help-33

[grave marten]

then how would you describe the length AC with the angle you have and the height of the tower

[nocturne wasp]

My picture

[grave marten]

yes but mathematicaly

[nocturne wasp]

Adjacent to the angles

[grave marten]

close but not quite

give me 2 sec imma draw something

[nocturne wasp]

Alr

[grave marten]

how could you use this

[nocturne wasp]

?

[grave marten]

you have in your drawing

[nocturne wasp]

No idea what that's saying

[grave marten]

$rsin(\alpha)$

[elfin berry]

spookyspaghetti

[grave marten]

you have this

its your 110

[nocturne wasp]

What's r and a

[grave marten]

r is your hypotenuse and that a is your angle

like the drawing i made

[nocturne wasp]

Alr

So the bottom side is cosine

[grave marten]

yes

but u dont have r yet

[nocturne wasp]

Ye and what's the right

[grave marten]

the right ?

[nocturne wasp]

Ye

Nim

Why does this not work?

My working is all over the place sorry

[grave marten]

be carefull u are using x for 2 different sides

[nocturne wasp]

O it's meant to be y for the right sides working out

O no I was trying to different ways for the same side

[grave marten]

so $AC = 110 \cdot \tan(62)$

[elfin berry]

spookyspaghetti

[grave marten]

thats already correct

[nocturne wasp]

Ye

[grave marten]

and i also see that u wrote $BC = 110 \cdot \tan(73)$

[elfin berry]

spookyspaghetti

[nocturne wasp]

Do I find the difference of the two

But I still don't get why it says B is south of the viewing platform and a is easy

[grave marten]

welp i just read ur question and they are not in the same direction

[nocturne wasp]

And the textbook answer was 415m

[grave marten]

a is due east and b is due south

[nocturne wasp]

I still don't unserstand

Understand

[grave marten]

this is the situation

u know AC and AB

[nocturne wasp]

O

[grave marten]

just gotta throw some pythagoras against it

and its solved

[nocturne wasp]

Alr lemme c

Did I do something wrong

[grave marten]

what is x and y and why did u do 244*36 ?

[nocturne wasp]

X is 110tan62 and Y is 110tan73

It’s 294.36 that what is got

[grave marten]

welp isnt Y = BC ?

[nocturne wasp]

Is what I got

O

Ye

O thanks I don’t quite get how that worked

[grave marten]

wdym ?

[nocturne wasp]

Like the level ground part

Is this a 2 diagram question

[grave marten]

thats just so that u dont have a vecrtical distamce between A and B

[nocturne wasp]

Alr thank you for helping

[grave marten]

did u get the answer ?

[nocturne wasp]

Ye

[grave marten]

can u show me ?

[nocturne wasp]

O it was all on calculator I’ll write it down

[grave marten]

yeah nice

its easier to just calc x and y and then use em

but this works

nicely done

[nocturne wasp]

Ye I wanted to use exact values

So I stored in calculator

[grave marten]

alr

dont forget to .close

[nocturne wasp]

.close

[marsh citrus]

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[marsh citrus]

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[pure compass]

A = (5,8), C = 1,-4
Find The Slope-intercept form of BD

[pure compass]

How can i do this?

its an rhombus

[lofty gyro]

in my mind, there are a few ways to do it.
The easiest one would be using the fact that diagonals of rhombuses are perpendicular and it passes through the mid-point of 2 opposite vertices

[lofty gyro]

where first property lead to finding the slope of BD using slope of AC, and second property would point to using point-slope form to find the straight line equation

[lofty gyro]

@pure compass

[pure compass]

i am back

i know that the M of of AC = 3

so

M of BD = -3

right?

[lofty gyro]

slope of AC is 3 is correct
however slope of BD is not -3

[pure compass]

oh

so how can i know slope of bd?

[lofty gyro]

recall: for slopes of perpendicular lines, let's say m1 and m2,
we have m1*m2 = -1

try it again with "slope of AC=3"

[pure compass]

Wait how do you know the m2?

if we only know m1

[lofty gyro]

do you know how to change the subject of the equation m1*m2=-1 into
m2= something?

[pure compass]

nope

[lofty gyro]

i see

how about 3*m2=-1?

and find m2?

[pure compass]

3m2 = 1

mhm

[lofty gyro]

nah, 3m2=-1

[pure compass]

oh

3m2 = -1

i thought i saw 1

alright

so the m of BD = -1?

[lofty gyro]

nah

[pure compass]

oh

[lofty gyro]

lemme type a bit

take some time 😛

[pure compass]

Alright

[lofty gyro]

.

,align
m_1\cdot m_2 &= -1 \
\frac{\cancel{m_1}\cdot m_2}{\cancel{m_1}}&=\frac{-1}{m_1}\
m_2&=-\frac1{m_1}

[elfin berry]

Biscuity

[pure compass]

mhm

[lofty gyro]

there we go

[pure compass]

oh

but we know that m1 = 3

[lofty gyro]

since if we plug m1=3 , we will have
m2=-1/3

[pure compass]

oh

yeah

oh so the m of bd = -1/3

cool

and how we can find the b

[lofty gyro]

well, we have the mid-point of AC is on the line BD

[pure compass]

yeah

[lofty gyro]

so, we'll just have to find that mid-point and then we can use point-slope form

[pure compass]

its 3,2

i already did it

[lofty gyro]

answer is?

