help-23

[safe parrot]

they even show an example of it

where they have n = 7 which is the stars

and k = 3 because we have 3 "boxes" / 3 parts / 2 lines

[covert yoke]

Ok, and the formula in that case is (n-1)C(k-1)

Which gives 16C3

For your problem

[safe parrot]

Oh

Is there several different versions of the formula for stars and bars?

[covert yoke]

They are two major ones, the version where there are no empty bins, and the version where there might be empty bins

[safe parrot]

Oh i see, so it's necessary for me to memorize them to be able to solve similar problems in the future

[covert yoke]

And the formulae given for each case should otherwise be exactly the same, provided the variables are defined in the same way

I don't have the stars and bars formula memorized

I just figure it out

[safe parrot]

what? o.o

How hahah

[covert yoke]

I just remember how the problem is formulated

[safe parrot]

This is so out of this world complicated

i really wish i understood

i sincerely dont

what do i need to do to be able to solve them myself?

[covert yoke]

Practice

[safe parrot]

Do i learn by not being able to solve them?

I'm not entirely sure if practice works

[covert yoke]

You learn by looking at examples and following along and then trying problems for yourself

[safe parrot]

I've spent roughly 36 hours the past 3 days now trying to learn combinatorics

And i'm still not able to solve a single one

People keep telling me that it will "click"

But i'm still as clueless now as i was over a year ago

[covert yoke]

I understand that you're frustrated, but surely you're overlooking things that you have learned and progress that you have made

[safe parrot]

I really wish that was the case

[covert yoke]

Well, at the very least you seem comfortable with the binomial coefficient

For instance

[safe parrot]

What's the binomial coefficient?

[covert yoke]

$\binom{n}{k}$

[flat frigate]

OmnipotentEntity

[safe parrot]

that i know n is the total and k is the "choose" ?

[covert yoke]

Right

[safe parrot]

hmm i got it wrong again

[covert yoke]

???

[safe parrot]

I dont think i am able to determine this

[covert yoke]

That's just a formula you can look up, or derive if needed

[safe parrot]

Determine the number of integer solutions to the inequality \ $x_1+x_2+x_3+x_4 < 40$ that satisfy the following conditions \
a) $x_i \ge 0 for i = 1,2 \dots , 5$

[flat frigate]

Merineth

[safe parrot]

I am honeslty not able to solve any correctly

here i have 4 boxes, x_1. . x_4

and i have 39 stars (since it has to be less than 40)

the condition a just says that there has to be 0 or more in each box

So i assumed n = 39 , k = 4

[covert yoke]

In this case if you have n = 38 it works as well

And n = 37

And so on

[safe parrot]

Yeah but if we choose 39 we get all the possible solutions ?

[covert yoke]

Only if you introduce a "leftover" box

[safe parrot]

so the number of possible solutions vary based on how many n we have?

n is between 0 and 39?

[covert yoke]

So think about it this way instead

If n < 40, and we add in a 5th box, then we can use n = 39

And 5 boxes

So if the first 4 boxes sum to 38 the 5th box will take the leftover 1.

If the first 4 boxes sum to 25 then the 5th box takes the leftover 14

Now we have a situation where we know how to approach it. We got rid of the pesky inequality

I get the feeling that I've lost you

[safe parrot]

mhm

i have no idea what you are talking about

[covert yoke]

Ok let's do a smaller version of the same problem, it's a common trick to make sure the approach works

Let's say I have x1 + x2 + x3 < 5

[safe parrot]

Ok

[covert yoke]

Now, let's count, we can have (0, 0, 0), (0, 0, 1), (0, 0, 2), (0, 0, 3), (0, 0, 4), (0, 1, 0), (0, 1, 1), (0, 1, 2), and so on

It's a little tedious, but you can just count them

[safe parrot]

Yeah

[covert yoke]

Now notice that the sum of each is either 0, 1, 2, 3, or 4.

If I were physically putting balls into bins, I would need at least 4 to do all combinations

So let's say I have 4 balls

I make (1, 2, 0) and I add it to my sheet

There's 1 balls in bin 1, 2 balls in bin 2, and no balls in bin 3, with 1 ball leftover

[safe parrot]

hmm ok

[covert yoke]

So what if I have a bin that I'm pulling these balls from?

[safe parrot]

(0,0,0),(0,0,1),(0,0,2),(0,0,3),(0,0,4),
(0,1,0),(0,1,1),(0,1,2),(0,1,3),(0,2,0),
(0,2,1),(0,2,2),(0,3,0),(0,3,1),(0,4,0),
(1,0,0),(1,0,1),(1,0,2),(1,0,3),(1,1,0),
(1,1,1),(1,1,2),(1,2,0),(1,2,1),(1,3,0),
(2,0,0),(2,0,1),(2,0,2),(2,1,0),(2,1,1),
(2,2,0),(3,0,0),(3,0,1),(3,1,0),(4,0,0).

