help-0

[plucky pier]

i mistook (4/5)^-8 as a seperate number and have to find x and make it equal to it

[left citrus]

Aah alright

[plucky pier]

i got x=-2

[left citrus]

Perfect

[plucky pier]

[left citrus]

Lol

[topaz scaffold]

Lmao nice emoji

[plucky pier]

lol, its from dis server

[alpine sable]

nice girl in ur pfp ;)

[topaz scaffold]

[upper pebble]

🍊

[topaz scaffold]

Lol

[orchid dock]

isnt it = 50 rounds then for 10 teams?

6 teams 1 round = 15
10 teams 1 round = 25
10 teams 2 rounds = 50 ?

[woeful pulsar]

no it's not multiplying by 2.5

the number of games in a round robin tournament is not proportional to the number of teams

[orchid dock]

oh well

have to reread it then

[cloud rain]

x^2+x^2 is 2x^2 right?

[shrewd otter]

Yes.

[cloud rain]

ok thanks

[ivory otter]

Hi

[shrewd otter]

Hello.

[alpine sable]

hi

[ivory otter]

Is this correct?

Question related to vectors

[alpine sable]

yes

[ivory otter]

ok so one question

what does the dot product give me as a result?

[thorn tapir]

A scalar quantity

[ivory otter]

what is a scalar quantity

[shrewd otter]

An element of the field.

We define a vector space V over some field F (...)
The dot product is the mapping <., .>: V x V -> F.

[thorn tapir]

A quantity which does not have any specific direction - like mass, volume etc.

[shrewd otter]

I really don't like this explanation, but I can't think of a more intuitive one.

[ivory otter]

if i use the cross product i will get a quantity with a direction ?

and thats the difference between cross product and dot product?

[shrewd otter]

Yes, one specific direction.

[thorn tapir]

yes, and not only it has a direction, it follows all vector laws - so it will be a vector

And it has a special property

it will be perpendicular to both of the previous vectors

[ivory otter]

ok nice i understand it now, but whats the point of a scalar then?

[shrewd otter]

To stretch and shrink vectors.

[thorn tapir]

Yeah that's a good answer

all magnitudes of vectors are scalar

[shrewd otter]

Namely, one of the key operations of a vector space is multiplication by a scalar.

. : F x V -> V.

[ivory otter]

so the scalar quantity tells me how much i can shrink or increase a vector ?

[thorn tapir]

not always

[shrewd otter]

No, you can shrink and stretch it as much as you want.

Multiplying a vector by 2 makes it twice as long.

[thorn tapir]

yeah ^

[ivory otter]

ye

[shrewd otter]

The scalar product is useful because it allows us to define a notion of length.

Formally called a "norm".

[thorn tapir]

you can also find projection using the scalar product

[shrewd otter]

Namely, the length of some vector v, denoted ||v||, is defined as the square root of <v, v>.

[thorn tapir]

yes

[ivory otter]

length = magnitude?

[shrewd otter]

Yes.

[ivory otter]

ok

[thorn tapir]

v . v = |v|^2

[shrewd otter]

We also study unitary spaces where the scalar product is defined.

And unitary operators which preserve the scalar product.

Namely if U is a unitary operator, then <Uv, Uv> = <v, v>.

And ||Uv|| = ||v||.

[wooden pier]

I don't have the question with me so I'm typing it out
A sphere is placed in a inverted, hollow cone with depth d and radius r .
The sphere is pushed down so that it's sides touch the inside of the cone and it cannot be pushed down any further.
After that, the top of the sphere is in line with the base of the cone, such that a flat piece of cardboard can be put over the inverted cone and remain flat.
Find the radius of the sphere in terms of d and r .

[fading shadow]

Can someone help with 23 and 24

[dawn wraith]

Any idea on how to start with 23?

[slender marten]

The vertex just lie on x = 3, so consider the generic quadratic equation form once you completed the square on it.

[dawn wraith]

Right, since it’s a quadratic curve, the coefficient of x^2 must be negative.

[coral cosmos]

For this equation to be perfect sqaure, both the roots should be same... which indicate that the discrimant should be 0
therefore b^2 - 4ac = 0 [m comes out to be 5 then]

[dawn wraith]

++

[fading shadow]

What abt 23

[dawn wraith]

Consider some function
y = a(x-p)^2+k

In which p is given, it is 3

You have two points that exists on the graph

From there you’ll have a system of equations, with 2 variables.

a and k.

Got it @fading shadow ?

[fading shadow]

Think so ye

Wait what do I write after a(x+3)²+k

[dawn wraith]

You just substitute in the points that are given

And get a system of equations

[fading shadow]

Alright

[dawn wraith]

Tip:
k won’t change even after the substitutions, the probability you’ll find a first is very high.

[teal epoch]

Are we trying to find how many grams per $1 or how many dollars per 1g?

Or none of these?

[neat ruin]

never mind it was a weird question since there isn't really a question

[manic glade]

question about set theory, when asked to prove or disprove

is this appropriate or too handwavy?

and what would be a better way to go about it

[dry thunder]

https://tenor.com/view/ダンス-屁こき-おなら-ガス-fart-gif-15787704

[pseudo surge]

hi! how can i understand how much solutions has differential equation?

[noble sinew]

Too handwavy imo - try and show they are equivalent by definition and using properties as de morgans law and so on until you arrive at an equivalent statement

Can sometimes be easier to show LHS is a subset of RHS and RHS is a subset of LHS

[manic glade]

well i can get to on the left side

but not sure what to do with the AUC part

some people just showed that the left side of that is contained in the AUC part but i feel that at that point its just the thing with the chart but with extra steps

not sure how you can reduce it to be exactly as the right side

went like this

[noble sinew]

Could do, let a in be arbitary and use definition to show subset of RHS and then same reverse

[karmic dew]

Can someone explain z-scores and why to use them

[alpine sable]

z-scores are used to compare data-values from two different datasets with different means. comparing them directly is not as enlightening as comparing their standard deviations. in other words, it's sort of a normalization that makes it possible to compare data-values from two different datasets.

[karmic dew]

Gotcha, and the equation to solve them?

