help-0

[slate kayak]

Do you know how i can calculate y-intercept? I cant find it in my teachers note she sent

[oak chasm]

You can either use the slope and go 4 to the left of t = 4.

[slate kayak]

Oh

[oak chasm]

Well, the slope is -50.

[slate kayak]

Yes

[oak chasm]

You want N at t = 0.

N at t = 4 is 1200.

So, you can walk 4 to the left.

[slate kayak]

So y intercepy is (0,4) ?

[oak chasm]

When you go to the left by one, how much does N increase by?

No.

[slate kayak]

When u go left by one it increases with 50

[oak chasm]

OK, so you know N at t = 4.

[slate kayak]

Yes

[oak chasm]

You can go to the left four times to get t = 0, right?

[slate kayak]

then at t = 0, it’ll be 1400

[oak chasm]

Right.

So, N = -50t + 1400.

The b is the y intercept, not a t value.

[slate kayak]

Oh okay i get these problems now thank you

[oak chasm]

No problem.

You can check your work, too.

[slate kayak]

What do u mean

[oak chasm]

1200 = -50(4) + 1400

At t = 4, you have 1200.

So, does your formula work?

[slate kayak]

Oh yeah true and for 10 it works too

[oak chasm]

Check it by filling in 4 for t.

Good.

Then you got the formula.

[slate kayak]

Thnx i’ll double check them from now on too

[oak chasm]

No problem.

[frank dome]

I’m going into 9th grade in a month and this is I ended with passing grades but not good, what are some things in math I should learn or prepare for for 9th grade?

[jaunty torrent]

everything of 8th grade..whats new isnt important now

[oak chasm]

@frank dome What math subjects have you learned?

Algebra, algebra 2, trigonometry, geometry, precalculus?

[frank dome]

We mostly worked on lines graphs and y=Mx+b stuff and some inequalities I had to do online class for the whole year so I’m 80% confident working with them

[oak chasm]

Oh, OK, that's algebra.

[frank dome]

We did do some algebra too

[oak chasm]

Can you afford like $40?

[frank dome]

Also what’s a block schedule ?

[wraith cairn]

imagine buying books

[oak chasm]

If not, I'd do Khan Academy algebra stuff.

Online course.

If you can afford it, I'd buy Schaum's Outlines "Elementary Algebra" and "Intermediate Algebra".

Schaum's Outlines have short explanations of how to do problems and then a bunch of problems and their answers.

Khan Academy (free) also has problems and will tell you if you got them right.

Though not quite as many problems as Schaum's Outlines.

Either way, you can get up to where you are now and start learning ahead if you want to.

You can also ask for help here if you get stuck on a problem.

[wraith cairn]

you can find the book's pdf on google

isn't the copyright gone

if the author's dead or something

[oak chasm]

No, it lasts for like 75 years past death, unless it's owned by a company or something.

[wraith cairn]

ah.

[alpine sable]

how do

what do i put below the 1

[ionic jewel]

notice how the bottom is 2(1) then 2(2) then 2(3)...

the i is the part that's increasing (1,2,3...)

but you need the other part

[alpine sable]

i tried putting 2(i) but it didnt work

[ionic jewel]

2i should work

[limpid spade]

try without parenthesis

[ionic jewel]

different formatting

[alpine sable]

oh okay

[ionic jewel]

eitohit parenthesis yes

[limpid spade]

yes

[alpine sable]

lmao

yes that worked

[ionic jewel]

✅

[final summit]

Reading this book on linear algebra. What does det mean?

[oak chasm]

@final summit Determinant: https://en.wikipedia.org/wiki/Determinant.

[final summit]

Thank you.

[glass lichen]

5 stems from the fact that you can laplace along any row / column of A and get the same det, so A and its transpose have the same det

[final summit]

Got you. Thanks, Mosh.

[livid mesa]

Hey guys I'm kind of confused on this question. Shouldn't this be 2 instead of 1/2? Because wouldn't 1/2 be greater than 1/4? Think I'm not understanding the function.

[limpid spade]

it's 2 and 3/2

[thorn kindle]

f(c)<c. (1/2)^2<1/2

Only true for 0<c<1

[livid mesa]

The book says the answer is 1/2.

[glass lichen]

$f(x)<x \ x^2-x<0 \x(x-1)<0$

[ocean seal]

Mosh

[glass lichen]

so the inequality is satisfied when $x\in (0,1)$

[ocean seal]

Mosh

[livid mesa]

Im still kind of confused on how its 1/2

[glass lichen]

cause 1/4<1/2

[livid mesa]

Ohhh ok I think Ik how they got it now

Thanks for the help

[floral sentinel]

How do I approach this?

[glass lichen]

approach... what?

[floral sentinel]

Oh I need to find the derivative

[queen wigeon]

use the exponential form of cosh and sinh

[glass lichen]

that, or hyperbolic trig identity

[queen wigeon]

$\cosh^2(x) - \sinh^2(x) = 1$

[ocean seal]

mchen10

[floral sentinel]

Ohh thank you!

Did I do this correctly? Implicit differentiation

[alpine sable]

I forgot how to do this

I took calc last sem

But make sure you find the der of each term

Then you isolote x and y

[gray isle]

no, looks wrong

[sage jacinth]

agreed, i did it out and i got something different

[gray isle]

[muted portal]

How do I plot a graph that looks like it’s twerking? Has to be one equation

@ me if you answer

[floral sentinel]

Which step did I go wrong?

