help-10

[severe reef]

Yes, but instead of memorizing them as coordinates I recommend memorizing them as trig values directly

[frozen jolt]

ok thanks

[severe reef]

Something like this

[frozen jolt]

ok

thanks

.close

[obtuse pebble]

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[mint arrow]

what is the logic in this

[mint arrow]

how to solve

OH WIAT

NVM

i get it

[shadow tangle]

Do you know how to add matrices?

Oh ok 👍

[mint arrow]

the answer is 7

right

[shadow tangle]

Yep

[mint arrow]

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[gloomy comet]

hey i jus need someone to verify my answer

[gloomy comet]

would the equation be

-28cos[pi/75(x-0)] + 28.5

[brisk matrix]

what is the maximum of your function

plug in x = 75

[gloomy comet]

here lemme show my work gimme one second

[brisk matrix]

well what do you get when you plug in 75

[gloomy comet]

oh i plug in 75 for x and make y = 0 right

[brisk matrix]

no just plug in x = 75

what value do you get

[gloomy comet]

31.3

i dont get it why would i plug 75 for x

[brisk matrix]

well you were supposed to get 56.5

which is correct. and if you plug in x = 0 you'll get 0.5, which is also correct

i was trying to help you check the answer

[gloomy comet]

on wolfram it said

31.3

[brisk matrix]

,w -28cos(pi * 75 / 75) + 28.5

[warm shale]

Results provided by WolframAlpha

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

Requested by maximofs#0

[gloomy comet]

Ohhh my bad

wait so the equation is acc correct?

i thought i was wrong

thanks a lot bro

[brisk matrix]

one thing to make a note of

actually 2

try to use "t" instead of "x" if it's in terms of time

and they didn't specify if x is in minutes or seconds or whatever, so your answer is correct if x is supposed to be in seconds, but otherwise you'd need to adjust

[gloomy comet]

cant i just write let x = seconds

[brisk matrix]

x is not equal to seconds

you could say "x is in seconds"

[gloomy comet]

got it 💯

.close

[obtuse pebble]

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[lapis gull]

we may never know what this zella person wanted to say

[obtuse pebble]

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[gloomy comet]

mb one more question

[gloomy comet]

for this we just plugin 5 for H and solve for t right

[severe depot]

yup and then look in t ε [0,60]

[prisma pasture]

yes

[gloomy comet]

ok so im doing that part rn

i got to the part

where im at

1/6 = sin(pi/25(t-8))

what do i do now

do i distrubute pi/25

[prisma pasture]

find the general solution for the equation sin(x)=1/6

[gloomy comet]

i dont understand

so i dont distrubute?

[prisma pasture]

What

Wdym in distrubute

First you need to find (both) general solution for the equation sin(x)=1/6

When equlize it with what you got inside you equation (pi/25*(t-8))

[gloomy comet]

how

[prisma pasture]

Write in your calculator arcsin(1/6)

In radians of course

This is one solution

To generelize it

You add 2pi*k

And you get the first solution

To get the another you do (pi-the number you got in the first time)+2pi*k

What I said now applies only for sin(x), for cos(x) is a little bit different

[gloomy comet]

quick question why do we add this

[prisma pasture]

Ok

How many radians there are in a circle?

[gloomy comet]

2pi

[gloomy comet]

got it so i got 0.167

[prisma pasture]

Good

If you start on some point on a circle

And you go around it 2pi radians

Where do you end up?

[gloomy comet]

the same place

[prisma pasture]

Indeed

And if you go another 2pi radians?

[gloomy comet]

same place

[prisma pasture]

Good

So no matter how many times you go around

You end up in the same place

This is what k stands for

[gloomy comet]

oh i see

[prisma pasture]

How many times "you went around the circle"

[gloomy comet]

ok so do i do 0.167 + 2pi(pi/25)

[prisma pasture]

No no

The first solution is

0.167+2pi*k

But this is not the only one

The get the another one

You need to

(pi-0.167)+2pi*k

And this is the another solution, you can calculate the number if you want to

[gloomy comet]

2.97

so the second solution is

2.9 + 2pi*k

[prisma pasture]

Indeed

Now you have 2 equations

[gloomy comet]

so what happened with the t-8

[prisma pasture]

Nothing

0.167+2pi*k=(pi/25)(t-8)

and

[gloomy comet]

also i have a question

[prisma pasture]

2.97+2pi*k=(pi/25)(t-8)

[gloomy comet]

s it possible

instead of 2pi *k i add 2pi/(pi/25)

bc that is the period

[prisma pasture]

No

k is an integer

Oh wait divide bu it

by

No it's still not an integer

You see

(pi/25)(t-8)

Is

One answer

from the infinite amount of answers

of the form

0.167+2pi*k

or

2.97+2pi*k

and you need to find which is relevant

Solve these 2 equations

For t of course

[gloomy comet]

okok lemme clear this up again once more

so rn i still havent wrote the 2 solutions im gonne in 1 second, rn im at

1/6 = sin(pi/25(t-8))

now i have to find the inverse

of 1/6

and add 2pi*k to it

for the first solution

right

[prisma pasture]

right

[gloomy comet]

ok so for the first solution

i got 0.167 + 2pi(k)

the second solution

(pi-0.167) + 2pi(k)

whats there left to do now

would it now be

one eqaution will be

0.167 = pi/25(t-8)

and then i solve for t

the other would be

(pi-0.167) = pi/25(t-8)

right

[prisma pasture]

no

0.167+2pi*k = pi/25(t-8)

the 2pi*k is important

[gloomy comet]

oh got it

but what does k equal then bro

is it a variable

[prisma pasture]

I explained to you what k is

I believe you can understand what is it

[gloomy comet]

ok i understand

[prisma pasture]

What you got?

