help-10

[safe egret]

<@&286206848099549185> is this question ok? or are physics questions not allowed?

.close

[obtuse pebble]

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[thorny kite]

Can someone explain what to do and give an example

How do I graph it

Alr I’m good

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[obtuse pebble]

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[thorny kite]

Uh

How do I unoccupy

[obtuse pebble]

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[raven gale]

What is the name of the type of question here? I'm trying to learn about it but I'm at loss as to what to google.

[spiral maple]

system of linear equations

[raven gale]

ok thanks

.cose

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[craggy herald]

Ecological footprint is a measure of the area
we humans use to produce it
we need and to take care of our waste.
Of the total area of the globe we can use
1,3 x 10^8 km^2 to this

[craggy herald]

An example of Ecological footprint per person in some countries :

Sweden's ecological footprint is 6.9 hectares (ha) per person.
How many globes would we need to have about the entire population of the earth
would have the same ecological footprint as we in Sweden have?

Earth's population: 7.5 -10^9 people

1 km^2 = 100 hectares (ha)

[obtuse pebble]

@craggy herald Has your question been resolved?

[obtuse pebble]

@craggy herald Has your question been resolved?

[obtuse pebble]

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[lean ingot]

hi i have a quick question

[lean ingot]

for ex. x to the power of 1 can just be written as x? correct?

hello?

<@&286206848099549185>

[hollow garnet]

yes @lean ingot

[lean ingot]

ok tysm

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[spring horizon]

b = -8

[spiral maple]

keep combining the like terms

and ignore people who feel the need to not help, like Lucas

[spiral maple]

.

you were right with combining like terms... you just then decided to stop

combine like terms

also why do you have -7

oh wait no, didnt see the -14

nvm

[hidden wigeon]

no, you are subtracting 4b from both sides

so you would get -7=1+b

[spiral maple]

You move all the b's to one side, and the constants to the other

[hidden wigeon]

ya

yes

yes

b = -8

you have to close it, you opened it

[obtuse pebble]

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[red dragon]

Hi have a combinatorial question: Is $\frac{((n+m)!)^2}{(2n)!(2m)!}$ bounded for natural numbers $n,m$? I've tried the Stirling approximation and that reduces it to showing that $\left(\frac{n+m}{2n}\right)^{2n+\frac12} \left(\frac{n+m}{2m}\right)^{2m+\frac12}$ is bounded. It's maybe a tedious problem so I was just wondering if someone with combinatorics knowledge maybe immediately sees an obvious strategy here.

[timid silo]

2

[red dragon]

fixed some things

[warm shale]

Golol

[obsidian isle]

take the derivative

[red dragon]

ooooh

in the Stirling approximated version?

[obsidian isle]

yeah

the great thing about this formula is the symmetry

[red dragon]

ok I'll try that but I'm not sure what to expect except the derivatives being eventually negative I guess?

[obsidian isle]

yeah exactly

the function should stop increasing at a certain point

so its derivative should stop being positive at a certain point

the product is symmetric so just take the partial derivative of one of the terms with respect to one of the variables

[red dragon]

ok seems like this will work out, thanks!

[acoustic pelican]

if f is injective and g is surjective then g of f is surjective?

[red dragon]

.close

[obtuse pebble]

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[ember rune]

Which is the solution of -34 < x < 10 in interval notation

[ember rune]

I said (-infinity, -34) ∩ (10, infinity) but it says the answer is (-34, 10)

[naive fossil]

It's just saying x is between -34 and 10

So it can be any values from -34 to +10

[ember rune]

oh wait i just reread it nvm lol

thx tho

[naive fossil]

yup

[ember rune]

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[timid silo]

how do i factor by using the gcf

[timid silo]

example question

i know that the gcf is 2a right

where do i go from there

now what

so do i like divide 2a from 2a^4

@grand oxide

@twilit bobcat

[timid silo]

@twilit bobcat

[karmic whale]

no

its factorize

so it will be $2a\times(a^3+4)$

[warm shale]

IVMC Gaming CH

[timid silo]

imma do this one on my own and just lemme know if i did it right

homework sheet/review

@twilit bobcat

[karmic whale]

yes

[timid silo]

@twilit bobcat now for like long ones like this where do i start

[karmic whale]

its $5\times(x^3-2)$

[timid silo]

gcf for all numbers?

