help-42

[unreal isle]

what seems to be the problem

[proper ocean]

AD

Actually

All

[unreal isle]

you've found the gradient correctly in the first part

[proper ocean]

X =0
y = ½x + 1

For d

[unreal isle]

now, in the second part, it asks for the eqn of line of AD

[unreal isle]

let's go part by part shall we?

[proper ocean]

Yes

This is the only example they gave🙏

[unreal isle]

you've done the first step correct by noticing it is perpendicular and hence the product is = -1

brb

[proper ocean]

...

[unreal isle]

alr im back

someone was at the door

okay so can you tell me what you need to form an equation of a line

[proper ocean]

Wtf

[unreal isle]

ignore him

[proper ocean]

Cross product

What!?!?

[unreal isle]

.

please chill

[proper ocean]

So

y=mx +c

And a point

[unreal isle]

a point and?

[proper ocean]

Parallel lines?

[unreal isle]

not quite

you need the m of the line

[proper ocean]

Perpendicular bisector

[unreal isle]

the "gradient"

[proper ocean]

Oh

[unreal isle]

to form an equation of line

you either need 2 points on the line

to find the gradient, and use it to find c

OR

if you have the gradient already and only 1 point

you can form the equation directly

[proper ocean]

Yes

[unreal isle]

do you know how to do that?

[proper ocean]

Sub-ing the first point + m numbers in
Y=mx + c

[unreal isle]

yep, so do you have that for AD?

[proper ocean]

y= ⅓(0) + c

Wait

No

[unreal isle]

you dont know the y coord of D yet!

there is a coordinate you do know on this line tho :)

[proper ocean]

x=9

[unreal isle]

erm

let's back track a little okay

[proper ocean]

Y= 4?

[unreal isle]

on this graph

we know the gradient of AB correct?

[proper ocean]

Yes

[unreal isle]

m=?

[proper ocean]

⅓

[unreal isle]

perfect, now what do we know about the relation bw AB and AD

[proper ocean]

That's they have the same gradient
L₁||L₂ therfore m₁=m₂

[unreal isle]

that's incorrect

but thats okay

[proper ocean]

Oh

AD

[unreal isle]

can you tell me the relationship bw perpendicular lines

[proper ocean]

Not CD

[unreal isle]

yeah...

[proper ocean]

m₁m₂ = -1

[unreal isle]

perfect so we can find mAD now right?

[proper ocean]

I think

M = -3

And y = ⅓x + 1

Do we use the point of (3,2) ?

Uh

[unreal isle]

i apologize i was afk again

[proper ocean]

Okie

[unreal isle]

where did this come from

[unreal isle]

this is perfect

[proper ocean]

I mean ⅓

[unreal isle]

and this is perfect

using these 2 ideas, can you find the eqn of AD now

[proper ocean]

Yes

[unreal isle]

that m = -3 and A(3,2)

[unreal isle]

perfect do that

[proper ocean]

C = -11

Wait no

11

[unreal isle]

that's correct, can you form the eqn of line since that's what the qs wants

[proper ocean]

y= -3x +11

[unreal isle]

you got it

[proper ocean]

And

[unreal isle]

yes?

[unreal isle]

perfect!

[proper ocean]

C

[unreal isle]

just part d left

can u give me a sec? i'll brb

im sorry i'm really busy

nvm it fixed itself

hi

[proper ocean]

Yes

[unreal isle]

ooo part D is very cheeky

the question tells us something about the line BC

can you spot it

[proper ocean]

⅓

[proper ocean]

M

BC
X=9

[unreal isle]

perfect!

the question tells us BC is parallel to the y axis

that allows us to deduce that the x-coordinate of B is the same as that of C

so if we form an equation for DC and plug in x=9 we should get the y coordinate of C

[proper ocean]

0= ⅓(9) + c?

[unreal isle]

not quite

first let's form the equation for CD

we know m=1/3 since it's parallel

do we have a known coordinate on the line CD

[proper ocean]

(0,11)

Wait no

[unreal isle]

why no

you're spot on

[proper ocean]

C
(9,y)

[unreal isle]

yes

[proper ocean]

As much i love maths I HATE geometry and matrices

Woah

Yay

Took only 1h

😲

[unreal isle]

i have some advice for you

[proper ocean]

Yes

Im her

[unreal isle]

don't panic when you dont get the answer

[proper ocean]

Here

[unreal isle]

taking a breather, have some water, reset, and look at the question as if you've never seen it

all that happened here was you mistook a perpendicular line as a parallel one

[proper ocean]

I sometimes redo it on a piece of paper

[unreal isle]

even though you knew the theory

your mind slipped

that's okay

you just need to reset

[proper ocean]

Do you think

That

[unreal isle]

i do not think

[proper ocean]

If i finish the grade 10 add maths book

[proper ocean]

No like general

[unreal isle]

i knew this was add math 😭 is this the hoo soo thong book

[proper ocean]

I go do grade 12 maths

(Pure maths)

[unreal isle]

are you talking about A levels?