[pure compass]

like the mid point

[lofty gyro]

ah

cool

[pure compass]

is (3,2)

[lofty gyro]

correct

so we will just have to plug back into
(y-2)=(-1/3)(x-3)

[pure compass]

oh

x+3y = 9 @lofty gyro

[lofty gyro]

well, it requires you to write in slope-intercept form

[pure compass]

3 = x + 9

[lofty gyro]

nope

[pure compass]

mhm

[lofty gyro]

XD

[pure compass]

oh

-9

3 = x - 9

[lofty gyro]

next, we have
y-2=(-1/3)x +1
then
y=-(1/3)x+3

[pure compass]

oh

[lofty gyro]

,align
y-2&=-\frac13 (x-3)\
y-2&=-\frac13x-\left(-\frac{1}{\cancelto{1}{3}\right)(\cancelto{1}{3})\

[pure compass]

mhm

[elfin berry]

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

[lofty gyro]

lol nvm

[pure compass]

what did you try to do

[pure compass]

oh thats cool

oh yes this is the correct answer

[pure compass]

and one more question how can i find B and D form that Slope intercept form

[lofty gyro]

B is easy, D is harder

B is on y-axis, so which coordinate is 0?

[pure compass]

i guess just put y = 0 in b

[lofty gyro]

nah

[pure compass]

oh

[lofty gyro]

try again

[pure compass]

oh

-1/3 * 0

y = 3

x = 0

[pure compass]

y = -1/3 * 0 + 3

y = 3

0,3

[lofty gyro]

so B is (0,3), right?

[pure compass]

yes

[lofty gyro]

correct

[pure compass]

yay

and how can we find

D

[lofty gyro]

D is harder, lemme draw something

[pure compass]

alright

[pure compass]

oh

[lofty gyro]

qait

wait

typo

[pure compass]

the distance formula

[pure compass]

you did it by the distance formula?

[lofty gyro]

B is moving from (3,2) to (0,3), so its
3 to the left and 1 to the top
now D is the opposite way, so it's
3 to the right and 1 to the bottom

[pure compass]

mhm

[lofty gyro]

nah, just walking along horizontal and vertical ways along the graph

[pure compass]

isn't it more easy to just use the distance formula

oh no

if i will do it

i will can't find the index

nvm

[pure compass]

so it the only way?

[lofty gyro]

you can try

[lofty gyro]

nah, but it's the easiest way i can think of

[pure compass]

okay

you helpd me a lot

thanks @lofty gyro

[lofty gyro]

cheers!

[pure compass]

.close

[marsh citrus]

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[marsh citrus]

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[twin ether]

A radioactive substance decays from 20g to 15g in 7h. Determine the half-life of the
substance
hmm how do I solve this

[twin ether]

half life problems are kinda confusing for me

so I'd appreciate any help

[valid cape]

apply radioactive decay formula

$N=N_0e^{\frac{-t}{T}}$

[valid cape]

where N is the remaining weight of the substance, N_0 is initial substance weight, t is time passed and T is the half life

you are given plenty information to find the half life

[twin ether]

$15=20 (\frac{1}{2}})^{\frac{t}{7}$

like this?

[elfin berry]

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

[valid cape]

um, whats the 1/2?

[twin ether]

we only learned this equation

[open kayak]

Yep, that's fine too

[open kayak]

Given the information in the problem, can you say what N_0 should be?

[twin ether]

20

initial mass

[open kayak]

Yes

[open kayak]

Now what's another meaningful thing to do here?

Can you create another equation

[twin ether]

yeah I think its
15=20(1/2)^7/t

[open kayak]

Shouldn't your T be the mean lifetime?

[open kayak]

Yep

[twin ether]

I solved for t too

[open kayak]

What did you get?

[twin ether]

it is 18.86

hours

I mean 16

.86

[open kayak]

Yep, .87 if correctly rounded

[twin ether]

16.87?

[open kayak]

Yes, if correctly rounded to two decimals

[twin ether]

oh I see, thank you! Do you mind mind helping me with another log problem? It's about the ritcher scale this time

[open kayak]

Just send it in a help channel (it's often better to close and open a new one by the way, since this one is now further down the channel list and less people will see it)

[twin ether]

oh k will do that

.close

[marsh citrus]

Channel closed

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[valid cape]

nope, its half life

at least, thats what ive been taught

[open kayak]

Really?

