help-0

[oak chasm]

@remote dagger So, what's the center coordinates and the radius?

[remote dagger]

ok i got radius 5 and center (3,1)

So how do i put the final answer

25=(y-3)^2+(x-1)^2

?

[oak chasm]

No, the 3 is for xs, right?

(x, y) is how coordinates are written.

If the center is (3, 1), then the x of the center is 3 and the y of the center is 1.

[remote dagger]

ah yes

x-3 and y-1

[ocean seal]

Chai T. Rex

[oak chasm]

,w plot (y - 1)^2 + (x - 3)^2 = 25

[ocean seal]

Results provided by WolframAlpha

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

Requested by Chai T. Rex#7323

[final crag]

Hey, is this statement false?

I have to say whether its true or false

[civic crypt]

What is the operator complement?

What means functionally complete?

[oak chasm]

@civic crypt See https://en.wikipedia.org/wiki/Functional_completeness.

Complement is probably the not operator.

But complement isn't actually functionally complete.

[left gate]

This is a very easy question but am new to sets is this the correct way to write question 5th and 6th? Is it [3,.....] And [-2,.....]

[civic crypt]

Thanks. The idea was that Rozio solves it 😄 . But I didnt know either 🙂

[oak chasm]

No problem.

[zinc vigil]

I have a question about number 5

should I do instantaneous rate of change or average rate of change?

[gloomy lintel]

Instantaneous rate of change because it says ‘at’ 3 minutes after the oil spill

So still differentiate

And sub in t= 3

[zinc vigil]

wouldnt I get zero though?

[civic crypt]

Perhaps better to use intersection instead of comma.

5. A={ y | yER ^ 3<=y}

I also prefer | instead of :

[left gate]

But that's the set builder form isn't that how you would write it?

Ahh

[civic crypt]

Yes, set builder form

I also see this:
A = {yER | 3<=y}

[zinc vigil]

can someonehelp explain the question?

I'm not sure if I'm overthinking it or missing something

[ionic jewel]

yours is right but I'd also use what vrafaeli said

[potent knoll]

You guys mean this ??

[ionic jewel]

his #5 is [3, infty)

[potent knoll]

Oh yes

I gotta buy glasses haha

[left gate]

👍

[civic crypt]

I also see: https://en.wikipedia.org/wiki/Set-builder_notation#Sets_defined_by_a_predicate

Comma can be used instead of intersection operator.
And the set from which is x taken can be written on the left side of the bar.

Oh, now I understand, you want to write it with brackets, not with set builder notation...

[ionic jewel]

oh lmao i thought he wanted the set builder too

[gentle marten]

Could someone explain truth tables to me in a simple way?

[manic quail]

What's the problem here? Don't you remember the logarithm rules?

$\log{(\frac{a}{b})} = \log{a} - \log{b}$

[ocean seal]

verysadperson

[stuck gate]

the exponent is throwing me off

[manic quail]

Why?

Just leave it in there.

[stuck gate]

oh

[manic quail]

Or split it up further, and then pull it out.

[stuck gate]

cause what i had was ln(8)/-ln7-lnx-y

[manic quail]

What?

$\log{(\frac{8}{7x^7y})} = \log{8} - \log{7x^7y}$

[ocean seal]

verysadperson

[manic quail]

@stuck gate

And you could expand the right thingy even further, if required.

[stuck gate]

ln(8)-ln(7)-7ln(x)-ln(y)

[manic quail]

Great.

[stuck gate]

😄

[final crag]

Is this statement false?

<@&286206848099549185> Could I get some help with this one

[oak chasm]

@final crag Can you build an AND with a bunch of NOTs?

[final crag]

I'm not ssure about this one

Do you happen to know what it means when it says operator complement?

[oak chasm]

It means NOT.

[final crag]

oh then it would be True right?

you could build an and and a bunch of nots

[oak chasm]

How?

Build an AND from a bunch of NOTs.

[final crag]

i googled ssomething it said like +, *, ' are functionally complete

[oak chasm]

OK?

[civic crypt]

Well, when you have some logical expression like A U B you can make a truth table for the result of the expression.

[gentle marten]

ok

[civic crypt]

A can be only true or false. B can also be only true or false.

[final crag]

nor is functionally complete right

[oak chasm]

@final crag Is this a homework problem?

[final crag]

yeah it is

i just have to state true or false

in my lecture it says nor is functionally complete

[oak chasm]

OK, so what is a known set of operations that are functionally complete?

OK, if NOR is functionally complete, then any set of operations that can create NOR is functionally complete.

And so NOR can easily be created from NOR, so NOR is functionally complete.

Similarly, can NOR be created from NOT?

[final crag]

i still dont get what operator complement is though lol

[oak chasm]

If so, NOT is functionally complete. If not, it's not.

@final crag Do you know what NOT is?

[final crag]

like false right?

opposite of true?

like in coding u say "if not"

[civic crypt]

You need to be able to express all possible truth tables.

[oak chasm]

@final crag Do you know what ! is in most programming languages?

[final crag]

yeah the not equal to

[civic crypt]

Yea, I guess this is from those programming logic "gates"

NOR gates alone can be used to produce any logic.

[oak chasm]

No, that's != in most programming languages.

[final crag]

yeah thats what it is @civic crypt

[oak chasm]

I asked if you know what ! is.

[final crag]

oh isnt that just not?

[oak chasm]

And is the result always false?

[final crag]

yes

[oak chasm]

Oh, so when you use !whatever, that's always false in a programming language you use?

[final crag]

oh no actually cuz 5 != 3 could return true

[oak chasm]

No, not !=.

Again, !.

[civic crypt]

But ! is a unary operator, so how can you combine more than one input with it?

[oak chasm]

@civic crypt Why are you asking me that?

