help-0

[autumn apex]

is the swapping of x and y throwing you off? I'm blind

[native temple]

IdK how to find vertex

[versed osprey]

oh ok, thanks, if you mind, could you please explain this again?

i dont get it

[gloomy lintel]

Complete the square on y and then that shows you the translation in the y direction for the vertex

[autumn apex]

yeah, so imagine rather than a particle moving around a circle you've got a piece of string that you're wrapping around a tube

the length of the string is what they mean when they say distance, i.e. the total PATH distance the particle has traveled

displacement though, you're not wrapping the string around, you're just holding the string tight between its start location and where the particle is after you've moved it

so you aren't measuring circles with displacement, just a line segment from position_old to position_new

so if you move the particle away from its starting position, then move it back, the total displacement is 0

but the path length it traveled isn't 0 if you ever moved it

[versed osprey]

OHHHH

holy shit

wow

thanks, and thats what makes the 1.5 and the 2.5 displacement, 20m right?

[autumn apex]

yep, any 'half round' would put it at the maximum displacement it can be along the circle

displacement caps at the diameter of the circle

[versed osprey]

thanks so much

[autumn apex]

np

[versed osprey]

i might come back again with the same doubt, dumb ik, but i just get confused again sometimes.

mmmbyeeeeee

[dense badger]

can someone help me in vc?

so i can screenshare

im doing a mini quiz on surface area and cant figure out some of the questions

[obtuse cove]

Can someone help me with this? Please ping me when you are ready.

[autumn apex]

@obtuse cove still need help?

[obtuse cove]

Yes.

[autumn apex]

so the costs of the cakes + cupcakes totals $420, right?

[obtuse cove]

I'm on a time budget too...

And yes.

[surreal delta]

@obtuse cove
X = amount of cakes sold
Y = amount of cupcakes sold

20x+15y=420

@autumn apex sorry

[autumn apex]

😛

that's the direct route

[surreal delta]

Yeah idk really how to explain that xd

[autumn apex]

yeah explaining it without giving away the answer is hard for this one

[surreal delta]

I'll try

[obtuse cove]

Lmao.

[surreal delta]

You need to have 2 variables
x and y cuz it's easy
You want an equation to know how many cakes you've sold (after looking at the data, this is the only possible equation situation thingy you can have)
Therefore you have
X + y = 420
But now you're saying that you sold 420 in total
You wanted it to be money
Now find a way to implement the price of them

Ayo hope that's a better answer 😄

[obtuse cove]

Ok.

[tranquil tulip]

What is The probability of getting 60 questions right in a row and each question has 5 answers?

[autumn apex]

assuming you pick randomly?

[tranquil tulip]

Yes

[autumn apex]

so that'd be (1/5) 60 times in a row, right?

what would the answer be if it were only two in a row?

[tranquil tulip]

yes so 60/300?

[autumn apex]

try to answer the easy one first, what is your probability if you're only given ONE question

and then answer for two, then for 60

[tranquil tulip]

1/5, 2/10, and 60/300?

[autumn apex]

those are all the same number

[tranquil tulip]

oh wait so is it 1/5 * 1/60

[autumn apex]

if you have two trials in a row at 1/5 probability each, you get the probability of getting them both right by multiplying (1/5)*(1/5)

[tranquil tulip]

ohhh

u have to do 1/5 * 1/5 60
times?

[surreal delta]

I'd like to add that this is binomial, therefore required to add a combination in front
If I'm not mistaken

[autumn apex]

(1/5)^60

[tranquil tulip]

oh thank u so much

[random crypt]

@autumn apex

[autumn apex]

I don't think so @surreal delta, but I could be doofing it up 😛

[random crypt]

I got that the abs max is f(4)=5

And no abs min

But I think I got the absolute maximum wrong because it says the value of F on the interval [2,5]

Does that matter

[autumn apex]

abs max is at x=4

[tranquil tulip]

wait is the answer still (1/5)^60

,calc (1/5)^60

[ocean seal]

Result:

1.1529215046069e-42

[tranquil tulip]

wait s rhat the percent or the decimal

[autumn apex]

yeah that applies if you're counting successes out of some maximum, but the maximum is the number of successes which simplifies it (so this is a simpler special case)

[surreal delta]

Decimal

[tranquil tulip]

ohhh ok , so the % is 0.115

[surreal delta]

Nono

It says e-42

[autumn apex]

it's extremely improbable to get all 60 correct, that's a super small number

[tranquil tulip]

ok tysm

[charred heron]

Could anyone tell me what I did wrong

[gray isle]

18/6 = ?

[alpine sable]

Not 4

[charred heron]

Oh

I’m slow

LOL

[random crypt]

What is the critical numbers here

[surreal delta]

I explained it in #help-2 😄

[random crypt]

Where

How do I know if the derivative is zero or undefined

[alpine sable]

No tangent line in such a point

[autumn apex]

the 'empty circle' is the symbol for 'undefined at this value'

[random crypt]

Would it be at the dots that aren’t filled in??

[autumn apex]

function is undefined at that value

[surreal delta]

That's with f', but that's just an explanation
You only have the graph
You have to look at the top and bottom of your graph

[random crypt]

Okay so then how do we find the derivative as 0

If we already got the undefined ones

[autumn apex]

in that example the empty circle can mean a discontinuity too

[random crypt]

How about that random dotthat isn’t even connected to the graph

[autumn apex]

derivative 0 means the tangent of the curve would be a horizontal line

and a discontinuity isn't differentiable

so the derivative isn't defined there

[random crypt]

Does the dot that’s underneath The graph that isn’t connected to anything is that a critical number or it doesn’t even matter

[autumn apex]

it can't be a critical point unless the derivative is defined there

[random crypt]

Ok

[alpine sable]

No tangent line on just a point

[random crypt]

How do you answer critical numbers. Can you answer like this (1,4) , (6,4), (6,2)

[autumn apex]

usually you'd just supply the x value that takes F to 0 (that is, y=0 for F)

[random crypt]

So x=1,6

[autumn apex]

there's no critical point at 6

there's a discontinuity => derivative undefined

[random crypt]

There’s an empty dot on 6,4

[autumn apex]

yep, empty dot means discontinuity

[random crypt]

So empty dot DOESNT mean a critical #???

