help-0

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[alpine sable]

Can I get help w this

[lone heart]

@alpine sable Has your question been resolved?

[alpine sable]

<@&286206848099549185>

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[alpine sable]

,help

[ocean seal]

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

[remote heron]

shocking no one told you that you should crop this to not have your name

i can help i think

have you been able to find the probability associated with any event?

[alpine sable]

yes

[remote heron]

which?

[alpine sable]

all of em

[remote heron]

you have the probability for all the events?

which is the smallest?

[alpine sable]

idk man i just want the answer

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[iron forge]

Hi

[iron forge]

can someone help me with my work

im trying to get the last row to all 0's as i believe thats how i would approach the problem

but im getting stuck on some simplification part

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@iron forge Has your question been resolved?

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@iron forge Has your question been resolved?

[worn fox]

@iron forge what is -18+(-6)*8 ?

[iron forge]

-66

@worn fox

[worn fox]

2nd matrix bottom right entry should be -66 not -42

[iron forge]

alright is everything else in the second matrix ok im going to retry from there

o wait

i see it

damn thanks

,close

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[worn fox]

yeah all else was fine

you see the 2nd row then becomes a multiple of the bottom one

giving you your zero row

[iron forge]

yeah makes sense thanks man

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[alpine sable]

I think ive found a new irrational number and i need someone to proof it

[quasi scarab]

new?

in what regard

[alpine sable]

Idk if it exists but i dont think so

[quasi scarab]

ehm

dont want to discourage you

but every number exists already

[alpine sable]

Ok

[quasi scarab]

and also, yea im pretty sure its irrat. too

[alpine sable]

Ok bye

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[cobalt kelp]

Am I missing something or should b not equal 7?

[worn fox]

How are you getting 7

[cobalt kelp]

Fact 8.11 made me think that Var(3X-2Y+7) = Var(3X) - Var(2Y) + Var(7). But this doesn’t make sense hmm. Okay wait this doesn’t compute

I can just use Var(aX +b) = a^2 Var(x)

[worn fox]

The thing here that they haven't told you is Var(X-Y) = Var(X) + Var(Y)

You still add variances even when you're taking away random variables

[cobalt kelp]

Ohhh

That makes sense

[worn fox]

And yeah when you pull the constants out they get squared

[cobalt kelp]

Yaah. So it equals 30 by saying

3^2*2 -2^2*3

Unfortunate formatting

[worn fox]

Escape them like \*

But I get what you said

[cobalt kelp]

Perfect thanks!

I’m stumped on Var(XY) though

Any hints that could lead me to the right direction?

[worn fox]

Uh I think there's some clapped formula for it

[cobalt kelp]

Hmm

Lemme browse

[worn fox]

Can derive it yourself if you like

Use the definition for variance in terms of expectation

Oh actually yeah just do that

They're independent and you know both their expectations

So just use the expectation formula for variance

[cobalt kelp]

Ohhh!! So E[XY] = E[X] E[Y] and use that to compute variance?

[worn fox]

Yep, always great to check independence before you do anything statsy lol

Makes your life alot easier when things are, but can make them hell when they're not 😅

[cobalt kelp]

Yeah it honestly is 🤣

Aight okay I been racking my brain. I’ve computer E[XY] but I realized, how do I find E[XY^2]

Wait maybe

Since I have Var(X) = E[X^2] - E[X]^2

I can isolate for E[X^2]? Do the same for Y and multiply them together

Let me try

Fuck yeah that was correct

Thanks for the help man!

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[supple sapphire]

How do I make a 3D graph from 3 functions

[supple sapphire]

Let me show you what functions I have

f(x) = -x + 10

g(x) = x

h(x) = -x + 10

[merry coral]

why do you want a 3D graph

and there are only 2 dimensions in ur equations lol

[supple sapphire]

Because I actually have 3 total variables, and yes there are only two I don't know how to explain what I'm doing with the proper notation

sorry

uhm let me try again

so for g and h, they both share the same y axis

fuck lmao

[merry coral]

y = -x + 10
y = x
z = -x + 10

?

[supple sapphire]

let me plug that in rq

this might take a minute to figure out lol

Actually it would be this (same graphs but different variables):
y = -x + 10
z = x
z = -x + 10

[worn fox]

That's gonna give you 3 planes, is that what you wanted?

[supple sapphire]

not exactly, I would like it to be a single graph but idk how to do that

[worn fox]

It's really not clear at all what you're trying to do

[supple sapphire]

I'm trying to find a relationship between 3 variables, will that simply result in 3 planes?

[worn fox]

Find a relationship in what way

[supple sapphire]

https://www.real-statistics.com/correlation/multiple-correlation/

I think this is what I was looking for, thanks for the help!