[covert yoke]

I'm transferring them from the initial bin to bin 1, etc

That means (1, 2, 0) is really (1, 2, 0, 1)

We secretly have 4 bins instead of 3

And we don't have an inequality, but an equality

[safe parrot]

[covert yoke]

You can see how x1 + x2 + x3 < n implies there exists an x4 such that x1 + x2 + x3 + x4 = n-1

Where all xi are non-negative and integer

[safe parrot]

No... i'm not smart enough i can't see it..

[covert yoke]

Well, unfortunately it is noon here and I have an appointment, so I do need to go

I'll try to flag down another helper

[safe parrot]

It's ok, thanks for your patience

.close

[safe radish]

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[safe radish]

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[indigo ruin]

.close

.claim

.reopen

[bitter monolith]

Can anyone explain how this equation led to f(x, y) -> 0?

are we supposed to set m or x to infinity?

[uneven agate]

x is approaching 0 as given originally in the example

[bitter monolith]

so set x to 0?

[uneven agate]

while solving for limits, its not ideal to think of it as setting x to 0 (you must think of x as slowly reaching 0 and the unique value it approaches as it gets closer to 0) but it works here, yes

[bitter monolith]

got it.

.close

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[noble frigate]

can someone explain the significance of the central limit theorem and how it's applied in real life?

[pseudo flax]

i don't even know what this is

[noble frigate]

lol

[pseudo flax]

i think i know what this is now

wdym how it's applied in real life

https://www.khanacademy.org/math/ap-statistics/sampling-distribution-ap/what-is-sampling-distribution/v/central-limit-theorem

[safe radish]

@noble frigate Has your question been resolved?

[noble frigate]

like how statisticians apply the theorem in real life

i don't get what it's used for/how it's useful

my textbook says a sampling distribution of sample means results from finding the means of every possible sample of size n from the population

which to me seems impractical

[safe radish]

@noble frigate Has your question been resolved?

[fathom adder]

Casinos

And physics

[fathom adder]

The interresting part is the way of proving and the multiple cases it opens

[safe radish]

@noble frigate Has your question been resolved?

[noble frigate]

not sure what this means

[fathom adder]

The result is not always the only thing useful, sometimes a proof involve new mathematic tools, which can be useful for other domain, or lead to another new domain (sometimes but more rarely now)

In central limit there a 50/50 between result and proof in terms of useful things in real life

The result is useful to study many random variables following probability law, economics and meteo are using those

And the way of prooving leads to some nuances in the central limit, so there is some new varient of it, useful in more theorical domain (statistic physics, boltzmann equation and stuff)

Thats what it means

The most easiest and lookable apply is the wall with marbles dropping and bouncing.

Where you have a gain at the end

Casinos using it such as extreme right and left are the best prize

Cuz indeed its the more rare to win according to central limit

( I dont remember if its binomial or normal law)

[safe radish]

@noble frigate Has your question been resolved?

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[past trench]

SOME ONE HELP

[past trench]

lol

[safe radish]

Please do not trust ChatGPT or similar AI tools for mathematical tasks, as they often generate output which "sounds correct" but has numerous factual or logical errors. Use of these AI tools to answer other people's help questions is strictly against server rules (see #rules).

[past trench]

lmao

tbh i saw a vid and thought

wtf gpt

[light shoal]

file under "not even wrong"

[split fulcrum]

hi bungo

[safe radish]

@past trench Has your question been resolved?

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[visual swift]

,rotate

[visual swift]

,rotate

[visual swift]

,rotate

[visual swift]

Having trouble with 16.

the probability that both are at the fair is (36-8-12.5)/36 = 31/72

so that's the denominator

but the probability of both conditions is a straight line

so P=0/

?

It doesn't feel right though because they're both there for an interval

Or is it because I'm only counting when they arrive and not the time they're there

[safe radish]

@visual swift Has your question been resolved?

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[cobalt tapir]

is this true?

[vocal briar]

(x-1)^n != n!

[cobalt tapir]

i want to solve b

idk how

[covert yoke]

@vocal briar I think you're missing that the nth derivative is taken, and the resulting function is evaluated at 1.

[vocal briar]

Oh....yea

Oops

[covert yoke]

@cobalt tapir I would need to verify, but it doesn't seem impossible to me

[cobalt tapir]

could you pls?

i mean is it true that (x-1)^n = n!

if so, why?

[covert yoke]

That's not true

What is true is the nth derivative of that expression evaluated at 1 is n!