[autumn apex]

correct, it can't be one

[alpine sable]

Empty doesnt mean critical

[autumn apex]

it explicitly means the opposite, empty dot strictly implies it is NOT a critical number

[random crypt]

Phhh

f(6)=4
f(2)=2 , f(5)=3, f(1)=3

So critical #s are 1,2,5,6

Right?...

[random crypt]

Talkin about this question

[autumn apex]

you listed discontinuities(empty dots) as critical numbers

there will be 2 critical numbers

[random crypt]

How. (6,4), (5,3), (2,2), (1,3) aren’t empty dots

[autumn apex]

(1,3) isn't a continuous portion of the graph, so the function is discontinuous at this value

[random crypt]

Ok

[autumn apex]

there being any empty dot in that vertical line counts

[random crypt]

As a critical #???

[autumn apex]

the opposite.

[random crypt]

So 1,4 is critical ??

Ohhhh

Wait

I thought we said empty dogs don’t ever count as critical numbers

[autumn apex]

there can't be a critical number on that vertical line (the vertical line through x=1)

[random crypt]

Ok ok

[autumn apex]

the graph needs to be differentiable at an x value to have a critical point there, among other conditions

they give you some examples of things that break differentiability, like discontinuities (x=1) and cusps (x=5)

[random crypt]

Ohh

A cusp on this graph is like 5,4

[autumn apex]

yes

[random crypt]

(5,3)*^^^

[autumn apex]

yeah I just noticed that too 😛

[random crypt]

So the critical points are (6,4) and (2,2)

[autumn apex]

why do you think (6, 4) is one?

[autumn apex]

this

[random crypt]

So if there’s a cusp then that whole line doesn’t count ???

[autumn apex]

don't mix up which points you're referring to

the cusp is at x=5

[random crypt]

Sorry I mean ...

[autumn apex]

there is a discontinuity at x=6

[random crypt]

Empty dot

Yeah

[autumn apex]

the empty dot tells you that it can't be differentiable for that x value, just like a cusp does

[random crypt]

Ok but why isn’t 6,4 a critical

Just Bc there’s an empty dot underneath it ??

[autumn apex]

so when I say "at x=6 there is a discontinuity"

do you know what I mean

[random crypt]

That whole line has an empty dot

[autumn apex]

the whole vertical line, identified as x=6 for all y values, can't have a critical point

[random crypt]

Ohhh

Because there’s a discontinuity (empty dot)

[autumn apex]

yes

[random crypt]

Gotcha

So basically there’s only 1 point that is a critical #

[autumn apex]

even if it's defined somewhere on that line, it won't be continuous with the rest of the function, so its derivative becomes undefined

no you missed one of them

you only found a minimum at x=2, but there's a maximum too

[random crypt]

4,5

[autumn apex]

keep in mind you only need the x values

[random crypt]

So 4

[autumn apex]

yep

[random crypt]

So x=2,4

[autumn apex]

correct

[sharp harness]

Can anyone help me with 2,3 and 4? Im stuck and dont have much time

[autumn apex]

@sharp harness still need help?

[raven crypt]

@autumn apex can u help

[autumn apex]

@raven crypt sure

so the exponent being negative -- do you know what that does?

if I have x^(-1), that's 1/x. Works the same if the -1 becomes a negative fraction

[sharp harness]

All good now, thank you

[autumn apex]

cool

[raven crypt]

so it's -1?

[autumn apex]

no

the exponent you're dealing with is (-4/7), not (-1) (nor is -1 the answer)

I'm just checking you know what a negative exponent means

[slate fossil]

show me the step, with explanations

[autumn apex]

usually people ask for help 😛

but you're in luck, the answer I just started giving the last person is the same for you

[slate fossil]

thats good to hear

[autumn apex]

so, for example, do you know what number 5^-1 is?

[slate fossil]

5 power of Negative 1

[autumn apex]

yes, but what is it equal to

[slate fossil]

Umm

Dunno lol

[autumn apex]

so if 125 is 5^3, how do you get 1/125? 5^x = 1/125

[slate fossil]

Ouh that's what you meant

5^3= 125

[alpine sable]

GET DOWNSTAIRS!

BLAKE, TAKE OFF HIS PANTS!

[devout tundra]

5^-3

@autumn apex

[autumn apex]

haha, I was trying to socratic method him @devout tundra

[devout tundra]

Uh

[autumn apex]

asking people questions so they reveal the answer to themselves

it's a way to avoid giving away the answer (and to get at where people are stuck)

[toxic cave]

can someone help me out?

7000 people will ski each day at a local ski resort if tickets cost $75 each. Attendance will decrease by 150 people for each $5 increase in the ticket price. The ski resort needs to make a minimum of $300000.

What is the highest ticket price the ski resort can charge and still make at least the minimum amount of money desired?

Enter the ticket price (NOT the number of price increases!) to the nearest whole dollar (do not include the dollar sign)

question for systems of equations and inequalities

[autumn apex]

@toxic cave still need help?

[mossy basin]

Would anyone be able to walk me through solving this so I have a better understanding to do the rest?:

Show that a ≡ b (mod m) if a mod m = b mod m

[finite spindle]

first maybe use the definition of ≡:
a ≡ b (mod m) means that (a-b) is divisible by n, or equivalently, that a-b (mod m) = 0 (mod m)

[dusk basin]

An airplane ticket has an area of 119 square centimeters. Its perimeter is 48 centimeters. What are the dimensions of the ticket?

[bold token]

is the fundamental theorem of calculus, and finding the area under a curve the same formula?

[bold token]

axb=119, 2a+2b = 48?

[glass lichen]

FTC II is the way to compute an integral

Integrals can be regarded as the signed area under a curve

[bold token]

Yeah, both are the same right? Def integ is the area?

