help-27

[devout snow]

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[quasi yoke]

hi

[quasi yoke]

Qn 8

,rotate

[quasi yoke]

Q8 pls

[quasi yoke]

<@&286206848099549185>

[rocky iris]

Dude

Wait for 15 mins

Then ping

Said in the rules

[quasi yoke]

its been 15 mins tho

[spice field]

which problem?

[ashen sigil]

hey chill

i got the answer

[quasi yoke]

number 8

[eager gate]

hi

[quasi yoke]

oh what did you get?

[ashen sigil]

do u want a pic of solution '

[eager gate]

can anyone ignore me?

[quasi yoke]

yea that’s fine also

[spice field]

hi!

[quasi yoke]

but can you work it through with me as well if I dont understand

[ashen sigil]

everything apart from [2,9,16,23,......2018]

is the answer according to me

[quasi yoke]

oh whats your answer?

i keep getting 288 but it’s not right

[ashen sigil]

so 1723

do i text on personal im

im new here

i dont know how to explain this to u

[quasi yoke]

Idk haha

[ashen sigil]

whats the answer tho

acc to the book

[ashen sigil]

well u gotta tell me . I wont be able to help otherwise

[spice field]

Hi Aashi

[ashen sigil]

umm hey

2[x]+1 + 5[x]+1 = 7[x] + 2

soo let 7[x]+ 2 be equal to m

and m has to be a positive integer acc to the question.
m is the +ve int that can be expressed as the above equation.
let [x]=y
y has to be an integer as gif gives int always. Any int
(m-2)/7=y
for y to be an int
only way y can be an int is m-2 is a mutliple of 7
so we have 0,7,14,..........................till 2016 that are multiples of 7 under 2022.
now we add 2 to each and we have 2,9,16,23,....................2018 as the values of m.
now we use the formula An= a+(n-1)d the A.P formula to get n.
the number of elements in the arithmetic progression.

n = 289

now we want the number of +ve int that are less than 2022 or equal which means we
2022-289=1733

[torn vessel]

how did you get this?

[devout snow]

@quasi yoke Has your question been resolved?

[devout snow]

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[pastel pasture]

Try using arithmetic progressions

[twin crescent]

what does same three decimal digits mean?

I am having a bit of a bruh moment here

[pastel pasture]

Stuff like 111, 222, 333 I'd assume

[pseudo basin]

it means that their three digits when written in decimal are the same

[twin crescent]

oh okay

so 9

.close

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[devout snow]

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[eternal marsh]

how can I find what number is under the black line, I tried some divisibility criteria but get nothing

[stone stump]

what did you get from your divisibility criteria

[eternal marsh]

the only thing that i can assume is that on the first arrow it's wether a 4 or 8

and like the sum of all is 3 congru to 0 mod 9

[queen zephyr]

,w 18!

Kek

[eternal marsh]

don't want the answer but the process, i can google it bro

[violet wind]

You found this because 18!/1000 is divisible by 4, right

[eternal marsh]

no

[violet wind]

oh that would be the last digit

[queen zephyr]

[violet wind]

yeah the last non-zero digit is a good place to start

[eternal marsh]

like i can remove 3 zero by $52$,10 and $154$

[woven radish]

phoestaclies

[eternal marsh]

so it it rest 2 and the arrow which is divisible by 4

so 4 or 8

[violet wind]

you're talking about the second digit of 18! ?

[eternal marsh]

yes the first arrow, the first number after all the zero

[stone stump]

not sure why you are only doing divisible by 4? there are enough factors of 2

[violet wind]

Usually we call that the last one

But ok

[eternal marsh]

it's divisible by 4 when the last 2 digit are divisible by 4

so only 24 and 28

[stone stump]

after that probably divisiblity by 9 and 11 will get you the other 2 digits

[eternal marsh]

i tried but get nothing

maybe i did it wrong

[violet wind]

you need to know the last non-zero digit exactly

[eternal marsh]

no

under the black line

[violet wind]

or the one you call the first arrow

Yes

But first

[violet wind]

You need to find this

[eternal marsh]

this

[stone stump]

you will be able to find that after finding the other one

so far you only used that 18! / 1000 is divisible by 4. not sure why you stopped there. why 4

[eternal marsh]

yes that's why I was trying to find the first and last arrow but I can only say that it will be 4 or 8 on the first one

