help-23

[dull rose]

I figured out those 2 were equal by doing a few brute force calculations. Just in case you wonder. So i wasn't able to go any further than what I have started with

[devout harbor]

huh

I'm trying to figure this out myself but aren't these sums typically just written as i=1 to the n?

it seems like your variables are just in different places so maybe try to switch the places of x and n

[peak estuary]

its not like it really matters how you name variables

you can probably do this via induction

[safe radish]

@dull rose Has your question been resolved?

[dull rose]

One is inside sigma and one isnt 😅

Basically these 2 are same (where x's are same)

Question is why and how

[buoyant shadow]

suppose x is 4

each row is (n+1)2^n

you just distribute the first column entirely, one number per column

[dull rose]

I am confused... Where does those rows come from ?

[buoyant shadow]

2+2 comes from (1+1)2^1

8+8+8+8 comes from (1+3)2³

[dull rose]

Oh I see. This is lot more easier than how I ended up calculating it lol. Thanks

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[lean otter]

Diophantine Equation

[lean otter]

Don't understand how it workers exactly

Did i ask a Doctorate lvl question wheres everyone

[spark oriole]

perhaps

[lean otter]

Its simple i just want someone to tell me how it work because i need it for a function of..... MD nuggets calculator

[safe radish]

@lean otter Has your question been resolved?

[lean otter]

Dosnt matter bot ill do it my was the most complex way ofc

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[cobalt flint]

Can anyone help me find the two numbers

[cobalt flint]

or like explain it in a way that would be easy for me

[merry sleet]

you should solve the quadratic real quick its the best way when you dont know any root

or you could try and guess one rtoot by trial and error if you can see one

and factorize from there

[cobalt flint]

Okay that was easier than I thought

thank you

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[warm onyx]

in problem 71

How can i find the recurrence relation?

I've come up with this

but doesn't seem like it

[compact ferry]

well if d1 = 80

what is d2?

[warm onyx]

40

[compact ferry]

no d2 would be 40 + 80

[warm onyx]

Oh

[compact ferry]

1/2 * d_n-1 + 80

[warm onyx]

So that's the recurrence relation?

[compact ferry]

if you write d_n = 1/2 * d_n-1 + 80 then yes

[safe radish]

@warm onyx Has your question been resolved?

[warm onyx]

What about problem (b)? It seems like I can't take a limit of {d_n}

I feel like I should take the 24 hour thing into account.

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@warm onyx Has your question been resolved?

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[glossy crest]

What is the difference between analitically prooving a theorem and synthetically prooving a theorem?

[safe radish]

@glossy crest Has your question been resolved?

[glossy crest]

<@&286206848099549185>

[glossy crest]

<@&286206848099549185>

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[lean otter]

How do I solve the powers

23 goes up

-23 +1

22

But my book says its -24

[obtuse plover]

Ye they put it into scientific notation

They did the 1.01/6.022

[lean otter]

Yeh

But the powers

Thats what im having difficulty in

[obtuse plover]

Which is 0.167

[lean otter]

yeh

[obtuse plover]

What’s the final answer ur book gives

[lean otter]

1.68 x10^-24

Actually its from a youtube video

See? -24

[obtuse plover]

Where’d u get the 10 in the numerator from

1.01*10^1 u have

[lean otter]

I dunno I added it by myself

Ah so confusing

[obtuse plover]

Lol u can’t do that

1.01 is not equal to 1.01*10

That’s where the confusion is coming from

[lean otter]

Oh

[obtuse plover]

So the yt video did (1.01/6.02)*10^(-23)

[lean otter]

Do the $ thing

[obtuse plover]

Which is 0.1677 * 10^-23

Idk how to lol

[lean otter]

Yeh

[obtuse plover]

And 0.1677 * 10^-23 in sci notation is 1.677 * 10^ -24

[round rover]

$\frac{a}{b}$ does fractions and $a^{b}$ does powers

[flat frigate]

Shell

[obtuse plover]

