not sure

[lofty pond]

First find coordinates of A by using M and B

[fluid inlet]

Can you like write and show the steps im not sure how to do it

[lofty pond]

Hmm wait

[fluid inlet]

Its not for me its for my younger brother hes in secondary school and idk how to do it for him. Im in uni studying cyber security lol so i forgot all of these stuff

[lapis valley]

is the first equation called the difference quotient ?

[stone minnow]

Plot the points on a geometric plane first

Then find the distamce

[alpine sable]

Question does anyone here know what is BMI?

[stone minnow]

At last use bh/2 formula

[alpine sable]

Or how to calculate it

So no one wanna help me fantastic

[lofty pond]

body mass index?

😅

[fluid inlet]

dude can you just do it for me i havent learnt math in ages and its not for me

[lofty pond]

@fluid inlet

[dense imp]

can someone send the solution for this p;z

[lofty pond]

first we can calculate x coordinate by using x cord of M and B , same for Y coordinate
then we get coordinates of A
then we plot triangle ACM
from that we can see that it's right angle traingle so we can just do Base*height /2

Not sure if I'm right
dispenser will fill 150+-7 grams so it gives 14 gram of deviation out of which we can spill it 1/20 times as we need min vol
so
14/20 grams can be spilled at max
which gives 150+7-14/20 grams of capacity

[barren shuttle]

Hello, just a quick question, if all outputs are unknowns, is it guaranteed that there's no unique solution here?

[alpine sable]

Yes I am that dumb

I haven't

Studied much

[lofty pond]

If a,b,c are not variable then it can have unique solution
But there will be no unique solution if number of variables>number of equations

[barren shuttle]

Thanks for clarifying, I got vars>eq. from row echelon thus no unique solution.

[fair zephyr]

f(x,y,z)=4.1x2+6xy+6.8z2+10. laplacian

plz answers anyone

[scarlet atlas]

can anyone help?

[lapis sluice]

there is no x

yeh like wtf

there is no conjugate to a real number

oh, ok

i have never seen someone use the notation * that has to be some american stuff

nah

From Europe

[scarlet atlas]

star and n is x

its a printing error

[lapis sluice]

what is 3 star?

[scarlet atlas]

my school is great

[scarlet atlas]

3 power x

[lapis sluice]

ah

[scarlet atlas]

some help with the ques then?

[lapis sluice]

considering the fact that you got multiple solutions you could just plot them in and eliminate them one by one

big brain

but you dont learn anything by that

[scarlet atlas]

exactly

thats why i wanted to solve

[strong furnace]

its a quadratic in 3^x

[lapis sluice]

yeh you should attempt to use logaritms

[scarlet atlas]

i just cant get -244 to be a power

i tried -2(12^2)

[glass lichen]

it's a quadratic in 3^x

244 is just one of the co-efficients

[scarlet atlas]

okk

lemme see

[scarlet atlas]

?

[lapis sluice]

for these simple equations you could go ahead and use photomath btw

[glass lichen]

Bruh

[lapis sluice]

they give explanations as well

xD

[glass lichen]

Or... explain how to actually do math

instead of being lazy and saying "use Photomath/symbolab"

[lapis sluice]

or just learn it and dont struggle

do it the ruski way

[scarlet atlas]

can anyone give a solution or not?

[lapis sluice]

sure

1 sec

[glass lichen]

we dont give solutions

[lapis sluice]

the solution is either 4, -2, -3 or 3

[scarlet atlas]

no shit sherlock

[glass lichen]

can you solve quadratics Y or N?

[scarlet atlas]

wait guys

[lapis sluice]

Why do americans have multiple choice though, it ruins the entire point of math

[scarlet atlas]

ques is wrong

lmao

[scarlet atlas]

im indian

[glass lichen]

It doesn't

[scarlet atlas]

it doesnt btw

[lapis sluice]

yes it does

it gives you hints

[scarlet atlas]

keep thinking that buddy

[glass lichen]

Yeah, cause then you can be more confident in knowing you're right vs wrong

[scarlet atlas]

multiple choice is also very confusing

[glass lichen]

A lot of good quality questions are formatted as "proofs" so the answer can be given, cause the mathematics is built into the logic of how to get the answer.

