help-13

[crimson sedge]

because u seem to be confused with what i am saying so maybe there is something i can do to help

its hard to describe it over text haha, it is way better if i can somehow visually show u it

[junior timber]

could u draw it maybe?

on like a paper and take a pic?

[crimson sedge]

yeah i can but i also dont want to just completely throw numbers in ur face because that will not make u understand it well either

maybe if i can draw it and show it to you at the same time

well okay

[junior timber]

okk

[crimson sedge]

@junior timber

alright

so this is what u have right now

lets redo what we just did earlier agian

What is AB?

[junior timber]

x

[crimson sedge]

no

[junior timber]

or 2x in its ABD

[crimson sedge]

yes

what is AD

r u there?

[junior timber]

oh sorry

like ABD triangle?

its x

[crimson sedge]

yes

what is BD

[junior timber]

x√3

[crimson sedge]

yes

btw if u r busy we can just do this later

[junior timber]

no no its ok

[crimson sedge]

this will take forever if u have to go every now and then

[junior timber]

i just need to check something before

im here now

[crimson sedge]

alright no worries

so with all of what we have said we have this

is this okay so far?

[junior timber]

yes

[crimson sedge]

alright so here is what i am going to do now

i will be splitting the triangles like this

its the same thing, i just split them off alright?

so now, i want u to ignore the left side of this picture

[junior timber]

okk

[crimson sedge]

meaning just focus on this

what is BD?

[junior timber]

okk

x

[crimson sedge]

alright but we already used x for the other triangle so lets give it another variable name

lets say y

is that fine?

[junior timber]

yea

[crimson sedge]

alright

so now what is BC

[junior timber]

BC is x√3

[crimson sedge]

what did we say about the variable name

[junior timber]

oh sorry

y√3

[crimson sedge]

okay

what is DC

also hold up no BC is NOT ysqrt(3)

recheck the triangle in yellow next to it

[junior timber]

oh

ohh right

oops

2y

[crimson sedge]

okay whaat is DC

[junior timber]

wait wait

for the yellow thing

isnt the shorter side suppose to be x

not x√3

[crimson sedge]

its not based on that

its based on the angles

[junior timber]

oh ok

[crimson sedge]

thats what i meant by this here

so like

opposite of angle 30 = x
opposite of angle 60 = xsqrt(3)
opposite of angle 90 = 2x

so anyways whats DC

[junior timber]

ohh ok

anyways

DC is

y√3

[crimson sedge]

okay at last

we finally wrote down the sides

now

what is the relation between those two sides

[junior timber]

BD = y = x√3

[crimson sedge]

yes!!!

so here is the idea

you see those y's in the DBC triangle?

we want to make them all be x's instead

and THEN we can get the ratio

[junior timber]

ohh ok

[crimson sedge]

so you already found the first one

y = xsqrt(3)

Now

what is BC

in terms of x

[crimson sedge]

look at this closely

BC is 2y

[junior timber]

yes

[crimson sedge]

we know y is equal to..

[junior timber]

x√3

[crimson sedge]

okay

so 2y is..

[junior timber]

2x√3?

i dont think thats right

[crimson sedge]

no you are right

it is

[junior timber]

oh ok good

[crimson sedge]

so now

what is DC

come on shu u got this this is like the last one

[junior timber]

uhh

[crimson sedge]

then we can be done

[junior timber]

so DC is y√3

[crimson sedge]

yes

what is y

[junior timber]

is it x√3√3

[crimson sedge]

yes

[junior timber]

[crimson sedge]

but what is

sqrt(3)*sqrt(3)

[junior timber]

uhh

3?

[crimson sedge]

yep!

which means this is...?

[junior timber]

3y

[crimson sedge]

why did it turn back to y 😭

[junior timber]

OH WAIT

LOL

3y

[crimson sedge]

did u

say the same thing

twice

[junior timber]

OMG

3x

there we go

[crimson sedge]

WOOOOOO GOOOD JOB SHUU

U R DONE

GOOD JOBB

[junior timber]

wait so

AD:AC

is

[crimson sedge]

okay so what is AD

[junior timber]

x

[crimson sedge]

first and foremost

what is AC

here is the final picture

[junior timber]

4x

[crimson sedge]

yes

[junior timber]

omg yay

[crimson sedge]

YAAAAAAY

WOOHO

took us a little under 2 hours but we are done finally haha

[junior timber]

lOL

SORRY

[crimson sedge]

okay but

whats the final thing u have

the ratio

that is

[junior timber]

x:4x?