[warm shale]

IVMC Gaming CH

[karmic whale]

correct

[karmic whale]

use HCF

so u know if $2^2 \times 3\times a^4\times b^3\times c^2$

then $-4 \times a^3 \times b \times c^2$

[warm shale]

IVMC Gaming CH

IVMC Gaming CH

[timid silo]

@twilit bobcat

right track?

[karmic whale]

yes

but

dont forget put 4a in front of it

so its will be $4a \times (3a^3 b^3 c^2 - a^2 b c^2 + 4 a c - 4b$)

[timid silo]

no other steps from here?

[warm shale]

IVMC Gaming CH

[karmic whale]

yes

[timid silo]

wow

thanks @karmic whale @twilit bobcat that was easier than i thought :))

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[pale gulch]

hi can someone tell me how the asymptote of the function (x+3)/(2x-1) is 1/2?

[pale gulch]

horizontal

uhh im 17 this year

functions and relations

yeah

infinity right

[warm shale]

KurtDee

[quaint glen]

you should also clarify whether you're talking about the horizontal asymptote y=1/2 or the vertical asymptote x=1/2

[pale gulch]

yeah

yeah my bad I meant y

ahh yeah i think i get it but i was jw bc i thought 1/2 would be possible when x= 1

oh ok

so if an equation was like

[warm shale]

KurtDee

[pale gulch]

$\frac 3x {4x}$

[warm shale]

joshu

[pale gulch]

oh ok bc it’s basically 1/0

[warm shale]

KurtDee

KurtDee

[pale gulch]

ahh ok so if an equation was like (4x+3)/(2x-1) it’d basically just be 4x/2x?

[warm shale]

KurtDee

[pale gulch]

oh

[warm shale]

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

KurtDee

[pale gulch]

yeah

both?

2 and 2?

ow

[warm shale]

KurtDee

KurtDee

[pale gulch]

oh so if the x’s in the numerator is higher than the denominator?

ohh ok yeah i get it now

thanks sm

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[timid silo]

@tiny phoenix

[junior inlet]

at t = 0, the ball is on top of the cliff

calculate the height of the cliff using the given function

then sketch the graph

[tiny phoenix]

a) Already given to you by the y-intercept

[junior inlet]

for the second b)
(idk why, the names are kinda bad)
just calculate the roots

[tiny phoenix]

b) convert to factored form

c) Complete square

[wanton iris]

SANDY!!!!

[tiny phoenix]

You’re right on track

-6(t^2-4t-12)

Put them all together

[wanton iris]

WE NEED HELP IN 384KBPS ANYONE GOOD AT MATH PLS JOIN!!!!

[final python]

#❓how-to-get-help

[wanton iris]

can u help me

pls

just join

[tiny phoenix]

-6(t-6)(t+2)

[junior inlet]

@timid silo what do you need help with??

hellO?

anyways

you know the quadratic formula?

[twilit bobcat]

yes

nvm

lmao

[junior inlet]

speech incomprehensible

[timid silo]

@tiny phoenix

[junior inlet]

when the ball hits the ground -6(t-6)(t+2)=0

we can just cancel out the factor of -6

[tiny phoenix]

Looks good

[junior inlet]

by dividing both sides

(but anyways you can just remove that factor)

(t-6)(t+2)=0

so one of these terms must be 0

[timid silo]

@tiny phoenix

[tiny phoenix]

(t-6) = (6,0) and (t+2) = (-2,0) on the graph

cmon

Man I’m trying to help 💀

[timid silo]

@tiny phoenix

[deft kestrel]

D=[-3,2] and R=[-2,4]

[tiny phoenix]

D = (x = Real | -3 <= x <= 1)

[timid silo]

D = (-4, 4)

R = (4, -4)

Function = No

[junior inlet]

for the circle?

yeah that's right

[tiny phoenix]

D = (-4 <= x <= 4)

[junior inlet]

@wanton iris seems like you've really lost it

NOOOOOO I HATE YOU :|\\\||||||||||\\\\

(although i'm not in the lgbtq community by myself)

<@&268886789983436800> @wanton iris seems to be spamming--

[wanton iris]

why was I @

[junior inlet]

please don't spam 😐

[wanton iris]

my bad

sorry 😦

[timid silo]

.close

[obtuse pebble]

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[timid silo]

@tiny phoenix

[final python]

plug in the values

bwdicalky

change the x values with the given values inside f

[obtuse pebble]

@timid silo Has your question been resolved?