[proper ocean]

But the problem I know there integration in grade 11

[proper ocean]

Yes

Taking all science and maths

[unreal isle]

yeah i assumed you were talking about A level, look AS math is TRIVIAL if you have taken add math in o level

as for the subject composition: phys chem bio math

that's what im doing rn

for me it's chill because i've always had a strong base in these subjs

but it's not for everyone

[proper ocean]

I don't wanna do bio sub in the future

💔

[unreal isle]

there's no 1 glove fits all answer

[proper ocean]

There's like 2 papers in AS maths?

[unreal isle]

you gotta see what works for you

[unreal isle]

yep, pure 1 and then either stats 1 or mech 1

[proper ocean]

Im asking YOU

[unreal isle]

i dont know you at all

[proper ocean]

I have dont the normal maths

[unreal isle]

im a stranger on the internet

[proper ocean]

For grade 10

[unreal isle]

isn't it a compulsory subject

[proper ocean]

Cool I had 2 of my best friend are strangers

[proper ocean]

NOO like self learning

For grade 10

I'm in grade 9 rn

I finish my grade 9 syllabus in 2024 Oct-Dec by self learning

Maths one only

[unreal isle]

im not qualified to give you a suggestion and I do not wish to misguide you

[proper ocean]

I know

I'm just asking

Is cal actually hard😔

[unreal isle]

to me it was the only fun part of Add Math, to some it was the bane of their existence

again

no one glove fits all

i urge you to try it out for yourself

[proper ocean]

Okie

[unreal isle]

without prior opinions on it

[proper ocean]

See you tmr fr cus I nan solving ts alone

Any tips for coordinate of a circle

Before I close ts

[unreal isle]

wdym
(x-h)^2 + (y-k)^2 = r^2
this equation?

[unreal isle]

yeah this

idk what you mean by "tips"

go through the examples to understand

do simple questions

watch some lectures onlineif you need to

ask here if you're stuck on a speciic qs

[proper ocean]

Okie

BRO

@unreal isle

Dream

Livestream

Im out

.close

[calm coral]

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[unreal isle]

just because i have a technoblade pfp doesnt mean i care 😭

[proper ocean]

💔💔💔💔

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[sweet meadow]

Hi, I just wanted to ask about the difference about calculus and analysis

[old falcon]

someone will correct me no doubt, but broadly calculus is contained within analysis which is a larger field

it depends on the context you're asking though

[primal smelt]

Calculus is the study of change, analysis is the study of functions and numbers in different spaces

iirc

[old falcon]

@sweet meadow clarify

[sweet meadow]

I was just curious. I was told that analysis is just calculus but its like more difficult

[drifting seal]

yea but eventually the things stop looking like calculus entirely

[old falcon]

in the context of like

[elder pawn]

calc focuses on computation. analysis focuses on the theorems that power the computation

[old falcon]

roketto

[primal smelt]

that really depends in my opinion

[drifting seal]

your opinion is wrong

[sweet meadow]

btw

how much time a day do you guys spend helping people in the server?

[old falcon]

7 hours

[drifting seal]

depends

[old falcon]

but im mostly silent offering emotional support psychically

[leaden thunder]

This isn't really a math question

[elder pawn]

for example in calc you simply use the chain rule to compute. but in analysis you will go through a proof of the chain rule

[sweet meadow]

so is analysis like calculus+its proofs

[drifting seal]

usually just when i’m on the toilet or procrastinating or tired late at night

[primal smelt]

I heavily disagree on that, I learned mostly proofs in calculus

[elder pawn]

yes the proofs behind calculus facts

[old falcon]

i do it on flights lol

[drifting seal]

are you on a flight rn

[old falcon]

no

[drifting seal]

switzerland

[old falcon]

nope

[elder pawn]

yeah it depends where you live. american calc is always computation while european calc may be proofs

[primal smelt]

Yea could be

[sweet meadow]

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[remote mural]

does the limit not exist?

[fringe reef]

yes, it doesn't exist

[glad parrot]

yeah from left it don't exist

[remote mural]

thankyou!

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[strong wave]

yo

[strong wave]

i dont understand how this is wrong

[mellow harbor]

what is wrong?

[strong wave]

i got x^6 + (6x^5)(2x^-1) + (15x^4)(2x^-1)^2 + (20x^3)(2x^-1)^3 + (15x^2)(2x^-1)^4 + (6x)(2x^-1)^5 + (2x^-1)^6

[mellow harbor]

You can use \frac to put fractions in

[velvet osprey]

you have not yet simplified it

[strong wave]

i have and its the wrong answer

I dont understand why tho

[velvet osprey]

wrong how

[dull wagon]

show your attempt at simplification

[velvet osprey]

are you 110% sure that you aren't screwing something up with the arithmetic?

[strong wave]

no

[velvet osprey]

ok then show us your simplification so that we can diagnose it

[dull wagon]

because what you have so far is right

[strong wave]

i got x^6 + 12x^4 + 30x^2 + 40 + 30x^-2 + 12x^-4 + 2x^-6

this is the answer

[velvet osprey]

how did you get from $15 x^4 \cdot (2x^{-1})^2$ to $30x^2$?