They don't know what the "complement operator" is.

[civic crypt]

Yea, this is suspicious 😄

[oak chasm]

What's suspicious?

[civic crypt]

@final crag Complement operator (negation operator). If you provide it something true it negates into false. If you provide it something false it negates it into true. It is like - but for logic.

For example let the statement be A="I'm pretty"

[final crag]

im not sure if i know about - haha

so if somethings true and u use !, it'll result in the opposite so false?

[civic crypt]

-A is the negation, and means "I'm not pretty"

[final crag]

ohh

i see what ur using

right yeah

[civic crypt]

So if A = "I'm pretty" then -A = "I'm not pretty"

[final crag]

so like if u use A = I'm not pretty

then u do !A

its im pretty?

[civic crypt]

Yes

[final crag]

yeah so its functionally complete

cuz it can return both types

So the operator complement is functionally complete statement is true

[civic crypt]

Well, It's a bit suspicious to me. But it might be.

[final crag]

yeah ima say true

i think its true

[civic crypt]

The concept of functional completness for unary operators does not make sense to me.

[final crag]

it should be functionally complete and im looking at my notes rn

[next void]

Can someone explain how to solve this? The numbers 1, 2, 3, 4, and 5 are written on slips of paper, and 2 slips are drawn at random one at a time without replacement.
(a) Find the probability that the first number is 5, given that the sum is 7.
(b) Find the probability that the first number is 3, given that the sum is 8.

[oak chasm]

@next void If the first number is 5 and the sum is 7, what numbers were drawn?

[next void]

@oak chasm It would be 5 and 2

[oak chasm]

OK, how many ways are there to choose the first number?

[next void]

1

[oak chasm]

I mean in total.

[next void]

It's not 1? Wouldn't there only be 1 way to choose 5 as the first number?

[oak chasm]

Do you know what "in total" means?

[final crag]

oh so thats why u were saying NOT. The operator named " complement" is NOT

[gloomy phoenix]

I don't understand why P, Q and X are non-coplanar. Could someone help me understand?

No flat surface contains all four points but why?

[oak chasm]

@gloomy phoenix It doesn't say P, Q, and X are noncoplanar.

It says P, Q, X, and Y are noncoplanar.

[gloomy phoenix]

Ok, so I could say P, Q, X and W are Coplanar but "no flat surface contains all four points"?

[oak chasm]

Again, they didn't say that no flat surface contains P, Q, X, and W.

So, "no flat surface contains all four points" doesn't apply to P, Q, X, and W.

It applies to P, Q, X, and Y.

[gloomy phoenix]

Thank you.

[oak chasm]

No problem.

[naive dock]

Can someone help me please with Algebra 2

[oak chasm]

@naive dock Do you know how to find average rate of change?

[naive dock]

Isnt it b1-a1/b2-a2

[ocean seal]

Chai T. Rex

[oak chasm]

Same with g.

In other words, the change in outputs over the change in inputs.

[naive dock]

So it would be -2?

Fort g(x)

[oak chasm]

Yes.

[naive dock]

And f(x) has the greater rate of change since 3 is greater than -2 or because 3 is farther from 0 than -2 is on the number line?

[oak chasm]

3 isn't the average rate of change for f.

[naive dock]

3/2 is correct?

[ocean seal]

Chai T. Rex

Chai T. Rex

[naive dock]

So 3/2 has a greater average rate of change than -2?

[oak chasm]

Yes, it is a greater rate of change than -2.

[naive dock]

Ok thanks

[oak chasm]

No problem.

[pallid cosmos]

How is x/0.5 simplified 2x?

[jagged imp]

multiply the numerator and denominator of x/0.5 by 2

[pallid cosmos]

Is the 2 taken from the denominator from 3 1/2?

[jagged imp]

no, 2 since 0.5*2=1

when dividing by a decimal like that it's probably best to write it as a fraction

since it might be more obvious what to multiply the numerator and denominator by if i write $\frac{x}{\frac{1}{2}}$ instead of $\frac{x}{0.5}$

[ocean seal]

111211211111221312211

[iron topaz]

Could someone help me with Algebra 2 please

[civic crypt]

I don't think NOT (complement) is functionally complete.

For functionally complete set of functions, you need to be able to express all the possible truth tables (for both 1, 2, 3, ... and more input variables) only with these given functions.

In your case you only have complement. You cannot express any truth table of 2 or more variables, because you cannot combine 2 or more variables with only NOT. Because NOT is a unary operator (function)

[final crag]

this is what my notes say about complement

[civic crypt]

@final crag So? Wdym?

[final crag]

wouldnt it be True because all cases are satisfied?

Like it could be both True and False

like i feel like if it said operators complement and boolean sum are functionally complete

that would be false, wouldnt it

but just with itself it should be true?

[final crag]

or do i have it switched lol

[civic crypt]

You cannot combine more than one input for NOT alone

[final crag]

wait it should be functionally complete because all values can be listed with bar? no

NOT can only have 2 values right

either 0 bar or 1 bar

so if its not 0, its 1. if its not 1, its 0

doesn't that mean its functionally complete?

[civic crypt]

No. For any number of inputs. You can make any pattern of outputs

For example, for 2 inputs
1 2 | Comb
F F | x
F T | x
T F | x
T T | x

You can use only NOT to produce any pattern on x column

[final crag]

so lets say xy bar = x bar + y bar

that would be true right

@stable knoll this channels being a used a little, do you mind going to another one pls

ty

[iron topaz]

Can someone help. Its Algebra 2

[rotund cairn]

Can someone help me with a basic trigonometry question?

[final crag]

@civic crypt Isnt there an online calculator that we can check with

[civic crypt]

I dont know why you used that example. It has +. In your question it says only NOT.

