help-0

[still estuary]

Now?

[alpine sable]

Now substitute A, B, and C into here

which will replace the fraction in this integral

[alpine sable]

pretty much

then you can distribute the integral to both terms

[still estuary]

I dint understand this part

[steep mortar]

if (x+iy)^((1)/(3)) =a+ib then what is (x/a) + (y/b)

[still estuary]

@alpine sable

Like this?

[alpine sable]

hold on

[still estuary]

Ooo

Now almost nearing tbe end

[alpine sable]

yup

just grind out the integrals and you're good

[still estuary]

F
For the left side what should I use

I can do the right one

[alpine sable]

oh hold on

[still estuary]

Nvm I can't do both I'm stupid

Or I can take log |1-x|/-1
On right

So I should vg t

-1/3× -log |1-x|

Which is
1/3log |1-x|

[nova bluff]

Hi everyone, I am creating a wallpaper for my pc but I have encountered the following problem:
My pc has a screen with an aspect ratio of 16: 9 and I want to insert the album covers without having to cut them, so with the same dimensions as height and length
what is the minimum number of covers I can put vertically and horizontally to fill the screen?

[alpine sable]

oh uh

@still estuary

and this is only for the left term

[nova bluff]

mhh

that the least?

and the dimension of the pic?

[still estuary]

Ok thx alot

[nova bluff]

got you

that was eay

easy but im dumb

thanks <3<3

[alpine sable]

yes this is right but don't forget the + C

[dull onyx]

um

[alpine sable]

i guess at the end once you're done

[dull onyx]

how do i get the derivative of a function i dont know😭

[still estuary]

Yea

[still estuary]

Which function?

[dull onyx]

i need to find the derivative of g(x) = f(x^2+1)

f:R -> R

[alpine sable]

do you need to plug things in or nah

what is riemann sum?

[heady tusk]

can this also be written as x=-2 ; x=8

[alpine sable]

like i know what the definition is

but how is it different from simply finding the integral?

and when is it used in place of simple integration?

[alpine sable]

just use this

[alpine sable]

riemann sums are an approximation of an integral when your step size is small

with a step size approaching infinity, it is an integral

why dont we take the last point

when calculating the riemann sum?

depends on which riemann sum you want to use

yeah i am talking about LRAM

why do we leave the last one out?

[dull onyx]

no

[alpine sable]

just because its an approximation starting from the left

i mean

excluding the right most point is like purposefully making it inaccurate

because you're leaving a section out from the area under the graph (between the end points)

basically, different graphs work best with different approximations, which is why 5 different types of approximations exist

this is mostly because the left Riemann sum amounts to an overestimation if f is decreasing on this interval, and an underestimation if it is increasing

LRAM (and RRAM) also provide a practical way to calculate the integral

this is also useful in multivariable calculus when proving integrals in 3D

i still don't understand how it is valid to leave one of the sections out

its just so there are multiple ways to approximate an integral

[sick lance]

Hi yall, I was solving a logarithm question and I got something like this (actually a equals to log 2 and all of theese in a big square root, but I only need to remember how to solve theese type of exponential numbers)

[dull onyx]

im so lost

[heady tusk]

an alternative method to write this?

[sick lance]

Didn't you asked the same thing on #help-1 ?

[heady tusk]

the person wasn't sure of their answer?

so do you know?

[sick lance]

If theese parentheses are same with [ ], the answer is -2 ≤ x ≤ 8.
But if it is ( ), it is -2 < x < 8
I've never seen such a parenthes like this, maybe because of I'm not american idk.

if it is { }, the answer is x=-2,** x=8**

[paper egret]

First of all, a is greater than 0
Because of a^(-2) = 1/a², so you may let t = a² (t >0), then a² + a^(-2) = t + 1/t
Assuming that t + 1/t = k (k > 0)
⟹ (t² + 1)/t = k
⟹ t² - kt + 1 = 0
Then you just solve this quadratic equation (remember to eliminate negative roots of the equation)
*Sorry if I made mistakes

[sick lance]

I can solve rest of the question now, thanks!

[heady tusk]

so this is incorrect?

is this correct?

please ping me

[jade birch]

Not quite

You are saying that, given a product AB, then AB is less than 0 if A<0 and B<0

But if A and B are negative, then their product is positive

For AB<0 you get two cases:
Case 1: A<0 and B>0 or
Case 2: A>0 and B<0

@heady tusk

[heady tusk]

so there is 4 answers?

[jade birch]

No, there is only one answer

It's an interval

[heady tusk]

ok

[jade birch]

However there are 2 cases, each giving you one interval, and the union of those 2 intervals is the answer

You don't usually solve quadratic inequalities this way

[heady tusk]

oh you dont

my notes don't show me how to do this specific type of question

[jade birch]

You graph the parabola with the x-intercepts and see where it is above and below 0, those intervals are the answers

,w graph (x-8)(x+2)=0

[ocean seal]

Results provided by WolframAlpha

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

Requested by .itsjustnai#9187

[jade birch]

From this graph, can you see for which interval of x, the quadratic is less than 0?

