help-0

[cunning locust]

ya feel

actually

[fast lichen]

-1/6-(-2/6)

[cunning locust]

no dont laugh

[frank apex]

yes I do feel that 0.3 - 1 = -0.7

[cunning locust]

ok lol

😅

is this because -1/6 is smaller

that ur subtracting it?

just curious

[fast lichen]

no this is always the order

[cunning locust]

cause if u were to ask me subtract y value 5 from 4. it would be 1

but u want the x value right

x value difference

[fast lichen]

no not yet

[cunning locust]

or we just simply doin

the slopes

subtract 1 from other

[frank apex]

yes

[cunning locust]

so the slope of 2nd mius the 1st

[fast lichen]

yes

[cunning locust]

ok

[fast lichen]

this is always difference

even wheny ou did rise/run

its y_2-y_1/x_2-x_1

[cunning locust]

ok so the answer

is 0.1666666666667

😅

[fast lichen]

yes thats the rise

run is 3

(1/6)/3

1/18

[cunning locust]

if u divide two slopes, that gives u the rise avg of both?

[fast lichen]

$f''(-2) \approx 1/18$

[ocean seal]

Køter

[cunning locust]

then divide that by run 3

[fast lichen]

its just

rise/run

but taken to the 1st derivative

[frank apex]

noo

[fast lichen]

f''=rise'/run'

[cunning locust]

shouldnt u be doing avg rise* of both/2?

to get the run

[fast lichen]

no just choose a value that somewhat makes sense

this is not a robust thing

its approximating

f'=rise/run so we just extend that idea

f''=rise'/run'

where the rise' is the difference in slopes

and run' you can choose i would say between 3 and 6

[cunning locust]

rise'/run' = subtract slope #2 by slope #1 / common distance of both, which is 3

?

[fast lichen]

sure

[cunning locust]

would this method

work for all the other ones

if i wanted to find

f''

like if they gave me graph

thats weird

w/ more than 1

curve

etc

[frank apex]

no
derivative of a fraction isn’t deriv of numer over deriv of denom

[fast lichen]

i am disregarding a bunch of notation

[frank apex]

fair enough

[fast lichen]

this is not rigorous

[frank apex]

just ensure it’s not “how much the rise changed divided by how much the run changed”

[cunning locust]

y not

[frank apex]

bc that doesn’t work

[fast lichen]

yea its how much the slope changed

[cunning locust]

we just did that

[frank apex]

yep

[fast lichen]

it works as an approximative eyeball test

to find out acceleration at some specific point

[cunning locust]

well i trust

it

with my life

koter take a break bro

u helped me so much

ily bro

@frank apex can u help me find out y i got this wrong

[frank apex]

you put values where the first derivative is 0

[cunning locust]

first deriv, is where x = 0

[frank apex]

no

[cunning locust]

f'(x)=0

[frank apex]

there’s no x here

[cunning locust]

t bro

lol

[frank apex]

and that’s the first derivative

[cunning locust]

ohhh

2nd dy/dx

[frank apex]

ye

[cunning locust]

should i do

what koter taught me

just now

[frank apex]

ye

[cunning locust]

bet

do i do that

for all 3 points

14,42, and 56?

[frank apex]

3?

you don’t know where P’’ is 0

[cunning locust]

not off the top of my head man

thats yi asked

koter

he told me how to find it

but

if u know a more obvious way

to get p'' is 0

please let me know

[frank apex]

one thing you can do is graph a sketch of P’ and see where it’s horizontal

[cunning locust]

ok

ngl zfn

my sketch

is horrid

i dont htink

u wanna see it

@frank apex

[frank apex]

hmm

[cunning locust]

fixed it

[frank apex]

from 0 to 14 the slope is positive

not negative

[cunning locust]

slope is increasing tho

[frank apex]

e

[cunning locust]

technically

its falling yea

below axis

[frank apex]

no

[cunning locust]

in my picture

is waht i meant

so i fked up

gotta fix it

[frank apex]

alr

[cunning locust]

is that better

@frank apex

[frank apex]

the slope is really high at x = 0

f’(x) shouldn’t go down as you go towards 0

[cunning locust]

but if i put it really high then it would be decreasing to t=14

[cunning locust]

it doesnt decrease from t=42-56?

[frank apex]

f'(x) is in fact decreasing from 0 to 14

[frank apex]

no it does

[frank apex]

edited

you just need 1 change to your graph

[cunning locust]

but from left to right you should be increasing

from right to left between 14-0, it makse sense

[frank apex]

basically at 0 the slope is high

so f'(x) should be high

[frank apex]

uh

[frank apex]

this was better

[cunning locust]

forget

about the overlapping

yes

im just showing like

the slopes

now i gotta

graph it

f'(x)

@frank apex

[frank apex]

yeah that's goodish

except it got kinda warped

so where is that graph flat

and why did you graph for values greater than 63

[frank apex]

(this is the main question)

[cunning locust]

21 and maybe 49?