!close

[worn fox]

.close

[supple sapphire]

.close

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[odd viper]

Hi!
I've a mathematics puzzle that i got out from a workbook i was doing
Could you please help me out and give me some tips on how to approach such questions?pray

Here's the question:

Two players, A and B, are playing an asymmetrical game. There are n points on the game board. Each turn player A targets a pair of points and player B says whether those two points are connected or unconnected. A can target each pair only once and the game ends when all pairs have been targeted. Player B wins iff a point is connected with all other points on the very last turn, while player A wins if any point is connected with all other points on any turn but the very last one OR if no point is connected to all other points after the last turn. For what values of n does either player have a winning strategy?

[odd viper]

<@&286206848099549185>

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[final totem]

If I have 2 identical cubes with one being made of plastic and the other being made of titanium and I only know the weight of the plastic cube then how would I find the weight of the other? The plastic one is 1.4oz.

[lone heart]

@final totem Has your question been resolved?

[placid zinc]

If you know the density of both plastic and titanium, this is easy.

[final totem]

0.9 and 4.5

g/cm^3

[placid zinc]

Sick. So you know the volume of the plastic, thus the volume of the aluminum, thus the weight of the aluminum

[final totem]

The numbers I'm coming up with don't make sense though.

Glasses Weight 25.5146 grams
Plastic Density 1.05 g/cm^3
Titanium Density 4.5 gm/cm^3
Glasses Mass 2.603530612 grams
Glasses Volume 0.5785623583 cm^3
Glasses Mass 0.002603530612 kg
Price in Titanium 0.7810591836

I converted the 0.9oz that the glasses weigh into grams to get 25.5146 grams.

And then plastic and titanium densities are given.

So mass should be weight divided by G.

25.5146/9.8

=2.603530612

Then volume is V=Mass/Density.

2.603530612/4.5 = 0.5785623583

But with titanium powder being $300 a KG that means I'm only paying 0.7810591836 which is definitely wrong.

[placid zinc]

You're converting grams to a mass?

[final totem]

Is that wrong?

[placid zinc]

Your densities are in g/cm³, so you want to be working in g

[final totem]

Which includes the gravitational constant.

Ah.

Okay.

So I should be using the 25.5146 grams as the mass for the volume calculation then right?

[placid zinc]

Ye

[final totem]

So this is correct then yes?

$300 per kg low price and $600 per kg high price for calculations.

Multiplied by 0.109... kg on the right there to get prices.

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[thorny lion]

what would 18!/12! be?

[merry depot]

write out 18!
write out 12!
cancel like terms

[merry coral]

I gotcha bro

let's think about it

with a smaller example

[thorny lion]

I already got it

[merry coral]

L

[thorny lion]

13366080

[merry coral]

which is?

[thorny lion]

that’s the answer

[merry coral]

but did u just use a calculator

🤨

[thorny lion]

I mean kinda the only way to

it’s factorial so the number is big

[placid zinc]

A smaller example that you don't need a calculator for:
What's 9!/8!?

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[shell frost]

The question is to solve for line AB. AB is tangent to Both circles. 4 and 2 are the lengths of the radius of their circles. I can figure out that line EF is 6 but the end bits is where I'm stuck. I know that radius DE would make a right triangle but from there I got nothing

[last ether]

Unless you're given the lengths of AD and CB I don't think there's a way to do it

As far as I'm concerned, AD and BC could be anything

[shell frost]

ok thank you

.close

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[jovial wave]

I'm not rly sure how to write the equation

[pure bolt]

cost of each page is the slope

[jovial wave]

So y=1.50x + 45?

[pure bolt]

(45/1.5 , 45) is a solution of the equation

[jovial wave]

But it wants the equation

[pure bolt]

set y=1.5x+c

[pure bolt]

plug in the values

solve for c

[jovial wave]

Ok

I also have another question

How would I solve for x

[pure bolt]

subtract 5 from both sides

divide both sides by a

because a is a positive number we don't need to change the direction of the inequality

[jovial wave]

So x > 3/a

[pure bolt]

ye

[nova niche]

Jill pays tax at 20c in the dollar for every dollar earned over $10 000. If Jill earns $x and
x > 10 000, write an expression for Jill’s tax in expanded form.

i dont know mayb im too dumb lmao

[pure bolt]

0.2(x-10000)

expand

[jovial wave]

Remember to close when u finish

The help chat

[nova niche]

.close

eh idk

[abstract fractal]

My brother in christ, this is your channel

[nova niche]

right?

i thought i was doing something wrong lol

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[fast cloak]

How to know if it's transitive or not

[tacit arch]

what's the definition of transitive

[fast cloak]

aRb
bRc
Then if aRc is there then it's transitive

[tacit arch]

what's bRc in this case?

[fast cloak]

1≤2³
2≤3³
If 1≤3³ then it's transitive

[tacit arch]

what if b^3 <= b ?

[fast cloak]

Idk

[tacit arch]

b = 0.5 is one such number

[fast cloak]

Oh

Yea

So... Is it not transitive

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[alpine sable]

Can you explain in very simple terms what Representation Theory is?