[heady tusk]

ohh

ofcourse

this method

thanks man! @jade birch

[jade birch]

Np

[heady tusk]

so it's - 2<x<8

@jade birch

[jade birch]

Yes

[heady tusk]

,w graph (2x+1)(x-3)(x-3)

[ocean seal]

Results provided by WolframAlpha

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

Requested by superpro#8907

[jade birch]

You might also see it written as $x \in (-2, 8)$

[ocean seal]

.itsjustnai

[heady tusk]

k thanks

[heady tusk]

this is my next one

asking for x>0

[jade birch]

$(2x+1)(x-3)(x-3)=(2x+1)(x-3)^2$

[ocean seal]

.itsjustnai

[heady tusk]

yes

ik

[jade birch]

(x-3)^2 is positive for any x

[heady tusk]

oh yes

[jade birch]

So you want to find for which x is (2x+1) also positive

[heady tusk]

so it's x=3

[jade birch]

x=3 is the x-intercept

[heady tusk]

yes

[jade birch]

You want (2x+1)(x-3)^2>0?

[heady tusk]

and - 1/2

[heady tusk]

yup

[jade birch]

Right

[heady tusk]

wait lemme try

[jade birch]

Alright

[feral zodiac]

If AB || DC
so DF || DE?

[jade birch]

@feral zodiac this channel is occupied, move to a free one

[feral zodiac]

Okay, do you help me in #help-4 ?

[heady tusk]

is it x>-1/2

but idk what to do with the (x-3) ^2

[jade birch]

What do you mean?

AB is positive if A and B are both positive

[heady tusk]

.

[jade birch]

A is positive for x>-1/3, B is positive for every x except 3

[heady tusk]

what is A and B?

[jade birch]

A: (2x+1)
B: (x-3)^2

[heady tusk]

-1/2 you mean?

[jade birch]

Yes

My bad

[heady tusk]

so its

[jade birch]

We dont check when both of them are negative because (x-3)^2 cant ever be negative

[jade birch]

Yep

,w graph (2x+1)(x-3)^2

[ocean seal]

Results provided by WolframAlpha

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

Requested by .itsjustnai#9187

[heady tusk]

,w graph (-x^2-1)(x-1)

[ocean seal]

Results provided by WolframAlpha

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

Requested by superpro#8907

[heady tusk]

@jade birch (-x^2-1) will always be negative right?

[jade birch]

Yes

[heady tusk]

OK nice

almost done with third

,w graph (-x^2-1)(x-1)<0

[ocean seal]

Results provided by WolframAlpha

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

Requested by superpro#8907

[heady tusk]

can't x be anything?

because it will always be multiplied with a negative

making it lower than zero?

@jade birch

[heady tusk]

this is the question

oh nvm

[jade birch]

No

[heady tusk]

because the other bracket has to eb a negative

so

positive I meant

it has to be a postive

because + x -

= -

so x always has to be higher than 1

@jade birch

am I correct

[jade birch]

The left is always negative

[heady tusk]

yup

so right has to be postive

[jade birch]

To get a positive result, the right term has to also be negative

To get a negative result, the right term has to be positive

[jade birch]

Yep

(-) (+) <0

[heady tusk]

so I'm correct

nice

so like

my notes only give a method where there is 2 terms on the right

for ex

8 + 2i

but now there's only 5?

@jade birch

[jade birch]

So you have a complex number on the left with Re(a-2b) and Im(2a+b)

But you also have a complex number on the right with Re(5) and Im(0)

[jade birch]

Two complex numbers are equal if their real and imaginary parts are equal

So you want a-2b=5 and 2a+b=0

[heady tusk]

I think I did that right?

[jade birch]

Looks correct to me

[heady tusk]

cool

@jade birch are you studying math at uni?

[jade birch]

Yep

[lapis valley]

how to plot this in gnuplot?

[heady tusk]

@jade birch i^2 is - 1 right?

but if I put it into my calculator it says math error

[quaint trout]

Yes i^2 = -1

[heady tusk]

(2-i)^2

[jade birch]

Because it treats i as a variable, not as the imaginary unit, I guess

[heady tusk]

is 3-4i?

[jade birch]

Yes

[heady tusk]

how do I make a calculation with this bot

[jade birch]

,w (2-i)^2

[ocean seal]

Results provided by WolframAlpha

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

Requested by .itsjustnai#9187

[jade birch]

You send a query to wolfram

[heady tusk]

,w (3-4i)(2-3i)

[jade birch]

Why did you ask me this?

[heady tusk]

idk

it seems liek you know a lot

about math

[jade birch]

Nah, just high school maths

[ocean seal]

Results provided by WolframAlpha

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

Requested by superpro#8907

[jade birch]

If you want to play around with the bots you can use #bots

[heady tusk]

why is the answer that complicated

(3-4i)(2-3i)

I just want to multiply that?

[jade birch]

It's not

Just expand it

[jade birch]

This gives you the polar form of the complex number

You don't want that

[heady tusk]

I want the normal form

[jade birch]

(a+b)(c+d)=ac+ad+bc+bd

Nothing changes

[heady tusk]

yes

I want to simplify that

I know it's worn g at the bottom

-6-17i/4-9i

nvm

[quaint trout]

@heady tusk

(a+bi)/(c+di) ≠ a/c + b/d i

[hard garden]

Why 3^x<=-5 has No Solution?