It seems Wikipedia says something else

Your T is their tau

Which is half_time/ln(2)

[marsh citrus]

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[valid cape]

yup, seems to be the case

[valid cape]

and i was taught to approximate e as 2 too

.close

[marsh citrus]

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[open kayak]

Ah, so what you learned approximates 1/ln(2) as 1

[spark otter]

for me ln(2) ~ 0.7 ~ 1/sqrt(2)

ln(2) ~ 1 is harsh

[marsh citrus]

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[ripe python]

Hi i need hint how to begin exercise
The question is :if (3sinx-cosx)/(sinx+2cosx)=1 find tgx

[knotty trellis]

Multiply both sides by the denominator of the fraction

[atomic ruin]

3sinx-cosx = sinx+2cosx

divide both sides by cosx to get tanx

then rearrange to solve for tan(x)

[ripe python]

Okay

Makes sense

Just second

Like this?

[atomic ruin]

u missed the -1

3sina - cosa to 3tana

[ripe python]

Ah i see

[atomic ruin]

should be 3tana - 1

[ripe python]

Just second

[ripe python]

Like this

[atomic ruin]

no

line 3 to 4 mistake

[ripe python]

Ah

[atomic ruin]

yep

correct

[ripe python]

Thank you

.close

[marsh citrus]

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[marsh citrus]

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[ripe python]

Hi it's me again lol
I need hint again
The question is if tgx+ctgx=3 find tgx-ctgx

[quasi minnow]

|a-b| = sqrt( (a+b)^2-4ab)

[ripe python]

Um sorry can you explain a bit

[quasi minnow]

use this formula

Replace a and b with tanx and cotx

[ripe python]

Alright

Please wait

[eager schooner]

what can you rewrite ctgx as

[ripe python]

Cosx/sinx

[eager schooner]

my WiFi

bruh

[eager schooner]

yes but I was also thinking 1/tanx

[ripe python]

Ah yeah

[eager schooner]

so tanx + 1 = 3
-----
tanx

[ripe python]

Aaaaa

And then quadratic equation ig

[eager schooner]

yeah

so multiply both sides by tanx

and rearrange to make it equal to 0

and it's a quadratic equation

[quasi minnow]

This will be a shorter method here

[ripe python]

Okay let me try both

[eager schooner]

I don't think they understood how that works

[ripe python]

Something like this?

[ripe python]

Did you meant this

[quasi minnow]

Yes

[ripe python]

And then i just solve it like... Irrational equation?

[quasi minnow]

You know tgx+ctgx=3 and tgx×ctgx=1

Put these values

[ripe python]

Aaa okay

[quasi minnow]

Yes

And put the ± sign in front of the sqrt

[ripe python]

How is that formula called

[ripe python]

Alright

[quasi minnow]

(a-b)^2 = a^2+b^2 - 2ab
= a^2+b^2+2ab-4ab
= (a+b)^2-4ab
|a-b|= sqrt( (a+b)^2-4ab))

[ripe python]

I see, so it's some type of quadratic

[ripe python]

Thank you

. close

.close

[marsh citrus]

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[marsh citrus]

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[frank eagle]

When computing the distribution of a \textbf{strictly increasing function} of some random variable $X$, that is $f(X)$, there is this equality $$P(f(X) \leq x) = P(X \leq f^{-1}(x)).$$ How come these sets are equal? We have \begin{align} \omega\in{f\circ X\in(-\infty,y]}&\iff\omega\in(f\circ X)^{-1}((-\infty,y])\ &\iff\omega\in X^{-1}\big(f^{-1}((-\infty,y])\big)\&\iff\omega\in{X\in f^{-1}((-\infty,y])}.\end{align}How do I continue here?

[elfin berry]

Philip

[wraith palm]

how do i do 2+2

[frank eagle]

.close

[marsh citrus]

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[brave spire]

Given, $ax+by=c, y>x>0, x,y \in {\mathbb{Z}}^{+}, a,b,c,d,e \in \mathbb{Z}$, What's the algorithm for finding the minima and maxima of $ex + dy$ with respect to the above conditions? All letters except x and y are constants

[upbeat sable]

Quite vague, what sets do a,b,c and d come from, what conditions are there on them?

[brave spire]

Lastly, there exists atleast one solution to the diophantine equation $ax + by = c$

[elfin berry]

rak³en

[brave spire]

There isn't much for a,b,c,d,e as I was hoping to find a general algorithm

[hushed egret]

what is d

[brave spire]

.

[hushed egret]

?

[crystal lintel]

?

[brave spire]

They are integers

[hushed egret]

set e and d to +- infinity

the quantity is unbounded

[brave spire]

Oh shit a massive chunks still missing

[elfin berry]

rak³en

[crystal lintel]

[upbeat sable]

Still, unbounded

[brave spire]

Why?

[hushed egret]

d and e are arbitrary

[brave spire]

Okay maxima makes sense

[brave spire]

So simply put, I am screwed because there's no general algorithm?

[hushed egret]

no, you are screwed because ex + dy is unbounded

[devout mauve]

wdym screwed, your question has an easy answer

[hushed egret]

you havent given any constraints on e or d

[brave spire]

They are integers..what else is needed?