[crimson sedge]

yeppie!

but

u can simplify that

[junior timber]

wdym

[crimson sedge]

okay so

what is a ratio

like

[junior timber]

its like a fraction

[crimson sedge]

yes!

so

what is x:4x as a fraction

[junior timber]

1/4?

[crimson sedge]

yesss

[junior timber]

ohhhh

[crimson sedge]

so

the moral of the story is that

the whole length is 4 times larger than AD

[junior timber]

phh ok

[crimson sedge]

and u r done

[junior timber]

tytyty

lixera

i have two more which is like similar but it gives numbers

i have one of the numbers but idk how to find the other one

can u help

[crimson sedge]

suree

also just call me lex

[junior timber]

okayy!!

question 10

[crimson sedge]

alright lets see what we got here

alright so ur BD value is right

CD meanwhile

alright so like

not sure if it is the intended method but it does it

u can find the length of BC first

[junior timber]

oh wait how

[crimson sedge]

okay this is gonna be a bit funky but

first

tell me what AB and AC are

[junior timber]

uhh

AB is 5√3

[crimson sedge]

yep!

[junior timber]

AC idk

[crimson sedge]

um

reread what the question says 😅

[junior timber]

oh

oop

LOL

5√3

[crimson sedge]

PFF lmaoo

math rotted ur brain yet? lmaoo

but yeah it is 5sqrt(3)

okay so here is the funky part

for that triangle

i want u to draw a dashed line of the height of the triangle

[junior timber]

realll

okk

[crimson sedge]

okay so question to u shu

if two sides of a triangle are equal

what is the triangle called

[junior timber]

isoscelence

[crimson sedge]

yep!

[junior timber]

lOL I DIDNT SPELL IT RIGHT

[crimson sedge]

cloooose enough pfff

but anyways

along with the two sides being equal what else is equal

[junior timber]

the height?

angle?

[crimson sedge]

angle yeah haha

but the angles of what

what angles are equal in an isosceles

[junior timber]

uhh

45

?

[crimson sedge]

err no no

dont give me numbers

just like

which two angles in an isosceles are equal

just like

the position of them

here is a picture of an isosceles

i think this should make it a bit clearer haha

also take a break if u r getting tired haha

[junior timber]

okk

u mean the sides?

are equal?

[crimson sedge]

yes the sides are equal

but thats not the only thing equal

[junior timber]

the angles?

[crimson sedge]

yes!

but how would u describe those angles

like they are equal

okay so basically

in an isosceles triangle

the angles opposite to the two sides that are equal are also equal

[junior timber]

yea

ohhh

[crimson sedge]

yeah so always remember this

When u look at an isosceles triangle similar to this

if u notice A and B are equal

then a and b are also equal

a is opposite of A

b is opposite of B

[junior timber]

ohh

[crimson sedge]

is this okay?

[junior timber]

yes

[crimson sedge]

alright thats good

now

i want u to draw the height

and show me

[junior timber]

on my triangle or this triangle

[crimson sedge]

Remember, the height will make a right angle with BC

[crimson sedge]

yours

[junior timber]

oh ok

one second

[crimson sedge]

was using this for an example

[crimson sedge]

yep u nailed it!

okay so lets call this new point the height makes with the base W

[junior timber]

okk

[crimson sedge]

i need u to like try and notate all of what i am saying so u dont get lost btw

so

what is angle AWB and angle AWC first and foremost

[junior timber]

right

angle

[crimson sedge]

yep!

note that down so u dont lost

also note down that value you found for AB and AC too

on the triangle

[junior timber]

okk i didon the side

not on the triangle

[crimson sedge]

yeah no worries

okay here is the question of the century

what is angle BAW and and angle CAW

[junior timber]

idkk

oh 60

[crimson sedge]

hint: look at angle ABW and angle AWB

[crimson sedge]

yep!

[junior timber]

yay

[crimson sedge]

note that down too

you are getting there shu !!

[junior timber]

yay

[crimson sedge]

okay so now

we are gonna find what BW and CW are

[junior timber]

okk

do we use the x, 2x, x√3

[crimson sedge]

you have everything you need, consider the following:

-you have a 30-60-90 triangle
-you know AB and AC

[crimson sedge]

yes!! u r getting the hang of it look at ya :D

[junior timber]

yayyy

so x = 5?

cuz AB = AC = 5√3

which is x√3

[crimson sedge]

yep!