[final crag]

yeah im just seeing if i understand the concept real quick

or like if we're on the ssame page with that one

would you say this is true?

[rotund cairn]

How do I find a missing angle when only given another angle?

[civic crypt]

777Ronin777 what is wrong with you

Dont you see this channel is used

[final crag]

lolll

[civic crypt]

#❓how-to-get-help read

[rotund cairn]

Lol what

[stable knoll]

Sum of all angles are 180•

[civic crypt]

You have 10 channels. You dont write on the same channel other people write at the same time

[stable knoll]

You are given two

[final crag]

ronin its 180 -32+90 brother

[stable knoll]

That square is meaning 90°

[final crag]

that was funny

vra had enough

[rotund cairn]

Thank you!

[stable knoll]

Also what is 0 with line in middle

I never saw that

[civic crypt]

Yes. Why?

[rotund cairn]

Theta, it’s for missing angles

[final crag]

okay i was just checking lol

i have true for that one too

[civic crypt]

How is that relevant to your previous question?

[final crag]

damn i dont know about this operator complement is functionally complete though...

[stable knoll]

Ye tottaly true

[civic crypt]

Put false.

[final crag]

its not i was just curious if we agreed that one was true

[final crag]

LOL

[stable knoll]

Lol

[final crag]

u think so

[civic crypt]

Yea

[stable knoll]

Its false

[final crag]

ahha

[stable knoll]

XY = X * Y

[final crag]

no that one is true

[stable knoll]

How

[final crag]

x+ y = xy

same thing

[stable knoll]

No

[final crag]

well bar xy

[stable knoll]

xy = x*y

Wtf man

[final crag]

yeah but its bar x bar y

not the same thing as normal x and y

[stable knoll]

Oh

[final crag]

i have 1 more question since u put false

for something like this statement

would that also be false because it says and?

[stable knoll]

I litteraly thought it meaned line of XY

[civic crypt]

This is true.

[final crag]

really wtf

i dont get it

but how though

the first part of that question is false isnt it

[final crag]

-___-

[stable knoll]

No one answerd my question

Lol

[civic crypt]

Wikipedia on Functional completness says, that {NOT, ^} is functionally comp.
Same for {NOT, V}.
Same of {NOT, ->}

[stable knoll]

):

[final crag]

choppa its cuz we're trying to figure this out

[civic crypt]

That is not how it goes.

[final crag]

or well @civic crypt is helping me

oh so ur saying

NOT, + is functionally complete

[civic crypt]

First question was, {NOT} operation alone is functionally complete - false
But the combination of operations {NOT, +} is functionally complete - true

[final crag]

but alone NOT is not

[civic crypt]

Exactly

[final crag]

ohhhh

[civic crypt]

Because NOT alone is not capable enough

But {NOT, +} are capable of produce any function you imagine.

[final crag]

operator NOR is complete tho

by itself

[civic crypt]

Exactly

[final crag]

ahh

god dammit

thanks loll

that makes sense now

[civic crypt]

yea

[final crag]

i was looking at it as two separate questions wtihin 1

if that makes sense

[civic crypt]

i know.

[final crag]

rip

i was stuck on this for the longest time

thanks

[civic crypt]

I mean, it is kind of strange question

[final crag]

it is

i was legit staring at it

trying to figure out wtf it was asking me

[civic crypt]

Because COMPLEMENT not only cannot produce every function, but cannot even produce any binary function. Cause with COMPLEMENT alone you can never combine more than 1 variable

[final crag]

yeah i see now

makes a whole lotta sense now

[civic crypt]

{+} is a much better example

With + you can produce many functions I would say, but not all.

[final crag]

yeah

do you know anything about maxterms btw?

[civic crypt]

No.

[final crag]

me either ill look into it though

[civic crypt]

Also I'm slightly confused about NOR. It cannot produce unary functions.

This is like a nice question. How is NOR func. complete, when it cannot produce unary functions.

[final crag]

"NOR is a functionally complete operation"

thats what it says on wiki

makes sense

[civic crypt]

Yes, but how, when it cannot produce unary functions.

You cannot have NOR A

[final crag]

"OR is the more complicated operation; it may use a NOR followed by a NOT."

[civic crypt]

I guess they take A NOR A in that case.

Yea

[final crag]

who tf knows

on wiki it says functionally complete

so ima just put true

[civic crypt]

So you need to be able to produce
A | result
F | F
T | F

A | result
F | T
T | F

A | result
F | F
T | T

A | result
F | T
T | T

You need to find a NOR combination to produce all these 4 functions (tables).

If you achieve, than you know NOR is functionally complete for 1 variable.
But this is not enough, it needs to be capable to do the same for 2, 3 and more variables.

1° might be achievable with (A NOR A) NOR A
2° with A NOR A
3° I think with (A NOR A) NOR (A NOR A)
4° I dont know. But 4 is equivalent with A + negA. negA = A NOR A and 3 is union.
So I have A + (A NOR A). And I have to apply 3° to that. So:
(A NOR (A NOR A)) NOR (A NOR (A NOR A))
Verification.
If A=false, (false NOR true) NOR (false NOR true) = false NOR false = true
If A=true, (true NOR false) NOR (true NOR false)=false NOR false = true

[final crag]

😦

[thorn kindle]

🙂

[alpine sable]

hey can someone explain how to solve this question

[alpine sable]

A

[covert glade]

Can someone help me with my calculator

[left zinc]

A

[gusty mural]

lmao this question kinda easy but my brains not working today

how do i solve this

[oak chasm]

@gusty mural What do you need to do to the left to get x by itself?