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[merry depot]

Turn really abstract algebraic questions into a linear algebra problem.

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[warm verge]

Find the indicated measure

Radius of a circle with circumference 36 ft

[naive valley]

probably you have a formula for the circumference of a circle?

[warm verge]

The formula is c=2πr

[naive valley]

ok, so 36 = 2πr

you should be able to solve that for r

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[boreal fractal]

Hi im stuck on this question

[tawdry portal]

It's correct but there is a simpler solution, can you find it?

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[vale wigeon]

...wait hold on

what

there is absolutely no reason why the homework system should be rejecting this answer

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[boreal fractal]

yeah thats what i thought

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[amber veldt]

how do you prove the dimension of the span is number of unique vectors in the span?

[bitter vault]

That's false. Take v = (1,0). Then span{v} is an infinite set consisting of all scalar multiples of v, but the dimension is 1, not infinity

[amber veldt]

i didnt mean that sorry

meant like the number of vectors that form the span

[bitter vault]

Still false. Take v=(0,0). Then span{v} is the zero subspace, and the dimension of the zero subspace is 0. There is one vector in the space, namely (0,0), and 1 vector "forms the span".

[amber veldt]

if vectors are nonzero and unique would it be true?

[bitter vault]

Still false. Take the set S={(1,0),(2,0)}. Then span S = span{(1,0)} and this is one dimensional

[amber veldt]

but isnt (2,0) = 2 * (1,0) making it not unique

?

[bitter vault]

(2,0) =/= (1,0) because 2 =/= 1

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[jade pond]

I require assistance

[jade pond]

Close

!close

Sorry I don't know how to close the door

[cobalt merlin]

.close

[jade pond]

close

.close

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[keen python]

hei

[keen python]

can someone help me or give me a tip how to solve this

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[austere leaf]

do i need to solve the integral of e^4x * f(x) dx?

if so how do they factor out the e^8, which is the answer

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[alpine sable]

Convert to a trigonometric number of an angle belonging to the first quadrant and note the related angles used. Give 2 different options. sec(240°20'10")

[alpine sable]

could someone help me with this please? thank you

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[tacit arch]

.close

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[grave solar]

Can anyone help me finding the Angle BDO

<@&286206848099549185>

Hello

?

Anyone out there Hello?

[hard patio]

you know what OBD is

and BOC is

so find the half of that

you have 2 angles of a triangle then

[grave solar]

I couldnot find of BOC

[hard patio]

Do you know what AOC is?

or COA?

[grave solar]

Yah 60

[grave solar]

60

[hard patio]

and angles on a straight line?

BOA is a diameter

[hard patio]

add up to?

[grave solar]

I know BOC

[hard patio]

....?

[grave solar]

Now i want to findBDC

[hard patio]

Ok, now that you figured BOC out, can you solve the problem?

[grave solar]

I dont think so

BD = CD we know

[hard patio]

if you connect O and D

then look at the triangles you get

[grave solar]

Using congruency

?

[hard patio]

nah for now just look at their angles

[grave solar]

Doesv OD bisects BOC

[hard patio]

or realise that BOC and BDC add up to 180

[hard patio]

yessir

The triangles will be congruent

[grave solar]

Noope

[hard patio]

wdym?

[grave solar]

Those angles doent add to 180

[hard patio]

is there a reason why they cant?

[grave solar]

Since BOA is only 180 degrees so by adding any acute angle to that will be more than 180 degrees

[hard patio]

sorry i wrote BOA

my bad

[hard patio]

...

sorry

or realise that BOC and BDC add up to 180

[grave solar]

Are they in cyclic quad?

[lone heart]

@grave solar Has your question been resolved?

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[alpine sable]

\begin{align*}
\lim_{n\to\infty} \frac{n}{2}\left(\frac{3}{(n+1)^2} + \frac{3}{(n+2)^2} + \cdots + \frac{3}{(n+n)^2}\right) &= \lim_{n\to\infty} \frac{1}{n}\left(\frac{3n^2}{2(n+1)^2} + \frac{3n^2}{2(n+2)^2} + \cdots + \frac{3n^2}{2(n+n)^2}\right)\
&= \lim_{n\to\infty} \frac{1}{n}\left(\frac{3n^2}{2n^2+4n+2} + \frac{3n^2}{2n^2+8n+8} + \cdots + \frac{3n^2}{2n^2+4n^2+2n^2}\right)\
&= \lim_{n\to\infty} \frac{1}{n}\left(\frac{3}{2\left(1+\frac{2}{n}+\frac{1}{n^2}\right)} + \frac{3}{2\left(1+\frac{4}{n}+\frac{4}{n^2}\right)} + \cdots + \frac{3}{2+4+2}\right)\
&= \int_0^1 \frac{3}{2(1+2x+x^2)} \text{ dx}\
&= \frac{3}{2(1+2x+x^2)} \Big|_0^1\
&= -\frac98
\end{align*}