[cunning locust]

can you show me you would graph it?

[cunning locust]

was trying to show u that slope was high idk

as in, it went straight down

@frank apex

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[lone heart]

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[alpine sable]

Find irrational no. between 0.71425 bar and 0.81 bar, how to solve? Can I write 0.81 bar as 0.81818 bar and then a no. between 0.71425 and 0.81818

[slender quiver]

!status

[lone heart]

What step are you on?
1. I don't know where to begin
2. I have begun but got stuck midway
3. I got an answer but I'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above

[alpine sable]

2

Someone help

Please

Find irrational no. between 0.71425 bar and 0.81 bar, how to solve? Can I write 0.81 bar as 0.81818 bar and then a no. between 0.71425 and 0.81818

[slender quiver]

can you show your work

[alpine sable]

Okay

It was actually 5/7 n 9/11

@slender quiver

[slender quiver]

ok

so

you want to find a irrational number

[alpine sable]

Yeah

[pliant cedar]

U can write both numbers with the same denominator first ig

[slender quiver]

but you are using fractions

[pliant cedar]

And then square them both

[alpine sable]

Yeah so?

How

Tell me a simple way sir

[slender quiver]

fractions are not irrational number

[alpine sable]

I'm a class 9 student

hello

[pliant cedar]

9/11 = 45/77
5/7 = 55/77

[pliant cedar]

R u okay with thay

Then u square both numbers

(45/77)² = (45²)/(77²)

(55/77)² = (55²)/(77²)

Then choose any integer between 45² and 55² that is not a perfect square

The (square root of that number)/77 is then between 5/7 and 9/11, and also irrational

[lone heart]

@alpine sable Has your question been resolved?

[lone heart]

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[vernal tinsel]

Find the value of 3g - 2c + 3b/2, when b = 1, c = 3 and g = 4. Answer as a fraction. I just need help on how I can solve these kinds of tasks.

[slender quiver]

plug in the values

[vale wigeon]

have you solved this kind of problem before?

[vernal tinsel]

Some basics, but not at this level.

[vale wigeon]

what sets this apart from the basics?

or to put it another way: what's causing you trouble?

[vernal tinsel]

I don't quite know how to solve it

[vale wigeon]

ok but you know how to plug in numbers for variables, yes?

[vernal tinsel]

And I am norwegian, so that's also pretty hard. Sorry I don't know what that means : (

[vale wigeon]

replace the letters with the values you're given for them.

[vernal tinsel]

Okay

[vale wigeon]

if you've done problems that are like this but basic then you know what i am talking about

i want to know what part of this problem is, to you, not basic.

[vernal tinsel]

Mostly the fraction part

3b/2

[vale wigeon]

so if there were no fractions you would be able to do it?

[vernal tinsel]

Probably

[vale wigeon]

do you know how to work with fractions?

[vernal tinsel]

Oh wait I remember now, I think

Just divide the upper number with the lower number?

[vale wigeon]

well if you wish...

fractions are a thing in their own right

[vernal tinsel]

Is there another way to do it?

[vale wigeon]

i mean, again, you just

replace the letters with the values you're given for them.

$3 \cdot 4 - 2 \cdot 3 + \frac{3 \cdot 1}{2}$

[ocean seal]

Ann

[vale wigeon]

and then this becomes an arithmetic problem that you can and should solve as normal

you're simply overthinking it, i think

[vernal tinsel]

I've got 12 - 6 and now I need to plug the fraction

[vale wigeon]

12 + 6...?

[vernal tinsel]

I meant "-"

Oops

[vale wigeon]

you have 12 - 6 + 3/2

and as far as i gathered you've either never worked with fractions before or have forgotten everything

[vernal tinsel]

I have worked with fractions, but I have indeed forgotten everything

So how do I work out 12 - 6 + 3/2?

12 - 6 is fairly easy, but the fraction part

[vale wigeon]

yes so 12 - 6 = 6

you can now add 6 and 3/2 by converting them to the same denominator

in this case 2

6 = 12/2

so 12/2 + 3/2 = ?

[vernal tinsel]

Don't you have to multiply 3/2 by two also?

[vale wigeon]

???

we aren't multiplying anything by 2

[vernal tinsel]

Oh, I just saw 6 and 12

[vale wigeon]

we may be multiplying the top and bottom of the fraction 6/1 by 2

but we are leaving the fraction 3/2 untouched

[vernal tinsel]

Alright

But it was 3b/2

[vale wigeon]

yes, and?

what value did they give you for b itself?

[vernal tinsel]

oops I wrote wrong again, so sorry

b= -1

[vale wigeon]

well then instead of 3/2 you will have -3/2...