[gloomy comet]

im still soving

[prisma pasture]

Ok

Do you need help?

[gloomy comet]

yes 💀

[prisma pasture]

So

let's start with the first one

What do you think the first step should be?

Remember you to "isolate" (I don't know the proper word in English) t

[gloomy comet]

multiply 25

on the otherside

[prisma pasture]

Well yes

But you can also

Divide both sides by pi/25

Which is the same as multiplying by 25 and then dividing by pi

But fine multiply by 25

What do you get on the left side?

[gloomy comet]

(0.167 + 2pi(k))(25)

[prisma pasture]

Well, multiply the numbers

[gloomy comet]

so

0.167 x 25

[prisma pasture]

Yes

[gloomy comet]

and 2pi x 25

[prisma pasture]

Yes

How much is that?

[gloomy comet]

4.18

[prisma pasture]

Ok

[gloomy comet]

and

50pi

[prisma pasture]

Awesome

Now you got 4.18+50pi*k=pi(t-8)

So divide by pi

[gloomy comet]

yes

i divide each number by pi right

so 1.33 + 50(k)

tthen we add 8

9.33 + 50k = T

[prisma pasture]

Awesome

Now solve the second equation

[gloomy comet]

i got

31.634 + 50(k) = t

[prisma pasture]

awesome

[gloomy comet]

can i include k in a let statement

what should i say it equals

[prisma pasture]

If you want to solve the question, you have to

So now you got 2 expression for t

[gloomy comet]

yes

[prisma pasture]

9.33 + 50k = t
31.634 + 50k = t

[gloomy comet]

yup

[prisma pasture]

You know that t is in seconds

and they ask you

in the first minute

so t is

0 ≤ t ≤ 60

right?

[gloomy comet]

yea i think so

[prisma pasture]

So

Now what you got to do

Is to "go around the circle"

Start plugging integers in k (starting from 0)

Until you get a t that is bigger than 60

[gloomy comet]

so its like a guess and check

[prisma pasture]

Yes

It's really short here

[gloomy comet]

do i do it for both

[prisma pasture]

Of course

You got your answers?

[gloomy comet]

for first one i got

k = 0.57

[prisma pasture]

What

[gloomy comet]

thats 60.134 which is bigger then 60

[prisma pasture]

What

[prisma pasture]

No no what

[prisma pasture]

.

k must be an integer

[gloomy comet]

OH mb integers are only whole nymbers right

wait im trippin

[prisma pasture]

If it's not an integer you didn't go a full circle

[gloomy comet]

so for the second one

its k = 1

[prisma pasture]

Em

I think you are getting confused

You shouldn't write the values of k

It's for you to find the answers

You should write the values of t you get

For exmaple

If I plug in k=0 in the first one

9.33 + 50*0 = 9.33

At 9.33s, h=5

Continue from here

[gloomy comet]

oh so i just sub in 0

for K for both equations

[prisma pasture]

Not just a zero

Every integer until you get t>60

[gloomy comet]

wdym

[prisma pasture]

I continue

k=1

9.33 + 50*1 = 59.33

At 59.33s, h=5

k=2

9.33 + 50*2 = 109.33

[gloomy comet]

ohhhhhhhh

[prisma pasture]

109.33s, h=5, but it's more than 60, so you ignore it

Now do it for the second one

[gloomy comet]

got itt

[prisma pasture]

You finished?

[gloomy comet]

yes

i got

at 31.634 seconds

h = 5

man ur a legend, is it ok if i ask u for questions when i have trouble, for the next hour or so, totally fine if u cant no worries

[prisma pasture]

you can ask me questions any time :)

I am very happy I was able to help

Omg first time someone replies with a super reaction to my message

[obtuse pebble]

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[crude estuary]

An alligator at the local zoo has a lower jaw that is 74 cm long and an upper jaw of 80 cm in length. If a long stick that is stuck between the tips of his jaws keeps the alligator’s mouth open at a 35 degree angle, how long is the stick? Round your answer to the nearest tenth.

c^2 = 74^2 + 80^2 - 2 * 74 * 80 * cos(35°)
I got 46.37cm as my answer

[crude estuary]

i took the values it gave me and plugged them into the cosine formula

and solved

[obtuse pebble]

@crude estuary Has your question been resolved?

[crude estuary]

<@&286206848099549185>

[timid silo]

Yes thats the way to do it

[crude estuary]

awesome

[obtuse pebble]

@crude estuary Has your question been resolved?

[obtuse pebble]

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[tame wing]

Consider a firm with the following information on prices and quantity demanded for its product.

Price Quantity demanded
$389 800
$339.00 1252
$409.00 395

a) What is the demand equation? Include a screenshot of your Excel work

b) What is the elasticity? Show equation used. Is demand elastic or inelastic?