Or might be true

[cobalt tapir]

could you work it out?

[covert yoke]

Is there more context north of the passage you posted?

Just want to make sure I'm not missing something

Like the original statement of the problem

It seems like what you posted is a solution, but I just want to make sure it's not a fragment of the solution

[cobalt tapir]

this is all their is to it

[covert yoke]

It might be easier for you to examine the derivatives yourself

Rather than going through the Taylor series

What is the derivative of 1/(2-x)?

Hint chain rule

And power rule

[safe radish]

@cobalt tapir Has your question been resolved?

[cobalt tapir]

1/(2-x)^2

using usub

[covert yoke]

Ok, what is the derivative of c/(2-x)^n for some constant c and some integer n?

[safe radish]

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[cobalt tapir]

.reopen

[safe radish]

✅

@cobalt tapir Has your question been resolved?

[safe radish]

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[clear sapphire]

I need help with this physics question

[clear sapphire]

.rotate

,rotate

[clear sapphire]

this is what ive done so far

<@&286206848099549185>

[woven hound]

$V_{fx}$ should just equal $v_{ix}$

[flat frigate]

Ari

[clear sapphire]

What?

no its not

the answer is C

which is not vix

[woven hound]

I'm not saying that's the answer

I'm saying that the final x-component of velocity equals the initial x-component

only the y-component changes

[clear sapphire]

ohh ok thank you

but how does that help me solve the problem?

[woven hound]

Since we're doing 2D motion, you need to find the x-component and y-component of the final velocity

The y-component is what you wrote on your paper

[clear sapphire]

oh ok

[clear sapphire]

which formula do i use?

[woven hound]

It's basically just the pythagorean theorem at the end once you get vfx and vfy

[clear sapphire]

ohhh i get it now ill try it thanks for the help

@woven hound

i still didnt get the right answer

[woven hound]

damn

$v_{fx} = v_{ix} = 120 \cos{35^{\circ}}$

[flat frigate]

Ari

[woven hound]

$v_{fy} = v_{iy} - 9.8t = 120\sin{35^{\circ}} - 29.4$

[flat frigate]

Ari

[woven hound]

did you get those

[safe radish]

@clear sapphire Has your question been resolved?

[clear sapphire]

,rotate

[clear sapphire]

This is what I got

@woven hound

[woven hound]

,wolf \sqrt{(120cos(35))^2+(120sin(35)-29.4)^2}

wait no

it should be adding 29.4 my bad

wait

no

I was right the first time lmao

[flat frigate]

Results provided by WolframAlpha

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

Requested by woshiari

[clear sapphire]

Yah lol

[woven hound]

anyway you should be getting this

[clear sapphire]

What’s 29.4?

[woven hound]

9.8t

[clear sapphire]

What did i do wrong here?

[clear sapphire]

Oh ok

[woven hound]

I'm not sure

did you make sure you also squared 120

[clear sapphire]

Oh ok thanks for the help tho

[woven hound]

when you squared 120*cos(35)

[clear sapphire]

I’ll try again on my calculator. But do the calculations look fine?

[woven hound]

assuming 39.43 is what you get for v_fy then yeah

,wolf 120sin(35)-29.4

[flat frigate]

Results provided by WolframAlpha

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

Requested by woshiari

[woven hound]

yeah

[clear sapphire]

But I’m not getting the right answer

I do vfx squares plus vfy squared

And then square root answer

And I get 40

.close

[safe radish]

Channel closed

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[clear sapphire]

Wait @woven hound

I don’t understand why I’m not getting the right answer

I’m doing the same calculations as you but in a different way

120cos35 squared plus 39.43 squared

And then I square root it and I get 40

Answer should be 106

[woven hound]

Do (120cos35)^2

[clear sapphire]

80.52

[clear sapphire]

Then what?

[woven hound]

everything else the same

I think you're forgetting the parentheses which is why your answer is way lower than what it should be

[clear sapphire]

Ohh that was it

Tysm for the help

I got the answer

.close

.close

.reopen

[safe radish]

✅

[clear sapphire]

.close

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[fierce pewter]

pls help

[fierce pewter]

i dont understand how to do it

nvm smomen helped me

.close

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[rare token]

hi

[safe radish]

@rare token Has your question been resolved?

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[livid crow]

could someone help me understand how to solve this sat question bc the collegeboard explanation makes no sense to me

[old chasm]

y-intercept is what?

what do you do when you want to find y-intercept of a line?

[livid crow]

just set x=0 right?

[old chasm]

yes

and by setting x = 0, you get....

[livid crow]

k=5?

[woeful flower]

yo gang could some1 please tell me what this question is im lost ash

[old chasm]

there you go.

