#help-23

1 messages · Page 364 of 1

obsidian tinsel
#

It s an optimal problem

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Where the : Y is the trajectory
Alpha admissible control
Phi the termina cost

safe radishBOT
#
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frozen quarry
#

Describe the elements of the following sets.

#

What is happening here??!

dreamy relic
frozen quarry
#

What do I do here

dreamy relic
#

Well for A the elements are all of the x that can solve the equation 2x+1=6

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This is pretty easy ngl

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Just find the values of x that solve the equations

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And then check if they're from the right set

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And ur done ig

frozen quarry
#

Also is

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

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@dreamy relic

dreamy relic
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Yes

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U don't really need it but if it can help u understand it better go for it

frozen quarry
#

Okay i have

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x^2 - 1 1/2x - 1

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Now quadric formula

#

.close

safe radishBOT
#
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gentle void
#

Hello, i need help with the Convert vertex form to general normal form (Quadratic equations)

fathom adder
#

Do you have a specific question ?

gentle void
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I have exam tomorow and i just want to understand it. as my teacher wrote that on the board i didnt understand anything

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btw i use translator for Technical terms

fathom adder
#

ok show us

gentle void
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I dont have a question, i just want a Crash course

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If i had f(x)= (X^2-3) + 1 how would i do that ?

fathom adder
#

Its not vertex form is it ?

gentle void
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I think it is i used translator

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Its the shifting of x and y

fathom adder
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Vertex form is a(x-k)² + h

gentle void
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i think

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Our formul is like this:
f(x)=(x^^2 - d) +c

normal moss
#

Square the brackets, then collect like terms

fathom adder
#

Can we have a Picture ?

gentle void
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1 min

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"e" should be "c" so ignore it

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I understand how they shift but not how to convert them to the general normal form

fathom adder
#

Well do you agree that it is y = (x+d)² + c

gentle void
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fx not y

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but yes i do

fathom adder
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But if you want i can say f(x)

gentle void
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ok

fathom adder
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Actually about the shifting you just consider the min point and you slide the parabola

gentle void
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but how do i do the converting, my teacher said something about "binomic formuls" or a "Pq" formul

fathom adder
#

for (x+d)² + c, the min point will be (-d,c)

gentle void
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why minus?

fathom adder
#

Thats what minimize the function

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We want the square to be 0

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x+d = 0 => x = -d

gentle void
#

i have to learn that formul?

fathom adder
#

Yeah

gentle void
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is there comming more or was that all?

fathom adder
#

Going from one form to another is better for both of us that you watch a video first and then maybe come with questions about the examples they show

gentle void
#

ok

fathom adder
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Like its something to see rather than read

gentle void
#

okay thx, have a good day

#

how to close this again?

misty owl
#

wait

gentle void
#

.close

safe radishBOT
#
Channel closed

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Use .reopen if this was a mistake.

normal moss
#

Converting from $f(x) = a \cdot (x - d)^2 + c$ to $f(x) = ax^2 + bx + c$

flat frigateBOT
#

USS-Enterprise

normal moss
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?

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where first c doesn't equal the second c

gentle void
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no

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.reopen

safe radishBOT
gentle void
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thats not that

gentle void
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yes but we didnt had "a" in it

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a was smth else

normal moss
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What are your formulas

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Vertex and General

gentle void
normal moss
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If there's no a in front of (x-d)^2 it implies the leading coefficient of the quadratic function is always 1

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Oh I see

gentle void
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wait, a means its wide, small, upside and downside right?

normal moss
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You are working with the leading coefficient being 1 constantly

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a is called the leading coefficient

gentle void
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we learned a but never used it really, we just know what that is

normal moss
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Hm

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Well a, the leading coefficient tells two things

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  1. Vertical stretching or compression
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  1. Direction of the parabola (facing or opening upwards or downwards)
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But it's interesting you don't learn about that

gentle void
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i know that but we never use a in our formuls

normal moss
#

So your vertex form is of $f(x) = (x + d)^2 + e$

flat frigateBOT
#

USS-Enterprise

gentle void
#

yes

normal moss
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And what is the General form?

gentle void
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but the + was a minus!

normal moss
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I don't see it in the photo

gentle void
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i remember

normal moss
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Yes sorry

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my mistake

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But this book also has both pluses

gentle void
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well if the x got shifted to the left its minus but if its shifted to the right, then plus

normal moss
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If d > 0, the parabola shifts left

gentle void
#

our teacher explained it wront then..