[alpine sable]

The z-score of a data-value $x$ is the number of standard deviations it is away from the mean. Given by $$z(x) = \frac{x - \bar{x}}{s_x}$$ where $x$ is the data-value, $\bar{x}$ is the mean, and $s_x$ is the standard deviation.

[ocean seal]

leadersheir

[karmic dew]

Gotcha thank you

[rich basin]

would anyone be able to help me at question 1?

[acoustic abyss]

anyone.

[undone dock]

$\frac{a^n}{a^m}=a^{n-m}$

[ocean seal]

K.

[alpine sable]

$\frac{ \cancel{(-1)} \cdot 7 \cdot \cancel{w} \cdot \cancel{y} \cdot \cancel{y} \cdot \cancel{y} \cdot y }{\cancel{(-1)} \cdot 8 \cdot \cancel{w} \cdot w \cdot w \cdot w \cdot w \cdot w \cdot \cancel{y} \cdot \cancel{y} \cdot \cancel{y}}$

[ocean seal]

leadersheir

[acoustic abyss]

yeo got it ty

[glass lichen]

dont just give solutions @alpine sable

[acoustic abyss]

7y/8w^5 right?

[glass lichen]

It does nothing to help

[alpine sable]

i thought it was junior high

[glass lichen]

??

what does the grade itself have anything to do with what I just said

[undone dock]

Yea

[acoustic abyss]

ok ty

[alpine sable]

i like.. gave da steps, basically

[glass lichen]

you didnt

[alpine sable]

👀

[glass lichen]

you posted 1 line of working with everything already done

ie the answer

and the steps*

[alpine sable]

wht do u suggest i should've posted instead?

[glass lichen]

K's response was better

reminding them of the needed exponent law

[alpine sable]

https://tenor.com/view/noted-note-the-office-gif-6207136

will keep dat in mind next time

thanks @glass lichen

[sharp epoch]

can someone help me find the y=mx+b form in #help-2

[upper pebble]

https://tenor.com/view/the-office-michael-scott-ryan-little-bitch-annoyed-gif-17430900

[alpine sable]

👀

[upper pebble]

the Helpers role should only be pinged 15 minutes after your question is unanswered #❓how-to-get-help

np

damn i feel like a moderator

[tawdry saffron]

Hi

[upper pebble]

hi

[tawdry saffron]

How do they go

Frim

This (ignore s)

To

In a cirkel

I don't understand how they split it

And how it's then put together

Again

Ping me when you answer

[noble sinew]

Because x^2-4x=(x-2)^2-4 you can replace x^2-4x with that

Same with the other thing

[noble sinew]

All that happens

[glass lichen]

they completed the square for both variables

[tawdry saffron]

Where does the -4 come from

Oh nvm

I get it ty

Dumb me

[glass lichen]

$x^2-4x=x^2-4x+4-4=(x-2)^2-4$

[ocean seal]

Mosh

[tawdry saffron]

Been 2 years since I had maths at a decent level and am learning it again to start physics in september

Still have a lot of work left

[native temple]

$$ 3n+1$$

[ocean seal]

Nerdy_Coder

[native temple]

Is this even?

If so prove it

[teal epoch]

uh- sometimes
3n can be either odd or even so the sum can be either even or odd as well

[arctic wren]

$3n + 1 = 2n + n + 1$ , 2n is always even, n+1 will be odd if n is even and will be even if n is odd and even + odd = odd , even + even = even

[native temple]

I got this from

oh

[ocean seal]

Guilhotina

[native temple]

I got this from $ 2n + 2n + 1 + 2n + 1 + 2n $ and then did this $ 6n + 2 = 2(3n + 1) $

[arctic wren]

Idk if this is correct, but it is what i got

[native temple]

$$ I got this from $ 2n + 2n + 1 + 2n + 1 + 2n $ and then did this $ 6n + 2 = 2(3n + 1) $ $$

[glass lichen]

3n+1 can equal 4 and 7 for valid n, so you cant conclude anything about 3n+1's parity

[native temple]

$$ I got this from $ 2n + 2n + 1 + 2n + 1 + 2n $ and then did this $ 6n + 2 = 2(3n + 1) $ $$

[arctic wren]

No text inside $

[glass lichen]

also 2+2+2+2 isnt 6

[teal epoch]

We have #latex-testing to test stuff if you already didn't know

[native temple]

no I need to make that latex

[glass lichen]

Is the question "Is 3n+1 even?"

if so, no, for the reasons mentioned.

[native temple]

oh

[teal epoch]

sometimes but in math terms no

[native temple]

I wondred of a odd + odd + even + even us even?

[glass lichen]

yeah, that;s literally what we've been saying

odd+odd is even, so yes

[native temple]

So I did that

oh

[glass lichen]

$o+o+e+e=e$ loosely speaking

[ocean seal]

Mosh

[arctic wren]

So i cant conclude that 3n +1 is even or odd i can just say that it will be odd for even numbers and even for odd number?

[glass lichen]

$(2a+1)+(2b+1)+2c+2d=2(a+b+c+d+1) {a,b,c,d\in\mathbb{Z}}$

[native temple]

ahhh

[ocean seal]

Mosh

[native temple]

I see

[glass lichen]

You cant say "3n+1 has this parity" full stop

[native temple]

so 2(3n + 1) = even

?

[glass lichen]

yes

cause it's 2*integer

[native temple]

Ou

[glass lichen]

$n\in\mathbb{Z}\implies 3n+1\in\mathbb{Z}$

[ocean seal]

Mosh

[native temple]

e?

[glass lichen]

\in

[native temple]

oh

[glass lichen]

"n is an integer implies 3n+1 is an integer"

[native temple]

ah

[glass lichen]

You can talk about parity in that sense, but generally speaking we tend to mean for all n instead of by cases

"2n+1 is odd" is a true statement for all n in Z

$2n+1$ is odd $\forall n\in\mathbb{Z}$

[ocean seal]

Mosh

[native temple]

ahh

another question

[arctic wren]

aaaaa ok

[native temple]

Why is the binomial theorim = The Binomial Distribution formula?

I tried to type it in texit but the cheatsheet didn’t show mw how....

sigma or choose works on texit

[glass lichen]

\sum_{}^{}
\binom{}{}

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

[ocean seal]

Mosh

[thorn tapir]

Yeah

[native temple]

Why is the binomial theorim $(a+b)^n=\sum_{i=0}^n\binom{n}{i}a^ib^{n-i}$ = to $ P(K successes) = \binom{n}{i}a^nb^{n-i}$

[ocean seal]

Nerdy_Coder

[native temple]

why?