Interesting, thanks

@lean otter do u see what they did now

[lean otter]

oh

OH

I remember what scientific notation is now

[obtuse plover]

Yeye

[lean otter]

Thank you both but you more

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[valid iron]

https://docs.google.com/forms/d/1gdo5yPGEMnoxiroQUp_QmrOWg0EXif-FYUlvYN9j4BY/edit?pli=1#settings

[valid iron]

pls fill out it is for a school project

i am doin a project on data management

i need a 100 responses

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[thorn fossil]

Given f(x) = -2x^2-7 find f(a-3)

[lusty widget]

yeyeye

wassup

you see the x?

replace it

with a-e

a-3*

and expand

boom

[thorn fossil]

so woudl it be f(x) = -2(x-3)^2-7

[lusty widget]

aye aye

nice

see you got this

aye aye

not c

x

I think u meant

to type

a

but ye

-2(a-3)^2-7

[thorn fossil]

ty

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[potent zephyr]

Hi!

[potent zephyr]

I need some help with part d of this question

<@&286206848099549185>

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[lusty widget]

aye aye

wassup

did u

try anything

or nah

where are u confused

[keen tusk]

So ik that y intercept is

1

[fossil vine]

Yes

[keen tusk]

But idk the y and gradient

[fossil vine]

You can see the gradient by looking at the boxes.

If it goes one to the right, it goes one up

That means the gradient is one.

[keen tusk]

And y

Oh wait

[fossil vine]

I think you mean the interception?

[keen tusk]

Y is y

[fossil vine]

yes?

[keen tusk]

Yes

Its 1

And the gradient is 1

[fossil vine]

yes

[keen tusk]

Y=x+1

[fossil vine]

Yes

That‘s the function

[keen tusk]

Got it thanks

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[sharp cypress]

what did we do here

where did (i + p - 1) go

[plucky elk]

(i + p - 1) = (i + p) - 1

[sharp cypress]

did we move the last sum to the other side

and then add the terms left

[plucky elk]

1 times this term was moved to the right

but the -v^2/x^2 stayed on the left

from splitting this

[safe radish]

@sharp cypress Has your question been resolved?

[sharp cypress]

wait a minute

almost

for me the right hand would look like this

[plucky elk]

use this

[sharp cypress]

so there will be a 1 somewhere if i use it

[clear blade]

factor out (i+p) from the first two terms in the square brackets

[sharp cypress]

take (i+1) out of the bracket ?

[clear blade]

(i+p)(i+p-1) + (i+p) = (i+p)[(i+p-1) + (1)]

[sharp cypress]

yes

[clear blade]

the right hand side is just (i+p)(i+p)

[sharp cypress]

where 😭

[clear blade]

(i+p-1) + (1) = i+p

[sharp cypress]

yes

okay

i see it now

Thank you everyone

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[finite widget]

I'm confused if there's a sharp change then there's no gradient?

why is the gradient not defined

can't you find the derivative and just work out the gradient

the second equation -x+3, x more or equal to 0

the derivative of that would just be -1

so wouldn't the gradient just be -1

[safe radish]

@finite widget Has your question been resolved?

[finite widget]

<@&286206848099549185>

[safe radish]

@finite widget Has your question been resolved?

[safe radish]

@finite widget Has your question been resolved?

[finite widget]

sorry but

a gradient cannot be defined at cusps and endpoints right?

[finite widget]

.close

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[lean thorn]

hi what have you tried so far?

[quiet stump]

Sorry I don’t understand the question

[lean thorn]

okay so let's break it down in steps:
What is the total of the first 4 natural numbers added together?

[quiet stump]

1+2+3+4 = 10

[lean thorn]

good!

now what is the sum of the first 5 even nubmers?

[quiet stump]

2+4+6+8+10 = 30

[lean thorn]

beatiful

now what are those things added together?

[quiet stump]

40

[lean thorn]

wait

hold on

I think I misread somethign

[quiet stump]

Ok

[lean thorn]

no wait I was right

okay so we had two numbers 10 + 30, so what would the average be between those two?