[hushed egret]

then they can be arbitrarily large/small

[devout mauve]

like them not being able to be bigger in abs value than 1000 or something like that

[brave spire]

Hmm

Its better I think if I just use dummy values

[upbeat sable]

You can have a,b,c,d and e be under 1000 and you can still have ex+dy unbounded

[brave spire]

(ie the values I saw on my sister's test)

[hushed egret]

are e and d held constant?

[brave spire]

Yes obviously

[upbeat sable]

Lets just say a=-1, b=1 and let c=1. so y-x=1. Let d=1,e=1 and you can see that there still is no bound for ex+dy=x+y

[hushed egret]

no it is not obviously

you should specify this

[brave spire]

Uhh okay mb

[hushed egret]

you can even do this over the reals

[brave spire]

Damn that's possible?

[hushed egret]

for fixed a, b, c, d, e, maximise ex + dy subject to ax + by = c

[brave spire]

Well I need to solve it for a=97, b=-299, c=50, d=1, e=100

[devout mauve]

can you post a picture of the original question

[brave spire]

Yes that should have been the language

[brave spire]

I can't cus it was on my sister's aimcat

[devout mauve]

ok so just a very different question. ok

[brave spire]

I just remembered the values

[brave spire]

These are the values I needed to solve it for, but I was hoping for a more general solution

[brave spire]

How do u do this tho?

[brave spire]

No? Its still optimization

[hushed egret]

well here everything is linear so its a linear programming problem whatever thats supposed to mean

layla probably knows about it from her optimisations class

[crystal lintel]

[hushed egret]

but then layla would probably suggest lagrange multipliers

[brave spire]

...

[crystal lintel]

i suggest the simplex method

[brave spire]

They r in 12th standard syllabus, u gotta make a big table or smthin

[hushed egret]

yeah so linear programming

[brave spire]

Yes that's what it's called

[devout mauve]

well simplex method on its own wont give you integer solutions

you need something like gomory cuts or something

[upbeat sable]

Are they looking for integer solutions?

[crystal lintel]

i thought the problem wasn't actually about integers

[hushed egret]

looks like it is

[devout mauve]

x,y positive integers

[brave spire]

Yes I mentioned that if u read the latex

[upbeat sable]

I did, you edited it a bunch of times. Just saying...

[brave spire]

Mb

But now that everyone gets it

Am I stuck with big table method?

[devout mauve]

are you asking whether you should do the stuff that you learned to deal with these problems?

[brave spire]

A) i haven't learnt simplex properly
B) I am asking for alternatives

[devout mauve]

well simplex is just way overkill. I dont know what method you learned but its probably specialized for this specific case

[brave spire]

I haven't learnt anything in a class, I was just challenging my sister on a test and this problem came up and both of us didn't know the proper algorithm for it

She chose the test, but she's not been taught any tools for LPPs either. Atleast not yet

My knowledge of simplex is based on just going thru the first few pages of a 12th class textbook my sister forgot to throw away

[novel juniper]

she would have just had the corner point method

[brave spire]

What's that

[marsh citrus]

@brave spire Has your question been resolved?

[marsh citrus]

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[marsh citrus]

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[still temple]

how is it wrong

it is literally thr highest common factor

how is it not

they said its 21

[fickle compass]

U write all the factors like this for finding lcm

basically u can see 7 and 3 factrs in 84 which gives 21 as well

so 21 is the hcf

[still temple]

what

broo

im confused

[stoic slate]

Highest common factor means highest

[still temple]

there are 3 factors that are common
7 2 and 3

[proper zodiac]

Your lists are only of prime factors

[stoic slate]

You didnt write all factors

[fickle compass]

isnt 84 divisible by 21

[still temple]

oh

[fickle compass]

oh yeah I couldnt remember the word

[proper zodiac]

Multiplying numbers in a list will give you bigger factors

[fickle compass]

prime factorisation method is only correct for finding lcm

for finding hcf u gotta do further stuff

[proper zodiac]

You can use prime factorisation for hcf

[still temple]

i have questions

[proper zodiac]

https://www.bbc.co.uk/bitesize/guides/z2dtfcw/revision/6

[still temple]

no 1
why do we have to multiply the 7 and 3 only

why not 7 2 and 3

[proper zodiac]

It's the factors they share

[fickle compass]

they ain tcommon

[proper zodiac]

Note 21 is not prime

[fickle compass]

aint common*

[still temple]

u mean 2 aint common?

[fickle compass]

yeah

see

[still temple]

so we multiply to find a non prime factor

[fickle compass]

105 is an odd number

[still temple]

yea igot it

i just realised

😂

[proper zodiac]

You start matching prime factors that the numbers have in common until you can't anymore

The product of those primes (in one list) will be hcf

[still temple]

wats hcf again

the defination

highest common factor ok but

like

[proper zodiac]

Like literally, the biggest number that is a factor of both numbers

[still temple]

thanks bro

[marsh citrus]

@still temple Has your question been resolved?