[alpine sable]

any idea what i did wrong

[ocean seal]

mahmooz

[tacit arch]

this is incorrect

[alpine sable]

no wait

i didnt integrate

[alpine sable]

its correct why isnt it correct

[tacit arch]

oh my bad it is

[alpine sable]

thanks ❤️

.close

[lone heart]

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[austere leaf]

.reopen

[austere leaf]

how do i do this

[tacit arch]

Use the definition of expected value

(4.3) here:
https://www.probabilitycourse.com/chapter4/4_1_2_expected_val_variance.php

[alpine sable]

you might also need this theorem

[austere leaf]

i know that i somehow need to factor out e^8 but idk how

[tacit arch]

show your work

[lone heart]

@austere leaf Has your question been resolved?

[tacit arch]

complete the square

https://www.cuemath.com/algebra/completing-the-square/

[lone heart]

@austere leaf Has your question been resolved?

[austere leaf]

@tacit arch like this?

complete this square?

[tacit arch]

write this as (x - a)^2 + b for some a and b that you have to solve for

[tacit arch]

@austere leaf you need to read this

[tacit arch]

this channel's occupied. read #❓how-to-get-help

[austere leaf]

its getting to messy

[tacit arch]

Yea it's a messy problem.

[austere leaf]

ther should be a minus before 16 instead of +

i guess -0.5 * -16 = 8

e^8

and the rest will be the density function of the normal distribution

how would the rest be ((x-u)/o)^2

[tacit arch]

You have a new mu and sigma

[tacit arch]

Also you should have started with standard normal here. Would have made the problem a lot easier

[tacit arch]

Standard normal means zero mean and variance one

[austere leaf]

omg this was even in teh question

so that will be e^ ( (-0.5x^2 ) + 4x)

is this it

the mu changed

but will still integrate to 1

right

[lone heart]

@austere leaf Has your question been resolved?

[lone heart]

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[latent mica]

need help with binoial expansion\

[latent mica]

$(2𝑥−𝑦^2)^4$

[ocean seal]

vanilla man

[marsh fog]

What about it is giving you trouble?

[latent mica]

i just want to make sure i got it right

[marsh fog]

Okay, whatd you get?

[latent mica]

lemme do this quick

[marsh fog]

No worries.

[marsh fog]

Looks good to me!

[latent mica]

u got the same?

[marsh fog]

Yep.

[latent mica]

ty man

[marsh fog]

No worries!

[latent mica]

.close

[lone heart]

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[stone dove]

hello

[stone dove]

i have this equation

and i want to separate the x from the y

so i did it like this

but the solution is like this:

how did they get that?

[limpid spade]

they just brought - 5 to other side

and swapped denumerator to switch sign

[stone dove]

oh

ok

[limpid spade]

weird question tho I'm pretty sure that's not how to solve a multivariable diff eq P(x, y)dx+Q(x, y)dy

[stone dove]

and is there anything i should be looking for to help me separate the x and y

[marsh fog]

It will be practice for integration by separation of variables I assume

They wrote it like that when I was in school then 'integrated both sides'

[stone dove]

ok, thanks

.close

[lone heart]

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[summer otter]

hey can i get help with this

[summer otter]

i wanna know how do you find the right points to use

[limpid spade]

any two points suffies

choose the points where there are little dots on

[summer otter]

is there suppose to be a range where i choose them?

i picked the first 2 points but it was th 1st and 3rd

[meager pagoda]

No there’s not a range, you probably would want it to be the most simplified version though

[summer otter]

oh okay

thanks

[meager pagoda]

Of course

If you need any other help lmk

[lone heart]

@summer otter Has your question been resolved?

[summer otter]

Yep

[lone heart]

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[alpine sable]

how to make equation with this

[remote heron]

with what

[alpine sable]

line prolly

[remote heron]

can you show the whole question

[alpine sable]

i was told to make a question with these

[remote heron]

do you want a line?

[alpine sable]

ye

.close

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[signal geode]

how do i do this

[signal geode]

any video recomendations? i dont know what to search to find it lol

<@&286206848099549185>

[wary stream]

You have to wait at least 15 minutes before pinging helpers

[signal geode]

i did 😐

[dawn birch]

calculator

[lone heart]

@signal geode Has your question been resolved?

[signal geode]

bruh

[lone heart]

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[last ether]

Nice image

If you're gonna ask for help, state the question too. Don't just post an image that does not have the question @boreal kernel

[boreal kernel]

the question was find the sa mb

[last ether]

Okay

Well this is a shitty problem because ACB doesn't seem to be a semicircle

[boreal kernel]

teacher said to split it into a triangular prism as the hint

thats about it

[last ether]

You could

You can make an equilateral triangle knowing your circle theorems

I guess that gives you an angle of 60°

[boreal kernel]

yea but im not sure what to do after that

[last ether]

So find the length of any of the two arcs

Actually lemme make this easier

You know that angle CAB = CBA and that if you make straight lines, CA = CB

So just find the length of arc BC or CA @boreal kernel

They're gonna be the same length so once you find one, you know the other

[boreal kernel]

alr

root 1875

do you need me to simplfy that

[last ether]

No keep it as that lol

Lemme check

That's not correct

Do you know your arc length formula (in degrees)?

