#help-13

1 messages · Page 72 of 1

steady wing
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I am wondering when negating the convergence of a sequence

steady wing
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First, when negating an implication a=>b, its "a and not b"

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So when we have a sequence converging, is it for all e, there is an n such that n>N => |un-l|<e

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Or is it for all e, theres an N, such that n>N, |un-l|<e

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Idk the statements seem equivalent to me

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But their negations will differ

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In the first one i get there's an e, for all N, n>N and un-l>e

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.close

cedar kilnBOT
#
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peak ether
#

Hi

cedar kilnBOT
peak ether
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Can anybody help me with this question

tropic oxide
#

what's troubling you

peak ether
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The question

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I dont know the process and how to start solving

tropic oxide
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Z is the number of bad chips in the tech's sample

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how many chips does the tech pick in total?

peak ether
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2?

tropic oxide
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he picks 2 chips?

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are you sure about that?

peak ether
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No im not

tropic oxide
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it says in the problem, at the beginning:

A technician has to choose three chips at random...

peak ether
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Oh

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3 it is

tropic oxide
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right

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so if you knew nothing else about the problem,

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what would you say the range of values for "number of bad chips in the sample" would be?

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this is not something you have to think too hard about or even do any calculations.

peak ether
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4 chips in which two are defective yet he has to choose three randomly.
{W, W, NW}?

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<@&286206848099549185>

tropic oxide
#

@peak ether you're overthinking it.

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massively so

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when all you know about the tech's selection is that it consists of 3 chips, how many bad ones could he possibly have picked up?

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anywhere between 0 and 3 bad chips, of course.

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does this specific point make sense to you?

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we cannot continue if you do not confirm or deny that this point makes sense to you.

peak ether
tropic oxide
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when all you know about the tech's selection is that it consists of 3 chips, how many bad ones could he possibly have picked up?
anywhere between 0 and 3 chips, of course.

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does this make sense to you?

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like really forget anything else and don't try to think of it until i tell you to. simple shit.

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if the tech picks up 3 chips the number of bad ones is between 0 and 3

cedar kilnBOT
#

@peak ether Has your question been resolved?

cedar kilnBOT
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balmy shard
#

Can someone pls double check to see if this is right

cedar kilnBOT
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@balmy shard Has your question been resolved?

balmy shard
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<@&286206848099549185>

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Hello anyone pls?

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Ive been waiting for ages

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<@&286206848099549185>

lethal jackal
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I've been waiting for ages for her to text me a goodbye

balmy shard
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Can u help me?

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Just make sure i got it right

lethal jackal
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how did you conclude that the radius of the cone is 10 cm

balmy shard
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I amde the radius 10

lethal jackal
#

so you're allowed to pick?

balmy shard
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We just need dimensions that fit

lethal jackal
#

wasn't obvious from the question how you were supposed to find a unique answer

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but yes if you just need that

balmy shard
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So we pick the radius/height and then figure out the other

lethal jackal
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well

balmy shard
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So its all good?

lethal jackal
#

yes, but are you aware that you could've done all of the checking yourself

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there are calculators on the internet

balmy shard
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Oh yea...

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Sorry for the disturbance.. thank you

lethal jackal
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np

balmy shard
#

.close

cedar kilnBOT
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humble oracle
cedar kilnBOT
lyric leaf
#

which part of the question are you confused about?

lethal jackal
#

literally awful question though

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these should all be called "sample mean" "sample variance" "sample standard deviation"

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or estimated mean, estimated variance, estimated standard deviation

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people get so confused because of it

lyric leaf
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those distinctions werent ever made to me until my third year of university 💀

lethal jackal
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yeah it's actually horrifying how they expect you to calculate the variance of the sample mean

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when you're literally told the mean is just add all of the numbers and divide by something

humble oracle
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I dont get any of it as its in a weird format

lyric leaf
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do you mean the notation?

humble oracle
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yeah

lyric leaf
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this, specifically?

humble oracle
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Both I havent rly studied this topic at all

lyric leaf
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Σ means 'to sum up'

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say we have xi where i=1,2,3,4,5 (any one of those values)

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Σxi means x1+x2+x3+x4+x5

humble oracle
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How do I know what to divide it by tho for the mean

lyric leaf
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here you are told you have 5 data observations, x1, x2, x3, x4, x5

humble oracle
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Oh god

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youre right

lyric leaf
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well with the definitions you are familiar with

humble oracle
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thanks lol

lyric leaf
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mean = [SUM of everything]/number of things

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so yea

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Σxi would just be that top part

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'the sum' of each squared data observations is something you should see in Variance and Standard Deviation, too

humble oracle
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thanks a lot i completely skipped past the 5 lol

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im blind

lyric leaf
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no worries, it happens

cedar kilnBOT
#

@humble oracle Has your question been resolved?

cedar kilnBOT
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silent finch
#

What are directed lengths? Context:

cedar kilnBOT
crystal raptor
#

I'd never heard of them, seem to just make sure you label/draw things correctly

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Or rather that it doesn't matter what labels you use

cedar kilnBOT
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@silent finch Has your question been resolved?

