help-0

[lilac stratus]

Nope. Every solution you get needs to be taken into account, otherwise the factorized polynomial and the original one won't be the same.

[lost coral]

like this?

[lilac stratus]

Like what?

[lost coral]

that doesnt help

[lilac stratus]

The 3x is positive, not negative.

[lost coral]

oh

i cant simplify this

oh wait

i've made an mistake

[lilac stratus]

Yep.

But wait.

You're factoring the wrong polynomial.

[lost coral]

u mean this 3x?

[lilac stratus]

Yeah.

[lost coral]

got it

[lilac stratus]

Even if it were negative though, your factorization wouldn't be right, since it's supposed to be (x-4)(x+1).

[lost coral]

like this?

[lost coral]

ye

[lilac stratus]

That's it. Now you can simplify the whole thing.

[lilac stratus]

Oh, hold up.

[lost coral]

3x-1

[lilac stratus]

Just realized it's (3x-1)

Yeah haha.

[lost coral]

haha

[lilac stratus]

There you go.

[lost coral]

im gonna try this

[lilac stratus]

Alright.

[surreal quarry]

.close

[lone heart]

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[covert agate]

you don’t need ‘.open’

[lilac stratus]

What do you mean "make a triangle"? Given three points or something like that?

[gray isle]

the triangle is a shape and it is nonsense to say that its 180°
however if you are referring to the interior angle sum then yes.
the interior angle sum of a triangle is 180°

[lilac stratus]

?

[gray isle]

no! i am NOT a robot if that's what you're suspecting.

[mortal trellis]

everyone is a bot except you

[covert agate]

• the interior angle sum is 180°
• the longest side’s length is shorter than the sum of the two smaller sides’ lengths

don’t tag helpers until no one has answered you for 15 minutes.

[covert agate]

all triangles satisfy these conditions

you verify whether these conditions are violated

take the first one for example

a triangle with measures 60°, 80°, 80°

ie angle sum of 60 + 80 + 80 = 220°

that’s not possible, triangles always have an interior angle sum of 220°

so immediately we don’t check the first box

[covert agate]

check condition 2

also, think before asking

exert some effort

[lone heart]

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@alpine sable Has your question been resolved?

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[oak perch]

x is the middle point
To see this you extend AB and DE, intersection point being O, take a look at triangle OAD. It’s similar to OBE, also similar to OCX

[alpine oxide]

the bit i did not get was

how he got dx

he doubled de

[oak perch]

Is that a problem? It clearly told you what x is

Read it

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[alpine sable]

Tan^2x/sin^2x = tan^2x + 1

[alpine sable]

do u have to prove it

yes

tanx=sinx/cosx

the squared one would be sin²x/cos²x

so (sin²x/cos²x)/sin²x

ya I got that but I can’t go from there to a tan +1

and this would simplify to 1/cos²x

uhh

ok

what next

Ohh I see it

1/cos^2x is sec^2x

And that is basically tan + 1

Tan^2x

Thank you

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[glass tree]

(Precalc practice test) Now I get how I got #9 wrong (rounding error) but I don’t get the others. I think the answer key may be wrong. My answers are:

1. C
2. C
3. B
4. D

[wary stream]

Key is correct

Like number 10, you did it wrong

[glass tree]

Wait I see my error on 1

[wary stream]

.

[glass tree]

did the last calculation wrong on 1. I don’t see my error on 10

[wary stream]

You did math wrong

Plug in x = 4

,w 4/(4 + 4)

[ocean seal]

Results provided by WolframAlpha

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

Requested by dldh06#2659

[wary stream]

,w 1/(4 - 5)

[ocean seal]

Results provided by WolframAlpha

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

Requested by dldh06#2659

[wary stream]

Pretty sure 0.5 isn't less than -1

[glass tree]

Oh it evaluates to -1 not 1

forgot the negative sign

[wary stream]

Like I said, you mathed wrong

Key is correct

[glass tree]

So the only issues I’ve had were just calculation stuff

[wary stream]

Most likely

[glass tree]

:/

well idk how to fix that

and in #6 I did 12am and 4pm not 1am and 4pm :/

well I’m just reading stuff wrong.

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[subtle seal]

I want to show that $(U_n)n)$ converges to l if and only if the two sub-sequences $(U{2n})n$ and $(U{2n+1})_n$ converge to the same l

[ocean seal]

planeboi

[subtle seal]

Can I say that $U_n=U_{2n}$ or $U_{2n+1}$ ?

[ocean seal]

planeboi

[subtle seal]

<@&286206848099549185>

[mortal trellis]

I hope the implication => is clear

so let's do the other direction. suppose that both U_2n and U_2n+1 converge to L

pick epsilon > 0. using that both sequences converge, we then get N_1 and N_2 such that for all 2n >= N_1 we have |U_2n-L| < epsilon and all 2n+1 >= N_2 we have |U_(2n+1) -L | < epsilon. what can we then say about U_n using the constant N_1 + N_2

[lone heart]

@subtle seal Has your question been resolved?

[subtle seal]

U_n such that n>N_1 or N_2 ?

