help-23

[lean otter]

OK

[mighty garden]

Then 155,000-100,000= 55,000

[lean otter]

with the first 80 000 : 1600$
from the 80 000 to 100 000: 700$

And the rest, 55,000?

[mighty garden]

Don’t you do 55,000 * 4% =2200

[lean otter]

Sure thing

[mighty garden]

I saw what I did wrong

I was doing
155,000 - 80,000 = 75,000
Then
80,000 * 2%

At first

So that answer should be $4500

[safe radish]

@mighty garden Has your question been resolved?

[safe radish]

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[lean otter]

I need help solving this problem

Ñ

I don't understand the explanation

<@&286206848099549185>

[safe radish]

@lean otter Has your question been resolved?

[lean otter]

Hello?

anyone

[safe radish]

@lean otter Has your question been resolved?

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[slim urchin]

how do I move forward with this question?

[safe radish]

@slim urchin Has your question been resolved?

[cinder viper]

@slim urchin Okay so we can choose P=0, Q=x

Right?

[slim urchin]

mhm, im trying to follow what looks like a solution for this on youtube

[slim urchin]

ill show you

[cinder viper]

You just have to integrate P dx + Qdy over the boundary

and the boundary is just made up of some lines

[slim urchin]

mhm so im guessing thats why we paramterise the line segment?

[cinder viper]

Yeah

[slim urchin]

okay that makes sense

i think i might be okay for now actually, your explanation really helped

[slim urchin]

thanks a lot

.close

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[slim urchin]

.reopen

[safe radish]

✅

[slim urchin]

i don't understand why he is trying to calculate what is in the red box here

[burnt bloom]

ok hol on

[cinder viper]

I'm thinking that <x,y> is just some vector on the boundary of some region

and then using that to find the area within the region

[slim urchin]

thanks a lot for that

im gonna have a look at it now

[slim urchin]

if you don't mind could you explain why you've replaced DA in green's theorem formula with dxdy?

[burnt bloom]

zzzz

[burnt bloom]

i'll just do it in this manner then

[slim urchin]

no no its fine

[slim urchin]

i just wanted to understand why conceptually but you dont need to redo it

.close

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[lean otter]

A fruit and vegetable retailer studies the evolution of his melon sales in order to anticipate his orders.
The retailer carries out a study on his customers. He finds that :

• among the customers who buy a melon in a given week, 90% of them buy a melon the following week
  the following week;
• among the customers who do not buy a melon in a given week, 60% of them do not buy a melon
  the following week.
  We randomly choose a customer who bought a melon during week 1 and, for n > 1, we note
  An is the event: "the customer buys a melon in week n" and pn = P(An). Thus p1 = 1.

1. Prove that for any integer n > 1, pn+1 = 0.5pn + 0.4.
   2.a. Show by recurrence that, for any integer n > 1, pn > 0.8.
   b. Show that the sequence (pn) is decreasing.
   c. Is the sequence (pn) convergent?
2. For any integer n > 1, vn = pn - 0.8.
   a. Prove that (vn) is geometric and give the reason and the first term v1.
   b. Express vn as a function of n.
   Deduce that, for all n > 1, pn = 0.8 + 0.2 × 0.5
   n-1
   .
   c. Determine the limit of the sequence (pn).

[elder loom]

do I need to know another directional vector to calculate the plane

then there is only one that is (-1, 4, -5)

[burnt bloom]

#❓how-to-get-help

[safe radish]

@elder loom Has your question been resolved?

[elder loom]

<@&286206848099549185>

[safe radish]

@elder loom Has your question been resolved?

[safe radish]

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[zenith pilot]

Hi

[zenith pilot]

This pls

[thin narwhal]

da options?

[zenith pilot]

I don’t wanna tell them coz I wanna see if the answer given is in the options

[supple aspen]

I guess:

10 * 6 * 2 + 10 * 5 * 2 + 5 * 6 * 2

[thin narwhal]

ok so i dont remember the surface area of a rect prism

but its probablt 2lw + 2lh + 2hw

280?

[zenith pilot]

280 is an option

Are u sure it’s 280?

[terse ether]

But do you understand why

[zenith pilot]

Kind of im gonna try to work out the next one

[supple aspen]

I also got 280

[terse ether]

Do you know how to calculate the area of a rectangle

[zenith pilot]

294?

[thin narwhal]

6*7²

[zenith pilot]

That’s 294 so ima go with it

[terse ether]

Do you know how to calculate the area of a square

[zenith pilot]

I just searched up the formula

[terse ether]

Sure

[zenith pilot]

This one I need help with fr

[thin narwhal]

what is this for btw

just a question

[zenith pilot]

It’s for a unit

Practice questions for a test

I’m trying to solve

[thin narwhal]

ok this one i might actually have to use my brain for a bit

oh nvm

[terse ether]

This prism is just basic shapes combined, you can find each shape's area individually

[thin narwhal]

its (12*5)/2

correct me if im wrong

oh wait no thats only for 1 side

[terse ether]

How?