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nvm then ill just freestyle this then

normal moss
#

Hmm

gentle void
#

bye!

primal bone
#

The quadratic with vertex form / Scheitelpunktform y = (x - d)^2 + e has vertex (d, e) / Scheitelpunkt (d | e)
Similarly the quadratic with vertex form y = (x + d)^2 + e has vertex (-d, e)

gentle void
#

👀

gentle void
primal bone
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The second part is not a new thing, though

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Take -d for d and rewrite

gentle void
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ok

primal bone
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Going from the vertex form to the general form should be the easier direction (you should be able to expand brackets)

gentle void
#

can u maybe give me an example and i try to slove it?

primal bone
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Sub-question - Expand the brackets (x + 4)^2

normal moss
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I still don't quite understand why leave out the leading coefficient, because then you just take in a very special case of parabolas. Also no clue why + inside the brackets, everywhere else I've seen it has been a minus as convention

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¯_(ツ)_/¯

primal bone
#

SCHEISSE that's a large embed

normal moss
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😂

gentle void
#

(x+4)(x+4)
x^2+4x+4x+16
f(x)= x^2+8x+16
thats how we learned

normal moss
#

8+2?

primal bone
#

just check what 4 mal 4 is?

gentle void
#

16

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xd

primal bone
#

So why 8?

gentle void
#

better

primal bone
#

Okay... and why the 2?

gentle void
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becuase it was (x+4)^2?

primal bone
#

I mean, why have you got a +2 there?

gentle void
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Ohhh i thought it was the c

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nvm

primal bone
#

(spielst du Uno oder was KEK)
-# (you playing Uno or sth? KEK)

gentle void
#

can u speak german?

primal bone
gentle void
#

well.

gentle void
primal bone
#

Now it is, yee

gentle void
#

OHHH YEAAAAAHHH

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thx

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have a good day

primal bone
gentle void
#

no

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1 last question

primal bone
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Ah well

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hm?

gentle void
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when a is for example 5,3 is the parable stretched or small?=

primal bone
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?

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wovon der "a"?
-# where's the a from?

gentle void
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it is f(x)= ax"2

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5x"2 + 4 for example

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it tells when it is downwards, upwards, and the widh

primal bone
#

well, if you take no translation, and stay with y = ax^2

gentle void
#

here is a pro explaining

primal bone
#

Supposing a>0:
You can probably see that, if x is positive and we fix that value, then as a increases, then so does y

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That is, a larger a forces the y values to shoot up faster

gentle void
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if a is a "0,2" number the parable is supposed to be wide

primal bone
#

That is, the graph gets narrow af

gentle void
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but if a is a full number it should be small

primal bone
gentle void
#

i understand it but i just wanted to know what happens if the number was 4,2 for example

primal bone
#

-# "parable" ist wie vom Bibel

gentle void
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f(x)= 4,2x^2 + 1 for example

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is it wide or thin the parable?

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i just want to know that

primal bone
#

larger a means narrower parabola

gentle void
#

so it is stretched?

normal moss
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I feel like dividing the quadratic function into this many parts "no leading coefficient first; then no linear coefficient" leads to just more confusion than starting with the whole thing

primal bone
#

soll ichs auf Deutsch

gentle void
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no

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need

primal bone
#

Wird a grösser, wird die Parabel enger

gentle void
#

ohhh

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ok

#

thx

#

that was all

#

we can close this now?

primal bone
#

So sagen auch die Beispiele hier

primal bone
#

!done

safe radishBOT
#

If you are done with this channel, please mark your problem as solved by typing .close

gentle void
#

.close

safe radishBOT
#
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safe radishBOT
#
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placid flower
safe radishBOT
placid flower
#

why are we supposed to take only taller than 20-feet trees in the denominator

#

they said that "a tree from one of these rows will be selected at random"

#

what does that line really mean here?

hardy lion
#

you are told it will be selected a random, but you are given more information later

placid flower
#

but technically if were to take only 20-feet taller trees in the denominator, then wouldn't it violate the statement where they say that it is selected at random?

hardy lion
#

no, you are given that information is true

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idk if it helps, but you can imagine parallel universes where each specific tree is selected a random

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if you are given that the tree is tall, the parallel universes where a short tree was picked cannot exist

fierce kernel
# placid flower

www.gradefultestprep.com Tutor personally with Alex Torres, Gradeful’s instructor, one of the world’s most specialized SAT® tutors. To book, text 347-474-7150 or email alex@gradefultestprep.com

Over 16 years, Alex’s online tutoring students have gotten into Harvard, Yale, Princeton, MIT, Stanford, Duke, University of Chicago, University ...

▶ Play video
#

this video explains it quite well

#

despite the shitty thumbnail

#

good luck on your SAT jug

safe radishBOT
#

@placid flower Has your question been resolved?

placid flower
placid flower
safe radishBOT
#
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safe radishBOT
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weary venture
#

FTC: Part I and II

safe radishBOT
normal moss
weary venture
#

I need help with them.

normal moss
#
Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck
weary venture
#

I don’t understand how indefinite integrals relate to derivatives

#

I would just like an explanation of them

#

I will ask such questions along the way

normal moss
#

Okay. Sorry, I can't do that because I need to go to sleep 🙂

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But yeah just wait around a bit

#

Someone will show up

weary venture
#

Okay

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Thanks, either way

normal moss
#

Although it is preferred if direct questions are asked, perhaps someone will walk you through it. I would however still suggest going over material you have available that covers this

weary venture
#

Real Analysis might explain it better

#

I could just look for that

normal moss
#

Yeah

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Good luck

#

🙂

weary venture
#

Good night

#

.close

safe radishBOT
#
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safe radishBOT
#
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steep magnet
safe radishBOT
steep magnet
#

For vertical asymptote we have sqrt(x^2 + 3x) + x = 0

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sqrt(x^2 + 3x) = -x

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

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3x = 0

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x = 0

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For the vertical asymptote we have the highest degree of x in the denom > highest degree in the numerator so we have y = 0

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And no oblique asymptotes either if im not mistaken

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So we only have x = 0 and y = 0 right?