[quiet stump]

20

[lean thorn]

there ya go 🙂

[quiet stump]

‘The average of the sum’ is what I don’t know really

[lean thorn]

so that's what we just did

[quiet stump]

Ok I need to read more

[lean thorn]

the average is the total divided by how many things you totaled together

so we had 10 and 30, so we divide by 2

[quiet stump]

Yes, but I was thinking I had to do something like 40 / 9

[lean thorn]

yeah that's what I thought initially too, but it asks you to find the sums separately first

[quiet stump]

Hmm

[lean thorn]

it's averaging the sums, not all the numbers all together

for example

[quiet stump]

Yeah that’s what I was confused about

[lean thorn]

say if you owned a store

and you made $100 on day 1, $110 on day 2, and $60 on day 3

what is the average total you made?

[quiet stump]

90

[lean thorn]

bingo

now do we need to know the average price of each item sold here?

nah

different question

[quiet stump]

Ok

[lean thorn]

does that analogy make sense?

[quiet stump]

Yeah its just hard for me to understand sometimes about the way questions are phrased

[lean thorn]

you'll get used to it

[quiet stump]

👍🏻

[lean thorn]

as you get further in math you get better at deciphering what people are actually saying lol

any other problems?

[quiet stump]

Ok thanks

Yeah I have a few more if you don’t mind

[lean thorn]

yeah go ahead

[quiet stump]

Ok wait

Both questions

[lean thorn]

okay so for question 15, we have some number p which is 1.5x larger than q. So we know that p = 1.5q. Good so far?

[quiet stump]

Yes

[lean thorn]

we also know that p is 18 bigger than q, so that means that p = 18 + q right?

[quiet stump]

Yes

Oh

I see it

[lean thorn]

🙂

[quiet stump]

36

?

[lean thorn]

seems reasonable. Want to show me how you got that?

[quiet stump]

So make both p’s equal to each other

[lean thorn]

good so 18 + q = 1.5q?

[quiet stump]

1.5q = 18 + q

0.5q = 18

Q = 36

[lean thorn]

okay good!

now we need to find p

we can do that by plugging it back into either equation

doesn't matter

[quiet stump]

Yeah

Got it

[lean thorn]

so we should get q = 36 and p = 54?

so we're looking for p + q, which should be 90

so it looks like the answer is none of the above

[quiet stump]

Yeah

[lean thorn]

unless we did something wrong lol, but the arithmetic seems fine

[quiet stump]

Yeah its good

[lean thorn]

dank

so for Q16, I'm assuming that the dancer is equally likely to step on any of the tiles

so if we have 1-Blue, 1-Green, 2-Red, 2-Orange, and 3-Grey, how many possible tiles can we potentially step on?

[quiet stump]

8

?

[lean thorn]

I count 9

[quiet stump]

Oh ya

Lol

[lean thorn]

lol

so the likelihood that the dancer will step on a grey tile is 3/9 then right?

[quiet stump]

Yes

[lean thorn]

so there you go

m = 3 and n = 9

[quiet stump]

Damn I missed the blue tile

I was saying 8/3

3/8

So then that is 1/3

1+3 = 4

[lean thorn]

hmm

well that depends if they want you to simplify or not lol

it's either 4 or 12

[quiet stump]

Yeah

They should say that right?

[lean thorn]

yeah I would maybe ask about that

or if you've been reducing in class

it's one of those two answers lol

go with your gut I guess

[quiet stump]

Yeah

[lean thorn]

hey I gotta head to bed actually

[quiet stump]

Ok

[lean thorn]

I recommend that you close this channel and re-open with this problem

best of luck

[quiet stump]

Thanks

[silver condor]

I’ll take a look as his replacement

[quiet stump]

👍🏻

[lean thorn]

teamwork makes the dreamwork!

[silver condor]

Give me a sec

[quiet stump]

Sure

[silver condor]

do you understand what this question is asking you for?

[quiet stump]

Not really

[silver condor]

well me neither

lol

[quiet stump]

I know that it goes up to ten

Lol

[silver condor]

Its the wording thats caught me

[quiet stump]

Same!

