help-0

[fiery bronze]

so at what point are you?

[jagged imp]

you can't solve this exactly in terms of "elementary" functions

[glossy nymph]

Here

[jagged imp]

you could use the Wlog/product log if you know what that is, but i'd like to know the exact context you have to solve this in

[sly mantle]

@modern aurora can you confirm this is a test q?

[jagged imp]

are you supposed to use a calculator?

[sly mantle]

@waxen shadow don't multipost

[glossy nymph]

No

[modern aurora]

oh he actually said it

but deleted lol

[feral wind]

yep, you get -x = ln(x+3)

[glossy nymph]

If I could just know how to get like an upper lower bound or an estimate of the value, that'll work

[feral wind]

and ln's range are positive numbers

so, can't try real numbers

the answer is a complex number

[jagged imp]

this reasoning isn't sound for x in (0,3)

[sly mantle]

@modern aurora yes he did, we have deleted msg logs, just wanted to hear it from you

[fiery bronze]

x=-ln(x+3)?

[jagged imp]

in that interval there is in fact a real solution

[modern aurora]

oh okay

[glossy nymph]

It was a question for differential equation, then in a subpart we had to check for critical points in a given range. This is the differentiated function I got so I was just trying to check for a critical point

[feral wind]

@jagged imp yeah you are right

[glossy nymph]

How can you determine this?

[jagged imp]

Wolfram Alpha

[glossy nymph]

Haha

[jagged imp]

also ivt would work to show theres a soln in there

[glossy nymph]

But like, if I had to solve something similar in a test, how can I get an estimate of the value?

[jagged imp]

an estimate? newton-raphson ig, I'm not too well versed in such approximation methods

[feral wind]

yeah there's a real solution, i was wrong

[glossy nymph]

Yeah

Just wanna understand how to intuitively know that the answer was in the interval (-1,0), as the answer key said

[jagged imp]

uh yeah first guess that its in there and then prove that using ivt probably

[glossy nymph]

Intermediate value theorem? How would that be?

[harsh acorn]

$|:−:2x+:3y+:11|:+\sqrt{x:−:y−:7}=0$

[ocean seal]

Hyl1s

[harsh acorn]

can someone help me to solve this?

[jagged imp]

define f(x)=e^(-x)-x-3. f(-1)=e-2. f(0)=-2. f(-1)>0 and f(0)<0 so somewhere in [-1,0], f has a zero

and obviously a zero of f is a soln of that eq

does that make sense?

[glossy nymph]

Ah yes I see, thank you!

[jagged imp]

nw

[stark lantern]

When is |x| = 0? When is sqrt(y) = 0? Think about it

[harsh acorn]

ohh i get it

[stark lantern]

Once you realize that both expressions have to be 0 for the sum to be 0 you can solve it

[harsh acorn]

let me try

$\sqrt{x−y−7}=0$

$({\sqrt{x−y−7}})^2=0$

$x-y-7=0$

$x=y+7$

oopsie

[ocean seal]

Hyl1s

[harsh acorn]

$|−2x+3y+11|=0$

$|−2(y+7)+3y+11|=0$

[ocean seal]

Hyl1s

[harsh acorn]

and i find $|y-3|=0$

[ocean seal]

Hyl1s

[harsh acorn]

y=3

and i replace y and solve for x?

is it right

[stark lantern]

sounds about right

yep, (10, 3) is the solution

[harsh acorn]

thanks

$|2x+:3y−:8|:+:|3x+:5y−:13|=:0.$

[ocean seal]

Hyl1s

[harsh acorn]

this one is different i cant determine x= or y=

should i write $|2x+3y−8|= -|3x+5y−13|$ ?

[ocean seal]

Hyl1s

[stark lantern]

No you can use the same method

both the equations in the abs value should be 0

since abs(x) is strictly non negative

[harsh acorn]

yep

[harsh acorn]

that proves this too

they must be equal to 0

so

how can i open abs

oh right root

[stark lantern]

you don't need to do that
just directly say 2x + 3y-8=0 and 3x+5y-13=0

[harsh acorn]

can i just delete abs?

why tho

[stark lantern]

which part are you talking about?

[harsh acorn]

.

why we deleted | |

[stark lantern]

Ok let's say we have |x| + |y| = 0. Can you give me the solutions?

[harsh acorn]

they are equal to 0
x=y=0

one solution

as i know

[stark lantern]

It's the same concept, the terms inside the abs value should be zero for the equation to be satisfied

[harsh acorn]

ahhh I understand now

answer is (1,2) right?

[stark lantern]

yes, that's correct

[harsh acorn]

$\sqrt{x+y−:57}+:\sqrt{x:−:y−:15:}=:0$ answer is (36,21)?

[ocean seal]

Hyl1s

[harsh acorn]

just want to check that i understand concept

[stark lantern]

yep that's right

[harsh acorn]

Thank you so much mate

another simple question, if question was like |x+y-z|+|y-z+x|+|z+x-y|=0 concept is same right?

they alone still equal to 0

[stark lantern]

Yeah, in fact if you're adding any number of non negative terms and the sum is 0, it follows that every term is 0

[soft condor]

How do you get architecural column in radians?

[spring harbor]

Channel is taken

[zinc ridge]

Z distribution?

[spring harbor]

Nah nvm my bad I think we have to use a calculator for this

[vapid viper]

would someone be able to help me solve this please

[spiral night]

how :9

😦

[random echo]

Isn't it just a linear diff eq? Find the integrating factor and you're done. If you find any integral tough to solve, you could mention that specifically

[vapid viper]

okayy, thank youuu

[lucid arrow]

Triangle Congruence Somebody help me

[sly mantle]

@lucid arrow don't multipost

and don't ping individuals for help

[alpine sable]

Quick Question lol

Ans is C

[civic hearth]

The momentum of a car with mass 2000kg traveling at 15 m/s is 30000kg m/s if I'm correct?