[gray isle]

the first one

[sage jacinth]

you applied the chain rule incorrectly

you need to add the parentheses because you multiply by the derivative of the inside

[gray isle]

the lack of parentheses led to committing multiple math crimes

[sage jacinth]

you should've just made the left side into a single fraction, then you can multiple the right side by 1+x^4y^2

and then it should be simple from there

distribute then factor out the dy/dx

[magic sphinx]

How would you solve 1? I’m so confused

[sage jacinth]

you just look for the type of function it is

[nocturne mirage]

its not constant since f(0) !=f(1)

not absolute value since f(1)<0

[magic sphinx]

Yea but I’m not sure what the 4 functions are could you explain

[sage jacinth]

i guess, but which ones have you heard of

[nocturne mirage]

that would be a step function

[sage jacinth]

most of these aren't talked about in an introductory algebra course

[magic sphinx]

This is a alg 2 course

[sage jacinth]

oh

[magic sphinx]

I’ve heard of the absolute value function

[sage jacinth]

constant function is a function that is constant everywhere

[magic sphinx]

Thank you

[sage jacinth]

step function is the on ethat valentin sent

[nocturne mirage]

a constant function would be .... constant

[sage jacinth]

except step functions aren't continuous

[magic sphinx]

Alright thank you

[nocturne mirage]

well yeah I kinda drew a curve instead of the function

just to clearly show the steps

[magic sphinx]

It’s alright lol

[nocturne mirage]

basically, an absolute value function would only give you positive values

[rocky dock]

my horizontal asymptote appears to be wrong

can someone help me

[carmine lion]

uh

shouldn't it be the other way around

why do u think the asymptote is y=1?

[rocky dock]

oh you're right

[carmine lion]

the graph goes down by 1

[rocky dock]

it's a negative 1

[carmine lion]

so the asymptopte also goes down by 1

yea

u got it

[rocky dock]

thanks!

[carmine lion]

👍

[gray isle]

no

[sage jacinth]

nein

[gray isle]

multiplied by the whole derivative of the inner function,
NOT multiply by the first term of the derivative and then add the second term

[sage jacinth]

it should be (2xy+x^2 * dy/dx)

or y' if you are into that notation

[carmine lion]

using y' in an exam is a bit eh

dy/dx is more easy to recognise

[sage jacinth]

agreed, it is also nice to recognize another great inventor of calculus, leibniz, who isn't really credited in the states

[floral sentinel]

I don’t really understand dx/dy

[fossil sedge]

You will realise y' just looks cleaner after a while imo

[floral sentinel]

My professor taught it with y’

[carmine lion]

in an exam

its hard to write it clearly

[sage jacinth]

^

[alpine sable]

what about newton's notation

[fossil sedge]

how so lel

[sage jacinth]

i have horrible handwriting

[carmine lion]

1's begin to look like dashes

[sage jacinth]

i can barely read my own handwriting sometimes

[sleek elbow]

is this handwriting? looks nice

[carmine lion]

and in the heat of the moment (exam) u could really mess up

[sage jacinth]

yes

[fossil sedge]

Well most university work uses y' as notation

but dy/dx works jst fine

[alpine sable]

help me to rewrite this pls

[floral sentinel]

Umm

[sage jacinth]

dont subtract something you need to multiply

you subtracted (1/(1+(x^2y)^2) when you needed to distribute

why not just make the left into (2xy+x^2 dy/dx)/(1+x^4y^2)

[gray isle]

redo everything after the first step

[floral sentinel]

Distribute that to every term in (2x*y+y’*x^2)?

[sage jacinth]

you dont need to distribute the fraction

just multiple 1 by the derivative of the inside

[floral sentinel]

So (2x*y+y’*x^2)/(1+(x^2y)^2.

[sage jacinth]

yes

[sage jacinth]

i would just leave the 2xy dy/dx on the right side since you are going to have to distribute the denominator anyway

[floral sentinel]

Oh I need a -1 on the left?

[sage jacinth]

you need to bring the fraction out of you want to take y' out

just your result from step 2 by (1+(x^2y)^2) on both sides

then solve

[sage jacinth]

you multiplied everything in the numerator in step 2

it should be 2xy+y'x^2

and dont forget the parenthesis on the right side

you are multiplying the whole right side i.e. (y^2 + 2xy*y')

[floral sentinel]

Isn’t that the same as 2x^3y*y’?

[sage jacinth]

theres an addition and not a multiplication sign

[floral sentinel]

;-;

[sage jacinth]

yes now distribute and solve for y'

[floral sentinel]

The right side?

[sage jacinth]

yes

[floral sentinel]

Why don’t I divide the (y^2+2xy*y’) ?

Move to LHS

[sage jacinth]

well if you try to factor it out that way, you would have to divide 2xy by y' in order to factor

the rhs is just adding y^2 + 2xy * y' to (y^2+2xy * y')(x^2y)^2

[floral sentinel]

Umm

I factor this?

[sage jacinth]

distribute then isolate the y' terms and then factor out the y' and divide in order to solve for y'

[floral sentinel]

Would it be x^4y^2

[sage jacinth]

yes

[sage jacinth]

you forgot the 1 * y^2 in your distribution

[floral sentinel]

Isn’t that what I wrote in the beginning?

[ocean seal]

(バカ) baka

[sage jacinth]

i have put an unsimplified solution above

[floral sentinel]

isnt y^2*1 = y^2

[glacial hedge]

Using the fundamental theorem of line integrals i get either +50ish or -50ish which isnt even remotely correct? f(x,y) = xy+y^2 right? because gradient of f(x,y) = <y,x+2y>?????

[twin haven]

it means that every 1 m^2 recives 1 litre of rain

[glacial hedge]

anyone know how to do this?

nvm im a ***ing idiot

[lusty pewter]

how

can i please have some help

[glacial hedge]

dude

100 m^2 * 1 mm

= volume of the water

which is

0.1 m^3 of water

which is 100 liters

[lusty pewter]

oh

[glacial hedge]

???????

how did you get $x^2-4x/5 - 3/5=0$ from the 1st equations

[ocean seal]

Elonmosqito96

[sudden nimbus]

two different questions

[glacial hedge]

oh'

[nocturne dove]

Can I get some help

[glacial hedge]

srously

[alpine sable]

if object contains 150,000 electrons and 125.000 protons what is the charge of that object?

[glacial hedge]

which one do you need help with

[sudden nimbus]

1

factorise

[glacial hedge]

uhh you cant really "factorize that" but you can solve for x

[nocturne dove]

I'm dying

[sudden nimbus]

yea

[glacial hedge]

channel being used

[nocturne dove]

[sudden nimbus]

i am just getting answers wrong

[nocturne dove]

Wut?