[glass lichen]

what's K?

[native temple]

been trying to type that

Umm i

Why is the binomial theorim $(a+b)^n=\sum_{i=0}^n\binom{n}{i}a^ib^{n-i}$ = to $ P(i successes) = \binom{n}{i}a^nb^{n-i}$

[ocean seal]

Nerdy_Coder

[native temple]

sigh

[glass lichen]

ok well let's do a simple example, I'll flip a coin 3 times and make the random variable # of heads

if I flip a coin 3 times i get $2^3$ possible outcomes in my sample space $$\Omega = {TTT, TTH, THT, HTT, HHT, HTH, THH, HHH}$$

[ocean seal]

Mosh

[glass lichen]

So we know that I can either get 0,1,2 or 3 from my random variable, how many options in Omega give them?

[native temple]

Omega?

[glass lichen]

well X=0 means TTT
X=1 means TTH, THT, and HTT
X=2 means HHT, HTH, and THH
X=3 means HHH

Omega is the sample space

like I defined

[native temple]

oh

[thorn tapir]

The sample space is named Omega

yeah

[native temple]

oh all possible outcomes

uhhh

[glass lichen]

so the values of the random variable follow 1 3 3 1

[native temple]

let’s see that)s 1/6 doe any outcome

[glass lichen]

which is a row of Pascal's triangle

which is where the binomial co-efficients arise

[thorn tapir]

and if you do the probabilities

[native temple]

oh

[thorn tapir]

same thing happens there too

[native temple]

isn)t the probability of getting any one of those rows 1/8

[thorn tapir]

Basically it's a case of experimental verification

[native temple]

as 1/2^3 = 1/8

[glass lichen]

$(a+b)^n=\sum_{i=0}^n\binom{n}{i}a^ib^{n-i} \ a=p, b=1-p \implies 1=\sum_{i=0}^n\binom{n}{i}p^i(1-p)^{n-i}, p\neq 0$

[thorn tapir]

you mean at X = 3?

or X = 0?

[native temple]

no to get any one of those possible outcomes

[thorn tapir]

nah the X = 1 and X = 2 would have a different probablity

they're more probable

[native temple]

carp they are

[thorn tapir]

Look at mosh's explanation for why it is even more correlatable

"Sum of all probabilities is 1"

so that also gives another evidence

because we did derive it from the distribution

[ocean seal]

Mosh

[native temple]

Not if x=3 is HHH

unless x = 2 is 3 in this case....

[thorn tapir]

no wait Mosh means probability

HHH is only one case

no matter how you toss, HHH can happen in only one way

[native temple]

probility of getting ttt?

[glass lichen]

X = # of heads in my example, so the only way you get X=3 means to get HHH

[native temple]

is 1/8

[thorn tapir]

yeah ^

[native temple]

oh to find probability of that is cominations

oh

where does the probability of failure come from?

the other ones

like probability of x = 1

do you have to find probability of x = anything else and raise that to 3-x?

[forest wasp]

I'm trying to find the coordinates of an incenter of a triangle and I read this but I'm confused by "each side of the triangle can be translated by the inradius". How am I meant to translate an entire side by an inradius?

Nvm I think I got it now

[idle sapphire]

i need help

[gray isle]

where are you stuck

[agile berry]

Mm

Are these recent ones from like 11th or 12th grade?

[river hearth]

I know hole is x=-1 but need the rest explained

[whole prairie]

What steps would one take to solve this?

[shrewd otter]

Factor out an x^2 from the numerator.

[whole prairie]

So it would then be x^2(4x-5) on top?

[shrewd otter]

Yes.

Try to see why that is useful.

[whole prairie]

Okay thank you

[crude hazel]

can someone explain how to simplify step by step: 1 - 2sin^2(2x)

[whole prairie]

The two x^2 would cancel making it unsolvable right?

[shrewd otter]

No, it would make it very solvable.

[gray isle]

why would that make it unsolvable?

[shrewd otter]

I believe this is an identity.

[whole prairie]

Oh wait I see now

[crude hazel]

which indentity is it, I'm so confused

[shrewd otter]

I don't know, it just looks familiar.

[gray isle]

||cosine||

[shrewd otter]

Well, right, you could factor this expression.

[whole prairie]

Like this then?

[gray isle]

,rotate

[gray isle]

missing dx

[shrewd otter]

But essentially, yes.

[gray isle]

(and you should have no issues integrating this now)

[whole prairie]

What would be the dx in this situation?

[gray isle]

dx is dx

[whole prairie]

From what my prof is showing it’s dx=du/2x is the general formula so then what would my du be?

[gray isle]

(to indicate that you're integrating with respect to x)

[shrewd otter]

You didn't make a substitution.

And there is no general formula.

[whole prairie]

Ohhhh yeah that’s right

[shrewd otter]

So it's just dx.

[gray isle]

if you made a sub, du would depend on what u was

[whole prairie]

Okay thank you

[wanton garden]

[2x^2 - 5x]2 1 = (2x4 - 10) - (-3) = 1 ig?

[whole prairie]

That’s what I got

[lethal ore]

,rotate

[ocean seal]

Couldn't find an attached image in the last 10 messages.

Jul 14, 2021, 3:11 PM

[river hearth]

what would this be?

"write a rational function given the characteristics"

[bitter yoke]

this function satisfies your conditions:
f(x) = (x-5)/[(x-2)(x-5)]

[river hearth]

/ is divided by correct?

[bitter yoke]

yes

[river hearth]

ok thank you

[bitter yoke]

np :)

[river hearth]

I actually have 1 last one do you know what this would be by chance?

[bitter yoke]

[1/(x-3)]+3

[river hearth]

Thanks once again :)

[bitter yoke]

np once again xd

[alpine sable]

How do i calculate the natural logarithm of i?

or what tools should one use

[rigid smelt]

Well try to convert i into e^(z)

Where z is some complex number

Also mind that if you choose ln to be principal-value, it should only output 1 value, whereas the multi-value will output a periodic result

[alpine sable]

ooo

alr alr thanks

i think i have to re learn everything about complex numbers lol

[rigid smelt]

What have you tried?