[harsh acorn]

yep

can someone help me how to solve this

[harsh swallow]

B = 2 C = 5

idk how to solve it

i just brute forced it

[alpine sable]

ty 🙏🙏🙏

[woeful pulsar]

well first thing you can do is see BBC has an odd number of factors, so it is a square
it's easy to brute force from here

[woeful pulsar]

please don't just give answers

[harsh acorn]

do all square numbers has odd number of factors?

[woeful pulsar]

yes

sort of

[harsh acorn]

wow idk that

[woeful pulsar]

that is if we are considering positive integers with positive integer factors

[harsh acorn]

so we need to find a number that its number's sum is divisible from 9?

i hope u understand what i said lol

[harsh swallow]

sorry bit spammy

😄

[harsh acorn]

what was that lol

[harsh swallow]

these are all the numbers that either work with the first condition or the second

and there's only one pair that works with both

but thats brute force

so ignore me 😄

as a double checking device or something 😄

how would you even go about finding this out without brute force

[gray isle]

if you consider 3 digit perfect squares where the first two digits are the same
there are only 2 that you need to consider

[harsh acorn]

answer is 225 right

[gray isle]

wdym by answer

[harsh acorn]

oh my bad lol

B is 2 C is 5

[gray isle]

yes

[strong furnace]

Since CBB is divisible by 9 BBC is divisible by 9 as well so you only need to consider square of multiples of 3

[gray isle]

did you double check whether the other perfect square satisfied those properties?

[harsh acorn]

not actually

[harsh swallow]

yes

in the list

it's only B = 2 and C = 5 that satisfies the first 2

[harsh acorn]

yep he/she is right

[harsh swallow]

7 lines of python 😄

shitty python i might add

[harsh acorn]

what about this question? i tried to write x^2-y^2 as (x-y)(x+y)... and did not work

[gray isle]

what's that stuff being cut off?

[harsh acorn]

oh question is like that

[gray isle]

uh...

[harsh acorn]

idk why lol

[harsh swallow]

EOL error

EOF while parsing

[harsh acorn]

anyway i tried to do like x(x+2)-y(y+4)-3 and did not work too

[gray isle]

question doesn't make sense

do you have similar questions in the same section?

[harsh acorn]

let me check

i found same question on different test lol

[gray isle]

what's below it

[harsh swallow]

could it be

[harsh acorn]

x^2+2x-3

we can factorize this

isnt it

[harsh swallow]

(x + a)(x + b) + (y + c)(y + d)

and somehow they all cancel out

[strong furnace]

This is something like a pair of straight lines

(x-y-1)(x+y+3)

[harsh swallow]

no cuz it would result in xy

oh no it wouldn't

[harsh acorn]

there is -y

[harsh swallow]

would it

[gray isle]

oh i overlooked something

[harsh swallow]

it's literally that

nyann is right

[harsh acorn]

okay okay i have another question, how did nyann figure that out that easily

[harsh swallow]

cuz he smart

???

[harsh acorn]

i think there are must be method

or formula?

can u share please if there are anything like that

[strong furnace]

We learn about this in 2D coordinate geometry for it to be factorizable it needs to staisfy the condition discriminant = 0 for 2 degree homogeneous equation
But since they ask you to factorize we can assume it is factorizable

[harsh acorn]

well im confused

isnt discriminant only for one variable quadratic equation

ax^2 +bx-c like that

[strong furnace]

The factors would be two linear functions and you can figure the coefficients of x and y by comparing only the pure 2 degree homogeneous terms

[harsh acorn]

what is the name of strategy that u used? i want to do research

[strong furnace]

We learned it as factorization of pair of straight lines but I am sure they are just expecting you to convert it into (ax+by+c)*(gx+fy+k) and then just compare the coefficients

[harsh acorn]

ohhh i understand it now

these questions are so different than our school syllabus lol

[alpine sable]

My brain is braindead please help

600n+1250 for 1 and 5n+150 for 2 @alpine sable

as for the 2nd parts just plug into the variable

[alpine sable]

Damn thank you g 😎

My brain ded

Dead brain

[clear pivot]

Hello guys , I want to ask a question that why it is n+1 in the percentile/quartile/decile formula ? I saw some with the only n in some another books. I have asked it on channel question 5 but no one has responsed. Sorry for re-asking the question over in this channel.

[vapid viper]

hello, can someone tell me if my part b is right please

[harsh acorn]

$if \overline{abcd}+\overline{dcba}= 16225, calculate, a+b+c+d$

[ocean seal]

Hyl1s

[harsh acorn]

can i write equation as 1000a+100b+10c+d=16225?

[muted raft]

What is the purpose of overline here?

[spring harbor]

is that average?

[muted raft]

this looks fine but how will you solve it though?

[harsh acorn]

idk :d

[harsh acorn]

abcd over line means a,b,c and d are digits of a number

1253
1 is a 2 is b 5 is c 3 is d

like that

[harsh acorn]

.

[feral raven]

There are 4 letters and 5 digits in the actual number

[harsh acorn]

whut

[feral raven]

16225

5 digits

[muted raft]

lmao

and 9^4 = 6561

[harsh acorn]

[muted raft]

[harsh acorn]

@bitter juniper

anyway, @muted raft what should i do then

[muted raft]

multiplication is commutative

Use this to create two system of equation like how you did for first one then solve for a+b+c+d

[harsh acorn]

oooh wait

i miswrite question

oh my bad lmfao

[muted raft]

lmao

[harsh acorn]

i get what leonkiller says now

$if \overline{abcd}+\overline{dcba}= 16225, calculate, a+b+c+d$

[ocean seal]

Hyl1s

[harsh acorn]

yep yep like that lol

then 1000a+100b+10c+1d+1000d+100c+10b+1a=16225

factorization maybe

[muted raft]

,w 9^4 + 9^4

[ocean seal]

Results provided by WolframAlpha

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

Requested by zslya#7821

[muted raft]

lol

[harsh acorn]

1001a+110b+110c+1001d

looks familiar

All Factors of 1001: 1, 7, 11, 13, 77, 91, 143 and 1001.