[boreal kernel]

uh

[last ether]

Lemme give the formula, and then I brb

[boreal kernel]

i thought u just meant cb as in the line isnt it just a straight line?

[last ether]

$2πr \cdot \frac{d}{360}$

[ocean seal]

Umbraleviathan

[last ether]

The arc

The arc, not the line

d is the angle

[boreal kernel]

is the angle just 60

52.3598775598? or is that not what you need

((50^2)(pi)(1/6)(2)-(50)(25root3)(1/2))(2) for both faces?

and then 2(pi)(r)(h) for the 2 curved faces

does that work?

[last ether]

Keep it in terms of π

Just so it's easier on my eyes lol

I'm gonna focus on the rectangular side

Whose area is just 2500/3 π. You have two of these.

Adding these two sides and the square bottom gets us $\frac{5000π}{3} + 2500$ cm squared.

[ocean seal]

Umbraleviathan

[last ether]

All we need to find are the front and back sides

You're following @boreal kernel ?

[boreal kernel]

yes

[last ether]

So this is gonna be a moment

Lemme draw something

[boreal kernel]

ok

[last ether]

Assume that the blue line is straight and isn't suffering from my drawing inabilities

You have a sector (red area) and then a hump (green)

I'm gonna focus on the red for now

What would the area of the red be?

[boreal kernel]

2pi50^2 times 1/6

[last ether]

Not 2pi, just pi

But yes

[boreal kernel]

wit

yea

pi

[last ether]

So uh

Time to do math

1250π/3 for the red

Now

The green is the area of the sector minus the equilateral triangle

So what would that look like

[boreal kernel]

so you find the area of the triangle and minus the total area of the sector?

[last ether]

Other way around

Sector - triangle

[boreal kernel]

yea ok

so 25root3 times 50 times 1/2

= triangle?

[last ether]

Uh lemme check

My laundry decided to not work so

Lemme fix it quickly

[boreal kernel]

ok

[last ether]

Yeah

So your green area is gonna be $\frac{1250\pi}{3}-625\sqrt{3}$

[ocean seal]

Umbraleviathan

[last ether]

Adding the red area:

$\left(\frac{2500\pi}{3}-625\sqrt{3}\right)$

[ocean seal]

Umbraleviathan

[last ether]

We have two of these sides to

so

$2\left(\frac{2500\pi}{3}-625\sqrt{3}\right)$

[ocean seal]

Umbraleviathan

[boreal kernel]

ok

[last ether]

And then we're gonna add up all the information we have

$2\left(\frac{2500\pi}{3}-625\sqrt{3}\right)+\frac{5000\pi}{3}+2500$

[ocean seal]

Umbraleviathan

[last ether]

just simplify this

[boreal kernel]

10806.912

thats the answer yea

tysm for your help

.close

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[last ether]

Np

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[sly comet]

How do u do 6aiv?

[last ether]

average slope formula

$\frac{x\left(4\right)-x\left(0\right)}{4}$

[ocean seal]

Umbraleviathan

[alpine sable]

aiv?

[last ether]

6, question a, application IV

[alpine sable]

Oh okkk

[alpine sable]

Ya this should be fine ^

[lone heart]

@sly comet Has your question been resolved?

[sly comet]

Apparently u minus x(4) by x(3)

Because it’s “during” the fourth second

[last ether]

yeah so it should be x(4) minues x(0)

idk why they would use x(3)

unless its like the average velocity between 3 and 4 (during 4)

[lone heart]

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[chrome sage]

Wtf does this mean

[chrome sage]

Like idk how I’m supposed to write it out?

[alpine kiln]

directrix is basically the line that the hyperbola curves away from

[chrome sage]

I’m asking how I’m supposed to write the ratio

[simple turtle]

I did search and this came up.

Here: https://byjus.com/hyperbola-formula/

[lone heart]

@chrome sage Has your question been resolved?

[chrome sage]

I’m assuming the directrix is x in that equation?

[lone heart]

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[lime moth]

I have no clue how to do this

[pure bolt]

complete the square

then trig sub

[lime moth]

When I try completing the square i get x^2-x+1/4-1/4-2 so wouldnt it be impossible to turn that into a trig sub?

[abstract fractal]

That's not a completed square. It should be of the form (x + a)² + b

[pure bolt]

complete the squate you get 9/4 - (x - 1/2)^2

try to get that first

then try x-1/2 = 3/2 sin theta

[lime moth]

okay so I got sqrt(3/2(cos^2 theta)) but im confused on what to do next

[pure bolt]

u mean sqrt(9/4(cos^2 theta)) ?

take the root

[pure bolt]

and differentiate both sides

rewrite the integral in terms of theta

[lime moth]

is the answer dtheta?