[violet wind]

no, you can go further

[eternal marsh]

yeah i know but how

[stone stump]

what is the divisibility rule for 8

[eternal marsh]

don't know really

[stone stump]

the last three digits form a number divisible by 8

[eternal marsh]

ok so the first arrow is 8 great

I think i get it, i will come back, I think I was just missing the criteria by 8

i find something like first arrow + black line congru to 4 mod 9 but with the criteria of 11 it gives me absurd result

the addition between the 2 hidden numbers is 4 and their difference is 7

I made a mistake but czn't figure it out

[stone stump]

their sum could also be 13

that would still work for mod 9

[eternal marsh]

no impossible

because we have an arrow which is 10

if the sum is 13

ok i figure it out thanks

I forgot that if the sum is 0 it's also divisible by 11

.close

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[half ledge]

How do I do question 6a and b

[left robin]

,rotate

[sonic smelt]

,rotate

[sonic smelt]

Try to turn the right hand side into a logarithm of some expression

Also, don't forget to mention that 11 - 6x and x - 1 both have to be positive

[left robin]

think about what log actually means
log_a(b)=c means a equals b when taken to the power of c, so a^c=b

[sonic smelt]

Otherwise the original equation would make no sense

Oh wait they asked for 6a too

[half ledge]

We’re you explaining 6b or 6a

[sonic smelt]

Okay just read what I said when you get to 6b

For now look at Martin's message

[half ledge]

So for a x = 8 if I’m correct

I’m not gonna lie logarithms confuse me a lot so I have no idea how to do b even after what you’ve said

[sonic smelt]

Okay, instead simply exponentiate both sides (base 2)

$2^{\log_2{(11-6x)}}=2^{2\log_2{(x-1)}+3}=(2^{\log_2{(x-1)}})^2\cdot{2^3}$

[woven radish]

A Lonely Bean

[sonic smelt]

And this has to hold because logarithms are defined for positive numbers in general

[devout snow]

@half ledge Has your question been resolved?

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[devout snow]

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[lucid oracle]

Losing sight of basic calculus haha, is integrating a real valued function just summing its continious y values?

[sonic smelt]

I believe what you are trying to recall is the reimann sum
[
\int_a^b f(x) dx = \lim_{n\to\infty}\sum_{k=1}^n f(x_k)\Delta x
]

[woven radish]

A Lonely Bean

[sonic smelt]

Visually it looks like this

[lucid oracle]

ahaha okey so my issue is actually a probability one. The probability density function maps events to probabilities in [0,1]. I dont understand how taking the integral of this function gives you the probability for an interval since that would imply the integral equals summing over the values of that interval

[sonic smelt]

Probabilities of all of the possibilities should equal exactly 1, right? (Same as 100%)

So the integral of the probability density function on its domain yields 1 as well

[lucid oracle]

but thats basically what im asking

why the integral and not the sum of f(domain)

But i realise i completely missunderstoof pdf's, they dont map from events but from the reals and im not sure why haha

Im gonna do some more studying and i'll be back if i still dont understand, ty for the help tho!

.close

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[restive river]

I tried x+5

and x-5

why is it wrong?

[cursive totem]

you realize its rotating about the y axis not the x axis

[restive river]

yeah

[restive river]

oh

so its y - 5

right?

<@&286206848099549185>

im jumping off the window

How can I help?

this question

[restive river]

.

how do I find the r

its not x- 5 5 -x or y - 5

Alright.

So, you should have been able to get an appropriate radius based off of your correct answer for the height, and input radius variables should be shown in the square root. Did you try y +5 instead of y - 5?

no

its hmw

Sorry if I can't be of much help, I am only in eighth grade but I am in trig, ahead three years.

3 times limit

[restive river]

alr

You are a hero

thanks man

you are 8th grade and teaching me calc

yea. You wanna see a question I got yesterday in class?

yes please

It took me two hours to get the answer:

i hated that

you are not 8th grade

[restive river]

u think i'm lyin?

I will quit engineering

if you are actually 8th grade

fo real

ok know im doubting

i look like a little boy

im 14

alright ur trolling me

no no no dm me rn

i show you

no thanks

alr

anyways.....

do you know the volume of the cylinder?

[untold lance]

Damn yeah this is that identity I did this in Grade 10

[restive river]

thats grade 12 stuff

the z wasnt even introduced

I got it btw

r is x

fml

[devout snow]

@restive river Has your question been resolved?

[devout snow]

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[feral agate]

firstly

expand the bracket

on the left side

no

you have to use the distributive principle

$a \cdot (b+c) = a\cdot b + a\cdot c$

[woven radish]

kheerii

[feral agate]

notice how the a is multiplied to both the terms inside the bracket

since they are being added

what?

how does that matter

oh

a, b, and c are just numbers

i just used letters instead of numbers to show you how it works

$3 \cdot (4+5) = 3\cdot 4 + 3\cdot 5$

[woven radish]

kheerii

[feral agate]

is this less intimidating

yes

well

you can plug in the value of b into your equation

and if both sides come out to be equal, it means you got the right answer

so 5(5-1) = 5x4 = 20

since both sides are equal, b=5 is the correct answe

r

yep

[devout snow]

@restive river Has your question been resolved?