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But im not sure what a one-sided asymptote or 2 sided one is

weary venture
steep magnet
astral glacier
#

I think they mean that that's what differentiates one sided and two sided asymptotes

#

You use the one-sided limits and see how many of those go to the value you need

steep magnet
#

Oh ok

astral glacier
#

If both, two sided asymptote. If one, one sided

steep magnet
#

Im not really sure how to do that tho

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Btw I figured out about the HA

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If you sub in x = infinity you get infinity, if you sub in x = -infinity you get infinity again

#

So it approaches from the top but not the bottom, right?

steep magnet
#

.close

safe radishBOT
#
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safe radishBOT
#
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sturdy drift
#

is this available?

safe radishBOT
sturdy drift
#

i need the boxes filled in

rigid inlet
rigid inlet
sturdy drift
#

a lot

#

i tried pert

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plugged the numbers into the formula but i just cant do it

rigid inlet
#

show what you plugged in and where

sturdy drift
#

i dont know whaty to do nezxrt

#

next*

rigid inlet
#

alright then

rigid inlet
sturdy drift
#

A=Pe^rt

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is

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a is the amount acfter time t

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p is the principle

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r is the annual interest rate

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and t is the time in years

rigid inlet
#

so if you tried to make use of this pert, why is there no e in your answer?

sturdy drift
#

so A=prt?

tardy mango
rigid inlet
#

you've already concluded that's wrong

#

you said "I tried pert" then showed an attempt that doesn't look like pert

sturdy drift
#

i dont know what to basically do after i turned the percent into a decimal

rigid inlet
#

your principal is fine

sturdy drift
#

so it would be like 520e^.045t

rigid inlet
#

indeed

sturdy drift
#

and then would i seperate it into 520(e^.045)^t

rigid inlet
#

sure

sturdy drift
#

when i did the e i got 1.046

rigid inlet
#

did the e?

sturdy drift
#

i did e^.045

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and it gave me that decimal

rigid inlet
#

,calc e^0.45

flat frigateBOT
#

Result:

1.5683121854902
rigid inlet
#

err

#

,calc e^0.045

flat frigateBOT
#

Result:

1.0460278599087
rigid inlet
#

cool

sturdy drift
#

and then would my decimal then be .046

rigid inlet
#

decimal for what?

sturdy drift
#

annual interest rate

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or would it be 4.60

rigid inlet
#

i assume you're asking about the second part now

sturdy drift
#

yeah

rigid inlet
#

it's asking for %, your answer is a decimal

#

how do you go from decimal to percent?

sturdy drift
rigid inlet
#

looks good

sturdy drift
#

tysm

#

my dogshit teacher just throws questions at me and answers them herself

#

so im so lost

rigid inlet
#

oh one possible wrinkle

sturdy drift
#

thanks!

rigid inlet
#

note how many decimals they want

sturdy drift
#

wym

rigid inlet
#

read the question again in full

sturdy drift
#

nearesrt hundreth of a percent

#

round function to the nearest 4 decimal places

rigid inlet
#

indeed

sturdy drift
#

Alright

safe radishBOT
#

@sturdy drift Has your question been resolved?

safe radishBOT
#
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#
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fair forge
safe radishBOT
fair forge
#

am i doing this right

safe radishBOT
#

@fair forge Has your question been resolved?

upbeat bay
#

No one came??

#

<@&286206848099549185>

safe radishBOT
#
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#
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eternal kelp
#

my brain aint functioning anymore pls help

eternal kelp
#

.close

safe radishBOT
#
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safe radishBOT
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kind quartz
#

Can i get some suggestions on how to deal with this? I think, to first solve the x equation, it would be the t root of that equation, yes? but how would i eliminate t in that circumstance?

quasi bison
#

from x = 3e^t, divide by 3, then take logarithms

#

get t = ln(x/3)

kind quartz
#

I will try that

#

i got no idea what im doing 😭

quasi bison
#

oh wait huh. i just saw the other written direction, my bad.

#

they want an exponential not a log

#

my bad

kind quartz
#

no worries

#

do you have any way to work it with the exponential?

#

i had thought i just misunderstood that written direciton lol

quasi bison
#

isolate t in the y equation first.

kind quartz
#

then insert it into the x equation, yes?

#

will do

#

alr i got t = (1-y)/3

quasi bison
kind quartz
#

should i then try to solve for y = something, as some simpler equations have it? because that feels wrong in my heart

#

i just put it in as is, and it was right! success

#

.close

safe radishBOT
#
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safe radishBOT
#
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crude falcon
#

Hey

safe radishBOT
magic junco
#

Hello

#

Anything we can help you today? catthumbsup

autumn sun
#

hiya. got a question for the channel?

magic junco
#

Alright

crude falcon
#

I’m in school and I have an exam next session

#

In sets

autumn sun
#

sure thing. what are you stuck on?

crude falcon
#

I’m getting mixed up between the cardinals

#

Yk?