[jade birch]

a^x, if a is positive is always positive, therefore 3^x cant ever be negative

It is an exponential equation

[hard garden]

Ahh yes. Thanks

[hard garden]

What about if a is negative?

[jade birch]

Well, for starters that is not an exponential function

And also it jumps into the complex numbers, if you had (-2)^(1/2), that would be isqrt(2)

[heady tusk]

👍

is this correct?

@jade birch

[quaint trout]

What was the question?

You did multiply out correctly

[heady tusk]

i have to calculate the quadratic eqaution

if one of the roots is x=3+7i

@quaint trout does it still look correct

[quaint trout]

Yes

But

There's no need to say it's equal to 0

[heady tusk]

ok

that's just how my notes is

[quaint trout]

You are just expanding (x-(3-7i))(x-3-(3+7i))

So, (x-(3-7i))(x-3-(3+7i)) = ... = x^2 - 6x + 58

You are simplifying an expression, there is no equation

[heady tusk]

OK thansk

@quaint trout

I hav e5o write this in poalr form

but do I use - 1?

or 1

[quaint trout]

Do you mind if I ask where you are from?

[heady tusk]

when calculating tan

[heady tusk]

South Africa

[quaint trout]

Cool

[heady tusk]

because then I get a negative degree?

[quaint trout]

-1

It should be a negative degree

Because it is clockwise to the positive x axis

[heady tusk]

alright

[quaint trout]

But use radians

[heady tusk]

so in my final answer I'll write - 45

degrees

[heady tusk]

we're not doing that yet

[quaint trout]

Ah okay

Then yes

[heady tusk]

we will later

[brazen plank]

It is known that the covariance of the variable X with Y is −143.8, with G 4 and with K 487.8. In addition, it is known that the standard deviation of X is 4.4. What is the covariance of X with a variable D defined by the formula D = 143K + 2.8G + 2X? Does anyone know what I should do with this task? 😄

[hard garden]

I'm stuck at this question

[primal ether]

on the 3rd line move the 1 to the other side to form a quadratic in terms of cosx

[quaint trout]

^

If you have trouble seeing it, let y = cos(x) then you have 1 = 2y^2 + y.

So solve for y

[primal ether]

but then remember to convert the y back to cosx once you find the solutions

[hard garden]

Thanks

[molten elk]

Why can't this be evaluated using the power rule for integration and then dividing by the derivative of the function under the square root?

[dry lava]

Because the 6-x^2 is not a linear function

That rule only works if the inner function is linear

[glass lichen]

You'd need a trig sub, however it's easier to just draw the graph then interpret as signed area

[sinful anvil]

guys which one is the correct answer

3.0 or 3.8

were working out x btw

[glass lichen]

3.8

since x > 3.4

[sinful anvil]

oh

damn

ok ty

and can anyone help me with the last 2 questions

i dont know what im supposed to do whatsoever

[polar barn]

what is 196883+1

[glass lichen]

do it yourself

[polar barn]

ok

[fading salmon]

second:
if you take the inner isoceles triangle you have one angle (56°) and one side 18cm, half it for 28°, 9cm and right angle -> rest you can work out

third:
bisector means it's half
so 30° and 28cm, find half the opposing side

[crystal narwhal]

wth am i doing wrong here? I had to find the perimeter. I divided the quadrilateral into 2 triangles one scalene and one right angled. I used the cosine rule on the scalene triangle to find the hypotenuse of the right angled triangle which I called B. I used Pythagoras to find the value of g by doing B^2 – 5^2 which gave me 304.39... which I added to 14,5,9 to get the perimeter. the real anwser is 45.4 btw to 1 decimal place

[dusky palm]

not sure how to do this

[sinful anvil]

its a

right

?

[dusky palm]

idk

[alpine sable]

what does the sentence "the ratio of fossils to artifacts is 2:9" means to you?

[dusky palm]

I think it means for every 9 artifacts, there are two fossils?

[sinful anvil]

its a

im sure

[dusky palm]

how'd you get to a?

[glass lichen]

dont give answers

[alpine sable]

then, what if there were 90 artifacts, how many fossiles ?

[upbeat gorge]

so yes this is correct

[dusky palm]

20 fossils

[sinful anvil]

so i divided 279 by 31

[upbeat gorge]

The idea is, find how many groups of 9 artifacts are in the 279

[dusky palm]

ah alright

[alpine sable]

the point is to help understand, just to give the answers

[sinful anvil]

ok

so divide 279 by 9

is 31

than 31 x 2

because

[glass lichen]

you're still giving the answer

[sinful anvil]

bruh

just wait

[glass lichen]

no

[sinful anvil]

im trying to explain

[glass lichen]

if you're not going to help, dont type

[upbeat gorge]

You wait buddy

[dusky palm]

so when I divided 279/9 its equal to 31 so in the original ratio it would be fossils to 31 artifacts

and now I just need to find the amount of fossils

[upbeat gorge]

Well no, the ratio is still 2:9
The 31 is like the number of “groups of 2 artifacts and 9 fossils you have”

[alpine sable]

the way got 20 earlier with what i asked is because you naturally got that 90 is 10 times 9, so you calculated 10 times 2 and you found the number of fossiles

[granite coral]

how would you find the zeros algebraically?