[mortal trellis]

let's use U_k instead of U_n just for some clarity. the idea is that if k is even, let's say k=2n then you can use the first condition. if k=2n+1 is odd then you can use the second. so if k > N_1 + N_2 then you can use both depending on which one you need

[subtle seal]

Oh that makes sense

thank you

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[grave saddle]

could some one please explain this? our Prof ran through it in no time and we are not allowed to ask questions during his lecture. So I literally don't understand anything q.q

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@grave saddle Has your question been resolved?

[grave saddle]

.close

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[stone dove]

Hello, how do I find the limit of this series?

[stone dove]

@proud cosmos why?

[proud cosmos]

because it is difficult

[stone dove]

huh?

yes, it is, but i need to solve it

[proud cosmos]

well, okay

[stone dove]

I found that it indeed converges, but I don't know how to solve it by hand

[proud cosmos]

take a pencil and start writing solution on the paper. that is how you solve it by hand

[stone dove]

well, i don't have a solution

that's what i'm here for

[proud cosmos]

ok. sorry

idk how to do it

[stone dove]

.close

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[edgy breach]

so, when integrating the differential of something - u still need the constant term?

so does it become e^bx/a * y + c = 0 ---> y = -ce^-(bx/a)

but in this case they couldnve just said + k instead of + c and then they're saying -k = c ?

if thats not the case then I dont understand where the c came from

[lone heart]

@edgy breach Has your question been resolved?

[lament glen]

you mean like
$$\int f'(x) \mathrm{d}x$$
?

[ocean seal]

Doggo

[lament glen]

you still need the constant, otherwise
$$\int 2x \mathrm{d}x = \int \frac{\mathrm{d}}{\mathrm{d}x} (x^2) \mathrm{d}x = x^2$$
which is missing the constant when it should be there

[ocean seal]

Doggo

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[bitter vault]

a is the gradient, which is 0

[coral moss]

are you sure it's the turning point and not the roots

[bitter vault]

then you need the tangent at x = 0, not the tangent at the turning point

[coral moss]

somebody has gone wrong somewhere

they're not the same

the gradient here will be h'(x)

h''(x) is like the "rate of change of gradient" if you get what i mean

depends what you're trying to find

but then the gradient will be 0 as stated earlier (for your tangent). Your turning points are at x = 0 and x = 4

A and B here are your turning points

seems like a very badly worded question (unless the translation is a bit off or you're actually looking for those 2 lines)

because then the tangents will just be y = -20 and y = 12

the straight lines are your tangents

what language was it translated from

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@sonic gate Has your question been resolved?

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[frosty pelican]

hi, so finals for my first year of high school are almost up and i have this little thing that i don't understand

[frosty pelican]

how does 1-4y + 4y^2 become (2y-1)^2

[karmic rapids]

what happens if you multiply out (2y-1)^2?

[frosty pelican]

i'm honestly not sure lmfao

i don't know how to put brackets with x and y raised in ^2

i mean with a number in them

[tacit arch]

have you heard of FOIL?
https://www.cuemath.com/foil-formula/

[frosty pelican]

mhm, but how does this apply here

[tacit arch]

$(2\lambda - 1)^2 = (2\lambda - 1)(2\lambda - 1) = (2\lambda)(2\lambda) + (2\lambda)(-1) + (2\lambda)(-1) + (-1)(-1)$

simplify that last equality

[ocean seal]

riemann

[tacit arch]

it's used to get the last equality

[frosty pelican]

im still a bit confused

how would you simplify the last equality

jesus i need to understand some basic shit xD

[tacit arch]

https://www.khanacademy.org/math/algebra-home/alg-intro-to-algebra/alg-manipulating-expressions/a/combining-like-terms-reminder

[frosty pelican]

ok so for this it'd be (2λ)(2λ)+2λ+2λ-1-1-1-1

by what im seeing in this

that feels very wrong lmfao

are we supposed to seperate the 2 from the λ too?

[lone heart]

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@frosty pelican Has your question been resolved?

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[weary wraith]

hello

[open folio]

[weary wraith]

i forgot how to solve unlike denominators im doing my brothers homework

youtube videos didnt help

hes in the 6th grade right now

i am stuck in 7_5 + 1_3

and 4_3 - 2_6

[open folio]

$\frac{7}{5} + \frac{1}{3}$

[ocean seal]

Breeziboi

[open folio]

https://www.khanacademy.org/math/cc-fifth-grade-math/imp-fractions-3/imp-adding-and-subtracting-fractions-with-unlike-denominators/v/adding-small-fractions-with-unlike-denominators

[weary wraith]

i just need help with figuring out the question and not the answer

alright thanks

[novel lintel]

you can add both when they have the same denominator. So just multiply both by the gcd(5,3)

[weary wraith]

thank you very much

[weary wraith]

that video helped so much

[open folio]

Khan academy is my go-to for math

[weary wraith]

they are amazing to be honest

i might donate

again thank you so much for the video have a good day

you can close the channel if you want

cya

[lone heart]

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[next flax]

why can't we simplify sqrt(65)

[wide niche]

Because it’s not divisible by any integer square numbers

[next flax]

because it only has prime factors ?