[devout snow]

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[devout snow]

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[dusk sand]

@dense jay i did (as a simplified example) 5x^2/3x^2, and there isnt a hole at 5/3?

[dusk sand]

can someone tell me what 3/4 top right is?

[dense jay]

5x^2/3x^2 =5/3 for all x besides 0 anyway

the x^2 cancel out

[dusk sand]

yes

so what does

5/3

mean

[dark dawn]

Plug in 2 what do you get

[dusk sand]

plug in 2 into 5/3?

what

[dark dawn]

The original function

[dusk sand]

5x^2/3x^2 ?

[dark dawn]

Yes

[dusk sand]

20/12

[dark dawn]

Or just 5/3

Now plug in 1?

[dusk sand]

5/3

[dark dawn]

Now plug in 0?

[dusk sand]

0

[dark dawn]

No

[dusk sand]

undefined

0/0

[dark dawn]

Undefined right

[dusk sand]

whats ur point

i dont speak math

[dark dawn]

But for all x’s other than that 0 there we would get 5/3 , so there absolutely would be a hole there,

I hope I didnt miss half a conversation and you already came to that conclusion

I just read the question

[dusk sand]

well

just trying to understand

what the purpose

of finding leading coefficients

then making it

5/3

well

i get that part

everything else

becomes

0*

but whats left over

the 5/3

is the limit

or 0 is the limit

im lost

[dense jay]

this isnt a good example to be working with though for this

[dusk sand]

how come

[dense jay]

because its always 5/3 when x isnt 0, even without the limit

[dusk sand]

5/3 is the slope

or what

legit im lost

[dense jay]

no

,w graph (5x^2)/(3x^2)

[woven radish]

Results provided by WolframAlpha

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

Requested by AℤØ#4979

[dense jay]

its essentially just a straight line but its undefined at x=0

[dusk sand]

parabola right

oh

[dusk sand]

strange thought it becomes just 5/3 since they both have x^2 common in num and denom

[dense jay]

try using $\frac{8x^2+5}{7x^2+4}$ as an example

[woven radish]

AℤØ

[dense jay]

it does for most x, but by having the x^2 in the denominator initially it becomes implicitly defined that x cannot be 0

since you cant divide anything by 0, even 0 itself

[dusk sand]

i found value of 8/7 and there is def not a hole there

btw are you saying that all fractions like this have a hole

at x= 0?

[dense jay]

no, but yes at any point where their denominator is 0

they would be undefined at such a point

[supple knot]

You're confusing holes with asymptote values

[supple knot]

This gives you holes

[supple knot]

You're calculating the horizontal limit here

[dusk sand]

to find hole gotta set denom to 0?

[supple knot]

Among other things yes

[dusk sand]

but here we have 2 same leading cofecients

coefficients

[supple knot]

A hole is more precisely a "removable discontinuity"

https://www.superprof.co.uk/resources/academic/maths/calculus/limits/removable-discontinuity.html

[supple knot]

That has nothing to do with removable discontinuities

[dusk sand]

horizontal limit? theres such thing?

[supple knot]

Horizontal asymptote is precisely what this paragraph is explaining

[supple knot]

Which is completely different from this link

You should read both

[dusk sand]

ok

horizontal asymptote is 8/7 which means a hole should be lurking too

well technically vertical asymptote = a hole?

thus a limit

[supple knot]

No

[supple knot]

No

[supple knot]

You're doing this again

[dusk sand]

asymptote is a huge hole man

[supple knot]

Nope

Don't invent your own meanings for words that already have meanings

[supple knot]

https://www.wikihow.com/Find-Horizontal-Asymptotes?amp=1

[dusk sand]

just trying to make sense of it all

[devout snow]

@dusk sand Has your question been resolved?

[devout snow]

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[solar ether]

(x ^ (5/6))/(x ^ (7/12))

[solar ether]

...

no- wait

much better

oh my no

i get it now

.close

[devout snow]

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[tiny coyote]

hey

[devout snow]

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[warm rapids]

Question iii

[fathom thicket]

,rotate

[fathom thicket]

@warm rapids let me guess

you have an issue

because

you dont know

which answer to use

[warm rapids]

yes

exactly

if this type of question pop up in the exam, i have to guess between 2 question. THen the possibility of me picking the wrong one is 50

;-;

[feral agate]

can lengths be negative?