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orchid oriole
cedar kilnBOT
orchid oriole
#

Someone pls help, idk how I’m getting it wrong

hardy island
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I’d use the AC method

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Multiply AC and find factors that add up to B

orchid oriole
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What will be AC and B in this case ?

quartz frost
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i would do complete the square, that is always nice

hardy island
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CTS is a waste

quartz frost
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😦

distant cedar
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😅

hardy island
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If you do AC you can re write it using the factors, so 10x^2 - factor 1 - factor 2 + 4 then continue from there

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Or you can do CTS

orchid oriole
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Is this ur method ?

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Is it the same as rhis

hardy island
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Yes

orchid oriole
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I’m confused on how they fit 5 and 8

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Bc they multiply to give 40

distant cedar
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It's 0.5 and 0.8

orchid oriole
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Or does that not matter

distant cedar
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Not 5 and 8

hardy island
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They multiply to give 40

orchid oriole
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Where did 40 come from is what I’m confused about

hardy island
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Multiply A and C

orchid oriole
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Ohhh

hardy island
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If it’s in quadratic form

hardy island
orchid oriole
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I forgot the formula, what is it again

acoustic vale
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hello

hardy island
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no formula really

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Just multiply a and c

orchid oriole
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Oh

hardy island
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Factor it so the terms add to b

acoustic vale
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( -b+-v/b2 - 4ac ) / 2a

distant cedar
acoustic vale
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just do a second grade ecuation

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@orchid oriole you know how to do that+

orchid oriole
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Also for the 6x (6x-3) equals 0 question

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Why do I divide only 6x

acoustic vale
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Second grade equation bro its so easy

hardy island
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I mean what else would you divide by

livid hound
# orchid oriole

x(10x-13) + 4 = 0
is NOT in the form ab = 0 where a = 10x-13 and b = x+4
you can't apply zero product property like this

distant cedar
#

Yes as Ramonov pointed out ,please understand when certain operations are valid

hardy island
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8 x 5 is 40

orchid oriole
livid hound
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writing x(10x-13) + 4 = 0 itself is fine, (it just doesn't really help you here)
the conclusion you reached from that is wrong

distant cedar
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We are supposed to write the equation such that the coefficient of x^2 is in the correct form

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Only then can we use the method

livid hound
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what?

orchid oriole
livid hound
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who said anything about multiplication of roots

distant cedar
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Not you Ramonov, I am replying to the method suggested by Meep

hardy island
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Still don’t get what you’re saying

livid hound
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the method they're referring to seems fine

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the ac method for factorising non-monic quadratics

orchid oriole
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For the first question why do i only divide 5a

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Like why does only 5a change

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Why not a-2

livid hound
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divide by 5 not 5a

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its just general clean up and simplification of the equation

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you don't need to if you don't want to

orchid oriole
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Ok, what’s the other way?

hardy island
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Also where or how did a change to x

livid hound
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apply zero product property directly

hardy island
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Or did the coefficient change

orchid oriole
hardy island
#

Oh

west zenith
orchid oriole
livid hound
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5a(a-2) = 0
is in the form pq = 0
applying zero product property directly to taht
5a = 0 or a-2 = 0

orchid oriole
#

Ohh

livid hound
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5a = 0 leads to a = 0

orchid oriole
#

I understand now

livid hound
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you can also first divide both sides by 5 to simplify the equation to
a(a-2) = 0

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and applying zpp there leads to the same end result

orchid oriole
#

Ok thank you

distant cedar
orchid oriole
#

.close

cedar kilnBOT
#
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quartz frost
#

just for good measure im gonna leave the completed square here @orchid oriole

cedar kilnBOT
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orchid oriole
#

Thank you

cedar kilnBOT
quartz frost
#

.close

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long mauve
#

.reopen

#

How to know the resistance is 9ohm

quartz frost
#

we know that the resistance of the whole plate is 3 ohm

long mauve
#

why ammeter reading is not 3/9 instead of 3/4.5

quartz frost
#

wait, in the picture they are connected parallel, not in series or am i wrong lol

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i think they mean parallel, no?

long mauve
quartz frost
#

in your task, they are in parallel i would say

#

but the task says they are in series

long mauve
# quartz frost

Oh I see if but parallel ammeter reading is what, how do you calculate it

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quartz frost
#

.