[glass lichen]

yes, definite integral is the signed area under the curved bounded by the integration variable axis

[bold token]

welp thx

[sick phoenix]

i need help for q b)

i got $x(x^2+x+1)>0$

[ocean seal]

dumpling

[sick phoenix]

then im not sure what to do next

[gray isle]

consider the result you reached in part a)

[sick phoenix]

i got -3 for 5 a

but im not sure how it comes in

[gray isle]

-3 is miles away from what 5a) asked for

[pseudo summit]

is it right to say that the decimal form of a fraction can never result in a number that is bigger than 1?

[gray isle]

-3 is NOT a proof of anything

[sick phoenix]

b^2-4ac<0

[pseudo summit]

Imaginary numbers goes brrrr

[gray isle]

oh... you meant the value of the discriminant

that alone isn't enough to prove that x^2 + x + 1 is greater than 0
you'd need an additional statement.

however I was referring

to the fact that (x^2 + x + 1) was confirmed to be greater than 0

try and use that in b)

[spark ibex]

can someone help me with this question

[merry coral]

Super-basic question, but my brain is breaking rn:
probability of rolling n amount of heads without rolling 3 tails

[remote heron]

its a binomial

[merry coral]

yeah something like

[remote heron]

i dont totally understand the question

they mean 3 total?

[merry coral]

yeah

[spark ibex]

can someone answer my question? i had my question first

[merry coral]

what is the probability of getting to a certain number of heads without hitting 3 tails

[remote heron]

oh geez sorry ak youre right

[merry coral]

il try

[remote heron]

@merry coral can you move to another channel

[remote heron]

bump

[spark ibex]

huh?

[merry coral]

@spark ibex 's question

"can someone help me with this question"

[remote heron]

these are just two uhh

paraboloids right

have you looked at their traces at all?

yea

theyre the same surface right

well sort of

ones just rotated

idk what else youre supposed to say here

[spark ibex]

what would the x,y, and z traces look like?

is it like an oval for the z trace?

[minor dagger]

can someone help me with these please?

alright, sorry

[tight locust]

what is the formula

for the V of a box?

[inner steeple]

I think it's V(x) = (12-2x)(20-2x)x

[minor dagger]

for the bottom one

[tight locust]

wow thanks for giving away the answer

[inner steeple]

you're welcome

[lost violet]

how can i show that the sequence $a_n=\frac{k^3}{3^k}$ is monotonic decreasing?

[minor dagger]

its finally correct

[ocean seal]

alef0

[minor dagger]

i need help with b and c tho as well

[tight locust]

show that the derivative is always nonpositive

[lost violet]

the thing i cant use derivatives because we have not seen that topic i was trying by induction for im stuck haha

[tight locust]

can you try using the ratio test?

show that k^3/3^k > (k+1)^3/3^(k+1)

[minor dagger]

can you help me with the last two

[minor dagger]

or can you help me

[inner steeple]

if you paypal me $20

[minor dagger]

I wasnt done with my question

[minor dagger]

I am unemployed.

[tight locust]

find when V(x) is greater than 210

get a job lmao

[minor dagger]

how can i do that

[tight locust]

lazy bum

[minor dagger]

do. i plug numbers into the v(x) equation?

[tight locust]

what is V(x)

[minor dagger]

(12-2x)(20-2x)x

[tight locust]

(12-2x)(20-2x)x > 210

[minor dagger]

volume of the box

[tight locust]

expand the lhs

[minor dagger]

what

[tight locust]

the left hand side

multiply it out

[minor dagger]

ooh

like

id ont get it

[tight locust]

do you know how to multiply?

what is (12-2x)(20-2x)?

[minor dagger]

4x^2-64x+240

[tight locust]

now what is (4x^2-64x+240) * x

[minor dagger]

4x^3-64x^2+240x

[tight locust]

4x^3-64x^2+240x > 210

4x^3-64x^2+240x-210 > 0

now find the roots of that polynomial

in the context of the problem, only the positive real answers should make sense

[minor dagger]

so this. is tthe answr?

[tight locust]

no

you have to solve the polynomial

[minor dagger]

ok

[merry coral]

probability of rolling n amount of heads without rolling 3 tails

no one ever came to a good solution for this

[hollow pelican]

for 1g can i leave my answer as this?

[merry coral]

(2x^5) was raised to the power of 1/3

not multiplied by it

[tight minnow]

Its supposed to be raised to that power tho

The answer is correct

[merry coral]

wut

[tight minnow]

It is called the power property

Google it

[merry coral]

ok sure

[tight minnow]

You can take the exponent and put it out in front

[pearl marlin]

try to solve $a_{n+1}-a_{n}$

[ocean seal]

learn4math

[merry coral]

so this is b

thats cool

I learned something

[tight minnow]

Correct

Great

[merry coral]

[tight minnow]

What grade are you in?

[hollow pelican]

ahh

okay

im year 1

[ionic jewel]

this is probably 6-9th grade somewhere

[tight minnow]

Alg 2

[ionic jewel]

might be alg 1 depending on curriculum

[tight minnow]

That is where this concept is learned

True

[hollow pelican]

engineering math 1

[merry coral]

8th grade geometry

logs have never been brought up

for some odd reason

[tight minnow]

You will learn it later

[merry coral]

I still have basic understanding of them

[tight minnow]

Thats good

[merry coral]

when doing charting / technical anylasis I use log charts a lot

[tight minnow]

Oh, cool

[tight minnow]

Seems complex

[merry coral]

for example

[hollow pelican]

thats

very complex

[merry coral]

8th grade btw

[hollow pelican]

oh i dont know whats that

[vital ravine]

<@&286206848099549185>

is this correct?

[merry coral]

yeet I boosted the server

[pearl marlin]

$\sec(\theta)= \frac{1}{\cos(\theta)}$ can you use this

[ocean seal]

learn4math

[vital ravine]

ummm

yeah i mean got the answers

i just need to clarify whether its right or wrong

[pearl marlin]

$\sec (\theta) $ should be $\frac{25}{24}$

[ocean seal]

learn4math

[vital ravine]

oo

[merry coral]

-7/24 should be tan?