[silver condor]

Is it asking for that?

[quiet stump]

The answer is 6

But I have no idea

[silver condor]

do you have a unit?

[mortal sandal]

That looks like 5 boxes to me

[silver condor]

6cm or 6cm^2

[quiet stump]

6 cm

[mortal sandal]

"A unit cube is in size"

probably inches?

[silver condor]

Im assuming the width doesnt change

[mortal sandal]

I think there's missing numbers though

[silver condor]

So it should just be 5 blocks long

[quiet stump]

Hmmm

[silver condor]

Thats my shitty diagram

But im assuming thats how they add the stairs

[mortal sandal]

lol

I love it

[silver condor]

But then width doesnt change at all

[quiet stump]

Yes

[mortal sandal]

nonsense unanswerable question tho

[silver condor]

Maybe its asking for that

but its still not 6

[quiet stump]

Yeah I thought exactly like you

[mortal sandal]

It says of each step

[silver condor]

Just skip this question

[quiet stump]

Yeah

How about these 3?

[silver condor]

21 what you can do is find the area of one rectangle

[quiet stump]

Yeah 12cm^2

[mortal sandal]

and then what else can you tell about them from the diagram

[quiet stump]

Hmmm

[silver condor]

brb

[quiet stump]

Ok

[silver condor]

tip, look at

What does that tell you

[quiet stump]

= 30cm^2

[silver condor]

Let’s say x is the longer length

And y is the shorter length

[silver condor]

What does this tell you of x and y

Does that help

[quiet stump]

X + 3y

?

[silver condor]

almost

x=3y

right

Now if you look back at the whole shape

can you get me the area of this in terms of x and y

[quiet stump]

2x+2y = 60

Xy=30

[silver condor]

area not perimeter\

area is base times height

[quiet stump]

Oh ya sorry

(2x)(2y) = 60

[silver condor]

almost

First tell me the height

[quiet stump]

X

[silver condor]

now base

[quiet stump]

Oh

X^2 x Y^2 = 60

[silver condor]

almost

Your getting close with each step

tell me the base

[quiet stump]

Oh

X(x2y) = 60?

[silver condor]

x(x+2y) = 60?

[quiet stump]

X(x+2y)

Yeah

[silver condor]

yep

[silver condor]

And rember this

[quiet stump]

So sub it in

[silver condor]

yes

and solve for x or y

[quiet stump]

Ok

[silver condor]

Then you can solve for the other variable

Then find perimeter with 2x+2y

[quiet stump]

Answer 16

[silver condor]

yes

[quiet stump]

Ok

[quiet stump]

Damn I wouldn’t have known to cut it in half and try things out

But anyway thanks

[silver condor]

The way i would go about this is turn the 54km/h into m/s

[quiet stump]

Ok

54000m/h

Then

[silver condor]

m/s

[quiet stump]

90

[silver condor]

is it?

[quiet stump]

9

9m/s

[silver condor]

The way to do it by hand is first turn hours into seconds
54 km/h = 54/60 km/m = 54/60 /60 km/d

Then turn km to m
54/60/60 = 0.015 km/s
0.015 x 1000 = m/s

So if the train takes 20seconds to pass him. And its going 15metres every second

how long is the train

[quiet stump]

300m

[silver condor]

yep

[quiet stump]

Ok

[silver condor]

Q23, you just try it by hand

[quiet stump]

Ok

6

[silver condor]

yes

[quiet stump]

I have two more questions

[silver condor]

[quiet stump]

Do you have time?

[silver condor]

yeah

[silver condor]

uhh you might need someone else to help you with this

i gtg

[quiet stump]

Ok

Thanks

[safe radish]

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[lean otter]

How can I make the function go through y=1.5?

[lean otter]

so that it looks like the blue one:

[thin bridge]

introduce a scaling factor if needed

but it already intercepts the y-axis at 1.5

it just might not be immediately obvious from your scale/markings

[idle parrot]

geogebra user

[safe radish]

@lean otter Has your question been resolved?