#

Card for AunionB

autumn sun
#

got an example question?

crude falcon
#

Is card A+ card B -card AintersectB

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Idk what Aintersect B is

autumn sun
#

mhm, inclusion-exclusion

crude falcon
#

Idk how to get it

autumn sun
crude falcon
#

He just put it on the board

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Said it’s a rule

#

I just don’t know how to get AintersectB

#

It’s like

#

He gave an example with 3 ven diagrams

autumn sun
#

your teacher is right in that inclusion-exclusion is indeed a rule, but if A \cap B is not given then A \cup B cannot be determined uniquely

crude falcon
#

total number 34
21 play football
12 play basketball
10 play volleyball
8 play football and basketball not volleyball
5 play basketball and volleyball but not football
4 play football and volley but not basketball

autumn sun
#

there we go

crude falcon
#

I think the numbers are wrong

#

I made that up

autumn sun
#

oh

crude falcon
#

It’s how he explained it

#

I just don’t remember the numbers

autumn sun
#

well yea the numbers here do not make sense

crude falcon
autumn sun
#

but I get the general idea of what you're pointing at

crude falcon
#

Yes

severe pond
#

Art of Problem Solving's Richard Rusczyk introduces 2-circle Venn diagrams, and using subtraction as a counting technique.

This video is part of our AoPS curriculum. Take your math skills to the next level with our advanced materials:

📚 AoPS Prealgebra Textbook: https://aops.com/store/book/prealgebra?utm_source=youtube&utm_medium=social&utm...

▶ Play video
crude falcon
#

I cant

#

Watch that

#

.

autumn sun
#

wait then finish your class first

crude falcon
autumn sun
#

can always ask later

severe pond
#

ask your teacher?

crude falcon
#

And I have an exam

autumn sun
#

your exam is today?

crude falcon
#

I’m not in math class rn and when I asked he didn’t explain it the best but I have the exam next session

crude falcon
#

It’s next session.

autumn sun
#

session can mean anything, didn't know it meant period in that case

crude falcon
#

It’s next period then

#

Which is in 35 minutes

magic junco
crude falcon
#

I know everything in set

magic junco
#

Oh nvm

crude falcon
#

We have multiple

severe pond
# crude falcon total number 34 21 play football 12 play basketball 10 play volleyball 8 play f...

Art of Problem Solving's Richard Rusczyk introduces 3-circle Venn diagrams as a counting technique.

This video is part of our AoPS Counting & Probability curriculum. Take your math skills to the next level with our Counting & Probability materials:

📚 AoPS Introduction to Counting & Probability Textbook:
https://aops.com/store/book/intro-cou...

▶ Play video
crude falcon
#

Only the part I mentioned

severe pond
#

just put on subtitles

crude falcon
#

It’s mixing me up

severe pond
#

and mute it

crude falcon
#

Okay

#

thank you so much

severe pond
#

you’re welcome

crude falcon
#

Bye bye wish me luck

severe pond
#

good luck

crude falcon
#

.close

safe radishBOT
#
Channel closed

Closed by @crude falcon

Use .reopen if this was a mistake.

crude falcon
#

.close

autumn sun
#

oh ok, cool

normal moss
#

Damn, last help channel closed

#

🙁

safe radishBOT
#
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orchid mirage
#

2x + 1/3x = 5 then what’s the value of 4x^2 + 1/9x^2

quasi bison
#

aight hol up

open wedge
quasi bison
#

do you mean:

\begin{enumerate}[a)]
\item $2x + \frac{1}{3}x$?
\item $2x + \frac{1}{3x}$?
\item $\frac{2x+1}{3x}$?
\end{enumerate}

flat frigateBOT
quasi bison
#

never appropriate to say in a help channel

open wedge
orchid mirage
quasi bison
#

right

#

2x + 1/(3x) then

#

!status

safe radishBOT
#
What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above
orchid mirage
#

actually I wanna change the question

quasi bison
#

bruh

#

okay send the new one in

#

as a picture preferably

orchid mirage
quasi bison
#

do i have to !status again or can you tell us your status without

orchid mirage
#

um

#

1

quasi bison
#

you have to send "1" 17 more times for it to be formally registered.

#

anyway okay

#

can you do some algebruh to 2x + 1/(3x) = 5 to write it as a quadratic in x

#

dont solve the quadratic but just get it to that form

quasi bison
#

no

#

you manipulate the thing algebraically

#

until you get a

quadratic in x

orchid mirage
#

ok I get it

open wedge
open wedge
orchid mirage
open wedge
#

Compare it to what you have now

orchid mirage
#

It’s +7

open wedge
open wedge
orchid mirage
#

so I do 21/7

#

?

quasi bison
#

$6x^L$?

flat frigateBOT
quasi bison
orchid mirage
#

my handwriting is that bad 😭

quasi bison
#

what's this capital L doing there

open wedge
#

$6x^2$

flat frigateBOT
#

1 divided by 0 equals Infinity

open wedge
orchid mirage
#

I don’t have any time to get bullied lol tmrw my exam

#

😂

open wedge
orchid mirage
#

21/7 no?

open wedge
#

Anymore questions?

orchid mirage
#

So 3?