[safe radish]

Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).

[woeful flower]

alr mb

[livid crow]

so how would i find b using that info?

[old chasm]

well, you know two points, you can create a line

because k = 5, that means you know that the line passes (5,13) and (12,-15)

[livid crow]

yea

was there a way to find y intercept using 2 points and slope? since desmos doesnt want to give me a line just a segment

i used the slope formula for slope

[old chasm]

I usually use $y-y_1 = m(x-x_1)$

[flat frigate]

nobody

[old chasm]

for point (x1,y1)

[livid crow]

oh yea i forgot that formula existed

y-13=-4(x-5) and just simplify

[old chasm]

so substitute that in, solve for the intercept and you got b

yes

[livid crow]

lemme try that rq

oh so i get y=-4x+33

which is the answer (b=33)

[old chasm]

yep

[livid crow]

tysm

.close

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[broken pecan]

I don't get why arccos is able to be to 7pi/4 when its range is only between 0<=x<=pi?

[old chasm]

there are different way to define the "inverse" here. The range of that is there to make arccos a function

because think about it... let say I want to solve cos(x) = 0, putting that to arccos(0) will results me in one value. However, you know that cos(2pi+x) = cos(x).

therefore x = arccos(0) + 2kpi

[broken pecan]

im so lost

so am I not supposed to use the function range and only go for the signs that make it valid (pi/4 and 7pi/4 being both positive for cos)

[old chasm]

well, would you say x = 5pi/2 a solution for cos(x) = 0?

that is the point, you don't care about arccos. You, however, care about the inverse of cosine

arccos is inverse function that only yield one inverse. But you know that there are multiple inverses as cosine is periodic function

therefore to find all the x, yes. you need to ignore the range of arccos

because arccos can only give you one inverse

[broken pecan]

hmm so arccos is not the inverse of cos? or rather its onlt the inverse for one value which would be between those bounds

[old chasm]

arccos is inverse of cosine. but not entire inverse

because arccos is function

it only map to one value

but you do know that multiple angle can get to the same cosine value

[broken pecan]

Wouldnt that mean that it would keep going if there are no bounds? how would I know that the number of x's are suffiencent?

or is 2pi the cap

[old chasm]

yes. it will repeat. In fact, there are infinite number of angles that satisfying the solution

but you can use the fact that cosine is periodic function (cos(2pi+x) = cos(x))

[broken pecan]

hmmmm gotcha, im assuming the first two are typically all I need then

[old chasm]

If you can get the first two, you can get the rest

by adding 2kpi to it

[broken pecan]

OHHHH

I was so lost on what the 2kpi did

ok that makes so much more sense now

thank you math guru 🙏

I felt like I had an ephiphany 😭

thats all I needed help on, again thank you

.close

[safe radish]

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[broken pecan]

.resolved

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[gaunt oracle]

I need help reviewing for calc exam

[gaunt oracle]

i just want someone to help me with this review sheet

[hardy lion]

!nopdf

[safe radish]

Please post images (such as PNGs or JPGs) of the question rather than other filetypes such as PDFs which have to be downloaded. Non-image downloads can potentially contain viruses or other security risks.

[gaunt oracle]

it might take a while, if anyone is available to help plz ping me

[safe radish]

@gaunt oracle Has your question been resolved?

[gaunt oracle]

.resolved

.close

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[wispy vortex]

hello can someone help me check a few of my answers

[wispy vortex]

radius length is 13

I first found the center point

took one of the points from the diameter line

then did

d = srt(x^2-x^1)^2+(y^2-y^1)^2

which is

srt(-10-2)^2+(6-1)^2

so

srt144+25

srt169

radius is 13

<@&286206848099549185>

[lean otter]

d = sqrt( (-10-14)^2 + (6- -4)^2 ) = 26
so, yes, r is indeed 13

[wispy vortex]

ok

can you check 2 others with me

[lean otter]

You mean 2 other problems?

[wispy vortex]

yeah

[lean otter]

Ok, just show them to me then. However, sorry if I cannot reply promptly. It is either due to family emergency or homework in my university

[wispy vortex]

this one I think I just put in y

[wispy vortex]

ok

so here

just putting in y to the equation

(x-1)^2 +16 = 25

(x-1)^2 = 9

then

(x-1)^2 = srt9

x-1 = +-3

idk how to do plus minus symbol

[lean otter]

(x-1)^2 + 4^2 = 25

[lean otter]

I think you should since there are 2 different answers, right?