Factors of 110: 1, 2, 5, 10, 11, 22, 55 and 110.

we can use 11 right?

[feral raven]

But is 16225 divisible by 11

[harsh acorn]

,w 16225/11

[ocean seal]

Results provided by WolframAlpha

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

Requested by Hyl1s#3863

[harsh acorn]

yep

[rough spear]

,calc 16225/11

[ocean seal]

Result:

1475

[feral raven]

You can then

[willow bluff]

Can someone help me 🥺?

[harsh acorn]

91a+91d+10b+10c=1475

what now

[feral raven]

The channel is taken

[harsh acorn]

what should i do now?

@gray isle can u help me too?

[harsh swallow]

? whatsup

[harsh acorn]

i pinged you for help

$if \overline{abcd}+\overline{dcba}= 16225, calculate, a+b+c+d$

[ocean seal]

Hyl1s

[harsh acorn]

question is this

[harsh acorn]

i tried these

[harsh acorn]

and get this

stuck there

[vague coral]

those lines, is it base 10 ?

[harsh acorn]

it means they are digits of a number

[vague coral]

of a number in base 10 ?

[harsh acorn]

yep

[gray isle]

you can start by considering certain restrictions of certain letters

[harsh acorn]

ohhh d+a=5

[gray isle]

not quite

[harsh acorn]

oh yes they can be 9 and 8

true

[gray isle]

just by looking at the last digit,
a+d could be 5 or 15

[harsh acorn]

a and d cant be zero

[gray isle]

however considering that the sum is a 5 digit number

[harsh acorn]

a+d=16

[gray isle]

a + d must be greater or equal to 9

hence a + d must be 15

[harsh acorn]

oh right

[harsh acorn]

well isnt there a chance =16?

[gray isle]

no

[harsh acorn]

if b+c<=9

[gray isle]

because a + d = 5 (mod 10)

[feral raven]

You have a+d for the last digit as well

[gray isle]

(from looking at the last digit)

[harsh acorn]

what does (mod 10) mean there? idk that

[gray isle]

ignore that notation then
the last digit of 16225 is 5
hence the last digit of the number from a + d must also be 5

[harsh acorn]

yep i understand that

[harsh acorn]

btw what is the name of that notation? what it called? i want to research it

[gray isle]

modular arithmetic

[harsh swallow]

what's the overline mean

[harsh acorn]

that mean they are digits

digits on a number

so a+d must be 15 bcs sum is 5 digit number

and they cant be 0

so b+c>9

and c+b+1= 12

[feral raven]

You have already have enough

[feral raven]

To solve this

For b+c

[harsh acorn]

c+b is 11 and a+d is 15

actually we dont need what i did early time

11+15=26

isnt it

Yep i think it is like that

better look at simple things at the first

like what ramanov did

[harsh swallow]

so i just figured out it doesn't matter

what the hell

[(6299, 9926), (6389, 9836), (6479, 9746), (6569, 9656), (6659, 9566), (6749, 9476), (6839, 9386), (6929, 9296), (7298, 8927), (7388, 8837), (7478, 8747), (7568, 8657), (7658, 8567), (7748, 8477), (7838, 8387), (7928, 8297), (8297, 7928), (8387, 7838), (8477, 7748), (8567, 7658), (8657, 7568), (8747, 7478), (8837, 7388), (8927, 7298), (9296, 6929), (9386, 6839), (9476, 6749), (9566, 6659), (9656, 6569), (9746, 6479), (9836, 6389), (9926, 6299)]
[26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26]

all pairs

and they all add up to 26

[harsh acorn]

well well math does not work like that i think

😳

[pastel idol]

Is this channel free?

[harsh acorn]

yep

go ahead

[gray isle]

is that the whole point of the question

[pastel idol]

why do they calculate values ​​and not or just whether the positive is infinite or negative infinity?

[harsh swallow]

no the a + b + c + d of all of them

[gray isle]

meant to write isn't instead of is

[harsh swallow]

i guess

i just found it interesting

[gray isle]

i really dislike $x→ \pm\infty$ notation

[ocean seal]

ℝamonov

[real sinew]

I don't understand what you're asking

Oh

[gray isle]

why do they calculate values ​​and not or just whether the positive is infinite or negative infinity?
wdym?

[pastel idol]

my math solution book is useless, they never write out the steps

[gray isle]

just because x approaches positive or negative infinity
doesn't mean your expression also approaches either infinity

[pastel idol]

I had this

[real sinew]

Have you learned L'hôpital's rule?

[pastel idol]

Sorry for the bad handwriting and the dutch language on the right

[pastel idol]

Nope

[gray isle]

don't use lhop here

why does everyone like bringing up lhop immediately

[real sinew]

That was my first reaction to the question

[harsh swallow]

the questions is rather easy

what it's saying is that when x becomes huge

the term becomes like the one on the right

[strong furnace]

limits at infinity use the basic idea of growth

[harsh swallow]

and then you get x/2x

[gray isle]

you also need to be careful when working with negatives and square roots

[harsh swallow]

but because the above one is the absolute value

when you plug in negative infinity it becomes -1/2

[daring obsidian]

Can anyone help me on this homework problem?

[harsh acorn]

draw the diagram first

[pastel idol]

I don't understand

[harsh acorn]

but M angle and m & n sides

[daring obsidian]

draw it?