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[raven bluff]

How would I solve this question

I found that they both have 1 n and a 4 in common

What now

[unique solstice]

Divide each term by the common factor

[raven bluff]

Including the -4n^2?

[final python]

it's a term yes

[raven bluff]

Would it be = 4n (-n + 2n)

[raven bluff]

My bad

[final python]

that would be -4n^2+8n^2=4n^2

so no

[raven bluff]

Damn

What did I do wrong

I divided

-4n^2/4n =-n

Is this correct at least

[final python]

yes

what's 8n/4n

[raven bluff]

2n

+2n

[final python]

why 2n

[raven bluff]

Oh nvm

[final python]

8n/4n is basically (8/4)*(n/n)

[raven bluff]

Is it just 2

[final python]

yes

[raven bluff]

Does n cancel

Alright

[raven bluff]

Could it be factored more

There’s still a 2 in common I think

[final python]

so we have 4n*(-n+2)

[raven bluff]

,rotate

[final python]

does -n have 2 in common?

[raven bluff]

No

4 does

[final python]

so no

[raven bluff]

Nvm there is no n in the 2

[raven bluff]

Thanks again

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[obtuse pebble]

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[brisk citrus]

What does closed form mean in part d of the question?

[brisk citrus]

Also I just realized that 3 exists in the inital problem so I am unsure if my first two answers are correct, any advice would be much appreciated

[obtuse pebble]

@brisk citrus Has your question been resolved?

[brisk citrus]

<@&286206848099549185>

[hybrid gull]

Closed form means that your answer isn’t an infinitely long expression

[brisk citrus]

Isn't it already in closed form because they don't have the limit?

[hushed moat]

Closed form probably means to actually evaluate the sum here

[brisk citrus]

The very next question is actually saying to evaluate

Here's a better picture of the entire question

[hybrid gull]

So part e?

Or d first?

[brisk citrus]

d

I can solve easily enough

[hybrid gull]

For d, you can use sum formulas on each of the individual terms of f

Oh okay

[brisk citrus]

(probably)

[hybrid gull]

Once you get d, you’ll then take the limit of d as n goes to ∞

[brisk citrus]

I just don't know how to put it in closed form

[hybrid gull]

What do you have so far?

[brisk citrus]

I know the actual equation which can then be used to solve but I don't know how to put it in closed form

The question above should have all the things needed for the next question

But... I have no idea how to express it in closed form because we never learned it and looking through the book I can't find any references to closed form

[hybrid gull]

If something is in closed form, then you can express it in a finite number of terms

Don’t worry too much about it

Basically, they don’t want you to start writing terms out

[brisk citrus]

I'm gonna be honest, I have no idea what that would look like. I understand that closed means it has finite values but how do I put that into text

[hybrid gull]

Do you know the finite sums for the first n integers, first n squares, and first n cubes?

[brisk citrus]

Is it literally as simple as just saying > infinity

[hybrid gull]

You can use those formulas to get an expression that represents the finite sum

[brisk citrus]

I think I understand

So since it is only progressing by 1, I believe the equation I need is (n(n+1))/2 but I don't know how to get rid of the 3+4k/n in order to get just the k

[brisk citrus]

.close

[obtuse pebble]

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[pallid dune]

teacher said not to worry about matching the y-intercepts

The function is good I just need help on figuring out where to put the exponents

[obtuse pebble]

@pallid dune Has your question been resolved?

[obtuse pebble]

@pallid dune Has your question been resolved?

[pallid dune]

<@&286206848099549185>

[obtuse pebble]

@pallid dune Has your question been resolved?

[pallid dune]

.close

[obtuse pebble]

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[pallid dune]

.reopen

[obtuse pebble]

✅

[pallid dune]

.close

[obtuse pebble]

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[pallid dune]

.reopen

[obtuse pebble]

✅

[pallid dune]

.close

[obtuse pebble]

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Channel closed

Closed due to the original message being deleted

[outer pawn]

.close

.reopen

.close

[obtuse pebble]

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[high lily]

don't multipost

what ahve you tried

@wheat igloo

[wheat igloo]

bro cuz im wondering whenever i post my questions then the channel will suddenly disappear

even tho im posting in the available section

[high lily]

timed out, maybe you and/or noone else posted frequently enough\

[wheat igloo]

no bro, i just answered someones question cuz i knew the answer and then when i sent it my channel disappear immediately

so i posted again

[high lily]

w/e. dw about that and get back to your question

what have you tried?