[fathom thicket]

@warm rapids when you choose x = -9. you get negative lengths in the triangle

so as @feral agate asked, do you think thats possible

[warm rapids]

ฺีะ ทั ฟืหไำพ รห ืนะ

[warm rapids]

but my answer is not negative

i got 10.63

[feral agate]

what?

[warm rapids]

forgot to change language

my friend keep talking to me that why i dont help him

i cannot even help myself

anyways

is my 10.63 wrong?

[fathom thicket]

enchanting table font

[fathom thicket]

your 10.63 is based on the negative length to begin with

apple from the poisonous tree

[warm rapids]

never heard that phrase

[warm rapids]

if in the exam,both number is positive what do i do?

[fathom thicket]

in an exam

there will

usually

be a compellling reason

to take one over the other

[feral agate]

he means to say that since you calculated the 10.63 length with the assumption the other lengths are negative, that already dismisses that answer to be wrong

[warm rapids]

so for preparation i just needed to read lots of english right?

[fathom thicket]

well 90% of the compelling reasons

is because

[warm rapids]

thank you?

[fathom thicket]

1 choice is obviously wrong

like x = -9 gives you negative lengths

which can never happen

[warm rapids]

so just keep in mind that if the X= negative numbers, its not that one for sure right?

[fathom thicket]

well its not necesserily that x is a negative number, but when you subsitute in the number to the sides of the triangle

it gives you a negative length

[warm rapids]

I dont get the negative length though

i got 10.63

i use the calculator to calculate too

[fathom thicket]

im talking about the sides of the triangle

[warm rapids]

oh

ohhhhhhhh

oh sorry

get it get it

my english just bad

[neon lark]

bro

need a little help with a trig equation

[warm rapids]

;-;

sorry

[fathom thicket]

!help

[devout snow]

Please read #❓how-to-get-help

[neon lark]

thank you

[devout snow]

@warm rapids Has your question been resolved?

[devout snow]

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[devout snow]

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[sterile wasp]

im just not understanding the first part of this question, translation: "See the limit value as the derivative in x=1 of a function f(x) .
Determine the function f′(x) and calculate the limit value."

[pseudo basin]

$f'(1) = \lim_{x\to 1} \frac{f(x)-f(1)}{x-1}$

[woven radish]

Ann

[sterile wasp]

how did you get to this answer?

hello?

[soft shore]

factor x^28-1

[sterile wasp]

still confused as to what f'(x) would be

[soft shore]

isn’t f(x) = (x^28-1)/(x-1)

if so, use the quotient rule

[violet wind]

I don't think so

[soft shore]

“See the limit value as the derivative in x=1 of a function f(x)”

oh wait

[violet wind]

Idk the language but I assume the limit is the derivative of some function

[soft shore]

my b

then f(x) = x^28?

[violet wind]

so what Ann does seems right

[sterile wasp]

yeah its in swedish but im having a hard time understanding it myself, my teacher is not originally swedish so idk if thats it or if my math is just too bad

this would be the derivative i guess? (28*x^27)/(x-1)-(x^28-1)/(x-1)^2

[violet wind]

I don't think so

[violet wind]

idk what you did but I assume this is what you're supposed to do

to see what f(x) is

[sterile wasp]

so i replace f'(1) with 28?

tbh im not getting it

[devout snow]

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[fringe owl]

Hi im new to this server and I wanted some help on this question here

[radiant dune]

What does PQ=PR tell you about angle PQR

And PRQ

[fringe owl]

theyre the same angle i think?

[radiant dune]

Yes

And side QR is same in both triangles

So we have proved one angle and one side to be equal

[fringe owl]

yes

[radiant dune]

Now we need another angle to prove congruency

Or another side

It is given that NQR=MRQ

Do you see any criterion of congruency being fulfilled?

[fringe owl]

I was thinking of ASA

[radiant dune]

Yes, there we go

[fringe owl]

because we know that MQR is the same as NRQ, so that means we got one of the angles

and that angles NQR and MRQ are the same

so we can prove this by ASA right?

[radiant dune]

Yes, and QR is the side

Yes

[fringe owl]

ok i will try to write this down thanks!

i dont see any problem with this but it still says its wrong

im not sure what i did wrong

[radiant dune]

Is this manually checked?

Maybe the system wants you to put it in a designated format

That's why it's saying it's wrong

[fringe owl]

but it is correct right?

[radiant dune]

Yes it is

[fringe owl]

as long i can explain this to my math teacher

[radiant dune]

Yep you can it's totally correct

[fringe owl]

Ill try to reformat it and see

thanks for the help

[radiant dune]

Np

[fringe owl]

.close

[devout snow]

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[brittle fossil]

.open

<@&286206848099549185>

[brittle fossil]

I need help to find y

I found x already:

x+2,5 5+2
--------- = ---------
2,5 2

x=6,25

[trail bison]

Are they similar triangles?