open wedge
orchid mirage
#

Okay one more

open wedge
orchid mirage
#

What will be the sum of the two angles produced when one side of a right angled triangle is extended on both sides

open wedge
#

💀

orchid mirage
#

I actually just don’t understand what it means

open wedge
#

Draw triangle ABC

orchid mirage
#

Maybe an English issue

open wedge
orchid mirage
#

Done

open wedge
#

Right triangle tho

orchid mirage
#

😭🙏

#

now what

open wedge
quasi bison
#

also can you send an image of the q

#

cause rn it sounds like you're trying to put your questions in plain text and not being very good at it

open wedge
orchid mirage
quasi bison
#

so we are confused at wtf you mean

#

ok sure

#

diabolical or not

#

if it's diabolical then we at least know it isnt your fault

orchid mirage
quasi bison
#

,rccw

flat frigateBOT
quasi bison
#

that paper is so bent

quiet igloo
# quasi bison ,rccw

prob not related, but 1) how does this cmd work, and 2) are there any similar cmds?

quasi bison
#

and they also dont tell us if we are extending a leg or the hypotenuse

orchid mirage
quasi bison
open wedge
quasi bison
#

there is ,rcw for clockwise or ,rotate [angle] for arbitrary rotations

orchid mirage
#

@open wedge

#

Which side

quiet igloo
quasi bison
open wedge
quasi bison
quasi bison
orchid mirage
open wedge
open wedge
quiet igloo
quasi bison
quasi bison
orchid mirage
quasi bison
#

i dont understand wtf is meant to be inferred

open wedge
quasi bison
#

if we dont know whether we are extending a leg or the hypotenuse then the answer can range anywhere in (180, 270]

quasi bison
#

extending a leg gives an unfindable answer

quiet igloo
#

AB or AC

quasi bison
#

WHY A LEG

#

nobody is answering this question, how do we know the problem wants us to extend a leg

orchid mirage
#

I think let’s skip it

#

do you see q7

quasi bison
#

y'all are so happy to just yap yap yap yap yap without understanding that the q is wrong

open wedge
quasi bison
#

anyway im out

quiet igloo
#

also does the sum refer to other the other angles beside the right one?

orchid mirage
#

in a triangle ABC angle B is 60 degree , Angle C is 40 degree and the bisectors of angle B and C mets at O, angle BOC is what

#

I’ve drawn it

#

Oh wait

open wedge
orchid mirage
#

Is it 130

open wedge
#

PLEASE LET US HAVE A DAMN MOMENT

open wedge
open wedge
orchid mirage
open wedge
#

You're correct

orchid mirage
#

ok I am done

#

thanks

#

.close

safe radishBOT
#
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safe radishBOT
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keen gate
#

i have a question about graphs. (its written in norwegian sorry for that) Task A is different function exressions. And which one is the correct one to the graph? I know its not F(x) but i dont understand if its g(x) og h(x)? Can someone explain it to me? I did the -b/2a formula and got -1 as an answer...

floral yew
lofty nebula
keen gate
lofty nebula
keen gate
keen gate
lofty nebula
floral yew
floral yew
keen gate
lofty nebula
lofty nebula
keen gate
#

yeah. I knew the formula but didn't know what i were supposed to do with it. But know i know!

#

I will learn the completing the square next!

#

Thank you so much for your time!

lofty nebula
keen gate
#

i will!

#

am i supossed to write a command to end the chat or smt?

lofty nebula
#

that would be .close

keen gate
#

ok see you soon!

#

.close

safe radishBOT
#
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safe radishBOT
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median drift
#

Okay be honest here does this really deserve a 46%?

median drift
#

Is the professor just unable to understand the proof the way I wrote it or is it genuinely just wrong

safe radishBOT
#

@median drift Has your question been resolved?

ancient quartz
#

you want to know whether you deserve a marking?

#

every teacher is different

#

just practice and the bias of the teacher will vanish too

quiet juniper
#

The last step (taking the limit as m goes to infinity of the sequence) subsumes that you know the sequence converges already.

safe radishBOT
#

@median drift Has your question been resolved?

#
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steep magnet
safe radishBOT
fathom jewel
#

real

steep magnet
#

u = 1 - r^3 | du = -3r^2

#

integral of (9r^2)/(sqrt(u))(-3r^2)

#

integral of -3/(sqrt(u))

#

Oh wait I see my mistake 🤡

#

.close

safe radishBOT
#
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fathom jewel
#

oh okayy

safe radishBOT
#
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thin lion
#

Can someone pls help me understand this

safe radishBOT
thin lion
#

This is CRT

#

I understand the general idea of it, given like examples but I don’t get the intuition behind this

safe radishBOT
#

@thin lion Has your question been resolved?

cedar widget
#

what do you want to know

thin lion
#

I don’t get what that remark is saying

cedar widget
#

do you have experience with groups

thin lion
#

Yes I know congruence classes

cedar widget
#

ahhhh this is not what I meant

#

but nvm

#

The remark is saying that there is a bijection between these two sets

#

so anything you can say mod N you can say simultanuously for all n_i

#

and vice versa (this is the non trivial part)

#

so you can solve an equation modulo 6 by solving it modulo 3 and modulo 2

thin lion
#

Is that like saying all integers can be in one of these sets [1]_3 [2]_3 [0]_3 ?