[wide niche]

I’m talking about it’s not divisible by 4, 9, 16, 25 ect

[next flax]

ahhh i seee

so for the quadratic equation

i got the answer (5/2) ± (sqrt(65) / 2)

is this the right answer?

[wide niche]

Yes

U can always sub it back into the equation to double check

[next flax]

thank you !

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@next flax Has your question been resolved?

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[lyric karma]

How many ways can we assemble five containers when water is in three containers and oil in two?

[keen bear]

Well, in cases like this we can brute force it. First we have to know a few things: can we distinguish the bottles of water?

As in is there a difference between water 1, water 2 and water 3?

[lyric karma]

no

There is no difference because they are all water

[keen bear]

Ok, well then, let's consider that we only have two options: oil, or water. We can just decide to care about where the oil is.

[lyric karma]

mhm

[keen bear]

So let's go through some examples:
If 1 is oil and 0 is water
11000
10100
10010
10001
...
00011

If you notice, we only have to care about 2 out of the 5 bottles

[lyric karma]

nhn

[keen bear]

So we can model this with 5 choose 2

[lyric karma]

so 10?

[keen bear]

Yep, which we can check via exhaustion by continuing the examples above

[lyric karma]

ahhh ok

I still need help for the other ones? If you can, we can vc?

[keen bear]

Can't vc, but I can help

[lyric karma]

Ah ok+

We have two identical pink balls and two identical white balls. We arrange them in a row in all ways. How many different arrangements are there?

My answer for that is 6, is it correct?

[keen bear]

Well, if we set it up just like the previous problem, we have 2 balls to care about out of a total of 4, so 2 choose 4, which is indeed 6

[lyric karma]

ah ok

Anya borrowed four books from the library. How many orders in which she could read them one at a time?

for this one, I am very confused

what does it mean by she could read them one at a time?

[keen bear]

She has 4 books, right? Let's call them a b c and d. She can't read multiple at once, so we have to think of how many orders we can put the books in

How many options does she have for her first book?

[lyric karma]

4 options

[keen bear]

Good, now she's read one, how many options would she have for the second book?

[lyric karma]

3

since she already read one

[keen bear]

Now how many for the 3rd book?

[lyric karma]

2 because she read the 2nd book and the first one

and for the last one 1

24 is the answer?

[keen bear]

4!=24, yep

[lyric karma]

Joline, Jenna, JM, and July went to a classical music concert. How many different ways can they sit in the four free seats if July wants to sit with JM?

How many characters can we create from two commas and four dots?
My answer here is 12

2 mins

[keen bear]

Characters? Like an ordering?

[lyric karma]

in any ways ig

[lyric karma]

for this one?

[keen bear]

For the commas and dots

[lyric karma]

12

right?

[keen bear]

I'm not sure, depending on what counts as a character

[lyric karma]

ah ok

but for Joline, Jenna, JM, and July went to a classical music concert. How many different ways can they sit in the four free seats if July wants to sit with JM?

[keen bear]

That one is less than 24, I know that.

But I don't know fast enough on it, srry

[lyric karma]

its ok

Thank you for the help!!

[keen bear]

It's a start

[lyric karma]

.close

[lone heart]

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[lone heart]

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[tidal magnet]

.help

[lone heart]

Commands:
clopen: .close, .reopen
factoids: .tag
help: .help

Type .help <command name> for more info on a command.

[tidal magnet]

.open

e

[tidal magnet]

The degree of polynomial

<@&286206848099549185>

[rotund garnet]

The degree of a polynomial is vocabulary to mean: the highest power of x
The degree here is 6

[lapis ingot]

ping helpers after 15 minutes

not right after posting the problem

[tidal magnet]

thanks

Find the sum.

[merry coral]

they wrote and not add

[rotund garnet]

Here you would add (find the sum --> addition) the two polynomials by combining the like terms.
Combine 2x^2 and -4x^2 --> -2x^2
Combine 5x and 6x --> 11x
Combine -7 and 3 --> -4

[merry coral]

the question wrote and

I think this is a system

[tidal magnet]

whats the answer mate?

<@&286206848099549185>

[swift shore]

@tidal magnet what’s the issue

[tidal magnet]

this man

[swift shore]

You add the like terms

[tidal magnet]

Tell whether the two figures are congruent.
*

im done with that

[swift shore]

Ah

Do you know what congruent means?

[tidal magnet]

nope

[swift shore]

It means they’re the same

Like if you cut out one of the triangles and placed it over the other triangle, the sides would line up perfectly

[tidal magnet]

ah

[swift shore]

So what do you think here? Are they the same?

[tidal magnet]

yea

ig

correct me if im wrong

[swift shore]

You’re right

They are

[tidal magnet]

thank you so much

[swift shore]

Same angles, same side lengths… they’ve gotta be the same

Yeah np

[tidal magnet]

If we multiply 5x and -(-4xyz) then we get?

[swift shore]

Well maybe simplify -(-4xyz)

What would that become

[tidal magnet]

-2x^2yz?

[swift shore]

What?