[vital ravine]

apart from that is everything good

[pearl marlin]

nop

[pearl marlin]

and this all happning in fourth quadrant because sin is negative and cos is positive

[merry coral]

sin fancy 0 is -7/25, cos fancy 0 is 24/25

[vital ravine]

ok ok i will redo it

please check again

[merry coral]

probability of flipping n amount of heads before flipping 3 tails

I'm trying to calculate odds in the form of 1:x for something

[vale wigeon]

it's not a fancy zero, it's the greek letter theta

[vale wigeon]

this feels weird and undersrated. are you flipping n+3 times in all, or are you flipping indefinitely until you hit n heads or 3 tails, whichever comes first? does "3 tails" mean 3 tails consecutively or 3 tails anywhere in your flip sequence?

[brittle grove]

why is √2/ 2 written as 1/ √ 2?

when in algebra I learnt about rationalization , that we have to eliminate √ from the denominator

[vale wigeon]

we do not.

[brittle grove]

What is the ratio of the side of a square that is inscribed in a circle , to that of the radius of the circle? if we let side of square = 1, then diagonal which is diameter of the circle = √2, so radius = √2/2..so the required ratio =
1 : √2/2
2 : √2

but answer is √2 : 1

[vale wigeon]

these three ratios are one and the same

[brittle grove]

how maam

can u please explain

[vale wigeon]

just as 5:7 is the same ratio as 500:700

so too are the ratios 1 : 1/sqrt(2), 2 : sqrt(2) and sqrt(2) : 1 all equivalent

[brittle grove]

yeah but my problem is I will calculate upto 2 : √2 then I won't find the answer,,how do I know these are the same..

[vale wigeon]

you already have the answer. 2 : sqrt(2) is the correct ratio.

you can multiply both sides of sqrt(2):1 by sqrt(2) and you will get 2:sqrt(2)

[vale wigeon]

these ratios are all distinct

anyway, what you can do is write your ratio in the form 1:x

and compare against b and c

or write it in the form y:1 and compare against a and d

to see what matches

[brittle grove]

ok thank u ann

[tight locust]

is there some sort of rule about derivatives of inverses?

if f(g(x)) = x

[tight locust]

then what can be said about f'(x) and g'(x)?

[hollow pelican]

guys how to simplify this?

[thorn kindle]

is that a z or a 2

[hollow pelican]

2

[thorn kindle]

log(x) + 2log(y) = 3log(2)

?

[hollow pelican]

yes

wait

no

log(x) + 2log(y) = 3log(z)

[thorn kindle]

why would you lie to me?

[hollow pelican]

my bad i didnt see properly

[thorn kindle]

is this even your own work?

[hollow pelican]

yea

[thorn kindle]

log(x) + 2log(y) = 3log(z)
log(y^2) = log(z^3/x)

y^2 = z^3/x

yeah that's all you can say

!

[brittle grove]

when a chord intersect a tangent at the circumference ..does it make 90 degree angle ..or it's only true for the radius?

[tight locust]

you tell me!

[brittle grove]

idk man

I know it makes 90 deg with the radius

[tight locust]

look at the image

please.

[brittle grove]

yeah it looks like it does

[brittle grove]

no' wth

sorry man I am dense

[tight locust]

yeah that sure does look like a 90 degree angle

[brittle grove]

no it does not

[tight locust]

yes.

[brittle grove]

are u being sarcastic

[tight locust]

no

[brittle grove]

ok enough discord for me today

[tight locust]

lol. you can actually prove that the only chord that makes a 90 degree angle with the tangent is the diameter

[brittle grove]

was it that hard man

thanks btw

[tight locust]

i try my best

[young ridge]

How do you eliminate a parameter in parametric equations?

On the interval 0<=t<=4

[jagged imp]

squaring both equations might help you see more clearly how you could do it

[lean bramble]

how do i do this

<@&286206848099549185>

[pearl marlin]

square both then add them

[young ridge]

oo thanks bruv

[pearl marlin]

image is not clear.

[errant dagger]

how tf do i show

(e^2 + 1) / (e^-2 + 1) = e^2?

nvm its ez

[ionic jewel]

do you know how polar integrals work

how so?

[ionic jewel]

the smart way to do this is just use the formula for the area of a circle

$\pi r^2$

[ocean seal]

bunny

itsDaman ඞ

[ionic jewel]

that's cursed

$A=\frac12\int_0^\pi(2\cos\theta-\cos\theta)^2 , d\theta$

[jagged imp]

\theta and \frac{a}{b} for a/b

[ocean seal]

bunny

[ionic jewel]

is what you meant to type

not sure why you squared that or added the 1/2 i don't remember having to do that

[alpine sable]

2cos minus cos

[strong furnace]

The squares should be seperated

[ionic jewel]

I'm ready not sure why we didn't just subtract the area of one circle from the other

pi(1)^2 - pi(1/2)^2 = 3pi/4

it's basic geometry

you want the area in between the two circles

take the area of the big circle, then subtract the area of the small circle

you definitely learned that stuff

just because you can solve something using a more complex method doesn't mean you have to

[ionic jewel]

but either way (afaik) nyannn is right if you wanted to do it this way

[alpine sable]

You can argue that it wasnt stated which method you should use to solve

[pale merlin]

Q- THE POINt P is on the intersection of the two planes given by x + y +z =1 and 3x + 2y +z = 6 which is closest to the origin.

My attempt
I've calculate intersection plane in parametric form like
x = 4 + t
y = -2t - 3
z = t

How do I convert parametric form of plane to standard form?