[lusty pewter]

$$hogrider$$

[ocean seal]

Blue Dude

[nocturne dove]

Average coc playa

[glacial hedge]

$6 \sqrt {3} x + 7x = \sqrt {3}$

$x(6 \sqrt {3} + 7) = \sqrt {3}$

$x = \frac {\sqrt {3}} {6 \sqrt {3} + 7}$

[ocean seal]

Elonmosqito96

[sudden nimbus]

is this it

@glacial hedge

[glacial hedge]

?

yes thats what x is

[sudden nimbus]

ohk

[lusty pewter]

can i have help woth another question

@glacial hedge

number 5

[glacial hedge]

dont ping me please

and that is the same principle

[nocturne dove]

Help me please

[glacial hedge]

as this

[lusty pewter]

$$whats-up-scoobs?$$

[ocean seal]

Blue Dude

[lusty pewter]

$$shaggy-in-da-house!!$$

[ocean seal]

Blue Dude

[rich basin]

I'm having trouble understanding pigeon hole principle

Like in regards to this question, you only need at least 2 cards

but the answer is like 5 cards because of 4 pigeonholes

however you can get like 2 cards in the start in one pigeon hole

It is possible to get two cards of the same suit

[thorn kindle]

,calc 52/4

[ocean seal]

Result:

13

[rich basin]

at least the probability for that is not 0, therefore it is possible

[thorn kindle]

Yep its 5 cards

[rich basin]

I'm confused why is it 5 cards and not 2 cards

Oh yeah nevermind

[thorn kindle]

Clubs spades hearts and diamonds

[rich basin]

I get it but there is antoher question that made me confused about the pigeon hole principle

[thorn kindle]

Ok

Post it

[rich basin]

Okay i get it, the question wasn't as vague as question i've seen before

And there is this one question which i don't get how they extract the answer for

I understand that you can't have 0 as the leading hence, it would be 9 factorial

but i don't get the reasoning behind multiplying the 9! by 9

how would that satistfy the non leading zero

[thorn kindle]

That is correct but misleading

It's not 9!*9

It is 9/10 * 10!

@rich basin

[rich basin]

How come?

[thorn kindle]

Consider all the permutations, including the ones with leading 0s, which would be 10!

Since there are 10 digits each used once, exactly 10% of those permutations will start with a 0

So only 90% of the permutations satisfy the condition

90%*10!

= 9/10 * 10!

10!/10 = 9!

So it is just 9*9!

[rich basin]

okay i get

thanks

and also with this question

[thorn kindle]

Such that each student shakes hands with each other student?

[rich basin]

yeah that is where i'm confused

i am confused with the line of why two students will each have shaken the same number of hands

[thorn kindle]

Wait no that cant be the case

Because then everyone will have shaken 24 hands

[rich basin]

Yeah

Well in the answer it says "Each student shakes hands with 24 other students, so 24 pigeonholes for 25 students, so two students must have shaken hands with the same nubmer of students."

it is saying that 2 students must have shaken hands with the same number of students

[thorn kindle]

Yeah that answer checks out

Provided each student shakes hands at least once

[rich basin]

i am confused, so each student shakes hands at least once

[silver yoke]

Hello what class would you guys pick for someone who is ok at math? College Algebra or Pre calc?

[rich basin]

however the answer says that 2 students msut have shaken hands with the same nubmer of students

[thorn kindle]

Yes

24 boxes

The numbers 1 thru 24

And 25 students

[rich basin]

So there will be of course 1 person left out in shaking hands

why does this show that two students must have shaken hands with the same number of students

[thorn kindle]

24 pigeonholes

25 pigeons

Dont overcomplicate things

[rich basin]

I am still quite confused how could this lead to two students must have shaken hands with the same number of studens

like i would of thought that would mean that there is at least 1 person who have shook a person twice

[thorn kindle]

No student shakes hands with the same person twice

[rich basin]

Okay with that condition, why would it be that 2 students would have shaken the hands of the same number of students

[thorn kindle]

It actually doesnt have to be 2

[rich basin]

like how could he of shook 25 people

[thorn kindle]

Just more than 1

The boxes are numbered 1 thru 24

So if you have 25 people then one box will have more than one person

[rich basin]

I think i'm starting to get it

so how i'd imagine it

you have 24 boxes line of up in a row

and then you have 25 students filling in with each of the boxses

however due to their being only 24 boxes

there would be a box with at least 2 people in it

and that 2 people would have the same amount of hand shakes

but the only problem is, wouldn't the odd one shaking with some other guy would mean he would of shook twice

unless all of them shook three times

and then it would mean that the two students would have 4 handshakes

Like shook three times for the same person

Do you think this is correct or not?

[thorn kindle]

Yes

[ionic jewel]

precalc is typically one step up

[rich basin]

Okay thanks

[thorn kindle]

This is called the "pigeonhole principle"

And in fact it doesnt matter if someone has not shaken hands

Because then it would just be from 0 to 23

Instead of 1 to 24

If someone has 24 handshakes then they have shaken hands with everyone else meaning that everyone has at least one handshake

[teal epoch]

hello, is this channel now free to ask?

[thorn kindle]

Sure

[teal epoch]

ok

[thorn kindle]

[teal epoch]

here
well I already have my answer which is 4/5
i don't know if it's right or wrong because there is no answer key to it and i'm dumb
if you want to know where i got my answer well sure thing i can explain

[ionic jewel]

4/5 sounds too high on first glance

oh wait i can't read

[pallid vine]

that question is phrased so weirdly

i think it means neither couples are next to their respective partner?

[teal epoch]

based on my understanding it seems so
also yeah i hardly understand this question at first

[pallid vine]

do you know how to approach this question?

[teal epoch]

i do
if you want me to show my solution sure thing

[pallid vine]

oh if you alreadyt have the solution and just looking to verify sure

[teal epoch]

ok thank you

[pallid vine]

if my mental maths is right it's close

[golden basalt]

,help

[ocean seal]

A brief description and guide on how to use me was sent to your DMs!
Please use ,list to see a list of all my commands, and ,help cmd to get detailed help on a command!