[thin narwhal]

top 10 idiot

[zenith pilot]

It’s not

Sadly

[terse ether]

Can you identify the shapes that make up this prism

[thin narwhal]

.

[zenith pilot]

Rectangle

[terse ether]

Can we not feed the dude the answer

[zenith pilot]

Triangle

[solid shell]

There's no reason to call each other idiots here

[thin narwhal]

im calling myself an idiot to be frank

[zenith pilot]

Y’all

[thin narwhal]

literally thought a triangle

[zenith pilot]

Bffr

[thin narwhal]

ok well back to the question

[terse ether]

Yes can you find the area for each of those shapes

[thin narwhal]

you have the lengths so you can find them

[zenith pilot]

Is it 920?

[thin narwhal]

howd you get there?

[zenith pilot]

Idk either

Tried a formula

[terse ether]

Can you do this

[thin narwhal]

the formula is what exactly?

[zenith pilot]

I used the google formula

[zenith pilot]

Uhm

[thin narwhal]

ah yes the google formula what is that

[terse ether]

What is the formula for the area of rectangle

[zenith pilot]

Easy

Lxw

[thin narwhal]

cool now the formula for the area of a triangle

[terse ether]

Alright can you find how many rectangles are there and find their area

[zenith pilot]

Hxb/2

[zenith pilot]

3 because of the other side as well

And the bottom

[terse ether]

Yes

[thin narwhal]

so how many?

[terse ether]

Find their areas

[zenith pilot]

150

X 3 = 450

[terse ether]

No

They aren't identical

Each rectangle is different

You need to find area for each

[zenith pilot]

Omg

[terse ether]

What's the bottom number

[zenith pilot]

190

[terse ether]

Huh

What did you multiply to find it

[zenith pilot]

150* mb

[thin narwhal]

that seems wrong

mb?

[terse ether]

Yeah

[thin narwhal]

oh nvm

150

[zenith pilot]

Now what

[terse ether]

Now

You have how many triangles?

[thin narwhal]

da triangles

[zenith pilot]

30

[terse ether]

Also are you sure of this

The other sjde

[thin narwhal]

30?

[terse ether]

Side

How did you find it

[zenith pilot]

5+12+13?

[terse ether]

Uh we will get back to that later

The other side area is wrong

[zenith pilot]

It’s 360

[terse ether]

Yes

[zenith pilot]

Fixed

[terse ether]

Now what's the formula of the triangle

[zenith pilot]

Bxh/2

[terse ether]

Yes

Apply it to the triangles

[thin narwhal]

theres 2 triangles, one on each side

[zenith pilot]

Keep getting 30

[terse ether]

How do you do the calculation

Ah

Yeah dunno why I thought it was wrong

Well

[zenith pilot]

My days

[terse ether]

Add them up

[zenith pilot]

It’s 960

[terse ether]

You did this which was weird

[zenith pilot]

Let’s try it

[terse ether]

So I got confused

[zenith pilot]

GOT IT WRITE

THANK YOU SO MUCH GUYS

[terse ether]

Gg

[thin narwhal]

Congartulations

[zenith pilot]

WAS IT TIME CONSUMING yes WAS IT WORTH IT yes

THANJ YOUU

[terse ether]

Yes but you can actually start solving the area of anything now once you divide it into basic shapes and getting area of each

Instead of people feeding you the answer

[zenith pilot]

Learnt that today thanks to

U

[terse ether]

:D

[zenith pilot]

Second last one

Is that right?

[supple aspen]

I get 791,68

[thin narwhal]

you can tell the shapes in the photo?

[zenith pilot]

Circle and something - cylinder

[thin narwhal]

ok ill introduce you to something

heard of nets?

[zenith pilot]

Yup

[thin narwhal]

you know the net of a cylinder?

[zenith pilot]

Yup circle and a rectangle

[thin narwhal]

ok that should be the shapes in the puzzle

so theres 2 circles right?

like back and front

[zenith pilot]

Yes

Correct

[thin narwhal]

calculate the area of the 2 circles

[zenith pilot]

24

[thin narwhal]

you probably know it

[zenith pilot]

Ones 12 so the total is 24

[thin narwhal]

howd you get that?

you know the equation for the area of a circle

?

[zenith pilot]

C=pi x R2

@thin narwhal

[thin narwhal]

sorry i gtg

bye

sleep

[supple aspen]

Imagine sleeping

weak

[zenith pilot]

Y’all

.close

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[thin crow]

find the quadratic function f whos zeroes are +-6i, a = 1

[haughty skiff]

when a=1, you will have x^2+bx+c=0

[thin crow]

yes

[haughty skiff]

when the zeroes are at +-6i, you will have (x-6i)(x+6i)=0

from there you can find b and c

[thin crow]

why

[haughty skiff]

the roots of the function are +-6i, right?