[potent lotus]

Ann

[strong wave]

oh

[velvet osprey]

$(2x^{-1})^2 \neq 2x^{-2}$

[potent lotus]

Ann

[strong wave]

I forgot to raise the number

💀

my bad thanks guys

.close

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[finite oasis]

\textbf{Question:} Let $G$ be a finite group of order 168. Prove that if $G$ acts transitively and faithfully on a set $X$ with $\abs X = 7$, then $G$ is isomorphic to $\op{PSL}_2(\vb*{F}_7)$. Furthermore, classify all possible such actions up to isomorphism.

\medskip
I’ve shown transitivity implies a subgroup of index 7, but I'm stuck connecting the action to $\op{PSL}_2(\vb*{F}_7)$ and classifying the actions. Could I get some guidance on this?

[calm coral]

@finite oasis Has your question been resolved?

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[sonic plaza]

is my working out correct, and also Im trying to find the value of t which im stuck

[primal smelt]

where did the 3 * go

3(t-1)^2

and then t^2 - 2t -1

[sonic plaza]

im confused could you take a screenshot of what ur talking about

[primal smelt]

look at the beautiful 3...

where did it go...

[sonic plaza]

ohh

oops

Let me fix that real quick

@primal smelt I didnt get a real solution for t

[dull wagon]

you distributed the 3 to something you shouldn't have

[sonic plaza]

the 2?

[dull wagon]

and you also did some duplicated addition there too

[sonic plaza]

but what im doing is on the right track overall tho right?

im using the correct method n all?

to solve for this question

[dull wagon]

after the initial set up, QF will get you what you want

but you gotta fix those initial steps

[sonic plaza]

QF?

[dull wagon]

quadratic formula

[sonic plaza]

oh

[dull wagon]

after expanding the $(t-1)^2$, you should have
$$3(t^2 - 2t + 1) + 2 = 8$$
try continue from there

[potent lotus]

ℝαμOmeganato5

[sonic plaza]

alr one sec

@dull wagon Im not sure if i did the last line right

I cant seem to factorise it

[dull wagon]

you dropped the ^ on the 3t^2

[sonic plaza]

could you screenshot it

[dull wagon]

and didn't factorise -3t - 3 correctly

[sonic plaza]

ooops

whats ur advice for my silly mistakes 😅

i loose about 8-10 marks on silly mistakes in exams

[dull wagon]

write things carefully

this shouldn't really be happening if you're writing stuff line by line as you have something directly above to compare

[sonic plaza]

didnt i do that tho?

I wrote line by line

[dull wagon]

yes. so the mistakes like this shouldn't be happening

they most likely arise from rushing and carelessness

as you have something directly above to compare

you aren't doing anything with the stuff like 3t^2 - 6t between those lines
so just copy that part directly/exactly

the 2 shouldn't mysteriously vanish

if you're doing that

perhaps also use a darker colour

as that light green is too bright

[sonic plaza]

thats true

[dull wagon]

and can get lost in the white background

[sonic plaza]

so anything dark

alr

[dull wagon]

get used to black or blue as those would be what you'd use in the exam/tests

use another readable colour for notes
and red for corrections after an attempt

[sonic plaza]

wdym readable colour for notes?

[dull wagon]

a dark colouor that isn't red, black, blue if you have one

to make comments

[sonic plaza]

tbh i just use black

for eeverything

but i should stop

[dull wagon]

that's fine, colour coding makes it easier to read what you did in the past

[sonic plaza]

yea

true

[dull wagon]

but if you're stuff is organised, a single colour is fine

[sonic plaza]

I woudnt say im organised

[dull wagon]

anyway try reattempting

[sonic plaza]

I also dont have a time table/schedule, does that really matter?

i just study

whenever i get time

[dull wagon]

also this can't be factored nicely

[sonic plaza]

btw my answer for q 7 is wrong

[dull wagon]

show y our updated work

[sonic plaza]

i got t = 1

[dull wagon]

show the work that led to taht

[dull wagon]

and didn't factorise -3t - 3 correctly

[sonic plaza]

.

oh my gaw

we were just talking about this

[dull wagon]

-3(t-1) would expand back out to -3t + 3

not what you started with

you can apply QF like you did in your original attempt

[sonic plaza]

could you take a screenie once again thank you

[dull wagon]

of what

[sonic plaza]

of my mistake in this screenshot

[dull wagon]

find the line where you had -3t - 3

your error was in what you wrote after that

[sonic plaza]

can i add you? I have to go sleep rn and ill continue this problem tommrorwo

[dull wagon]

no

[sonic plaza]

👍

[dull wagon]

just post when you come back and someone will come and assist

[sonic plaza]

ok

[sonic plaza]

does this ticket stay opened or does it get deleted?

I want to continue from this chat

[dull wagon]

the channel gets recycled if you don't use it for a period of time

you can copy a message link that'll bring you back here

and use it for reference when you come back

[sonic plaza]

how long is that period of time

[dull wagon]

around 15minutes of non-responsiveness (extendable depending on activity)

if you know you're going to be away especially going to sleep,
just close

[sonic plaza]

alr

[calm coral]

@sonic plaza Has your question been resolved?