[alpine sable]

when i take the second derivative of a function with a chain, why does the chain not turn into 1? and instead I get a second chain that multiplies by the the first chain...

[rigid smelt]

Channel is busy, please move

[river hearth]

I dont know how to try its a 5 page homework assignment and this is the last question Im stuck on I havent done this in 3 years so im kind of blanking

could you explain how to do these?

[rigid smelt]

Look at the x axis, every values that has an according y value is in the domain

[alpine sable]

ok....?

[river hearth]

y=3?

[rigid smelt]

Wdym y=3

[river hearth]

I am very confused

[rigid smelt]

Basically you just need to look for x values that doesnt have its y values

For example, at x=2, imagine a straight vertical line going thru x=2

Does that line ever meet the curve?

[river hearth]

yes

[rigid smelt]

Where?

[river hearth]

near 2.3

[rigid smelt]

I dont think so

[river hearth]

oh

so domain is x=2?

[rigid smelt]

Not very straight, but thatll do it

Does it meet the curve?

[river hearth]

no

[rigid smelt]

Yes

So that means x=2 is not in the domain

Because where there is an input there needs to be an output

But x=2 does not have any output value

Can you find other values like this?

[river hearth]

only for x?

[rigid smelt]

Yes

Look at the x axis

Which x value does not have an output

[river hearth]

0 doesn't touch

[shrewd otter]

Isn't that just 1 / (x - 2)?

[rigid smelt]

Are you sure?

Draw a line going thru x=0

Does it meet the curve?

[river hearth]

no

[rigid smelt]

...

[river hearth]

...

nevermind

Ill ask the teacher later

Im lost

[noble sinew]

seems like you are confused on what is the x-axis and what is the y-axis

[river hearth]

isnt that the y line

[shrewd otter]

It is.

You only care about lines.

Not points.

That's what asimptotes are.

[rigid smelt]

It is the line that goe sthru x=0

Ok, since i gtg, take a look at x=3

Imagine a line going thru x=3

Does it meet the curve?

Verify it with others

[twin pine]

The domain are all the values that x can take

[idle sapphire]

i need help

i dont understand how to do this

[shrewd otter]

This chat is clearly occupied...

[river hearth]

no Im done

[idle sapphire]

so can someone help me?

[noble sinew]

use formula for interest and then solve an equation

namely if she invest x in saving account then she will invest the rest in a bond, so (3800-x)

set that equal to 180 and solve

[bitter yoke]

yes, except its not defined at x = 5 which is what they wanted

[sterile widget]

myt be easy for u guys but bro i am not being able to understand this at all

[glossy tendon]

Do you know double angle something?

[stray jewel]

A biologist is studying the growth of a particular species of algae. She writes the following equation to show the radius of the algae, f(d), in mm, after d days:

f(d) = 11(1.01)d

Part A: When the biologist concluded her study, the radius of the algae was approximately 11.79 mm. What is a reasonable domain to plot the growth function? (4 points)

Part B: What does the y-intercept of the graph of the function f(d) represent? (2 points)

Part C: What is the average rate of change of the function f(d) from d = 2 to d = 7, and what does it represent? (4 points)

how would one do this?

<@&286206848099549185>

[noble sinew]

step 1 read the rules

[stray jewel]

and?

[noble sinew]

then you will notice you have broken them and maybe fix it?

[stray jewel]

this isnt an exam

[noble sinew]

1 rule is find an empty channel (not one having a msg 1 min before you post)

another rule is not ping helpers

[sterile widget]

Nope

[glossy tendon]

check the picture I sent

that should help you get x

[glossy tendon]

and for w

TP and TQ is tangent to the circle, that means TP is perpendicular to OP, same goes for TQ. And do you know what angle does it make?

[alpine sable]

What would be the most overkill way to find the area of a square?

The most unnecessarily hard and complex way to find it

If its possible to make that a complex thing

[agile compass]

@alpine sable https://youtu.be/Y2cBpBLJlfU

[alpine sable]

oh shit its 16 minutes long lmfaoo

ty ty

[hollow merlin]

how to do this

[shrewd otter]

Have you heard of Cramer's rules?

[hollow merlin]

nop

[alpine sable]

They must be parallel for no solution means same coefficient for x and y

[hollow merlin]

ye

same slope ig then

[alpine sable]

Yeah that's it slope of 2nd equation is 4/5

And first one is k/3

[hollow merlin]

oh u just rearrange for y =?

[alpine sable]

Yeah

[hollow merlin]

o bruh

i thought it was harder

[alpine sable]

(lol)

10+3?

[small holly]

can someone help me with b and c

idk why its like that

[alpine sable]

10+3? Pls :c

[shrewd otter]

You don't know why what is like what?

[small holly]

13

how is the y intercept 12

[alpine sable]

Entre + me la mamás + me crece jsjsjsj

[small holly]

i dont get how they got it

[shrewd otter]

It says so, the y intercept is when x = 0.

You just plug in x = 0 and find y.

[small holly]

oh

why did they say when x = 0

[shrewd otter]

Which x value does the y axis go through?

[small holly]

0

ohhh

and thats what they did with c

[shrewd otter]

Yes.

[small holly]

alright ty

[shrewd otter]

Square both sides.

[alpine sable]

ok

[small holly]

1 question, for c, why did they square root 4?

[alpine sable]

cause they wanted x-1

[alpine sable]

thankss

[small holly]

oh alright ty

[shrewd otter]

Because the right side is a square.

[small holly]

and where did the -16 go

[alpine sable]

wdym

To get (x-1)^2 they had to get -4 to the LHS

-16/-4=4

[strong furnace]

@alpine sable bro

[alpine sable]

yeah

[shrewd otter]

They divided by -4.

Basically they're doing everything to isolate x.

[small holly]

ohh alright thanks

[shrewd otter]

The angle is 45 degrees.

[winter salmon]

im struggling to find the domain

i tried x>-3/2 and x>1/3 but it didnt work

[shrewd otter]

There's nothing to try, this is a fully deterministic process.

Divide both sides by the right side of the inequality.