[thin crow]

yep

ohh

right

how do i find b and c from that

[haughty skiff]

expand this

[thin crow]

x^2+36

whats after that

oh wait

is that the answer

already

[haughty skiff]

ye, from that, b=0 and c=36

[thin crow]

thanks bro

love u

.close

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[lean otter]

I don't get this question. I simplified the brackets and then took 12 from both sides but idk what to do afterwards.

[grave flint]

why expand when you have it in perfect square form

[lean otter]

Can you explain further? I don't understand what u mean by that.

[grave flint]

you have $(5-c)^2$

[flat frigate]

dog.

[lean otter]

I expanded it to then get 2 different answers from c

[grave flint]

you can get the two different answers by considering both branches of square root

for example

$(x+3)^2 = 25$

[flat frigate]

dog.

[grave flint]

$x + 3 = \pm 5$

[flat frigate]

dog.

[grave flint]

$x = -3 \pm 5$

[flat frigate]

dog.

[grave flint]

$x = 2, -8$

[flat frigate]

dog.

[grave flint]

see i didnt need to expand got both solutions

much easier as well

[lean otter]

Yeah I see that

it is much easier

[grave flint]

so just do that with your inequality

just be careful with the plus or minus

when you take the minus sign itll reverse the inequality

[lean otter]

oh

I see

so this is what I think I understand

by reverse inequality u mean that when u do -3-5 the sign goes from "<" to ">"?

[grave flint]

yeah

[lean otter]

alrrrr

Thank u very much

[grave flint]

$(5-c)^2 > 12 \newline 5 - c < -\sqrt{12}$

[flat frigate]

dog.

[grave flint]

but for the positive you keep it the same

[lean otter]

I see

I'll try the question now

tysm

[grave flint]

no prob

[lean otter]

.close

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[lean otter]

is this the correct order to study? : Algebra 1 ➡️ Geometry ➡️ Algebra 2 ➡️ Trigonometry

[solid shell]

It really depends on curriculum but from my experience that is the order in which I did those classes

I think some schools do Alg 1, Alg 2, then Geometry

And trig is often synonymous with precalc afaik

[lean otter]

what does that mean?

[solid shell]

Precalculus is another name for the Trigonometry class

That's what it was called for me

[velvet flax]

afaik = as far as i know

[lean otter]

ohhh okay thanks

.close

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[last sphinx]

Show that 1004001 is a prime number

[last sphinx]

I don’t know how to start

[halcyon carbon]

Don’t know either

Because it’s not prime

Lol

[lean chasm]

1004001 is divisible by 3

[last sphinx]

So it was a trick question thank you

[solid shell]

I mean you could do a proof by contradiction by assuming it is a prime number and finding an inconsistency

I'm not as well versed in proof though

[last sphinx]

I mean yeah but it’s pretty obvious now since it’s divisible by 3

[halcyon carbon]

Easy to check digit sum is divisible by 3

[last sphinx]

I was trying to prove it was a prime number so I didn’t think about doing digit sum lol

.close

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[wary dock]

.open

hello i really want to solve this i know i am a kid but can anyone help me please?

[wary dock]

anyone?

.close

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[iron dock]

To find the sum you just split this right

[iron dock]

Or is there a different method

Split it into 1/9^n + 2^n/9^n

Then use a/(1-r)

[fierce ore]

easier

1/9^n = (1/9)^n, 1/9 ≤ 1 so it converges

2^n / 9^n = (2/9)^n, 2/9 ≤ 1 so it converges

[iron dock]

Yea but how do you find the sum

[iron dock]

Do you do this

[stray socket]

Split it into two sums

[thick sparrow]

You may not need to split it. Consider that $1 + 2^n < 3^n$, then the expression collapse to a single fraction, which then can be concluded convergent by the ratio test.

[flat frigate]

jimmy1234

[stray socket]

Well they wanna find the sum

Not just determine whether it's convergent or not

And the easiest way I see it is to split the fraction up

[iron dock]

Okay that's what I thought

Just want to know if that's the right method or if there's a different method

The answer works

.close

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[iron dock]

Thanks guys

[safe radish]

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[lean otter]

||x - 5| -5 | <= 1

I got 0 <= x <= 10 and (x <= 8 or x >= 2)

[lean otter]

but that was incorrect

and idk how

<@&286206848099549185>

[safe radish]

@lean otter Has your question been resolved?

[safe radish]

@lean otter Has your question been resolved?

[stoic garden]

might give you some ideas

@lean otter can you get the intersection points

in this image

also for reference

[safe radish]

@lean otter Has your question been resolved?