[pallid vine]

I believe its 5/6 but show me ur solution bc i could have fumbled the math in my head

[teal epoch]

ok give me a min

[vagrant kayak]

can anyone reply to the question

what is the question?

[pallid vine]

channel busy dude

[vagrant kayak]

no

i wanna help

-_-

[pallid vine]

i already have it covered lol

[vagrant kayak]

ok

[pallid vine]

im sure someone needs help in another channel though

2!2! * 5 is the amount of ways they are not seated together

5! is total ways

[teal epoch]

let P(a) be the probability that neither of the couple sits together yada yada
P(a) = 1 - P(a')

Instead I'm just going to calculate the complement instead
So there are two couples lets call it couple A and couple B
the ways couple A can be arranged is 2!
same goes for couple B
let's call the single person C
the ways A, B, and C can be arranged is 3!
so overall the number of ways are 2!2!3! based on the condition
the total number of ways is 5!
so the chance is 2!2!3!/5! which is 1/5
subtract it from 1 and i got 4/5 which is my answer

i'm sorry if my explanation is terrible

[pallid vine]

That's a little convoluted lol, the method of calculating the compliment was correct though

that is the proper approach

let me draw something real quick

can we agree this sort of pattern

is the only way no couple can sit together

[teal epoch]

wait there are 5 people right?

[pallid vine]

with the random person somewhere in there

yeah just imagine they are between one of them

or on the end

[teal epoch]

oh ok

[pallid vine]

im wrong

woops

they can

i said something stupid

mental maths failed me, the second i drew something i realized i was wrong

[teal epoch]

i think the random person can seperate a couple
just put them inbetween i think

[pallid vine]

yeah

they can

it adds a net 4

and you're right

[vale wigeon]

are y'all doing combinatorics?

[pallid vine]

your working is correct

[pallid vine]

i would of done it a different way but this is completely fine

the math is all correct

good job dude

[teal epoch]

so is my answer correct?

[pallid vine]

yeaha

[teal epoch]

oh thank you dude

[bronze dust]

A boat is to be manned by 8 crew members of whom 2 can only row on bow side and 3 can only row on stroke side, total number of arrangements possible?

[oak chasm]

@bronze dust Pick the places for the stuck members.

Arrange the nonstuck members in the remaining places.

So, there are four places each side.

[bronze dust]

how about i do it like this

there are 4 places each for bow and row

5 members are restricted to either bow or row

i select 2 unrestricted members out of 3 unrestricted members for bow side (i need 2 there)

then 1 unrestricted members out of remaining 1 unrestricted members for row side ( i need 1 there)

and then i arrange bow and row seperately

3c2 * 1c1 * 4! * 4!

is this correct?

[fresh lake]

3! * 2! * 3!

i thought

i mean like you can assume there's 3 boats, one for 3, one for 2, one for 3

[bronze dust]

why this?

[prime badge]

i don't understand the task

[fresh lake]

3 restricted is 3! and 2 restricted is 2!

the remaining is 3 unrestricted, so 3!

[prime badge]

ah ok, 8 spots, 8 people, i get it

[fresh lake]

that's just what i think but i'm not sure

[bronze dust]

i think thats wrong

[fresh lake]

wait idek what bow and stroke are

[bronze dust]

add another 2! here

[oak chasm]

@bronze dust No, you have too few possibilities because you don't account for the ways of placing the nonstuck people in various sides. You just assume they're already sorted to sides.

[prime badge]

(4c3 * 3!) * (4c2 * 2!) * 3!

[bronze dust]

@oak chasm what is the correct answer according to you then

[nocturne dove]

a good probability question.

Care to try anyone?

[bronze dust]

we have to find the correct option?

or mark them true or false

[nocturne dove]

If you're asking me then I would say mark the correct option.

[prime badge]

also 3 * (4!) * 4!

same answer as (4c3 * 3!) * (4c2 * 2!) * 3!

[bronze dust]

thats my first answer too

but i guess we have to multiply it by 2 as well

to account for both arrangements

RBRBRBRB

and BRBRBRBR

[prime badge]

sure

[bronze dust]

b = bow, r = row

[oak chasm]

@bronze dust I've checked with a program and it looks like your answer was correct.

There are 1728 suitable arrangements.

[bronze dust]

and multiply it by 2 also right?

[bronze dust]

what if pattern starts with green

[rich basin]

I need some help with b

do i take this into cases?

[teal epoch]

i think not

[crystal tapir]

u basically do it like 2 3 2 1 = 12

[rich basin]

for part b

[teal epoch]

i think its 3(4!)(2)

[crystal tapir]

oh its hould be 1 2 3 2 so in then end u need 2 even numbers to be even

[teal epoch]

you have 4 choices on the first 3 digits, and only 2 on the last

[rich basin]

the answer is 128

[crystal tapir]

so do u know the answer from the book

what does that say?

[rich basin]

It only has a number

128

[prime badge]

it's 4³ × 2

or 4^4 / 2

[crystal tapir]

i think or this u need to 4 x 4 x4 x2

[teal epoch]

oh wait my bad-

[crystal tapir]

cuz

[rich basin]

why is it 4^3 x 2

i get the 2

because there is only 2 even num bers

[crystal tapir]

2 even nmbers

[teal epoch]

yeah that thing is right

[crystal tapir]

yea

[rich basin]

and i get the 4^4/2 because 50 percent of it is even

but i don't get the 4^3

[crystal tapir]

cuz

u have 4

choices

and they can be repeated

[teal epoch]

the first 3 digits have 4 choices

so basically it's 4^3

[rich basin]

Okay i get it thanks

[teal epoch]

then multiply it by 2 for the last one

[rich basin]

and also for the division by 2 right

is it determined based on a ration within the set

like forexample you want to calculate a 4 digit number that is greater or equal to 4 for the first digit

i mean like how many combinations can you make with a 4 digit number that has the first digit being greater or equal to 4

it would be like 75 percent times 4^4

[teal epoch]

um kinda-ish?
I honestly don't get what you mean sorry

[rich basin]

Like what if the question is that you want to find the permutation of a 4 digit number from like 3,4,5,6 and that it must be greater or equal to 4000

it would be like 75 percent

of 4^4

[teal epoch]

can you tell us where do you get the 75% thing
I want to get this straight

[rich basin]

Nevermind, the next question had a similar question to what I'd imagined

thanks

[teal epoch]

oh ok...