[junior timber]

ohh ok

so

BW = WC = 10?

[crimson sedge]

mmm not quite!

recheck ur 30-60-90 triangle

[junior timber]

oh oops

it should be 5√3 then

wait but AB and AC is 5√3

[crimson sedge]

yeah maybe we did an error let me scan thru all of it again to make sure

[junior timber]

okk

[crimson sedge]

oh @junior timber

i figured it out haha

i am dumb

[junior timber]

ohhh

what happened

[crimson sedge]

it went past me too

[crimson sedge]

it was this step

[junior timber]

ohh

[crimson sedge]

look at the triangle AWB closely

so you know that the opposite of the right angle is 5sqrt(3)

but what is the opposite of the right equal to in the 30-60-90 triangle

for reference sake

[junior timber]

ohh ok

[crimson sedge]

yeah so what is it do u think

[junior timber]

uhh

[crimson sedge]

its in this pic

haha

[junior timber]

uhhhuhh

[crimson sedge]

u r really getting tired huh haha

but anyways just look at whats opposite to the right angle

we are like

pretty close to finishing

[junior timber]

okkk

[crimson sedge]

so lets just go thru it

[crimson sedge]

do u really have no idea

[junior timber]

no

[crimson sedge]

like

draw a line from the right angle to the place opposite to it

where do u end up

[junior timber]

oh so 2x?

is that what u meant

[crimson sedge]

yes

when i say "the opposite of" just draw a line from whatever i am talking about in the other direction

anyways

in our triangle

AWB

the side AB is opposite to the right angle

which means that AB = 2x

right?

but what is AB

we know AB already

[junior timber]

ohh

yea

5√3

[crimson sedge]

yes

so find x

what is x

[junior timber]

isnt x 5 tho?

[crimson sedge]

no

[crimson sedge]

i said its wrong here haha

we did it wrongly

[crimson sedge]

so solve for x knowing this equation

[junior timber]

oh

wait is AC 2x too then?

[crimson sedge]

yep!

but like

lets find x first pls 😅

[junior timber]

okkk

[crimson sedge]

you know AB is what

ok i am getting pretty tired so i might have to go rest soon

[junior timber]

oh ok

[crimson sedge]

so if u want to we can finish it off now or later?

[junior timber]

now

[crimson sedge]

okay then lets keep up

[junior timber]

okk

[crimson sedge]

What is AB

[junior timber]

2x

[crimson sedge]

yes its a multiple of x

but we knew from the start

[junior timber]

yea

[crimson sedge]

that it is what

you wrote it down

i told u to note it down if possible

[junior timber]

yup

[crimson sedge]

sooo?

[junior timber]

wait was it AB or BW

[crimson sedge]

AB

just

i need to know what AB is

we wrote it down

[junior timber]

oh 2x?

[crimson sedge]

nooo

at the start

what did we write AB as

[junior timber]

i had it as 5√3 and then i changed it to 2x

so i dont think i got it

[crimson sedge]

yes

it is 5sqrt(3)

[junior timber]

oh

[crimson sedge]

so

AB = 2x

we know that right

[junior timber]

yea

[crimson sedge]

we also know that AB= 5sqrt(3)

can u plug in that

and solve for x

in that equation

[junior timber]

so 2x = 5√3

[crimson sedge]

yes!!

so x is?

[junior timber]

uhh

x = 5√3/2?

(5√3)/2

[crimson sedge]

YES!

wOOO

now

find BW and AW using that

oh wait

u dont need AW i forgot

Just find BW

u found it earlier with the wrong x = 5

[junior timber]

yea

[crimson sedge]

but we found the right x this time which is what u wrote

so like

what is BW

[junior timber]

uhh so BW is x√3 right

[crimson sedge]

yep!

so plug in x u get...

[junior timber]

one second

wait so

u mean

[crimson sedge]

yeah?

[junior timber]

(5√3)/2√3

[crimson sedge]

yes!

so what do u get?

[junior timber]

15/2?

[crimson sedge]

YESSSSS

GOOD JOBBB

so we know BW but what is CW?

hint; think about it for a second u will realise something

[junior timber]

isnt BW = Cw?

[crimson sedge]

YES!

thats the whole point of why we did all of this!

so

AT LAST

what is BC?