[calm coral]

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[crisp minnow]

In many real-world scenarios, organizations must evaluate multiple proposals to determine the most cost-effective solution over time. This analysis often involves comparing financial expenses, considering both initial investments and long-term operational costs. In this case, we examine three different proposals—Tom’s, Dick’s, and Sally’s—to assess their cumulative costs across a specified timeframe.
To model this situation mathematically, we will define cost functions for each proposal, accounting for changes in expenses at key intervals. By analyzing these functions, we can compare financial impacts using graphs, tables, and calculations, allowing us to make an informed recommendation on the most cost-efficient option
is this a good introduction?

[finite oasis]

This relates to mathematics how exactly?

[crisp minnow]

its maths

read the problem

its explaing maths in words

[odd moon]

idk how long your question is gonna be but to me its a lot of yap

is it gonna be like the example

the example is different since the introduction is short but every sentence in the other paragraphs tel you something about the problem

[crisp minnow]

im writing an intro about the problem

[odd moon]

ok

[crisp minnow]

so im introducing the problem

.close

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[blazing coyote]

Trying to integrate x^2dy - y^2dx over (0,0), (1,0),(1,1) orietented counter clockwise

[blazing coyote]

usinge green's theorm

we first have the function -(y^2dx-x^2dy)

so we have

,w integrate 2x+2y over the triangle bound by (0,0), (1,0),(1,1)

[potent lotus]

Wolfram Alpha doesn't understand your query!
Perhaps try rephrasing your question?
Click here to refine your query online

Requested by math_rocks

[blazing coyote]

,w integrate 2x+2y over 0≤y<x; 0≤x<1

[potent lotus]

Results provided by WolframAlpha

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

Requested by math_rocks

[blazing coyote]

.close

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[granite cypress]

.Solved by WolframAlpha, I hope helpers' lounge took note

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[remote mural]

What if x=5 and n=1 for example? Wouldnt that integral be 0?

[remote mural]

im stupid

.close

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[brisk pelican]

how can i show that limsup of (logn)^(logn/n) is 1?

[brisk pelican]

as n goes to inf

[mellow harbor]

!showyourwork

[calm coral]

Show your work, and if possible, explain where you are stuck.

[brisk pelican]

ive been treating it as a limit instead of limsup

i tried lhopital and wound up with at the exact same spot

i cant think of anything else to do

[mellow harbor]

Have you looked at the limit of log(n)/n here?

[brisk pelican]

oh yea i should have said

i took log of everything before doing lhopital

so im trying to show that logn*log(logn) /n goes to 0

[mellow harbor]

No I mean, do you know what this approaches?

[brisk pelican]

0

[mellow harbor]

Do you think you can use that?

[brisk pelican]

here?

i dont see how

log(logn) goes to infinity

[mellow harbor]

What happens if you apply Lhospital again?

[brisk pelican]

i just get the same thing

[mellow harbor]

You don't

[brisk pelican]

with an extra +1/n but that goes away in the limit

wait but how are you using lhopital on the whole thing

i was taking d/dn of numerator and denominator separately

[mellow harbor]

Ignore that I was trying something else

[brisk pelican]

i dont know what to do

[mellow harbor]

I mean don't you get (log(log(n)) + 1)/n for the numerator tho?

[brisk pelican]

yea

but the 1/n goes to 0 as n grows

and the d/dn of n is 1 so

lhopital just runs me in a cycle

[mellow harbor]

Um... log(log(n)) grows slower than log(n)

[brisk pelican]

ohh wtf true

im blind

thank you

thanks for all the help

.close

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[sonic plaza]

Need help with the whole subset questions

[naive meadow]

How do you think we should start (a)?

[sonic plaza]

1st one is percentage increase

I forgot how to

[naive meadow]

Percentage increase is $\frac{[\text{new value}]-[\text{old value}]}{[\text{old value}]}\cdot 100$

[potent lotus]

Buzzing Hornet

[naive meadow]

What will this be equal to in our case?

[sonic plaza]

It will be

100-114/11 x 100

Sorry 11 is 100

[naive meadow]

Almost

As you've said, 11 should be 100, but there's one other thing not quite right here

[sonic plaza]

Percentage symbol?

[naive meadow]

No, you haven't quite applied the formula correctly

Look back at the numerator

[sonic plaza]

Oh it should be 114-100

/100

X100

[naive meadow]

Right

Which is?

[sonic plaza]

Let me calculate that

[jagged agate]

erm actually 🤓

Don't forget to minus 100%

[sonic plaza]

Hi Maddie

Wdym

[sonic plaza]

14?

[naive meadow]

Right

[sonic plaza]

14%

[naive meadow]

This is already in the formula

And in xxx's calculation

[jagged agate]

o aight bett

[naive meadow]

Alright, now let's do (b). How do you think we should start this?