[tidal magnet]

o

multiply

sorry

[swift shore]

No no, what’s this

Start with this

[tidal magnet]

aight

[swift shore]

Don’t overthink it it’s easy lol

[tidal magnet]

-20x^2yz?

ig

[swift shore]

Not quite

How you do figure that

[tidal magnet]

is that right?

[swift shore]

Not quite

[swift shore]

?

[tidal magnet]

lets say

multiple choices

[swift shore]

Wdym

[tidal magnet]

multiple choice

wait

[swift shore]

What about it

[swift shore]

I’m asking how you got to this answer

Wait are you just throwing random answer choices at me? lol

[tidal magnet]

idk man

my brain is melting...

[swift shore]

What? Did you come up with this or not? Yes or no

[tidal magnet]

i didnt

i have multiple choice in my question...

[swift shore]

Ok

[lone heart]

@tidal magnet Has your question been resolved?

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[sharp prairie]

Hi guys. I dunno if this task is too large, but I don't understand a single thing that is happening in this review, can someone help me with finding resources to learn this within 12 hours?

[sharp prairie]

thanks in advance <3

[lone heart]

@sharp prairie Has your question been resolved?

[tacit arch]

Just screenshot and share.

[lone heart]

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[opal spindle]

Hello, I would like to know if I can solve for 2 unknown vectors if I know their sizes and dot product

[opal spindle]

*cross product

more specifically i have a 3x3 matrix with known elements

trying to find the 1x3 and 3x1 matrix that multply for it

is it even possible?

[velvet pelican]

if you think about it, you end up with 6 unknowns and 9 equations

and since you can scale solutions by a factor, you wither have 0 or infinite solutions

[opal spindle]

yeh i thought it was infeasible

spent like 30 mins tryna work out similtanous equations

ah well thank you

[velvet pelican]

the best attempt you have is to maybe find integer solutions

by factoring out the 1/30 and dealing with it later

but i dont think there are any

[opal spindle]

I've actually figured it out with the context

it was a joint probability distribution matrix

i just need to add the values in the columns lol

[velvet pelican]

nice

[opal spindle]

thank u!!

[velvet pelican]

my pleasure

[opal spindle]

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[loud rover]

Could someone explain what g(y^2) would mean in this case?

[loud rover]

im a bit lost and ive got an exam in 5hrs

[vale wigeon]

g(y^2) is what happens when you evaluate the function g at y^2

[loud rover]

so 2y^6 + 5y^4 +5y^2 -4 = 0

cheers ty

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[wheat crystal]

Hi does anyone know how to simplify this square root?

i thought u would make 8 2sqrt2

and then factor but its wrong

[gray ingot]

try to create a square inside

so that the outer sqrt gets cancelled

[wheat crystal]

how

[gray ingot]

using a^2 + b^2 + 2ab

[wheat crystal]

2sqrt2+15^2?

[gray ingot]

no

ab = sqrt(15)
a^2 + b^2 = 8

try to find a and b

then your answer would be a + b

[wheat crystal]

2+6? idk

[gray ingot]

hint what are the factors of 15, that add up to 8

[placid zinc]

There's some way to express it like:
8 + 2√15 = (a + b√15)²

Finding that gets rid of the √

[wheat crystal]

5 and 3

[gray ingot]

yep

now (sqrt(5) + sqrt(3))^2 is?

[wheat crystal]

3sqrt5?

wait

no special product

uh

[gray ingot]

use (a + b)^2

$(\sqrt{5} + \sqrt{3})^2$

[wheat crystal]

5

uh

2sqrt15

+3?

[ocean seal]

Swas.py

[wheat crystal]

8 2sqrt15

[gray ingot]

8 + 2sqrt15

yes

yes and that is your answer

[wheat crystal]

Ohhhh

why does the simplify calculator not do that?

symbolab

im so confused

[gray ingot]

[wheat crystal]

Thanks for your help. 🙂

[gray ingot]

$\sqrt{8 + 2\sqrt{15}} = \sqrt{(\sqrt{5} + \sqrt{3})^2} = (\sqrt{5} + \sqrt{3})$

[ocean seal]

Swas.py

[gray ingot]

@wheat crystal ^

the general trick to simplifying double radicals is this

[wheat crystal]

special products?

what if they dont work

can completing the square work lmao

[oblique pier]

there's actually a trick for these kind of simplify problems

you have calculator?

[wheat crystal]

yeah

[oblique pier]

what's the type of calculator?

[wheat crystal]

symbolab 😂

when simplifying these

they dont let us use a calculator tho

[oblique pier]

bruh

then

you have have to remember by heart

[gray ingot]

its already a complete square

most of the times

you just need to find it

[oblique pier]

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

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

[wheat crystal]

Yea

alright

Ty

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[alpine sable]

im confused to solve for y on 2y-4/3=x

[gray ingot]

what have you tried?

[alpine sable]

Multiplying by 3

but it didn't work

[gray ingot]

why not

you'd get
2y - 4 = 3x

[alpine sable]

then idivided by 2 and got

y=3x+2

but it was wrong

[gray ingot]

it is wrong

2y - 4 = 3x
2y = 3x +4
y = (3x+4)/2

[alpine sable]

do i have to isolate

[gray ingot]

or $y = \frac{3x}{2} + 2$

[alpine sable]

y before idivide?