[junior timber]

15

[crimson sedge]

YEPPIE

so back to why we were doing all of this

we wanted to find out what DC is

we now know BC

first we need to find BD

so let's go back to before we had the height thing

what is BD?

same story

30-60-90 triangle

you know BA

[junior timber]

yea

[crimson sedge]

yeah

[junior timber]

so then

we take

BC

BD

= 5

[crimson sedge]

Nope!

recheck it

wait

oh

i thought u were talking about what BD was haha

i didnt see u subtract them

but yep! its 5!

u got itt

ad u r done!

[junior timber]

yayy

tyty

[crimson sedge]

phew that took a bit

do u understand what happened all in all?

[junior timber]

i think so

i need help with another question but i think u should go take a break

[crimson sedge]

okay send it why not

lets just power thru it

[junior timber]

question 9

[crimson sedge]

oh the one above it lol

i thought u had solved that

[junior timber]

nope i just wanna to do the one where i got one of the answers

[crimson sedge]

okay

so this one isn't bad

first question

what are the angles of an equilateral

[junior timber]

the same

[crimson sedge]

so?

what is it?

[junior timber]

60

[crimson sedge]

yes

okay

second question

what is angle BAD

[junior timber]

30

[crimson sedge]

right

angle ABD?

[junior timber]

60

[crimson sedge]

and finally

Angle BDA?

@junior timber

[junior timber]

90

[crimson sedge]

okay

so that makes a 30-60-90 triangle, correct?

you know AB, the opposite side of the right angle

find BD

[junior timber]

yea

so AB is 8

is 8 x√3 or 2x

[crimson sedge]

its opposite to the right angle

what do u think

look back at the pic

u need to memorise this so it becomes second nature

[junior timber]

uhh

oh its 2x

so x = 4

[crimson sedge]

yes

yse

yes

aye u r getting good at this :D

so what is BD

[junior timber]

34

*4

oops

ohh wait

so now

BED is 90 degrees

and BD is 2x

so x = 2

so BE is 2

[crimson sedge]

yep!

[crimson sedge]

Ayee look at you go :D

you solved it all without my help

good job !!

[junior timber]

yayy

tyty

tysm for helping me

:D

[crimson sedge]

yesss it was great talking with ya! :D

3 and a half hours long pff but i hope u learnt something at least

[keen yew]

<@&286206848099549185>

[cedar kiln]

@junior timber Has your question been resolved?

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[strong zephyr]

how can you figure out (6x²+8x+9)/(2-x)(3+2x)² in partial fractions?

[strong zephyr]

.close

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[light pine]

im a bit confused on what Z5 acc means here

[dire geode]

https://www.whitman.edu/mathematics/higher_math_online/section03.02.html

[light pine]

so Z5 is just the set 0 1 2 3 and 4?

[dire geode]

you can think of it that way yes. more precisely it's the equivalence classes [0], [1], [2], [3], [4]

[0] = {..., -5, 0, 5, 10, ...}
[1] = {..., -4, 1, 6, 11, ...}

etc

[light pine]

kl thx

.close

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[lone fjord]

Q × {5}
{Q} × {5}
how would i find for the cartesian products of these two sets?

[lone fjord]

Q is the set of rational numbers

[velvet mortar]

Wouldn't it be Q * {5} = {(q1, 5), (q2, 5)... (qn, 5)?

Basically a set of all possible ordered pairs

[crimson sedge]

!nosols

[cedar kiln]

As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.

[crimson sedge]

This is a minor solution but I feel like this could've been explained by simply asking them to give the definition of the cartesian product :/

[lone fjord]

i think so? i'm not sure 100% on the difference between Q and {Q}.
if it were Q i think it would basically go on forever

and if it were {Q} it would have a cardinality of 2

[crimson sedge]

Q is the set of rational numbers, {Q} is a set containing the set of rational numbers

[crimson sedge]

Okay, so what would be the cartesian product between {Q} and {5}?

[lone fjord]

{Q,5}?

actually i think it would have a cardinality of 1? { {Q,5} }

[crimson sedge]

Sorry, I forgot to check in on this channel. Yes, that is correct, {{Q,5}} is the cartesian product of {Q} and {5}

[lone fjord]

thank you

.close

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[crimson sedge]

Hmmm, I see you deleted that last question

Honestly I'm no set theorist, I have no idea how cardinality is formally defined, but I always understood it as a more generalized idea of size

It has the benefit of being able to compare infinite sets

For example, the set of reals has greater cardinality than the set of natural numbers

[cedar kiln]

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[somber brook]

will it not be 3 (3/x) in last line

[digital cliff]

why?