[safe radish]

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[robust jetty]

Can someone help me find the class intervals and class size for this?

[safe radish]

@robust jetty Has your question been resolved?

[void plank]

Where did you get stuck?

[robust jetty]

Just need the class intervals and class size

[real charm]

Cant you just make up the interval? Might be wrong

Like do:
81-90
91-100
101-110
111-120 etc.

With class size 9

[safe radish]

@robust jetty Has your question been resolved?

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[quiet stump]

Can someone explain why the answer is the third one?

[tiny wraith]

high school math enthusiasts must also be students

so a part of the students are math enthusiasts

and soccer players can be anything

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[quiet stump]

Thanks

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[solemn vault]

How to do this??

[flat frigate]

Basudev

[cosmic grove]

then calculate $\vec{a} \cdot \vec{b}$

[flat frigate]

Ｈｅｒｅｌｓ

[solemn vault]

I did it and I go $50-6m=\sqrt{161+m^2}$

[flat frigate]

Basudev

[solemn vault]

And I get the m value in decimal

But the answer in book says its -3

Ok it got it

I did a simple mistake

[cosmic grove]

$| a | \cdot | b | = \sqrt{25 + m^2} \sqrt{136} = 50 - 6m$

[cosmic grove]

oh ok

[solemn vault]

Yes

Thx

.cloae

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[flat frigate]

Ｈｅｒｅｌｓ

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[fallen oriole]

a²×b²=(a×b)²

[fallen oriole]

Is this accurate?

[solemn vault]

Ye

[fallen oriole]

Okay thanks

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[barren ledge]

uhh that looks wrong

[tiny wraith]

no, it's correct a^2 + b^2 is not equal to (a + b)^2

with multiplication it works

@barren ledge

[fallen oriole]

,calc 9^2 * 9^2

[flat frigate]

Result:

6561

[wild copper]

Is that vector cross product?

[fallen oriole]

,calc 81^2

[flat frigate]

Result:

6561

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[wanton rock]

can anyone help me with this

[tiny wraith]

they count in a way that's like reading, left to right and then top to bottom

just start counting in that way with the numbers below and you will probably spot a pattern

[wanton rock]

got it

thanks

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[meager quail]

is $(8){10}$ the same as $(8){19}$ base expansions are breaking my brain

[flat frigate]

Bonjoeri

[split ether]

Yes

[meager quail]

ah okay thanks

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[upbeat swan]

Do quadratic functions have a maximal output value?

[upbeat swan]

I think not

[glass carbon]

f(x) = ax^2 + bx + c then it has maximal output value if a < 0

[upbeat swan]

How

[glass carbon]

so parabola need to open downwards

do you know what is vertex?

something like that

[upbeat swan]

A point where an angle is formed?

Oh ok i understand that

And if a >0 ?

[glass carbon]

then it has minimal output value

[upbeat swan]

Ok

1 more question

Is the slope of a quadratic function different in each point?

[glass carbon]

yes

[upbeat swan]

So you first find the derivative of the function and then substitute the x value of the point you want to find the slope of?

[glass carbon]

yep, generally slope is 2ax + b if f(x) = ax^2 + bx + c

[upbeat swan]

Ok

Can 2 different functions have the same derivative?

[glass carbon]

of course, since derivative of constant is 0, we can take for example x^2 and x^2 + 1

[upbeat swan]

Ok

Thanks

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[bleak yacht]

wait

.close

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[robust lantern]

Hi I have some problem solving the b, and c. Don't know if I'm doing it right or wrong.

A straight line passes through the point (3,5) and has a slope of 3/5.

Determine a so that the line also passes through
a) point (5,a)
b) the point on the y-axis where y=-4a
c) the point on the x-axis where x = 3 - a

[foggy salmon]

whatve u done

[robust lantern]

I'll send my work, wait a sec.

https://media.discordapp.net/attachments/1027663613558784072/1029810731870339172/20221012_193917.jpg?width=702&height=936

https://cdn.discordapp.com/attachments/1027663613558784072/1029810943384879194/rn_image_picker_lib_temp_e384f84f-9708-4252-98ed-6d893106221a.jpg

Sorry it's not english, but I don't know what I did wrong in b. and c.