[ocean seal]

Swas.py

[alpine sable]

so i isolate y

before i divide

then

[gray ingot]

yes isolate y

then divide

[alpine sable]

that was my mistake

thanks you

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[hushed mica]

guys someone tell me how did it get converted from

n^2 + 1 to n^2 - 1

[merry depot]

it didn't

If a|b and a|c then a|(b-c)

[hushed mica]

so those r two different fractions

[merry depot]

if you assume n+1|n^2+1 and you know (by factoring) n+1|n^2-1, then n+1|(n^2+1-(n^2-1))

[lone heart]

@hushed mica Has your question been resolved?

[lone heart]

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[strong juniper]

I get to

[last ether]

Set it into standard form

First

[strong juniper]

yeah

[last ether]

Make that question into standard form

[strong juniper]

i got it into slope form

[last ether]

What do you get

Don't do slope form

Standard form is easier

[strong juniper]

standard form?

[last ether]

$$4x - 3y = -24$$

[ocean seal]

Umbraleviathan

[last ether]

You know that the x intercept is (a, 0) where a is the intercept; the y intercept is (0, b) where b is the intercept

That means that for the x-intercept, y must equal 0; for the y-intercept, x must equal 0

[strong juniper]

ok, let me digest this for a second

[last ether]

Solving for y-intercept:

$$4(0) - 3y = -24$$
$$-3y = -24$$
$$y = 8$$

[ocean seal]

Umbraleviathan

[last ether]

I hate latex why is it shoving it to the right

[strong juniper]

yeah I can get to y = 8

y intercept

= 8

So ok.

4(x) - 3(0) = -24

4(x) = -24

24 / 4 = 6

x = 6

wait.

-4(6) = -24

idk if it should be 4(-6) = -24

but im guessing its -6

[last ether]

Yeah it's -6

[strong juniper]

ok

[last ether]

So it would be A

[strong juniper]

yup

just typing another question hold on

actually no thats a dumb question

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[chrome prism]

Suppose y is directly proportional to x^3, what happens to y if x is increased by 20%?

[flat ore]

what is the value of x increased by 20%

[chrome prism]

wdym

[flat ore]

exactly what I said

what is the expression for x increased by 20%

[chrome prism]

y directly proportional to x^3

[flat ore]

ignore that

first tell me what is 100 increased by 20%

[chrome prism]

120

[flat ore]

100 + (20/100)* 100

correct?

now do the same for x

[chrome prism]

wdym

[flat ore]

instead of 100, do it for x

what is x increased by 20%

[chrome prism]

x + (20/100) *100

?

[simple turtle]

x+.2x

[chrome prism]

why is it .2x?

[simple turtle]

20/100=.2 x is increased by 20%

[chrome prism]

wait

so shouldn't it be only .2x

instead of x+.2x

oh wait nvm

it is x+.2x

[simple turtle]

no. if you increase 10 by 20%, it is 2. it is 10 + .2(10) = 12

[chrome prism]

ok ik now

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[vagrant rover]

f(x) = sqrt(x+4)/x-4 is x here nonnegative too? @lofty oriole

[vagrant rover]

And x =/= 4, right?

[rotund garnet]

x =/= 4 from the denominator, and (x+4)>=0 or x >= -4 from the sqrt.

in interval notation, that's
[-4, 4) U (4, inf)

[lofty oriole]

x + 4 is nonnegative, and x =/= 4

[vagrant rover]

Can you say that x is nonnegative thoguh? Since you can't have two different value for each x.

Like do you have to say x+4 is nonnegative

or is x itself nonnegative in both x+4 and x-4 since it is nonnegtaive in one of them.

Like are these classifications universal or relative?

[rotund garnet]

you're focusing in on the word nonnegative I think too much. You have two things going on here

1. Dividing by (x-4)
   You can't divide by zero. That means x cannot be 4. Hence, x=/=4

2. Taking square root of (x+4)
   You can't square root negative numbers. That means (x+4) must be greater than or equal to zero. Hence, x>=-4

Combining these restrictions into one domain, we say
x: [-4, 4) U (4, inf).
or in other words,
x>=-4, but x =/= 4.

[vagrant rover]

Makes sense

Is it okay to write it as 0 <= x =/= 4?

Or is that a nono?

[rotund garnet]

naw that's saying something completely different, the number zero should be nowhere in your answer 😛

[vagrant rover]

Oh I see

Question

This says that all real numbers for this functions' domain are less than -4 excluding 4.

[rotund garnet]

"less than" is a typo. That should say greater than.

[vagrant rover]

Is that correct? I thought it was all real numbers greater than -4 excluding 4.