[glass lichen]

in use, and dont ping helpers instantly

[alpine sable]

now, you know that 279 is 31 times 9, so what calculation would you have to make to find the number of fossiles?

[granite coral]

oh sorry

[dusky palm]

so you multiplied 9 times 31 groups to get 279 total artifacts

so I would need to multiply 2 * 31

to get 62

i get it now thanks

[upbeat gorge]

well done

[alpine sable]

you can already factorize by x, then set X=x² and see what it becomes 😉

[severe marlin]

Anyone know surds? A bit advanced

completed every question apart from the last 2

[alpine sable]

what's the question there? simplifying the fractions ?

[upbeat gorge]

Have you heard of rationalizing denominators?

[severe marlin]

Of course that’s the method.

[upbeat gorge]

do you remember how to?

[severe marlin]

I do indeed but I’m getting mixed up

As the numbers are weird

[upbeat gorge]

What methods are you thinking of

[severe marlin]

multiply by the denominator with a different sign

[upbeat gorge]

alright you’re on the right track

[severe marlin]

Yes, however just getting mixed

I’ve done too many of these

[upbeat gorge]

If you’re getting lightheaded solving math, try taking a break for a while and coming back to it later refreshed

[severe marlin]

I have and I’m back now

[upbeat gorge]

ah

[north needle]

You need both of them?

[severe marlin]

just stuck in the last 2 yeah

[north needle]

For the fist one keep the bottom as one function

So you would just need to times by:
(root 2 / 2 ) - 1

[severe marlin]

on the top or on the bottom?

like let’s say to begin

I have to multiple by the denominator right

different sign this case subtraction

How should the top and bottom be

How should the numerator and denominator arrive

[north needle]

Can’t you just do that

Think about the bottom as one function

[severe marlin]

let’s say you can

let’s continue

[north needle]

So just expand it

[glass lichen]

more efficient way $=\frac{\sqrt{2}}{1+\sqrt{2}}$ then rationalize

[ocean seal]

Mosh

[severe marlin]

Alright gimme a sec

[north needle]

Being used sorry

[grave solar]

What?

[north needle]

Need to move to different channel since this one is in use

[severe marlin]

I think I got it

What did your answer arrive to @north needle

Show me your expanding working

I need to compare and contract

[grave solar]

How can i delete this message

[north needle]

Gis a sec

[severe marlin]

Don’t worry haris

lol

[severe marlin]

YES MY GUY

top class

There we go

My working agreed with yours and I just checked the answer

perfect

[north needle]

Advice for the second one is expand the denom first

I gtg for a bit so gl

[severe marlin]

yeah yeah thanks that acc helped

What a leggy

Ty

[crude hazel]

how do I find the work done by gravity to a satellite in orbit

[alpine sable]

can u solve these

[severe marlin]

@alpine sable

Simple

I’m also in the same topic

for a) do this

5 is already done so what is 5 the root of?

25

25x3 = 75

1. = square root of 75

Do you get it?

let’s go to no. 2

[alpine sable]

oh got it

ty

[severe marlin]

yep yep

same procedure

Easy

[alpine sable]

i missed some classes

so i didnt get it

[severe marlin]

No worries always get back on track

[alpine sable]

ty

[hard garden]

Any ideas? I can't figure out how the given angle can help

[autumn dock]

Hi, Mr/Ms.MilkyWare
My proposal for you is to draw triangle first

Did you ?

[gentle ocean]

is this channel taken?

I don’t get how question ii is worked out here

Cause I did not solve it like this so I’m abit confused

[small bear]

What's confusing you?

[gentle ocean]

i took the derivative

of the equation

but they didnt?

[small bear]

You don't have to take the derivative, and even if you did, did you get that the function is minimum at the same point?

[gentle ocean]

but its amplitude is not at -1

but they just put it at -1

[gentle ocean]

yes i got same answer

[small bear]

The amplitude here doesn't matter. We need to find when h is lowest.
We know that -1 <= sin(theta) <= 1 right?

Since we want to minimize the function, we put (-1) in place, as the smallest value

that, multiplied with 0.7 which is the amplitude, gives the minima

[gentle ocean]

ohhh

so is it cause amplitude wont change the points of the maximum and minimum

originally i thought you have to take first derivative and equate to 0 to find maxmum and minimum

[digital needle]

can anyone help me solve this pls

[small bear]

The length of the amplitude doesn't change where the minima and maxima are

[gentle ocean]

I seee

thanks for the clarity

[small bear]

Usually yes, you do. However the sine function is periodic and its properties are very simple. Therefore we can just plug in -1 for it

[gentle ocean]

i see

they just took a shortcut

lol

thanks for the help c:

[digital needle]

uh

anyone

pls help?

[small bear]

No problem ||also it isn't a shortcut, we know when sine is minimized by the inequality above, therefore the minima has to be reached somewhere||

[digital needle]

peacgiant can u help me

[sturdy walrus]

where is the question from? @digital needle

[digital needle]

a test my instructor gave me

a practice one

https://www.mathcounts.org/sites/default/files/2019 Chapter Competition Team Round.pdf

[charred flint]

The total perimeter before gluing is 19*3

What sides should you glue to remove the least amount of perimeter?

Haha definitely felt like a mathcounts question

[digital needle]

u mean gluing right?