[gusty mural]

u divide the right side by (sqrt5 + 3)

[oak chasm]

You divide both sides by that, but yes

[gusty mural]

but the bit that is screwing me up is expressing x in the form of that

like in a sqrt b + c

[ocean seal]

Chai T. Rex

[gusty mural]

yep i got that

[ocean seal]

Chai T. Rex

[gusty mural]

hold up ill write it out

[vestal widget]

3-√5

Multiple by conjugate in both numerator and denominator

U will get the answer

[gusty mural]

oh lmao

i got it

thanks

lmao

wait

is that right

no

there

this is right

i think

[oak chasm]

The conjugate is where you change the sign of the term with the square root in it.

[gusty mural]

yeah

@oak chasm tysm :))

[ocean seal]

Chai T. Rex

[gusty mural]

this is the definition of conjugate surds on my textbook

so i used that

[tiny agate]

oh

well if you take a class with complex numbers, conjugate will mean something else

[oak chasm]

Conjugate means something else here.

They didn't start with a pair of surds, so this is fairly inapplicable.

[tiny agate]

there are no bad students, only bad textbooks

[gusty mural]

im working through my high school calculus textbook and i just started the chapter on complex numbers

lmao

well i got the correct answer with the textbook method but thanks yall

[tiny agate]

oh WELL DONE

hold on, i'll dm my method for these

[livid crypt]

can someone explain what they did here

[oak chasm]

@livid crypt What are you confused about?

[livid crypt]

I just have no idea how they did this problem

[ivory nest]

Since x goes to 0, it's going to be coming from the left (since you're taking away from 2)

2 - x^2 at small values of x will be less than 2, never going to be anything greater than 2

So this turns into the left side limit

[ocean seal]

Chai T. Rex

[livid crypt]

ok so I understand that part

so you get the left side limit as 2 and then what

[ivory nest]

well what does f approach as you go to 2 from the left?

remember, approach doesn't mean equal

[livid crypt]

it approaches 3 right?

[oak chasm]

Yes.

[ivory nest]

Yep!

btw, it's important to note that this is 2 - x^2

could we say the same thing if it was 2 - x?

what does squaring x yield us?

it's pretty integral to this question

[livid crypt]

0^2 = 0

im kinda of understand it

is there a name for this concept?

my teacher never taught me this

[ivory nest]

well also limit of x -> 0
it could approach from x is negative or x is positive

squaring makes it only positive

cause if we subtracted a negative number from 2

[livid crypt]

oh

[ivory nest]

We could actually be bigger than 2

Right?

and then that would put us on other line segment and make this a lot more complicated

[ivory nest]

Not a formal name but it's just limit approaching from different directions

[livid crypt]

i feel like I understand it

but the notation they used confused me a bit

tysm

[ivory nest]

Still confused by the notation?

[livid crypt]

a little

how did they do the f(u) thing

did they just take the 2 minus

from this

and make u approach 2-

[ocean seal]

Chai T. Rex

[livid crypt]

so u in this case is 2-x^2

[oak chasm]

Yes, when x approaches zero.

[livid crypt]

oh ok I understand it

ty everyone

[carmine lion]

how do i approach this problem

$\tan(\theta-\frac{\pi}{3})=-\sqrt{3}, 0\leq\theta\leq2\pi$

is the first step adjusting the domain?

[ocean seal]

Chai T. Rex

[carmine lion]

what i've done is

let $x=\theta-\frac{\pi}{3}$

[ocean seal]

abe

abe

[carmine lion]

my bad it was wrong question

so yea

let x= theta - pi/3

tan x = -(sqrt 3)

x=-pi/3, 2pi/3

[oak chasm]

,calc atan(-sqrt(3))

[ocean seal]

Result:

-1.0471975511966

[oak chasm]

,calc -pi/3

[ocean seal]

Result:

-1.0471975511966

[oak chasm]

OK, looks good.

[ivory nest]

that would be my approach abe

substituting with x = theta - pi/3 is good

the rest kinda falls out which you showed

[carmine lion]

$-\frac{\pi}{3}\leq x\leq\frac{8 \pi}{3}$

[oak chasm]

So, you have $n \pi - \frac{\pi}{3}$ where $n \in \mathbb{Z}$.

[ocean seal]

Chai T. Rex

abe

[carmine lion]

there is a given domain

and i haven't learnt the general formula stuff yet

,calc 5pi/3

[ocean seal]

Result:

5.235987755983

Chai T. Rex

[carmine lion]

for an acute angle yea

[oak chasm]

For any angle, I mean.

[ocean seal]

Chai T. Rex

[oak chasm]

So, you can add as many half revolutions as you want and it'll give an angle at the same slope, so the tangent will be the same.

Does that make sense?

[carmine lion]

nope

[oak chasm]

Does the part about tangent giving the slope for an angle make sense?

[carmine lion]

thats only if you have it in the form

-tan(x+pi)

[oak chasm]

No.

[carmine lion]

this question is tan(x)

[oak chasm]

Thanks, I didn't see that before.

[ocean seal]

Chai T. Rex

[vapid smelt]

This is the data: 10,15,20, 25, 30, 35
We are supposed to find out the median, which I got 3.5, but idk which is the median among the data, how do I fid that out?

[oak chasm]

@vapid smelt Sort the values in ascending order.

OK, now are there an even or odd number of elements?

[vapid smelt]

i am confused because i got the median in decimal

[ivory nest]

You got 3.5 because you're looking for the item in between element 3 and 4, which doesn't exist (since you have 6 datapoints). How do you get around this issue?

[vapid smelt]

right

that i don't know

[ivory nest]

oh ok

if you have an even number of elements

you'd average the 3rd and 4th element

to get the median

in this case, you gotta start by sorting the data (which you've done)

so the 3rd element is what? and the 4th element?

whats the average of those two

thats ur median

[vapid smelt]

oh

thankyou

[carmine lion]

sorry about that

[bronze trench]

Find PU and QS if ΔPQR is isosceles with vertex Q, bisects ∠PQR, ||, TU = 11, QT = 21, PR = 15 and PQ = 12.5.