[tame wing]

I got -3.207 as my elasticity, believe this is wrong.

Got it from Demand elasticity = ((1252 - 800) / 1026) / (($339 - $389) / $364)

[night glacier]

did you do the demand equation

if you draw it you can see whether it is inelastic or not

then that can help decide if your answer is reasonable

[obtuse pebble]

@tame wing Has your question been resolved?

[tame wing]

It's elastic just wanted someone to verify my approach.

[night glacier]

i believe your answer is right

[obtuse pebble]

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[long hedge]

how is -9 wrong

[long hedge]

ohhhh

.close

[obtuse pebble]

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[obtuse pebble]

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[forest glade]

help! i cant do simple proofs to save my life

[obtuse pebble]

@forest glade Has your question been resolved?

[hollow schooner]

they are symmetric. thank me later

[trim saffron]

a=b <=> b=a

[rich hemlock]

How is proving the symmetric property for line segments simple?

it's not

Does congruence not imply symmetry since congruence is an equivalence relation?

jk i don't what this problem wants

[obtuse pebble]

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[obtuse pebble]

@timid silo Has your question been resolved?

[brisk grove]

try writing $\parens{1 + \frac{1}{2x}}^n$ as a summation

[warm shale]

redstoneplayz09

[brisk grove]

@timid silo

It's a sum

Things added together

You can do it in terms of n

Have you heard about newton's binomial?

$(a + b)^n = \sum_{k = 0}^n \binom{n}{k} a^k b^{n-k}$

[warm shale]

redstoneplayz09

[brisk grove]

does this look familiar to you

huh

the title of your page says

"binomial expansion"

have you went over the material before trying the question..?

that's very wrong

you can't do it without knowing what the binomial expansion is..

ask your teacher about it

[brisk grove]

so you DO know this?

show me what you know

I can't help otherwise

[brisk grove]

that's exactly this

but written... badly

do u know what the symbol

$\sum$

[warm shale]

redstoneplayz09

[brisk grove]

means

okay

so..

[brisk grove]

look at this

can u see its the same thing as what u sent?

okay

so use it to rewrite $\parens{1 + \frac{1}{2x}}^n$

[warm shale]

redstoneplayz09

[brisk grove]

well okay thats correct but I suggest letting the 1 have a power of n-k

and 1/(2x) have a power of k

because the 1 just stays 1 anyways, so the ugly n-k power disappears

also make sure u write the index

$\sum_{k=1}^n$ is summing over $k = 1$ to $k = n$.

[warm shale]

redstoneplayz09

[brisk grove]

well the point is that you do it yourself

$\sum_{k=1}^n f(k)$

[warm shale]

redstoneplayz09

[brisk grove]

you have something like this

a sum,

and inside it some expression with k and other stuff

this just means:

$f(1) + f(2) + ... + f(n-1) + f(n)$

[warm shale]

redstoneplayz09

[brisk grove]

so k is what's called the "index"

you plug in each value between 1 through n

into k

and add up the results

that question is meaningless

[brisk grove]

this represents a sum

why did your sum disappear, and also why did you just copy f(k)? that has no relation to the question

I just used it to try and explain what a summation is

ok lets scrap this

seems like summation are just confusing you

use this

and write out the first 3-5 values of the sum

k...?

why do u have k

look in your paper

use this

,rotate

[brisk grove]

alright

now try to simplify it a little

for example

$\frac{1}{2x} = \frac{1}{2} x^{-1}$

[warm shale]

redstoneplayz09

[brisk grove]

write every x as having negative exponent

that will help later

ok

what's

$\parens{\frac{1}{2} x^{-1}}^2$

[warm shale]

redstoneplayz09

[brisk grove]

and you also have the same thing to the power of 3

simplify that

(using exponent rules)

yes, good

now you have that very big expression

and you multiply it by (2 + 3x^2)

so its the same as first multiply by 2

and then multiplying by 3x^2 and adding the results

so you should think "what are the different ways to get a term without x"

how could x cancel out here

well, later

they tell you the term independent of x is 17 + 3/4

so we can use that to make an equation and solve for n

THEN after we have n, we can find the coefficient of 1/x

[obtuse pebble]

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[unreal steeple]

Can someone explain to me why we need to divide 1000000 since the answer is C?

[fierce lagoon]

100 cm = m

Therefore:

100^3 cm^3 = m^3

And 100^3 is 1000000

[obtuse pebble]

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[prisma glacier]

I need someone to help me all of 32 please

[obtuse pebble]

@prisma glacier Has your question been resolved?

[obtuse pebble]

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[stable prairie]

Hello, so I have an equation system, and using the Gauss-Jordan elimination method this was obtained $f(v)=f(v_1)=f(v_2)=f(v_3)=f(v_4)$. I encountered this method used on linear equations but I'm not sure if I clearly understand how the method was applied in this equation system. Can someone please explain? Thank you so much.

[warm shale]

chobu nomu

[obtuse pebble]

@stable prairie Has your question been resolved?

[obtuse pebble]

@stable prairie Has your question been resolved?

[mint tendon]

so first get all your terms on one side

so you have a bunch of equations equals 0

[mint tendon]

then row reduce that matrix

[stable prairie]

Thank you so much!