[brittle fossil]

ja

yess

its about radiation theorem

[trail bison]

Then same things

[sage burrow]

german?

[brittle fossil]

ja xd

[trail bison]

CD/AB = CZ/AZ = DZ/BZ

[trail bison]

Lol

[sage burrow]

strahlensatz: y:2 = 4:5

[trail bison]

Keep going

[brittle fossil]

wait i try this

[brittle fossil]

wie meinst du

das ergibt gerade alles keinen sinn

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[brittle fossil]

.close

[devout snow]

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[deft jay]

First question has me stuck on what to do first

[solid spire]

So to find the angle what do we need?

[deft jay]

minus 90 and 45 out of 180

[solid spire]

That would be angle DCA

[deft jay]

oh

idk

[solid spire]

You're doing trigonometry right

[deft jay]

yeah

My minds blanked icl

@solid spire ??

[solid spire]

So what do you know about the relationsships using sin cosine and tangent?

[deft jay]

The fractions with the opposite hypotenuse and adjacent

What does it mean for find the measure of

[manic sedge]

You need to find the magnitude of the angle ABC and BAC

Use inverse Trigonometry that's it

[deft jay]

icl I don’t know what that is 😂

[manic sedge]

Like $cos^{-1}(x)$

[woven radish]

𝓐𝓡𝓝𝓐𝓑 𝓟𝓐𝓛

[deft jay]

oh

[manic sedge]

Trig functions with negative exponents

You can say it like that

[deft jay]

still don’t know what to do

[manic sedge]

Oh I didn't see you don't need to use it

[manic sedge]

Find Angle ACD then you would get angle ACB

When you get ACB you would observe that in ∆ACB angle CAB and CBA are equal

So you could solve it by using basic geometry too

[deft jay]

Ok so the angle for B is 45

Wait no

[manic sedge]

,w 90+45+2x=180

[woven radish]

Results provided by WolframAlpha

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Requested by 𝓐𝓡𝓝𝓐𝓑 𝓟𝓐𝓛#6985

[manic sedge]

Partially correct

[deft jay]

what is x in this context

[manic sedge]

Both equal angles

You solve it yourself @deft jay

I was checking

[deft jay]

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[devout snow]

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[round pecan]

is 2/5 the fraction equal to 2 : 5?

[foggy wing]

yes

[round pecan]

im sorry man i cannot take u seriously with that pfp

[polar chasm]

yes

can you take me seriously with my pfp btw?

[round pecan]

thank you

yeah i can

[devout snow]

@round pecan Has your question been resolved?

[devout snow]

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[rapid coyote]

Can anyone help me?
The speed of the cars on a specific road is normally distrubated. The observations shows that $95%$ of the cars ride slower then $120 km/h$ and $10%$ slower then $90 km/h$

[woven radish]

Jacob_

[rapid coyote]

Question:
a) What is the average speed of the cars
b) How much % of the cars go faster then 105 km/h

I don't know how to start this question

[devout snow]

@rapid coyote Has your question been resolved?

[sage burrow]

try to find the parameters for the normal distribution as you knpw 95% and 90%-quantiles.

[rapid coyote]

Do you mean with the z-score or?

This is the graph right

[sage burrow]

yes

but p(X<90)=0,9

[rapid coyote]

Then the z-score is:
1,64 and 1,28

[rapid coyote]

isn't it P(X>90) = 0,9?

[sage burrow]

sorry, you are right.

[rapid coyote]

I now know the z-score but how can i calculate the parameters with that?

[sage burrow]

do you have a table for normal distribution with 0 and 1 as parameters?

[rapid coyote]

yeah with all the z-scores for 2 decimals

[sage burrow]

look at the values for 0.9 and 0.95 and fit your parameters so that you get 90km/h für 0.9 and 120 km/h for 0.95

[rapid coyote]

So

$P(Z < \frac{120-\mu}{\sigma}) = 0.95$

And then:

$P(Z < \frac{90-\mu}{\sigma}) = 0.10$

[woven radish]

Jacob_

Jacob_

[sage burrow]

yes

[rapid coyote]

and then:

$\frac{120-\mu}{\sigma} = 1.64$

[woven radish]

Jacob_

[rapid coyote]

And the same with

$ \frac{90-\mu}{\sigma} = -1.28$

[sage burrow]

with this, you should be able to answer the qeustions for the average speed, and the percentage with respect to 105 km/h

[rapid coyote]

Yeah ill try rq

Like this way right

[sage burrow]

yes

[rapid coyote]

Wait i get a negative sigma

that isn't right

[sage burrow]

,w solve 120-a=1.64b and 90-a=-1.28b

[woven radish]

Results provided by WolframAlpha

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Requested by ThM#7271

[rapid coyote]

Thanks, answer on b) was 42,85%

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[weary pebble]

So here x is the age of the grandson and y the age of Mr.Stevens

first one is right

For the second , in 3 years means x+3 = 4(y+3)

Because 3 years + x will be 4 times y+3years

Ok

We will consider the ages of MrS and the grandson threeyears after the present

We will write them as x' and y'

The text says to you that x' = 4y'

do you get that ?

that's because the age of MrS will be 4 times greater than the age of the grandson

Why Y on the left ?