[sonic plaza]

@naive meadow sorry back

Hmm

we just sub t = 15

[naive meadow]

Yup

Now you will want to use a calculator for this instead of doing it by hand

[sonic plaza]

yes

I got 713

and c is 8

im pretty sure

8h

[naive meadow]

It's like 8.2 but yeah

,calc 1.14^15

[potent lotus]

Result:

7.137937978388

[naive meadow]

Yeah this is right too

[sonic plaza]

oh so yeah approx 8.2

let me try this

first one is we just sub t = 0

which is 10

[naive meadow]

It is, yes.

[naive meadow]

Now how should we do (b)?

[sonic plaza]

next one is 2.6

[sonic plaza]

basically just sub t = 15

[naive meadow]

,calc 10*0.9^15

[potent lotus]

Result:

2.0589113209465

[naive meadow]

Not quite 2.6

How should we round 2.058 to 1 decimal place?

[sonic plaza]

it should be 2.6

oh

2.1

[naive meadow]

Yeah

[naive meadow]

"Trial and error" is a horrifying exercise

[sonic plaza]

for C, 6 and 5 are close answers

fr

[naive meadow]

,calc log_0.9(1/2)

[potent lotus]

The following error occured while calculating:
Error: Undefined symbol log_0

[naive meadow]

Well notice that 0.9^5 and 0.9^6 are both greater than 1/2

So we need to check some more values

[sonic plaza]

so something less

[naive meadow]

Not quite

0.9^t gets smaller as t increases, and we want to know (roughly) what t gets us 1/2

Since t=5 and t=6 both get us things larger than 1/2, we're not sure if we've gotten as close as we can

[sonic plaza]

its not exactly half tho

[naive meadow]

For instance, how do you know the closest integer isn't t=8?

[sonic plaza]

hmm not sure

[naive meadow]

Well the answer is "keep checking until we get something too small"

[sonic plaza]

its asking half of the initial right

which is 10

half of 10 = 5

[naive meadow]

That is true

[sonic plaza]

shoudnt it be 10(0.9)^6

which gives 5.31441

and we round it

[naive meadow]

Well how do you know 7 doesn't get us 5.1? Or 4.9?

It's important to check the next value too (in this case especially because 7 actually does end up being closer)

[sonic plaza]

trial and error

@naive meadow I checked the answer it was 7 but

i dont understand how its 7

[naive meadow]

Well, what happens when you plug in t=7?

[sonic plaza]

oh nvm

ok i gt it

they rounded it up

[sonic plaza]

like 4.782..

[naive meadow]

Right, which is closer than 5.31

[sonic plaza]

yup

Ill move on to the next q, i think this is a bit trickier

[naive meadow]

How should we start (a)?

[sonic plaza]

well i mean question c

a is 60

b is 4860

[naive meadow]

,calc 20*3^5

[potent lotus]

Result:

4860

[naive meadow]

Right.

Now how should we go about drawing the graph?

What kind of graph should this be?

[sonic plaza]

its an exponential first of all since it has a

exponent

[naive meadow]

Right, this is an exponential function

[sonic plaza]

yup

[naive meadow]

So we should find the y-intercept, find one or two more points, and then just sketch the rest

[sonic plaza]

so to find the y intercept, we let t = 0?

[naive meadow]

Right

[sonic plaza]

but i thought

exponential always start with 1

when its 0

[naive meadow]

Well, a^t is 1 when t=0

But c*a^t isn't going to be quite the same, is it?

[sonic plaza]

yeah true

the exponentail function is being mulitlplied

[naive meadow]

Right

So instead of being 1 at 0, it will be?

[sonic plaza]

alr

i draw the graph

[sonic plaza]

20

whats the next part of the question asking?

[naive meadow]

I'm not totally sure why this part of the question is mathematical. The answer that comes to mind is something about limited resources on the island, I guess.

It's basically asking "why might the population growth eventually not be exponential?"

[sonic plaza]

first of all

[sonic plaza]

ohh ok

it also said draw the graph for t equal/greater than 0

i also found subbed t = -1

basially found some negattive t values for the graph

it should be only positive right?

[naive meadow]

Yeah you only need the nonnegative half

[sonic plaza]

including 0

[naive meadow]

Yes, nonnegative means greater than or equal to 0

[sonic plaza]

yep

[sonic plaza]

Yeah because its a small island

and limited resoruces

[naive meadow]

That's what I was thinking yeah

[sonic plaza]

the population might also compete each other

for resources which reduces the population size

yea

this was the answer

why cant it grow large? is it only for this scenario or

for every scenarios in life

[naive meadow]

Well in general population cannot literally grow arbitrarily large because the resources in any given place are finite

[sonic plaza]

Yeah true

its not like they are in heaven, receiving endless resources

this one is hard

Ive been strugglig to find the constants

[keen flare]

were you able to find A?

[naive meadow]

How do you think we should try to find A?

Hint: remember the y-intercept thing we were discussing earlier

[sonic plaza]

Is A when x = 0?

[naive meadow]

Yes

Do you see why?

[sonic plaza]

isnt A = 0.08

[sonic plaza]

why?

[naive meadow]

Well, what is A(2^kt) equal to when t=0?