[charred flint]

Right

[digital needle]

hmm

[digital needle]

okay i understand this

[digital needle]

i dont this

[charred flint]

If I glue two sides together, those 2 sides stop being perimeter

[digital needle]

yes

bc they are inside the polygon?

[charred flint]

Yea

[digital needle]

got it

so which sides would u glue?

[charred flint]

So with 2 triangles you can choose either the 5 or the 7

Which is best to go for the greatest perimeter?

[digital needle]

7?

[charred flint]

Nah, because that would subtract 7*2 from the perimeter

[digital needle]

i see

5x2=10

so that would leave u with the greatest

when u subtracy

[charred flint]

Now, what can you glue with those 2 triangles and an extra one?

Might have to draw it

[digital needle]

for the the two triangles when glued together do they make a rhombus shape?

[charred flint]

I think so, not sure on what sides are parallel

[digital needle]

the base

[digital needle]

is it what or where?

[charred flint]

Like what length sides cane be glued now

[digital needle]

well, if the shape is a rhombus we can glue the side with a 7

to any of the existing sides with a length of 7

[charred flint]

Yup, thats the best shape

Subtracting 10 and 14 for the answer

[thick kernel]

Um

I need help with my math homework

[glass lichen]

https://dontasktoask.com/

[surreal sinew]

why is it true that $n!=\int_0^\infty e^{-t} t^n dt$

[sturdy walrus]

@digital needle is the answer 33?

[digital needle]

thats what i got

[ocean seal]

TheToadSage

[glass lichen]

repeated IBP

or differentiating under the integral sign, which a professor from Oxford has done a video on the exact problem

[surreal sinew]

i dont get how to do it by IBP

[glass lichen]

https://www.youtube.com/watch?v=4RIHTHYD2SQ

you just do IBP n times

[surreal sinew]

its supposed to be done with ibp

oh

[glass lichen]

or prove it by induction

however that restricts yourself to n in N

[lapis sluice]

$\left | \left (\frac{n+1}{n} \right ) ^n - e \right | < \epsilon$

[ocean seal]

Danajax

[glass lichen]

No

[lapis sluice]

why not?

[glass lichen]

the stuff inside the abs value isnt necessarily positive

[lapis sluice]

so how should i proceed on that inequality then?

[glass lichen]

you never posted a problem

you posted a random inequality

[lapis sluice]

yes,

[ionic knoll]

One dumb question, x-2 is the same as 2-x?

[lapis sluice]

no

[lapis sluice]

proove it yourself $x-2 \not = 2-x$

[ocean seal]

Danajax

[ionic knoll]

bc I thought that -x is the same as -1*x, so I could take the -1 and multiply it by the 2

lmao

[lapis sluice]

think that x is a variable

any number

so easy number 100

test with 100

[alpine sable]

can i have help with this radical equatio

[lapis sluice]

is 100-2 equal to 2-100?

that is what you are asking

[crisp grove]

take x=2

[ionic knoll]

oh I see

[lapis sluice]

xDDDD

[alpine sable]

that was fast

[crisp grove]

lol it wasn't for you

[alpine sable]

but idk if it was for me ;-;

hahahahah

[lapis sluice]

nopr

[lapis sluice]

hax

[sick lance]

Can someone explain me how did this happened?

[dull storm]

hi guys

how is this possible

i keep getting different results and he got 0.947241

i have no idea how though

h=4.8 btw

so tg(4.8*1.804219591) is supposed to equal 0.947241

or should 4.8*1.804219591 i tried to times 180/pi but still no result

any idea about this? 😦

same goes for here

how in living hell does he calculate that tg and cos is beyond me

R=5,h=4,8 though

though it is: cosh1.804219591

oh my god...

it's cosh (x) function

and tanh (x) function

i can't believe this 😄

[still sundial]

does anyone know how im supposed to find this base

am i supposed to end up with a quadratic formula?

[minor solar]

I know this is a stupid simple questions, but i wanted to double check. If i had .003% of people out of 15,510 people. That would be 46 people? Because it would be 15510 * .003% = 46 people

[sharp sable]

yes

[minor solar]

thank you!

[tidal lion]

help

[alpine sable]

smash?

Yo i have problem with algebra

[dull storm]

@minor solarwait

[alpine sable]

Can u help

[dull storm]

was that % actually 0.3%?

[minor solar]

nope!

it was .003%

[dull storm]

if u want 1%, then that is 1/100 = 0.01

if u have 0.003% then that is 0.003/100

so 15510*(0.003/100)

=0.4653

[minor solar]

so its .46 people?

[dull storm]

(illogical since it can't be half a human?)

[tidal lion]

help

[sharp sable]

46 humans and a 🤣 baby

jk

[dull storm]

maybe they have converted original 0.3% into 0.003 already ready for u to calculate i don't know

[minor solar]

so that statstic would make it half a human>

[dull storm]

you need to ask

[minor solar]

im calculating dick size lmao. trying to figure out how many people have 9 inches and above

so that means .46 people will have dicks biggetr than 9 inches

[sharp sable]

that's rare

[dull storm]

significant research i must say...