#

this is how i would do it

cedar kilnBOT
quartz frost
#

@long mauve

long mauve
#

Ty

quartz frost
#

.close

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zealous tapir
#

How do I find x?

cedar kilnBOT
tropic oxide
#

!status

cedar kilnBOT
#
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'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above
#

@zealous tapir Has your question been resolved?

zealous tapir
#

1

clear berry
#

try expanding using cos(a+b) formula

#

@zealous tapir

cedar kilnBOT
#

@zealous tapir Has your question been resolved?

distant cedar
#

@zealous tapir Use this identity: cos(a+b) = cosacosb + sinasinb

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,, cos(a+b) = cosacosb + sinasinb

wraith daggerBOT
#

RaphaelZZZ

distant cedar
#

Once you simplify using this , you will be closer to getting x

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green jungle
cedar kilnBOT
green jungle
#

how do i continue?

timber mauve
#

Do it graphically

leaden ledge
#

Graph can only help in the no. Of solutions..

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keen estuary
#

$$tg({2x + π})$$

my solution is:
$$\frac{1}{cos^{2}(2x + π)} * 2$$

wraith daggerBOT
#

sla-ppy

keen estuary
#

wolfram is telling me i done messed up

#

i believe there is a common rule where you are usually supposed to switch most tg() into sin()/cos()

cerulean sail
# cedar kiln

[get a new channel btw as this one will close and may get hidden]

cedar kilnBOT
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drifting solar
#

I need to prove for all real numbers n, if n is greater than 3, then $n^{2}>9$

drifting solar
#

I let $n=3+k$, such that $n^{2}=(3+k)^{2}$

wraith daggerBOT
#

Matt.Rey

drifting solar
#

my bad lol

wraith daggerBOT
#

Matt.Rey

versed kayak
#

Bro n^2 = 9+k^2+6k

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Obv this is > 9

red pumice
#

induction doesnt work on the reals

drifting solar
#

I'm not doing induction

#

I was going to get there and I showed my work like $k(k+6)+94$, but that would be fine to show since the +9 is there anyways

wraith daggerBOT
#

Matt.Rey

drifting solar
#

.close

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hollow garnet
#

I'm having trouble finding my b variable here

#

This is integration with partial fractions

#

The problem is the thing on the top left

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normal thorn
#

Anyone here good with computers

cedar kilnBOT
normal thorn
#

I know its not maths but i cant find anywhere to get tech help

viral cloak
#

This is for maths - I suggest trying a different server.

normal thorn
#

They kinda overlap

#

Im in dire need of help and noone else is replying

crimson delta
#

you didnt even ask a proper question

#

how are people supposed to help you if they dont even know if they can help you because you didnt say anything specific

cedar kilnBOT
#

@normal thorn Has your question been resolved?

normal thorn
crimson delta
#

for that type of question this really is the wrong server

#

something something turn off and on again

#

plug everything in and out again

cedar kilnBOT
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vagrant condor
#

how can i determine wether a given vector a is a scalar multiple of a given vector b in R^N?

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plain badge
cedar kilnBOT
plain badge
#

I know we have to use the
Cauchy criterion to begin this problem

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it's what comes after that i'm not sure

cedar kilnBOT
#

@plain badge Has your question been resolved?

cedar kilnBOT
#

@plain badge Has your question been resolved?

plain badge
#

anyone, anyone

#

bueller?

cedar kilnBOT
#

@plain badge Has your question been resolved?

wind glade
#

$a_1 + a_2 + \cdots + a_n \ge na_n$

wraith daggerBOT
#

please request a new nickname

plain badge
#

shouldn't it be epsilon not na_n

ripe siren
#

a_i>=a_n for all i<=n

plain badge
#

i had written down that cauchy's convergence criterion yields for every epsilon >0 there exists N, such that a_n+ a_n+1 + a_n+p < epsilon

cedar kilnBOT
#

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idle elm
#

Does anyone have any advice on how to solve this? I get what its asking but I don't have any idea how I would find fk. I dont really understand math with factorials

proud torrent
#

determine what C_1 is

idle elm
#

-x^3/3!

#

assuming it wants the bottom series to be similar to the top one

proud torrent
#

that's not C_1, that's the term from mclaurin series

idle elm
#

Is C_1 not a term in the mclaurin series?

proud torrent
#

the only things you know about C_j are that C_0 = x and that further C's can be obtained by using the recursive formula

idle elm
#

But we are also told that the recursive formula can compute the maclaurin series

proud torrent
#

if you know what coefficients f_k to put in, sure

#

but you said that you have a problem with that

idle elm
#

I dont understand what you mean

proud torrent
#

can you compute C_1 using the recursive formula?

idle elm
#

If I replaced f_k with -3! then it would give me C_1

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But that only works for C_1

proud torrent
#

well you figured out what f_0 is equal to

#

what if you repeat the same process for C_2

proud torrent
cedar kilnBOT
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heady osprey
cedar kilnBOT
muted bear
#

find the number of ways to not choose C

#

then subtract that

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vernal shoal
cedar kilnBOT
vernal shoal
#

help pls i dont know where to start

lethal jackal
#

what's the increment method?

vernal shoal
#

apparently this one

lethal jackal
#

oh interesting

#

always thought of this as just using the definition of the derivative

vernal shoal
#

pls help on how to start

#

im really confused

#

bcs its a fraction

latent bloom
#

Hmm

#

Okay first write y = f(x)