[sonic plaza]

0.08

[naive meadow]

Well I was trying to get you to explain why it's equal to A

But yes, it's 0.8

Now how should we try to find k?

[sonic plaza]

because in the question it gives us a graph and a formula, we know the function will equal to 0.08 when t = 0

[sonic plaza]

rearranging?

[naive meadow]

I was looking for something along the lines of $A2^{k\cdot0}=A2^0=A\cdot 1=A$ but sure

[potent lotus]

Buzzing Hornet

[naive meadow]

What should we rearrange?

[sonic plaza]

make k the subject

[naive meadow]

Well I was more asking what equation we should rearrange

[naive meadow]

Sure, that works. Now how should we rearrange it?

Like concretely what should we do to it

[sonic plaza]

divide by A so it will be N/A

[naive meadow]

Right, then what?

How should we get k out of the exponent?

[sonic plaza]

isnt this index equations?

[naive meadow]

It is, yeah

But how do we solve those?

Wait, I lied

This is not

We have x=y^z and want to solve for z, how should we do that?

[sonic plaza]

isnt this the answer

wait

nope i got it wrong

wait maybe it is correct

I forgot to assign a value for t

[naive meadow]

Yeah no you can't do it like this

A, N, and 2 are different bases

You can only use tricks like this if you have something like $a^x=a^ya^z$

[potent lotus]

Buzzing Hornet

[naive meadow]

Are you familiar with logarithms?

[sonic plaza]

@naive meadow sorry my mum was calling me

[sonic plaza]

I heard it like 3 times but no

[calm coral]

@sonic plaza Has your question been resolved?

[naive meadow]

Hmm I'm not totally sure how you're supposed to go about this then

[sonic plaza]

No worries, i dont think my exam will be heavly focused on that question but I do want to go over the harder questions I coudnt solve from before from the other topic

[naive meadow]

What do you think we should start with?

[sonic plaza]

expand the bracket (k+2)x

[naive meadow]

Hmm

What's the general way to find the solutions to a quadratic?

[sonic plaza]

x^2-xk+2x-3k-11=0

[sonic plaza]

factorisation

[naive meadow]

Well, that's one way to do it

[sonic plaza]

ax^2+bx+c=0

[naive meadow]

But the way that usually tells us how many real solutions an equation has is...?

[sonic plaza]

the discriminant

[naive meadow]

Well the quadratic formula yeah

So what happens when we put this quadratic into the quadratic formula?

[sonic plaza]

we can solve for

x

-b+-(b^2-4ac)/2

a

[naive meadow]

Right, but like what do we actually get when we put in the coefficients

[sonic plaza]

to put it into the quadratic formula we need to

expand the braket first

so we could see clearly waht the a, b and c term is

[serene talon]

that would make it harder, not easier

(why?)

[sonic plaza]

Not sure tbh

[serene talon]

what are a, b, and c?

conceptually

for any quadratic

[sonic plaza]

the coefficients

[calm coral]

@sonic plaza Has your question been resolved?

[sonic plaza]

<@&286206848099549185>

[calm coral]

@sonic plaza Has your question been resolved?

[alpine stone]

Any progress so far?

[sonic plaza]

Oh nope

I coudnt solve that since 2 weeks

[alpine stone]

A quadratic equation has two distinct solutions iff the discriminant is positive, so, in this case it’s equivalent to (k+2)^2 + 4(3k + 11) being positive

Do you know how to solve quadratic inequalities?

[sonic plaza]

I think so

[calm coral]

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[rocky flower]

What’s the minimum distance from any vertex of an edge of a cube to the cubes space diagonal? I have an answer but idk how to prove it

[leaden thunder]

What does cubes space diagonal mean

[rocky flower]

A space diagonal of a cube is the diagonal from one corner of the cube to the directly opposite corner of the cube

[swift laurel]

presumably you mean one of the vertices that the space diagonal doesn't pass through

[rocky flower]

Yeah

Oh wait, I should’ve clarified that, thank you

[swift laurel]

so what was your answer?

[rocky flower]

I didn’t produce an answer myself but the answer happens to be || x/sqrt2 || where x is the side length of the cube

[calm coral]

@rocky flower Has your question been resolved?

[rocky flower]

Actually it’s alright, idk how to approach this problem with pure geometry

.close

[calm coral]

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[sharp oxide]

I'm a bit confused where to go with finding b

f(x) decreases from x=-11/7 to -2/7
& increases from x=-2/7 to 9/7

[calm coral]

@sharp oxide Has your question been resolved?

[calm coral]

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[fickle flume]

Hello!

[fickle flume]

I have decided to memorise some kind of convergence-test flow chart

Does this flow chart look okay, or is it missing some information? I don't want to memorise something that won't cover all scenarios

When I write "all scenarios", I don't mind if there is some niche exception

but it would have to be very niche

[glass heart]

the root test is missing

[velvet osprey]

also for alternating series i'd say test them for absolute convergence first, THEN apply AST if you get divergent on that

[fickle flume]

where in the flow chart would i be using the root test, is it after seeing if I can use DCT or LCT?