Ah okay, yeah

Smarter than the answer key

Very based

thank you

[rotund garnet]

5 yrs of private tutoring, 500 students, in my experience answer keys are only right some of the time xd

[vagrant rover]

xd

By the way, how do you get to the point where you just know all of these fundamentals

[rotund garnet]

5 yrs of private tutoring

[vagrant rover]

I just feel like there is so much I don't even know yet

[vagrant rover]

ahhhhh

[rotund garnet]

and I'm working on a math major

[vagrant rover]

Oh I see

[rotund garnet]

I do math 10 hrs a day every day haha

[vagrant rover]

Dang, super cool

Chad

[rotund garnet]

[vagrant rover]

I wish I was good enough to do that

I'm trying 🤷

I put in like 15 hours today

It's actually 9:11 AM and I haven't slept lol

I have too much school work

[rotund garnet]

dam bro, get sleep. 8 hrs of sleep is the best thing you can do for an exam score. Don't cut into sleep for study!

sleep is prio #1 your brain needs it

[vagrant rover]

Oh there isn't anything I can do, I have 1 1/2 months to finish half a school year so that I can submit my final transcript to the uni that I got into so that I can start

It's not by choice

But it's the right thing in this case

ANyways, back to it

Tysm for the help

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[cedar field]

Why is the answer to cos in this a square root if this is how you calculate cos?

[astral vessel]

the square root is the adjacent side length over the hypotenuse

if that is what you mean

[vale wigeon]

@cedar field do i understand correctly that your point of confusion is: "i learned that square roots are irrational, i.e. cannot be written as fractions, and yet here we are with x/r somehow equaling sqrt(3)/2; what gives?"

[cedar field]

how can lets say 4 divided by 1 be a square root?

[cedar field]

and yes maybe

[rotund garnet]

x/r doesn't specify x or r need to be integers. x is sqrt3. r is 2.
so x/r is sqrt3 / 2

square roots cannot be written as fractions of two integers. there's nothing wrong with writing a square root in a fraction

[vale wigeon]

here x is sqrt(3)/2 and r is 1, but yes, that was my point

[cedar field]

why does it sound so complicated if its just this?

[vale wigeon]

well... ok, would you like to go through why cos(30°) is what it is? a derivation that uses geometry and nothing else?

[cedar field]

ok

[vale wigeon]

is that a yes or a no

[cedar field]

yes

please

[vale wigeon]

okay

let's start with an equilateral triangle

it'll be convenient for us to take its side length to be 2

i'll make a diagram in just a moment

do you follow so far?

[cedar field]

yes i do

[vale wigeon]

now i will draw a line from B to the midpoint of AC, which i will call D

since this equilateral triangle is also isosceles, this line will be the median, the altitude and the bisector all in one.

[cedar field]

so from b to the 2 at the bottom

[vale wigeon]

"the 2 at the bottom" is nothing more than a length label. it doesn't refer to any point.

and in fact i will now get rid of it to make room for length labels of the two halves.

do you understand this diagram?

[cedar field]

yes

i do

[vale wigeon]

alright

now tell me

are you familiar with the pythagorean theorem

[cedar field]

yes quite

fimiliar

[vale wigeon]

okay

can you go ahead and use it to calculate BD then?

ping me when you're done

[cedar field]

maybe im not that good I know 22+b2=c2

[vale wigeon]

that sounds nowhere near the pythagorean theorem

[cedar field]

oh I think i meant the Pythagoras theorem

[vale wigeon]

same difference.

what i was hoping you'd go for is:

AD^2 + BD^2 = AB^2

[cedar field]

oh

ok so ad 2=2

bd 2=2

[cedar field]

is that right?

[gray isle]

what's ad 2 supposed to mean

[cedar field]

squared

[gray isle]

what's bd 2 supposed to mean

[vale wigeon]

the symbol ^ exists, you know.

[cedar field]

oh

[gray isle]

what's the length of AD?

[cedar field]

1

[random beacon]

can i know the question

[gray isle]

and what happens when you square that value?

[random beacon]

what is that value

[vale wigeon]

i am trying to walk kangaroo rat through rederiving from scratch the value of cos(30°), and to this end i've drawn them an equilateral triangle in which i've drawn one median to split it into two 30-60-90 triangles

and we are currently at the point where kangaroo rat is trying to apply pythagoras' theorem to a right triangle whose hypotenuse is 2 and one of whose legs is 1, to find the other leg

[random beacon]

yeah

i can get it

ima wait if kangaroo rat can come up with the answer

[cedar field]

wait i gotta go can I or you DM you in about 12 hours to continue?

or i can do it now for two minutes

and also ad^2=2 bd^2=2

is this right

[random beacon]

just uhh keep this conversation ?, i just need to know what u have learn and come back later, we can all help your problem

but wait, ad^2 = 2 when ad = 1 , uhh do u see it wrong

[vale wigeon]

if it really is in about 12 hours then i will be available (though 11 might spell some trouble)

[random beacon]

and bd^2 isnt 'bout = 2 due to pythagoras theorem

[glass python]

ouh

[random beacon]

since bd^2 + ad^2 = ab^2 (pythagoras theorem)
and know ad = 1 and ab = 2
u know that bd^2 cannot equal to 2

[glass python]

ax2+bx+c=0 is what ?

iam grade 10th and learning this now

[vale wigeon]

@glass python please open your own channel

[glass python]

mean?