.close

[obtuse pebble]

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[opaque galleon]

Recall the Fundamental Theorem of Calculus fo find $f_{x}$\\
$f(x,y) = \int_{y^2-x^2}^{2} \sec^3(t+1) dt$\\

$f_{x} = 0 - [\sec^3(y^2-x^2)][-2x]$\\
$f_{x} = 2x\sec^3(y^2-x^2)$

Did I do this correctly

[warm shale]

casiofx991exz

[opaque galleon]

pls say if wrong 😭

or right

🙂

[timber island]

it looks wrong ngl..

[opaque galleon]

😭

[sage geode]

Are you sure t + 1 is y^2 - x^2 when t = y^2 - x^2?

[plain owl]

Just missed a small +1

[opaque galleon]

oh yeah lol

[polar fossil]

and sec^3(1) is 0?

[timber island]

its 2 not 1

[polar fossil]

oh right

[plain owl]

Still that doesn't matter

[opaque galleon]

why I gotta evaluate sec^3

if you gonna multiply it to 0

[polar fossil]

you don't, i was confused

[opaque galleon]

thanks

[timber island]

why am i getting this 💀

OH

nvm

its not f(x)

[polar fossil]

we're not looking for the integral here

it's $\pdv{x}f(x,y)

[elfin burrow]

that’s an antiderivative of the answer we want

[timber island]

yeah i just saw it, its 2 variables

[opaque galleon]

Recall the Fundamental Theorem of Calculus fo find $f_{x}$\\
$f(x,y) = \int_{y^2-x^2}^{2} \sec^3(t+1) dt$\\

$f_{x} = 0 - [\sec^3(y^2-x^2+1)][-2x]$\\
$f_{x} = 2x\sec^3(y^2-x^2+1)$

Did I do this correctly now

[warm shale]

casiofx991exz

[opaque galleon]

nice

B)

😎

this is me ^ rn

[obtuse pebble]

@opaque galleon Has your question been resolved?

[obtuse pebble]

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[summer arrow]

Hello, can someone please help me understand what exponential 2^x means? or exponential functions? My first language is not english and for the first time, im gonna transfer to an english school. Im having trouble with these mathematical terms.

[ruby path]

It means that the variable is in the power of some non negative number

Or positive number

Whatever you wish

[summer arrow]

those are exponents right?

whats the difference between exponents and exponential I mean whats the difference between the two words

[ruby path]

Well they are basically the same

[summer arrow]

oh

so exponential functions are also the same?

[ruby path]

An exponential function is when you have the power as a variable

$$2^3$$
$$f(x) = 2^x$$

[warm shale]

neonperseus

[ruby path]

In the first example, 3 is the exponent, and in the second example, x is the exponent

But the second function as a whole is an exponential function

[summer arrow]

what does the f even meann

[ruby path]

That's just the name of the function

[summer arrow]

I dont understand how do they ask questions on this topic I mean do they ask which one is a function and give options

[ruby path]

Well

If you see "x" in the power, it's an exponential

I don't know if it's of any use for a question to be asked solely on what an exponential function is

[summer arrow]

I dont understand how this is a topic what is it even used for

[summer arrow]

if its not a variable its just an exponent right? okay thats the impoprtant part

[ruby path]

anything in the power is an exponent

But it's only an exponential function if the variable (x) is in the power

[summer arrow]

ooh I think I get it

sorry for asking this much It doesnt make sense when you dont speak english

[ruby path]

all good

[summer arrow]

.close

[ruby path]

.close

[obtuse pebble]

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[hasty lily]

Consider points A, B on a circle with center O. Let K be the intersection of the tangents drawn from A, B and KCD, KEF be secant lines.
Let P be the intersection of CF and DE. Prove that A, P, and B are collinear.

[obtuse pebble]

@hasty lily Has your question been resolved?

[hasty lily]

<@&286206848099549185>?

[candid yarrow]

What have you tried

[hasty lily]

well i don't really have any ideas yet

[night glacier]

[hasty lily]

i've tried taking the intersection P_1 of AB, CF and P_2 of AB, DE and proving that AP_1/P_1B = AP_2/P_2B
but that didnt really lead anywhere

[granite quartz]

Sorry but no

[hasty lily]

i feel like you'd probably need to draw something extra to solve this problem (edit: @novel grotto?)

[obtuse pebble]

@hasty lily Has your question been resolved?

[tranquil sonnet]

The problem is purely projective so we can just take a homography sending AB to the diameter and the rest is trivial

Another less “cheesy” way is to just use brocards theorem (on cbef) to say that the pole of K goes through P and we are done

[old path]

You use the angular property of secants, ie angle subtended by two intersecting secants is equal to sum of the two angle subtended by the arcs at centrE DIVIDED BY 2. Use the property for angles APD, DPF, FPB. you will prove that angle is 180 degree. hence three points are collinear

[novel grotto]

it's homothety

not homography

[tranquil sonnet]

No, I’m not referring to homothety, I’m referring to homography.

[novel grotto]

Oh I didn’t know that existed 😅

thanks

[tranquil sonnet]

It’s basically a projective transformation

That preserves incidences and tangencies

[novel grotto]

intriguing

[obtuse pebble]

@hasty lily Has your question been resolved?

[hasty lily]

hmm (sorry, i just got back here)

oh yeah

but wont you need A, P, and B to be collinear to be able to calculate angle APD like that?