@foggy salmon

The right answer of b. and c. are b. a = -4/5 and c. a = 25/3

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[lean otter]

divergent right?

because u sub gets you to the integral from 0 to (e-1) for the function 1/u^2

so thats divergent

ye?

[exotic ember]

no

u = e^x -1

du = e^x dx

so du/u^2

[zinc berry]

yes it's divergent.

[exotic ember]

What is divergent

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@lean otter Has your question been resolved?

[lean otter]

thank you

[lean otter]

something you have not learned yet apparently lol

its about improper integrals

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[exotic ember]

I haven't

[lean otter]

u good

youll cover it in calc 2

[exotic ember]

I'm not in the us

[lean otter]

calc 2 isnt US-only

[exotic ember]

I'm a jee student

[lean otter]

ye i know a few of em

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[lean otter]

.close

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[lean otter]

thats easy

[thorny echo]

Answers are either : 225pi cm squared , 267pi cm squared , 281pi cm squared , 239pi cm squared 303pi cm squared

[thorny echo]

im relieved

[lean otter]

okay i need like 10 mins to solve this

but just to make sure

[thorny echo]

okay thats good

thankyou so much

you're a good person

[lean otter]

the sum of the diameter of B and C = diamete of A right?

[thorny echo]

hold on

doesnt mention

only areas of b and c = area of a

[lean otter]

1 sec

if the 2 circles were above each other

then the sum of their diametes would be equal to A

visual aid is the green line

[thorny echo]

yes

your right since they are tangent

[lean otter]

so now you can get the raduis of A, calc its area

get the area of C and B and add them

compare to the area of A

BOOM BOW you got it

think you can do it?

[thorny echo]

youve opened my third eye

[lean otter]

its what i do

[thorny echo]

yes i got it from her

here

[lean otter]

great

[thorny echo]

i will never call myself smart ever again

[lean otter]

lmao

[thorny echo]

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[errant terrace]

im tyring to solve this using the cast diagram

@errant terrace

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[safe radish]

Please don't occupy multiple help channels.

[kind edge]

How do you do the second to last one

Why do you need R

This isn’t geometric right?

!close

How do you close the channel

[mellow star]

use .close

but wait for somone

they will help

you can ping for helpaswell

<@&286206848099549185>

[arctic locust]

It's a telescoping series

[kind edge]

I see

[arctic locust]

Develop the $\ln$ in function of $n+2$ and $n$

[flat frigate]

black_couscous

[arctic locust]

Then separate the sums

Reindex

And you'll get your result

You could also use the asymptotic behavior of $\ln$

[flat frigate]

black_couscous

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[still fern]

What is Z in this case, is it just the summation of both X and Y?

My program calculating this equation sometimes gets an error due to division by zero.

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[lean otter]

Someone please explain me this example:

[lean otter]

Will the initial conditions mean that:

a) t = 0
   u = 2

b) t = 0
   v = 3

If yes, then please explain to me the x(n), f(n) and f'(n),

Thank you 🙂

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[lean otter]

<@&286206848099549185>

[lean otter]

<@&286206848099549185>

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[lean otter]

<@&286206848099549185>

[lean otter]

<@&286206848099549185>

[lean otter]

<@&286206848099549185>

[lean otter]

<@&286206848099549185>

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[late wagon]

If the first urn has 6 blue balls and 4 red balls, the second urn has 4 blue balls and 6 red balls, and the third urn has 6 blue balls and 4 red balls. What is the probability of drawing 2 blue balls?

[late wagon]

how to solve this problem

?

note:it's not homework or exam

i tried to draw tree and calculate the possibility

but i'm not sure if it's the right numbe

r

[lean otter]

wouldn’t this just be ||2/total balls||

[late wagon]

lmao i don't think so

[lean otter]

idk lol Im 9th grade so i jus thought that

Or wait no

Probably ||2/amt of red balls||

or nah that wouldn’t work either

actually I have no idea anymore probably just amt of blue balls/total balls or something idk

[late wagon]

i tried the last one BUT i'm not sure if it's correct

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[lean otter]

Anyone can explain me?