[somber brook]

ohhhh nvm,

i get it now

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[solar tendon]

To solve the derivative I just substitute 3 to the x

?

[dire geode]

Show your work

[burnt leaf]

First off, you need to transform the equation. Once that is done, then you can plug in the 3 as x

Take the derivative of that equation. If you don't know what that means, we can help!

[solar tendon]

This is what I did

Is correct?

<@&286206848099549185>

[cedar kiln]

@solar tendon Has your question been resolved?

[cedar kiln]

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[silk quest]

wait

[silk quest]

nvm

wait

nvm

thought I had something

.close

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[crimson sedge]

2 is not element of B so can this be true??

[dire geode]

The underlined statement is false

[modest lichen]

it iisnt true

[crimson sedge]

ok

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[merry tinsel]

is the formula
for left sum
a+(k-1)deltaX
or a+kdeltaX

[tiny wing]

left riemann sum?

[merry tinsel]

@tiny wing yea

[tiny wing]

it's the former

if I've got your variables right

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[calm hedge]

WHy is the derivative of sin is cos

im new to this

I know product rule and constant rule

[slow thicket]

probably a google question

you can also just look at the slope of the tangent line of sin at every point x

and compare it to the value of cos at that x

[calm hedge]

ok ty

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[ashen peak]

I know that i have to get (log3)^n in the denominator to simplify this but im not able to inject the e^x form into the summation as suggested by question

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[sturdy gale]

Hi again

[sturdy gale]

I have another question

I have done (a), I need help with (b)

I have determined the point of intersection to be [3,6,-7]

but I don't know how to find the angles between L1 and L3

I have done dot product

but came up with 157 degrees, whereas the answer says 90 degrees

Any help would be appreciated thanks 🙂

I'll be waiting...no rush

[radiant topaz]

You have direction ratios tho

[radiant topaz]

Can ya'll show how?

You do get dot product equal to 0

[sturdy gale]

hey sorry

Yep just did that dot product is in fact 0

I used a.b=|a||b|costheta

Honestly don't know what I'm doing

Just really confused

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[sonic seal]

Hi I'm stuck

[radiant topaz]

Hi

Do you need help?

[sonic seal]

Yes

Howw

[radiant topaz]

How did you get log 30

[sonic seal]

5^2 + 5 = 30

i squared 5 = 25

then i added 5

then its 30

is that correct?

[radiant topaz]

The 5 is seprate

Not in log

[sonic seal]

ohhhh

sooo it should be log 25 +5??

[radiant topaz]

Yes

[sonic seal]

thenn whats the base of log 25

is it 5???

[radiant topaz]

The base is e I guess

[sonic seal]

what do I do to proceed further?

[radiant topaz]

Find values given by log terms

[sonic seal]

May I ask how?

[frail needle]

for log(5^2) use log exponent rule to re-write as 2log(5)

[sonic seal]

ohhhhhh

[frail needle]

then log with nothing else is log base 10 so log10=1

[sonic seal]

oaky ill try it

[frail needle]

you already have that nvm

[sonic seal]

what is log 5 base 10

[cerulean sail]

(As mentioned before the log base depends on context, but assumedly it’s base 10 from the previous context)

[sonic seal]

it came out like this

what is the next step ;-

[cerulean sail]

Well you can work out 1+5 of course

Do they ask for the final answer in any particular form?

[sonic seal]

nopp not rlly

can i remove parenthesis??

[cerulean sail]

You could in some places (though there’s a place where they should have remained!)

You could evaluate 5-2 of course too

(Then I won’t complain about the )

[sonic seal]

it gave me 4+ 2 log 5 - log 5

i added 5+1

then subtracted 2

sooo 4 + 2log 5 - log5

is that correct?

[cerulean sail]

If you had log(x-2) in your original expression you can’t do it like that when you’re doing log(5-2)

[sonic seal]

ohh

[cerulean sail]

That’s why I complained about here

[sonic seal]

ahh i see isee

so it should be

(6+2log5) - log (5-2)

[cerulean sail]

Yep, of course you can evaluate the 5-2

[sonic seal]

(6+2log5) - log(3)

howw do i evaluate the logss?