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[marsh citrus]

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[wary bluff]

I dont understand this part

(n k) because we have n tosses and we want k heads. and then what is P^k ?

its the probability of head appearing?

and then whats (1 - p)^(n - k) for ?

(1 - p) would be the prob of not a single head appearing right?

if so then whats the ^(n-k) for?

[limber hearth]

this is the probabity of the sucess from you binomial law

in this case this is the probability of head appearing raised to the power of k

[wary bluff]

ohhhhhhh thats why they said define that last part as q

I was so confused

lastly

there is another part I dont understand

[limber hearth]

i don't remember very well but it comes from the binomial theorem ig

where p is the same probability tho

[wary bluff]

how exactly did they go from all that to (p +(1 - p))^n

[tired oxide]

the binomial formula

[wary bluff]

how do they know that we should let x = q and 1 = p

is it always like that?

[tired oxide]

like $$\sum_{i=0}^\inftyn\choosek a^ib^{n-i}=(a+b)^n$$, because the terms in the sum stop being nonzero and you get the usual binomial formula, which i encourage you to look up

[wary bluff]

I seee

tysm

🙏 bless u

[elfin berry]

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

[wary bluff]

I get it lol

[limber hearth]

only in case of a discrete law

[wary bluff]

[limber hearth]

wait

[wary bluff]

well we arent doing continuous in this course anyways so i shouldnt worry abt that for now ig

[limber hearth]

the function written here is the probability mass function, often the primary means of defining a discrete probability distribution and that's what they're doing here

[limber hearth]

yes my answer wasn't that accurate rigor

[wary bluff]

howwww

$\frac{n \cdot (n-1)!}{(k-1)!(n-k)!}$

[elfin berry]

Calc III Victim

[wary bluff]

this is what we are left with after simplifying right

and then they take out the n?

but even then we have (n - k)! down there instead of ((n-1) - (k - 1))!

so how can they say n * (n - 1, k - 1) ?

oops im slow I get it

.close

[marsh citrus]

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[marsh citrus]

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[warped jay]

How do I calculate the sum of a convergent and divergent series?

[warped jay]

specifically this series:

1/(n(n + 1)(n + 2))

i used partial fraction decomposition and rewrote it to 1/2n - 1/(n + 1) + 1/(2n + 4)

[proud ice]

The sum would diverge

[warped jay]

?

oh right divergent series dont have a sum right

cus they're infinite

how would i calculate the sum of a convergent series then?

: (

.close

[marsh citrus]

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[proud ice]

It's just the sum of the two converging values

[marsh citrus]

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[rocky lark]

Can I see this as a tan and sec?

[limber hearth]

try to reduce the fraction

[rocky lark]

Ok

$x=tan(\alpha)$

[elfin berry]

Fluffy McGiggles

[limber hearth]

more like that

[rocky lark]

I derive the tangent

I have a faster way

[rocky lark]

🤦

I can show you a method for a moment pls

[limber hearth]

yeah show me

[rocky lark]

So i am here

$dx=sec(\alpha)^2 d\alpha$

[elfin berry]

Fluffy McGiggles

[rocky lark]

Now substituting into the integral

I get everything based on these things

Right?

[limber hearth]

show me how you substitute it

into the integral

(btw don't forget to define alpha)

[rocky lark]

This

[limber hearth]

looks good

[rocky lark]

Ok then I'll solve it

What was your method?

[limber hearth]

this

[rocky lark]

Okay

[limber hearth]

and integrate x + 1/x²

which is x²/2 - 1/x +c

[rocky lark]

Wait

But we can't do that

Like

[limber hearth]

?

[rocky lark]

Look

I have a faster method

[indigo lagoon]

you can

but i like yours

method

it looks cool

[limber hearth]

kinda giga chad method

[indigo lagoon]

yes

[limber hearth]

approved

[rocky lark]

However I don't have another method

Well

Thanks

.close

[marsh citrus]

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[marsh citrus]

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[stable portal]

i have this cube which attached to this axis

[stable portal]

this axis rotates on it's own z

without knowing the rotation of the axis just by looking at the positon of the cube how can i figure out the global axis it's on?

so if this is point A and here it is after rotating on the Z

can't i take the global positon of the cube and figure out the axis of the rotation

[marsh citrus]

@stable portal Has your question been resolved?

[marsh citrus]

@stable portal Has your question been resolved?

[proud ice]

I do not understand what you are asking exactly

[stable portal]

if i could a cross b that's the axis it rotated on

i want to take a 3rd vector or point and see how much it's rotated on that axis

[proud ice]

Where are you seeing a and b?

[marsh citrus]

@stable portal Has your question been resolved?

[proud ice]

@stable portal

[stable portal]

the pictures

i ended up getting it

took a cross b to get the axis, then projected A onto the axis
then took c and projected that to the same axis.
then acos projectionA dot projectionC

[marsh citrus]

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[slender trout]

Idk how to approach the two problems

[slender trout]

The ones that have a slash on them are wrong

the first image is the formula, the second is the givens, the third are the two problems

[marsh citrus]

@slender trout Has your question been resolved?