#

@vernal shoal

vernal shoal
#

yeaaa

latent bloom
#

Okay

#

Now write f(x+h)

vernal shoal
#

okk

latent bloom
#

Did you get there yet?

vernal shoal
#

yes

latent bloom
#

Okay what did you get so far?

cedar kilnBOT
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crimson sedge
#

hi - if you had to do r = 2cos4theta, can you multiply the 4 by theta?

crimson sedge
#

wait that doesnt make sense sorry

#

i have to graph points on polar coordinates by taking angles not on the unit circle like 16 degrees or 27 degrees and plugging them into the equation to find r so i can get a point (r, theta)

#

so if I had to do r = 2cos4theta where theta is 16 degrees, would it be r = 2cos(64 degrees) or r = 2cos(4(16 degrees)) ?

gilded elm
#

ooh a plot?

#

also hello spideygirl

crimson sedge
#

i feel better about being dumb now

gilded elm
#

lol yes i frequent these help channels

#

idk why

#

lol ur not dumb

crimson sedge
#

but yea a plot

#

true, but regardless familiarity tends to be a plus

gilded elm
crimson sedge
#

it evaluated differently when i plugged it into the calculator

gilded elm
#

can you take a pic of the calculator

crimson sedge
#

wait

#

now it did smh

#

i am dumb. my apologies

gilded elm
#

no worries lol

crimson sedge
#

.close

cedar kilnBOT
#
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crimson sedge
#

i appreciate the help re: stating the obvious

gilded elm
#

lol nw

cedar kilnBOT
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crude scroll
#

what would be the contradiction assuming $\alpha^2 > 2$?

wraith daggerBOT
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crimson sedge
#

How do I go about solving this?

cedar kilnBOT
long swan
#

Pythag

#

Be careful with sign

lyric leaf
#

cos(x) = sin(pi/2 - x)
sin(x) = cos(pi/2 - x)

cos(pi/2 - x) = 0.707
arccos(0.707) = 0.785549163

pi/2 - x = 0.785549163

x = 0.785549163

#

so do cos(0.786)

crimson sedge
#

Sweet thank you

lyric leaf
#

feel a little weird about my sol. though, wouldnt mind being double checked

crimson sedge
#

Alright, not sure if I should round it or not

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crimson sedge
cedar kilnBOT
crimson sedge
#

@uncut veldt

cosmic steppe
#

!15m

cedar kilnBOT
#

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near trout
#

how to do this quadratic graph?

cedar kilnBOT
crimson sedge
#

what class is this for

#

@crimson sedge do you know about transformations

#

?

crimson sedge
near trout
#

the teacher introduced a new topic to us but didnt explain it. he just gave the worksheet right away.

#

so i dont know- most likely algebra

crimson sedge
#

what class is this for though?

near trout
#

10

crimson sedge
#

alr

#

you havent done derivatives right?

near trout
#

i have

crimson sedge
#

oh

near trout
#

derivative function?

crimson sedge
#

so its a calculus class ?

near trout
#

dy/dx?

crimson sedge
#

yeah

#

find the derivative of f(x) and plug in 0.5

#

that will be the gradient of the tangent line

near trout
#

oh alright thanks

#

❤️

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#

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worldly vault
#

need help proving this

cedar kilnBOT
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dusky marsh
cedar kilnBOT
dusky marsh
# dusky marsh

just need help on understanding 1/7 of the GST inclusive price

#

this question is basically asking which one i should rather take to get a better deal of the shoes. so either take 1/7 of the GST inclusive price or refund the GST which at this moment would be 158.50 x 0.85= 134.725

cedar kilnBOT
#

@dusky marsh Has your question been resolved?

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@dusky marsh Has your question been resolved?

dusky marsh
#

.close

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gilded oracle
#

hello

cedar kilnBOT
gilded oracle
#

i had like 20 questions in statistics to solve and i did solve all except 4 questions, can you guys help me out with answer for the remaining 4, the due is in 15 minutes

#

The relationship between two data series, with 38 data points per series, is investigated. Calculated correlation coefficients are Rs = 0.87 and R= 0.82.

Which of the following question statements is/are correct?

There is a monotonic relationship between the data series.
When one variable increases, the other variable can be expected to increase.
There is a linear relationship between the data series.
There is a causal relationship between the data series.
There is a statistical relationship between the data series.

#

.close

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steady wing
#

Nature of the series defined by $a_{n+1}=1-e^{-(a_n)}$

steady wing
#

With an >0

wraith daggerBOT
#

dabble

steady wing
#

.close

cedar kilnBOT
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sturdy barn
#

PLEASe HELP

cedar kilnBOT
sturdy barn
#

<@&286206848099549185>

devout galleon
#

expand it

crimson sedge
cedar kilnBOT
# sturdy barn <@&286206848099549185>

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sturdy barn
#

alr

#

i did and now i have 2xcubed +2pxsquare+1xsquared+8X+pX+4

devout galleon
#

coefficients of x = 2 * coefficients x^2

#

solve it

sturdy barn
#

p=2?