[vernal tinsel]

okay

[lone heart]

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[bronze helm]

I’m a bit confused as to what M is?

[lone heart]

@bronze helm Has your question been resolved?

[bronze helm]

Is it just the labelling of each seed

[lone heart]

@bronze helm Has your question been resolved?

[lone heart]

@bronze helm Has your question been resolved?

[grizzled musk]

i have a problem

[lone heart]

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[grizzled musk]

i need help

[lone heart]

Please don't occupy multiple help channels.

[grizzled musk]

.close

[lone heart]

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[arctic mortar]

lim x->2

[arctic mortar]

$$ \frac{1}{(x-2)^2} $$

[ocean seal]

sytez

[arctic mortar]

of that

the limit is infinity

from both the left and right side

[wild trail]

$\lim_{x \to 2} \frac1{(x-2)^2}$ ?

[arctic mortar]

but my teacher says if the limit is infinity it does not exist…?

[arctic mortar]

x->2

[wind cloak]

x to 2

[arctic mortar]

this is the thing i don’t get

[ocean seal]

numbpy

[arctic mortar]

yes

[wild trail]

The point is that when we say limit exists, we mean that lhl, rhl exists, are finite and equal

infinity is not a real number, it's just a symbol

[arctic mortar]

why finite

[wild trail]

That's the definition of limit

[arctic mortar]

hm

[wild trail]

finite here means that the limit should be a real number

[arctic mortar]

is it because if L is infinity f(x) - L cannot be less than epsilon

[worn fox]

note there are conflicting conventions. a limit "not existing" does sometimes mean "is not a finite number or plus/minus infinity" for some people

[arctic mortar]

i see

[glacial rover]

Are you trying to evaluate the equation with the limit as x tends towards 2?

[arctic mortar]

yea

i already know it’s infinity

[glacial rover]

Have you heard of L’hopitals rule?

[wild trail]

I mean if we are in real number system then there's no concept of infinity. It's just when we move to extended real system that infinities are introduced and we need to add the finiteness clause

[arctic mortar]

but i’m trying to understand why if the limit equals infinity then the DNE

[arctic mortar]

yes

[arctic mortar]

it’s a trivial limit, i know how to solve it

[glacial rover]

Oh okay I get you

[wild trail]

doesn't apply here cause there's no indeterminate form

[glacial rover]

Yeah that was kinda goofy of me ooops

[arctic mortar]

i see

alr thanks

.close

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[languid latch]

About this one @wild trail

I asked my teacher, he said its a trapezoid

[tender arch]

Which number are you needing help on?

[lone heart]

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[languid latch]

66

[lone heart]

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[junior relic]

Can someone please help me with no 4

[junior relic]

I don’t understand what to do in this math

[coral thorn]

!status

[lone heart]

What step are you on?
1. I don't know where to begin
2. I have begun but got stuck midway
3. I got an answer but I'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above

[junior relic]

<@&286206848099549185>

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Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.

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[lone heart]

@junior relic Has your question been resolved?

[lone heart]

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[pale spade]

i need to know how to rotate a 2d vector

[strong compass]

Do you know about linear transformations?

[pale spade]

no

[strong compass]

Do you have the exact question?

[pale spade]

i have an x and y value of a vector and with a given anlge i need to rotate it and then get the X and Y value of that rotated vector

[scarlet oriole]

post the question

or is this a problem you created?

[pale spade]

this is a problem i created

[alpine sable]

is this for a programming project?

https://en.wikipedia.org/wiki/Rotation_matrix

[pale spade]

i just need it for making a program

[scarlet oriole]

ah Okay

[alpine sable]

python?

[pale spade]

c#

[alpine sable]

https://stackoverflow.com/questions/22818531/how-to-rotate-2d-vector

[scarlet oriole]

linear algebra is usually used to rotate, but i think there are libraries that will do math for you

[alpine sable]

(first result on google)

[pale spade]

ok i will look at this

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[flat oxide]

hey guys, i need hep with making an equation for a business
Say a business invests x in ads and gets 1.2 x back in profits, knowing that the customer retention of said business is 85%, what is the function of that determines the profits of the business obver time, assuming x is the trimesters and y is the profits expressed in x

[lone heart]

@flat oxide Has your question been resolved?