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[elfin cove]

"...sind teilerfremd" means are coprimes :)

This is the descriptive set notation which i was suppose to write down for the certain exercise but at the end the question is: "What notation did you describe" - what does that mean? 😅

[elfin cove]

Would that be a symmetric difference or something else?

[safe radish]

@elfin cove Has your question been resolved?

[elfin cove]

<@&286206848099549185> is this a symmetric difference or a real set because i am not quite sure what type of set i just described there... :O

[safe radish]

@elfin cove Has your question been resolved?

[peak estuary]

so I assume you missed a closing bracket

$M={ (x,y) | x\in \bZ, y\in\bN \setminus{0}, x, y \text{ sind teilerfremd}}$

[flat frigate]

Denascite

[elfin cove]

oh yea i see thx :D

[peak estuary]

hmm how to give a hint for what this set represents without just saying it 🤔

where else in math do you encounter pairs of numbers, where the second one can't be zero

and they have to be coprime

[elfin cove]

prime (numbers)?

[peak estuary]

no

ok lets take it one step at a time

where do you encounter pairs of numbers, where the second one cant be zero

and they are both integers

[elfin cove]

i know that in division you cannot divide by 0

[peak estuary]

yes good

correct direction

[elfin cove]

i dunno in germany we have a own topic for coprime

but division is the correct direction u said 🤔

but it's not product quantity/set?

[peak estuary]

no. you might be thinking too complicated

you said you can't divide by 0. and our second number cant be 0. so maybe that second number is something we divide by. what might the first number be

[elfin cove]

a natural number?

[peak estuary]

how many numbers do we need for a division

[elfin cove]

2

[peak estuary]

good so if our second number might be the number we divide by, what might the first number be?

[elfin cove]

i think i am confused 😅

[peak estuary]

if we have the pair (1,2), what division might that correspond to

[elfin cove]

i am not sure what the second part means... my english is good but yeaa...
i am not even sure if i ever had this in school completely... 🥹

[elfin cove]

For me it sounds like that there is like more than one division type which is not possible, so i dont know...
Its just this little question left for my paper... I wrote down difference set but don't think that's correct either...

.close

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[keen pebble]

Ayo i need some help

[keen pebble]

My equation is 1/2 x^4+x^3

And i need the zeros

How do i solve this one?

I started with factoring out one x^2 out

[vast obsidian]

Better: Factor out x^3

[keen pebble]

Wait

So x is 1

Holy

Is x 1 then?

Holy that is pretty sick

Thanks lad

[lethal musk]

nope

its not 1

factor properly

[keen pebble]

x^3 is the same as x^3 multiplied with 1 isnt it?

@lethal musk

So when i factor with x^3 i get 1/2x+1

[lethal musk]

yeah so you have x^3(1/2x+1) = 0

you have a product of two terms equal zero

one of them must be zero

either x^3 = 0 then x =0

or 1/2x + 1 = 0

which gives what x?

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@keen pebble Has your question been resolved?

[keen pebble]

-2

I just meant that if you factor that out you have instead of the x^3

1

Thats what i meant yk

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[steep oasis]

0 = x(8-5x)

how do I find x without the trial and error of plugging in numbers for x until I get 0
inverse operations wouldn't work in this case

[solid shell]

I imagine you could expand the right side and hit it with the quadratic formula if you're familiar with that

[steep oasis]

thank you for the tip, lexitorius

[tall bough]

Or say x=a and 8-5x=b
We have 0=a*b
Now right side will be zero if a or b are zero or both are zero.
Now when is a zero and when is b zero?

[steep oasis]

thank you, fucktalogist. I think that'll be the quickest way to the answer

.close

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[tall bough]

<@&268886789983436800>

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[devout glade]

just a quick question

[devout glade]

my teacher is marking class tests as 90 percent of the grade and some other assignments 10 percent of the grade

if i were to get a 60 percent in class tests and 100 in the assignments what would my final grade be?

[solid shell]

Is this a homework question or just a legit math question?

[devout glade]

legit math question lol

[nova creek]

You can just do a weighted average of the grades

[solid shell]

^

[devout glade]

okay thanks

.close

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[empty carbon]

help

[nova creek]

An ambulance is on its way

[tall bough]

Wee woo wee woo

[obtuse plover]

🚨

[empty carbon]

i understand how they got (x-4)(x^2+48x+780)>=0

x=4

but i dont understand why there are testing x=5

[nova creek]

To see if larger values for x are valid, or smaller values

[empty carbon]

so it can be any # rit?

[nova creek]

If x = 5 gave a negative number for example, the solution would be x ≤ 4, which would have whatever minimum makes the smallest side 0

[nova creek]

Theoretically yes

[empty carbon]

if it gave a negative # how would it be x<= 4?