[slender trout]

<@&286206848099549185>

[brisk copper]

Anyone can have answers for these.

[slender trout]

why did u ask in this channel

[brisk copper]

Which channel can I ask?

[slender trout]

go to #❓how-to-get-help

[brisk copper]

Thank you.

[slender trout]

<@&286206848099549185> can someone help my problem

[still temple]

how would i help your problem

do you want me to make it harder?

and

[still temple]

!15mins

[marsh citrus]

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.

[slender trout]

mb

idk how to solve it

[marsh citrus]

@slender trout Has your question been resolved?

[marsh citrus]

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[slow pollen]

I need help with these angles, i don’t know what the curve on the BC means,

the question says, “the following circle has D as center. Suppose that m BC = 84 degrees. find the following:”

[analog dawn]

aw hell no aleks giving me cancer

[slow pollen]

😭

[analog dawn]

its either half or double

i literally remember doing this like 3 years back

[slow pollen]

which one?

[analog dawn]

the bdc is ofc 84

i think bac is 42 or 168

prob half

[slow pollen]

i assume it’s 42

yeah

thank you

[analog dawn]

test it also what lang is that

[slow pollen]

spanish!

[analog dawn]

ok ok

i thought i couldn't read math

[slow pollen]

i still can’t..

i was wondering what the curve on the letters means

bc it’s always like a straight line but i assume it’s because it’s a curve

[analog dawn]

also aleks is so bad. the order of the angle matters like they'll acept
bac but not cab

like wth

[slow pollen]

oh i got it right thank u

just one left

[analog dawn]

yes yes

u cant mess up or u restart all over

[analog dawn]

oh

uh

this is pretty fine but the shift

[slow pollen]

i think i can do this one with my graphing calculator

[analog dawn]

ight use the dot grpahing thing

i swear i cant trust the pencil thing

[slow pollen]

ikr

[analog dawn]

i counted 1 square off for a parabola and i had to start over

[slow pollen]

it’s asking to mark every point in the intersections on x axis and mínimums and maximums inside the cicle

[slow pollen]

😭😭

[slow pollen]

this is what i translated it might be wrong

that looks pretty good

[analog dawn]

ye looks right

[slow pollen]

alright it’s my last one 😭

it’s not even my homework i’m getting paid to do this

[analog dawn]

WHAT

luckyyy

[slow pollen]

yeahhh

this is my first time using aleks

i’ve gotten all of them right for now

[analog dawn]

smarty pants

[slow pollen]

mannn they were easy

i had a hard time on like 3

i don’t know how to graph this

like where do i put it…….

[analog dawn]

use the point thing

that x thing

below the eraser

then u can input x and y coordinates

[slow pollen]

ohhh cool

thank u

.close

[marsh citrus]

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[thick dagger]

Hello, I don't know how to do b, should I define a maping and prove it is bijective? I have no idea how to define such.

[marsh citrus]

@thick dagger Has your question been resolved?

[thick dagger]

<@&286206848099549185>

[marsh citrus]

@thick dagger Has your question been resolved?

[marsh citrus]

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[willow yarrow]

can anyone help me pls

[still temple]

@willow yarrow what have you tried so far?

[willow yarrow]

I tried AM-GM and substituted 2017^2 with z1 x conj(z1)

i dont know what to do with the numerator

[marsh citrus]

@willow yarrow Has your question been resolved?

[serene spoke]

P = A² + B²
P = (A+B)² - 2AB

@willow yarrow try this way

[marsh citrus]

@willow yarrow Has your question been resolved?

[willow yarrow]

doesnt seem to work

it kinda overcomplicates the expression

[marsh citrus]

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[wet jetty]

i found the three paralelogram

possible

but i dont know the Quantity relationship

help

[nova totem]

You'll have a linear system of 3 equations

2a + 2c = 33
2a + 2b = 24
2b + 2c = 35

They tell you perimeters of the parallelograms

[wet jetty]

How to solve it

damn i haven’t learn yet

[marsh citrus]

@wet jetty Has your question been resolved?

[marsh citrus]

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[loud hornet]

Equation of the straight line containing the LaTeX height: CD
𝐶
𝐷
LaTeX triangle: ABC
𝐴
𝐵
𝐶
with vertices at the points LaTeX: A=left(-1,- 2), LaTeX: B=left(2,- 3) and LaTeX: C=left(8,- 1) has the form:

[open kayak]

Can you give a sketch please? We don't know what D is

Or show the problem exactly as stated

[loud hornet]

D is the point between A and B, theres a height from C

[loud hornet]

so how should I do that task @open kayak

[open kayak]

Like this?

[loud hornet]

ah thx

[open kayak]

What's the task?

[loud hornet]

i think so

[loud hornet]

..

[open kayak]

Ah, you just need to draw that?