#

is my answer

#

correct?

devout galleon
#

show your equation

#

coefs of x: 8 + p

#

coefs of x^2: 2p + 1

#

8 + p = 2 (2p + 1)

#

solve

sturdy barn
#

yes thats it

#

did you get 2

devout galleon
#

thats it

sturdy barn
#

how do you do this

devout galleon
#

divide to (y-3)

sturdy barn
#

how

#

oh ok

devout galleon
#

you know column division?

sturdy barn
#

no

devout galleon
#

hey are you sure?

sturdy barn
#

no

#

is column division dividing everythig by 3?

#

also why y-3?

#

OH I GOT IT

devout galleon
#

see
3xy-9x+4y-12
3x(y-3)+4(y-3)
(y-3)(3x+4)

sturdy barn
#

you can use long divison too

devout galleon
#

not me you

sturdy barn
#

also how to do this

#

lets work out together

devout galleon
#

try yourself first

sturdy barn
#

alr

#

factorise but stuck on the inverse part

devout galleon
#

factorisation is already done

sturdy barn
#

alr i got x=e cubed

#

and x=-4/3

devout galleon
#

show your solution

#

right

sturdy barn
#

yeah

#

alr thanks boss

#

seriously

#

have a good day

#

.close

cedar kilnBOT
#
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shell beacon
cedar kilnBOT
shell beacon
#

for part (ii), i wrote that due to y = 1 being a line of symmetry for C1 and C2, the only way to have one intersection point is for the point to be at the left vertex of the ellipse. i can solve for k (k = 6), but i then i tried to approach it differently by setting up a quadratic equation and setting discriminant = 0, but i cant seem to get the same answer.

#

Is the discriminant approach not possible in this question? If so, why not?

tribal sparrow
#

discriminant approach should work, maybe some calculation mistake?

shell beacon
#

wait my first step is already wrong fml

tribal sparrow
#

well, tried it myself, but it doesn't seem to work lol

shell beacon
#

Is there a reason why it shouldn’t?

tribal sparrow
#

I can't think of any reason to say so

shell beacon
#

did you get the same equation as i did

tribal sparrow
#

nope

#

I mean almost same, just difference of a sign

shell beacon
#

oh oops yeah the last equation should be -1 not +1

tribal sparrow
#

I mean, I got, 36k^4 + 4(1296 + k^2)(1296k^2) = 0

shell beacon
#

but ultimately the discriminant is still never 0

tribal sparrow
#

apart from k = 0

shell beacon
#

rip

#

would it matter if the equation was in terms of y?

tribal sparrow
#

nope, D would still have to be 0

#

since you only want one x, and one y

shell beacon
#

Is the discriminant approach impossible?

tribal sparrow
#

that's what I am trying to think, that if it's really not possible, then why not

cedar kilnBOT
#

@shell beacon Has your question been resolved?

cedar kilnBOT
#

@shell beacon Has your question been resolved?

cedar kilnBOT
#

@shell beacon Has your question been resolved?

cedar kilnBOT
#

@shell beacon Has your question been resolved?

cyan wren
#

gimme a sec

#

ye it should be just about how (-x)^2 = x^2 aka extraneous root shenanigans

cedar kilnBOT
#

@shell beacon Has your question been resolved?

cedar kilnBOT
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upper root
#

#chill

cedar kilnBOT
#

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balmy raft
#

Hello guys my camera is dookie so I'll send pictures instead written on an app

balmy raft
#

I need to verify this identity

fallen moat
#

i guess it's in degrees

balmy raft
#

I've tried changing tan and cot to their formule which is cos/sin and sin/cos and then work it out by canceling etc but I can get nowhere near 1

#

And yes the identity is true

balmy raft
burnt pumice
#

Working on it

fallen moat
#

did you try things like
sin(90°-a)=cos(a)

balmy raft
#

U can't use those here

#

I think...

burnt pumice
#

Have you tried using these?

balmy raft
#

I can't use those here cuz my math teacher will ask me to prove these formulas and she'll count them wrong

burnt pumice
#

I'm pretty sure you can't do this without these formulas

Why not just learn the proofs?

#

And what do you mean, "she'll count them wrong"?

balmy raft
burnt pumice
#

Oh

#

Okay

balmy raft
#

It's pure math like fractions etc but it's just that I'm stuck and can't do a thing

burnt pumice
#

Yeah man, you cant solve it without those formulas

#

I'll send u the solution in a minute

balmy raft
#

Thanks a lot I'll try explaining it to hzr

cedar kilnBOT
#

@balmy raft Has your question been resolved?

balmy raft
burnt pumice
#

Hmmm

cedar kilnBOT
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green grove
#

2 independent quality tests are applied to a product, the probability of the project passing the first successfully is 0.3, the probability that a product doesnt pass any quality test is 0.1, given that a product has passed the first test what is the probability that it has passed both tests

green grove
#

A - passes first check - P(A)=0.3\
B - passes second check\
$P(A \cup B)=0.9$\
$P(A \cup B) = P(A)+P(B)-P(A \cap B) \implies P(A \cup B)=P(A)+P(B)-P(A)P(B)$\
$P(B \mid A)=P(B)$

wraith daggerBOT
#

metnal

green grove
#

did i solve this correctly?