[flat oxide]

<@&286206848099549185>

[slate monolith]

@flat oxidewhat class is this

this question requires an understanding of financial equations

which the high majority of people here dont have

[flat oxide]

goddamnit

i thought it was just a math question

[slate monolith]

it has math in it

but in the math on this server there is no variable like customer retention

[flat oxide]

i was asked to do a business plan for a company i am working for and i need help determining the function that i can use to apply it as a general rule instead of calculating each trimester

[slate monolith]

damn thats a first, youre asking someone to do your literal job

meaning even fewer people would know

[flat oxide]

it's not my job

[slate monolith]

ask in an econ/finances server

[flat oxide]

i am a volunteer

thanks man

sorry for the trouble

[slate monolith]

#old-network

no worries

good luck figuring it out

.close

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[flat oxide]

there is no econ server though @slate monolith

ill figure it out

[slate monolith]

hm, try googling then

or maybe find a finance server

[flat oxide]

just to be clear, it's not my job and i was asked to do this for the first time in my life today

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[jolly lintel]

I need a second opinion on my solution for an exercise I made

THE EXERCISE:
Two sharpshooters, one of whom (A) hits a target 75% of the time and the other (B) only 25% of the time, aim at a target. Exactly one bullet hits the target. What is the probability that this bullet came from A?

My thinking process went as following:
We are looking for P(A | H)

1. Assign given probabilities
   P(A) = 0.75
   P(B)=0.25
2. Calculate conjunction (exactly one hits target)
   P(H) = P(A) + P(B) - (A ∧ B) = 0.75 + 0.25 - (0.75 * 0.25)
3. Applying Bayes Thorem:
   P(A | H) = P(H | A) * P(A) / P(H) = ((1 - 0.25) * 0.75) / 0.8125 = 0.6923 (approx.)

Is this correct?

[foggy copper]

no

P(A) isn't 0.75, it's what you're trying to find.

[foggy copper]

P(H|A) is 0.75, and P(H|B) = 0.25

[jolly lintel]

You're absolutely right, I will reconsider my calculations rq

H means "exactly one hits the target". Wouldn't this result in a value different from P(H | B) = 0.75, since all two hits aren't included?

And I'm a bit confused about that we are looking for the value of P(A), aren't we looking for the probability that the exactly one bullet that hit the target come from A (resulting in P(A | H))?

[foggy copper]

Ah, I was using H differently.

[jolly lintel]

Ah, no worries. Given this meaing of H, would the process as shown above be correct?

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[alpine sable]

Why did they reduce the fraction from 100/8 to 25/2 how did they even get that

[slender quiver]

divide both the numerator and the denominator by 4

[alpine sable]

I am so stupid how did I not see that

thanks a lot for making me see the vision

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[shrewd vault]

Good Evening I was wondering if this is correct?

[shrewd vault]

I need help. could someone tel me if my asnwer is correct

[alpine sable]

yes its correct

[lone heart]

@shrewd vault Has your question been resolved?

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[lone heart]

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[steel crescent]

which is correct, BODMAS or PEMDAS?

[sharp thorn]

What is pedmas

[steel crescent]

parentheses, exponents, multiplication, division, addition, subtraction

[sharp thorn]

Both are correct

Bodmas doesn't talk abr exponents

[steel crescent]

bodmas does talk about exponents

"o" = orders
orders = exponents

[sharp thorn]

Then yea both are literally the same

They never thought me order was power

[steel crescent]

how are both the same?

one has division first and then the other as multiplication first

[sharp thorn]

Oh

If an equation has only multiplication and division, you can go left to right or right to left or any order it doesn't matter

If it has more than those two, division is first

[steel crescent]

alright that's what i was wondering because

i saw this video and it was like this math issue no one can solve

6/2 (1+2)

for me i just got 9 i only use BODMAS

but if you go the other route and multiply the 2 by the 1 + 2 first you'd get it wrong, but

this is why we put things in fractions right

anyway thanks a bunch! :D

[alpine sable]

Well our board of education only preffer BODMAS So ye

[vagrant lichen]

is the same

[lone heart]

@steel crescent Has your question been resolved?

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[fierce prairie]

what is the question

[carmine reef]

note the two things in the parentheses are different

one is x+y and the other is x-y

so it's not 4a^2-a^2

[ivory pendant]

Ye

[ivory pendant]

56

[fierce prairie]

I mean what are you asked to do

[ivory pendant]

Factor

And simplify

[fierce prairie]

There's not anything to factor here but yeah, it can be simplified

[ivory pendant]

Ye

[fierce prairie]

So you want to expand it out

[ivory pendant]

Simplify

[fierce prairie]

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

Can you simplify this?

[ivory pendant]

No

[fierce prairie]

Does multiplying polynomials sound familiar?

[ivory pendant]

yes

[vagrant lichen]

use that FOIL method

easy as pie

[ivory pendant]

@fierce prairie

[ivory pendant]

yo!

[vagrant lichen]

!

[ivory pendant]

I put in the 4

now what

[fierce prairie]

can you type what you wrote here?

I'm having trouble reading

[ivory pendant]

(4x + 4y) to the power of 2 - (x-y)

[ocean seal]

Kihei

[fierce prairie]

You cannot distribute the 4 because the exponent must be simplified first

so you should first simplifiy

[ocean seal]

Kihei

[ivory pendant]

(x+y) (x+y)

[fierce prairie]

yeah

have you learned FOIL?