[harsh acorn]

give attention to the name of Triangle too

[harsh acorn]

yep

[harsh acorn]

you must consider the name of triangle when you draw diagram

[harsh swallow]

,rotate

[harsh swallow]

when x becomes much bigger than 11

the term becomes the one on the right

@pastel idol

and then you evaluate both limits

seperately

[pastel idol]

I understand

[harsh swallow]

so with infinite

infinity

you fill in and get x/2x

= 1/2

i put it in brackets next to it

because you cannot really do it like that

but for illustration purposes it's fine

but when you go to negative infinity

you get something different

the top infinity gets squared and then rooted

aka absolute value

but the bottom negative infinity

still has a negative

so it becomes

• x/2x

= -1/2

[daring obsidian]

can someone help me get side o

[harsh swallow]

oone sec

[daring obsidian]

ok

[stable mango]

Lets move to another channel

[daring obsidian]

ok

[harsh swallow]

That make any sense @pastel idol

[pastel idol]

Yes thank you

[harsh acorn]

answer is 9 right?

it cant be 8 because it wants us to take a nonwhite chopstick atleast

so it is not 8

[strong furnace]

pair and pieces might be something you need to take into consideration @harsh acorn

[woeful pulsar]

imagine you get 8 white and one yellow oh no

[harsh acorn]

my english is not that good, is pair mean 2

[harsh swallow]

if you want a guarantee of a non white chopstick pair you have to at least grab all white chopsticks and then 2 more

right

[strong furnace]

does yellow and white count as pair

[woeful pulsar]

probably not lol

[strong furnace]

if not you will need 3 more

[harsh swallow]

interesting point

[harsh acorn]

so answer is 5 pair

[harsh swallow]

if you say a pair is only the same colour it would be different still

[harsh acorn]

if same color are in same pairs

[harsh swallow]

if you just want 2 non white chopsticks

guaranteed

it's all white chopsticks + 2

[strong furnace]

all white chopsitcks + 3 for same color in same pairs

[harsh acorn]

it asks for atleast, so we can say that he can take 1 pair of full of white color chopsticks

isnt it

so we need to take 4 times so no white left

[harsh swallow]

so there is a chance that you grab a non white pair on the first 2 chopsticks

[harsh acorn]

+1 because he wnats to take nonwhite

[harsh swallow]

but guaranteed it's either 10 or 11 chopsticks

depending on whether you want a nonwhite pair of the same colour or either colour

[harsh acorn]

so answer is 1?

i am confused so much lol

i tought it was easy question

[gray isle]

you need to take the amount needed in the worst case scenario

[real sinew]

At says at least how many are needed. At least 2 are needed

[harsh acorn]

shouldnt we take it when it says maxium

but it says at least?

or am i wrong

[gray isle]

if you want to get a pair

tbh, the question is worded poorly

[real sinew]

I think the answer is 2

[harsh swallow]

like i said if you want to be guaranteed to get a pair of non white chopsticks you need to grab at least 10 chopsticks

because if you grab all 8 white chopsticks

[real sinew]

You need at least 2 since the first two can both be nonwhite

[harsh swallow]

you will still have a pair of non white chopsticks

[harsh acorn]

why 10 tho

[harsh swallow]

8 white chopsticks + 2 non white chopsticks

[harsh acorn]

oh

i read it as *** how many times*** lol

[thin ice]

hey i have a questions can anyone help me

[harsh acorn]

so answer is what

10 or 2

i think 2 is more sensetive bcs there are chance a pair of chopsticks are non white

and it says at least

[woeful pulsar]

no, at least how many to guarantee

[gray isle]

tbh, the question is worded poorly

[harsh swallow]

it's a terrible question

because you could have 3 answers

[harsh acorn]

and it is a past paper of HKIMO lmfao

[harsh swallow]

and all would make sense in a way

[strong furnace]

I think its a translation barrier

[harsh acorn]

i can share chinese if u want

oh wait false text

[gray isle]

lol

[strong furnace]

I was really confused xD

[harsh acorn]

why it copy paste wrong lol

when i copy paste it gives me wrong things

珷最發艸黎艸棙艸的筳孒刁利最 8 栰:10 栰咍 7 栰－抏宎倚淳圦丂赳佢覊圦門丏眽睕的惉
it gives me that

[strong furnace]

I am pretty sure its either 11 or 10 depending on how they define non white pairs

but the idea is

if you choose to take k amount of chopsticks all the possible selections for k chopsticks should satisfy the condition of two non white pairs

[gray isle]

yeh, guaranteed is implied.
when you lift your blindfold you really want to have a pair of non-white chopsticks in front of you

if you lift your blindfold and only see a white and brown, you failed

[harsh acorn]

so we choose worst case

[gray isle]

yeh

[harsh swallow]

idk if you can give explanation

but if you can

[gray isle]

if you consider the worst case, you'll defintiely have a pair you want

[harsh swallow]

100% say the question is garbage

cuz it is

[gray isle]

(but you may also have multiple pairs of non-white chopsticks which is fine)

[harsh acorn]

so there are must be 1 white chopstich left so when we take there are not all white

or

[gray isle]

so here, you want a pair of non-white chopsticks

the simplified worst case would be to
first pick those 8 white chopsticks that you don't want immediately

then one of each of the remaining colours, brown and yellow

[harsh acorn]

isnt taking random

[gray isle]

this is considering the worst case

you can take those 8white, 1 brown, 1 yellow in any order

[harsh acorn]

oh i get it

[gray isle]

but the worst case will always consist of that combination

[harsh swallow]

when you've taken the 10 chopsticks it could be no whites there but it could also have 8 white and 2 non white

the point is you want 2 non white chopsticks

so you have to grab enough so that if you take all white chopsticks you also have 2 non white chopsticks

[gray isle]

well for pair, i think they mean a pair of the same colour

holding non-matching chopsticks is a no-no

[harsh acorn]

i think it wants to take non white pair chopsticks but when we start to take, we can take one by one or what

ah just forget it

[alpine sable]

Is this section free for a question?

[harsh acorn]

last question from me, how can i solve this?

[alpine sable]

What do those dots mean

[harsh acorn]

it means it goes to (1-1/4072324)

[muted raft]

the denominator are whole squares

[harsh swallow]

the dots mean also all the ones in between

[harsh acorn]

yep

[woeful pulsar]

the product should simplify nicely

think about making those 1-1/n^2 into a nice fraction

[harsh acorn]

wait a min i see a thing

1-1/4- 3/4 and 1-1/9= 8/9
3/4x8/9=1/2

and others will cancel too

[woeful pulsar]

can you rigourise this cancellation?

how does it cancel exactly?