#

the answer is just P(B) right?

cedar kilnBOT
#

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buoyant latch
cedar kilnBOT
buoyant latch
#

,rotate

wraith daggerBOT
buoyant latch
#

,rcw

wraith daggerBOT
buoyant latch
# wraith dagger

Shouldn’t this one be linear combinations of (1, 2, 3) and (2, 2, 4)?

buoyant latch
# wraith dagger

Since here we say the vector z is a linear combinations of its vectors x and y

buoyant latch
#

(Well now that I think about it, R is a vector space so each element would be a vector, but I don’t think that’s the point here)

lethal jackal
#

what's z

#

oh

#

wait what's your question

#

oh

#

yeah c(A) is the set of vectors that are linear combinations of the columns of A

buoyant latch
#

Did I/lecturer write down the wrong thing

lethal jackal
#

c is the column space yeah

buoyant latch
#

So it should say C(A) is the set of vectors that are a linear combination of (1, 2, 3), (2, 2, 4)

lethal jackal
#

what does C(A) mean though

#

like the notation

buoyant latch
#

Oh is it supposed to be small c

#

Column space of A

lethal jackal
#

is it the column space of the matrix A

buoyant latch
#

Oh it doesn’t say

#

Fuck I missed the first part

#

Yes

lethal jackal
#

like I'm just assuming that it is

#

then yes it is the set of all linear combinations of the columns of A

#

otherwise known as the span of the columns of A

buoyant latch
#

Yeah yeah

lethal jackal
#

or maybe you could call it Im(A) if you think about the associated linear transformation

buoyant latch
#

I don’t know what Im(A) is

lethal jackal
#

like the set of all vectors that Ax can produce

buoyant latch
#

Anyway I either wrote down the wrong thing or the lecturer did

lethal jackal
#

yeah

buoyant latch
#

Would it be correct to say that the column space of matrix A, denoted as C(A) is the set of all possible linear combinations of the column vectors of A, and is a vector space

#

Do we know it’s a vector space or should I try and prove that to further my understanding

cedar kilnBOT
#

@buoyant latch Has your question been resolved?

royal loom
buoyant latch
#

Is this a good start

buoyant latch
#

Hmm is it for some or for any

#

And do I have to say that at least 1 of the c’s have to be non zero?

lethal jackal
#

no

#

a vector space has to contain the zero vector

buoyant latch
#

Oh true

#

Hmm I’m kinda stuck on showing the sum of 2 column spaces is another column space

#

Not sure how to get a ci out

buoyant latch
#

.close

cedar kilnBOT
#
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misty tinsel
#

This chem but

cedar kilnBOT
misty tinsel
#

How he divide 0.010/15.0 x 1000000

#

And get 670?

#

I got a decimal

obsidian coral
#

What did you type in your calculator?

cedar kilnBOT
#

@misty tinsel Has your question been resolved?

misty tinsel
#

<@&286206848099549185>

obsidian coral
misty tinsel
#

Isn’t rounding to the nearest tenths

#

666.7

#

(Just to show)

#

@obsidian coral

#

Nearest whole number is just 667

obsidian coral
#

Not tenth

#

Tens

#

The tens place

misty tinsel
#

Oh

#

.close

cedar kilnBOT
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misty tinsel
#

,close

#

Ok

#

Thx

#

,close

#

.close

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echo osprey
cedar kilnBOT
echo osprey
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i have to find a polynomial that factors into these

#

but i don't know how

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i got it

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weak mountain
#

Let X be a topological space

cedar kilnBOT
weak mountain
#

Can the closure of $X\setminus{x}$ be X if no sequence in $X\setminus{x}$ can converge to x

wraith daggerBOT
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wind whale
#

How do i do this? i have no idea where to even start

wind whale
#

along with these i have no idea where to even begin

forest sparrow
fallen moat
#

,rotate

wraith daggerBOT
fallen moat
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crimson sedge
#

I got that I need 27 steps to calculate the cube root correctly w/ bisection method but it doesn’t sound right. Can I have a second opinion?