[wispy vortex]

no

i don't know

how to type it on keyboard

that's what I meant

so I'm going to just say +-

x = 1 +- 3

[lean otter]

(x-1)^2 = 25-16
(x-1)^2 = 9
(x-1) = +-3

x1 = 3+1 = 4
x2 = -3+1 = -2

[wispy vortex]

yeah

[lean otter]

I don't think you need +- symbol anymore

[wispy vortex]

ok

[lean otter]

just (4, 2) and (-2, 2)

[wispy vortex]

last one

[lean otter]

I think what you did is all good

[wispy vortex]

ok

[lean otter]

ok. let me check...

[wispy vortex]

this one I just need to find midpoint

I did

(-6+2/2 , 5-1/2)

so

[lean otter]

( (-6+2) /2 , (5-1) /2)

[wispy vortex]

-2,2

[lean otter]

Right.

What more can I help?

[wispy vortex]

hm

for this one I got

y-3 = -2(x-5)

the formula

we are suppose to write it in

is

y-y1 = m(x-x1)

so x1,y1 is the midpoint

midpoint is 5,3

slope of the original line

is 1/2

but negative reciporical

procal

is

-2

[lean otter]

I give you screenshots from what I type in MS Word. It is clearer than typing on Discord directly.

[wispy vortex]

ok

[wispy vortex]

is the bottom right picture

slope intercept form

[lean otter]

Yes, depend on what the quiz or assessment interface ask

[wispy vortex]

and the top right picture is point slope form?

[lean otter]

Yes, first you input into point slope then solve it in slope intercept

[wispy vortex]

yea

they just ask for point slope form

[wispy vortex]

thank you for your help

.close

[safe radish]

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[safe radish]

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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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[hexed widget]

help me idk what to do after adb = bdc

[hexed widget]

proofs

[white umbra]

please don't ping helpers before 15 minutes

[safe radish]

@hexed widget Has your question been resolved?

[hexed widget]

<@&286206848099549185>

[sleek plank]

what does it mean if BD is a bisector

[hexed widget]

ad = dc?

[sleek plank]

yes

which means the triangles have atleast one equal side and one equal angle

do you notice another side the triangles share?

[hexed widget]

ab = bc since they perpendicular bisector form isosceles triangle

[sleek plank]

they both share bd

since it's the same exact side

which means that the 2 triangles share a side, an angle, and another side

[hexed widget]

how do i prove that angle bad = angle bcd though

[sleek plank]

you don't need to tho, since you've proved angle adb = cdb

[hexed widget]

no

thats not bad = bcd

[sleek plank]

you don't need to prove they're equal

[hexed widget]

what but its asking me to

[sleek plank]

oh i thought that meant triangle

although this still works

[hexed widget]

ohh its ok

[sleek plank]

since the 3 things we found earlier can help us prove that the 2 triangles are equal

which would then mean the corresponding angles are equal

[hexed widget]

cant i say this

and then angle bad = angle bcd since isoscdeles triangle have equal angle base

[sleek plank]

uh i feel like you have to prove it's isoceles first

but otherwise yea

[hexed widget]

like ab = bc since perpendicular bisector form isosceles triangle

[sleek plank]

idk if that's sufficient enough
i was thinking more along the route of using pythagorean theorem

since the half triangles are right triangles and have the same legs

which means they have the same hypotenuse

[hexed widget]

okayy rtyyy!!

.close

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[tender shore]

Find a polynomial function​ f(x) of degree 3 with real coefficients that satisfies the following conditions.
Zero of 0 and zero of 2 having multiplicity​ 2; ​f(3​)equals18

[quiet plume]

You have the roots, so if we write $f(x) = a(x-r)(x-s)(x-t)$, what would r,s,t be?

[flat frigate]

Azyrashacorki

[tender shore]

i got 2x^4-8x^3+8x^2 but it was wrong at this point I just need the answer

[quiet plume]

That would have a root of multiplicity 2 at 0. And your polynomial has degree 4.

[tender shore]

I dont know what that means does anyone know the actual answer?

Ive been pluging this thing in for hours now

[quiet plume]

The pointing isn't to give you the answer.

[quiet plume]

Find r, s and t that give a root of 0, a root of 2 and another root of 2, and then plug in 3 to solve for a.

The roots of that equation are exactly r, s and t.

[safe radish]

@tender shore Has your question been resolved?

[safe radish]

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[sick violet]

I need help with this problem

[sick violet]

I'm stuck because it has to be simplified more and i dont know how to add these two numbers (after 5) because they dont share the same base

[flat frigate]

faiyrose

[sick violet]

HI

OMG THANK YOU

huh

OH

THANK YU

wait no im confused

this is 1/3cbrt2

[flat frigate]

faiyrose

[sick violet]

Yes

2 to the power of 5/3

[flat frigate]

faiyrose

[sick violet]

can you help me combine these together

I'm forgetting how

im losing my mind

[flat frigate]

faiyrose

[sick violet]

so combine the 1/3 and 5/3 because they are multipied?

wait nvm its addition. cant

Yes

so 2^-1/3

[flat frigate]

faiyrose

[sick violet]

5+2^4/3

wiat no

yes

i realized.