[woeful pulsar]

also it's not 1/2

[harsh acorn]

oh

it is 1

my bad

[harsh swallow]

no

not that either

[muted raft]

2/3

[harsh acorn]

how did u solve that explain please

@muted raft

[gray isle]

its not 2/3

[harsh swallow]

3/4 * 8/9 is not 2/3?

[gray isle]

oh thought they meant the final answer

[harsh swallow]

nonono

[muted raft]

no

I meant 3/4 * 8/9 = 2/3

[harsh swallow]

only the one hyl1s said was 1/2

and then 1

[harsh acorn]

oh right

[muted raft]

the whole expression can be written as $\frac{n+1}{2n}$

[ocean seal]

zslya

[harsh acorn]

how can i find n then

[strong furnace]

approximations

the square is really close to 2000^2

[harsh acorn]

i know i ask to much questions but what do you mean "square is really close to"

[strong furnace]

4072324

[harsh acorn]

oh i get it

[strong furnace]

my bad

[harsh acorn]

i dont think they would give a question that has approximation

[strong furnace]

I don't remember the algorithm but I am pretty sure there is one to get really close to the square of any number

you're not supposed to approximate 2000

you just know it is close to 2000

then from there you look at the difference of squares

[harsh acorn]

oh right

[woeful pulsar]

what you want is $\sqrt{4072324}$

[ocean seal]

Element118

[woeful pulsar]

so you are trying to estimate it to find some way to work it out

[harsh acorn]

the first 2 digit must be 2 and 0 bcs it is 40

as i know

[gray isle]

teachers also like being "smart" and use values based on what year it is

[muted raft]

big hint

[harsh acorn]

then answer is 2018 lol

[gray isle]

so it feels like its from a past paper form 3 years ago

[harsh swallow]

$\prod_{n = 2}^{2018} (1^2 - (\frac{1}{n})^2)$

[harsh acorn]

yep thats right

[ocean seal]

Katharine

[harsh acorn]

this Big letter is multiplication type of sigma right?

?

[harsh swallow]

ye

product

pi

capital pi

[harsh acorn]

oh okay good to know

[harsh swallow]

instead of capital sigma

[gray isle]

$\Pi \pi$

[ocean seal]

ℝamonov

[strong furnace]

you had first 2 digits 20 and the last digit could either be 2 or 8 from the last digit

[harsh acorn]

yep you are right

and we can find 1 of 2018 from 4072324's 24

or we cant?

[strong furnace]

you can divide the difference of that number with 2000^2 and divide it by 4000 to get a close limit for 2000+x

(2000+x)^2=4000x+(400000)+x^2

4000x must not exceed that difference

[harsh acorn]

$(2000+x)^2=4000x+(400000)+x^2$

i love my life

[strong furnace]

I don't know Latex myself but I am pretty sure thats not how it works

[muted raft]

no space before and after $

[ocean seal]

Hyl1s

[harsh acorn]

yay

[strong furnace]

wait what ? texit works without all those /{} signs as well?

[harsh acorn]

yep

[strong furnace]

limit comes out to be 19 so you have to only check for 2002 2008 2012 and 2018

[harsh acorn]

can u write all the equation? i did not get it very well

[strong furnace]

lets say the number is 2000+x

then (2000+x)^2-2000^2=4000x+x^2 right?

[alpine sable]

Hi i have a problme To solve Please help me

[strong furnace]

use a different channel

[harsh acorn]

oh right

[strong furnace]

now we find the actual difference on LHS

[harsh acorn]

what is the opening of LHS? :s

[strong furnace]

72324

$72324=4000x+x^2$

[ocean seal]

nyann

[harsh acorn]

solve with quadratic formula?

[strong furnace]

which gives us $4000x<72324$

oof

[harsh acorn]

try to write with _

idk will it work

[ocean seal]

nyann

[harsh acorn]

oh right :d

so we can say from that x is >15

and 20>x

[strong furnace]

which gives us $x<18.(something)$

[ocean seal]

nyann

[harsh acorn]

oh right dividing is the choice too

okay we find x is 18

[strong furnace]

no

now we have only 4 numbers that fit the bill

2002 2008 2012 and 2018

and since the square of none of those number is greater than 4000

we can conclude the floor of 72324/4000 is our x

[harsh acorn]

which is 18 yup i understand

so 2000+18=2018

so what now

[strong furnace]

use this

[harsh acorn]

if it is the solution idk how to solve this

oh

[strong furnace]

you get this by eliminating terms

something similar to telescoping series

[harsh acorn]

btw how did he know that expression can be written as this

[strong furnace]

1-1/a^2

write this as (a-1)*(a+1)/a^2

now write the same thing for a-1 and and a+1

you'll get (a-2).a/(a-1)^2 and a(a+2)/(a+1)^2

if you multiply these three you get (a+2)(a-2)/(a+1)(a-1)

[harsh acorn]

i think i understand

[strong furnace]

another way would be to start doing this from the first term

[harsh acorn]

so last answer is 2019/4048 which is unsimplifiable

[strong furnace]

huh?

how did you get 4048

should be 4036

[harsh acorn]

oh i took it as 2024 lol

i am tired :s

[harsh acorn]

and what is the name of that thing? i see these as different types

is there any general name for this method or formula or whatever

[strong furnace]

I don't really know what you call this in exact terms , for sums the equivalent is telescopic method of evaluating sum

[lament fable]

Anyone knows?

[alpine sable]

how would I find EF

[strong furnace]

go to another channel since lightgrim just asked his question

[alpine sable]

he asked in #1 too

lol

[harsh acorn]

anyway thanks for help nyann

[strong furnace]

welp

I guess he is getting help

[alpine sable]

DE is 40

[strong furnace]

GD and CF are diameters?

[alpine sable]

CD = GF

[lean rose]

GD and CF are diameters, then <GBF = <CBD

[alpine sable]

looking for arcs

specifically EF

[alpine sable]

ik that

[lean rose]

look

CF is 180 degrees

then GF is 65

= CD

also CF = CD + DE + EF

EF = CF - CD - DE

= 75 degrees

[alpine sable]

right

thanks

[pearl wraith]

the rat uses 60ml / day

so do i only need to worry about the percent of the water right?