I know that I have to use ratios but could use some help

[bronze trench]

<@&286206848099549185>

[dawn wraith]

Would you like a hint?

~~ @bronze trench ~~

Oh well, I’ll just wait

[foggy onyx]

can someone help

i forgot how to solve a kite ;-;

[alpine sable]

uh hold up

i can't read ur handwriting

dude 2 is probably 90 degress

[jaunty jasper]

Can someone help me with 1-3

[carmine lion]

u kinda need to show the triangle

[jaunty jasper]

It doesnt give it

[hoary zinc]

Do you need to solve for A?

[jaunty jasper]

No u just have to prove both are equal

[oak chasm]

@jaunty jasper Use law of sines for the first one.

[jaunty jasper]

Wait how

[oak chasm]

Well, what's the law of sines say?

[jaunty jasper]

SinA/a is SinB/b is SinC/c

Pls someone help

Im kinda confused

[dawn wraith]

Now try and make a common denominator

[jaunty jasper]

But dont i have to like pretend that they aren’t equal

Cause in try a prove that they are

[dawn wraith]

When you want to prove identities, the main objective is to use a formula that may get you to the identity given to you in a question

You don’t have to pretend as if things were equal or anything like that

You have a formula, get to the given identity.

You’re in point A, get to point B

[jaunty jasper]

So like that right

[dawn wraith]

How so?

[jaunty jasper]

Cause its a common debate

Denominator

[dawn wraith]

What does the law of sines say?

[jaunty jasper]

SinA/a is SinB/b is SinC/c

[dawn wraith]

Now explain how’d you get to that

[jaunty jasper]

Multiply one side by (5b+2c) and the other side by a

[onyx cargo]

Finding the derivative of this function, stumped here, I must use the first principles IROC method tho

[rigid smelt]

try to apply a^2-b^2

or so called conjugate

[formal canyon]

I’d suggest rationalizing the rooted denominators first, think that might make it easier or also that ^

[rigid smelt]

that would just make it actually a bit longer

u just need to multiply by the conjugate and you are good to go

[dawn wraith]

That is invalid, if you multiply the LHS of the equation by something, you also multiply the RHS by that value

Otherwise it’ll become an indefinite inequality

[jaunty jasper]

So how would u find the common denominator

[jagged imp]

what's your question then? Are you struggling to find dy/dx?

[dawn wraith]

I would firstly look at the denominators and try to make the denominator in the question

[jaunty jasper]

Wdym

[dawn wraith]

Oi, channel is occupied

[tranquil helm]

Can anyone please help me with its solution asap?

[jagged imp]

why asap?

[tranquil helm]

Yup.. I need it by tomorrow.. That's why

😅

[jagged imp]

then again, what's your question

[dawn wraith]

The 5b+2c is the denominator we’re trying to get

So try and plug that in

[jagged imp]

You've stated the problem and the method for solving it

[tranquil helm]

Okay

[jagged imp]

dy/dx = u / v and at points where v = 0 and u does not = 0, the derivative is not defined because the tangent is vertical.
use this

so look for points where the denominator is 0 and those are your vertical tangents

(and make sure numerator isn't 0 at those points

[tribal geyser]

Can someone explain 27a)?

How is it 140? Like where does the bearing of 50 go from? Can u draw it in?

I’m confused

Pls help thanks

The answer says this but I don’t understand

<@&286206848099549185>

[soft echo]

Tea at $2.40 per kg is mixed with tea at $3.20 per kg in the ratio 1:3
a) Calculate the weight of each type of tea in 40kg of the mixture.
b) Calculate the price of per kg of the mixture.

<@&286206848099549185>

[tribal geyser]

Sorry Channel taken

[soft echo]

oh

ok

[tribal geyser]

Could someone help with my question thank you

[grim heath]

a) 2.4$ tea weight = 10 kg
3.2$ tea weight = 30 kg
B) 56$

[vale wigeon]

@grim heath do not give out answers

also your answer to b isn't even correct

[graceful lance]

What will be the steps ?

How to do it

[misty raptor]

@vale wigeon can I dm you?

@graceful lance

1) you know one of the root is -1. So you can divide polynomial in (x+1)(some quotient).
2) you can find this quotient polynomial by dividing polynomial/(x+1) 
3) the quotient polynomial will be a simple quadratic polynomial whose roots can be found by formula
let me know if you still can't find it

[graceful lance]

okie

its done

[alpine sable]

is this right?

[subtle mango]

Thank you

[noble bolt]

Wrong it's 408

[stable knoll]

In some theater all rows have same amount of seats. If a number of seats is 4 less then a number of rows what is the total number of seats: 90, 92, 96, 95. Is it 96 i tried plugging all the numbers in this equation: x(x-4)=number and only logical one is 96.

[alpine sable]

how did u get that?

[slim sun]

Are the ten question channels different?

[noble bolt]

I balanced All the forces

Mg-F-Ma= 0

[vague coral]

mg - F - ma = 0
then F = mg - ma

$$ \sum F_{ext} = ma $$

[ocean seal]

Herels

[alpine sable]

F= 588-198

which equals to 390

[vague coral]

,calc 609.8 - 603

[ocean seal]

Result:

408

[noble bolt]

Calculation error

Bread check calculation

[alpine sable]

1 sec

[vague coral]

the result is 408 if you take g=9.8m/s^2

[alpine sable]

i did F=60 times 9.8 - 60 times 3.3

nvm i got it

ty

[stable knoll]

In some theater all rows have same amount of seats. If a number of seats is 4 less then a number of rows what is the total number of seats: 90, 92, 96, 95. Is it 96 i tried plugging all the numbers in this equation: x(x-4)=number and only logical one is 96.