[rich basin]

So for the front seat, there is really only 2 people that are able to sit in the front

because there is only 1 person which is the driver is able to sit there

as well as fixed people in the back

so it is basically 4! [For the switching from front seat and backsword in between of the 4 people] * 4! [people swapping around in the back]

but the answer is 288

which is half of the result here

,w solve 4! * 4!

[ocean seal]

Results provided by WolframAlpha

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

Requested by Travelling Salesman#4998

[rich basin]

I am looking at the answer and they made it such that it is 4*3 * 24

and they got 4*3 because "only four are able to sit in the front passenger seat"

Is this because once you find out how many permutations for the front seat, it would mean for the one seated at the back

like there are 10 strawberries, and you ate 4. And because you know you ate 4, there are 6 strawberries left

But the problem is with my solution is that it is repeating

Is this correct?

[tough hatch]

u can divide this experiment into two

1. choosing 2 out of 4 to seat in the back seat
2. choosing 2 out of 3 to seat in the front seat
   since u are essentially taking away the 'particular people' who will seat as given

e.g. we choose only 2 ppl to seat in the back seat because 2 out of the 4 slots have already been taken by the particular ppl

similar logic applies for the front seat

[jovial reef]

Question: If $\log{x} + \log{y} = 6$ what is the minimum value of $x+y$?

[ocean seal]

oño

[jovial reef]

I got 2000 but idk if 2000 is correct. I got it by assuming x=y

[cursive yoke]

u still need help ?

[jovial reef]

yeah im not sure with that answer

[red phoenix]

I think I got something that might help ya

[cursive yoke]

Do you know the Sum to product rule of logarithms

[jovial reef]

yes

[jovial reef]

I would like to know what you have in mind

[red phoenix]

I think its where Pajo is going

[tight sphinx]

Uhhh how do I do Q14

[red phoenix]

But you can do the log product rule and get xy = 1-^6

10^6

[cursive yoke]

yeah

[red phoenix]

And then y = 10^6/x

[cursive yoke]

thats where i was going

[red phoenix]

Thus you get x + 10^6/x = the product

And from there, you can see where to solve

[jovial reef]

ohhh I see thank you

[cursive yoke]

the one with the acres

is that how you spell it

[tight sphinx]

yea

yea, that one

[cursive yoke]

so first write 7 1/2 as a fraction

[tight sphinx]

so 15/2

right?

[cursive yoke]

yep

[tight sphinx]

then what

[cursive yoke]

now you need to see how many blocks your going to have

do you have an idea how you re gonna get that

[tight sphinx]

nope, not at all

[cursive yoke]

so if you have 10 acers and you divide them in to blocks of 2 acres

how many blocks of 2 acres will you have

[tight sphinx]

wait how is it 10 acres

[cursive yoke]

im just giving a simpler example

[tight sphinx]

oh

[cursive yoke]

the principle is the same

[tight sphinx]

oh, okay

[cursive yoke]

were just using natural number rn

we are*

[tight sphinx]

mkay

soooo, what do we do after that?

[cursive yoke]

after what

?

[tight sphinx]

after converting the mixed numeral to a improper fraction

we finmd the amount of acres right

but how many acres are in the question

[cursive yoke]

nah we find the NUMBER of blocks of the requested size which is 3/5

[tight sphinx]

how do u do that

[cursive yoke]

okay thats why i was asking this

[tight sphinx]

o

so how many acres would there be in this question? 10?

[cursive yoke]

the one u asked or the one i asked 😄 ?

[tight sphinx]

the one i asked

[cursive yoke]

15/2 : 3/5 = 15/2 * 5/3 = 25/2 => 12 minus the 2 for the frogs so 10

[tight sphinx]

im confused at that part

what do u mean by 12 minus the 2 frogs

ohhhhh

i get it

[cursive yoke]

ok

[tight sphinx]

mkay tysm

[serene lily]

:]

is there any way to simplify 3ab-2 further? we have this speed solving activity in our math club and i said "cannot be simplified" yet they marked me wrong...

[cursive yoke]

3ab-2 ?

not as far as I know

you most probably made a mistake somewhere before that

[dry thunder]

a tractor puts a force of 1000N the pressure exerted is 40Pa find the area in m square

can anybody help?

[cursive yoke]

how do you define pressure

?

[wicked ember]

h mm

[plush shuttle]

The formula for Pressure is Force = Pressure x Area
So you just have to rearrange that formula and then put the numbers you were given into it

[rich basin]

I don't get why it is just 5!

and not 5! *2

because you are making one of the judge the point

and not the entire judge becoming as one unit

therefore within the 3 groups, they are able to swap around

Nevermind, thank you

[cursive yoke]

u sure its 5! ?

[rich basin]

I reread the answer it is 5! * 6

6 in which they permutate within their small group

I don't get how we can approach q22 b

[untold sequoia]

you can just subtract the cases where they r together

you'll get the number of cases where they're separated

[rich basin]

I got the answer for this but I want to look for a more efficient way

Yeah, i just found out the cases when they are together

That is good

[untold sequoia]

👍

[rich basin]

But then i still don't get

it

So the part a is suppose to help you find b

[untold sequoia]

number of ways in which they can be arranged when no conndition is given is 5!

[rich basin]

Okay i got it

[untold sequoia]

k

[rich basin]

I thought the answer for a would be 24

[untold sequoia]

oh

[rich basin]

and then i was like how is 120 - 24 be 74

Thanks, that was gave me good insight

[cursive yoke]

wouldn't it be 6! if no condition is palced

[untold sequoia]

circular permutation

(n-1)!