[scarlet atlas]

like there are multiple correct answers but you have to choose the prioritised one

what about this/

[lapis sluice]

in one of my exams i got the following question. Integral(nroot(tan(x), 5), how should you write multiple answers to that, the answer is: ,ask int root(tan(x), 5) dx

,ask int root(tan(x), 5) dx

[glass lichen]

your notation is shit

[ocean seal]

Results provided by WolframAlpha

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

Requested by Danajax#1235

[lapis sluice]

mine

[glass lichen]

yes "Integral(nroot(tan(x),5))"

[lapis sluice]

that is CAS notation not mine

[glass lichen]

Ok, and you wouldn't make that MC obviously

[lapis sluice]

MC?

[glass lichen]

"Show that (this) = (that)" where (that) is the answer is a fairly common formatting.

[lapis sluice]

what are you supposed to find?

Hhaha, yes like then what...

[karmic rapids]

hey sorry for the stupid question, but this is how graph should be drawed when i want to solve this inequality?

[small bear]

Looks good, on the left at -1 you can continue the graph under the x-axis just so it looks complete and doesn't abruptly stop

[karmic rapids]

yea forgot to continue that line at -1 😅

ty👍

[oblique trench]

I wanted to see if somebody could help with a solution and explanation on this:

[minor crane]

Does anyone here do revision often

Ask I’m failing my gcses lol

[bitter kite]

anyone?

[vocal olive]

calvin has 2/3 x cards

kia has x cards

[bitter kite]

i did block modeling and i am left with 5 boxes aand 2976 is not divisible to 5

what should i do?

hello?

[alpine sable]

(not homework i am practicing my calculus skills) how do i go about solving this?

[lapis sluice]

substitute maybe

[lapis sluice]

holy shit

this is some serious shit

partial integration

[raw shard]

wow i’ve heard of that but never actually seen it

[alpine sable]

🤔

[lapis sluice]

$f(x) = \frac{xe^x\cos x + xe^x \cdot \sin x - sin x \cdot e^x}{2} + c$

integrate partially and you should get something like that

my final result may be wrong

[ocean seal]

Danajax

[raw shard]

cool but terrifying

lol

[acoustic shale]

can someone help me

Please

[raw shard]

wait can i ask something dumb @lapis sluice

[acoustic shale]

I got question

[raw shard]

how is this partial integration if there’s only one variable

[lapis sluice]

u = x

dv = e^x cos(x)dx

[raw shard]

oh

[lapis sluice]

du = dx ofc

[acoustic shale]

I wanted to know how to find the correct one

[raw shard]

this channel seems to still be occupied @acoustic shale

[lapis sluice]

@raw shard if you really want a terrifying integral, you should try $int nroot{tan x}{5} dx$

[acoustic shale]

I sent this early nobody helped

[ocean seal]

Danajax

[acoustic shale]

@lapis sluice Are you advanced in math ?

[raw shard]

oh i think i saw that earlier @lapis sluice

it was an insanely long solution right

[lapis sluice]

yup

[raw shard]

like 3 or 4 lines

[acoustic shale]

do you know the math I sent ?

[lapis sluice]

,ask int root(tan(x), 5) dx

[ocean seal]

Results provided by WolframAlpha

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

Requested by Danajax#1235

[lapis sluice]

xD

[acoustic shale]

dana

yo

[lapis sluice]

yes, i am looking at it now sorry

[acoustic shale]

read this

do u understand it ?

[rigid wind]

literally boolean algebra but + for | and * for &

[acoustic shale]

can u make me understand it

I litarly not understanding it 100% to know the answer

[lapis sluice]

you should attempt to rewrite the expression for X and Y as you now that A' * A = 0

[raw shard]

@rigid wind i see that you’re blue now, lol congrats

[lapis sluice]

so you could shorten the terms

[acoustic shale]

A' * A = 0 ?

[lapis sluice]

yes

[acoustic shale]

but its A' * A'

what is it

[lapis sluice]

that is A'^2

either 1 or 0

[acoustic shale]

then how can i know if its 1 or 0

what about 1 * (A' + A )?