[pure bolt]

yep

[lime moth]

awesome the only thing im confused about is at the end i got (-3/2 cos theta)/(3/2 cos theta) *d theta did I do one of the calculations wrong since the negative didnt cancel out

[pure bolt]

how did you get the negative sign

derivative of 3/2 sin theta is 3/2 cos theta

[lime moth]

oh im dumb thanks for the help

[lone heart]

@lime moth Has your question been resolved?

[kind sierra]

Close the thread

[lone heart]

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[alpine sable]

Hello, as this was in an exam, I’m not able to get my worked solutions, but the question is: if x^2 +bx +1=0, show that it will never have a positive or a negative real solution.

[tacit arch]

Depends on b

[alpine sable]

They didn’t give b

[tacit arch]

,w plot x^2 -5x+1

[ocean seal]

Results provided by WolframAlpha

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

Requested by riemann#2529

[tacit arch]

Look two positive solutions

[alpine sable]

Yes, but we needed to shiw that

Or prove

It

Sorry btw

[tacit arch]

You said prove that it doesn't

[alpine sable]

Oh sorry prove that it doesn’t

For any value of b

[tacit arch]

🤦‍♂️

[alpine sable]

Sorry bruh

Brains fried

[tacit arch]

Rephrase your question

[tacit arch]

This is clearly wrong

[alpine sable]

Hello, as this was in an exam, I’m not able to get my worked solutions, but the question is: if x^2 +bx +1=0, show that it will never have a positive or a negative real solution for any value of b

[tacit arch]

As given by this counterexample

[alpine sable]

It was written like this tho…

And it will never have a positive or a negative x solution

[tacit arch]

You probably just remembered it wrong

[alpine sable]

And the above proves

That it doesn’t have (x-something)(x+something)

Rather it’s either (x+sometting)(x+something) or (x-something)(x-something)

Sorry if I’m being rude

I really didn’t want to come off that way

[tacit arch]

You're not rude

Just imprecise

[alpine sable]

But the above graph

That you showed

[tacit arch]

You prove it by calculating the discriminant

And showing the two roots has the same sign for both roots

For all b

[alpine sable]

So discriminant is b^2-4

But that only says that there are 2 solutions

If b is smaller than -2

And bigger than +2

It says nothing about the positive or negative x

Or maybe I interpret ur explanation wring

Wait

Oh i did

Sorry

Brains fried

[tacit arch]

Just show that the square root of the discriminant is smaller than b

Then do cases for positive and negative b

[alpine sable]

Wait u mean + and - x?

Sorry I’m super dumb

So it’s like, I’m not even sure how to show that the square root of discriminant is smaller than b

Do you just rearrange?

The quadratic formula

And infer?

[tacit arch]

Yes the roots are given by the quadratic formula

[alpine sable]

So you just prove that the + and - don’t matter

Basically

In quadratic formula

For this quadratic

[lone heart]

@alpine sable Has your question been resolved?

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[alpine oxide]

Can someone please talk me through a fraction question?

[alpine oxide]

the one I got wrong

I used fractions to solve it

or tried to anyway

[lone heart]

@alpine oxide Has your question been resolved?

[dusty rivet]

Your answer is the fraction of pizza left (like 0.2 of 1 pizza + 0.25 of another pizza)

However, the question says “what fraction of the total original amount of pizza is left? There are 4 pizzas, so it would be

Your answer/4 pizzas

In other words, 0.85/4 = 17/80

Overall your way of going about it was correct, but you likely didn’t read the question correctly

I hope this makes sense

[alpine oxide]

Thanks, so bare with me I'm a little dumb so I thought I already did that

However so what we saying is we have 4 and another 4 pizzas?

[dusty rivet]

I’m saying that your answer was 0.85/1 and you were only thinking about 1 pizza, but it should be the fraction left of 4 pizzas, 0.85/4

Part/whole but you messed up the digit for the whole

[alpine oxide]

Ok interesting because when I was doing the fractions I said to myself ok 4 pizzas thats 4/1

Which is now 400/100

Then - what they had

So I guess I looked at it like George had 77% of the 4 pizzas combine

As a unit I suppose

[dusty rivet]

Ohh I think I kind of understand

[alpine oxide]

So to my head its like I got the 4 pizzas whats the problem 🤣

[dusty rivet]

Ohh so you did 4 - 0.8 - 0.75 - 0.77 - 0.83 = 0.85

I think

[alpine oxide]

Yes but fraction form

[dusty rivet]

I see

[alpine oxide]

Here 1 sec

Excuse the terrible writing I was rushing

How do we rotate that on here

[dusty rivet]

I don’t know

[alpine oxide]

,rotate

[dusty rivet]

Ohh cool

I get what you did

[alpine oxide]

https://tenor.com/view/jimmy-butler-jimmy-buckets-basketball-gotcha-yes-you-are-gif-18752639

[dusty rivet]

With that essentially you got the top part of the fraction so then just divide by 4 and that’s the answer

[alpine oxide]

Yeh see now I'm lost again after you said that because I already took from 4 pizzas now another 4?