[cursive yoke]

u re right

[bleak igloo]

can anyone tell me how to calculate imperfect roots without calculator

[cursive yoke]

any root or just the square root

[bleak igloo]

any root including sqrt

I just came to alg1 so..... pls dont include any alg2 ehh......

[cursive yoke]

well boy if you dont know calc i cant help u sorry

[bleak igloo]

uhh k

[cursive yoke]

there could be a method i just dont know it sorry

[glass lichen]

You can usually get a rough approximation by assuming the values are evenly distributed

ex sqrt(7)~2.6

[neon berry]

Where can I find good online math books

I seriously need to improve my maths

[bleak igloo]

how did you calculate

[glass lichen]

7 is between 4 and 9, so sqrt(7) is between 2 and 3

[bleak igloo]

ohk that thing I ve studied

[glass lichen]

7 is the 3rd integer between 4 and 9 out of the 5 total ones, so it's 3/5 along

so 2+3/5

,w sqrt(7)

[ocean seal]

Results provided by WolframAlpha

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

Requested by moshill1#9771

[bleak igloo]

yeh its much precise ty

??

I didnt undrstand the question

[glass lichen]

dont crosspost.

[cursive yoke]

Hey man something just came to mind

do you know how to do polynomials

[bleak igloo]

umm no

but going to study

in alg1

i have that in my textbook

[cursive yoke]

ohhh too bad I just rembered lagranges interpolation polynomial for aproximating functions

[bleak igloo]

whats it

can I ddo it

in alg1

[cursive yoke]

not without polynomials

[bleak igloo]

ok after polynomials

?

[cursive yoke]

yeah

[bleak igloo]

tell me

I will save it in notepad

[cursive yoke]

https://www.youtube.com/watch?v=WCGKqJrf4N4 this

[glass lichen]

Lagrange Polynomials / Interpolation is a uni concept...

[cursive yoke]

Really ?

sorry then

[bleak igloo]

will try

[glass lichen]

Yes, at least I only learned about them in linear

[bleak igloo]

Bye I am going to spam my textbook to reach polynomials

[cursive yoke]

we did it at end of HS

as it requeires calc only to find the error

something he doesn't seem to be concerned with

[glass lichen]

Told you already.. stop crossposting

[teal epoch]

Please don't post the same question on different channels
Please only ask when a channel is free
Please translate it in English.

...

[gray gorge]

Dw I took care of them

[dense violet]

Help please

[rigid smelt]

sum of angles in a quadrilateral is always 360

you can find BDO and BEO

oh oops

brainfart

[dense violet]

will BDO and BEO would be 90?

[rigid smelt]

yes

[dense violet]

alr thanku

[rich basin]

I am having trouble in obtaining the answer for this question

The last part for which the two particular artist must not sit next to a particular writer

So i was tryinng to find the case when the artist sit nexts to the writer

and then minusing the case where there is no restriction

so i did this $2880-4!\cdot3!\cdot2$

[ocean seal]

Travelling Salesman

[rich basin]

but unfortunately i did not get the correct answer

2880 is from no restrictions

and the 4! *3! *2 is the total permutation of when the two particular artist are next to the particular writer

I think i didn't take the case for which one of the artist is sitting next to the wrtier

[rich basin]

Still confused

[strong citrus]

How to solve this?

[bronze dust]

4! * 5!

is this the answer?

[wraith cairn]

Neither of them want to sit next to the writer, it doesn't have to be both

[dense violet]

How to calculate w

[nocturne mirage]

isnt that just the whole square minus the 310° arclength minus the triangle ABO ?

prob use pythegoras theorem find the area of the triangle ABO

[dense violet]

i just need to find w why would i find area?

[nocturne mirage]

wait

I thought w was the grey area

[dense violet]

no it's the base of the rectangle

[nocturne mirage]

sorry >.<

[dense violet]

The answer is coming 11.4

[dense violet]

no worries

[nocturne mirage]

you can get x using cos(theta) here

theta is 35 degrees

(i'm using the angle bisector of <AOB

[dense violet]

yes i did that but will i multiply it twice to find w, or add 6 into that

[oak chasm]

No, it's 25 degrees. (360 - 310)/2

[nocturne mirage]

add 6

true 25°

[dense violet]

why

[nocturne mirage]

mb

[dense violet]

can i not multiply it?

[nocturne mirage]

w = x+6

[dense violet]

Oh ok thanku

[crimson raven]

send help for (a) pls

this is what i worked so far

[oak chasm]

You don't know if that's some sort of midpoint.

There isn't really enough information.

You can tell that the x value of R is greater than 6. You can tell that the y value of R is greater than 5 and less than 10.

[crimson raven]

cant figure it out unless they said they were midpoints

[oak chasm]

You can assume that the points are drawn to scale and use a ruler, I suppose.

But in your answer, you should write that you're assuming the points are to scale.

[crimson raven]

ok i try that

[viral peak]

ello i just land to this server

im 14 years old . i really like math tbh . i found this server by searching it :D.

[coral cosmos]

lol same

this server contains some highly complex questions which are out of my scope lol

[viral peak]

nice. and hello there

[coral cosmos]

Hello

[viral peak]

yep

im top 10 for form 2 student

for math only tbh

:/

i suck at langguage

lol

[crimson raven]

found the value for x in R but not so well in y

[coral cosmos]

couldn't get you

[coral cosmos]

lol, I am preparing for an engineering exam... so I only have to focus on Math , Phy, Chem

[viral peak]

owh nice

good luck

[oak chasm]

@crimson raven Well, use a ruler and find the vertical distance between P and U.

[coral cosmos]

Thanks : )

[crimson raven]

hol up

[viral peak]

np =).

[oak chasm]

@crimson raven Is that the same distance as between U and S?

[crimson raven]

a sec

how couldnt i didnt notice this

if X is midpoint of RQ

then RX=6/2=3m

and 4+3=7

[oak chasm]

Yes, but that's not what I meant.