[brave geyser]

thanks but i don't understand

[winter salmon]

i get 1/3 < x < 2/3

[glossy tendon]

$4^{\log_4{(3x-1)}}<4^{\log_4{(2x+3)}} \implies 3x-1<2x+3$

[ocean seal]

robin

[shrewd otter]

@winter salmonFigure it out from here.

[winter salmon]

[brave geyser]

@shrewd otterc

[brave geyser]

could you explain that, please

[shrewd otter]

No idea tbh.

I don't really understand the problem.

[raw nexus]

could someone help me with this please 🙂

[shrewd otter]

Find the first derivative.

Find its roots.

Those are your turning x values.

For y, just find f(x).

[raw nexus]

(-3x^2) + (10x) + 0 ?

@shrewd otter

[shrewd otter]

Okay, that's the derivative.

[raw nexus]

how would i find its roots

@shrewd otter

-6x + 10

[brave geyser]

i found right now, it's my answer. thanks dude

[raw nexus]

1.666

8.333

@shrewd otter is that right for min and max

[shrewd otter]

It's a quadratic equation.

[raw nexus]

im confused

[shrewd otter]

Just use the quadratic formula.

And find solutions.

[raw nexus]

coul u give me a hand

[alpine sable]

I dont know the exact English geometrical terms, angles on the left and right are equal to each other, and when you give the equal angles letters it becomes
2x+2y=90
x+y=45
a=x+y
a=45

[blissful tinsel]

Can someone explain to me how to determine the order of zeros?

[shrewd otter]

?

[blissful tinsel]

For example why does $\frac{1}{z^2-1}$ have simple poles at z_0 = 1 and z_1 = -1

[ocean seal]

Julian42
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[shrewd otter]

Because 1^2 - 1 = 0.

And (-1)^2 - 1 = 0.

[blissful tinsel]

ok but $\frac{1}{(z-1)^2}$ has order 2 poles

[ocean seal]

Julian42

[shrewd otter]

Does it now?

[blissful tinsel]

it does or am I confused

[shrewd otter]

Seems like it has just 1.

,w poles of 1 / (z - 1)^2

[ocean seal]

Results provided by WolframAlpha

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Requested by Hurubon#6899

[shrewd otter]

See, just one pole of order 2.

[blissful tinsel]

yeah thats what i meant

the order of the pole is 2

but for

,w poles of 1 / (z^2 - 1)

[ocean seal]

Results provided by WolframAlpha

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

Requested by Julian42#2130

[blissful tinsel]

its only two simple poles

[velvet pelican]

does it have something to do with the multiplicity of the root?

z^2 - 1 = (z+1)(z-1) so roots are z=+/- 1 with multiplicity 1

(z-1)^2 = 0 has root z=1 with multiplicity 2

[shrewd otter]

Yep.

[blissful tinsel]

ahh ok now it makes sense

thank you 🙂

[strong citrus]

$(n + 2) + [3n+2 - nx]/[x - 3] = [2x - (n + 3)]/[x - 3]$

[ocean seal]

Aadil Gillani

[brave geyser]

@alpine sable thanks <2

[warped phoenix]

abs(12 - 3x) - 4 = 11

12 - 3x = 15, 12 - 3x = -15

and i solved for x and got x = 1, x = 9

but that was none of the options? so im curious what i did wrong

[glass lichen]

$\abs{12-3x}=15 \ 12-3x=\pm 15$

[ocean seal]

Mosh

[warped phoenix]

right

ohhhhhhhhhhhh wait i just made a stupid mistake

🤦‍♂️

nvm, sorry

[winter salmon]

im pretty sure its x=-1,x=9

[warped phoenix]

yeahhh i forgot to divide by -3 and instead did 3 for some reason, ty!

btw, should i be checking for extraneous solutions with absolute value equations? is that a rule of thumb for all equations or only certain ones

[glass lichen]

you generally check for extraneous when there's a restriction or manipulation that can introduce solutions

[winter salmon]

im confused why the answer isn't x=5;x=1 when i simplified the left side i got (x-3)^2 = 4

[topaz wharf]

Can someone quickly help me with this, im confused with the first 3

[winter salmon]

i can barely see the questions could you take a closer picture

[topaz wharf]

I'll just write it out since I'm helping a friend but its

Use ^x^ = x² + 6x + 9

What is the value of ^2^

[winter salmon]

just plug in 2 to the equation

and solve

2^2 + 6(2) + 9

4 + 12 + 9

25

so for #4 the answer would be C

do the same thing for #5

and then for #6 plug in 64 on the left side

64 = x^2 +6x +9

[topaz wharf]

Wait so for 5

I did -9 plus -18 plus -27

[winter salmon]

you don't multiply 3 to 9 at the end and it would be +9 since the exponent is a even number and the -3 is in parentheses

[topaz wharf]

So it would be 0

[winter salmon]

ye

have you or your friend covered the quadratic formula? @topaz wharf

cause you need that for #6

[inner sentinel]

can u help me im confused on this lesson with discrete math @winter salmon

[topaz wharf]

Notnyet

[winter salmon]

i don't know what discrete math is sorry

[topaz wharf]

Could you show me how to work it out since I'm a bit confused

[winter salmon]

so what you do first to get from to the picture i showed above is pretty simple actually

so you first switch sides

and then subtract 64 from both sides

you would get x^2 + 6x - 55 = 0

which is similar to the picture above

then what you do is apply the quadratic formula

you find out what a/b/c are

in this case a = 1 b = 6 and c=-55

then you just plug it in the bottom formula

@topaz wharf do you understand everything so far?