[nova creek]

Because the volume can't be negative

[empty carbon]

oh ye

[nova creek]

So that would mean values larger than 4 are invalid

[empty carbon]

okok i think i get it

thx

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[chrome parcel]

Need help

[misty coral]

well its a straight velocity time graph

so the acceleration has to be uniform

what have you done so far

@chrome parcel

[chrome parcel]

Nothin

I dead dont know how to do this

[misty coral]

well lets say a car is completely stationary and moves to a velocity of 10 in a space of 5 seconds

how much did its velocity change by each second to get to that velocity

[chrome parcel]

2

[misty coral]

right

what is that 2? acceleration

its the rate of change of the velocity of an object with respect to time

now read of your graph

this time we have an object, starting at a speed of 0, and moving to a speed of 8 in 4 seconds

and since we know a = (v-u)/(t)

a = 8/4

= 2 ms^(-2)

@chrome parcel make sense?

[chrome parcel]

Nah I still dont get it

so am I just dividing

[misty coral]

hmm

well what is velocity to you

[chrome parcel]

isnt it like

How fast someone is going without changing their speed

sumn like that

[misty coral]

well I would say it is the distance they travel per second

so if someone has a velocity of 15 metres per second, then each second they get another 15 metres away from me

velocity is not so much about actual VELOCITY to me personally, it is about how much distance they travel and in what time they do it in, (also what direction)

[chrome parcel]

so velocity is how long it takes a person to go somewhere

or how long it took

[misty coral]

in a way yes

if we ignore acceleration and say I ran 100 metres in 10 seconds

I would have a velocity of 10 m/s because that is how far I travel per unit time in order to travel 100m

so does velocity make sense?

[chrome parcel]

yeah

[misty coral]

ok now for acceleration

if velocity is the change in distance per second

[chrome parcel]

Ik what acceleration is

[misty coral]

acceleration is the change in velocity per second

ok nice

well now you should be able to answer your question

if you finish with a speed of 8m/s

and started with 0m/s

and it took 4s

what is that objects acceleration

[chrome parcel]

4 seconds

?

[misty coral]

yes it took 4 seconds

to go from a velocity of 0 to 8

[chrome parcel]

alrr

[misty coral]

how much would I have to change my velocity by each second to get from 0 to 8

if I had to do it in 4 seconds

[chrome parcel]

2

[misty coral]

exactly

that is your acceleration

now for the second part

if you have a constant velocity

that means it is not changing right

and if acceleration is change in velocity per unit time

then what must your acceleration be?

[chrome parcel]

so A is 8 and B is 2

[misty coral]

no A is 2 and B is how you worked it out

[chrome parcel]

o

[misty coral]

gotta go do my laundry real quick

whilst im gone someone else might be able to help

[chrome parcel]

alr

[misty coral]

<@&286206848099549185>

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[ripe summit]

I'm trying to find the max/min values and saddle points of the function f(x,y)=xy+e^(-xy) however i don't understand how the answer is minima f(x,y) = 1 at all points (x,y) on x- and y-axes

[ripe summit]

i was able to find the partial derivatives (will list) and when i tried finding the D value i got D=0 which is inconclusive via the second derivatives test

fx = y(1-e^(-xy))
fy = x(1-e^(-xy))
fxx = y^2e^(-xy)
fyy = x^2e^(-xy)
fxy = 1 + e^(-xy) * (xy-1)

im not sure what to do after this since obviously the second derivatives test isn't working

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@ripe summit Has your question been resolved?

[safe radish]

@ripe summit Has your question been resolved?

[safe radish]

@ripe summit Has your question been resolved?

[gleaming grove]

Since the second derivatives test was inconclusive, you must check the extreme values (x and y at plus and minus infinity) along with the critical points (here just (0,0),). At the infinity's, the function goes to positive infinity. At the critical point (and all point where either x or y is 0), the function has a value of 1. Therefore, the function has no maximum, but a minimum of 1 all points along the x and y axes.

[safe radish]

@ripe summit Has your question been resolved?

[gleaming grove]

What are you confused on?

[ripe summit]

I was confused in this specifically

Like I guess I’m not understanding how they came up with the answer of saying minima at f(x,y)=1 for all x and y along the x and y axes

btw cool pfp

[gleaming grove]

You have to take the values of all the critical points and check to see if it is bounded. Here, the function has not maximum because it behaves sort of like a parabola, but a minimum because it never gets smaller than 1. So just because this occurs along both axes, that still is the minimum value of the function

[ripe summit]

ah that makes sense ty

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[mint veldt]

Can someone help me fill in the steps that were skipped?

[foggy salmon]

where

[dusty tendon]

I'm not sure what you're asking mate

what blanks, and what are you trying to show?

[mint veldt]

For the last part, where it says now E(X) and E(Y) are constants.

I drew a line to show what I'm looking at.