[cerulean sail]

Yep, that’s pretty much the most you can do, you could use log rules to combine them I guess

In this case they don’t come out nicely I don’t think

[sonic seal]

can i remove the parenthesiss now?

oakyy

[cerulean sail]

Yea you could’ve done so some time ago (apart for the ones that were around 5-2)

[sonic seal]

6+2log5-log3

is this the final answerr?

[cerulean sail]

I mean, it’s a final answer

[sonic seal]

but it could go farther??

[cerulean sail]

One I would accept unless I asked otherwise

You could, but overall it’s not much of a big or useful change - as mentioned before, you could combine the logs all together if you wanted to

hey pulse!

[sonic seal]

how do i combine the logs? like subtract themm? im sorry im new to this lesson ;-;

[crimson sedge]

hint: 2log5 - log3 can be rewritten

[sonic seal]

(log 5/3) ^2?

[cerulean sail]

So like you know how you brought down the power of 2, you could “put it back”, and also remember that log(a) + log(b) = log(ab) and log(a) - log(b) = log(a/b)

[sonic seal]

ahhhh

soo the finalizee finalest answer is

6+ (log5/3)^2?

alrighty thanks guyss!

[cerulean sail]

You can’t combine them like that!

[sonic seal]

oop

[cerulean sail]

(The cats are saying no )

[sonic seal]

i thought it was a yes emoji :sobb

what do i doo instead?

[crimson sedge]

hint 2: you might be overthinking it

[sonic seal]

hmm

[crimson sedge]

what would be 2log5 - log3 ?

[sonic seal]

2 log(5/3)???

ahm

2 log2??

2 log 5 - log 3 is as is?

[cerulean sail]

First work on 2log(5)

[sonic seal]

log 5^2 - log 3??

ahhhh

[cerulean sail]

Now carry on

[crimson sedge]

and there’s more you can do with that!

[sonic seal]

log 25 - log3??

soo the finalest answer is 6 + log 25 - log 3?

[cerulean sail]

More

[cerulean sail]

You can keep going!

[sonic seal]

6 + log 25/3?

i dontt see any more steps in this one is this the final answer?

[cerulean sail]

It’s another final answer

As before it really depends on what you get asked for but that’s an alternative one

[sonic seal]

ahhhhhh

okayy

thanks guys !

i learned a lot

bye!

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[echo jasper]

Can anyone see what went wrong here? Have restarted question several times with same answer but it's incorrect

[dull oxide]

For starters, they're not normalized

[gritty viper]

,w orthogonal basis

[wraith dagger]

Results provided by WolframAlpha

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Requested by RedstonePlayz09#0205

[gritty viper]

do they need to be?

[dull oxide]

Back in my day, yes.

I guess definition has changed

[radiant topaz]

Orthonormal are

[radiant topaz]

Show your work

Please

-8-8=-16 btw

[echo jasper]

I can't take pictures of it atm but I just applied the x2 - ( (x2*x1)/x1^2 ) * y1 thing

[radiant topaz]

Yeah I can see you have done it right

Maybe do it the other way round, cuz I think the computer doesn't accept this response for some reason

Still can't see anything wrong with this response

[echo jasper]

Guess system is broken, it told me exactly what I typed but said it was wrong :/

Thanks for looking it over

[radiant topaz]

That's unfortunate

[echo jasper]

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[novel stone]

Any tips on integrating this function?

[novel stone]

Exercise p

[cedar kiln]

@novel stone Has your question been resolved?

[cedar kiln]

@novel stone Has your question been resolved?

[long swan]

this is pretty tricky ngl

maybe let x = tan^2(u), then dx = sec^2(u) du, then:
sec^2(u)/(1+tan(u)+sec(u)) du

[novel stone]

💀

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[proper plaza]

I am pretty sure I am having an incorrect y calculation, I am being asked to calculate this question, for my first iteration I am getting 5.E-14 for y_1 but I am getting -1.6569 via my algorithm.

[proper plaza]

x = (1-sqrt(1-x^2))/(1+sqrt(1-x^2))
y = y_1*(1 + x)^2-(2^(iterator+1))*(x+1)

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[tropic oxide]

you fucked up and deleted your original message

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[tall wraith]

Trying to fix my mess

[tall wraith]

Red box is the assignment.
The solution says, this is a tautology, however when I run it on the bottom, I get 2 false values.
What have I done wrong?

I worked the wrong problem.

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[rustic verge]

What is that function shaped like a thing having three branches?