[wheat igloo]

wait a minute

this one but im confused

[wheat igloo]

my answer in number 1 is 106 since the arc is equivalent

the rest idk bro

[high lily]

try and determine as many angles as you can from basic angle sums

[wheat igloo]

like what bro i dont have any ideas what ur talking about lol

give me some clue to the answers bro cuz the deadline is in 30 minutes

[high lily]

do you know basic geometry and angle sum theorems?

angle sum on a line?

[wheat igloo]

like what example

[high lily]

angle sum of a triangle?

[wheat igloo]

idk bro

we may have different terms used but give me some examples

[wheat igloo]

is that also 50? or 25?

[high lily]

neither

[wheat igloo]

oh my bad

more clues bro

[wheat igloo]

i went here to learn equations from these

[high lily]

basic angle sum theorems

this is like the bare basics of geometry

[wheat igloo]

is it like the congruent angles

[high lily]

no

how big is that angle

[wheat igloo]

wtf is that bro hahaha

[high lily]

well that black line is a straight line

[wheat igloo]

ohh

[high lily]

and that curved red arrow is the angle i want you to state the size/measure of

[wheat igloo]

yea bro im sorry if im slow

is that 90 degree

[high lily]

no

[wheat igloo]

180?

[high lily]

yes

[wheat igloo]

if you complete this curved line to the other side of the angle it will perform a 360 degree circle right?

okay so whats next bro

[high lily]

apply that to your question

[wheat igloo]

how : (

[high lily]

and try and determine <TOL

[wheat igloo]

bruh if tor is 106 how do u get tol

thats my question bro

okay i have an idea tell me if this is correct

[high lily]

apply angle sum on a line and basic (angle) addition/subtraction

[wheat igloo]

S = (n − 2) × 180° ?

[high lily]

what

why are you trying to apply the angle sum of a polygon here

[wheat igloo]

hahaha

wait broo

i cantttt

[high lily]

calm down

and have a think about what you have

mark on your diagram what you know, i.e. that <TOR = 106°
what you want to find <TOL (because as you implied at the very start, that will have the same measure as the arc TL)

and how you would be able to apply that the angle sum on a line is 180° to find out what you want

[wheat igloo]

okay i will try bro

bro i still cant

im not focused and i cant brooo

i really cant broo

im doing coding at the same time the deadline is in 15 minutes

pls help me find the answers bro

[karmic whale]

@wheat igloo hi

[karmic whale]

before he says the degree of this is 180

[high lily]

i am helping...

it takes effort from you as well

[obtuse pebble]

@wheat igloo Has your question been resolved?

[obtuse pebble]

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[obtuse pebble]

@timid silo Has your question been resolved?

[final plaza]

Hi

Are you familiar with domain and range of the sin function

@timid silo

Good

But what if we restrict the domain?

Look at valid values of b

What are the valid values of a then?

Good

What do we do next

How about just regular substitution?

If we need our answer in terms of b

Why not just replace a with sin b

Nope

You skipped steps

One step at a time

Trig functions are tricky this way because

The domain and range stuff will skewer you

Yeah

The functions are not one to one

Exactly

Now what

Perfect!

Can you take it from here?

Well you have a restriction for b

B can only be certain values

N is any integer

But we want solutions within a certain range right?

Can we determine any information about b or n

If x must be those specific values?

Er, we don't need to determine anything about b whoops

B is just b

But n is not something that's allowed in our final answer

We can have our answer in terms of b, but not n

Sorry for the confusion

What must n be

Can it be 0?

Let's say n is zero

Choose a valid value for b

Does x fall into the desired range?

So what does that tell you

Yep!

So the final answer is?

Bingo!

Just remember

Be very careful when cancelling a trig function with it's inverse

Pay very close attention to the domain and ranges

A lot of students slip up and really just want them to straight cancel

And forget the 2pi or pi

;)

[obtuse pebble]

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[vernal atlas]

https://cdn.discordapp.com/attachments/765252568842371153/915572482642169886/20211201_145641.jpg

i keep on getting A

the answer key lists it as B

whats wrong with my steps?