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[pure agate]

Did you still need help?

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[plucky moon]

I can combine the constants here right?

And solve c_1 and afterwards intgrate x(t)

And then solve c_2

And then the question/problem is done

Is that correct?

Im still kinda bad at differential equations so Im making sure I understand it

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[lean otter]

yo

[lean otter]

what does this /3 mean?

does it mean divided by 3?

[halcyon carbon]

Like fractions?

Yeah

[lean otter]

oh ok just written weird idk ty

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[sonic jewel]

can i get some help for this?

[white hollow]

hint, inverse is the function reflected about the line y = x

[sonic jewel]

ok and?

[white hollow]

so at the point of intersection the x and y coordinate will be the same

[split ether]

So if y = f and y = f^-1 intersect at one point, then so do y = f and y = x at that point

[sonic jewel]

so do i solve f(x) = x

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[spiral pine]

Is this legal?

or bad notation?

or can i simply remove 0

[broken pewter]

I sure as hell have never seen this notation

[halcyon carbon]

Why not from 0 to n

Or 1 to n

[spiral pine]

Because im doing it the other way around lol

[broken pewter]

so ig just remove the 0 if the context implies the natural numbers

[broken pewter]

sums are commutative over the natural numbers

[halcyon carbon]

$\sum_{i=1}^n 2i = n^2 +n$

[broken pewter]

so the other way around should be the same as the regular way

[spiral pine]

ooh it cant go down?

[flat frigate]

Pure

[spiral pine]

yeah i know its the same but in my context its kinda the other way around

so i was kinda freestyling

[broken pewter]

what I'm sayin is that
$$2n + (2n - 1) + \cdots + 0 = 0 + \cdots + 2(n - 1) + 2n$$

[flat frigate]

Duhon

[spiral pine]

yeayea i know

thansk though

I use both

but one goes from 0..n the other is n..0

Writing the same for both situations is correct but not as intuitive when reading

so can i use the bottom notation or is it just no go

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[spiral pine]

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[topaz scarab]

I just saw a question where someone asked how to write a piecewise function (first image) in one line, and another person responded using characteristic/indicator functions (second image). However, is the response actually correct? I mean, shouldn't the numbers replacing A be sets, not numbers?

[topaz scarab]

So it'd be $f(x) = a1_{{0}} + b1_{{1}} + c1_{{0, 1}^c}$.

[flat frigate]

JaimermXD

[topaz scarab]

And what about piecewise functions were the condition is that x belongs to an interval (a, b)? Could I write $1_{(a, b)}$ directly, or would $1_{{x \mid a < x < b}}$ be better?

[flat frigate]

JaimermXD

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[mental patrol]

I am trying to find the p value and HSD :/

I tried many times cannot figure it out

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[lean otter]

Please explain me this definition:

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[lean otter]

me neither

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[safe radish]

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[fleet forge]

We learned factorials today, but I want to know why 0! is always 1?

[lean otter]

what definition of factorial did you use?

[fleet forge]

What’s a definition?

[lean otter]

how did your teacher explain factorial to you?

was it 5! = 5*4*3*2*1

[fleet forge]

Yes

But I don’t understand why 0 is 1

[lean otter]

can you see that $\frac{5!}{5}=4!$

[flat frigate]

Toby

[fleet forge]

🤔

You remove 5 from multiplication

[lean otter]

yeah

[fleet forge]

And at 0

[lean otter]

so $\frac{1!}{1}=0!$

[flat frigate]

Toby

[fleet forge]

😲

Yeah

It makes sense

Thanks

[lean otter]

yw :)

[safe radish]

@fleet forge Has your question been resolved?

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Remember:
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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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[brittle verge]

hi, why is this:

[brittle verge]

not the same as this?

[white hollow]

there's not a minus sign in front here?