[hasty lily]

sorry i'm new to competition maths, i still dont understand how that can be used yet

[tranquil sonnet]

if you are new you should try to find an angle chase solution

Once you get better this configuration will become very familiar, but for now I will try to find an elementary solution

[hasty lily]

and unfortunately after reading descriptions of brocard's theorem for like 5 minutes i still don't understand *how it can be applied here

[tranquil sonnet]

You need to know what a polar is

I’ll tell you

So basically, the pole of a point A with respect to a circle W is the line connecting the tangents from A to W

Does that make sense?

So for example the polar of K is line AB

[hasty lily]

yeah

[tranquil sonnet]

hmm, there is actually a bit more theory (complete quadrilaterals), I think it’s best we just angle chase

[hasty lily]

are there any books that i can read to understand these concepts? because i don't think the course i'm taking covers high school knowledge just yet

[tranquil sonnet]

There are mainly 3, Euclidean Geometry in Mathematicals Olympiads (costs money), A Beautiful Journey through Olympiad Geometry (free), and Lemmas in Olympiad Geometry (free)

[hasty lily]

thank you!!

[tranquil sonnet]

I highly recommend the first 2

The second is the most beginner friendly

[hasty lily]

i'll try to buy/get them

[tranquil sonnet]

Ok let me try to angle chase

[tranquil sonnet]

Yeah honestly idk how to do this without projective

[hasty lily]

its fine

thank you

[obtuse pebble]

@hasty lily Has your question been resolved?

[obtuse pebble]

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[echo gazelle]

i’m very confused what i’m doing wrong

[plain stag]

where is -4 coming from?

[echo gazelle]

dx/dt

oh my go

my imagination apparently

[plain stag]

such is the bane of all calc students

[echo gazelle]

lmao

thanks for pointing that out

.close

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[calm lotus]

Hello! I have got an interesting problem.
There is a group of 12 people far from home. They all want to return home, but they only have 1 car which can carry only 4 people, including the driver. If 4 people drive home, 1 of them has to come back with a car to pick up other people.
The question is: What is the minimum number of rides required to take all people home? (Rides home and rides back are counted separately)
How would you solve this problem?

[prime reef]

so lets put 1 person in the car and we are left with 11...now with every 2 drives we get -3 ppl

11-3*3=2 so with 3(2)=6 drives we are left with 2 ppl +driver

so 7 drives

[obtuse pebble]

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.

[prime reef]

mb

[obtuse pebble]

@calm lotus Has your question been resolved?

[calm lotus]

Thank you

[obtuse pebble]

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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

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[distant otter]

Could someone tell me how to this question using a ba2 plus calculator i only know using the formula

Someone do this and show me the steps on a ba2 calculator so I can try it as well please I heard it's a huge time saver

[obtuse pebble]

@distant otter Has your question been resolved?

[obtuse pebble]

@distant otter Has your question been resolved?

[obtuse pebble]

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[golden hamlet]

Write an algebraic expression that represents the following algebraic computation.
Draw a right triangle first. Assume that x > 0.

sec(arcsin 3x)

[obtuse pebble]

@golden hamlet Has your question been resolved?

[golden hamlet]

<@&286206848099549185>

besides names, r = 1, y = 3a, x = sqrt(1-9a^2)

not sure if i get the right

so sec is 1/sqrt(1-9a^2)?

can anyone confirm? :c

.close

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[north forum]

what’s the reference angle for sin(345)?

[north forum]

is it sin(15)

[hybrid gull]

Helps to draw it out

[north forum]

my math teacher told us that the reference angle has to be equal

but sin(345) and sin(15) aren’t the same

[hybrid gull]

correct

[north forum]

does that mean sin(15) is the reference angle?

or is it -sin(15)?

[shrewd wasp]

it is -sin(15). Use sin(a+2pi)=sin(a) and sin(-a)=-sin(a).

[obtuse pebble]

@north forum Has your question been resolved?

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[hollow imp]

Hey I'm trying to solve this integral:

[hollow imp]

Gamma is the line from 0 to i. Note this is a complex integral

[warm canopy]

what have you tried?

[hollow imp]

So far I have tried the following. We use the paramaterization of gam(t) = ti and then this contour integral is equal to this:

Now I am trying to find an antiderivative of -t - 1/t which I think would be:

But we can't plug in 0 into ln(t) so I'm not really sure what to do now

[warm canopy]

uh im not sure that integral is even defined then

let me call the cavalry

[wild swallow]

that integral doesnt converge

[hollow imp]

Do you think that it was meant to be written as (z - 1)/z ?

[muted delta]

probably

[zenith raft]

would that still diverge

[obtuse pebble]

@hollow imp Has your question been resolved?

[hollow imp]

Assuming it was meant as (z - 1)/z and using the paramaterization of gam(t) = ti, then we would have

Any ideas for the antiderivative ?

[shrewd wasp]

$-t-i \ln (t)$

[warm shale]

adzetto

[obtuse pebble]

@hollow imp Has your question been resolved?

[obtuse pebble]

@hollow imp Has your question been resolved?

[slim cove]

that doesn't converge either

It still has the same 1/t singularity

[muted delta]

This has been up

forever

[obtuse pebble]

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[plush bear]

For a), what is the value of theta?