[ocean seal]

itsDaman ඞ

[strong furnace]

In case you want the way of doing it using integration the formula would be ((2cosx)^2-(cosx)^2))/2 integral of this from 0 to pi

[pearl marlin]

$\frac{e^2+1}{e^{-2}+1}$ $\frac{e^2+1}{\frac{1}{e^{2}}+1}$\ $\frac{e^2+1}{1+e^2}\times e^2$

[pale merlin]

pls have a look at my ques

[ionic jewel]

it's not the same thing

[pale merlin]

i need just some tips

[errant dagger]

ask a question in a channel where a question was not asked 30 seconds before yours

[strong furnace]

No

[pale merlin]

oh ok

[strong furnace]

That would be freshman's dream

[ionic jewel]

$A=\frac12\int_0^\pi(2\cos\theta)^2-(\cos\theta)^2 , d\theta$

[ocean seal]

bunny

learn4math

[strong furnace]

,calc 3*pi/4

[ionic jewel]

,calc 3/4 *pi

[ocean seal]

Result:

2.3561944901923

Result:

2.3561944901923

[ionic jewel]

lmao

you should have used the circle method

[alpine sable]

You should listen to bunnies

[strong furnace]

Circle method is the better method

[ionic jewel]

took me about 5 seconds in my head and didn't have the trouble with all this

this is fair, but always be on the lookout for simpler solutions

[alpine sable]

Simple solutions is how the brain grows

[ionic jewel]

ngl my first thought when i read this was a double integral with f(x,y)=1

then i was like wait this is a circle

that's like saying all numbers are even

becuase it's true sometimes

yeah i suppose it actually makes sense when you derive it from the double integral

hmm

super interesting, just made that connection

you could also solve this problem with

$\int_0^\pi\int_{\cos\theta}^{2\cos\theta} r , dr , d\theta$

[ocean seal]

bunny

[ionic jewel]

so you can see how this simplifies into the "weird" 1/2 integral r^2 dr form

[pearl marlin]

c

[ionic jewel]

do you mean (x-1)/4 or x-1/4

yours reads like the latter

[alpine sable]

He meant first

[ocean seal]

itsDaman ඞ

[ionic jewel]

i know but I'm pointing out that it's wrong

your writing of it was wrong

x-1/4 is not the same as (x-1)/4

you use $\pm$

[ocean seal]

bunny

[pearl marlin]

wait i solve on paper

[ionic jewel]

$\pm(\frac{x-1}4)<1$

[ocean seal]

bunny

[ionic jewel]

so for positive we get x < 5, and for negative we get x > -3

[pearl marlin]

Use libnitz rule for x=-3 and for x=5 it is divergent becuse of harmonic series

[pearl marlin]

that is (-1)^k not -1, alternating sequence of 1 and -1

not -4^k its (-4)^k

k with both -1 and 4

$(-4)^k = (-1)^k \times (4)^k$

[ocean seal]

learn4math

[pearl marlin]

alternating series test

sorry for typo, (great mathematician name its Leibniz's test,)

[uneven root]

Need help, could someone explain my homework to me pls?

[vale wigeon]

isn't this navier stokes??

@uneven root

[uneven root]

What's a nevair steak?

[strong furnace]

Should call the mods I think

<@&268886789983436800>

[vale wigeon]

you sound like a troll, soap.

[sly mantle]

@uneven root don't post troll questions

[uneven root]

Aight

[tight locust]

@uneven root

[uneven root]

Ah hah! At least somebody doesn't mind helping XD

[vale wigeon]

@tight locust is that lowres on purpose?

[alpine sable]

Funny people 👏

[tight locust]

[alpine sable]

How do I factor this:

$x^{3} - 3x^{2} + 3x -1$

[ocean seal]

Bleidorb

[alpine sable]

my books says this is a perfect cube?
but I don't recognise it as a perfect cube?

[vale wigeon]

it is

(x-1)^3

[alpine sable]

but it does not have the form of
a^3 + b^3
or a^3 - b^3?

[vale wigeon]

those aren't perfect cubes

a perfect cube is (a ± b)^3

[alpine sable]

how did you get the x-1?

[delicate bear]

Quick maths

[vale wigeon]

(a+b)^3 = a^3 + 3a^2 b + 3ab^2 + b^3

[alpine sable]

$(x - 1)^3 = x^3 - 3x^{2}(-1) + 3x(-1) + -1^{3}$

[ocean seal]

Bleidorb

[alpine sable]

I need to check this, if I am doing this right.

I forgot that

$a^2 + b^2 \neq (a + b)^2$

[ocean seal]

Bleidorb

[alpine sable]

https://image.slidesharecdn.com/11x1t0105cubics-110204003417-phpapp01/95/11x1-t01-05-cubics-2011-5-728.jpg

[ocean seal]

Akhandanand Tripathi

[alpine sable]

yup

[sacred vigil]

Just try to substitute

Finding the identities are easy if you practice to do so

[alpine sable]

thanks man (:
Ann and Akhandanand .

https://www.dummies.com/education/math/algebra/how-to-factor-the-difference-of-two-perfect-cubes/
why is a^3 - b^3 called a perfect cube 🤔

or is it just a mistake.

[vale wigeon]

a^3 - b^3 is not a perfect cube, it's a difference of cubes

[vague coral]

Someone knows an easier way to prove that $(-1)^n$ diverges ?

[ocean seal]

Herels

[vale wigeon]

do you mean the sequence or the series

[vague coral]

the sequence

[woven sphinx]

easier than what

[vague coral]

I just want a way to prove it that is easy to understand

:/

[alpine sable]

If you accept the fact that if a sequence converges, then any subsequence of that sequence converges to the same thing as the original, then it’s easy

[vale wigeon]

is there a proof you're looking at rn which is hard to understand?

[vague coral]

I saw a proof by contradiction but I didn't understand a single thing

[vague coral]

oh I forgot about subsequence :o

yeah that must be a good idea

[vale wigeon]

did it not boil down to 'if the limit exists, all subsequences will have to approach it too. but the even subsequence is a constant 1 and the odd subsequence is a constant -1, and 1 ≠ -1'

[vague coral]

hmmm that makes sense

thank you guys

[vale wigeon]

did your proof not boil down to that?

[vague coral]

no it was using an other thing

If I want to prove those things now, I'll just use subsequences then

[alpine sable]

guys im having a very basic confusion

Should we put value of 0 normally here or instead ignore that

[pearl marlin]

hope this is question about rational number between -3/4 and 1/3 if yes then you can put zero there

[alpine sable]

yeah it is

thankyou sir

[digital maple]

Can someone help me with 3b)? I already finished 3a but i seem to be stuck on b.

[pearl marlin]

what problem you are facing while solving?

[digital maple]

Do you when you try to reduce the equation to like row echelon form?

It should look like this

but the top middle and middle right part cannot be reduced to 0

or at least i tried to reduce it to 0 but it just wont let me keep the whole thing as reduced echelon form

this is all the work i was able to do so far

[pearl marlin]

no need to look like this just make 1 on piviot in each row

[pearl marlin]

you are trying to make it identity matrix it may not be possible if matrix is singular.