[glass heart]

next to the ratio test

they are very similar tests

[calm coral]

@fickle flume Has your question been resolved?

[fickle flume]

okay thank you!

and ty too Ann

.close

[calm coral]

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[rare inlet]

Hello!

I solved this problem correctly but i am unsure if my proof is ok

At the end i got it right a = 15 this is the right answer but can someone please tell me if what i wrote is ok? like for a test if i write this on my exam is this accepted?

[calm coral]

@rare inlet Has your question been resolved?

[rare inlet]

<@&286206848099549185>

[calm coral]

@rare inlet Has your question been resolved?

[calm coral]

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[inland ice]

i got this wrong, i used a graphing calculator and am wondering if i entered it in wrong?

[inland ice]

i entered 2013 as 0 since its the years since 2013, 2014 as 1, 2015 as 2, etc.

and then entered the second row in the next column as it is

[radiant plinth]

try rounding it to the nearest hundredth

and see if it takes that answer

[calm coral]

@inland ice Has your question been resolved?

[inland ice]

WAIT I THOUGHT THAT WAS THE NEAREST HUNDREUTH

ITS NOT??

[leaden thunder]

https://d138zd1ktt9iqe.cloudfront.net/media/seo_landing_files/decimals-place-value-chart-1637578922.png

[inland ice]

omg i feel stupid 💔💔 help

km literally in high school i should NOT be learning this rn…

well thankyou heh

.coose

omg

.close

[calm coral]

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[slender socket]

Can someone help me with part b?

[bold hatch]

It says to assume that all igniter failures are independant.

So try to view this as a geometric distribution

Does that help? If not, feel free to ping me and I'll explain more.

[slender socket]

I don't really remember anything about geometric distributions sorry

[bold hatch]

Sorry, i messed up

This is actually a binomial istribution

Ok disregard that. First, whats the probability that an igniter succeeds?

[slender socket]

.85

[bold hatch]

Its good to visualize the question in part B as:
What is the probability that the 31st and 32nd shot will both succeed?

And once you find that probability, you can use P(!A) = 1 - P(A) formula to find the probability of at least one of those shots failing.

[slender socket]

I thought it is asking if they both fail?

Oh wait so the total probably is the probability of them both succeeding and the probability of one or another failing?

[bold hatch]

No, it's asking for the probability of at least one of them failing

Ill give you a table to demonstrate

[slender socket]

Is this correct then?

[slender socket]

?

[bold hatch]

✅ this is correct

[slender socket]

Wait so are you saying instead of doing all that that you just find the probability of one of them failing?

Let say the probability of the 31st failing

Because isnt the fail rate .15 and it is independent so wouldn't all of them have a fail rate of .15

[bold hatch]

No, you should find the probability of both of them suceeding

Because if you try to find the probability of one of them failing, you risk double-counting the overlap where both fail

[slender socket]

Isn't or for non mutual exclusive events then or probability - them both happening?

In our case how could both fail since if the 31st failed we wouldn't go to the 32nd

[slender socket]

?

[bold hatch]

You can do that too

[bold hatch]

Wait, you might be right

So this is actually a geometric distribution, like i said before

And if X is a geometrically distributed variable, you can use the formula P(X >= x) = (1 - p)^x

P is a probability function
X is the geometrically distributed variable
x is the number of tries
p is the chance of something happening

[slender socket]

(1-.15)^32?

[slender socket]

.

[bold hatch]

You shouldn’t use x = 32, because it’s given that the first 30 shots succeeded

[slender socket]

So 2?

[bold hatch]

✅

[slender socket]

Ok thank you

[calm coral]

@slender socket Has your question been resolved?

[calm coral]

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[remote mural]

Anyone this plz help

Hi

[remote mural]

Anyone help plz

[twin raptor]

what is $1 + \frac{1}{n^2} + \frac{1}{(n+1)^2}$?

[potent lotus]

flying_fly

[remote mural]

Yes we have to apply summation on this nth term

[twin raptor]

try simplifying this expression

[remote mural]

Main problem it's not getting simplified

I hv just done this much I am sending

[twin raptor]

that's good progress! can you get rid of the square root now?

[remote mural]

Yes

But not getting my ans

With this

I am sending u the ans

[twin raptor]

once you get rid of the square root, try taking the 1 back out of the numerator

[remote mural]

Yes I know I hv done till the last but not getting the ans

[drifting seal]

nice

[remote mural]

Ans is n=2000

[twin raptor]

as in you are stuck on the final step? or your answer differs from the one given?

[drifting seal]

paid via crypto

[remote mural]

Not getting the equation to get n=2000

In the last

[twin raptor]

can you detail your progress?

so that i can understand where you are stuck

[remote mural]

Sending u the progress

I hv done it on rough

What to do now

[twin raptor]

it looks like you have entirely solved the problem, but are just confusing yourself with notation at the end

you defined the sum to be from 1 to n, and the answer extraction in the problem also asks for n

these are NOT the same n

so what you should really get at the last step is (m+1) - 1/(m+1) = n - 1/n, where m = 1999

[ancient grotto]

<@&268886789983436800> Look who we have here, another free monkey money generator

[dreamy lance]

Free monkeys

[ancient grotto]

In all seriousness they do produce monkeys which I consider bots

[calm coral]

@remote mural Has your question been resolved?