[loud hornet]

there are four answers and i didnt know how to eliminate @open kayak

[open kayak]

Can you show the original question

A screenshot just like that one

[loud hornet]

do you know Polish language?

[open kayak]

No but still send it

I might know it from context

[open kayak]

And after this, there are the answer options?

[loud hornet]

yep

[open kayak]

Is the question to find the equation of the line through C and D?

[loud hornet]

the equation of the line that contains CD

[open kayak]

Is there a picture?

[loud hornet]

no

[open kayak]

If you sketch the triangle and all the lines that are given, you get this

None of these lines is the height

Atleast one line goes through C (the orange one)

Is maybe the orange one meant? Or does it really say something like "height"

[loud hornet]

it says height

wysokość

is height

always

[open kayak]

Hm, weird

[loud hornet]

this also

[open kayak]

Is it about the same as this?

[loud hornet]

no

its median of the triangle

[open kayak]

Oh

[open kayak]

Ok, then everything is fine

It will turn out to be the orange one

[loud hornet]

how to make equation of this orange line

[open kayak]

So, the requirement for the height is that we have a 90° angle

[loud hornet]

ye

[elfin berry]

Kepe

Kepe

[open kayak]

Does this make sense?

If we have m_A * m_B = -1 for two lines, then they are perpendicular/form a 90° angle

[open kayak]

You probably had this in class, @loud hornet, right?

[loud hornet]

yeah

[open kayak]

Do you know how to find m_{AB}?

[loud hornet]

also another problem

[loud hornet]

no

[elfin berry]

Kepe

[open kayak]

You know this, right?

@loud hornet

[loud hornet]

yeah

thx

1/3

simple

[open kayak]

Wait, I meant A(-1, 2)

[open kayak]

A(-1, 2) and B(2, -3)

[loud hornet]

ah sorry

[elfin berry]

Kepe

[open kayak]

Can you simplify this further @loud hornet

[loud hornet]

yeah, 3/5

[open kayak]

Exactly

[open kayak]

Ok, so we are almost done. We know the orange line is of the form $y = \frac 3 5 x + c$, we just don't know $c$ yet

[elfin berry]

Kepe

[open kayak]

But we have one more information:

The orange line goes through the point C

So we can plug in its coordinates

C(8, 1)

[elfin berry]

Kepe

Kepe

Kepe

[open kayak]

First one can't be it

Third one also not

[elfin berry]

Kepe

[open kayak]

Exactly that!

So it's the second one that's correct

@loud hornet

[marsh citrus]

@loud hornet Has your question been resolved?

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[modern geyser]

sin(y/2)+e^y=4x

[modern geyser]

Find dy/dx

[shadow warren]

do you know how to do implicit differentiation?

[modern geyser]

yes

when i derive the x its going to be dx/dx

so 1

and when i derive the y its going to be dy/dx

then solve algebrically for dy/dx

[shadow warren]

yes

[modern geyser]

correct me if i am mistaken

[shadow warren]

so apply that concept here

[modern geyser]

yeah when i do it i have a problem

derivative of sin is cos

[shadow warren]

yes

[modern geyser]

and i need to apply chain rule

[shadow warren]

yep

[modern geyser]

so cos(y/2)

and the derivative of y/2

[shadow warren]

and then multiply by the chain rule

yep

which is?

[modern geyser]

im having a problem in fugiring out how to derive the y/2

[shadow warren]

how would you normally differentiate y/2

[modern geyser]

it can be turned to 2^y-1

[shadow warren]

no need for that

it’s just $\frac{y}{2}=\frac12 y$

[elfin berry]

y0shi

[shadow warren]

1/2 is a constant multiplier

[modern geyser]

oh ok

[shadow warren]

so if you differentiate it

you’ll get?

[modern geyser]

1/2 dy/dx

[shadow warren]

yep that’s it

[modern geyser]

next

[shadow warren]

so $\cos\left(\frac{y}{2}\right)\cdot\frac12\dv{x}y$

[elfin berry]

y0shi

[modern geyser]

and +e^yd/dx=4

[shadow warren]

yep

[modern geyser]

and now we solve for dy/dx

by factoring

[shadow warren]

e^y(dy/dx)

yes

[modern geyser]

dy/dx

and taking the cos to the right

by dividing

[shadow warren]

well factor it out first

and yeah

[modern geyser]

dy/dx(1/2+e^y)=4/cos(y/2)

[elfin berry]

y0shi

[shadow warren]

this is what you have after factoring right?

[modern geyser]

no

dy/dx ( 1/2+e^y) = 4/cos(y/2)

[shadow warren]

what did you get?

why is the cosine on the right

when we differentiate sin(y/2)

[modern geyser]

cos(y/2)*1/2dy/dx

[shadow warren]

yes

so when we factor the dy/dx

[modern geyser]

oh ok

[elfin berry]

y0shi

[shadow warren]

so this makes sense yeah?