[digital maple]

What does that mean?

are u saying this form can still be correct even if it doesn't look like that?

[pearl marlin]

you have solved the question

[digital maple]

Ohhhh. SO wait my teacher wont say anything if these aren't zeros?

[pearl marlin]

remove the last coluom ,they just said to make rref of cofficient matrix

[pearl marlin]

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

[digital maple]

So my final answer should only look like this?

[pearl marlin]

made -2 zero

[digital maple]

-2 needs to be 0?

[pearl marlin]

yup

[pearl marlin]

i have not checked you calculations i am answering this question on the basis of your last step

[digital maple]

If i turn that -2 into 0 then the 0 next to it turns into 2

[strong furnace]

if you are going fro the reduced row echelon form

only the columns with leading entry = 1 needs to have all other coefficients 0

[pearl marlin]

its ok

[pearl marlin]

that will be your final answer

[digital maple]

alright

thank u so much

[golden bridge]

Hello I'm having troubles with this question
I need to find A,B the information I have are: A is y=2x + 1 and B is y= -0.5X-1 also the AB length is 6 and he answers are the following A ( 0.4,1.8) (-5.6,1,8)

[prime ice]

so i figured out A,B,C but now they ask to determine the value of m and c. I dont fully understand what i have to do

[pearl marlin]

If line is intersection y axis at 3 ,then c is 3 , now y=mx+3, put this in function f , find m

[prime ice]

thanks let try

[golden bridge]

;-;

[prime ice]

should i put it in function f or g?

[glass lichen]

you have 2 points you know are on g(x): (0,3) and C

thus you can find the slope of the line m

[golden bridge]

can someone help me with this

[glass lichen]

distance formula

[golden bridge]

can you send it

oh

nvm I know it

But I don't have the Y or x for either of the points

[glass lichen]

right, yeah

[pearl marlin]

Does they are making a right angle triangle?, Or something more instructions are given in question

[prime ice]

sorry but im still having issues

[glass lichen]

slope formula.

[golden bridge]

No triangles

and no more instructions

[prime ice]

Like this ???

[glass lichen]

how do you know (3,18) is on the line?

[pearl marlin]

These are othogonal lines because their slop product is =-1 , may be we will get a hint from here

[prime ice]

yoh im lost

[glass lichen]

ok well im asking about your work

so if you have no clue what you wrote, why did you write it?

[prime ice]

So I did this for the first question

[glass lichen]

did you arbitrarily pick (3,18) out of thin air?

right.. so (3,0) and (0,3) are on the line

not (3,18) like you made up

[prime ice]

oh ok

let me try again

[glass lichen]

no

[ocean seal]

Mosh

[prime ice]

would -1 = m

[glass lichen]

yes...

$m=\frac{3-0}{0-3}=-1$

[ocean seal]

Mosh

[prime ice]

im really sorry i took so long im genuinly lost my teachers are not the greatest

[pearl marlin]

Both are intersecting at x axis where y is zero so put y=0 , in g it will give you X=+-3, take +3 , now point is (3,0) pUt in line 0= 3m+3 m= -1

[prime ice]

thanks guys sorry but ima be troubling u guys alot more

[pearl marlin]

Its ok , atleast you are learning something

[reef karma]

Which grade question was this?

[prime ice]

11

[reef karma]

Which country?

[prime ice]

south africa

[reef karma]

Oh nice

Ig u have learned quadratic equations and linear equation s?

[prime ice]

no not yet

[reef karma]

I solved this using quadratic equations

It was easier

[prime ice]

ill quicky google a tutorial thanks alot

[glass lichen]

I wouldn't say using quadratics is easier, given they already had C...

[strong wing]

what does this stand for?

[glass lichen]

#old-network and ask in chemistry?

[strong wing]

ah ok srry

[prime ice]

what formula do i have to apply to find D

[golden bridge]

<@&286206848099549185> ;-;

[glass lichen]

Solve for the intersection of the line and quadratic

[prime ice]

how do i do that

[worldly void]

can anyone help me

[pearl marlin]

Intersection of both line and curve. Just put line in curve

[fervent grail]

6x⁴+x³-3x²-9x-4 = 0

Pls help

[worldly void]

<@&286206848099549185>

[pearl marlin]

Roots or factors ?

[fervent grail]

Roots

Rational roots

[fervent grail]

@pearl marlin

[pearl marlin]

I have sloved ,

Just wait

[fervent grail]

Pls send the sol

[prime ice]

im so lost

[fervent grail]

Ohk

[gray isle]

solve
y = 18 - 2x^2 and
y = -x + 3

[reef karma]

How did you already have 3

[prime ice]

first one is y=18

[fervent grail]

How have you done the second step ?

[pearl marlin]

Rational root test,

After that division use karna

[prime ice]

i still dont undertsand

[fervent grail]

Long division method ?

[pearl marlin]

Yes

[gray isle]

have you solved systems of equations before?
found where (in a simpler case) where two straight lines intersect algebraically?

[prime ice]

i have not

[gray isle]

that is a pretty big issue

[fervent grail]

Acc to rrt 6/4 ke factors uske roots ho skte hai pr uske baad ka smjh me nhi aya🥲

[gray isle]

have you solved quadratic equations before?

[prime ice]

no

[gray isle]

ugh...

how did you find C?

[fervent grail]

Uske baad ka thora sa explain kr skte ho pls🙃

[fervent grail]

@pearl marlin

[gray isle]

well what you did there was solving a relatively simple system of equations involving a quadratic

[prime ice]

ok

[gray isle]

i.e for B, C,
you were effectively solving the system
y = 18-2x^2 and y=0

[prime ice]

ok let me quicky try

[gray isle]

similarly, here the system you want to solve is
y = 18-2x^2 and y=-x +3

[alpine sable]

hi

[gray isle]

ugh...

[fervent grail]

Ramanov can u pls help me in this.......

[gray isle]

you're going backwards

[prime ice]

what x value would i use

[pearl marlin]

It will take time , i have to make its rrots properly.