[random beacon]

we will moving to your own channel, read #❓how-to-get-help

[glass python]

ouh

tq

[cedar field]

ok ill DM you then

[random beacon]

or me if u're sooner, 12hour more is my 3AM so if u avail sooner than expect and cant contact Ann u can dm me, im avail until my 11PM

[cedar field]

ok

thanks

[random beacon]

u can close the channel if you want, for other people use

[cedar field]

.close

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[thorn vessel]

hey

[thorn vessel]

On a meadow there are sheep and geese

And there are 18 heads and 58 legs

How many sheep and geese are there?

[spark creek]

Let the number of sheep be x and the number of geese be y

Start from this and form 2 different equations using the data about the heads and legs

[thorn vessel]

so like

x + y = 18 and
x + y = 58 ?

[spark creek]

The first equation is correct
x+y=18

Second one is incorrect

How many legs does a sheep have? And how many legs does a geese have

[thorn vessel]

well sheep has 4 and goose has 2

[spark creek]

Yup

So if you have x sheep then total sheep legs is how much?

Similarly how many goose legs

[thorn vessel]

4 times x? and 2 times y ?

[spark creek]

Yup

So now what will be the second equation

[thorn vessel]

4y + 2y = 58 ?

[spark creek]

Correct

[thorn vessel]

4x*

[spark creek]

You can solve it now

[thorn vessel]

yes thank you very much

i appreciate the help

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[errant hinge]

how a = yi

yi = a

trw i have an exam

Please some on help so i get some good marks

[vale wigeon]

$y_i$ is either $a$ or $-a$ depending on the point

[ocean seal]

Ann

[vale wigeon]

by definition of your system really

[lone heart]

@errant hinge Has your question been resolved?

[errant hinge]

oh

but in here can yi be either a or -a

if so then 2summationi=1 mi xiyi

@vale wigeon

x = 1 y = 1 leads to 2m but how -2m

[vale wigeon]

...

[errant hinge]

like

in 3x3 matrix

a11 = 2||(upperlimit)||summation1||(lower limit)|| (y^2+z^2)*m. Since z=0 it will be

2summation1( y^2)*m

y can be 1 or -1 by your point right

so a11 = 2m(1)^2 = 2m

ok wait let me first confirm the formulae

@vale wigeon thanks

trw my exam it is furstating

😢

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[lethal cairn]

is this correct? had this question on a test yesterday but i feel like this solution is just too simple for it to be right...

and no i don't have the answer key or my grade yet

[vale wigeon]

that first substitution you made looks very very suspicious

[lethal cairn]

is it?

[vale wigeon]

i mean, you now have a summation in the right-hand side whose number of terms is 1/y

which i personally would've been very cautious with

you then just blithely expand it and say that since each term approaches 0 so does the sum, even though the number of terms is variable and even approaches infinity as y goes to zero

which... no, you can't do that.

[lethal cairn]

oh i see

i also tried to write the limit as a series but that didn't get me very far

[vale wigeon]

i mean ok

have you worked with riemann sums yet

[lethal cairn]

nope i don't know what that is

[vale wigeon]

...right ok so we are to take this at face value

[lethal cairn]

this was on a practice test for college entrance

[vale wigeon]

so you have $\frac{1}{n} \sum_{i=1}^n \paren{3\paren{\frac{2i}n}^2 + 2\paren{\frac{2i}n} + 1}$

[lethal cairn]

yes

[ocean seal]

Ann

[vale wigeon]

which, after some simple algebra, expands into $$\frac{12}{n^3} \sum_{i=1}^n i^2 + \frac{4}{n^2} \sum_{i=1}^n i + \frac1n \sum_{i=1}^n 1$$

[lethal cairn]

right

[ocean seal]

Ann

[vale wigeon]

do you know how to calculate $\sum_{i=1}^n i^2$, $\sum_{i=1}^n i$ and $\sum_{i=1}^n 1$?

[ocean seal]

Ann

[lethal cairn]

i don't know the first one i could do the rest

the second one is n(n+1)/2 and the third is just n right

[rotund garnet]

Ye

[vale wigeon]

yes

the sum of the first n perfect squares is n(n+1)(2n+1)/6

[lethal cairn]

i see

so if you expand that you get (2n^3 + 2n^2 + n)/6n^3

1/3 + 1/3n + 1/6n^2

[vale wigeon]

careful with the lack of parentheses around the denominator

[lethal cairn]

oh sorry times 12

[vale wigeon]

though the exact values are somewhat beside my point here

once you substitute everything in, you will have this:

$\frac{12n(n+1)(2n+1)}{6n^3} + \frac{4n(n+1)}{2n^2} + 1$

[ocean seal]

Ann

[lethal cairn]

yeah

[vale wigeon]

and from here you can either do it the honest way and expand it out, or note that both fractions here have the same degree in the num and denom and so really all we're after is the ratio of the leading coefficients

but either way this is an honest to goodness rational function in n

[carmine lion]

limit should be 3?

[lethal cairn]

so you get (4n^3 + 6n^2 + 2n)/(n^3) + [4n(n+1)/2n^2] + 1 = 4 + 6/n + 2/n + 2 + 2/n + 1

shouldn't it be 7?