[brittle verge]

no

in the second one just 1 -

[white hollow]

??

[fossil vine]

The minus in the second one should be a plus.

Then it would be correct.

[white hollow]

no

it's already correct

[fossil vine]

Because you divided (or multiplied) both sides by -1

No

[white hollow]

use log laws it's correct

it's the first one that's wrong

[fossil vine]

Okay, sorry

[brittle verge]

like this no?

[fossil vine]

I was looking for a transformation from the first one into the second one.

[white hollow]

yeah fair enough

[white hollow]

yeah I think it should be this for the first one

[brittle verge]

thanks 😀

.close

[safe radish]

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[safe radish]

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Remember:
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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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[fossil vine]

,rotate

[thorny echo]

Question 3

And no the diameter for a is not 25

[thorny echo]

Do you understand the question?

[white hollow]

I'm working on it

[fossil vine]

Somebody asked the same question yesterday.

Where did you get it?

[white hollow]

I've seen this question a long time ago as well

[fossil vine]

Okay

I thought it might be a competition or something like that.

[thorny echo]

That was me

[thorny echo]

Idk about that

[white hollow]

nah I'm sure

[thorny echo]

Me

[white hollow]

I've solved this before

I vaguely remember how, you use right triangles

[thorny echo]

Could u help now

[fossil vine]

Okay

[thorny echo]

Right triangles?

[white hollow]

all the lines you drew alreayd, make them hypotenuse of right angle triangles

[thorny echo]

It’s for a tutor😭😭😭

[fossil vine]

Do you have a new profile picture?

[thorny echo]

Yep

My old one was the default

[fossil vine]

That's why I didn't remember you.

[thorny echo]

What do you mean

[white hollow]

like so

[thorny echo]

Hm

[white hollow]

have to go so won't be able to help further

sry bye

[thorny echo]

But when you make the right triangle

[thorny echo]

Ok bye

@fossil vine do you have any ideas

[fossil vine]

No

Sorry

[thorny echo]

Ok

It’s alright

,rotate

[thorny echo]

Question 3

[safe radish]

@thorny echo Has your question been resolved?

[thorny echo]

You might have to https://www.ics.uci.edu/~eppstein/junkyard/tangencies/three-circles.html

[safe radish]

@thorny echo Has your question been resolved?

[safe radish]

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[safe radish]

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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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[quiet shard]

For 127 i got posirive cos and tan but theyre supposed to be negative

[quiet shard]

And im not sure why loll

[stray socket]

Look at your domain for theta

[quiet shard]

It was in the first quadrant right?

[stray socket]

No

Look how it's restricted

[quiet shard]

Why

[stray socket]

I'm going to rewrite what your problem says verbatim

[quiet shard]

If its greater thab pi/2 shouldnt it be toward the right of pi/2

[stray socket]

For theta? No

You're taking about angles, not X-Y stuff

Angles don't work like that

The angle is greater than 90 degrees, less than 180 degrees

[quiet shard]

So if the angle of theta is greater than pi/2 its to the left?

[stray socket]

You always go anticlockwise from the positive x axis

[quiet shard]

Bc its greater in value over the circle?

[stray socket]

So past 90 degrees, before 180

So second quadrant

[stray socket]

Depends

It can also be in the 4th quadrant

[quiet shard]

So toward the right?😭

[stray socket]

No

[quiet shard]

Isnt anticlockwise downward

[stray socket]

No that's clockwise

Clockwise goes "downward"

[quiet shard]

Ohh i was confusing anti clockwise bc i always call it counterclockwise

Okay so bc theta is greater than pi/2 its a greater angle so past where 90 degreees is so thays why its in second quad?

[stray socket]

Yes

[quiet shard]

Okay so id still solve it the same way just make sure my cos is nevaitve and sin is pos?

Like at the end?

[stray socket]

Yes

[quiet shard]

Tysmmm

.close

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[fiery valley]

Is this proof correct?

[solar hazel]

I might not be following it right but this looks like what you're trying to prove?

[fiery valley]

Right

.close