[fringe rivet]

whats is theta

?

[plush bear]

that greek letter after "sin"

sin "theta"

So, if sin(θ)=-sqrt(3)/2, what is the value of θ?

[fringe rivet]

so $x=sin^{-1}(-\frac{\sqrt{3}}{2}})$

[plush bear]

but you know that exact value

[fringe rivet]

no it say undefined

[plush bear]

there is a trignometric table for this values in specific

[fringe rivet]

60

[plush bear]

if you see, sin(60º) is sqrt(3)/2 right?

[fringe rivet]

degrees

but what about the negative sign?

[plush bear]

what about it? What do you think it will change?

[fringe rivet]

the value

[warm shale]

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

[fringe rivet]

Finnaly

[plush bear]

right
Do you know the trignometric circunference?

[fringe rivet]

no

[plush bear]

wanna make quick call and i share screen?

[fringe rivet]

ya sure

I cant use my mic tho Im on my pc

[plush bear]

It's okay

[obtuse pebble]

@fringe rivet Has your question been resolved?

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[pearl charm]

I have a few matrix questions

[pearl charm]

<@&286206848099549185>

<@&286206848099549185>

[obtuse pebble]

@pearl charm Has your question been resolved?

[static furnace]

what have you tried?

[pearl charm]

Nothing

yet

I just don't know

how to start

the first question

[gilded needle]

the first one's not really a matrix question

what operation between two vectors can you think of that involves the cosine of the angle between them?

[warm shale]

adzetto

for Q2, use $\overrightarrow{\mathrm{P}}=\left(\frac{\overrightarrow{\mathrm{v}} \cdot \overrightarrow{\mathrm{u}}}{|\mathrm{u}|^2}\right) \cdot \overrightarrow{\mathrm{u}}$ and $\overrightarrow{\mathrm{r}}+\overrightarrow{\mathrm{v}}=2 \overrightarrow{\mathrm{p}}$

[pearl charm]

i do'nt know

[gilded needle]

does this look familiar: $|a||b|cos(\theta)$

[warm shale]

Bungo

[pearl charm]

oh wait yea

that's the dot product

isn't it?

[gilded needle]

yep

[pearl charm]

so what do i do with it

[pearl charm]

<@&286206848099549185>

<@&286206848099549185>

[timid silo]

Don't need to ping 4 minutes apart bud

[pearl charm]

ok

can you help me?

[shrewd wasp]

use $\cos (\angle B A C)=\frac{A B \cdot A B}{|A B||B C|}$ for Q1

[warm shale]

adzetto

[shrewd wasp]

can you calculate AB vector and vector length?

[pearl charm]

how

idk how

[shrewd wasp]

$\text { If } A=(1,0,2), B=(2,-2,4) \text {, and } C=(4,4,2)$

[warm shale]

adzetto

[shrewd wasp]

I assume these are point in space

[pearl charm]

yea

[shrewd wasp]

So you have the initial and terminal points.

[pearl charm]

right

@shrewd wasp

what do i do with them

@shrewd wasp

[static furnace]

isn't there something you can do in order to find the distance using those two points

[pearl charm]

i know i got the distance

i got AB and BC

but BC is like a decimal

[pearl charm]

and i also do'nt know whether the top part is a dot product or multiplication

and i also do'nt get why there's like an absolute value

@static furnace ?

[shrewd wasp]

first find two vector like
$$
\begin{aligned}
A B & =\langle 2,-2,4\rangle-\langle 1,0,2\rangle \
& =\langle 1,-2,2\rangle \
A C & =\langle 4,4,2\rangle-\langle 1,0,2\rangle \
& =\langle 3,4,0\rangle
\end{aligned}
$$
Now
$$
\begin{aligned}
\cos (\angle B A C) & =\frac{A B \cdot A B}{|A B||B C|} \
& =\frac{\langle 1,-2,2\rangle \cdot\langle 3,4,0\rangle}{\sqrt{1+(-2)^2+(2)^2} \sqrt{(3)^2+(4)^2}} \
& =\frac{3-2 \times 4+2 \times 0}{3 \times 5}=\frac{-5}{3 \times 5}=\frac{-1}{3}
\end{aligned}
$$

[pearl charm]

that's wrong though

cos (BAC) isn't -5/3

i just submitted that and it says it's wrong

[shrewd wasp]

no its -1/3

[warm shale]

adzetto

[pearl charm]

yea that's correct

thank you

.close

[obtuse pebble]

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[strong atlas]

why isnt ABC = 75degrees by alternate segment theorem as PAB = 75

[hybrid gull]

BC isn't parallel to AP I don't think

[strong atlas]

but in alternate segment theorem it doesnt need to be parllel

[hybrid gull]

It should

What does the alternate segment theorem say?

[strong atlas]

“For any circle, the angle formed between the tangent and the chord through the point of contact of the tangent is equal to the angle formed by the chord in the alternate segment”

[hybrid gull]

I would need a diagram to see this

[hybrid gull]

Ah that's helpful

Lemme look

why isnt ABC = 75degrees by alternate segment theorem as PAB = 75

From what youre saying I think you're right

Maybe I'm missing something

,rotate

[hybrid gull]

Oh wait no we switched them up

PAB = 75 -> ACB = 75

@strong atlas

[strong atlas]

Why not ABC tho

O wait

Damn

Ok thnx

.close

[obtuse pebble]

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[vale dirge]

Let x be a scalar and A be a nxn matrix.