[remote mural]

Yes

[remote mural]

Thank u sooo much done it

[remote mural]

Love u bro

[calm coral]

@remote mural Has your question been resolved?

[calm coral]

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[cursive canyon]

https://youtu.be/tCV9VyIIaw0

I get how to restrict the domain to make it an inervtible but im not that much famiIiar with intervals and the video provided to me never showed an example on how to restrict it with the ch0ices

[cursive canyon]

https://cdn.kastatic.org/ka-youtube-converted/tCV9VyIIaw0.mp4/tCV9VyIIaw0.mp4#t=247

[calm coral]

@cursive canyon Has your question been resolved?

[calm coral]

@cursive canyon Has your question been resolved?

[serene talon]

at the end of the video Sal shows you a solution

[calm coral]

@cursive canyon Has your question been resolved?

[calm coral]

@cursive canyon Has your question been resolved?

[remote mural]

<@&268886789983436800>

[calm coral]

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[coarse tundra]

How many marks am I looking at /64 for this past paper I did. The course is GCSE Level Maths course. In England.

Based on this past paper, is my mathematics knowledge excellent?
( for my level of Mathematics )

Can you provide any advice how I can keep improving?

@supple ferry

Did I get nearly everything correct ?

@velvet osprey

[calm coral]

Please do not ping individual helpers unprompted.

[coarse tundra]

Do I get nearly full marks?

The ai told me I have got 60/64 marks

The pass mark for my course is around 6p%

60%

Ann

Am I welcomed to the proper Maths club now?

[lucid junco]

I don't think alex will

[coarse tundra]

How many marks do I get /64 ?

For this paper

Can u tell me?

[coarse tundra]

Can u tell me?

[tropic moth]

😭 how old are u

[coarse tundra]

Did I do wekk

Well

[lucid junco]

What am i looking at 😭

[coarse tundra]

With this paper?

@tropic moth

Did I do well with this paper?

How many marks will I get /64?

93%?

[tropic moth]

If you did 60/64 you will get around 93% yeah

[coarse tundra]

What?

Oh

I mean by looking through them

Does it seem 93%!

[tropic moth]

sorry man I cant check every single one

if there is one u think u did wrong i can check that

[coarse tundra]

Do they overall seem correct and good?

By skimming?

[tropic moth]

sure

doesnt seem wrong

[coarse tundra]

Will u feed me like in ur PFP?

[tropic moth]

😭 😭 😭 😭

[coarse tundra]

@tropic moth

Are my answers to Q6, Q4 correct?

I did complete the calculate

[tropic moth]

send a photo again for those

[coarse tundra]

They are correct? @tropic moth

I did the calculated

[pale blade]

Q12 is wrong. Your work is unintelligible but the final answer is definitely incorrect. Don't trust chatgpt to check your work, especially when its written so poorly.

[coarse tundra]

I would get how many marks /6?

@pale blade

How many marks /6?

For Q12

And do all other seem correct?

[tropic moth]

Q6 is pretty much missing

[coarse tundra]

Yes

Wait

Is Q6

[pale blade]

Your work is unintelligble. I'm not a GCSE marker, so I have no idea how many points you would get. Either way, your answer is wrong and you should redo it.

[coarse tundra]

And this

Is

The answer

For Q6

:

[tropic moth]

yeah i mean there is no answer here

[coarse tundra]

Yeah, its Jere

Here

The answer

Q6

Is it full marks

Correct ?

@tropic moth

Do I get full marks

Correct

Anyway

For my full works

What is mark /64 total marks

If anyone were to guess ?

Like

58/57

Out of 64 yes?

<@&286206848099549185>

From all pics

[lilac maple]

Its correct ig

[coarse tundra]

How many marks /64

?

[lilac maple]

I think the answer would be no she didnt

[pale blade]

Q6 is also wrong.

[lilac maple]

But the % is right

[coarse tundra]

15.63% is less then 18

[lilac maple]

The question is if

She sold 18% fewer ice creams

But she didnt

[coarse tundra]

No

She sold 15.63%

Anyway

Out of this paper what rough mark I get ?

/64. Total marks

[untold summit]

if you cant mark the paper yourself then you probably didnt get 60/64 fyi

if the paper doesnt have the mark scheme released then do a different paper

[calm coral]

@coarse tundra Has your question been resolved?

[calm coral]

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[remote mural]

I don't understand what went wrong

[remote mural]

this is what i solved for

book says this is the answer

<@&286206848099549185>

this is the right answer apparently but why

did they only want the lower part here lol

[tranquil bone]

what us your integral setup?

is*

[remote mural]

here

[tranquil bone]

so isnt that correct?

[remote mural]

f(2) 6.67

yeah but

what does teh question even mean

does it have to be an enclosed space between

all 3 lines

or something

[tranquil bone]

pretty sure they’re asking about the area of region between orange and blue line and the green curve

[remote mural]

lol