[alpine sable]

what does this mean, with hillside is inclined to the horizontal?

is the horizontal a plane that is on top of the hill?

is this it?

a hillside inclined at 25 degree to horizontal sounds pretty steep to me

[civic hearth]

How to get 9.8m/s

[gray isle]

what is gravity

[civic hearth]

Idk

Look at the given there was no gravity

[gray isle]

g

[alpine sable]

gravity on earth is on average 9,8 m/s²

[gray isle]

represents gravitational acceleration

^ is something you should know

[civic hearth]

Help i want to understand this

[gray isle]

its pretty much a value that you just have to know

[civic hearth]

It's 12:41am i need to sleep now but i choose to make this

[gray isle]

,w gravity on earth

[ocean seal]

Results provided by WolframAlpha

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

Requested by ramonov#0921

[lunar fern]

When you fall on Earth you undergo gravitational acceleration and her value is 9.80665 m/s^2

[civic hearth]

9.8m/s^2 gravity???

[lunar fern]

This is an accelaration

[civic hearth]

But how did they get 9.8m/s

[gray isle]

its pretty much a value that you just have to know

[lunar fern]

It's a constant value

[gray isle]

physics

general knowledge

[civic hearth]

...

[gray isle]

you could go more precise like above:

9.80665 m/s^2
some questions may tell you to use 9.81m/s^2
but unless stated otherwise, 9.8m/s^2 is the generally accepted value to use for g

[strong furnace]

there are experiments to determine that value

[lunar fern]

Gravitational acceleration depends on the mass of the star/planet that attracts you

[strong furnace]

some of the simple experiments include the timeperiod of a pendulum

[civic hearth]

How

I don't understand this book

[strong furnace]

Cavendish's torsion balance is what was used to determine the value of G and then they used newton's gravitational law to get 9.8

[civic hearth]

Ohhh

[hardy vault]

How far were you able to get?

[distant dune]

help?

[urban pilot]

REPOST

[spring rapids]

64%?

[urban pilot]

$ 64/(64+32) = 64% $

[civic zinc]

help

[real sinew]

Sine returns the same value when you add or subtract what is inside by a multiple of 2*pi

So choose the answers that have a multiple of 2pi added or subtracted

[urban pilot]

exactly

the sine function is 2*pi periodic

[lone folio]

Hello, can someone help me with this question? My teacher hasn't explained how to do this type of questions yet, but we have it for a take home exam.

[urban pilot]

try first by calculating f(a^2) and g(2a) and try to solve f(a^2) - g(2a) = 0

[lone folio]

Thanks! I'll try it and see where that gets me.

[urban pilot]

go for it

[worn rapids]

Can someone explain the trig identities used in the first step, im super confused

[shell widget]

$\cos(2x) = 1 - 2\sin^2 (x)$

[ocean seal]

Sup?

[shell widget]

Hence, $\cos(6x) = 1 - 2\sin^2 (3x)$

[ocean seal]

Sup?

[worn rapids]

ahh ok

[loud frigate]

Is this y = 3x - 2

[worn rapids]

yes

[lone folio]

I tried doing the steps but I'm still a bit stuck. Could I get a bit more help, if possible?

[urban pilot]

@lone folio what is the lesson you are doing this exos for?

second degree equation ??

[lone folio]

It's our third class of our functions unit

[urban pilot]

Are you familiar with second degree equations ??

[lone folio]

Somewhat. Quadratics, right?

[urban pilot]

yes

[lone folio]

I've learned transformations and factoring, but not much beyond that.

[urban pilot]

when you will calculate f(a^2) - g(2a) = 0 you will get an equatioin of the form ax^2 + bx + c = 0

and you will need to write something like this (x - A)(x - B) = 0

using transformations and factoring

[sour lynx]

i dont know how to do expiremental probability and i need a sentence with an answer

heres the question

i dont know how to do it

[civic zinc]

Wym?

[lone folio]

12/20 = 60% chance to hit the a ball, apply that 60% chance to 30 throws

[urban pilot]

18

[sour lynx]

so the answer would be 24?

[lone folio]

30 x 60%, or 0.6 = 18

[sour lynx]

thank you

[lone folio]

Oh okay, I got it. Thanks f_911! The steps were pretty helpful

[urban pilot]

anytime

[alpine sable]

27. Find the following sum : 1/1 * 2 + 1/2 * 3 + 1/3 * 4 + ............ + 1/ 99 * 100

Options : (A)1/100 , (B) 99/100 , (C) 1/99 , (D) None of these

[alpine sable]

I think the answer should be B

But I just guessed the answer after finding a pattern

[alpine sable]

So anyone knows how to do it in the normal way or something?

Like a formula or way

[lone folio]

https://gmatclub.com/forum/what-is-the-value-of-229663.html

I think someone explained it pretty well here.

[ionic jewel]

you use summations

$\sum_{i=1}^{99} \frac{i+1}{i}$

[ocean seal]

bunny

[strong furnace]

you get general term 1/((n+1)*(n)) and then use Sn-Sn-1 = Tn where Tn is general term and Sn is sum of n terms

[alpine sable]

Ohhhh

[strong furnace]

you can also use telescopic method of evaluating sums

[alpine sable]

What's that?

[alpine sable]

Thanks for showing the link! I will check it later

[strong furnace]

http://www.math.pitt.edu/~sparling/23021/23021sums2/node5.html#:~:text=One elegant way to compute sums is the method of telescoping sums.&text=In this sum we see,with the next positive term.&text=We say that the sum has telescoped.&text=Looking at this formula%2C we,term with a minus sign.

[alpine sable]

Thanks!👍

[alpine sable]

I didn't get it lmao

[lunar garden]

Does anyone know how to do this? if so i can use the help

[alpine sable]

Ohhh

how would I solve this?