[ivory pendant]

Yes

But I dont think we are doing that here

because my teacher was talking about difference of squares

[median oar]

Is the instructions to factorise?

[ivory pendant]

Yes

[median oar]

You should include that when you’re showing the problem

Anyhow, use difference of squares to factorise this, do you know what difference of squares is?

[lone heart]

@ivory pendant Has your question been resolved?

[ivory pendant]

Yes

[median oar]

Ok use it

[lone heart]

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[ivory pendant]

.reopen

[lone heart]

✅

[ivory pendant]

What would I do with the 4?

@median oar

Could you show me how it would look using difference of squares?

[lone heart]

@ivory pendant Has your question been resolved?

[median oar]

4 is but 2²

Then you can factor the squares from the 2 and (x+y) using exponent rules

@ivory pendant

[lone heart]

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[ivory pendant]

.reopen

[lone heart]

✅

[ivory pendant]

Could you show me what the equation would look like?

Using difference of squares

[median oar]

2²(x+y)² - (x-y)²

= (2(x+y))² - (x-y)²

Difference of 2 squares here

[ivory pendant]

Sorry for late responses

@median oar

I am praying

[lone heart]

@ivory pendant Has your question been resolved?

[ivory pendant]

What do I do here?

[median oar]

well, what is the difference of 2 squares?

[ivory pendant]

What does that mean

@median oar

Now I am home

I can focus

[median oar]

you said you knew what the difference of squares is

[ivory pendant]

A^2 - B^2 = (A-B) (A-B)

[median oar]

brackets?

[ivory pendant]

Yeah my bad

Now what do I do

[ivory pendant]

@median oar

[median oar]

that's not difference of squares

[ivory pendant]

Could you give me the definition

Of difference of squares

Alright

[median oar]

https://demonstrations.wolfram.com/DifferenceOfSquares/

[ivory pendant]

So how do I go from this to my answer

[median oar]

use the difference of squares

[ivory pendant]

What do you mean by that

[median oar]

what is the difference of squares

[ivory pendant]

Sorry I got a final tommorow. And difference of squares is really tripping me

[median oar]

difference of squares is that

a^2 - b^2 can be factorised to be (a-b)(a+b)

do you know this

[ivory pendant]

Yes

[median oar]

then why have you written (A-B) (A-B)

when it should be (A-B) (A+B)

[ivory pendant]

Oh shi

I forgot about opposite signs

How would I use this to solve my question

[median oar]

so we know A^2 - B^2 = (A-B)(A+B)

[median oar]

look at these steps

[ivory pendant]

The thing that confuses me is that when we have a number outside the brackets

What would we do to the 2

2^2

[median oar]

look at this next line

[median oar]

i said this

earlier

[ivory pendant]

Would it be

(2(x+y)- (x-y)) (2(x+y) + (x-y))

Without the ^2

My bad

@median oar

[median oar]

remove them

[ivory pendant]

Like this

[median oar]

you're still missing brackets

brackets brackets brackets

they are absolutely necessary

DO NOT ever slack off on your brackets

[ivory pendant]

My bad big bro

Like this

@median oar

[median oar]

yes

that's right

[ivory pendant]

Ya

[median oar]

now expand the inside brackets first

[ivory pendant]

One sec

Can you give me like 10?

I will brb

Don’t leave plz

[ivory pendant]

@median oar

I’m am back

[median oar]

did you simplify

[ivory pendant]

(1x + 3y) (3x + 1y)

@median oar

[median oar]

ok

now what

expand

[ivory pendant]

3x^2 +10xy + 3y^2

@median oar

[median oar]

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

[ocean seal]

Results provided by WolframAlpha

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

Requested by Frosst#1111

[median oar]

good job

you did it

[ivory pendant]

Let’s goo

Since my final is tomorrow

What tips do you have for me

[median oar]

do you know sums and difference of cubes

[ivory pendant]

No

I don’t think we did that

Only squares

[median oar]

it's cool

[ivory pendant]

Should I do one more question

And you check

(M^2 - 5m - 6) (m^2-5m +6)

Ughh trinomial

@median oar yo

Would 6 need its own bracket?

[median oar]

it does but it wouldn't matter

((m^2 - 5m) - (6)) ((m^2-5m) +(6))

[ivory pendant]

Yeah

That’s what I was wondering

Alright back to the question

(M^2 -6m) (1m -6)

M( m -6) 1(m-6)

(M+ 1) (m-6)

[median oar]

where did this come from

[ivory pendant]

I factored 6

[median oar]

what does the question say

can you repeat it word for word

[ivory pendant]

Factor

[median oar]

anything else?