[lapis sluice]

where does this appear

so you could per example redefine X: $X = A^2 + 1(A'^2)$

[ocean seal]

Danajax

[acoustic shale]

Its in the picture

[lapis sluice]

whch would just be $X = A^2 + A'2

which is 1

so X = 1

[acoustic shale]

I see so that means

since there in Y + 1

its 2 ?

Y = 2?

[lapis sluice]

yes

[rigid wind]

no

[lapis sluice]

?

[rigid wind]

boolean algebra only takes 0 and 1

for Y, notice there's +1 at the end

anything + 1 = 1

[lapis sluice]

i dont think this is boolean algebra

[rigid wind]

so Y = 1

and you don't need to define any complicated function to solve for X

[lapis sluice]

ahhh nvm

i didnt see 1+1 = 1

my bad

[acoustic shale]

so X = 1 and Y = 1 ?

The A' thing

[lapis sluice]

Yeh I think so, i have never had boolean algebra, but from the rules i suppose that 1+1 = 1

so yes Y = 1

[acoustic shale]

but

does the A' means 1 and A means 0 ?

or A means 0 or 1

[rigid wind]

no

A' is opposite of A

so A + A' = 1

[acoustic shale]

and A * A is 0?

[rigid wind]

A' * A = 0

[lapis sluice]

because anythying +1 equals 1

yup

[acoustic shale]

what about A' * A '

[lapis sluice]

A'^2

[rigid wind]

you can collapse to A'

[lapis sluice]

true

[rigid wind]

notice 0 * 0 = 0 and 1 * 1 = 1

[acoustic shale]

yes

[lapis sluice]

these weird rules are confusing me, i should be doing boolean algebra,

It is giving me the same feeling as when i first started with complex numbers

[raw shard]

lol complex numbers are easy this is like impossible to follow though

[acoustic shale]

yes

There something complex also but not sure about it

[lapis sluice]

depends what you mean about complex numbers being easy

I don't excactly like Digamma functions

[acoustic shale]

tes

yes

look at this one

[lapis sluice]

or complex functions in general are a mess

[raw shard]

bruh that’s a calculus thing

[acoustic shale]

yeah

I thought of increases

but there one its somehow complex wait ill show u it

I didnt get it 100%

This one

This one I didnt get it

[lapis sluice]

Jesus christ, the question is like reading a textbook, what are you studying?

[acoustic shale]

A textbook

And I dont understand this

I was wonder one of two

1000% or 900%

[acoustic shale]

what do u think

[lapis sluice]

i cant be asked to read it honestly im sorry. Just give me one sec

[acoustic shale]

okay

[acoustic crest]

Hey I need help with this

What’s the solution?

[dull onyx]

take the left and right hand limit

[lapis sluice]

Honestly idfc

[lapis sluice]

doesnt exist

[acoustic shale]

is it easy?

[dull onyx]

literally so lost

sorry for my ugly ass handwriting 🥱

[lapis sluice]

no i dont think so

[acoustic crest]

same

[acoustic crest]

but this is what I actually wanted to know :) thx, appreciate it

[dull onyx]

WHAT

thats a different one

[karmic wraith]

huh lmao

[dull onyx]

this is how ull solve urs @acoustic crest sorry if u got confused with my question 😭

[karmic wraith]

theres no limit

[ocean seal]

Maple

[gentle prism]

Can someone help plsss

[open meteor]

Do you see the pyramid at the bottom?

[gentle prism]

Yea

[open meteor]

How would you begin calculating its area?

[gentle prism]

A=lwh

[open meteor]

*trapezium sorry

[gentle prism]

Oh

Yeah

[open meteor]

there is a formula for the area of a trapezium, do you know it? if not you can just divide it into simpler shapes and go from there

[gentle prism]

Yes i know it

[open meteor]

do you have all the values you need to plug into the formula?

[gentle prism]

Yeah i have the formulas

But idk which ones to use

[open meteor]

$$A=(1/2)(a+b)h$$

[ocean seal]

Maple

[open meteor]

right?