[minor solar]

wow, so even less than 46 people

[sharp sable]

oh yeah

am so dumb

lol

[dull storm]

no u're not

well it is rare

because it's irrelevant to have bigger than average

more than that it is just weight in life

nothing more

and if u think ladies are impressed with such a thing, no they are not

only the sluts

and you want to avoid them really, because they are not a keeper ey?

xD

[tidal lion]

help me

[grizzled path]

wise words

[dull storm]

you can calculate this in wolfram alppha man @tidal lion

[sharp sable]

for

this

[dull storm]

-0.25

[tidal lion]

?

[dull storm]

7x+5y=331
4x+9y=398

[sharp sable]

i got 7X+5Y=331 and 4X+ 9Y=398

[sharp sable]

yeah i did that

but how to answer that

is it by elimination

[dull storm]

u can have many approaches

just use one equation to solve second

[tidal lion]

is the first part 16²

or 4⁴

[dull storm]

7x+5y=331 / 5

[buoyant kayak]

both are the same

[tidal lion]

hm

ok

[dull storm]

1.4x+y=331/5

y=331/5-1.4x

then u use that y in second equation

[sharp sable]

oh

[dull storm]

also u can use system of linear equations

[sharp sable]

just divide both sides that convenient

[dull storm]

@sharp sablein that second equation u have 4x+9y=398

so u will now have when u transfer that y u got in first equation

[sharp sable]

yeah

[dull storm]

4x+9(331/5-1.4x)=398

[sharp sable]

yes

[dull storm]

u get X and then u put that value X in first equation 😄 and u get Y

u can use matrices as well

[sharp sable]

that's awesome

thanks

[dull storm]

no probs mate

[silver dew]

what do you mean

lol

[tight locust]

sec = 1/cos

tan = sin/cos

sectan = sin/cos^2

[alpine sable]

how i solved this was:
I found a factor for the large buses (5 and 9)(i should have done 45, the least common factor), 90.
Then I wrote
(7s+5l=331)*-18
I got 18 from 90 divided by 5.
(4s + 9l=398)*10
I got 10 from 90 divided by 10.
Then I multiplied them and got
-126s + 90l = 5958
-40s + 90l = 3980
I subtracted them and got
-86s + 0 = 1978
Divided 1978 by 86 and I got how many people the small buses can carry.
Then to get how many people the large buses can carry,
I did 331 - 7s divided by 5.
There's another way to do it if you want.

[sharp sable]

damm

that's pretty good too

thanks

[alpine sable]

oh lfc was 45

oops

[desert fable]

uh is this occupied

[dawn heart]

hi

[sharp sable]

no

[desert fable]

ah good

[alpine sable]

i don't think so

[desert fable]

oki thats good

https://artofproblemsolving.com/wiki/index.php/2016_AMC_10B_Problems/Problem_21

[dawn heart]

umm

hi

[desert fable]

for this question lol its easy once u can come up w the graph but i cant

hi

is there a way to solve this using calculus idk

;-;

[dawn heart]

can anyone help

how this group works

[desert fable]

uh

[dawn heart]

uh

yeah

hello?

[cerulean grotto]

yo

can i just send the text

[dawn heart]

bro im so lost

[cerulean grotto]

to see if someone knows how to help me ?

[dawn heart]

which level math u guys doing

[late parcel]

AP Calc AB

Is this channel open

[tight locust]

SURE

[late parcel]

That’s defiantly E right?

[cerulean grotto]

bro

my question must be a easy leve one

[late parcel]

It definitely has 3 POI

Oh wait does it have 4 POI

<@&286206848099549185> I have this graphing question

So on this graph on the very left would you consider the stretch at -5 a POI

[sharp sable]

can i use the channel

[alpine sable]

I’m trying to understand what it means for a functor to be full. If f wasn’t mapped to F(f), that would mean that not all morphisms of the domain or mapped to the morphisms of the codomain, therefore the functor is still a functor but no longer full right? Sorry if this question sounds stupid but I’m still new to functors.

[dawn heart]

wait

do tehy help for algebra

here

9th grade math

i in 7th grade and doing 9th grade

math

[twilit dune]

Can you please show your work?

huh?!

what is your first step?

is this a given?

As I understand, shouldn't it be $(a^{2}+2abi-b^{2})^{2}$?

[ocean seal]

alshfik

QLightningWolf44

[twilit dune]

oh, i see

[ember sluice]

is asin(x)+bsin(x) equal to (a+b)sin(x)?

[civic jungle]

f has to be mapped to something in order for F to be a functor, so not mapping f to anything is not an option

Since there's only one arrow in D between F(X) and F(Y), there's really no choice in the matter except to map f to that arrow

[velvet osprey]

Guys the spectrum of A is the set of proper values right ?

[alpine sable]

Yes

[ember sluice]

I sorted it out using desmos but thanks for confirmation

[simple dragon]

how do i do this

is it basically asking to find f'(x) then make x=pi/2

[glass lichen]

yes

[simple dragon]

oh ok thanks

[odd obsidian]

to get 1-cos^2x they used the Pythagorean identity

sin^2 (x) + cos^2 (x) = 1

sin^2 (x) = 1 - cos^2 (x)

yep! in fact, many of the identities are found through this main identity

for instance:

is derived from that identity, and you can see that by dividing all three components by cos^2 (x)

or

which is derived the same way, but by dividing all three components by sin^2 (x)

[alpine sable]

hi need help

[odd obsidian]

no worries!