#

But in this case

#

Sorry bad wording

cedar widget
#

that is not related to CRT

#

but that is true and important

thin lion
#

Oh

#

Hm well the first set is Z/NZ what does this represent

cedar widget
#

equivalence classes under modulo N

#

and 0, 1, ...., N - 1 form a complete set of representatives

thin lion
#

Ah alright

cedar widget
#

likewise for Z/niZ

thin lion
#

And this is bijection to f(x)

cedar widget
#

f induces the bijection

#

this is the important part

thin lion
#

That’s the bijection right?

cedar widget
#

yes

thin lion
#

Alright, I somewhat see it, ima try do an example to understand it more

#

Ty

#

.close

safe radishBOT
#
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safe radishBOT
#
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mighty prism
#

I am using gapminder to calculate some statistics. But I stumble across a problem where I'm one decimal off but can't figure out why. I am calculating death by measles for children per 1000 births for Nigeria. According to Gapminder it should be around 0.117

mighty prism
#

I use gapminder to get the data for total births in Nigeria, and total death by measles to make me own death by measles per 1000 births

#

I had 6 310 000 births, and 10800 total deaths for the same year

#

10800/6310 = 1.7 deaths per 1000

#

How am I one decimal off? I don't get it, I can link the gapminder data I'm looking at if someone could help

safe radishBOT
#

@mighty prism Has your question been resolved?

prisma wren
flat frigateBOT
#

Basel
Compile Error! Click the errors reaction for more information.
(You may edit your message to recompile.)

#

Basel
Compile Error! Click the errors reaction for more information.
(You may edit your message to recompile.)

flat frigateBOT
#

Basel
Compile Error! Click the errors reaction for more information.
(You may edit your message to recompile.)

safe radishBOT
#

@mighty prism Has your question been resolved?

normal moss
#

0.117 and 1.7 aren't 1 decimal off

mighty prism
#

Not completely, but some error is understandable since I'm using approximate numbers of total births and total deaths

#

so it not being exactly 0.117 isn't that big of a deal

#

but being a decimal off approximately is a bit of a bigger deal

normal moss
#

I see, but still even if we move the 'correct' answer one decimal to the right we get 1.17, or rounding up to 1.2? Which is still a ~40% difference

#

Is this expected?

mighty prism
#

Sure

#

The numbers from gapminder is like 6.31 million

#

for total births

#

We wouldn't obviously have such an even number in reality

#

where it is exactly 6 310 000

#

So I'm expecting some error, as long as I'm within a 50% margin

normal moss
#

Huge margin but I am in no way an expert about these things so okay

#

Well to me it seems a huge margin*

#

Also quick question

mighty prism
#

I mean could be, the issue is that I don't have any knowledge of knowing how gapminder estimates their values or what model they use. I'm just taking their numbers and data to try and ''rederive'' an answer they have

normal moss
#

I haven't deep dived into the question really, but just off the face of it I see the statistics can be sorted by year

#

And I don't see you mentioning any year

#

Might the mistake be here?

mighty prism
#

Ya, I picked 2008

#

for both

#

The links should send you to the exact same year

normal moss
#

Oh I see, yes

mighty prism
#

or if you prefer to open gapminder tools yourself and sort the y axis

#

I appreicate a new pair of eyes looking at it

#

Maybe I've tunnel visioned staring at this question for a while

normal moss
#

Yeah I am looking give me a second

#

Just a bit harder on a phone

mighty prism
#

I could also share my screen if that makes it easier

normal moss
#

I doubt it 😅

#

Okay I looked at it

#

And best I can say is that either Gapminders statistics for measles death / 1000 births is calculated, or rather modeled differently than simply dividing the two quantities

#

Or, different sources were used

mighty prism
#

I tried to find the sources for the data since they typically link it

#

But the sites were unvailable

#

probably taken down after this many years

#

:/

#

But thanks I guess, I was kinda at the same conclusion as you. But I wanted another pair of eyes to analyse it with me

normal moss
#

Yeah

#

I don't know, perhaps leave it open

#

For someone with more expertise in this area

#

But that would be my top guess after looking into it

mighty prism
#

Should I trust my number more or gapminder?

normal moss
#

Probably gapminder

mighty prism
#

I'll try to ask around a bit more just in case, before I decide to abandon my approach and use gapminder's numbers. I have a handin, if I'm lucky then my teacher won't ''fact check'' the calculations

#

and then question why the two numbers don't align

normal moss
#

Because the data is probably modeled and corrected for things like underreporting, etc.

mighty prism
#

Most likely, it is valid what you are saying

#

My issue is that I then make a comparison to Germany and calculate the precentage difference. Since Gapminder says Germany has 0 deaths per 1000 births

#

Most likely because the number is so small they just rounded it to 0

#

so I had to ''get the real number'' myself by using their total deaths in 2008 + total births

#

and I was like ''fact checking'' to see if I would get the same number if I did it for Nigeria, but I didn't