[gentle prism]

Yeah

[open meteor]

do you know what a, b and h are here?

[gentle prism]

A is area b is base h is height

[open meteor]

yeah, and a is the other side, parallel to the base

[gentle prism]

Oh ok

[open meteor]

like this

[gentle prism]

Ok

[open meteor]

it even works when the sides aren't symmetrical like in this diagram

[gentle prism]

Ok

[open meteor]

can you find a, b and h in your question?

it might help to draw out the trapezium separately

[gentle prism]

Ok

B is 16?

[open meteor]

yeah

[gentle prism]

A is 20?

[open meteor]

yep

[gentle prism]

H is also 16 or would it be 10

?

[open meteor]

it's 10, because you're looking for the perpendicular height

[gentle prism]

Ok

[open meteor]

also the order of a and b doesn't matter either. b can be greater than a and the formula would still work

[gentle prism]

Ok

[open meteor]

so can you calculate the area of the trapezium now?

[gentle prism]

Idk why but my teacher gave this formula

Would it work

The one on the left

Is for area

[open meteor]

yeah, that's the same thing really

[gentle prism]

Ok

[open meteor]

your teacher just used different letters

[gentle prism]

A=180?

[open meteor]

yep, good

[gentle prism]

Thanks

[gentle prism]

So In the end the area will be 260 right

Because the other 2 40's

[open meteor]

yep

[gentle prism]

Ok

[open rampart]

Could someone help me solve this?

[lime tangle]

R u doing logs

cuz u can log both sides if u want

[lucid oriole]

On January 1, 2000, the Netherlands had about 15.9 million inhabitants.
On January 1, 2011, the Netherlands had approximately 16.7 million inhabitants.

By what percentage has the population increased?

Round to whole percentages.

can someone help me

[lime tangle]

just do 16.7/15.9

[alpine sable]

end value minus start value gives you the evolution

if you want the percentage of evolution, you divide that by the start value

[lime tangle]

u need to use logs

log both sides

well

do this

$log9^x - log5(2^{x-1.5}) = log2^{x+0.5} + log2(3^{2x-1})$

[ocean seal]

IAMTHEFARMER

[lime tangle]

ye thats how i would do it

@open rampart

[open rampart]

Ohh imma try and do that, thanks @lime tangle

[lime tangle]

no problem

just remember these properties plz

$logab = loga + logb$

[ocean seal]

IAMTHEFARMER

[lime tangle]

$loga - logb = log\frac{a}{b}$

[ocean seal]

IAMTHEFARMER

[lime tangle]

2 more properties u might use

[open rampart]

Thank you :))

[lime tangle]

$loga^x = xloga$

[ocean seal]

IAMTHEFARMER

[lime tangle]

and one more

$log_ba = \frac{loga}{logb}$

[ocean seal]

IAMTHEFARMER

[lime tangle]

thats all u need

@open rampart

enjoy

and good luck

[void anvil]

How do I get the answers on the right when solving?

The symbol I think is suppose to be Pi but not sure

[amber sage]

Each interior angle of a regular polygon, when rounded off to the nearest degree, is n degree. How many possible values of n are there?

[alpine sable]

first, get to know what's the angle of a regular polygon is in function of the number of sides

[scarlet shell]

Hi can anyone help me with this one?

[amber sage]

(k-2)*180/k where k is the number of sides

i dont know how to approach the question

[scarlet shell]

How can show Euler's formula without any degree?

[amber sage]

@alpine sable

[alpine sable]

first pick k = 3, take than number

then k = 4, and so on

as you're rounding the number you got, you'll quickly get all the values you want

[scarlet shell]

<@&286206848099549185>

[amber sage]

n is already an integer if k=3

shouold i try this by trial and error

[alpine sable]

some times it will be, but it wont be for any k

you'll see the number getting smaller, so when you get to 1, it's ended

[amber sage]

ok

[fresh parcel]

well e^3+i is just e^3 x e^i

[scarlet shell]

What does e^i equals to?

[fresh parcel]

and then you can just use moivre formula

e^ix = cosx + i sinx

for all x

[amber sage]

i still dont quite get it

[scarlet shell]

But there is no x