2?

wait no

explain what u mean by factoring

Yes

i dont know if i take out the coefficient or the exponent

2^1/3?

wait no

2^-1/3

so then it iwll be 1_

1+

um

1^-5

i think

1/4

i used a calculator, dont know how to do manually

im from america

[flat frigate]

faiyrose

[sudden void]

oh

[flat frigate]

faiyrose

[sick violet]

4

[sudden void]

phew

i was stressing out tryna solve this 😭

[flat frigate]

faiyrose

[sick violet]

4

i mean 5

[sudden void]

where did the 1+4 come from

[sick violet]

u mean 2^-1/3?

[flat frigate]

faiyrose

[sick violet]

Its okay

so now what

[flat frigate]

faiyrose

[sick violet]

5+ 2^-1/3(1+4)

?

is that my final answer? i have to have simplest form

[flat frigate]

faiyrose

faiyrose

faiyrose

[sick violet]

0.7937

i cant have decimals, must be simplifed full

[flat frigate]

faiyrose

[sick violet]

yes

[flat frigate]

faiyrose

[sick violet]

I'm so confused, thats what i worte?

should final answer just be 5+ 5(2^-1/3)

[whole rivet]

sorry to interrupt you guys, what math is this

[sick violet]

umm algebra 2 advanced

why?

[whole rivet]

Im studying for the test out, and that looked awfully familiar so I asked lol

[sick violet]

ahh im doing summer school so i can go to pre calculus haha

my teacher is bad

its 12:30, so tired and i know nothing.

[whole rivet]

sounds terrible. I'm trying my best to speed run un6 of this thing

I think we're on the same unit but different area

[sick violet]

bro ppl told me it would be easy but

they changed the curriculum

to make it harder

ah this is unit 4 for us, out og 6

[whole rivet]

oh

we have 13 units

but rn this one is Rational exponents and Radical functiosn

[sick violet]

wow, thats a lot. my school broke it down to 8 units but this is different, summer school

I understand why yours would be 13. ours just combines everything together

yes same, thats our unit

[whole rivet]

my work seems a lot easier tho

unless I havent gotten there yet

[sick violet]

@hasty mason are you still here

[flat frigate]

faiyrose

[sick violet]

yes

[sick violet]

true, going to one of the best schools is tough. maybe thats why mine is so hard since mines also advanced

yes

[flat frigate]

faiyrose

[sick violet]

yeah.. back to where we started

so now what?

im not understanding what you're trying to do

and how?

i think i need more of an explanation, im so confused

yes, i already have that

1/3cbrt2

[flat frigate]

faiyrose

[sick violet]

yes..

whats that

umm

multiply by 3cbt2

then it becomes 1??

[flat frigate]

faiyrose

[sick violet]

so cbrt2 over 1

[flat frigate]

faiyrose

[sick violet]

1

right?

wait no

2^2/3

[sudden void]

yep

[sick violet]

now what

[sick violet]

pray for my math grade to be an a plz

[sudden void]

i will pray for you

[flat frigate]

faiyrose

[sick violet]

yes

i dont know

[flat frigate]

faiyrose

[sick violet]

2^3

[flat frigate]

faiyrose

[sick violet]

2^2/3

huh

ah okay so

2^2/3 / 2

[flat frigate]

faiyrose

[sick violet]

yes..

i dont get where this is going

it feels like we're doing the same thing but different formatting an that im doing in circles

actually do you think you can just solve it and send me a picture? so i can see ur thought process

[flat frigate]

faiyrose

[sick violet]

did you see the image i sent you

the very first one

so

now that i have 2 ^ -1/3 + 2^5/3

right?

honestly thats all i understood

i understnad how to do the rest but i dont know why you're doing this,

yes please

yeah

[flat frigate]

faiyrose

[sick violet]

mhm

[flat frigate]

faiyrose

[sick violet]

yes'

[flat frigate]

faiyrose

[sick violet]

mhm

[flat frigate]

faiyrose

[sick violet]

Yes

yes

everything has to be simplified to the max

[flat frigate]

faiyrose

[sick violet]

mhm, so 125/2

oh

what?

[flat frigate]

faiyrose

[sick violet]

i dont understand-

actually its okay

ill ask my teacher about this tomorrow.

but i have 3 pages to do

that i don tknow

if u can help

i made terrible mistakes

Just tell me which ones are wrong…..

i know lots are. i messed up

wasnt thinking right

[flat frigate]

faiyrose

[sick violet]

can you help me?

lets start with q. 8

ive simplified, 10root8 - 3root2

20root2

20root2-3root2

oh it equals 17?

root2/

wait why?