[alpine sable]

question: Find the smallest value of N, for which S∞ − SN < 0.5
not sure where i went wrong tbh but the answer seems so wrong

[odd obsidian]

what's the sequence

anyway your second step doesn't seem to make any sense... how did you divide 160 by 0.5?

you should have subtracted it just guessing based on your operations here

[alpine sable]

lol idk what i did

whats wrong with me

i dont know what to do

i know i need to use logs thats it

What should I do

[mild plover]

If (x+yi) = re^theta(i)
Does -(x+yi) = -re^theta(i) for

[alpine sable]

yes

omg i know where i went wrong

thanks anyways

i should have used the equasion

20/1-7/6 = 160

so i can cancel them out

[final tartan]

I need help for question 1

[alpine sable]

why

just search the definitions of union and intercept

[final tartan]

well im just confused since its 4 diagrams

i only done 2 diagrams

[alpine sable]

just draw a seperate diagram for A and B then for B and C then C AND C AND D if ur confused

but its the same concept i dont get you

[final tartan]

so is the answer for 1.a 4?

@alpine sable

[normal carbon]

HCF OF 450 AND 180 AND HOW DID U GET 90? HELP

[shut scaffold]

u not gonna sleep huh

[quartz osprey]

how do i solve for 0 on this

i swaer im dumb or something

iset = to 0

can i u multiply the demonimator/

?

i jsut do lnx=1?

isnt ln 0=1

ln 0 = 1-1 = 0

the answer isnt e either

kinda dont know what to do from here

[mystic kindle]

What seems to be the problem?

[quartz osprey]

i have no clue how to dolve for -

0

my algebra is kinda weak dont know how to get started

i mean i can umltiply entire thing by e right ?

[mystic kindle]

You mean when x = 0?

[quartz osprey]

solve g'(x)=0

[mystic kindle]

Oh ok

[quartz osprey]

when that equation = 0

[mystic kindle]

Gotcha

[shut scaffold]

its quotient rule

[mystic kindle]

It's the quotient rule

Yeah what he said

[shut scaffold]

(vu'-uv')/v^2

[quartz osprey]

wait what

why do i find the derivitive again

[shut scaffold]

u is ln(x) - 1 and v is (lnx))^2

use the quotient rule

[shut scaffold]

^

[quartz osprey]

to solve for when it = 0?

[shut scaffold]

yeah

[quartz osprey]

what

[shut scaffold]

get the derivative and set it = 0

[quartz osprey]

werg uwrgjkb;

dude

[shut scaffold]

wait u already have g'x

that's the derivative

[quartz osprey]

ok let me say again

im trying to sovle for when the derivitvve = 0

and i kidna dont know how

here is the q

[shut scaffold]

lol

u just say ln(x) = 1

[quartz osprey]

well yea

then its 0

oh wait

no it isnt

yea when is ln x= 1

[shut scaffold]

when x is e^1

so they want e to the nearest hundreth im guessing

[quartz osprey]

oh

i cant just put e

[shut scaffold]

instead of just e like u type

[quartz osprey]

__--

[shut scaffold]

d

[quartz osprey]

well here how do you even get that from the derivitve

cuz what i did is multiply the bottom

[mystic kindle]

I think e isn't an acceptable input in whatever site this is

[quartz osprey]

to both sides

[shut scaffold]

that's right

[quartz osprey]

oh ok

thaknks

let me find what e is lmao

[shut scaffold]

2.71828

i forgot what hundreth means

[quartz osprey]

2nd place

[glass lichen]

$e\approx 2.72$

[mystic kindle]

2 decimal places

[quartz osprey]

tens hunddrehs

[ocean seal]

Mosh

[quartz osprey]

thanks

my god im so dum udmm

xd

[mystic kindle]

Lol wait until you join engineering school

[shadow reef]

Quick question would inc be (-oo, -2] [2,7]
Dec(-1, 2]

[quartz osprey]

iirc if its closed point then its included

yea looks right to me

[alpine sable]

im doing implicit differentiation. is the derivative of 2y = 2 or = 2y(dy/dx)?

[vague coral]

it's 2(dy/dx)

[carmine cobalt]

Hi can anyone help me with this problem pls

[somber moat]

i assume this means the probability of getting the same amount of aces in each hand

[glass lichen]

you have k aces b/w them

[somber moat]

that means that the max is 2 aces per hand

[glass lichen]

4 aces in 1 hand and 0 in the other is 4 aces b/w them

[somber moat]

oooh okay

tbh i dont even know how to approach this

halp

theres like 6X10^12 or something like that different combinations for hands you can get but I cant figure out how to get all the ones w/ aces

you have a 2/26 chance of getting 4 aces out of the deck

3/52 chance of getting 3 aces

1/26 chance of 2

[ebon steeple]

A AND G and J can some one please do them as an example

[somber moat]

and 1/52 chance of getting 1 ace

am i right?

[ebon steeple]

@somber moat can u pls help

[somber moat]

these are pretty common squares, the first on is 8. remember that sqrt(ab)=sqrt(a)*sqrt(b) to break them down into easier square roots

[ebon steeple]

@somber moat

Is this right ?