#

so I could just calculate Germany's death per 1000 births, and then be like ''I took the data for Nigeria from Gapminder'' and do the comparison there

#

But that's risky business

dull sequoia
#

Especially real world data

normal moss
#

Well looking at Germany specifically, 8 deaths have been registered from measles between 2001 and 2018

#

No age given

mighty prism
normal moss
#

Assuming an answer from them would be bestowed upon you

mighty prism
dull sequoia
#

You have a deadline? Is this like a project or something

normal moss
#

Well anyway, I should probably go to sleep, given that it's 00:26. Best of luck Basel!

mighty prism
mighty prism
dull sequoia
#

Even if they respond after the deadline youd learn something if they respond

mighty prism
#

I can send the email anyways to see if I can get some information. Honestly seems like the data is very lacking when it comes to deaths per 1000 births

#

Since that is the ONLY year gapminder has any data on deaths per 1000 births for measles

#

You can't scroll or analyse it for any other year

#

And maybe their model takes other factors into consideration?

mighty prism
#

.close

safe radishBOT
#
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#
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loud wren
#

gaaaaaaaaaaah

safe radishBOT
loud wren
#

FIRSTLY, wtf is the $\kappa(\mathbf{v})(\mathbf{w})$ notation??

flat frigateBOT
raven heart
#

well k(v) is supposedly a linear form in (K^n)*, so you can evaluate it on a vector in K^n

#

hence the k(v)(w)

#

@loud wren

safe radishBOT
#

@loud wren Has your question been resolved?

safe radishBOT
#
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serene portal
#

this looks easy but i can't do it 😭

safe radishBOT
magic junco
#

Have you heard of sine law?

serene portal
#

no i dont think so

magic junco
#

What are you learning recently?

magic junco
serene portal
#

idk we've been doing trig equations like cos theta= .8

serene portal
magic junco
serene portal
#

yeah i dont think so

#

i think it's probably just a challenge question

magic junco
#

Right….are you allowed to use unlearned theorem or additional tools like a calculator?

#

If they’re allowed, I can introduce sine law rq

serene portal
#

yeah they're allowed

magic junco
#

Alright, let’s talk about sine law

#

So for every triangle\
\
$\frac{\text{its relative side}}{\sin(\text{certain angle})} = \frac{\text{its relative side}}{\sin(\text{the other certain angle})}$

serene portal
#

i see

flat frigateBOT
#

HungryChomper

magic junco
#

9/sinA = 8/sinC

#

Do you have any doubt so far?

serene portal
#

so it would be like 8/sin(34) = 9/sin(C)?

magic junco
#

Exactly

serene portal
#

i get it now

#

thank you

magic junco
#

Alright, anything else?

#

Feel free to post your work for verification after you’re done catthumbsup

serene portal
#

I could probably do it by myself but if you want could you help me solve for the angle of c?

magic junco
#

Why not

magic junco
serene portal
#

ohh yeah

magic junco
#

Ping me when you’re done

serene portal
#

@magic junco sin(c)=4.5/8 i think

magic junco
#

Where is your sin34

#

,w 8/sin(34 degree) = 9/sin(C) find C in degree

serene portal
#

well i multiplied both sides by sin(34)

magic junco
#

,w 8/sin(34 deg) = 9/sin(X) find X in degree

flat frigateBOT
magic junco
#

ok, I give up using wolfram lol

magic junco
#

yeah that works

#

but taking sin34 as 0.6 instead of 0.5 looks more precise imo

serene portal
#

yeah also because it says to round to the nearest tenth

#

anyways once im there im not quite sure what to do

#

i use arcsin right?

magic junco
#

use inverse function

#

yes

#

Be aware that there can be two possible answers

#

sin 120 deg = sin 60 deg

#

The angle can possibly be at second quadrant

#

when the angle is obtuse

serene portal
#

oh ok

#

am i supposed to get .64

#

i feel like im missing a step

magic junco
#

.64?

serene portal
#

from arcsin .6

magic junco
#

no, I'm not sure what does .64 mean

#

0.64?

serene portal
#

yeah from arcsin(.6)=.64

open wedge
serene portal
#

oh i shouldve put the 0 in front lol

magic junco
#

,w arcsin(9/8*0.6)

serene portal
#

ahh

#

but then what do i do with 0.7

magic junco
#

As I mentioned, the value can possibly be (180-42.450443)

#

because they yield the same sine value

serene portal
#

yeah so we have all the angles

magic junco
#

which, by default, indicates that the other scenerio does not work

#

it's up to your teacher, tho. Idk if the diagram is just for reference

magic junco
#

now it looks pretty simple

serene portal
#

yeah

magic junco
#

Just find angle B and play the same trick again

#

I believe that you can finish it from here on out catthumbsup

serene portal
#

yeah tysm

magic junco
#

no worries, anything else?

serene portal
#

no that's all

#

.close

safe radishBOT
#
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sick plume
#

This is a question that I got incorrect on and exam I have already taken. I do not understand why I got it wrong. Could you help me figure out if its incorrectly marked wrong, or if I actually did it incorrectly?

sick plume
#

We are specifically told to use the formula A = P((1+r/n)^nt -1) / (r/n)

plucky elk
#

Then what did you use to get your answer

sick plume
#

I used that formula

#

95((1+.0625/12)^480 - 1) / (.0625/12)