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silent plover
cedar kilnBOT
silent plover
#

hi can someone help with the last part

cedar kilnBOT
#

@silent plover Has your question been resolved?

silent plover
#

<@&286206848099549185>

wind pewter
#

if p and q are 90 degrees from each other r=1, if they are 0 degrees from each each other then r=0

silent plover
#

yeah i did that but it says its wrong

wind pewter
#

hm

wind pewter
silent plover
#

ah

wind pewter
#

that should be correct, since you can get negative values

silent plover
#

forgot about negative

#

yep its correct

#

@wind pewter ty

wind pewter
#

np

#

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wind pewter
silent plover
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sorry i forgot

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cinder bluff
#

how to i’(x) = ((4x+6)^4(2x-5)^2))’

vagrant elbow
#

$i(x) = (4x + 6)^4(2x - 5)^3$

wraith daggerBOT
#

NEONPerseus

vagrant elbow
#

If you're meant to differentiate this, use the product rule

cinder bluff
#

i honestly don’t know how to arrive to the solution

vagrant elbow
#

$(uv)' = u'v + v'u$

wraith daggerBOT
#

NEONPerseus

cinder bluff
#

4(4x+6)^3 X 3(2x-5)^2 ?

vagrant elbow
#

Not quite

cinder bluff
#

but there’s no + in the solution

#

so I’m lost

vagrant elbow
#

They probably did some factoring maybe

#

4(4x + 6)^3(2x - 5)^3 + 3(2x - 5)^2(4x + 6)^4

#

You should have this

cinder bluff
#

ok

#

but from this to 32(2x+3)^3(2x-5)^2(14x-11) I’m lost

#

shit makes no sense to me

cedar kilnBOT
#

@cinder bluff Has your question been resolved?

cedar kilnBOT
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@cinder bluff Has your question been resolved?

cedar kilnBOT
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@cinder bluff Has your question been resolved?

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tidal wasp
#

can someone explain to my why the graph of -2^x looks like this?

tidal wasp
#

isnt -2^2 = 4 not -4?

leaden ledge
#

You have to out -2 in a bracket

#

(-2)^x

#

Like that

#

It drew the graph of y = - 2^x

tidal wasp
#

it just shows this then...

leaden ledge
#

Its actually kind of ungraphable as it will be undefined onn the real axis at infinitely many points between any two even powers

#

Is what I think kind of

tidal wasp
#

hmm

#

i kinda get it

#

i guess

#

so when i graph -2^x it actually graphs -1 * 2^x?

leaden ledge
#

Yeah

tidal wasp
#

i see

#

thx

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tidal wasp
cedar kilnBOT
tidal wasp
#

by doing it manually i got the value to be 1102.5

#

but the formula given is giving me 36000

#

nvm im supposed to take r as 0.05 instead of 5

wary hamlet
#

The answer is d?

#

Yes

tidal wasp
tidal wasp
#

thx

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chilly bolt
#

does the negation of a statement reverse its quantifier

chilly bolt
#

like negation of a for all statement changes to there exists ...

crimson delta
#

Yes

chilly bolt
#

would that also be a counterexample

crimson delta
#

"For all numbers something holds" gets turned to "there exists a number for which it doesn't hold"

#

And that number is then precisely a counterexample

#

If that's what you are asking

chilly bolt
#

ok thanks

cedar kilnBOT
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shrewd blaze
#

.

#

How do you solve/calculate the percentile?

shrewd blaze
#

I know how to solve that but i forgot one step

quartz frost
#

can you post an example of what you are doing/where you are stuck?

shrewd blaze
#

Wait let me make a problem

#

I dont have a problem yet but i need it for exam tomorrow

#

So i need to review

#

There i made a small problem

#

I just want to know on where to place / where the percentile located

#

Here i added the cf

#

Can you find the percentile of 23?

#

. Close

#

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shrewd blaze
#

Ill just study my self

cedar kilnBOT
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peak dome
#

how did he factorized it ?

cedar kilnBOT
#

@peak dome Has your question been resolved?

cerulean gyro
#

u can do it with your calculator

#

or if your fractions is really good, use any method you want

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waxen agate
#

so in question #4 how did they get 2x?

cerulean gyro
#

probably by isoceles triangle property

waxen agate
#

whats that

cerulean gyro
#

it's a circle, so all the lengths from the centre to the side of the circle are the same lengths

#

when u join the edges, they form isoceles triangles

#

the 2 non-centre angles in the triangle are the same

#

using that, u can calculate the centre angle

#

the 2 triangles' centre angles are related, as when u add them up you get 180 degrees

#

do the reverse to get 2x

waxen agate
#

sorry if im being dumb

#

but wdym by

#

do the reverse

cerulean gyro
#

isoceles triangles' angles in this case are " 2 side angles + 1 centre angle = 180 degrees"

cedar kilnBOT
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cerulean gyro
#

if u know the centre angles, u can solve for both side angles

cedar kilnBOT
#

Please don't occupy multiple help channels.

waxen agate
#

ok thanks

#

.close

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#

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crimson sedge
#

math help in polygons uve all those sides that r basically equal to each other like a pentagon shape having five sides so how do i know or i can prove that all sides are equal to each other?