I don't mean assume midpoints.

[crimson raven]

ik

[oak chasm]

I mean measure with a ruler.

[crimson raven]

seems not kinda legiting but do it anyways

[oak chasm]

Is XV the same length as VR?

Right, that's why you have to write "assuming everything is to scale"

[crimson raven]

measured and yes

[oak chasm]

That means that a ruler can be useful in this way.

OK, then what are R's coordinates?

[crimson raven]

probably (10,6)

bc VX=1 cm and VX=VR

[oak chasm]

OK, here's how I'd answer it:

Assuming everything is to scale, R is approximately (10, 6)
If everything is not to scale, R's x coordinate is greater than 6 and R's y coordinate is strictly between 5 and 10.

Do you know what "to scale" means and how I got the second part's numbers?

[crimson raven]

for x bc it lies on the right side of P so value of x should be greater than 6

[oak chasm]

Right.

[crimson raven]

but not sure for y tho

ik its greater than 5 but i didnt find its smaller than 10

[oak chasm]

Well, it has to be greater than U's 5. And the height of the rectangle is 6, so it can only be 6 above P's 4.

Does that make sense?

[crimson raven]

kinda

[oak chasm]

If it was greater than 10, it would be more than 6 higher than P, right?

[crimson raven]

yes

[oak chasm]

But the rectangle is only 6 high, right?

[crimson raven]

yep it says that

[oak chasm]

Do you see why that's impossible?

If not, I have another way of explaining.

[crimson raven]

if P lies on under the line would be impossible

[oak chasm]

Right, P would have to be under the rectangle.

Another way to see it is that the bottom of the rectangle is under P's 4, right?

[crimson raven]

yes

[oak chasm]

So, if you add 6 to the bottom of the rectangle, that's under 4 + 10.

Wait.

That's under 4 + 6.

[dense violet]

,,

[oak chasm]

@dense violet Sorry, channel is busy.

Let me start again.

The bottom is under P's 4.

The top is 6 higher than the bottom.

The top is under 4 + 6.

The top is under 10.

Does that make sense?

[crimson raven]

kinda know the concept

[oak chasm]

Oh, OK.

And do you understand "to scale"?

[crimson raven]

like 1cm to 1m, 1:2 or sth

[oak chasm]

Yes.

Do you understand why it lets us use a ruler?

[crimson raven]

maybe scaling?

to find the ratio or sth

[oak chasm]

Yes. "To scale" means that you take an exact picture of the thing and then you exactly scale it up or down.

So if two things are the same distance apart on an exact picture, they'll be the same distance apart if you exactly scale that picture up or down.

So that's why we can use a ruler.

If the ruler says that the distance between S and U and U and W are the same, then when we scale that up to the exact picture of the real thing, the distances will still be the same as each other, just scaled up.

Does that make sense?

[crimson raven]

yep

[oak chasm]

That's why we say "Assuming the picture is to scale" so that, in that case, we can use a ruler.

And that's why we also say, "But if it's not to scale, then this less exact result."

Then we've covered all the bases.

[spring harbor]

Consider in an orthonormal coordinate system a circle passing through point B(−1,0) and tangent at point A(1,2) to the line with equation y=2x. What is the area of this circle?

Could someone help me out please? I'd very appreciate it.

[eager surge]

hey guys. might seem really random, but does anyone know where i can start learning about the Whewell equation?

[spring harbor]

This channel is taken ._.

[oak chasm]

@eager surge Sorry, channel is busy.

[eager surge]

oh my bad. do you know where i should ask this question?

[spring harbor]

#❓how-to-get-help

[eager surge]

thanks

[spring harbor]

Consider in an orthonormal coordinate system a circle passing through point B(−1,0) and tangent at point A(1,2) to the line with equation y=2x. What is the area of this circle?
Could someone help me out please? I'd very appreciate it.

<@&286206848099549185> Anyone?

[oak chasm]

@spring harbor Well, one of the basis vectors could point in any direction.

So, let's see.

You have A(1,2) on the line y = 2x.

[spring harbor]

Mhm

[oak chasm]

@alpine sable Sorry, channel is busy.

[alpine sable]

oh sorry

[oak chasm]

@spring harbor So, the direction of vector A has to correspond to the direction of the slope 2.

So, that's 2y per x.

So, A(1, 2) is also 2y per x.

Now a slope points in two directions from the origin.

So, the basis vectors are either (1, 0) and (0, 1) or (-1, 0) and (0, -1).

Does that make sense?

[spring harbor]

I mean.. sure, but we're not really supposed to do this with vectors

I think we just have to make usage of some basic concepts like the circle equation and other things

[oak chasm]

Well, that makes things harder.

I think.

Wait.

[spring harbor]

Yeah I am really thankful but i'd rather do this in a method I understand, I don't want to just nod my head and go along with what you say

We learned how to use vectors and such but not at the level you're showing there (i think at least)

[oak chasm]

That's trigonometry.

[spring harbor]

Oh ok.

my bad then

I didnt get to read all of it

[viscid compass]

HI, i need some help with a problem

[ocean seal]

Chai T. Rex

[oak chasm]

@viscid compass Sorry, channel is busy.

For the x component of A in the standard basis, you add together the x component of the rotated components of A in the orthonormal basis.

An orthonormal basis will just be the standard basis rotated somewhat with the components reordered perhaps.

[ember lava]

@viscid compass u can go to #help-7｜zen1thxyz

[sleek elbow]

https://dontasktoask.com btw

[spring harbor]

@oak chasm I handed in without giving an answer and this is part of the solution they showed

[strong furnace]

@oak chasm may* I ask what you just did?