[oak chasm]

@stable knoll Do you mean that the number of seats in a row is 4 less than the number of rows?

[stable knoll]

Yes

[graceful lance]

How to do it

[oak chasm]

@graceful lance Sorry, channel is busy.

[graceful lance]

okie

sorry

[misty raptor]

@graceful lance put x = 2

[graceful lance]

and LHS as 0

[oak chasm]

@misty raptor Sorry, channel is busy.

[graceful lance]

and then solve

[misty raptor]

Yes

@oak chasm okay

[graceful lance]

Thank You

[oak chasm]

@stable knoll OK, I know a way to do it.

[ocean seal]

Chai T. Rex

[stable knoll]

I will try

[carmine lion]

how to prove this identity

[oak chasm]

@carmine lion Sorry, channel is busy.

[carmine lion]

oh ok

[stable knoll]

This is middle school question from high school competition test.

[oak chasm]

Oh, OK.

[ocean seal]

Chai T. Rex

[ancient bear]

I'm wondering why does this exercise mention the 2nd derivative test

If the relative extrema are found through 1st DT?

[oak chasm]

What's the second derivative test?

[ancient bear]

You look for concavity and inflection points

I.e. the rate of change of the functions rate of change.

We get relative extrema by finding where the velocity is zero

[oak chasm]

OK, and what can concavity tell you about extreme points?

[ancient bear]

Well

I don't know.

[oak chasm]

It can tell whether they're a local maximum or local minimum.

[ancient bear]

O.

Can you elaborate so I can see it clearer?

I mean I get it. But u could show a way to think of it so that I can learn it right in this moment

[tame stirrup]

If you do the second derivative test well it is not compulsory but you get whether a point is maxima or minima just by using formula

You can find the extremes using both

[oak chasm]

If a function is concave up at an extreme point, it's a local minimum.

[ancient bear]

So if the extrema's concavity is down then it's a rel max

[tame stirrup]

But in complex problems its easy for second derivative

[ancient bear]

I see!

[oak chasm]

This is because the function is coming from above on the left and leaving to above on the right.

[harsh acorn]

The length of a truck, L metres, is 8.2m, correct to 1 decimal place.
Complete this statement about the value of L

what does this mean i did not understand it

[lament wyvern]

what does "to 1 decimal place" mean

[harsh acorn]

idk thats why i asked it

it was practice test and answer was 8.15 and 8.25

[lament wyvern]

well, might be worth looking in your textbook to find out what to X decimal places mean 😛

[harsh acorn]

i wouldnt ask there if I found it in internet or textbook sir.

[lament wyvern]

to N decimal places mean you round the stuff past the decimal place.

so if you had 8.17 and you needed it to 1 dp, you'd look at the 2nd place - 7 - and round it

in this case, you'd round 7 up

so you'd get 8.2

[harsh acorn]

but why in answer there are 8.25

it must be 8.24

isnt it

[lament wyvern]

if we had exactly 8.25, then it'd be 8.3

but what if we had 8.249? or 8.249999? or 8.24999999999?

every number less than 8.25 and greater than or equal to 8.15 rounds to 8.2

[harsh acorn]

ah i understand it but why they just write 8.15 and 8.25 lol

[lament wyvern]

maybe it's a book that treats 8.25 as rounding to either one lol

but the way I'd see it is that 8.15 <= L < 8.25

[limpid spade]

Inflection points u find by 2nd and first derivative right?

[acoustic shadow]

No just the 2nd derivative

[limpid spade]

Yes switch signs

[alpine sable]

Easy ass question

that i forgot how to do

[vale wigeon]

do you know what the integral of x^2 is

[alpine sable]

what can you change x^2/3 to

Yes

1/3x^3

[vale wigeon]

okay then divide that by 3

[alpine sable]

o

SO

1/3X^3/3

Yes?

[limpid spade]

No

When u take the constant 3 out the integral the constant in the integral is removed

So it's just 1/3int(x^2)

[alpine sable]

Uh

1/3X^3/3

[vale wigeon]

you need parentheses

[alpine sable]

worked for me

[vale wigeon]

there are better ways of writing (1/9)x^3

[alpine sable]

got the correct answer so

that works to, I think i will stick to my way for simplicity

[limpid spade]

Oh nvm x^3/3 you took the integral already thought you didn't

[graceful lance]

How to do it ?

[acoustic shadow]

Sum of roots = -b/a product of roots= c/a

[graceful lance]

yes

then ?

[ocean seal]

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

[crude tendon]

Oops

[crude tendon]

Let $x_{1}, x_{2} $ be the zeros of the polynomial $x^{2}-px+q$. Then you have: $\frac{x_{1}}{2}, \frac{x_{2}}{2}$ are the zeros of the polynomial $2x^{2}-5x-3$, which are 3 and $-\frac{1}{2}$. So the zeros of $x^{2}-px+q$ are 6 and -1.

[ocean seal]

NPKA

[graceful lance]

ohhh

okie

[crude tendon]

Hence $6^{2}-6p+q=0$ and $(-1)^{2}+p+q=0 \rightarrow p=5, q=-6$

[ocean seal]

NPKA

[graceful lance]

Thank You

[crude tendon]

You're welcome

[crude tendon]

Ok

ABC and DEF are equilateral triangles right?

[stable knoll]

yep

[alpine sable]

Hello someone good at real equations?

[limpid spade]

Yes

[crude tendon]

Excuse me

This server is still in use

please wait just a few minutes

[limpid spade]

[safe chasm]

Hello, just found this server

[limpid spade]

Hi

[alpine sable]

I mean something like this:

[limpid spade]

Yes

[alpine sable]

I need more examples

[safe chasm]

So I'm currently learning Integration, where may i ask questions related to it?