[gray isle]

the x value of D is what you're trying to find

have you done stuff with substitution before? or familiar with the transitive property of equality?

[prime ice]

i have

[alpine sable]

anyone here from malaysia I need help wit my math

[gray isle]

apply that to:

y = 18-2x^2 and y=-x +3

[fervent grail]

Okay pls send me when u will complete

[abstract breach]

[prime ice]

so x is 3 right

[reef karma]

I got x as -5/2 in D

[gray isle]

x = 3 is one of the solutions to that system,

which you already have, (i.e point C)

[reef karma]

Is this correct?

[gray isle]

you are interested in finding the other solution (that's according to the graph, less than 0, for the coordinates of D)

have you done stuff with substitution before? or familiar with the transitive property of equality?
i have
apply that to:
y = 18-2x^2 and y=-x +3
currently what I'm asking of you requires a single step

don't overthink this part

[prime ice]

hmm

[prime ice]

yeah no i dont understand

[gray isle]

have you done stuff with substitution before? or familiar with the transitive property of equality?
you said you have

do you know the basic idea of substitution?

[prime ice]

no

[gray isle]

you can replace something with something of equivalent value

transitive property of equality
is pretty intuitive too

things equal to the same thing are equal

[prime ice]

ok

[gray isle]

and here since you are looking for values where:

y = 18-2x^2 and y=-x +3
and either by substituting the value of y from one equation into the other,
or noticing that both 18-2x^2 and -x +3 are equal to y,
that logically leads to the equation
18-2x^2 = -x + 3

[plucky crow]

ramonov

[prime ice]

ok i get this

[gray isle]

would you have been able to arrive at that without my explanation?

[prime ice]

nope

Would I solve like this

[plucky crow]

huh

[gray isle]

no wtf how

[fervent grail]

6x⁴+x³-3x²-9x-4 = 0
How to factorise it ?

[uneven root]

Can't do 2x^ - x

@prime ice

[prime ice]

Ok let me retry

[gray isle]

this is a quadratic equation

[plucky crow]

@prime ice you can not mix x^2 and x

you can not add x^2 and x

[fervent grail]

6x⁴+x³-3x²-9x-4 = 0
How to factorise it ?

[plucky crow]

you can not - x^2 and x

[gray isle]

you can rearrange into general form
and then factorise or be lazy and apply QF

but I'm highly recommend that you put this on hold, and go back and review basic algebra as you're heavily ill equipped to solve these types of problems

[fervent grail]

6x⁴+x³-3x²-9x-4 = 0
How to factorise it ?

[rocky tinsel]

Hey, what's a one sentence answer as to why you cannot log negative numbers

[gray isle]

rational root theorem
combined with polynomial long division / synthetic division

[uneven root]

@prime ice basically, the variable AND power have to match to add or subtract

[plucky crow]

oh hi hannah

lol

[torn glacier]

can i ask a question here

[prime ice]

oh ok

[rocky tinsel]

hhiiii syphax :))

[gray isle]

logs aren't well defined for negative arguments

[rocky tinsel]

wdym by well defined

[torn glacier]

how can i calculate this if im given f(x)'s and f'(x)s graphs?

[uneven root]

Substitute the equations for f' and f (please correct me if i'm wrong lol)

[prime ice]

would i factorize

[plucky crow]

you wouldnt get real solutions ig

[prime ice]

write it like this −2x^2 + x + 21 = 0

[torn glacier]

wdym

[uneven root]

You'd get 2 answers for x since it's quadratic so yeah, you need to factorize

[prime ice]

ok so x=-3 and x=3.5

[gray isle]

−2x^2 + x + 21 = 0
isn't right

[prime ice]

eish

[gray isle]

how are you getting that from:

18-2x^2 = -x + 3

[prime ice]

−2x^2 + x + 15 = 0

[gray isle]

yes

and then factorise or be lazy and apply QF

[prime ice]

so

(2x+3)(x+5)

[gray isle]

no

[prime ice]

is my eqaution even possible to factorise

[gray isle]

your quadratic is definitely factorisable

if you're not confident with your factorisation skills

be lazy and apply QF

[prime ice]

eish

ima take a break

ill be back later

[uneven root]

You're really really close, you just missed 2 things and you've got it

[gray isle]

wlog (2,4) and (4,2) would be considered the same solution
usually for something like this, you'd assume something like a > b or b > a

there are also infinitely many solutions if you're allowed a=b

[prime ice]

x=-3

or x=5 over 2

[gray isle]

not quite

how are you getting those?

[prime ice]

i factoised 2x^2+x+15=o

[uneven root]

wasn't it -2x^2 +x + 15 = 0

You can't just throw away the "-"

[alpine sable]

do you guys know any science server

looking for a specific science?

go to the explore public servers

and search science

we do have some connections

#old-network

@alpine sable

i did

but i got banned lol

for no reason

from that stem thing

same

got banned last year

cause i evaded ban

messed with the mods

uh was being annoying

but i was popular with some people

ig

2 months ago when i needed help so i asked qs and they thought i was trolling

got a question to ask here though?

no

[alpine sable]

i'm writing a paper on dark matter

mk

what does that mean

@alpine sable join homework help server

thank

u

[brave fossil]

im not sure what do do here

[pearl marlin]

$A^{3}+A^{2}=I$ \ take inverse on both sides we will get A^{2}+A=A^{-1}$ i'm considering that A is invertible

[ocean seal]

learn4math
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[brave fossil]

what do u mean take the inverse of both sides

(A^3+A^2)^-1 =I^-1?

[pearl marlin]

multiply inverse of A on both sides

[brave fossil]

ohhh i see

ffs what a stupid question

cheers big man

<3

[sudden tulip]

hi

anyone can teach me how to find intercepts

[novel granite]

X intercept is the point where the line touches X axis ie where y=0 and similarly for y intercept

[sudden tulip]

ok

[lucid ember]

can anyone explain how this is true?

[merry coral]

probability of flipping a total of n amount of heads before flipping a total of 3 tails (you stop when either condition is met).