[modern geyser]

yeah

[shadow warren]

alright

so just divide the entire thing on both sides

to solve for dy/dx

[modern geyser]

we get an answer of dy/dx = 4/1/2cos(y/2)+e^y

[shadow warren]

yeah

remember to put parenthesis

but if you’re writing it on paper, just make sure that the entire thing is in the denominator

[modern geyser]

yeah got it tysm

[shadow warren]

if you want to get rid of the complex fraction at the bottom

[modern geyser]

can you help me with 2 question also

[shadow warren]

you can also multiply by 2 in the top and bottom

yeah sure

[modern geyser]

next question is
lnxe^3y=2y^2

[elfin berry]

y0shi

[modern geyser]

yes

[shadow warren]

alright

so just use the same process

[modern geyser]

when i derived the whole thing

i got

1/x+e^(3y)3dy/dx=4ydy/dx

[shadow warren]

mm not quite

we have a product of two functions on the left hand side

we have to use the product rule here

[modern geyser]

oh ok

[shadow warren]

this would be correct if it was an addition sign instead of multiplication

[modern geyser]

oh i missed it

anyways i did the product rule

and got

1/x*e^3y+lne^3y3dy/dx

[shadow warren]

$\frac{1}{x}e^{3y}+\ln(x)\cdot 3e^{3y}\dv{y}{x}$

[elfin berry]

y0shi

[shadow warren]

this?

[modern geyser]

i think yes

[shadow warren]

yeah that’s good

so now differentiate the right hand side as well

then move all the dy/dx terms to the same side

and just factor like we did before

[modern geyser]

ln(x)*3e^3ydy/dx-4ydy/dx=e^3y/x

[shadow warren]

yep

and now factor it

and divide the other factor on both sides

[modern geyser]

dy/dx(3lnxe^3y-4y)=-e^2y/x

divide (3lnxe^3y-4y) by both sides

then we'll get an answer of -e^2y/x/(3lnxe^3y-4y)

i think there is something wrong

<@&286206848099549185>

.close

[marsh citrus]

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[marsh citrus]

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[slim nest]

Hi

[serene spoke]

Hii

[slim nest]

Please dont wait

[serene spoke]

Ok

[slim nest]

I will be typing down the question for mintues.

[serene spoke]

Okk whats it about ?

[slim nest]

It is long

Uh

[serene spoke]

Ok type !

[slim nest]

Solving for func using x and y

I think...

I also got a garbage wifi, so please do not wait 😭

[slim nest]

Omg 😭

[scenic path]

bro can you answer my doubt meanwhile

ill try to help him

[slim nest]

Mount Everest is the highest mountain on the planet. In 1999, the highest point on the mountain was measured to be 29,035 feet above sea level. Scientists believe that Mount Everest is still growing and estimate that the height of the mountain is increasing between 0.16 and 2.4 inches every year. (Note: 1 foot= 12 inches)

If the height of Mount Everest increase 2.4 inches each year, how many years after 1999 would the mountain be expected to have a maximum height of 6 miles above sea level? (Note: 1 mile= 5280 feet)

[slim nest]

Thanky uouuu

[serene spoke]

I.can try

[slim nest]

You guys are so sweet 😭

[scenic path]

just a min trying grabbing my pen and paper

[slim nest]

What can I say xdd

[slim nest]

Ofc! Take your time!

[serene spoke]

Hey see 2.4 inches = 1/12×2.4 foot = 1/5280 × 1/12× 2.4 mile

[slim nest]

Oh

Yep!

[serene spoke]

We need a max height of 6miles above the sea level

Already we have a height of 29035 feet

[slim nest]

Yes

[slim nest]

True

Chatgpt got it wrong

😭

[serene spoke]

29035 feet = 1/5280 × 29035 miles

[slim nest]

Yes

[serene spoke]

,calc 1/5280*29035

[elfin berry]

Result:

5.499053030303

[slim nest]

Cool!

[serene spoke]

it would be better if we convert everything to feet

[slim nest]

Ofc!

[serene spoke]

6 miles = 6* 5280 feet

,calc 6*5280

[elfin berry]

Result:

31680

[serene spoke]

We need an height increase of

[slim nest]

31680 feet!

[serene spoke]

,calc 31680-29035

[elfin berry]

Result:

2645

[serene spoke]

Already the mountain is 29035 feet above sea level

[slim nest]

Slope intercept form?

[slim nest]

Yep!

[serene spoke]

I grows 2.4 inch per yr that is 1/12 × 2.4 feet /year

[slim nest]

Yep

[serene spoke]

,calc 1/12 * 2.4

[elfin berry]

Result:

0.2

[serene spoke]

Now if we divide this by 0.2

We should get required number of years

[slim nest]

Okay! Tysmm

[serene spoke]

,calc 2645/0.2

[elfin berry]

Result:

13225

[serene spoke]

Thats 13225 yrs

[slim nest]

This is correct! Ty again

[scenic path]

aight imma wait for another 13225 i guess

to check wether that scientist is true

[slim nest]

😭

[scenic path]

[serene spoke]

I think the scientist said