[flat frigate]

faiyrose

[sick violet]

ahh

okay so

578

wait a minute

i thought i got that somwhere

nvm

mahbe that was smth else

anyway moving on

no. 9

[flat frigate]

faiyrose

[sick violet]

1512 and 189

um

im so lost

is this not what i did?

[flat frigate]

faiyrose

[sick violet]

ahh

okay

so now i have 1512 +189

do i add them together and then cbrt

or what

[flat frigate]

faiyrose

[sick violet]

isnt it just

3 cbrt 63

??

[flat frigate]

faiyrose

[sick violet]

so i have to add htem first

??

thats 1701

so cbrt1701

?

[flat frigate]

faiyrose

[sick violet]

oh!

do u mean like simplify

not cube right

6 cbrt 7

and

3 cbrt 7

9 cbrt 7!

oh!!

[flat frigate]

faiyrose

[sick violet]

huh

im so confused

we have to cube it?

nono the original problem doesnt say cube it, i just wrote it there because thats what i thought to do

so y cbrt 7b is final answer

now lets go q10?

can u try to let me do it and ill tell u what i get

umm no

so it is juts 17 rt 2 then right

none of them square

sorryyyy

wait

this one is 4th root now

i go tit

got it

first number

5 4root 2

2 4throot 2

for seocnd one?

third one

oops

answer is 3 4throot 2

and for no. 11 is 7 root 3?

oh

for 11?

sqrt 27 is 3root3 tho

and 3root 48 is

ohh

i see

12root 3

so then its 15root3

umm

no12 now..

i have 3 pages

i think im gonna stay up all night

6 4throot 5

idk the other one

9root5

wait no

idk.

whats that

ahh yes

i do

i took out root 5 and 9?

yes

thats what i did

i took out root5 and it give me 9

9root5 squared is 405

45

i mean

81

[flat frigate]

faiyrose

[sick violet]

so

6 4 rt 5

• 4 81

• 4 rt 5

um

3

[flat frigate]

faiyrose

[sick violet]

Yes

so

3

4throot 5

no. 133333

idk this one tbh

nut how

this is ^5

ah

the first number is

wait nvm.

i dont know

um

i got 64..

64 and 3

not gonna owrk

4 4 4 3

2 2 2 2 2 2 3

[flat frigate]

faiyrose

[sick violet]

yes

i hope so

nvm i dont

i got 3^6 and 2

yea

too lazy to type it all out

for 1458

im really tired

i think ill do one more page

ill skip this problem..

can u check 16

[flat frigate]

faiyrose

[sick violet]

huh

sum of cubes.

nevermind

is 15 and 16 right

huh

ive heard of them

yes?

kinda

ive done all

hep with rationalization please

its okay, ill check my answer tomorrow

i jut want to sleep

im so tired

actuallyi cant

its due in 6 hours

tysm

ill bookmark it rn

okay one more assignment

its okay

thanks for your help!

goodnighttt

.close

[safe radish]

Channel closed

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[sick violet]

wait what

so confused

how do you close it?

.close

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• Show your work, and if possible, explain where you are stuck.
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[lean otter]

To check continuity at (0,0).

How do I check the continuity of the function at (0,0) ?

[gusty trench]

check if the limit at (0,0) equals the function's value at (0,0)

[lean otter]

How do I check the limit at (0,0) ?

If I put x=0, y=0. The limit is undefined

It is of 0/0 form

[gusty trench]

one approach might be to taylor expand cos(x+y) since you know the input is close to 0

1 - (1 - (x+y)^2 / 2 + ...)

1's cancel, the higher powers of (x+y) vanish to 0

and the (x+y)^2 term cancels to leave just the coefficient

[lean otter]

Ok I am trying

Yes it is continuous

[lean otter]

Is there any condition of Taylor Series Expanding a function ?

[gusty trench]

it was useful in this case since i know cosine has a well known expansion and the input was approaching 0, and there was already a 1 in the numerator

you could probably look up when a taylor expansion holds

luckily cosines expansion converges everywhere

[craggy sedge]

Convergence mentioned

[lean otter]

.close

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[light shoal]

what sort of answer is desired?

blue = a region

blue = a color

[dull sequoia]

i think it's safe to assume area?

it's either area of perimeter

[light shoal]

i never assume

[dull sequoia]

that's why you're better than me at this

[light shoal]

well i do sometimes, but it doesn't usually go well

[dull sequoia]

well what have you tried

is a great place to start

let's have a look at where you got up to then

[safe radish]

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[knotty anchor]

H

[drifting knot]

@knotty anchor can u send the pic clearly

[spiral saddle]

!original

[safe radish]

Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.