[topaz wharf]

Yeah im getting it

[winter salmon]

lets solve this part first

what would you do first @topaz wharf theres multipple things you could do

[topaz wharf]

I would do (6²-4) x (1 x (-55))

[winter salmon]

o i didn't think of that

so we know that 6^2 is 36 so we can just solve the left side easily and get 32

wait

[glass lichen]

what??

no

[winter salmon]

that

wouldnt

wait

[wary stream]

Apply proper order of operations, PEMDAS/BEMDAS

[glass lichen]

you cant just change the question

[winter salmon]

what i would do instead is multiply -4 by 1 which is just -4

since -(-x) = x

-4 * -55 would be 220

then solve 6^2 which is 36

then add 220 and 36 which is 256

sqrt256 is sqrt16^2 and then you can just cancel the sqrt and the exponent

[winter salmon]

then from here you have -6 +- 16 / 2 * 1

[wary stream]

Also, another thing to point out, I understand that you're helping someone, but technically, you're not supposed to show step by step on how to solve the problem. Give the person tips on how to solve it, then let the person try it out by themselves, and if they get stuck, see what they are stuck on and correct them from there

[winter salmon]

[topaz wharf]

Oh I asked him for the step by step since I was quite confused

[wary stream]

Well, what should have been done is, (s)he explained that you set that equation equal to 64, then applied quadratic formula, then let you try it out, and if you got stuck, ask for more assistance instead of showing all the steps

[winter salmon]

you then would separate the solutions and get

solve both of them and tell me what you get

[topaz wharf]

First one is 5 and second one is -11

[winter salmon]

correct and based on your packet here only 5 is shown so B would be the right answer

[topaz wharf]

Oh

Wait yeah that makes sense

[wary stream]

If you look at #❓how-to-get-help, number 7, in the list, it does state "explain and elaborate instead of giving the answer", and that also indirectly includes showing the full steps

[winter salmon]

i literally showed them how to do it with full steps when i literally could've just said the answer is B

[wary stream]

I'm saying that you should have pointed them in the proper direction instead of showing them how to do it

[hushed rune]

i hv a question on this

here is my work and answer

teacher says its wrong, but i dont think i made a mistake can someone help pls and ty

[warped phoenix]

In a function, why does compressing it make it wider? shouldn't it be making it narrower, due to "compression"? and vice versa with stretching

[hushed rune]

i had the same problem but if thats how ur teacher or textbook explained it then just try to remember it what they mean is compressing vertically which makes it wider and stretching vertically which makes it taller. your thinking horizontally which makes more sense in my opinion

[winter salmon]

since you only get money if you land on heads whats the probability you land on heads if you toss 1 coin

[hushed rune]

1/2

theres 32 outcomes

and only 1 is all heads and only 1 is all tails

[winter salmon]

it says whats the expected payoff

so it basically is saying whatever outcome is the highest probability is the expected payoff

[hushed rune]

oh for us its like the expected gain or loss on average from it

like this

[noble sinew]

yes normal definition

but 30/32 gives 1 dollar

and 2/32 loses 20 dollars

so expected value is 30/32 * 1 + 2/32 * -20

[hushed rune]

but in the second sentence doesnt it say $1 for each head

key word each?

[noble sinew]

oh

[winter salmon]

yea and only heads tails don't give money but you dont lose money either

[hushed rune]

thats why i multiplied by 4 3 2 and 1 for the different amounts of heads

[noble sinew]

yes looks good then

[hushed rune]

i think my teacher did that

but i wasnt sure if im making a mistake reading the question

okayy thanks yall

[winter salmon]

im confused why the answer isn't x=5;x=1 i simplified the left side and got (x-3)^2 = 4 which is x-3 = +- 2

[noble sinew]

how did you simplify it like that

[winter salmon]

well

sqrt of x is x^0.5

and theres a formula where a^loga(b) is equal to whatever b is

[noble sinew]

what is that even an exponent

looks like x * log...

[winter salmon]

its not x * log

its exponent

[noble sinew]

the answer is x=5 then

[winter salmon]

thanks :) why would x=1 not work?

OHHHHHHHHHHHHHHHHH

nvm

[noble sinew]

domain of log

[winter salmon]

yep

[noble sinew]

and also sqrt, and log base

[alpine sable]

can anyone help on this

[warped phoenix]

Can someone explain this? I completely understand why the domain would be (-7, 7] but before the range was shown I guessed it would be (-4, 4], i dont get how it's (-4, -2), [-1, 4]?

the lowest a function goes for the range is (-4, and the highest is 4]

[glass lichen]

range of a function is allowed y values

[opal pier]

so every whole number is the sum of two prime numbers

right

?

[velvet citrus]

Natsano has at most $65,000 to invest in the common stocks of two companies. He estimates that an investment in Company A will yield a return of 10%, whereas an investment in Company B, which he feels is a riskier investment, will yield a return of 20%. If he decides that his investment in the stocks of Company A is to exceed his investment in the stocks of Company B by at least $20,000, determine how much he should invest in the stocks of each company to maximize the return on his investment.

anyone know how to do this?

[merry coral]

Well, this guy should be looking at the Sharpe ratio, fundamentals, and technical analysis.

but for this purposes of this question

we know that company B is better

so we want as much money in it as a possible

[merry coral]

.

so follow the rules of the question

and see what you come up with

[glacial hedge]

How do I do this problem?

<@&286206848099549185>

[void yoke]

Um, what is your opinion?

[glacial hedge]

i am not sure

how do i aproach this

[void yoke]

Okay. Er … Do you understand all the mathy words in the problem?

[glacial hedge]

yes

e1 is like the first column in the identity matrix

linear transformation is Ax and its asking to solve for A

[fading rover]

𝑥𝑑𝑥=(7−2𝑡)𝑑𝑡
why is this non-linear
all terms are to the power of one

differential equation

[glacial hedge]

@fading rover channel occupied

[void yoke]

Hi. You are interrupting someone else’s problem 🙂

[fading rover]

Sorry, didnt see any activity for a couple of minutes.

[glacial hedge]

@void yoke how would you do the problem?

[glass lichen]

How do you compute the matrix representation of any linear transformation?

[glacial hedge]

uhhhh, not quite clear on that

[glass lichen]

if $T: V\to W$ and ${v_1,...,v_n}$ is a basis of V and ${w_1,...,w_m}$ is a basis of W, then the matrix representation of T wrt those 2 basis is found by mapping each basis vector of V by T, then taking the scalars of $T[v_i]$'s linear combination representation in the W basis, making that the ith column of the matrix

[ocean seal]

Mosh

[glacial hedge]

is $v_i$ the ith column of v?

[ocean seal]

Elonmosqito96

[glass lichen]

ie if $T[v_i]=a_1w_1+...+a_mw_m$ then the ith column of the matrix will be $\begin{bmatrix}a_1 \ \vdots \ a_m\end{bmatrix}$

[ocean seal]

Mosh

[glass lichen]

v_i is the ith basis vector for V

[glacial hedge]

Uh could you just walk me through the problem? that chunk of math doesn't make that much sense right now

[glass lichen]

so in this example, the 1st basis vector of R^2 maps to e_1+e_2+3e_3

right?