So from where the line is, how did he get from there to the last step?

Hope I'm making sense

[dusty tendon]

Try multiplying the first line from Cov(X,Y) inside the expectation

Treat E(X) and E(Y) as constants, since they're population parameters.

Like, don't break apart the expectation yet

[mint veldt]

Ummmm

Okay

[mint veldt]

Like would I distruste X with Y and E(Y)?

[dusty tendon]

distruste?

I'm sorry, I don't recognise that word.

[mint veldt]

Distribute *

[dusty tendon]

Yeah distribute the multiplication

but don't break apart the expectation

leave everything inside

[mint veldt]

Okay!

I can do that

E{XY+XE(Y) - E(X)Y+E(X)E(Y)}

[dusty tendon]

Do you know the rules for expectations?

[mint veldt]

Hmmm

[dusty tendon]

Like if y is a constant, X is a random variable, then E(y)=y, E(yX)=yE(X)

This sort of thing

And E(X+Y)=E(X)+E(Y)

Linearity of expectation

[mint veldt]

I'll have to look through the book again for that.

[mint veldt]

I recognize that

[dusty tendon]

use that and the one with constants

Remember, E(X) itself is the population mean, which is treated as a constant.

So E[E(X)]=E(X)

[mint veldt]

E{XY+XY - XY+XY}

Is that correct so far?

[dusty tendon]

Wait wot

[mint veldt]

😭

[dusty tendon]

Where's your E(X)

Some of the terms should be something like this: $X\cdot E(Y)$

[flat frigate]

Memiya

[mint veldt]

Well X is also a constant no? So I thought the same would apply like you said for E(Y)

[dusty tendon]

E(X) is a constant, but X is a random variable

$E(X)\neq X \iff X is random$

[flat frigate]

Memiya

[mint veldt]

Noted

[dusty tendon]

to reduce confusion, sometimes what I do is write E(X) as $\mu_X$

[flat frigate]

Memiya

[mint veldt]

Reduce confusion with X and E(X)?

I'll keep that in mind

[dusty tendon]

Yeah, in order to remember than E(X) is a constant, I write it as $\mu_X$

[flat frigate]

Memiya

[dusty tendon]

So I don't confuse it with X

[mint veldt]

Okay

Ty for you help. I feel too unsure about this so I'm gonna just reread some stuff.

I don't wanna waste your time.

.close

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[earnest wagon]

Period of function f(x)={2x} where {} denotes the fractional part function is 1 or 1/2?

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[inner carbon]

how to integrate sinx*ln(tanx) dx

[cinder viper]

By parts

[tall bough]

yes

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[lean otter]

Is my vector multiplication and addition correct? (Ignore the graph)

.close

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[dusty cave]

hi guys, can I find center of a circle if i knew 2 points on circumference? if so what would be the equation?

[tiny wraith]

No, you can't you would need 3 points for that

[halcyon carbon]

Any point along the perpendicular bisect or of the two points can be the centre of a circle which contains those 2 points

[dusty cave]

Yeah, how to find that intersecting point?

I mean can you point me to something that I can check online

To get the eqaution

[sudden forum]

Say perpendicular bisect of the two points is AB.
Then, for all points on AB, there is a circle such that the point is centre

so there can be infinite circles

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[safe radish]

@tropic wharf Has your question been resolved?

[tropic wharf]

<@&286206848099549185>

[toxic stratus]

,w simplify cos(arctan(x))

[flat frigate]

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Requested by 夢雪#2250

[toxic stratus]

that kinda just looks like its gonna be B

wait im being totally pepega

just draw a diagram

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@tropic wharf Has your question been resolved?

[tropic wharf]

Wait whysom

Why so*

[toxic stratus]

because this kinda turns into

[toxic stratus]

but also just draw a diagram

clearly cos(arg(z)) is gonna be x/|z|

[tropic wharf]

Yea

[tropic wharf]

Is |z|^2 = (z × conjugate z) a identity? I don't rmeeber seeing it

Mbmb

[toxic stratus]

[tropic wharf]

Is that yes? XD

[toxic stratus]

you could even say that its the definition of |z|

[tropic wharf]

Oh. Lol

[tropic wharf]

Thankss

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[edgy rover]

do i now use y=mx+c?

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[edgy rover]

.close

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[pine dove]

Can someone explain to me how to know when to use a histogram than a bar graph when given a Statistics question?

[pine dove]

Question: The human resources manager of an automotive supply store has collected the following data showing the number of employees in each of five categories by the number of days missed due to illness or injury during the past year.

Missed Days: 0-2 days, 3-5 days, 6-8 days, and 8-10 days
Employees: 159, 67, 32, 10

At first, I thought the best data to use is a bar graph but the answer key says histogram

I'm just confused when to use a histogram

Correct me if i'm wrong but, bar graphs is only used when you're comparing different things like different dog breeds?