#

can you help me understand with an image of a shape that how are those sides actually equal is i dont get?

cosmic steppe
#

What

#

You need to state your problem clearer

#

Are you asking how to prove a polygon is regular?

crimson sedge
#

yes that

#

how do one proves that the polygons all sides are equal to each other or like angels thing

cosmic steppe
#

Send me a photo

#

You most likely have to use SAS and then CPCTC

crimson sedge
#

what is sas and cpctc

cosmic steppe
#

"Side-angle-side" and "corresponding parts of congruent triangles are congruent"

#

But like

#

I need to see the full problem

#

Send a photo

crimson sedge
#

it has said the pentagon has five sides and all those sides are equal to each other as in a polygon

#

so how do one knows that they are equal in a polygon shape?

#

how are five sides equal

cosmic steppe
#

If you're given that it's a regular polygon then by definition the five sides are congruent

#

But

#

If you were to take all the radii of the polygon

#

They should all sector the polygon into 5 congruent isosceles triangle whose vertex angle is 360/5

cedar kilnBOT
#

@crimson sedge Has your question been resolved?

crimson sedge
#

thanks so much @cosmic steppe

cedar kilnBOT
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quasi plover
cedar kilnBOT
quasi plover
#

mark scheme

south juniper
#

can u find the gradient of the given line first?

quasi plover
#

im not sure

south juniper
#

5/2 because you need to isolate y first

#

that is done by dividing both sides by 2

quasi plover
#

how do we do that

south juniper
#

for a line y=mx+c, the gradient/slope is always m

quasi plover
#

y = (3+5x)/2

south juniper
#

Yes, so the slope is 5/2

cosmic steppe
#

Well there's a nicer way of doing it

quasi plover
#

what about the 3

cosmic steppe
#

I can show you a little trick

south juniper
#

its the y-intercept you dont need it

#

sure!

quasi plover
cosmic steppe
#

For the linear equation $Ax + By = C$, the perpendicular gradient is $\frac BA$

wraith daggerBOT
#

Umbraleviathan

quasi plover
#

what about the C?

cosmic steppe
#

Don't care

quasi plover
#

we just ignore it?

#

oh

#

graet

cedar cypress
#

The constant just controls the intercepts and shifts the line while keeping the slope same

quasi plover
#

sounds unreasonable but i like it

cedar cypress
cosmic steppe
#

Well yeah. The constant just shifts the line up or down but has nothing to do with slope

floral forge
#

the inverse of a line will have slope perpendicular to the initial line, hence why this works

#

so its like solving for x=my+c

quasi plover
#

should I understand this, or i should just remember the equation up there and use it

cedar cypress
#

Another thing I'd like to add, product of slopes of two perpendicular lines is always -1

floral forge
#

def should understand it

#

as always in math

quasi plover
cedar cypress
# quasi plover ?

Let's say i have two perpendicular lines with slopes M1 and M2, then M1 times M2 is always -1

#

Comes handy

quasi plover
quasi plover
cedar cypress
cedar cypress
#

If the lines are perpendicular

quasi plover
#

oh oh sorry my bad

cedar cypress
#

Only with perpendicular

#

It's converse is also true

#

If product of gradients of two lines is -1, then they are perpendicular

quasi plover
#

oh wait, the question is asking me to find the gradient of the other (opposite) lines of the equation right?

#

which so gradient A times gradient B is always -1

#

so why i cannot just do -1/5

cedar cypress
#

Why -1/5?

quasi plover
cedar cypress
#

The gradient of the first line is 5/2

#

Not 5

cedar cypress
#

Need to get rid of that first

cedar cypress
#

Yes get it in the form y=mx+c

#

M is 5/2

quasi plover
#

2y = 5x + 3?

#

now its in the form

cedar cypress
#

No

#

The 2

#

Isn't there in the mx+c form

#

you need to divide it

#

Both sides by 2

#

The form is y=MX+c, not 2y=MX+c

quasi plover
#

but the it would be (5x+3)/2

cedar cypress
#

Yes and take the 2 inside

#

5x/2+3/2

#

So m is 5/2

#

And c is 3/2

quasi plover
#

?

#

whats C in the y=mx+c again?

#

i think i forgot

#

and is this the way to find the gradient of the another line right?

#

;-;

cedar cypress
quasi plover
#

i rememebr the M is gradient

cedar cypress
#

What do you understand by the y intercept?

quasi plover
#

the point where the line pass the Y axis

cedar cypress
#

Yes so logically shouldn't it the point (0,c), where c is the value of y at x=0?

#

So the y intercept is c

quasi plover
#

whats 0,c

#

0 and c

#

y=mx+b

cedar cypress
#

Of the y intercept

quasi plover
#

what???

#

im not sure did i understand you

cedar cypress
#

Can you plot this line? That way you can understand yourself

#

What I mean by 0,c

quasi plover
#

its the middle

#

the point where y and X interceppt

cedar kilnBOT
#

@quasi plover Has your question been resolved?

cedar kilnBOT
#
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knotty wagon
#

(Q.25) Had this question for an exam, is the answer 72m? (7200 cm)

gritty galleon