[quartz frost]

the letter is "Psi"

[rustic verge]

Ohk

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[sonic seal]

Can someone tell me how did it become the encircled number?

[sonic seal]

like how did the limit above it became the encircled one

[fair mortar]

That's how fractions work?

2x/x is just 2

[sonic seal]

ahhh

alrr i see it now

thankss

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[tepid bramble]

hello- forgive me- i hope yall r able to assist me do this

[bright bridge]

e

[tepid bramble]

huh-?

wha-

[bright bridge]

how would you solve it

[tepid bramble]

i-

im still afraid tbh-

[bright bridge]

nothing

[tepid bramble]

id first uh

minus 180-131

and get QTS

[bright bridge]

ok

then

[tepid bramble]

180 - 131 is wait

49

i get 49

[bright bridge]

then uh you find SQP

[tepid bramble]

180 - 49 - 103

28

[bright bridge]

uh now what

[tepid bramble]

and the rets im not sure

:]

rest*

[bright bridge]

im gonna guess ***RPT is 90 degrees

[tepid bramble]

why is it 90 degree?

its not a diameter-

wait its a tangent-

[bright bridge]

maybe

[tepid bramble]

r u familiar with solving thi-

[lethal jackal]

you can partition the circle into these three arcs of different colours

[tepid bramble]

uh huh

[lethal jackal]

by messing around with the angles, you can solve for the measure of the pink arc

the light blue arc is across a diameter, so you know its measure

[tepid bramble]

i still dont get it why did u separated it-

[lethal jackal]

the measure of the yellow arc can therefore be found

[tepid bramble]

😭

[lethal jackal]

that is related to the angle x

[tepid bramble]

i thought we're finding the angle-

i still dont get it at all

[lethal jackal]

if you find the measure of the yellow arc, you can find the angle x

[tepid bramble]

wait

[bright bridge]

ohhh

[tepid bramble]

HAH?

😭

why am i endin up finding the arch

[lethal jackal]

do you know the relationship between the arcs and the angles?

[tepid bramble]

i uh- only angles, im only familiar with the 8 theorems-

[tepid bramble]

yea-

that theorem

[lethal jackal]

that's the relationship between the measure of the arc and the measure of the inscribed angle

do you see how if you find the measure of the yellow arc, then you can find the measure of angle x?

[tepid bramble]

the arch represents the angle itself

im sorry sir

i only see a right angle

😭

in the yellow arch

[lethal jackal]

do you see how the angle x is an inscribed angle corresponding to the yellow arc?

[bright bridge]

oh

[tepid bramble]

uh huh

o well

i've found it-

tyy ya

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[worthy vale]

Is the question and solution wrong?

Why doesn't it x the expected winnings by -1

As we are meant to do the optimal mixed strategy for B, and the pay-off matrix is in the perspective of A

When I times the expected winnings by -1 the value of the game to B is the the same as what they got for A

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[worthy vale]

<@&286206848099549185>

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[fallow ravine]

need help with some math a simple function to get a value
example of the raw function
150+300+450+600
each time a new value with the count 150 gets added it will be added to the number before. the number 150 is static and wont change
so i need a value to check how many times as example 74 will be if i use this princepil

[fallow ravine]

on 150+300+450+600 we have a value of 4

[bright bridge]

what

[fallow ravine]

yea its hard to explain

[fair geyser]

how many times 74 what

[fallow ravine]

74 this function where 150 gets added to the value before

and it starts with 150

150+300+450+600+750 <--- i dont want to add this 74 times

[bright bridge]

ok lets divide everything by 150

[fair geyser]

oh it's easy

[bright bridge]

what do you get

[fallow ravine]

150 divide to waht?

74?

[storm mural]

divide this

[bright bridge]

^

this

[fair geyser]

the last number is 11100
last plus first is 11250
now second plus second to last is still 11250
37 times you add 11250

and from this you can algebra a general formula

maybe, i don't remember it

[bright bridge]

150( 1+2+3+4)

[fair geyser]

right triangle numbers i remember

n(n−1)/2

[bright bridge]

o yeah

[fallow ravine]

ah yes

but -1?

[fair geyser]

plus one sorry

[fallow ravine]

so when you wire the function down how would it look like
when you wanna know what the base value of 150 10 times is?

so i get a example

n = 150
n(n+1)/2

right?

no

im confsued

[cedar kiln]

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[copper crest]

Innit 1/2

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[copper crest]

Can summon Xplain the question