[spring harbor]

So they got point M(-3,4)

and then they found the length of |MB| which is sqrt(20)

and used that to find the area of the circle

but I am not very sure I understand the first step, how they got the first two equations

they are the tangent line equation I know, y-f(a) = df(a)(x-a)

but im not so sure i understand why they used it *in the way they did

[strong furnace]

consider the fact that tangent is perpendicular to radius

[spring harbor]

Fair, so their slopes multiplied gives us -1

[strong furnace]

yep

[spring harbor]

but where do the -2 and -1 come from?

and the -1 and -1/2

[strong furnace]

it needs to pass through (1,2)

[spring harbor]

Hmm

[strong furnace]

it is the line along radius

[spring harbor]

but it should be f(a) there

[strong furnace]

passing through (1,2)

[spring harbor]

I understand 2 but why 1

[strong furnace]

a line with slope -1/2 passing through (1,2)

[spring harbor]

yeah no im totally lost

[ember lava]

xD

[oak chasm]

The -1/2 slope comes from being the perpendicular slope to 2.

[wraith cairn]

draw the center of the semi-circle, connect it to the tangents, get a square.
connect the radius of the large circle to the corners of the semi circle. See what you find.

[spring harbor]

Oh I see

what about the -1?

[oak chasm]

Not sure about that.

[strong furnace]

(y-2)=(-1/2)(x-1) slope-point form of line

[oak chasm]

It looks as if they're making equations for the lines from A and B to the center of the circle.

But I don't know how they know the slope is -1 for point B to M.

[strong furnace]

does not make sense to me either

but you can get a different line

perpendicular bisector to the one joining A and B

[spring harbor]

"A tangent to a circle is, at the point of tangency, perpendicular to the radius of the circle through that point. We therefore find the center M of the circle as the intersection of the perpendicular in A on the line y=2x on the one hand and the perpendicular bisector of the chord [AB] on the other. To find this intersection, we need to solve the following system:"

google translated so dont mind it very much

[strong furnace]

ohh wait that is exactly what it was

[oak chasm]

Ahh, OK.

[ember lava]

[strong furnace]

misread y-1 = -1(x-0) as y = -1(x-1)

[oak chasm]

How did they convert the slope for the standard basis (2) into a slope for the orthonormal basis?

[spring harbor]

no clue

[strong furnace]

orthonormal coordinate system implies standard basis

[oak chasm]

No, it just says that the basis vectors are unit vectors and orthogonal.

They could be rotated from the standard basis.

[spring harbor]

I think it means a cartesian coordinates system

[oak chasm]

Like if I rotate the x and y axis by 30 degrees clockwise, it's still cartesian.

And the basis vectors are unit vectors and orthogonal to each other.

[strong furnace]

(1,2) how would you interpret this position vector in your system

[oak chasm]

Yes, that's what I mean.

I mean, I showed earlier how to do it, but I was wondering how they did.

(1, 2) has a slope of 2 as well in the orthonormal basis.

So, you don't need to convert, but they should show that it's that way.

For this one, everything's rotated 180 degrees: https://www.desmos.com/calculator/fw7y6v96lq

[strong furnace]

since every vector is rotated equally and they didn't ask for actual coordinates just the radius , you can use this solution WLOG

[oak chasm]

Well, the problem is that the coordinates are in the orthonormal basis and the slope is in standard basis.

You need to convert the slope into the orthonormal basis.

This only converts without change if the rotation is 0 or 180 degrees.

[strong furnace]

if you interpet y=2x as standard basis

you are forced to use the same for (y,x)

[oak chasm]

Otherwise you need to do an arctangent to get an angle from the slope, add the rotation, and use tangent to get the slope.

No, the points are said to be in the orthonormal basis.

But x y is standard basis.

[spring harbor]

I think it's just a mistranslation

[oak chasm]

Could be.

[spring harbor]

it's just a cartesian coordinate system

[oak chasm]

Oh, OK.

That makes the problem easier.

[spring harbor]

i did mention it a bit earlier

xD

[oak chasm]

Oh, I didn't know that that was for sure.

[strong furnace]

its a communication problem on their end but when they don't mention any other frames(using cartesian terms) and mention (y,x) its for a general point

[spring harbor]

thanks for the help though, both of you.

[oak chasm]

No problem.

[ivory otter]

hi

so lets say you got this question

$\sin 2x = \frac{2 \tan x}{1 + \tan^2 x}$

[ocean seal]

MEOWBRO 父

[ivory otter]

and you are asked to show that sin 2x does equal the right hand side

but!

you can only use these formulas

you cant do any cot or sec

etc

id perefer if someone can walk me through it step by step and like ask me questions

but ill take any help ofcourse

[jagged rapids]

Take everything in terms on sine and cosine

[woeful pulsar]

sin(x) and cos(x) to be precise

[lavish cypress]

Then, instead of using sec you can use 1/cos, etc. so, for example: 1 + tan²A = 1/cos²A

[ivory otter]

where does it say that sec is 1/cos

in the formulas

[lavish cypress]

What

[woeful pulsar]

well if they show you sec you can do that, but it looks like they didn't cover sec

[ivory otter]

exactly!!!

thats the point

[woeful pulsar]

don't worry too much

[lavish cypress]

I'm saying you can leave everything in terms of cosine without converting to secant

[ivory otter]

thats the problem*

[woeful pulsar]

if it doesn't show up then you don't use sec

[ivory otter]

no it wont show up

but on youtube

[woeful pulsar]

then you don't need to use it

[ivory otter]

they only solve these questions with sec and stuff

[lavish cypress]

Then don't copy off of YouTube.

[ivory otter]

and i have no idea

[ivory otter]

i cant find a single youtuber that doesnt solve it without sec and other stuff

[lavish cypress]

Well, there you go I guess

[woeful pulsar]

are you just giving answers here

[lone heart]

From

#❓how-to-get-help

Rule 7

When asking for help, do not insist on getting just the answer; we are here to help you learn, not cheat. Likewise, if you are providing help to others, try your best to explain and elaborate instead of simply giving away the answer.

[next scroll]

Let f(i) denote the minimum positive integer x such that x is not a divisor of i. is there a term for this??? I have some problem in programming regarding this.

[woeful pulsar]

there's no mathematical term for that i think

unless you mean mex

mex {k | k divides i}

https://en.wikipedia.org/wiki/Mex_(mathematics)

@next scroll ?