[alpine sable]

To understand it

[limpid spade]

That's a rational equation

[alpine sable]

Oh yes

[limpid spade]

Me I'm an integration God

This channel is occupied

Go to other channels

[hushed berry]

You from romania?

[safe chasm]

Oh my YES

[alpine sable]

Moldova

[limpid spade]

Or npka is gonna spank yall

[safe chasm]

Nice

[crude tendon]

Let G be the intersection point of AB and FD. We have: $\angle GAD = 180 - 60 - 70 = 50; \angle GDA = 180 - 60 - 68 = 52. Hence \angle AGD = 180-52-50=78.$
Let H be the intersection point of BC and DF. We have: $angle BHD = 180- \angle CBA - \angle HGB = 180 - 60 - \angle AGD = 120 - 78 = 42$

[ocean seal]

NPKA

[alpine sable]

Ok fractalogist

U have more examples to explain and to train

?

HELP

ME

[stable knoll]

Thank you

[limpid spade]

....

This channel is occupied

[alpine sable]

.... 😭

He said thanks!

and moved on

[limpid spade]

Go to an unoccupied channel

[alpine sable]

OOP

[limpid spade]

Go to an unoccupied channel

[crude tendon]

what's wrong with you

[limpid spade]

?

[tawny lion]

read the rules

[tawny lion]

just integrate 5x^3

[safe chasm]

Since this channel is empty ima ask here. I missed my class and can't figure out how to do. Someone pls explain part b?

[tawny lion]

the image is upside down bro.

lmfao

I turned it around

make a bounded integral

with bounds 9 and 0

integrate 3x^1/2 - x

[limpid spade]

,rotate

[tawny lion]

,rotate

[tawny lion]

nice

[limpid spade]

a is 0 to 3

B is 0 to 9

C 1 to 3 and d 0 to 1

Then u just integrate the simple integrals

d is the only 'difficult' integral others should be ez

[safe chasm]

Ye can u tell d as well with like steps?

[limpid spade]

U know how to do integral of exponentials?

[alpine sable]

Uhh i still cant get the answer

I got 42

when the answer is 54

I did take one of the X

[limpid spade]

Did u do (x^4)/x - 3x/x

[alpine sable]

what

no

how did you get that

[limpid spade]

Do 5hat

That

Partial fractions

[alpine sable]

i still dont know how u got thart

[gray isle]

basic property of fractions

$\frac{a+b}{c} = \frac ac +\frac bc$

[ocean seal]

ℝamonov

[alpine sable]

yes

but how is that

[alpine sable]

this

[limpid spade]

?

[gray isle]

a = x^4
b = -3x
c = x

[alpine sable]

Yes

why break it up tho?

Wouldnt you cancel 2 X

[limpid spade]

To make it solvable

[alpine sable]

that way?

[gray isle]

simplification

[limpid spade]

You will get 2 solvable integrale

integrals

[gray isle]

you end up with two terms that are easily integrateable

(using power rule)

[alpine sable]

Ow okay, gonna try it and I'll let you know

can some1 help me seperate out the tan term?

the tan is the variable in this

[limpid spade]

xtan(o)*((sqrt()-1+b(x)/sqrt())

xtan(o) is common

[alpine sable]

i dont get what you are trying to say sorry

[limpid spade]

Well I made xtan(o) the common factor

[alpine sable]

how?

[limpid spade]

xtan(o) comes 2 5imes

Times

[limpid spade]

^

[alpine sable]

but what about the tan in the sqrt?

[limpid spade]

1+tan^2 is the same as?

[alpine sable]

i dont remember exact

but its cot i guess

[limpid spade]

sec^2x

[alpine sable]

oh nvm

[visual dew]

You write tan(0) like its tan (a)

[alpine sable]

but theta is a variable itself

thats the problem

[limpid spade]

and the sqrt(sec^2x) is just secx

So all sqrts are gone

Then simplify further

[alpine sable]

okay lemme try

Um

i got 60

Ended up with

(1/4x^4-3)

[gray isle]

doesn't look like you integrated the 3

[alpine sable]

no

idk what to do with the 3

[gray isle]

integrate it

[alpine sable]

How

ooo

RIGHT

Hi, can anyone describe how to solve this question? "3 new members joined to group and amount of members was increased by 2%"

bingo!

[limpid spade]

Multiple 3 by 80

No

50*

[alpine sable]

why

[limpid spade]

Nvm

Check #help-1

[pure hill]

Someone please help

[tardy kelp]

Since sqr(x) is defined when x>0 and log a b is defined when a,b>0 and a!=1

you can say x !=1 and log n (( 5*x - x^2)/4) >= 0

from here you get x != 1 and (5*x - x^2)/4 >= 1

[pure hill]

I just don't understand what condition should I put on x this is in the base of log

[tardy kelp]

it is x not n?

sry

is the same

[pure hill]

all of them are x

[tardy kelp]

instead of n is x

i thought it is n

the same thing , just replace n with x

[lunar fern]

Love the way you write "x"

[pure hill]

but if x in the base of log is negative then whole of the conditions will change for log

[tardy kelp]

hm

[glass lichen]

Base of a log is positive and not 1

[tardy kelp]

x has to be positive

and x can't be 1

[glass lichen]

thanks for repeating

[tardy kelp]

sry

[tardy kelp]

but i said it too 2 times

[glass lichen]

yeah I have no clue what log a b is suppose to mean

[tardy kelp]

log base a of b

[glass lichen]

log_a(b)

[tardy kelp]

i am not sure how to use that bot

[pure hill]

sorry sorry I wanted to say that x has two conditions 0<x<1 and x>1 and for both of these graphs are different

[tardy kelp]

oh that way

[pure hill]

and also this is what I am getting by taking different conditions for x in base

[tardy kelp]

i am not sure if i understand everything cuz i am not so good at english, but you have to use 2 cases and myb one of them is wrong ( when x > 1 and the other when 0 < x < 1)

if x > 1 then 5*x - x^2 > 4

and the other when 5*x - x^2 <= 4 and 0<x<1

or am i wrong

[pure hill]

yes you are right but I guess after getting these equation we should take their intersection for the values of x

[tardy kelp]

no

not the intersection

[pure hill]

union?