[turbid wolf]

(a - b)/-3 = -(a - b)/3 = (b - a)/3

you have to multiply the negative sign to the whole of (a - b) not just a

and when you do that b becomes positive

and a becomes negative

[vernal atlas]

ohhhh

[turbid wolf]

so (a - b) turns to (b - a)

[vernal atlas]

thank you so much

i asked a couple of my friends and they were so bad at explaining

thank you!

.close

[obtuse pebble]

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[dusty steppe]

@timid silo I'm kinda stuck. You said you could help maybe?

[jolly ginkgo]

It's better if you write n=2k+1 instead of changing like that

[jolly ginkgo]

Looks good

[dusty steppe]

it's just a continuation of a previous problem, but i can't acces the channel

check #help-5 for context

[jolly ginkgo]

You just have to find q right

[jolly ginkgo]

No its okay it's done already

Isolate q

[timid silo]

My bad, told them to use 2n+1.. I forgot

[dusty steppe]

No problem. Just trying to understand the logic

[jolly ginkgo]

Alright your thoughts are right just the anomaly that n=2n+1 so I just rectified it a bit otherwise it's all good

And btw when you take n=2k+1 , k={0,1,...}

[dusty steppe]

q is isolated, but i don't get how this:

Proves this:

[warm shale]

it's Sam

LabyrinthSplash

[jolly ginkgo]

Wdym?

[timid silo]

...That means the natural numbers without 0, right?

[jolly ginkgo]

Z+ is N

[dusty steppe]

The part i don't get is the natrual number union with -1

[jolly ginkgo]

No 0 involved

[dusty steppe]

In our lessons 0 is natrual number btw

[timid silo]

A lot of people consider N to include 0. I guess that's where the confusion came from

[jolly ginkgo]

For k=0 , k²+k-1 = -1

The lowest possible value

And if the lowest possible value is in the set Z itself then we are done proving

[warm shale]

it's Sam

[warm shale]

it's Sam

[dusty steppe]

okay so because k=0 then k^2+k-1=-1 and -1 is in Z then we can conclude the proof

[warm shale]

it's Sam

[jolly ginkgo]

Just to complete the proof

[jolly ginkgo]

k²*

[warm shale]

it's Sam

[dusty steppe]

I think i misunderstood a bit, but here is what i got from it.

[jolly ginkgo]

If you are writing in latex use \Rightarrow rather than \rightarrow

[dusty steppe]

I kinda get the logic that we need to prove that k is in Z because q is in Z

[dusty steppe]

Yeah i have it corrected. But would the rest of the proof be correct? or is it set up wrong?

Right now the proof is structured so that i prove that k is in Z before concluding the proof. Is that structure correct?

[jolly ginkgo]

For the last line write k \in N imply that k in Z therefore k²+k-1 \in Z , so there exists q=k²+k-1 \in Z

Such that n²=4q+5

[dusty steppe]

Seems alright now?

@jolly ginkgo If you think we are done i will close it down?

[jolly ginkgo]

Yes

[dusty steppe]

Thank you for the help.

.close

[obtuse pebble]

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[warped moat]

13. A water tank at a filtration plant is built in the shape of an inverted cone with height 5.2
    m and diameter 5 m at the top. Water is being pumped into the tank at a rate of 1.2 m3
    /min.
    Find the rate at which the water level is rising when there is 8π m3
    of water.

[warped moat]

I can't tell if this question is asking dr/dt or dh/dt

[timid silo]

Water "level" and water "height" mean pretty much the same thing, so it's dh/dt

[spiral maple]

rate of the height

[obtuse pebble]

@warped moat Has your question been resolved?

[obtuse pebble]

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[timid silo]

Please tell the answer

[timid silo]

Let's start from the bottom. Do you have no idea how to calculate 1+1/4-1/2 in the first place? (PS: Not telling you the answer right away. If that's what you want, use a calculator)

[nocturne minnow]

Use a calculator

[obtuse pebble]

@timid silo Has your question been resolved?

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[timid silo]

Yeah ok I calculated

Thx

[obtuse pebble]

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[timid silo]

6ab - d = b(4+a)

[timid silo]

which is the dependence of a on b and d

[obtuse pebble]

@timid silo Has your question been resolved?