#

Here's the work I did

plucky elk
#

,calc 95((1+.0625/12)^480 - 1) / (.0625/12)

flat frigateBOT
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Result:

2.0253168890788e+5
#

Result:

2.0368154145427e+5
sick plume
#

yeah 202,531.68 rounded up is the answer I picked. So is it actually marked wrong incorrectly?

plucky elk
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Yea I don't see any mistakes

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It could be that they rounded early in between calculations but yours is correct

sick plume
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Are you kidding? This was a final.... okay thank you. I got to go write an email.

plucky elk
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I used P=0 and C=95 and it matches your answer

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Even if you of set P=95, you don't get any of the other answers

sick plume
#

That question was the difference between a 92% and a 96%.

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anyways thanks you

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fast bolt
safe radishBOT
magic junco
#

Tried anything yet?

fast bolt
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yeah im getting 1

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but the solution says something else

magic junco
#

Can you show your work?

rigid blaze
#

oh my god

fast bolt
magic junco
rigid blaze
#

wait isn’t logx(logy(z)= logxy(z)?

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or am I tripping again

fast bolt
#

this the solution provided

rigid blaze
#

eat

#

log3(log2(a)) became log3(log3(a))?

fast bolt
#

my one:
after simplyfying : log3(log2a/log(1/2)b) = 1
= 3 = log2a/ -(log2b)
= -3 = logb a.
this give ab^3 = 1

fast bolt
rigid blaze
#

The question asked log3(log2(a))

fast bolt
#

ah

#

i get it

rigid blaze
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however in their solution it became log3(log3(a))

fast bolt
#

the solution is wrong.

rigid blaze
#

obviously they’re not the same number

#

so yeah

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Their solution is incorrect

fast bolt
#

thanks

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rigid blaze
#

Wait @fast bolt

fast bolt
#

?

rigid blaze
#

was log3(log3(a)) = 1 a given statement

#

I’m not able to understand that part

fast bolt
#

no

#

its a typo

rigid blaze
#

maybe they assumed

safe radishBOT
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steep magnet
#

test

safe radishBOT
steep magnet
#

Oh

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My image wasnt sending

#

1 sec

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Still not 🙁

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Its not working idk

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magic junco
#

👀

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green ivy
#

Can anyone please help with this question

safe radishBOT
green ivy
#

How can we say that A,B,E will be collinear

quasi bison
#

!occupied

safe radishBOT
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@green ivy Has your question been resolved?

mossy lotus
# green ivy How can we say that A,B,E will be collinear

its pretty easy to see that AB bisects CD (use the power of a point on the two circles about that point of intersection)
And from then on, you just play the fact that diagonals of a parallelogram bisect eachother to your advantage

green ivy
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use the power of a point on the two circles about that point of intersection, wdym by this ?

mossy lotus
#

do you know a geometric result by the name of Power of a point?

green ivy
#

Ohh tysm I got it the line AB acts as the radical axis

mossy lotus
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yep

green ivy
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Hence it passes through the mid point of the diagonal CD

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And is collinear to point E due to that

mossy lotus
green ivy
#

😅 this was pretty self explanatory i guess my mind was just not working

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Thanks!

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glossy creek
#

how can i solve the inequality
x^2 + 3x + 10 <= 0
when there isnt any real solutions to the quadratic

opaque fern
#

Then the statement is false for any real value of x

glossy creek
#

so should i just put down "no real solutions"?

ancient quartz
#

that works

near atlas
glossy creek
#

is it the same for just < not <=?

near atlas
vagrant ice
#

$x \in \varnothing$

glossy creek
#

thank you

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flat frigateBOT
safe radishBOT
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patent laurel
#

hey, in this question how can I solve this integrals? I tried to substitution but i found it hard to do

safe radishBOT
#

@patent laurel Has your question been resolved?

patent laurel
#

<@&286206848099549185>

upbeat bay
#

Is this the exact question?

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Like what is asked in yr question exactly?

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Cause this integral's answer can't be expressed

patent laurel
#

The exect question is first linear order differential equations

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But in the step is both integral both sides

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i am being stuck

ancient quartz
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this seems to be of the form y' + Q(t)y = P(t) to me

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try an integration factor perhaps

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but you'd still have to integrate

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hmm

patent laurel
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hmmm what is mean?

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this is a key of that

upbeat bay
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$y(t) = A e^{-\int_{0}^{t} \sqrt{1+t^4},dt}$

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all good here?

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Now, as $y(0) = 0; \implies y(0) = A e^{-\int_{0}^{0}\sqrt{1+t^4},dt}$

flat frigateBOT
upbeat bay
#

@patent laurel Does this solve yr question?

patent laurel
#

ah yeh I got it, thanks a lot

safe radishBOT
#

@patent laurel Has your question been resolved?

patent laurel
#

Yes

upbeat bay
#

!occupied

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terse atlas
#

got stuck proving BxA^2 = (A^2)xB (square matrices) not sure where to go on from here

terse atlas
#

if not familiar |A| = det(A)

cedar widget
#

what are you trying to do