[tardy kelp]

yes

in case 1 i thing Δ = 9

[pure hill]

but union will give all the real values!

[tardy kelp]

think*

yes

that is the domain

[pure hill]

this is the answer

[tardy kelp]

i know

the domain is the union of the solutions of case 2 (1;4]

and case 1 where it is (0;1)

[pure hill]

should I send what I worked out and maybe you guys could tell where I am doing it wrong!?

[tardy kelp]

i can try to help

[pure hill]

okay

[tardy kelp]

it doesn t work like this

when 0 < x < 1 u showd that x^2-5x+4>=0

so from there

u find if x has solution in the inequality and u get R / (1;4]

but 0 < x < 1

so the solution for that case is (0;1)

[pure hill]

you mean to say that I should have factorised the equations?

[tardy kelp]

yes

or use Δ

[pure hill]

I reached the conclusion on second page by factorisation only I just didn't show it there

[tardy kelp]

hm, i don t think i said it right

you get an inequlity after each case right?

[pure hill]

I don't think that is the proper way because for 0<x<1 the values of log become negative if the value that we put inside log is not smaller than one

[tardy kelp]

yes

but you didn t write all

there

[pure hill]

like log(0.1)2 is negative but log(0.1)0.5 is postive

[pure hill]

what did I miss??

[tardy kelp]

you didn t get the solutions of each inequality

[pure hill]

okay wait

[tardy kelp]

i repeat
from x^2 - 5x + 4 >= 0 and 0<x<1 you get S = (0;1)
and from x^2 -5x + 4 <=0 and x>1 you get S=(1;4]

[pure hill]

it will be (x-4)(x-1)>=0 and (x-4)(x-1)<=0 and x(x-5)<0 and x>0 and x!=1

[tardy kelp]

after you verify the first things you found out like x can t be 1

and you do the union thing

[pure hill]

ohhh okay let me try that

[tardy kelp]

ok

[jaunty nova]

Can anyone point me in the right direction wit the question highlighted in green. I've looked all over the internet and I cannot find out how to do this. It is in the field of Mathematical Ecology.

[chilly zodiac]

is there a way to simplify $k! * j!$ ?

[ocean seal]

lightzkin

[jaunty nova]

If you knew the difference between j and k you could just write in terms of one variable I believe

[potent swift]

,ti lightzkin

[ocean seal]

This user hasn't set their timezone! Ask them to set it using ,ti --set.

[chilly zodiac]

lemme set it

[potent swift]

,ti --set

[ocean seal]

Your timezone has been set to Europe/Lisbon!
Your current time is 01:55 PM (WEST) on Sun, 02/05/2021.

[chilly zodiac]

thanks i'll try it

[jaunty nova]

Where can I ask a question?

[chilly zodiac]

#❓how-to-get-help @jaunty nova

[still crest]

<@&286206848099549185>

[bleak ibex]

m/n +n/m

=(m+n)/mn

Now apply the formula for sum of roots and product of roots

[bleak ibex]

Even I am curious about this

[still crest]

🥲

[graceful lance]

how to solve this one

what steps to take

[bleak ibex]

Umm bro, there's an unanswered question here

Move yours to another channel

[still crest]

Any guesses?

[bleak ibex]

Nothing till now

[still crest]

What about this one?

I have found the first a and b

But no idea what to do with c

[bleak ibex]

I am actually weak in coordinate geometry😂

[still crest]

Everyone must hate geometry heh

Even I do

[thick yoke]

You need to mark A as A(x1,y1)

And find y1 with x1

[still crest]

But we already know A

[thick yoke]

Sorry

[still crest]

It's A(16,-8)

[thick yoke]

I meant B

After that

Find the slope of AO and BO

[still crest]

Okay

x is on top or bottom, i forgot

[thick yoke]

Multiply them and that should be equal to -1

Because they are vertical to each other

[still crest]

Is the formula (x-x1)/(y-y1) or the opposite

[thick yoke]

It doesn't matter

The slope will be the same

[still crest]

I'm working it out, give me some time

I found 2*x2 = -y2

[still island]

1. Given 5 coin tosses of a fair coin, what is the probability that we have at least one run of size 3?
   Here a run of size 3 is a consecutive set of HHH or T T T.
   I dont understand the problem can anyone help me? I know it is easy but I am new to this so i am having difficulty even understanding the problem

[thick yoke]

The parabola is: y²=4x

@still crest

[still crest]

Correct

[thick yoke]

Good

[still crest]

Oh and I do the system

[thick yoke]

Good

[still crest]

Do you have any idea for this one?

[thick yoke]

Not really

[still crest]

Okay thank you!

[still island]

hmmm okay

thank you I didnt see it

[still crest]

np

@worn trail 1+1?

[drifting kindle]

So I have the answer

But I don't really know how the steps are

[still crest]

Thank you!

[drifting kindle]

The 2nd image I sent is the answer

[slow citrus]

How do I calculate the amount of possible paths to take?

[still crest]

there is an unanswered question here

[slow citrus]

ah sorry

[drifting kindle]

It's fine, I sent it to another one

[hard harness]

Hmm