[velvet stratus]

From what I understand, histograms are usually used for ra nges of data,compared to bar graphs which are used specific categories of data

And yes, bar graphs can be used to compare data from different categories, like dog breeds

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[still charm]

A 16 lb object stretches a spring 8/9 ft by itself. There is no damping and no external forces acting on the system. The spring is initially displaced 6 inches upwards from its equilibrium position and given an initial velocity of 1 ft/sec downward. Find the displacement at any time t, u(t).

[still charm]

i just don't get it

i thought i signed up for a math class but now i have to learn physics again

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[still charm]

<@&286206848099549185>

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@still charm Has your question been resolved?

[foggy salmon]

this is shm i think

the relavent ones shld b

T = 2pi sqrt(m/k)

X = Acos(2ip ft)

zz idk whats f, this is bad LOL

https://en.wikipedia.org/wiki/Simple_harmonic_motion#Dynamics

well this looks good

ok well a lot of constants r sus

uve to go find out what they mean

whys physics so hard

:c

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[weary aurora]

$\binom{n+2}{n-1}$ = 4(n+1)

[flat frigate]

Standardmodellen

[weary aurora]

alright so ive used the formula for combinations and gotten

[flat frigate]

Standardmodellen

[weary aurora]

but i dont get further than that

oh wait

(n+1)! = (n+1)n!

how do i use that with +2 tho

oh wait i got it

(n+k)! = (n+k)(n+(k-1))(n+(k-2))…(n)

.close

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[slender haven]

I am given tanB=1/2, A+B=90

then im given SinA+cotB / CosB-TanA

I put them all under "Alpha"

so cotB = tanA | cosB = sinA

Now I don't know how to continue

or even if this is the right step

the tanB = 1/2 is making me confused

idk how to find the tanA

okay I made a mistake, tanB=1/2 therefore ctgA=1/2

and I Can go from there on

I think the + there should be a - it's a printing mistake, i put them in beta and found cosb and solved it...

.close

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[full hazel]

Is this no solutions?

[halcyon carbon]

Show your work

[halcyon carbon]

You can’t just multiply both sides by x+5

[full hazel]

Why not

[halcyon carbon]

That’s the first thing

It can be negative or positive

You don’t know that so the best thing to do is move 3x to the left hand side

Then combine the fractions

$\frac{35-x}{x+5} -3x<0$

[flat frigate]

Pure

[full hazel]

What do you mean by combine the fractions?

[halcyon carbon]

$\frac{35-x}{x+5} -3x \cdot \frac{x+5}{x+5}<0$

[flat frigate]

Pure

[halcyon carbon]

Find common denominator

Then combine them

[full hazel]

This is what i got

[elder garden]

ahhejevrjavehhehwwhrke

idk what i am doing

[full hazel]

@halcyon carbon

[halcyon carbon]

Wait

$\frac{35-16x-3x^2}{x+5}<0$

[flat frigate]

Pure

[halcyon carbon]

You have this yeah?

[full hazel]

Yea

[halcyon carbon]

We split this into two cases

Either the numerator is negative and the denominator is positive

Or the numerator is positive and the denominator is negative

Solve them individually

Then find the union

[full hazel]

Did i already solve the one with the positive denominator ?

[halcyon carbon]

Not really you have to solve this system

[full hazel]

I mean positive denominator

[halcyon carbon]

Wait a sec

$\begin{cases}
35-16x-3x^2>0\
x+5<0\
\end{cases}$

[flat frigate]

Pure

[halcyon carbon]

This is one case

You have to find the interval where both inequalities hold

$\begin{cases}
35-16x-3x^2<0\
x+5>0\
\end{cases}$

[flat frigate]

Pure

[halcyon carbon]

This is the other case

[full hazel]

What if i try graphing the zeroes and plugging in adjacent values?

[halcyon carbon]

Solve this first and yeah graphing will help

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[lean otter]

'

[lean otter]

having trouble figuring out the theorem, its not consecutive interior or corresponding

[thin bridge]

do you have a visual guide for all these angle pairs / angle theorems?

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@lean otter Has your question been resolved?

[lean otter]

thats all that was given to me

[thin bridge]

do you know all those descriptions listed?

do you know how they look visually?

[lean otter]

OH

yes

right angles converse theorem and vertical are the only ones im iffy on

[thin bridge]

what describes the relationship between the angles marked by those red arcs?

[lean otter]

ummmmmmmm kinda lost on that

[thin bridge]

hence why I asked you

do you have a visual guide for all these angle pairs / angle theorems?

it would help to look up images online (or in your book) and compare that to what you have

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@south badger Has your question been resolved?