[carmine lion]

oh fuark forgot u could cancel the n and n^3

[vale wigeon]

7 sounds correct actually

[lethal cairn]

oh awesome

thanks so much for your help!

[carmine lion]

welp how many marks

was this in ur test

[lethal cairn]

all the questions were worth 4 points

[carmine lion]

oh

ok

[lethal cairn]

yeah it was a practice test though that's what they're for

[carmine lion]

nice nice

[lethal cairn]

thanks for the help guys

.close

[lone heart]

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[carmine lion]

yeah

[lone heart]

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[deep harbor]

Malin says that the probability of rolling a regular dice four times without getting a six is ​​approx. 50%. How does maline reach this value?

[vale wigeon]

have you made any progress so far?

[deep harbor]

no

i'm comfused

I know it has something to do with 5/6

[rotund garnet]

Nice. 5/6 is the probability of not getting a 6 on a single roll.

[deep harbor]

yes

[rotund garnet]

To get the probability of independent events, like rolling a dice, you multiply the probabilities.
In this case, that's (5/6)(5/6)(5/6)(5/6) or just (5/6)^4.

[deep harbor]

wait

(5/6)^4

?

[rotund garnet]

Ye

[deep harbor]

.close

[lone heart]

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[sick smelt]

the function is 2arcsin(2x+ (pi/2))

and i just kinda want to know what im trying to be finding

[lone heart]

@sick smelt Has your question been resolved?

[sick smelt]

<@&286206848099549185>

[lone heart]

@sick smelt Has your question been resolved?

[sick smelt]

gave up

.close

[lone heart]

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[lone heart]

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[half topaz]

How to find a, b and c

[lone heart]

Please don't occupy multiple help channels.

[wary stream]

You have to close your other channels before opening new ones, using .close

[half topaz]

Done

[wary stream]

So if you recall the last problem, there was a set, the values from 1 - 10

And P was the set of powers and Q was the evens

This problem is similar, you have the set from 2 - 10, and A is the set of primes from 2 - 10

B is the set of values greater than or equal to 5

And C is the set of values less than 4

[half topaz]

Why does it say x;x

[wary stream]

It's just notation

The value of x, for when x is >= 5

[half topaz]

B=5 6 7 8 9 10

[wary stream]

Yes

[half topaz]

C=1 2 3

[wary stream]

Yes

Think you can handle the rest now?

[half topaz]

A= 2 3 5 7

[half topaz]

Yes

Shall I close it

.Close

[wary stream]

Lower case c

[half topaz]

.close

[lone heart]

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[earnest violet]

bruh i dont have math help room

[lone heart]

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[earnest violet]

how to obtain

[wary stream]

Just take

[earnest violet]

oh

[wary stream]

You took this channel, you have this

[earnest violet]

ok

[wary stream]

Read #❓how-to-get-help

[lone heart]

@earnest violet Has your question been resolved?

[lone heart]

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[half topaz]

Can someone explain this to me
Q j

<@&286206848099549185>

[woven crane]

,rotate ccw 90

[woven crane]

what exactly is the issue?

[half topaz]

I can't understand how to do question j

.close

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[tidal trout]

$$\frac{5^{a+3}-55\cdot 5^{a-1}}{5^{a+2}+89\cdot 5^a}$$

[ocean seal]

Nayan RBLX

[tidal trout]

$$:\frac{5^{a+3}-55\cdot 5^{a-1}}{5^{a+2}+89\cdot 5^a}=1$$

[ocean seal]

Nayan RBLX

[tidal trout]

how do we solve this

[astral pebble]

What did you try?

[tidal trout]

I tried taking the 5^a common

[woven crane]

and?

[tidal trout]

and i tried solving it

but the ans didn't come

[woven crane]

show your working?

[tidal trout]

I rubbed it

I was doing with pencil

[woven crane]

try again and show where you get stuck

[tidal trout]

alr

[astral pebble]

Yeah we're not going to solve it for you but we can help you identify your mistakes.

[tidal trout]

my phone has no charge

🗿

but basically I got 25-55/10+89

-30/99

-10/33

[astral pebble]

And how did you get to that answer

Also do you have the correct answer

[tidal trout]

i took 5^a common

no

its a prove that question

[tidal trout]

.

[astral pebble]

You have to be more specific.

[woven crane]

that is the right approach though^ I guess you made a mistake in doing that, so we'll need to know what you did specifically

[tidal trout]

5^a(5^3-55 * 5^-1)/5^a(5^2+89*1)

[gloomy stream]

if you're solving for a, then it can be any real number

[gloomy stream]

that's right

[tidal trout]

its a prove type question..

I have to get 1

[gloomy stream]

you did

[tidal trout]

how?

[gloomy stream]

solve that, it equals 1

show your next step to see where you're going wrong

[tidal trout]

nvm me dumb

I was doing - before / in the numerator

I want to die

anyways thanks for the help

[gloomy stream]

np

[tidal trout]

.close

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[thorny solar]

Hello, was recently reviewing some math-physics based notes my friend shared with me, (i was absent from class), i asked where the minus came from and she wasnt sure.