[lone folio]

You can try finding the lowest common factor and check if the two triangles have the same sides as each other. So for example, side FE is 18, and side ST = 27. That scales at 1.5 times, so you can check if the other sides also scale at 1.5x. If they all scale at 1.5 to each other, then the triangles have SSS congruency.

[alpine sable]

long arc - short arc / 2 = ?

[lunar garden]

Thank you so much!

[halcyon ginkgo]

This is all I was given but we have to find the slope

[alpine sable]

the slope is 1

according to the graph

[lone folio]

I don't think it's one, x and y aren't 1-1

[alpine sable]

or if you zoom in

[lone folio]

it'd be 50/30 I think

[alpine sable]

5/3

[alpine sable]

I was just looking at the grid

but it’s 5/3

[lone folio]

Yeah no worries

[civic zinc]

Am I right

and what would the others be?

[glossy current]

Is it 65°

[alpine sable]

I’m not sure

how would it be 65

[halcyon ginkgo]

So the slope is 1 ? Or 5/3 ?

[alpine sable]

5/3

[wheat rampart]

can someone tell me how u get from 6+2/3 to 20/3?

I forgot how its done

[lone folio]

Are you sure that's the question? I'm pretty sure you can't do that

oh, unless you formatted it wrong

6 + (2/3) right?

[junior ferry]

6 is the same as 18/3

[strong furnace]

does not matter in this case

[lone folio]

6 = 18/3

+2

[strong furnace]

the format is correct

[lone folio]

=20/3

[wheat rampart]

oh i feel stupid now

anyways

thankyou a lot

[strong furnace]

read the rules no test problems

6. Do not ask for help on tests. Any violation of this will lead to appropriate action being taken at mod discretion.

[lone folio]

Hey, can someone help me with this transformation? I'm not sure how the sqrt and fraction affect transformations

[junior ferry]

nvm ignore that

[alpine sable]

Nvm

[strong furnace]

take it down please or you'll be kicked/banned

[alpine sable]

...

[strong furnace]

<@&268886789983436800> .

[sly mantle]

what's this

[strong furnace]

he posted a test problem even after being told not to

[night geyser]

should be resolved, thanks

[alpine sable]

Also it is clearly written in rules that we shouldn't ask for help in tests!

[shell widget]

@lone folio after some simplification, it's just $\frac{-3}{\sqrt{2}} \cdot \sqrt{x-1}$

[ocean seal]

Sup?

[shell widget]

now compare this to sqrt(x)

[civic zinc]

$25 to whoever helps me with a few math problems

[shell widget]

boo hoo

[urban pilot]

hahahaha

[pastel idol]

how do we solve this again?

i forgot

[shell widget]

solve or graph?

[pastel idol]

solve

[urban pilot]

solve what ?

[civic zinc]

Im serious, Venmo or Cashapp

[alpine sable]

@civic zinc

let’s see

[pastel idol]

how you get from the function to the 4, 4x and -4

[urban pilot]

you are going to work on different intervals and substitute the absolute value and you will get the result

[pastel idol]

i only have this

whats the first step

[trim hull]

is this ocuppied

[shell widget]

@pastel idol you dont need to do anything

[trim hull]

need help on 2

[shell widget]

The function is defined that way and we cant do anything

[alpine sable]

@pastel idol are you making a function table?

you would plug in a number then solve

then graph

[frosty vigil]

can anyone help me convert this into a rectangle equation?^

[pastel idol]

i have to become this

[lapis harness]

Find a recurrence relation a_n, where a_n is the number of series of length n made from {0,1,2,3}, where 0 can't be next to 1, or next to 2

got this on a test, the only question i didn't answer. Anyone has a tip ? ( test is over now 🙂 )

[frosty vigil]

thanks!

[lapis harness]

split it into cases and then draw your linear functions in appropriate domains

[frosty vigil]

@lapis harness qq, so to convert these polar equations into rectangle

i basically have to use the x=rcos, y = rsin, and r^2 = x^2 + y^2 within my polar equation right?

[vague coral]

yes that's the way

[frosty vigil]

The final form should be a circle equation right?

[lapis harness]

https://www.desmos.com/calculator/xjylsogtmw

[vague coral]

maybe, maybe not, you should see

[lapis harness]

trivial form acost + bsint yes

[frosty vigil]

meaning after i convert the polar coordinate to a rectangular equation it should take form as a circle equation basically right?

[frosty vigil]

cause ive been seeing this trend and it looks like it takes form of a circle equation

[lapis harness]

if you convert circle equation to another form its still gonna be a circle equation 😄

[vague coral]

basically

[frosty vigil]

yeah cause polar coordinate is a type of circle equation right?

[vague coral]

things like hyperbola, ellipse, parabola, etc..

[frosty vigil]

yeah

[strong furnace]

I am still not near the solution but the idea I think might work is taking a_(n-1) and then looking at ways of adding 1 term of 0/(1,2)equivalent/3 into every series to get a relation between a_(n-1) and a_n

if that makes sense

[alpine sable]

Is anyone free

I need help

<@&286206848099549185>

It’s sending

[strong furnace]

4. If your question has not been answered for a minimum of 15 minutes, you may use the @Helpers tag once. Please do not try to bump your question using this ping unnecessarily. Do not abuse this ping. Do not individually ping users with the Helpers tag without their express permission.

[alpine sable]

I need help oa😭

30-60-90 stuff

Pythagorean theorem

I need help

😔😔😔

[lapis harness]

google eq triangle height formula

[lapis harness]

dunno if it's right but not an recurrence relation anyways lul

[lapis harness]

https://en.wikipedia.org/wiki/Equilateral_triangle#Principal_properties

[eager fern]

https://media.discordapp.net/attachments/490557019623915520/838922455635984414/image0.png?width=335&height=447

idk how to do e and f

it says x->-infinite

[pastel idol]

look at the part where x is negative

and follow the function

you will see that the function will never and because it keeps going down to the left

resulting in - infinite

(the above is e)

[wise jewel]

uhhh
im struggling to understand how my teacher got this
like...why would finding the square root of 960 and 375 here to get the scale factor and volume ratio not work?

but yet it works here?:

[pastel idol]

and i think f is 4 because it intersects with x=4 when going to infinite to the right (correct me if i'm wrong)

[civic crypt]

It should work. You have surface areas given. The scale factor is the square root of the ratio of surface areas.