[ivory pendant]

Just factor and simplify I guess

Yeah factor

[median oar]

does it say simplify?

it's really important

you tell me WORD FOR WORD

what the instructions say

[ivory pendant]

Read the top

[ivory pendant]

Why is it important

[median oar]

because

it just says factor

you dont have to expand

[median oar]

this

= 0 marks

this is incorrect answer

completely wrong

if i was marking i'd give u a 0

[median oar]

this

this would get full marks

you have to do what the question asks

[median oar]

from here just factorise once more

[ivory pendant]

What do I have to do to simplify

@median oar

[median oar]

there;s no simplfy

anywhere

just factorise

[ivory pendant]

If a question asks me

@median oar to simplify

[median oar]

then u simplify

[ivory pendant]

Alright

See ya bro

Thank you

One more thing

@median oar

Does collecting like terms mean simplifying?

[median oar]

no

it means factorisinig

[lone heart]

@ivory pendant Has your question been resolved?

[lone heart]

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@regal cliff Has your question been resolved?

[regal cliff]

.close

[lone heart]

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[rapid frost]

could anyone help me wit this homework problem?

[rapid frost]

so far i have A = {3 0 -1}, {-1, 2, 1}

not sure how to forrmat but i think you get the idea

im kinda stuck here now tho

like what am i supposed to do next

is the A matrix the answer?

.close

[lone heart]

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[rapid frost]

i realize this is for pre-unviersity questions 💀

[worn fox]

It's for any questions

[rapid frost]

oh

.reopen

[lone heart]

✅

[rapid frost]

here is the problem:

so far i have A = {3 0 -1}, {-1, 2, 1}
not sure how to forrmat but i think you get the idea
im kinda stuck here now tho
like what am i supposed to do next
is the A matrix the answer?

[worn fox]

You wanna write (3,0,-1) in terms of the standard basis and then use the fact that T is linear

[rapid frost]

i dont think my professor went over standard basis

did a quick google search tho

are they just unit vectors? is that right?

[worn fox]

They're (1 0 0) (0 1 0) (0 0 1)

The ones that you have information about

[rapid frost]

got it

oh

i see what ih ave to do

i got it 😎

(10, -4)

thanks for the clarification

.close

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[coarse skiff]

is this done correctly

[worn fox]

Sure

[lone heart]

@coarse skiff Has your question been resolved?

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[outer vector]

how do i do the last 2?

[worn fox]

What's the arg of z³?

[outer vector]

3pi/4?

[tight steeple]

do you know the euler's identity?

[outer vector]

yea but we werent rlly taught what it was

this is my first time seeing qns about arg like this im so lost

[tight steeple]

then it's easy as z^3w^2 becomes 4^3*5^2 e^i3pi/4e^i(10pi/6) using power rule its(3pi/4 +10pi/6=29pi/12)

[strange solstice]

is it not pi/4^3 X5pi/6^2 ?

[strange solstice]

oh, maybe thats right instead

[outer vector]

is this for the second last one?

[tight steeple]

yep

[outer vector]

cuz zthe ans says 5pi/12 for some reason

[worn fox]

Do it yourself, they added fractions wrong

And then you also need to perhaps be considering the principal argument

Because of the capital A

So if your calculstion takes you over π you take the complementary angle

[tight steeple]

my bad it was 29pi/12 or 24pi/12 +5pi/12 , 2pi+5pi/12 hence the answer

[lone heart]

As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.

[outer vector]

ah ok got it

thanks

[lone heart]

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[boreal crypt]

Can someone tell me how I solve this

[boreal crypt]

and yes i know the answer is 2 i just want to know how to get there

d

[chrome salmon]

First get the value of product in denominator

[boreal crypt]

can you show what i calculate

[boreal crypt]

$-2/-2/4$

[ocean seal]

demo

[boreal crypt]

<@&286206848099549185>

[harsh ferry]

2 multiplied by -1/2 is -1

dividing -2 by -1 is +2

[boreal crypt]

thank you

[boreal crypt]

better than the helpers

.close

[lone heart]

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[chrome salmon]

I'm not helper son

[lone heart]

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[alpine sable]

ohh

[lunar palm]

what you described before deleting that is correct

[alpine sable]

i thought i was wrong

[alpine sable]

ohh

[lunar palm]

do you understand where to go from the substitution stage?

[alpine sable]

well intersection point is a,a

therfore does the equation become a = root a-b + c

[lunar palm]

Yes

[alpine sable]

and then u substitue it into the equation

[lunar palm]

well this is your substitution

you have substituted y=a and x=a

in terms of substitution, you are finished

[alpine sable]

omg

[warped horizon]

yo the options here are wrong ryt ? or am i just dumb

[chrome salmon]

Just get the form

[lunar palm]

#❓how-to-get-help

[chrome salmon]

What makes you think this is your domain?

[warped horizon]

i was blind

pardon

[alpine sable]

wdym

should i try and simplify the equation a^2 - (2c-1)

[warped horizon]

i T pose to assert dominance

[chrome salmon]

Sorry my bad

[chrome salmon]

Is that an equation?