No that's an x

the age of the grandson

yes that's it

kind of but I think you got it

oh yes mb

You're right

It shows me that you understood

yes

mb i'm tired

xD

that's right

Yep

3x = 54

x= 54/3 = 18

yep

[devout snow]

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[weary pebble]

@scenic ether Do you know $\sum_{k=0}^{\infty}x^k$ ?

[scenic ether]

hello

[woven radish]

ByShaDowZ

[scenic ether]

i am back

[scenic ether]

yes

so i use the infinite sum formula?

[weary pebble]

Yes because you have an infinite sum here

Do you see it ?

[scenic ether]

for geometric sequence

[scenic ether]

yes i can see it

[weary pebble]

yep that's it

[scenic ether]

ok

so S_inf=a_1/(1-r)

[weary pebble]

what's r here ?

[scenic ether]

common ratio

[weary pebble]

yes but in the question, what's r and what's a_1 ?

[scenic ether]

r=x and a_1=-1

[weary pebble]

are you sure ?

[scenic ether]

but for some reason it doesnt work

[scenic ether]

hold on

let me check

what do u think it is

[weary pebble]

I'd write it as $-1 + \frac{1}{x} + \sum_{k=1}^{\infty}x^k = -1 + \frac{1}{x} + \sum_{k=0}^{\infty}x^k -1$

[woven radish]

ByShaDowZ

[weary pebble]

$= -2 + \frac{1}{x} + \sum_{k=0}^{\infty}x^k$

[woven radish]

ByShaDowZ

[weary pebble]

And here the formula is $\sum_{k=0}^{\infty}x^k$ = $\frac{1}{1-x}$

[woven radish]

ByShaDowZ

[scenic ether]

why are we subtracting 1 on the right side?

[weary pebble]

because i put k=0

I add up $x^0 = 1$ to the sum so i substract it with a -1 in order to keep the same value

[woven radish]

ByShaDowZ

[scenic ether]

ok

i might have to study more on that

[weary pebble]

maybe

[weary pebble]

Do you agree with the formula I wrote ?

[scenic ether]

so $\frac{-10}{3}=-2+\frac{1}{x}+\frac{1}{1-x}$?

[woven radish]

m64sky

[weary pebble]

Yes that's it !

[scenic ether]

looks good

[scenic ether]

ohhh

[weary pebble]

And I hope from here you know how to solve it ?

[scenic ether]

yes I do know how to solve it

[weary pebble]

if not say it

nice

[scenic ether]

thank you for your help

[weary pebble]

So here the trick is to see the infinite sum

and to apply the formula in the right conditions (k=0 !!!!)

[scenic ether]

ok

.closed

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[tawny horizon]

B(3,10) C(6,4). I worked out m of BC = -2 and AB: y = 1/2x + 8.5. how do i work out coordinates of A?

[scenic ether]

oh i understand that part

[weary pebble]

@tawny horizon Here you need 2 informations to solve this

First of all , you have to notice that A = (x,y) satisfies y = 1/2x + 8.5

[tawny horizon]

what does that mean?

[weary pebble]

It means that A is on the line y = 1/2x + 8.5

[tawny horizon]

it does satisfy 👍

[weary pebble]

so its coordinates are such that y = 1/2x + 8.5

but an other info is important to notice here

do you have it ?

it's on the graph

[tawny horizon]

no I'm stuck

[weary pebble]

Why is there a line between A and C ?

[tawny horizon]

it is parallel to the x axis

[weary pebble]

Yes

[weary pebble]

What can you deduce from this ?

Remember you search the coordinates of A

and you have the coordinates of C

[tawny horizon]

well I'm still stuck

[weary pebble]

Here you have to see that the y coordinates of A and C are equal

does that makes sense to you ?

[tawny horizon]

yeah

thank you very much!

[weary pebble]

do you know how to end ?

[tawny horizon]

give me a sec

[weary pebble]

^

[tawny horizon]

Yeah I got it

[weary pebble]

nice

[tawny horizon]

thank you good sir

.close

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[umbral roost]

Would you agree with these calculation? Unit conversion/ dimension analysis? I’m asking because numbers seem wrong.