Vice versa the surface areas ratio is the square of the scale factor, and the volume ratio is the cube of the scale factor.

[wise jewel]

yeah nvm im stupid

[eager fern]

ah ok

[wise jewel]

LMAO, thanks

[pastel idol]

do you understand?

ok np

[eager fern]

thanks

[civic crypt]

Yea, the teacher just reduced the fraction a bit, to make it more simplified, before going on. Luckily when the fraction got reduced the taking of the root became easy 🙂

[tranquil tulip]

does anyone know how to make (x-3)^2 - 25 into standard form

for a quadratic equation

[wise jewel]

@civic crypt wait hold on...finding the cube root of 648 and 1029 and then dividing the 2 doesn;t give me 6:7 for the scale factor does it?? it just gives me the decimal .8571428572

i understand that the cube root of 216 and 343 gives you 6:7

but if it's just a reduced version of 648/1029, i dont see why that changes the answer to be correct

oh wait

.8571428572 is 6/7

when i tell my calculator to turn .8571428572 into a fraction though it just puts it back into a decimal 😭

[frosty vigil]

anyone get this one?^

[pastel idol]

That means that there isnt a useful fraction to turn .8571... In

[thin charm]

Please join its dead

[alpine sable]

i dont know how to start on this

like my head says -81 make it on the other side

[noble sinew]

try finding the derivative because the derivative tells us when the function is increasing or decreasing

then set the derivative equal to 0 and solve

[signal adder]

If the derivate is egal to 0, that can also be the minimum right ?

[noble sinew]

indeed he technically needs to check if it is in fact a maximum (but using how a polynomial of degree 2 looks when a is negative and b is positive could also be enough)

[signal adder]

Yeah ok

[stiff vortex]

how do i answer this

i got 8 for the height

<@&286206848099549185>

[muted scarab]

no

[stiff vortex]

<@&268886789983436800>

[fading zephyr]

what's the matter

[heavy otter]

@thin charm Don't post unsolicited adverts here

[pastel idol]

Someone help

You need to calculate for p

<@&286206848099549185>

[lapis harness]

isnt this like solved ?

[pastel idol]

Yes but i dont understand the steps

[candid ferry]

oo

[pastel idol]

If you could explain each step a little it could help me

[candid ferry]

are you aware of L lopithal rule

or idk what is the spelling

?

[pastel idol]

Nope

[candid ferry]

oo so you kno differentiation?

[pastel idol]

Nope

This is the basics of limits

[lapis harness]

you factor top and bottom

and cancel out the paranthesis

[candid ferry]

using that rule you are allowed to differentiate both numerator and denominator if its 0/0 or number/0

oo

not aware of it yet

then factorize

[civic crypt]

Well, conversion decimal -> fraction can be problematic, because you lose some decimals at the end, and your calculator is not sure if it is a fraction or not.

You should calculate it in one go.
third_root( first_number / second_number)
This should be able to output the fraction.

[civic crypt]

@rugged lynx the channel is occupied. Please try some other channel 🙂

[lapis harness]

https://www.mathsisfun.com/geometry/complementary-angles.html

read the first sentence

[candid ferry]

make an equation and put their sum = 90

[rugged lynx]

i dont see anybody responding?

[candid ferry]

x + 5x = 90
6x = 90
x =15
larger measure = 15 * 5 = 75

[latent reef]

Is there anyone to help me with 2nd order partial derivative ? I'm doing homework but I dont know where my answers it went wrong ?

[lapis harness]

@latent reef just send it

[latent reef]

I don't know why are steps are wrong ?

[lapis harness]

playing league rn maybe someone can help but try to insert individual steps into wolfram and see where it fucks up

[latent reef]

when are you available haha

[candid ferry]

okay so your a) is wrong

?

[latent reef]

No all of them were wrong

[candid ferry]

oh no you did introduce negative

oke

so imma solve and sent it to you. dm?

[latent reef]

I just learn about partial deriative so idk how to plug them in wolfram

[latent reef]

sure, if possibly could you please explain where i did wrong and show me the correct answers?

[velvet pelican]

the basic idea is to treat y as a constant when you differentiate wrt x

and vice versa

[alpine sable]

Is anyone here familiar with linear algebra?

I am trying to find a basis, and cannot understand why I am not getting the right answer!

Why won't it reduce!?

x1 = 1/4 x4
x2 = 1/4 x4
x3 = -1/3 x4

What am I doing wrong?

[lapis harness]

it can be an answer

your x4 is a parameter

[alpine sable]

Hmmm

Isn't x4 = x4???

I just don't get it

[lapis harness]

make your x_4 equal t or sth and your answer is
x1 = -1/4 t
x2 = -1/2 t
x3 = -1/3 t
t in Reals

use this site for your linear algebra problems https://matrixcalc.org/en/slu.html#solve-using-Gauss-Jordan-elimination({{0,4,0,2,0},{0,0,3,1,0},{-4,12,-3,4,0}})

[muted raft]

aren't they all positive?

[lapis harness]

i mean just flip the t sign no ?

[muted raft]

well yeah

Ah no I am wrong

ah thats a nice website

it gives you the solution set

[distant bay]

Could someone help me with 8) it’s confusing me what does it mean. Is the reasspsitive property the same as distribution.

[wide talon]

it means, you have an equation on the form a*b*c, use that to prove that (a*b)*c = a*(b*c)

[peak gorge]

We had this discussion in math class today, what is formula to find the probability of a royal flush?

[urban thistle]

can i get some help please

[distant bay]

Ok, that’s easy we know that multiplication will always yield the same result and it doesn’t matter what you do first, whereas addition and subtraction you can’t interchange those qualities an example is. 1 x 4 x 7 I could write this 7 x 1 x 4 and it still will equal 28

[midnight marsh]

can anyone solve this