[knotty anchor]

I haven’t got it

[drifting knot]

@knotty anchor what is 0 to 3 f(x)dx can't see whats written on other side

[safe radish]

@knotty anchor Has your question been resolved?

[mental hawk]

There must be some more info on the function maybe?

[safe radish]

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[indigo marsh]

Hey

By the definition of multiples (at least what I found), a multiple of a number is the product of the multiplication of that number by a WHOLE NUMBER.
whole numbers = {0, 1, 2, 3, 4, ...}
Now, I saw in some places things like: 2 * (-3) = -6 so -6 is a multiple of 2, but -3 is not a whole number but an integer.
So the question is: is it correct that -6 is a multiple of 2, so integers are accepted and the definition is incorrect or rather the saying -6 is a multiple of 2 is incorrect?

Thanks

[peak estuary]

-6 is a multiple of 2 under most definitions

for a lot of people whole numbers and integers are the same thing

[minor flax]

even though they aren't...

-6 is a multiple of 2, because in \mathbb{N} there's no such thing as -6 lol, so it's assumed you're working in \mathbb{Z} ig

[peak estuary]

depends on your definition ¯_(ツ)_/¯

[indigo marsh]

Hmmm ok

[peak estuary]

wait until you find out that a lot of people consider 0 to be a natural number

[indigo marsh]

💀

[indigo marsh]

btw, should I see it translates to latex or it should stay like this (I am new)

[peak estuary]

it doesnt have $ in it so the bot doesnt translate it

[indigo marsh]

ohh ok thanks guys

.close

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[somber pier]

6.no please solve it

[covert zealot]

A real-estate agent receives a base salary of P 28,000 per month plus a commission. The commission in 2% of the sales up to and including P 1,250,000 for the month and 5% of the sales over 1,250,000 for the month. a. Write piecewise function that relates the salesperson total monthly income hused off or his/her sales for the month

[covert zealot]

Hello can you help me with this?

[river oriole]

!occupied

[safe radish]

Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).

@somber pier Has your question been resolved?

[somber pier]

No

[safe radish]

@somber pier Has your question been resolved?

[blazing fjord]

yo

[blazing fjord]

need help?

[somber pier]

Of course bro

[blazing fjord]

aight lemme read it

[blazing fjord]

this one right

[somber pier]

Yes

[blazing fjord]

kay

so

first up, we know that 15 men can build the house in 21 days

so in 1 day, those 15 men get 1/21 of the work done, which is their working rate

now in 15 days those men will complete 15/21 or 5/7 of the work

so they still have 2/7 work to finish

the guy then adds 9 additional men after 15 days, making 24 men

and then these 24 men finished the remaining 2/7 of the work in 5 days

(since they finished one day earlier)

the working rate of these 24 men in 1 day is 2/35 (since 2/7 of the work was done in 5 days, so (2/7)/5 = 2/35)

but now we need to find out whatwouldve happenede without those addifitonal 9

-first, the 15 men would continue their work (obviously)

• the work rate of 15 men per day is 1/21

woah how did i make that dot?

anyways

-with 2/7 of the work left , we need to see how many days the 15 men wouldve taken

so

(2/7)/(1/21) = 2/7 x 21 = 6 days

so if the 15 men had continued it wouldve taken them 6 more dyas

they only had 6 days to finish

but since they finished a day earlier,

(21-15=6, they wouldve still finished)

[blazing fjord]

Answer: they wouldve been behind by 1 day

@somber pier

[somber pier]

The answer in my book is given 2 days

[blazing fjord]

its probably incorrect

[somber pier]

Yeah

Thank you for your precious time and writing it step by step

[blazing fjord]

its not possible to be behind 2 days, cuz they finished 1 day earlier

[blazing fjord]

np

[somber pier]

I will do the math later to let you know if I have understood it or not because I am studying a different subject now and don't want to switch since I have already did much math today.

[blazing fjord]

ok, got it.

[safe radish]

@somber pier Has your question been resolved?

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[shadow cobalt]

How do I calculate the cost and selling price when dollar markup ($4.70) and percent markup on cost (102.17%) are given?

[safe radish]

@shadow cobalt Has your question been resolved?

[shadow cobalt]

.close

[safe radish]

Channel closed

Closed by @shadow cobalt

Use .reopen if this was a mistake.

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Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[slate quail]

I’m looking to go over this together with someone

[rain bear]

seems like f(x) = kx^2 where k is most prob 1

you can ask anything you want

[slate quail]

My first question as for e and f,

There is an open circle at 0