Is that the bit I don't get

[dusty rivet]

So with your equation the answer you got is how much of the 4 pizzas left

But you don’t have it as how much of the 4 pizzas left out of the 4 pizzas

Does this make sense?

Sorry but I gotta go somewhere now

[alpine oxide]

Ok Thankyou

[dusty rivet]

I hope you get it

[alpine oxide]

I nearly grasped ya

OOOO Thers my 4 pizzas

Oh

Wait

So I worked out how much of the 4 pizzas are left. but it wants to know how much is left of the 4 pizza okay

Why is my head not clicking

What fraction of the 4 pizzas is left

Ok I get that now written like that

I see

What fraction is left of those 4 pizzas

Ok

So

We know the 4 pizzas have 85/100 left combined

So it's whatever pizza is left /4

Ok solved

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[dull cypress]

What is the probability that a random password of length 20 contains exactly three digits?

[dull cypress]

i got (10^3 * 26^17 * c(20,3)) / (36 ^20)

but idk if thats correct

only lowercase letters and digits are allowed in the password

my thinking is 10 digits and 3 slots -> 10^3

and we arrange them with c(20, 3) since order doesnt matter

then the rest of the digits are lowercase letters which is 26^17

then since its probability we divide that by the total number of outcomes

which is 36^20 since 36 possible characters and a length of 20

on a calculator the probability equals about 0.097

can someone verify if I'm doing this correctly?

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[vale wigeon]

this sounds correct yes

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[wanton kiln]

Hey, I just wanted to make sure that the series
$$\sum_{n=1}^{\infty} \frac{\sin(n)}{(2i)^n}$$
converges.
WolframAlpha says it diverges because of the limit test, which seems weird because the limit test clearly gives that it is inconclusive since
$$\frac{\sin(n)}{(2i)^n} \to 0$$
as $n\to \infty$.

However, since the series of the absolute values
$$\sum_{n=1}^{\infty} \left| \frac{\sin(n)}{(2i)^n} \right| \leq \sum_{n=1}^{\infty} \frac{1}{2^n} = 1$$
the series is absolutely convergent and hence convergent.

Or have I missed something?

[ocean seal]

CoffeeMan

[worn fox]

,w sum from n=1 to inf sin(n)/(2i)^n

[ocean seal]

Results provided by WolframAlpha

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

Requested by iCaird#6258

[worn fox]

maybe you put it into wolfram wrong?

[wanton kiln]

Weird

Anyhow, clearly it's just some problem with wolframalpha and the series converges. Thanks.

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[worn fox]

yeah strange i typed what you typed on wolfram pro on mobile and it said it diverges

then when I clicked "show steps" it decided it converges

whack

[wanton kiln]

Yeah

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[marsh shore]

Is it possible to construct a sequence of irrational numbers with subsequences converging to each real number

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[limber ruin]

please help me identify the error and solve it

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@limber ruin Has your question been resolved?

[viscid cloud]

How did you get step 6

[limber ruin]

i tried differentiating step 3, but i made a mistake at the end with adding the 4

but i was wondering why my h is equal to the b

<@&286206848099549185> please help

[viscid cloud]

ur 2nd derivative is wrong

[limber ruin]

my new answer is 4+(34560/b^3), is it correct now?

[viscid cloud]

Could you show ur steps

[limber ruin]

its the same as the one here, i just used the exponent rule after and did not add 4 to the 34560

[viscid cloud]

The image is correct

[limber ruin]

is the optimal shape of a square prism a cube? because normally the height would be half or double the width

[azure garnet]

I have a question: What would the formula to this e.g. "every day mark adds 2 more euros into his balance than he did the day before.. Monday he had 2, Tuesday 4, Wednesday 6, Thursday 8 and so on.. How much would he have all together by the end of the year?"

[ocean seal]

potatology

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[azure garnet]

@safe needle Thanks man

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[alpine sable]

Hi, I don't understand what question a is asking for or how to do this

[alpine sable]

Can someone please help me, I am stumped

I would appreciate some form of guide or something that can help me understand what this question is asking me

I could help you a year ago. Alas. I forgot everything about stats

surely something you remember?

I just need like a small push

[mortal trellis]

what is the definition of F_W(w)?

[worn fox]

what must the value at the end point of a CDF be?

[mortal trellis]

that's even easier

[alpine sable]

is it the upper limit?

[worn fox]

if you have a CDF with inputs from a up to b (interval)

what is the value of the CDF at b?

eh bad choice of variable letters, nothing to do with the question a,b

[alpine sable]

would it be b=1-Pr(X>a)?

or is it something to do with integration?