[south badger]

<@&286206848099549185>

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[chrome remnant]

hey so

[chrome remnant]

I remember when learning to find the roots of complex numbers

to add multiples of 2pi to the argument to find the other roots

but i also remember them saying that you had to make sure that it was in this certain space on the argand diagram?

to be careful with -ve signs ??

i cant remember what exactly it was and i cant find other examples online does anyone know what it might have been exactly

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[visual patio]

So I wanna make this into a sumation form but Im not sure how

[visual patio]

Im not sure if thats the right term but its the E symbol

[flat frigate]

Pure

[visual patio]

where did this come from

what if it was like this?

that would mean its B correct? @halcyon carbon

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[upbeat ridge]

Hi

[upbeat ridge]

I was writing an essay, and I was wondering how I could explain this expression in words

$\int_{0}^{\pi}\sin\left(x\right)dx$

[flat frigate]

AirToastie

[quasi bison]

this is not an equation

[upbeat ridge]

Uh

Formula?

[quasi bison]

expression, maybe.

[upbeat ridge]

Yeah

That one

[quasi bison]

"the integral of sin(x) from zero to pi"

if you really wish to put it into words

[upbeat ridge]

No "respect to a to b"?

[quasi bison]

what?

[upbeat ridge]

Integral of sin(x) respect to zero to b

Not like that?

[quasi bison]

you misunderstand what "with respect to" means

[upbeat ridge]

Orderly

[quasi bison]

that phrase indicates the variable of integration

[upbeat ridge]

I'll go with this one

Ah okay

Thanks!

.close

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[leaden wyvern]

hey

can anyone help me out I don't remember how to solve for vectors

[weary lotus]

you use the trig ratios

for a), N 40 degrees means that the angle from the y axis to the vector is 40

so the angle from the x axis to the vector must be 50

[leaden wyvern]

yep

and where do I go from there

[weary lotus]

you know vector a has a magnitude of 30 m

so you can use the cosine ratio to get x

[leaden wyvern]

adjacent over hypotenuse?

[weary lotus]

ye cos 50deg = x / 30

[leaden wyvern]

what is deg

degrees

[weary lotus]

yeah degrees

[leaden wyvern]

so i did cos 50

and what do i do next

[weary lotus]

you solve for x

[leaden wyvern]

when you say deg is that a button i press on my calculator or are you just clarifying that 50 is a degree

[weary lotus]

im saying cosine of 50 degrees

deg is just short for degrees so 50deg is 50 degrees

[leaden wyvern]

i did cos 50

whihc is 0.642

which is equal to x/30

so multiply by 30

so 19.2?

or 19.3 cause of rounding

and then for Y

also use cos because Y is the adjacent

Y= 23

thanks a lot dude appreciate it

[weary lotus]

np

[leaden wyvern]

B is confusing

because its just flat east

[weary lotus]

yeah its asking for delta y, which is 0, since the y value does not change

[leaden wyvern]

yeah so x is 20

y is 0

right

[weary lotus]

yup

[leaden wyvern]

cool that's not too hard

can I keep this thread open incase i have more questions later

or do i close it and open another later

[weary lotus]

this trhead will eventually timeout, so if you have another question, it might be better to close it and ask later

[leaden wyvern]

ok thanks

.close

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[crude star]

How do you find inverse of (ln(2x))/(5-ln(2x))

[crude star]

I was trying solve it and im stuck at

x(5-ln(2y)) = ln(2y)

[plucky elk]

Distribute and move the terms with y to one side

Then you'll be able to factor out that term

[crude star]

distribute x?

Wont it be something like 5x- ln(2)x - ln(y)x ?

If I expand x(5-ln(2y))

How will I single out the y in that case

[lean otter]

Okay so

It will be come 5x-ln(2y)=ln(2y), right ?

Make it so that it is

[crude star]

What about x * ln(2y)

since its inside the bracket

[lean otter]

Yes sorry, forgot to write thar

Anyways

[crude star]

or can I do e^ to both sides

to get 2y on right side

[lean otter]

xln(2y)+ln(2y) = 5x

[crude star]

ye

[lean otter]

Factoriss ln(2y) such that

[crude star]

Ohhhhhhhhh

[lean otter]

ln(2y)(x+1) =5x

[crude star]

and then move

x+1

to other side

[lean otter]

Yes

[crude star]

and then can I set both sides to e^?

[lean otter]

Yes

And divide by 2

[crude star]

omg tysm man

[lean otter]

And u got your y

[crude star]

Yea ty I get it

.close

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[lean otter]

🙏🏻

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[elfin tusk]

it gives you two equations to use for different x

ye was doing something mb

pick the right equation,

then you can find out the probability by doing p(x=<3) - p(x=<1)

[robust stream]

$$P(a < x < b) = \int_a^b f(x)dx$$

[flat frigate]

lems

[robust stream]

when f is a probability density

this is how you solve the question

[flat frigate]

aٴ