[devout snow]

@umbral roost Has your question been resolved?

[umbral roost]

Okay I’ll shorten my question. How should I convert GJ to Gw?

I know W is J/s

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[lofty monolith]

How do I differentiate y=arcsinx

[lofty monolith]

Nvm

.close

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[jolly swan]

what is this formule

[rare mantle]

Slope formula

it's essentially what MVT says

f'(c) = rate of change at c

[restive river]

https://en.wikipedia.org/wiki/Mean_value_theorem

[jolly swan]

thx

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[spark ruin]

how do I convert 3x+2y=6 plane to vector parametric form? missed a lesson and im lost now

[true geode]

Do you know how to find the direction vector of a line ?

[spark ruin]

not quite

[true geode]

Ok imagine there is a line with gradient 2
What do you think will be the direction vector for that ?

[spark ruin]

(1,2)?

[true geode]

Yes

Now what is the gradient of the line in question ?

[spark ruin]

3/2

[true geode]

Nope
Check again

[spark ruin]

mm

-3/2?

[true geode]

Yes

Now what will be the direction vector for that ?

[spark ruin]

(1,-3/2) ?

[true geode]

Well yes that is correct
But i would recommend writing it in a simpler form so it is easier for everyone

(2, -3)

[spark ruin]

ah

[true geode]

I have basically multiplied both by 2
Which is scalar multiplication and doesn't change the direction

Now do you know whats the next step or no idea?

[spark ruin]

as far as i know so vector form is usually (x,y)=(something)+scalar(2,-3)

now i have no idea how to find that something

[true geode]

You find a pair of values of x , y from the original equation

And put it instead of the "something"

[true geode]

The scalar is the parameter
When you set the parameter to 0 you just get
(x,y) = (something)

[spark ruin]

?

[true geode]

Yes

[spark ruin]

ah

oki thx

[true geode]

Note that you chose the value of x for the (something)

That was arbitrary
So this can have different looking solutions but they will all be equivalent

The (something) can be any point on the line not just (0,3)

[spark ruin]

btw

r u also familiar with "point normal form"

im not sure what that is

[true geode]

Yes
But that is more work i think

It is of the form

a.n = x.n
Where n is the normal vector to the line , "x" is the variables vector (x,y)
And "a" is any random point on the line

[true geode]

Are you familiar with dot products ?
Or scalar products ?

[spark ruin]

learnt about them but havent used it very much

[true geode]

Well this uses these dot products

[spark ruin]

.close

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[unique inlet]

Hii, can someone help me how to evaluate the limit of a complex function along the path from coming from the origin?

Idk how to solve for it. I've tried solving for the y=mx eqtn. but don't know how to plug it in ind the eqtn. Or someone knows how to solve it in any ways?

[devout snow]

Please don't occupy multiple help channels.

[warped relic]

.close

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[wooden axle]

Can anyone tell me what approach I can use for solving this question?

[polar bolt]

That notation what

[devout snow]

@wooden axle Has your question been resolved?

[wooden axle]

It says integration

[polar bolt]

And? How can a function have dx and dy in the definiton?

What is f(1,1)? According to what they wrote its (1+1)dx+(1+1)dy

Does that make any sense?

[devout snow]

@wooden axle Has your question been resolved?

[devout snow]

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[ocean yacht]

I have a doubt in 1st question

[ocean yacht]

.close

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[restive river]

i have a little question

[restive river]

do this function

[uneven heron]

what's ur question abt it

[restive river]

has a oblique asymptote

[uneven heron]

no its horizontal asymptote is y=3

[restive river]

Ok

thank you

.close

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[chrome creek]

how to do the algebra for this

[chrome creek]

~how does the left equal the right

[restive river]

1 = (1 + sqrt(5))/(1 + sqrt(5))

[pseudo basin]

$\frac{1+\sqrt{5}}{2} = \frac{2-1+\sqrt{5}}{2} = 1 + \frac{\sqrt{5}-1}{2} = 1 + \frac{1}{2/(\sqrt{5}-1)} = 1 + \frac{1}{\frac{2(\sqrt{5}+1)}{(\sqrt{5}-1)(\sqrt{5}+1)}}$

[woven radish]

Ann

[chrome creek]

thanks

.clsoe

.close

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[ember turtle]

How would I complete the square here? Doesn’t the technique require to have a 1 at the 1st position?

[scarlet sequoia]

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

[ember turtle]

Do I use that every time it’s not 1x^2?