[somber moat]

so for (g) 441=49*9

and for (j) 900=9*100

^them there factors can be easily broke down

[somber moat]

would you be able to help me pls?

[glass lichen]

how big are bridge hands?

[somber moat]

13 cards

so between 2 hands thats 26

[glass lichen]

so you need P(k aces in 26 cards)

[somber moat]

ye

desired outcome/total sample space yeah?

[glass lichen]

Pretty sure permutations is better here

[somber moat]

P(a)=mod(a)/mod(capital omega)

[somber moat]

how so?

[craggy elbow]

how was the range found out here?

[keen mulch]

Sub x = 1 into equation

[craggy elbow]

but why specifically 1?

[keen mulch]

Because that’s the lowest value x can be

Otherwise you’ll get a negative square root

So to get lowest value of y

[craggy elbow]

ok 👌 thx

[keen mulch]

You can sub in lowest value of x

No worries

[vast ore]

how would we do f

[jade birch]

Orient yourself around point C, it is the only one that doesn't move. Also notice that C is on the y-axis. Points A and B lie on the same horizontal line (they have the same y coordinate) and the distance between A and B to the y-axis is the same.

If you can't imagine the triangles formbed by f), give some values to coordinates a and b and see what you get

[vast ore]

so just find values for a and b and put it into a distance formuila?

how would we do this with the formula

[jade birch]

Oh you need to use the distance formula

What is that formula again?

[vast ore]

square root of x2-x1 + y2-y1

wait u square the two terms

[jade birch]

Ohh right

And you're finding the distance of all 3 sides and then the type of triangle?

[vast ore]

yes

[jade birch]

Lemme try writing it out

[vast ore]

ty

[jade birch]

Ok so you get that AC=BC

[vast ore]

can u tell me the values of the 2

thats where im getting confused

[jade birch]

Just plug the coordinates in the formula

[vast ore]

yes

[jade birch]

You don't get anything nice

[vast ore]

and what do u get?

[jade birch]

except for AB

[ocean seal]

.itsjustnai

.itsjustnai

[vast ore]

how do u know there equal??

[jade birch]

Well because they have the same equation?

[vast ore]

oh

i musta made a mistake then in my own work

[jade birch]

Send a picture if you want

[vast ore]

no i think its good

ty for the help

[jade birch]

np

[vast ore]

@jade birch would it be isoceles then?

[small bear]

The triangle will always be isosceles, yes. That is because AC = BC.
As a bonus, you might want to try and figure out, which condition should we have for a and b so that the triangle is equilateral.

[vast ore]

i saw taht in the answer key

but it was wierd

wat does this mean?

[small bear]

Yes, that is precisely what we get for the equilateral case

[vast ore]

how would we figure it out'

[small bear]

So what we know for certain is that AC = BC, that is true always (by using the distance formula)

Now we try and see when does AC = AB

Can you calculate the distances and write the equation?

[vast ore]

one sec

2a=a^2+b^2+4?

[small bear]

Hmm, some terms are missing, and the square root is missing

Did you mean 2a = sqrt(a^2 + b^2 - 4b + 4)?

[vast ore]

yes i did

mb

[small bear]

Alright, we can square this equality, what do we get?

Try to simplify as much as possible

[vast ore]

4a^2=a^2+b^2-4b+4?

[small bear]

Yes, I'll move all a terms to the left

We will be left with 3a^2 = b^2 -4b +4

This is also 3a^2 = (b-2)^2

Alright, let's take the square root of both sides

[vast ore]

did u minhus a from both sides here?

[small bear]

(this is also where we introduce the plus minus sign, since we need to do that when square rooting)

[small bear]

I did yes

[vast ore]

ok so wat does that sign mean?

[small bear]

When we square root something, for example sqrt(x^2) isn't just x. I won't get into the whole thing but in equations you can also write plus minus x

It comes from the absolute value, but we needn't talk about that

[small bear]

So taking the square root of this equation yields +- sqrt(3) a = b-2

[vast ore]

how do u square root -4?

-4b

[small bear]

Why would we need to square root -4?

[vast ore]

as in taht

[small bear]

We don't take the square root of individual terms, we take the sqrt of the whole expression

So we took the square root of b^2 -4b +4

which is the same as the sqrt of (b-2)^2

Are we good so far?

[vast ore]

kind of

[small bear]

Ask me anything that bothers you

[vast ore]

OH

wait

i get it

b^2-4b+4 is in the format of that thing where u square a term

so we ignore the middle term?

[small bear]

It isn't ignoring, it is rewriting

b^2 -4b + 4 = (b-2)^2

[rustic delta]

?

[small bear]

these two things are the same

[vast ore]

i get it tho

ty for the help

[small bear]

Np

[dire jetty]

Hello I've got a question regarding a normal distribution example with μ = 35 and δ = 2
and have to find out the ? from the statement below:
P(X <= ?) = 0.2

The answer for the example is given to me but I have no clue what formula I have to use to reach the result.
Result for ? = 33.316

[ashen anchor]

what is your understanding of domain?

[rustic delta]

The domain of a function is the set of its possible inputs

[alpine sable]

@dire jetty do you have a table for the cdf of a standard normal

you can just normalize and then look it up in the table