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@alpine sable Has your question been resolved?

[alpine sable]

os ir is the total area? which is 1?

@worn fox

[worn fox]

1 yes

because the CDF is "adding up" the probabilities as it goes along, so once its gone all the way along itll have added up all the probabilities and we know they add up to 1

you should be able to use that fact to find b in terms of a in the question

[alpine sable]

I can

I can't see how though **

[worn fox]

$F_W(w)$ is a CDF

[ocean seal]

iCaird

[worn fox]

figure out its end point

[alpine sable]

yup

wouldn't the endpoint just be 1?

oh wait

the value at the endpoint is 1

not that the endpoint is

1

[alpine sable]

I tried to find how to find the endpoint but I could not

could you please help me @worn fox

[mortal trellis]

if X ~ U(1, a) and W = sqrt(X), then how large can W at most be

what is F_W at that point

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[copper flicker]

How do I draw a graph between two values in GeoGebra?

[copper flicker]

I have this and I'm supposed to draw the graph for f(x) between 0 and 12

Managed to do it in normal algebra field

But how do I do it in CAS?

.close

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[hexed crystal]

angle BMN

[hexed crystal]

how to find, i literally tried everything..

[gray ingot]

You'll need to use angle cmn

And the fact that cma is a straight line

[gray isle]

looking up adventitious triangle may help

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[hexed crystal]

thx guys

[hexed crystal]

tried, doesnt work

[hexed crystal]

it works

thx

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[rigid junco]

Anyone know the slope? I'm a little confused on this question

[thick talon]

you have points A and B right

[upbeat tulip]

Yea, use the formula

-8/3 ?

[thick talon]

A with coordinates (2,4) and B with coords (5, -4), u can use the slope formula as maeve mentioned

[alpine sable]

Don’t just give answers

[rigid junco]

alright ill do that thank you

[upbeat tulip]

The formula is

Wait

I'm gonna try to use latex

Nevermind

(yB - yA)/(xB - xA)

Imagine the capital letters to be subscript lmao

[alpine sable]

$\frac{y_2-y_1}{x_2-x_1}$

[rigid junco]

so

m=−83

right?

bruh the fraction wont work

[ocean seal]

Critzzzy

[rigid junco]

just to make sure

this is how it would look right?

[upbeat tulip]

$-\frac{8}{3}$

[ocean seal]

Maeve

[rigid junco]

great thank you guys so much it makes a lot more sense now

[upbeat tulip]

Yes

[rigid junco]

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[brave aurora]

Hey yall, got a quick question

[brave aurora]

So in this problem, wouldn't the spring force be F(x) = k * -x ?

because the spring is being compressed, not stretched

[merry coral]

well let's define the variables

and solve this logically

what does k represent

and what does x represent

?

[brave aurora]

K is the spring constant

X is the distance it's stretched or compressed

I would just think that x would be negative when compressed

Like in the problem

[tacit arch]

Just flip the x coordinate axis

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@brave aurora Has your question been resolved?

[brave aurora]

But would x be negative lol

[tacit arch]

There's nothing wrong with that

Coordinates don't affect the physics

You can set your origin to be anywhere

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[thick lynx]

Is it even possible to accurately solve this

[thick lynx]

It's not straight, so it's not a triangle, right?

(solve for d)

[merry depot]

i assume that's just a correction for drawing the angle slightly off

[slate jolt]

its just badoy drawn but assume its a atriangle

[thick lynx]

This is a "hard exercise" in my book, so I dont think its just tan(23°), one calculation and done

[slate jolt]

like you cant do anything

[thick lynx]

that would be considered "easy"

[slate jolt]

if you dont know what this weird shape is

[thick lynx]

hmm

maybe it wants me to figure out that this is unsolvable like this?

[thick lynx]

well I could form 3 triangles ig, right?

[slate jolt]

to me its just a wiggle

its not even straigth

like either you assume it was meant to be straight

or you cant do anything

[slate jolt]

yeah thats not maths

thats gzssing lines

[thick lynx]

you cant do anything with that tho, right?

[slate jolt]

yeah and how do you know you drawing is the good one

like your lines are arbitrary

[thick lynx]

you drawing is the good one
wdym

[thick lynx]

ok ima look at the solution, imma tell you, wait a sec

[merry depot]

where did this drawing come from? What is the full question? Are you sure the 200 referes just to that one triangle side?

[thick lynx]

Oh, I looked at the start of the solution and the 200m refers to the whole above line

and the squiggle thing

they just ignore in the solution lol

they draw a straight one

thx

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[supple fiber]

how is the parallel component 50sin15

shouldn't it be 50/sin15

[slate jolt]

imagine if the angle is 0

your formula gives that the parrallel component is infinite

whereas 50sin(angle) gives that it is 0

which makes sense

[supple fiber]

how do you reach that