[scarlet sequoia]

not really, that's general formula

you always can do

$$\int \frac{1}{2x^2-x+1} \dd{x}=\frac12 \int \frac{1}{x^2-\frac{x}{2}+\frac12} \dd{x}$$

[woven radish]

Modus

[scarlet sequoia]

and now you have 1x^2

[gleaming socket]

What is this called?

[ember turtle]

Remixed quadratic

(Pt2!)

[devout snow]

@ember turtle Has your question been resolved?

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[hard pike]

anyone got an idea how i would work this out?

its a vector question but i dont know where to start

<@&286206848099549185>

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[restive river]

So i drew the triangle

And i used cos

but it didnt worm

<@&286206848099549185>

[mental rover]

Can you write it a bit neatly so i can tell whats going on?

[restive river]

um the 55 and 33 are both angles

and the 25 is the distance away

Also i cant rlly draw any neater than that

Umm <@&286206848099549185>

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[calm hill]

Could someone help me solve this

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[high chasm]

trying to do df/du

but it doesnt seem like ive done this correctly

cant see what ive done wrong

any ideas?

acc

nvr mind

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[random vine]

Given a code C generated by a generator matrix how would I find the minimum distance?

[random vine]

Is there a little shortcut for it or is brute force the only method?

[stone stump]

its a nontrivial problem

NP-hard iirc

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[sharp oar]

.

[wintry vine]

By equivalent fraction property we know if we multiply numerator and denominator of a fraction by same quantity we get fraction with same value does it hold true if we multiply numerator and denominator by square root of certain whole numbers because square root can either have positive value or negative value . So it could be like you can multiply numerator by positive value and denominator by negative value .

[tired thistle]

no

a square root is only positive

there is no positive and negative value

[wintry vine]

I mean square root 4 can have two values either 2 or negative 2

[tired thistle]

no

$sqrt{4}=2$

[woven radish]

REY

[tired thistle]

but if $x^2=4$ then $x=+2$,$x=-2$

[woven radish]

REY

[tired thistle]

because $x=+/-sqrt{4}$

[woven radish]

REY

[wintry vine]

That is what i am trying to tell

[tired thistle]

?

[feral agate]

Whenever you see $\sqrt{4}$ it always represents the principle root ie the positive value unless you specifically see $-\sqrt{4}$

[woven radish]

kheerii

[feral agate]

In most cases

[wintry vine]

Ohk yeah i forget this

Thx both of you

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[queen zephyr]

state your question

[inland river]

how to get a

a is angle btw

[feral agate]

Use a calculator

[queen zephyr]

ikik

[feral agate]

No other way

[queen zephyr]

$\tan\alpha=\frac{4}{3}$

[woven radish]

bettim

[inland river]

idk how to, do i just divide 8/6 then is placed in tan?

[queen zephyr]

so approximately

$\alpha = \tan^{-1} 1.33$

[woven radish]

bettim

[queen zephyr]

put that in a calc

,w tan^-1 1.33

[woven radish]

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[queen zephyr]

0.,w 92 in angle

[feral agate]

,w 0.926093 radians in degrees

[queen zephyr]

,w 0.92 in angle

[woven radish]

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[queen zephyr]

i fked lo

[inland river]

ok I got it now, thankyou

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[iron horizon]

I keep getting something other than 2x , can someone help to see where i went wrong here

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[vast rain]

hmm your general solution is a little off

remember if the roots are repeated

you do something slightly different

[iron horizon]

thanks

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[scenic surge]

is this a partial fractions question?

[upper schooner]

Seems to be I would think!

[scenic surge]

well then

what I got so far is

[quaint citrus]

Simplify off the bat tho

[scenic surge]

the denominator?

[upper schooner]

Hey @lusty sapphire

[quaint citrus]

Nah the numerator becomes 3(x^2 - 1) right

[lusty sapphire]

Hi hi.

[scenic surge]

oh does that rlly help that much?

[quaint citrus]

Then u can cancel

[wind vale]

yes

yes

[scenic surge]

wait cancel what i dont get it

shit

[wind vale]

swr besst

[quaint citrus]

Try expanding x^2 - 1

Into factors

[scenic surge]

(x-1)(x+1)

oh and then

cancel one of the (x+1)

i mean

[quaint citrus]

Ye

[scenic surge]

omg lemme retry the question brb that would make it alot better

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[trail apex]

Hi

[trail apex]

i got 0 marks when i tried it on a test

i know how to find nth term in a geomtric sequence

but i dont rlly understand this question

[stuck field]

Well you have two equations and two variables.

Your variables are,
The first term.
Common ratio.

Do you realise that?

[trail apex]

no i dont rlly understand what u mean tbf

[stuck field]

Do you know what a geometric progression is?

[trail apex]

no