I need odds in the form of a decimal

[noble sinew]

start for n=1,2,3 then deduce a general formula after

[merry coral]

ok bet here are some rough numbers

[noble sinew]

I meant actual exact calculations not a simulation

[merry coral]

3 is obvi 50%

[noble sinew]

you can't deduce a formula from that

[merry coral]

you can check your work doe

[proven flare]

Hey guys I have a question, why are power functions considered transcendental?

Also are all periodic functions trancedental?

[merry coral]

t t t
h
t h
t t h

[proven flare]

?

Also where do you place reciprocal functions?

Like is it under rational functions?

[merry coral]

this problem is harder than I thought

there are only 4 ending possibilitys:
zero tails (yay)
one tails (yay)
two tails (yay)
three tails (sad)

but the probability gets scewed

Going for one heads odds are 7/8

Three odds are 4/8

[noble sinew]

heard of binomial distribution?

you wont get anywhere if you just simulate anyway

[merry coral]

yesn't

that would be plotting all values of n right?

forming an arc I think

[noble sinew]

that would be calculating it exact instead of simulating it

and would allow us to find a formula for n

[merry coral]

[proven flare]

Oh well I guess my question is just there, do you guys know here I should post it?

*where

[prime badge]

there are 3 positive outcomes (n+2 flips, n+1 flips and n flips) and a lot of negative ones (3, 3+1 ... 3 + n − 1)

tricky one

[noble sinew]

if you start calculating it exactly (not simulating!) for n=1,2,3

the answer should follow

[proven flare]

https://www.quora.com/What-is-the-expected-number-of-coin-flips-until-you-get-3-heads-in-a-row

Maybe this will help?

[prime badge]

i mean it's a lot of work to do n = 1,2,3

[noble sinew]

it isn't

with binomial distribution

[merry coral]

probability of flipping a total of n amount of heads before flipping a total of 3 tails (you stop when either condition is met).

I need odds in the form of a formula

[prime badge]

n=1 is 4 different lengths

[merry coral]

we have another condition doe

[noble sinew]

im aware

[prime badge]

so, that's a lot of work

[merry coral]

yesn't

[noble sinew]

no

[prime badge]

i'm literally not gonna do it

[noble sinew]

didn't ask you to do it

[prime badge]

i mean it as evidence lol

[noble sinew]

and it would take me 1 min to find for n=1,2,3

[merry coral]

and....

just trying to calculate odds for a game I made lol

anyways, ping me I gtg

[noble sinew]

so for n=1 the prob of flipping 1 head before 3 tails is 1- the prob that we hit tails 3 times - agree?

that we can calculate with binomial distribution

1-dbinom(3,3,0.5) is for n=1

(or type pbinom(2,3,0.5))

[merry coral]

agreed

[noble sinew]

for n=2 you can do 1-(dbinom(3,4,0.5)+dbinom(4,4,0.5))

[merry coral]

how can I graph this

[prime badge]

1 = 4/5
2 = 10/16
3 = 20/42
4 = 35/99
5 = 56/219

idk what's the pattern

[noble sinew]

your probabilities are wrong and there is a pattern in the formula

[prime badge]

which one is the first wrong one?

[noble sinew]

4/5 is wrong

[prime badge]

good

easy to check

[noble sinew]

here you go

@prime badge @merry coral

[drifting mural]

ohh nvm

i got it nvm the question

[alpine sable]

What's this GUI?

[noble sinew]

RStudio

[alpine sable]

Thanks

[safe jacinth]

This is probably more of an Excel question. But maybe not really... In Excel I can generate a random number with RANDBETWEEN(). But this will generate a number within the specified interval with an equal probability for any number. Is it possible to apply some kind of bell curve-like probability for the generation of numbers within the interval? For example If RANDBETWEEN(1;100), I would like 50 to be the most probable outcome and 1 or 100 to be the least probable. And if possible, I would like to be able to adjust the "probability curve" so that it isn't necessarily a normal distribution.

[vale wigeon]

youre gonna need to be a little more specific about what distribution you're looking for here.

[safe jacinth]

I don't know how to be more specific. Can you make an assumption and provide an example?

[vale wigeon]

sure...

you want to generate numbers between 1 and 100, right?

so no zeros

[safe jacinth]

Sure

[vale wigeon]

RANDBETWEEN(1,50) + RANDBETWEEN(0,50) will do the job, i think

tho it will have both 50 and 51 as modes

but it will have the property that values toward either end of 1:100 are less likely

[safe jacinth]

Damn that was not at all what I expected, but that might be quite genius.

I will test it out, Thanks

[hollow pelican]

guys how do u do this? im confuse

[small pumice]

Question 45 please

<@&286206848099549185>

[abstract breach]

[small pumice]

<@&286206848099549185>

[prime badge]

thank you

for n=2 you can do 1-(dbinom(3,4,0.5)+dbinom(4,4,0.5))
was that wrong?

[noble sinew]

they are equivalent

[prime badge]

maybe i don't understand what's dbinom

[noble sinew]

just nicer to look at the other formula because otherwise for larger n it gives a very big expression

[prime badge]

is 1-(dbinom(3,4,0.5)+dbinom(4,4,0.5)) same as (dbinom(0,4,0.5)+dbinom(1,4,0.5)+dbinom(2,4,0.5))?

[noble sinew]

yes

[prime badge]

oh

i got it

[sly escarp]

Hi, i need to find multiplicative inverse of 13 mod 79

Ive tried a method but am confused :- 79 = 13 * 6 + 1. where di I go from here?

[prime badge]

you write 6 as answer

[sly escarp]

oh that's it, thank you very much

[prime badge]

wait

i write first, think later

no, that's not right

[sly escarp]

I saw a lec on yt and it said you do this backward chaining till you hit 1 at the right, I hit in first step

[prime badge]

it has to be minus 1

[sly escarp]

any idea how can I get there?

[tender geyser]

this might sound pretty dumb now but:
a local minimum is a minimum within a certain interval
whereas the minimum or global minimum is the minimum value across all numbers

gimme a second to illustrate it 😄

in this example, the global minimum is obviously to the left because its overall the lowest value

but lets say you only look at positive x
then the local minimum is to the right (because we dont care about anything thats to the left of x=0)

correct!
and the global minimum would be -inf because it goes to -infinity in one of the directions ^^