[glacial hedge]

mhm

[glass lichen]

ill take that as a yes.. since that info was given..

[glacial hedge]

yes xD

[glass lichen]

so what are the scalars of the linear combination for the R^3 basis?

[1 1 3] right?

[glacial hedge]

wait wha?

oh

wait what?

[glass lichen]

$T[e_1]=1e_1+1e_2+3e_3$

[ocean seal]

Mosh

[glacial hedge]

im a little confused

[glass lichen]

about what?

[glacial hedge]

we arent putting the basis vector into t?

[glass lichen]

we are

[glacial hedge]

wait doesnt e_1 represent

[glass lichen]

the basis of $\mathbb{R}^2$ is ${e_1,e_2}$

[ocean seal]

Mosh

[glacial hedge]

?

[glass lichen]

that's e_1 in R^3

[glacial hedge]

yes and isnt that what we are pugging into t?

[glass lichen]

$e_1=\begin{bmatrix}1\0\end{bmatrix}$ in $\mathbb{R}^2$

[ocean seal]

Mosh

[glacial hedge]

oh 😆 we are in r^2

[glass lichen]

yes you plug in a R^2 and get out an R^3

[glacial hedge]

so how do we get this>?

[glass lichen]

well you read it off, what's the scalar in front of e_1 in the output?

[glacial hedge]

1

[glass lichen]

and e_2?

[glacial hedge]

1

[glass lichen]

and e_3?

[glacial hedge]

3

[glass lichen]

right, so those are the scalars of the linear combination

[glacial hedge]

yes

[glass lichen]

and we take those as the entries of the column for the input basis vector. We inputted the 1st basis vector, so those scalars fill the 1st column of the matrix

[glacial hedge]

im a little confused why this works

OH

wait i see

since we are inputting a basis vector, the other terms in the linear combination are 0

[glass lichen]

not quite

if we input any vector from the input space, we will get a vector from the output space, correct?

[glacial hedge]

yes

[glass lichen]

now the output space has a basis that we're working with, and since bases span the space, there is a unique representation of any vector in the output space relative to the basis (definition of basis)

so I can write T[v] as a linear combination of basis vectors in the output space, for any v in the input space

[glacial hedge]

yes

[glass lichen]

Now we define something called the co-ordinate vector which is simply in that unique linear combination, write the scalars as a [blah blah blah] vector, so all the matrix is is the collection of these co-ordinate vectors

[glacial hedge]

mhm

[glass lichen]

likewise you could imagine multiplying the matrix representation by say [1,0] and quickly realize that multiplication will just return the 1st column

[glacial hedge]

yes

[glass lichen]

so loosely that's why it works

[glacial hedge]

sorta what i meant 🙂 I probably used the wrong words tho

ty

[glass lichen]

Yeah, so the first column of the matrix will be [1,1,3] for the reasons said

[glacial hedge]

Ok I can do the rest ty!!

[glass lichen]

yeah you get an answer of ||C||

[alpine sable]

Can someone help with this

[late bridge]

uh.. is that a test?

[alpine sable]

no

it's homework

[alpine sable]

I don't think you get 6 chances to get a test question right lol

[karmic dew]

Any suggestions on improving math act score?

[glass lichen]

study

practice questions

[karmic dew]

Specific subjects?

[glass lichen]

well depends on the content of the ACT

and whether it's a contest style exam or standardized curriculum exam

[karmic dew]

Standardized

[glass lichen]

Then just look at the curriculum / previous ACTs

if you see something you cant solve, try finding a simpler variation

[karmic dew]

Ok, thx, what about science?

[glass lichen]

similar thing

[karmic dew]

Is there a strat involved

Cuz u dont get much time

[glass lichen]

Ill be honest no clue exactly what the ACT is, but generally just understanding what to use when is the trick

(and of course how to do it)

[karmic dew]

K thx

[left echo]

<@&286206848099549185>

[thorn tapir]

The graph is uh slightly unclear

By that I mean

in between 0 and -5

how is it divided

Never mind I think I can guess it

You know what are asymptotes?

[left echo]

SORRY i should deleted it i already got the answer for that

[thorn tapir]

oh lol

[left echo]

thanks tho

[thorn tapir]

👍

[torpid lagoon]

oiii

hi

got 291 as the answer for this

[thorn tapir]

are you sure $\frac{1\pi}{4}$ is not a typo

[ocean seal]

rikusp2002

[thorn tapir]

I'm assuming it's correct and proceeding

[torpid lagoon]

whats a typo?

[ionic jewel]

$S = r\theta$

[ocean seal]

bunny

[ionic jewel]

,w 3.7pi/4 meters to cm

[ocean seal]

Results provided by WolframAlpha

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Upgrade to WolframAlpha Pro!

Requested by 兔子#6562

[ionic jewel]

yep 291 is right given that its not a typo

[torpid lagoon]

ye so im correct

[ionic jewel]

yes

[thorn tapir]

i meant - wrongly typing something else than what was intended

like "gost" instead of "gist"

[ionic jewel]

1pi/4 = pi/4 so it seems odd for the 1 to be there

so rikusp thought it might have been meant to be a different number

[thorn tapir]

i thought it was 11pi/4 but then again there comes the question of minor and major arc

[torpid lagoon]

ty 👍

[torpid lagoon]

oh

[gaunt magnet]

got 2.8 as a radian for this question

correct?

[thorn tapir]

damn, this needs calculator

[ionic jewel]

sounds about right though

[thorn tapir]

but yeah, it should be in 2nd quadrant

[ionic jewel]

,w tan(x) = -0.35553, sin(x) = 0.354988

[thorn tapir]

so 2.8 isn't wrong

LMAO

[ionic jewel]

[ocean seal]

Results provided by WolframAlpha

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Requested by 兔子#6562

[thorn tapir]

...wait a minute

[ionic jewel]

fine

its not exact decimals

[thorn tapir]

nah wait

[ionic jewel]

,w tan(x) = -0.35553

[ocean seal]

Results provided by WolframAlpha

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Requested by 兔子#6562

[thorn tapir]

for real.

i think

just get cos(x) and solve it

no i know

wait]

[ionic jewel]

anyways its pi - 0.pi lol

[thorn tapir]

,w arcsin(0.334988)

[ocean seal]

Results provided by WolframAlpha

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Upgrade to WolframAlpha Pro!