If |xA|=b

Is it possible to extract the scalar from the determinant?

And have an equation that looks like y|A|=b?

Without knowing anything about A

[vale dirge]

I know that if A is a diagonal matrix, then x^n|A| gives the coreect result. But i don't know if it's possible for every A

[grizzled shore]

That’s true for any A

[vale dirge]

Is that a theorem or a result of one?

[grizzled shore]

It has to do with how you define the determinant

It’s just an immediate result from what the rules are for determinants

[vale dirge]

Yeah i think i can see it.
Since i multiply the factor by n, then the submatrix, then the factor in that submatrix and so forth

[grizzled shore]

Multiply the factor by n?

[vale dirge]

Pardon, i'm not learning in english.

What i mean is that since detM=(-1)^ijMijsub....

Mij is mutiplied by x

so the result of the submatrix determinant is also multiplied by x. And the result of that matrix's determinant is also multiplied by x.

So forth for a total of n times

[grizzled shore]

Yeah each of the submatrices will have an x in front

And there’s n submatrices

So you get an extra x^n factor at the front

[obtuse pebble]

@vale dirge Has your question been resolved?

[obtuse pebble]

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[next reef]

Using the least square approximation, find the length of the projection vector p of b onto the column space of A.

[next reef]

(Status - 1)

[fathom flicker]

[royal basin]

ain't this just gonna be (A^T A)^-1 Ab?

[next reef]

[royal basin]

i have vague recollections of that being how you find the least squares approximation

[next reef]

How can A be multiplied with b?

A is of order 3x2 and that of b is 3x1, no?

Nvm, I referred to the lecture summary and got the answer

.close

[obtuse pebble]

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[slate kayak]

.close

[obtuse pebble]

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[slate kayak]

.reopen

[obtuse pebble]

✅

[slate kayak]

would arc ABC in this case = arc ADB?

If so, can i know the theorem linked to this?

[glossy basalt]

nope, since fixed length (x) of arc AD can move towards (or away from) B , so those arc you've given can be arbitrary

[obtuse pebble]

@slate kayak Has your question been resolved?

[slate kayak]

right, but what i don't understand is why you can just move AD around?

[glossy basalt]

well, since there's no restrictions

[slate kayak]

is it because there's no constraints to it other than the length of AD should be x?

oh

[glossy basalt]

unless it's a "to scale" diagram

which usually it's not the case

[slate kayak]

what would change in a to- scale diagram

[glossy basalt]

and which is uncertain in this case whether ir not it is

[slate kayak]

i thought to scale only is concerned about the lenght

what stops it from moving anywhere then?

[glossy basalt]

all lengths of the diagram to be exact

[glossy basalt]

all lengths including measurements of "empty spaces"

[slate kayak]

ah okay that's just too pedantic ig lol

[glossy basalt]

kek

[slate kayak]

but then moving AD is kinda weird as well

but i'll take your word on it

tbh i thought AD and BC (they both seem straight so they should be assumed straight) are parallel

and since parallel they should both be equal

let me show you

[glossy basalt]

if you consider AD and BC are chords, then they are straight lines because of definition of chords

[glossy basalt]

while there ain't any phrase saying they are parallel

[slate kayak]

AC is a diameter so ABC = 180 degree = ADC

[glossy basalt]

so, we can't tell if they are parallel or not

[slate kayak]

even if they're straight lines?

[glossy basalt]

yep

[glossy basalt]

this is another info though

[runic cape]

this problem has a chance of being true 1 in a million

[slate kayak]

I made that up

the question is only limited to what i mentioned above

[glossy basalt]

i see

[slate kayak]

what would the question need so that it's well defined and you can actually choose the difference between arc ABC and ADC?

mention that they're parallel?

and if they're parallel then they're both equal?

[glossy basalt]

this is a good one

[glossy basalt]

this is also good

[slate kayak]

wait what

shouldn't AC being a diameter be implicit

oh wait it doens't have to pass through the center

ngl i wrote that as an explanation not a question lol

okay makes sense

thanks

.close

[obtuse pebble]

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[gilded dragon]

Can somebody help me compute this pls?

,rotate

[obtuse pebble]

@gilded dragon Has your question been resolved?

[gilded dragon]

.close

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[warm shale]

.miles12345

[timid silo]

And alpha is some constant

.close

[obtuse pebble]

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[long jetty]

There is an array S of numbers from 1 to 10 {1,2,3,4,5,6,7,8,9,10}.
4 numbers get extracted from this array. Determine the probability that number 6 will be one of those 4 numbers AND second place by greatness in ascending order.

[royal basin]

so we take 4 numbers from the array at random?

like it's a deck of 10 cards that we shuffle and then draw 4?

[long jetty]

Yes

[royal basin]

ok

!status

[obtuse pebble]

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

[long jetty]

1

[royal basin]

ok

do you know what it means for 6 to be the second-highest in our selection of 4?

[long jetty]

Yeah, but it's in ascending order, meaning if there are for example extracted 3 6 8 9
6 here is second place

Ascending

Right?