[alpine sable]

no i wrote ... for the extra part

[chrome salmon]

As far as I know equation has an "=" sign

[alpine sable]

i

ik

[lunar palm]

so, from there, try and rearrange into the required equation

you should have all you need

[alpine sable]

yep

i have all i need

quick quesiton tho

why is it the first

not the second

cuz they aren't equal to each other

[lunar palm]

well, yeah

you're missing a term

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

[alpine sable]

true

but how do i know that they were supposed to be groouped together

cuz lets say it was a = 5+ x

then i would group together

a^2 = (5+x)^2

but like a = 3+ 5

a^2 = 3^2 + 5^2

[lunar palm]

think of back to when you first learnt algebra

the fundamental idea when you have an equation is

what you do to one side, you must do to the other

to go from a^2 you square the entire side

so a = 5+x would go from (a)^2 to (5+x)^2

or (LHS)^2 = (RHS)^2

[alpine sable]

ahh right

[lunar palm]

hence, when we have

a = sqrt(a-b) + b

it is again (LHS)^2 = (RHS)^2

not each term individually squared, which is different

[alpine sable]

yep

makes complete sense

thank you @lunar palm

[lunar palm]

👍

[alpine sable]

rlly apprecate ur help

have a great rest of the year

[lunar palm]

you too

[alpine sable]

thanks

.close

[lone heart]

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[alpine sable]

me need help

[alpine sable]

;D

Its an IB question

Don't tell its ez

my maths is weak so yeah

[nimble latch]

do you know cosine rule?

[alpine sable]

OH wAIt

we have to use that?

[nimble latch]

yea since cosABC is given

you find 'a' using that

and find the area using 1/2 × a × 3a × sinABC

[alpine sable]

Ohhhh tysm!!

[lone heart]

@alpine sable Has your question been resolved?

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[hexed topaz]

hi can some1 explain partial fractions to me...im a secondary 3 student from Singapore following the Cambridge o level syllabus thanks

[hexed topaz]

<@&286206848099549185>

[hexed topaz]

under polynomials thanks

[median oar]

$3\frac{2}{3}$

[ocean seal]

Frosst

[median oar]

Partial fractions like that?

[hexed topaz]

with algebra

[median oar]

Can you show me an example

[mortal trellis]

do you mean stuff like $\frac{1}{(x-2)(x-3)} = \frac{A}{x-2} + \frac{B}{x-3}$ ?

[hexed topaz]

sure

[ocean seal]

Denascite

[hexed topaz]

yes

[mortal trellis]

then be more specific about what you want help with

[hexed topaz]

sorry mb

[hexed topaz]

there are 3 cases for there fractions right

[mortal trellis]

just like the picture shows

[hexed topaz]

i dont understand how they work

[mortal trellis]

be more specific about what you dont understand

[hexed topaz]

idek how to explain in texts ( skull issue fr ) is it possible to vc?

[mortal trellis]

maybe someone else is willing. also we dont have vc on this server

[hexed topaz]

ah its fine

ill ask my teacher next week then

[lone heart]

@hexed topaz Has your question been resolved?

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[red raptor]

guys im putting sin (pie/4) and also sin(3pie/4) and its giving the same answer anyone know why? maybe setting on calculator?

[red raptor]

guys im putting sin (pie/4) and also sin(3pie/4) and its giving the same answer anyone know why? maybe setting on calculator?

[mortal trellis]

well they are the same

so that's pretty much expected

btw it's pi

[red raptor]

how is a quarter pi

[tiny cipher]

sin(pi - x) = sin x

[red raptor]

same to 3 quarters

pie?

[mortal trellis]

its not

but sin of them is the same

[red raptor]

but then the function is wrong

[mortal trellis]

just like 3 and -3 are different but 3^2=(-3)^2

[red raptor]

i need to graph this

and i have x as pi then 3/4 pi half pi and quarter pi

if i graph this i cannont find the period

or range

here

[red raptor]

see?

[mortal trellis]

I dont see what the problem is, no

[gray isle]

are you implying that you would be unable to graph y=x^2?

[red raptor]

? Look if I graph this the wave is getting smaller going outwards therefor its not a trigonometric function

[red raptor]

What's x^2 got anything to do with this

[gray isle]

you implied that there was an issue with getting the same output when inputting two different values into the function

? Look if I graph this the wave is getting smaller going outwards therefor its not a trigonometric function
can you show your table and your graph

[red raptor]

These are the points I got

[red raptor]

See the square root two over 2?