Requested by rikusp2002#9261

[ionic jewel]

,w pi - .34159

[thorn tapir]

now

add

[ocean seal]

Results provided by WolframAlpha

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Upgrade to WolframAlpha Pro!

Requested by 兔子#6562

[thorn tapir]

pi/2 to it

[ionic jewel]

yep

its 2.8

the answer is $\pi-0.\pi$ this is very legit math

[ocean seal]

bunny

[thorn tapir]

or yes pi - theta works too

[gaunt magnet]

would the answer be 2.8
,w π-arcsin(0.334988) in radians

,w π-arcsin(0.334988) in radians

[ocean seal]

Results provided by WolframAlpha

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Requested by Usman#0988

[tacit mortar]

hi

this question

for this question u need to sketch the angles

would this be correct

[fervent island]

reflecting the triangle over the y axis would give the same result, so there exists 2 angles theta that satisfy $\sin \theta = -0.5$

[ocean seal]

Green4Applez

[tacit mortar]

so its correct right?

[fervent island]

Yes, but you need to specify the values of theta that satisfy the equation as well

[tacit mortar]

ye so
Theta is -30
sin of (-theta) = -sin(theta)
So we know that from a 30-60-90 triangle, for sin to be 1/2, theta has to be 30degrees.

sin of (-30) = -1/2
If you want to verify, type this into your calculator:

sin^-1(-0.5)
you should get -30degrees or -1/6pi radians

[fervent island]

well, keep in mind the range that theta is in given by the problem

it says that theta is between 0 and 2pi

[tacit mortar]

yea the 30 degree in the picture is -30

[fervent island]

ik

but the value for the given range of theta would be 330 deg

or 11pi/6

and also 7pi/6 also gives the same result

which is found by reflecting the triangle u drew over the y-axis

[tacit mortar]

so mine is also good?
so overall mine would be considered correct

[fervent island]

it's correct in general but it's not correct in terms of what the problem is asking

[tacit mortar]

what am i doing wrong in terms of what the problem is asking?

[fervent island]

you didn't give theta in the range the problem asked u for

additionally, u left out an angle that also works

[tacit mortar]

where should i put that

in the picture

[fervent island]

just reflect the already existing triangle over the y-axis

to have 2 triangles

[tacit mortar]

i see just make another triangle?

[fervent island]

correct

[tacit mortar]

wait 1 min ill be right back

[fervent island]

ok

[tacit mortar]

so like this just had to draw 1 more triangle on it (ill make it neater later

[fervent island]

no

one moment i'll draw it out

[tacit mortar]

ok ty

[tacit mortar]

what does this part say?

[fervent island]

60 degrees

sorry for it being a bit messy

[tacit mortar]

np tysm and this is 11pie/6 right and 7 pie/6

[fervent island]

yes

does this make more sense now?

[tacit mortar]

yes

[fervent island]

Awesome!

[harsh solstice]

Three times five more than the positive difference between ninety and eighty-four. what will this be as a mathematical statement?

[late vapor]

34 = 7k what is k?

[harsh solstice]

<@&286206848099549185> its been a bit above 15 mins so according to #❓how-to-get-help i'm allowed to ping so can any1 help?

like also explaining it would be good so i can learn to not forget next time

rip

pls help

[vapid edge]

Please help me with no.2

[thorn kindle]

3*(5+(90-84))

[harsh solstice]

oo ok but is their an explanation to it?

this is 7th standard maths btw so ye

i'm supposed to be in 8th (i'm 13 not underage)

[thorn kindle]

Three(Five+(difference between ninety and eightyfour))

[harsh solstice]

OHH OK

[thorn kindle]

There is not much to it

[harsh solstice]

oki

[thorn kindle]

Just learn how to read lmao

[harsh solstice]

thx

[harsh solstice]

ok

[thorn kindle]

👍🏻

Gg

[strange beacon]

Helpeee me

How to get P and Q

[harsh solstice]

from what i know u need to decipher them using oposite angles

[twin haven]

you can use properites

of cyclic

isosceles triangle

use these properties and then you can solve

[thorn tapir]

try to divide both sides of the equation by 7, you'll get k = 34/7

[mellow frigate]

why cant we solve root x = -2. wouldnt it be 4. I mean we always take +- value of any root right? so theoretically root of 4 can give -2 also....so why is root x = -2 undefined? Is there something i am missing?

[thorn tapir]

It's not undefined.

But

if you say

$f(x) = \sqrt{x}$

[ocean seal]

rikusp2002

[thorn tapir]

For this, to be a function - you must ignore the negative values.

for this function, you can't have a value of -2.

Why? Let's say you include them.

so, by that

f(4) = 2

and f(4) = -2

This becomes a one to many mapping.

And whatever happens to the world, an one-to-many mapping can never be a function.

But if you say sqrt(x) = -2, you can solve it and get x = 4 - that's clearly correct.

[alpine sable]

may i get some help please

[thorn tapir]

have you studied half angle formulas?

or even, multiple angles?

[alpine sable]

no but should i?

[thorn tapir]

definitely.

Which grade are you in?

[alpine sable]

going into 10th soon

[thorn tapir]

Oh, most countries make students learn this in around 10-11

I can just state the formula for you but maybe that's not good

[alpine sable]

ya im taking like an advanced summer class thats why

@thorn tapir yes please though

[thorn tapir]

$\sin (2\theta) = 2 \sin \theta \cos \theta$

[ocean seal]

rikusp2002

[thorn tapir]

Put x = 2theta

you'll get

$\sin x = 2\sin (x/2)\cos(x/2)$

[ocean seal]

rikusp2002

[thorn tapir]

Now just

write cos(x/2) in terms of sin(x/2)

you'll get a relation.

put x = 30 degrees and solve the equation to get your answer.

and if it becomes hard that way

$$\sin \theta = \sqrt{\frac{1 - \cos (2\theta)}{2}}$$

This is your finished prodict

[ocean seal]

rikusp2002

[thorn tapir]

So