[royal basin]

aight hold on

did you translate the problem from another language?

[long jetty]

Yeah

[royal basin]

"second place by greatness in ascending order" appears to be ambiguous -- i am reading it as "second biggest" but you are reading it as "second smallest".

so please show the problem in its original language.

[long jetty]

It's romanian language

In brakets it says in ascending sense

[royal basin]

i put "the second-biggest element" into google translate and it came up as

al doilea element ca mărime

so i think that it really does mean second-biggest

and your selection of {3,6,8,9} won't do because 6 is the third-biggest in it

[long jetty]

Hmm then I'll go this way
But would it make a difference in final answer if its 2nd biggest or smallest? After all its complete randomness

[royal basin]

these are different events

so yes it potentially makes a difference unless it's just by coincidence that their probabilities are the same

and "after all its complete randomness" is not an argument either way

anyway

that 6 is second-biggest means that the selection consists of:

• precisely one number bigger than 6
• 6 itself
• precisely two numbers smaller than 6

[long jetty]

Yes

Makes sense

Should i go here by the formula P= m/n

[runic cape]

the 6 being selected is 4/10 but second place...

let us list all possiblities

[long jetty]

We just multiply the probability of these cases with each other

Right?

[runic cape]

not sure

[long jetty]

4/10 (4 numbers are bigger than 6) * 4/10 (6 itself) * 5/10 ( 5 numbers smaller than 6)

[royal basin]

wrong on two counts

or on three, depending on who's counting...

[long jetty]

Where is wrong?

[royal basin]

well if you wanna go this route then the probability of picking 6 is

not 4 but 1

and not out of 10 but out of 9

[long jetty]

But number 6 can be 1st or 2nd or 3rd or 4th positional wise

[long jetty]

I wonder what routes there is

[long jetty]

And why out of 9? Why doesn't the number itself count as a probability?

[royal basin]

wording...

the reason it's out of 9 is because we already picked the high number

so there are 9 numbers, and not 10, left to choose from

[royal basin]

no, we've fixed it as second-greatest.

[long jetty]

No i am talking here as position wise, not which one is bigger

[royal basin]

then there are no posiitons

positions*

i think you've made your own life a lot more complicated at this point

[runic cape]

,w 10!

[warm shale]

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[runic cape]

,w 2^10

[warm shale]

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[royal basin]

pointless calculations

[runic cape]

sorry the first was a mistake but the second one is the number of all sub sets of {1,2,3,4,5,6,7,8,9,10}

[royal basin]

and again,

pointless calculations

[runic cape]

so we subtract {} to get 1023

[royal basin]

no, chaka, we are not picking a random subset of {1,...,10}.

we are picking a random subset of {1,...,10} OF SIZE 4.

please do not floor the channel with your own poor understanding of the problem.

[runic cape]

and the sets with two terms to get 1023-55=978

[royal basin]

chaka, please stop.

you are flooding the channel.

[long jetty]

;)

[royal basin]

the way i would do this is:

• there are (10 C 4) ways to select four numbers out of ten
• the number of ways to select 1 number higher than 6 and 2 numbers lower than 6 is 4 * (5C2)
  [there are 4 numbers above 6 and 5 numbers below 6]

[runic cape]

i love you ann

[long jetty]

There is no need to count the probability of 6 itself?

[royal basin]

what probability

i am doing it combinatorially

[novel grotto]

Sorry if I'm wrong but it says second place in ascending order, this should mean there are 2 numbers higher than 6 and 1 number lower i think

[royal basin]

.

[novel grotto]

oh

sorry, i looked at the pinned message and not the other messages. what you sent is correct i believe

[long jetty]

This is the favorable cases
What about total cases?

[royal basin]

no, the favorable cases are the second bulletpoint

the first bulletpoint is the total cases

[long jetty]

Ohh

Thanks a lot

You helped me

[obtuse pebble]

@long jetty Has your question been resolved?

[obtuse pebble]

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[obtuse pebble]

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[queen cloak]

How do I do b)

[polar fossil]

p, q, and r are real, and there's at least one complex root...

[tranquil sonnet]

Complex roots come in conjugates since all of the coefficients are real

So you know alpha, beta, and gamma, so just use vietas to find r

[queen cloak]

So isn't Σαβγ=-r

[tranquil sonnet]

Not the sum

Just the product

[queen cloak]

Yeah the product of the roots,

[tranquil sonnet]

Yes

[polar fossil]

you have a sum symbol in there
which I guess is fine just nonstandard since there's only one triple of roots

[tranquil sonnet]

Yea I think it’s cause q = cyclic sum alpha beta

[queen cloak]

So how can I use the fact that one,of these roots is 3+I to find r

[tranquil sonnet]

This

[queen cloak]

I don't think I really understand-

[tranquil sonnet]

Do you know what conjugates are

Complex conjugates

[queen cloak]

I just started roots of polynomials yesterday sorry if I'm being dumb

[queen cloak]

Nope

[tranquil sonnet]

learn about complex numbers and then tackle this problem

[queen cloak]

Ok thanks

[obtuse pebble]

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[obtuse pebble]

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[dense stirrup]

Can anyone explain me why nP5 is taken as n !

[severe reef]

nPr=n!/(n-r)!

[royal basin]

it is not?