If I graph this the wave gets smaller

[gray isle]

did you make any attempt to graph this?

instead of what seems to be assuming it doesn't work

[red raptor]

I did try graph it

[gray isle]

can you show your graph

[red raptor]

Ah nvm found mistake graphed in wrong order 😶

[red raptor]

No wait

[red raptor]

No def did mistake

[gray isle]

yeh, many mistakes there,
try again

[lone heart]

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[pseudo lily]

if im integrating lnu (u-2)^3/2 am i doing by parts twice

[ocean hawk]

what is "lnu"

[last ether]

ln(u)

Probably

[ocean hawk]

please use parentheses to clarify the equation, or share a screenshot @pseudo lily

[pseudo lily]

nvm i think i got it

.close

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[limpid flicker]

Is this the right answer for this question ??

[glass tree]

(Wow their LaTeX formatting sucks) Your answer does seem to be correct.

[alpine sable]

Nothing wrong w trad paper and pencil

[foggy copper]

it might be word, not latex

[glass tree]

No I’m referring to who wrote the question. The spacing is all off, they don’t use parenthesis, and they didn’t backslash their functions

[alpine sable]

[glass tree]

I doubt that given the “arcsin” and “arccos”

[foggy copper]

maybe

[glass tree]

LaTeX is the only formatting tool I know that defaults to italics.

[foggy copper]

maybe

[glass tree]

Anyway @limpid flicker Your answer is right and you can close this help channel now

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[tawny imp]

shouldn't the correct answer be 329.9?

[prime badge]

yes

i get the same

no way they mean like, capacity

[tawny imp]

for some reason it marked my answer as wrong?

i'm not sure why

[waxen flame]

How did you calculate your answer?

[tawny imp]

i found the area of the outside and inside cylinders

then i subtracted the inside one from the outside

and i got 329.87

and it says "round to 1 d.p." so i rounded to 329.9

[prime badge]

maybe they want units

not just number

[tawny imp]

it says not to

[prime badge]

🤷

[waxen flame]

Contact your teacher. It's possible they have the wrong answer entered.

[tawny imp]

.close

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[high wolf]

Not sure what I'm doing wrong:

[high wolf]

This is my work:dP/dt = (3/500) * P * (5 - P)

dP/(P * (5 - P)) = (3/500) * dt

Integrating both sides:

∫[1/(P*(5-P))] dP = ∫(3/500) dt

Using partial fraction decomposition, we can write:

1/(P*(5-P)) = (1/5) * [1/P + 1/(5-P)]

Substituting this back into the integral:

(1/5) * ∫[1/P + 1/(5-P)] dP = (3/500) * t + C

Taking the antiderivative, we get:

(1/5) * ln|P/(5-P)| = (3/500) * t + C

Multiplying both sides by 5 and exponentiating, we get:

P/(5-P) = Ce^(3t/500)

Solving for P, we get:

P = (5Ce^(3t/500))/(1 + Ce^(3t/500))

Using the initial condition P(0) = 4, we can solve for C:

4 = (5C)/(1+C)

C = 4/1

C = 4

Therefore, the solution to the differential equation is:

P = (20e^(3t/500))/(1 + 4e^(3t/500))

To find P(77), we simply substitute t = 77:

P(77) = (20e^(3(77)/500))/(1 + 4e^(3(77)/500))

P(77) ≈ 4.8752

[pseudo ice]

Taking the antiderivative, we get:

(1/5) * ln|P/(5-P)| = (3/500) * t + C

Multiplying both sides by 5 and exponentiating, we get:

P/(5-P) = Ce^(3t/500)

[ocean hawk]

prob copied it from chatgpt

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@high wolf Has your question been resolved?

[vale wigeon]

this isn't your work. this is chatGPT.

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[quiet vector]

You see spirals in the ocean’s shells and the far-reaches of space. And you can create them from polar functions. The general form for a spiral is r = aθ, where θ is the angle measure in radians and a is a number multiplier. In the graph of r = 1/3θ. The 1/3 multiplier makes the spiral tighter around the pole. A larger number will make it spread out farther more quickly. And what about a negative number multiplier? It makes the spiral move out in the opposite direction — clockwise instead of counterclockwise. The figure shows you an example of just such a spiral.

[quiet vector]

is it?

i dont see the direction changing; can anyone tell if its wrong

[carmine reef]

?

the graph looks like r=-theta or something

[quiet vector]

is the direction of r=theta and r=-theta the same

[carmine reef]

no

[quiet vector]

it is

[carmine reef]

theta would look like this rotated by 180 degrees

[quiet vector]

yes!

rotated

but the direction of rotation is the same

"It makes the spiral move out in the opposite direction — clockwise instead of counterclockwise." so this is wrong?

[carmine reef]

ah yeah that's wrong

hmm

it would be right if the range of theta displayed was itself negative

so you display theta<0 on the graph

or hmm

[limpid field]

The spirals in the ocean shells are literally the Theodorus Spiral

[carmine reef]

maybe it wouldn't be

no I think that's the problem here

[quiet vector]

ok wait

[carmine reef]

yeah yeah I'm right