[obtuse pebble]

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[sullen saddle]

hello, i seem to be forgetting the methods to mess w and malipulate integrals, so if someone could help me I'd really appreciate it

[sullen saddle]

here's the problem. all i know is that i can flip the integral to get the opposite answer, and i can express an integral as two or more other integrals, as long as they have the same start and end points. my main issues i'm having are i don't remember how to set the bounds to what i want (in this case, i'm not given an integral with a bound of 5/6), and i don't remember what to do with the function inside

[high lily]

consider doing substitution

[sullen saddle]

substituting what

the g(x)'s?

[high lily]

the inside of the function

[sullen saddle]

so do u = 12x or something?

that's the lcm right

[high lily]

don't worry about the lcm

do a different sub for each integral

e.g
for the first one try 2x = 6u

[sullen saddle]

okay just to make the inside u

well that's the same thing

is it not

[high lily]

same thing as what

[sullen saddle]

2x = 6u same as 12x = u

[high lily]

no

[sullen saddle]

$\int _{\frac{1}{2}}^3\frac{g\left(u\right)}{12}du:$

[warm shale]

ski

[sullen saddle]

ok here it is subbed in

well have to change bounds

$\int _6^{36}\frac{g\left(u\right)}{12}du:$

ok there

[warm shale]

ski

[sullen saddle]

wait am dumb again

[high lily]

where are you getting that

[sullen saddle]

yeah idk

ignore let me redo pls

[high lily]

there are multiple approaches to how you choose your subs here

[sullen saddle]

$\int _{\frac{1}{6}}^13g\left(u\right)du:$

[warm shale]

ski

[sullen saddle]

ok here

[high lily]

for the first one try 2x = 6u
that aims to convert all arguments to 6u
alternatively you could do the appropriate sub for each to get the arguments to u instead

[sullen saddle]

k?

okay

[sullen saddle]

well the first one would be this

[high lily]

or w/e as long as they're the same

[sullen saddle]

so use 2x = 6u for all of them?

[high lily]

no

[sullen saddle]

okay how did you get 2x = 6u

should i do 4x = 6u for bottom left

and x = 6u for bottom right

etc

[high lily]

replacing 2x with 6u get you 6u for the argument

[sullen saddle]

what?

[sullen saddle]

it turns it into this

i don't see any 6u there

[high lily]

show your work

recall that in the sub
2x = 6u
2x = 6u NOT u

[sullen saddle]

yeah just saw that

and fixed when did work pic sending

[high lily]

yes

[sullen saddle]

ok now for bottom right

i need to make 4x = 6u

right

[high lily]

you mean bottom left

[sullen saddle]

yes

[high lily]

yes

[sullen saddle]

$\frac{3}{2}\int _0^{\frac{2}{3}}g\left(6u\right)du=2:$

[high lily]

its probably less tedious to get all arguments as u. but this still works

[warm shale]

ski

[sullen saddle]

this right ? @high lily

[high lily]

looks ok

[sullen saddle]

alright, what do i do now?

do i need to convert the integral im looking for to u

with x = u

[high lily]

you can if you want.

also manipulate your equations so that you don't have a (non 1) constant being multiplied to the integral

[sullen saddle]

yeah i was going to do that as well

ill try it rn

[high lily]

and then do some integral addition/subtraction to match the required bounds

[sullen saddle]

sweet i got 1 which is the right answer

thank u bro

.close

[obtuse pebble]

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[keen dove]

Hi there! So for some reason I just have no clue what to do here. I think I'm supposed to find the cube root of 108 which I think is 27y but I don't know what to do with the ^3 and ^5 after that?

.open

.help

[obtuse pebble]

Commands:
clopen: .close, .reopen
factoids: .tag
help: .help

Type .help <command name> for more info on a command.

[brave bramble]

You'd then have y^(5/3)

[keen dove]

OH

See I was wondering that but I wasn't sure

[brave bramble]

Which is another way to write the cube root of y⁵

[keen dove]

so would it be 27y^5/3

:DD Awesome!! Thank you so so much!

If youre still here

For this one, Im confused about the ^5 on the left side

Do I divide 50 by that? so it becomes 10t^22/5

Or would it be like 50/2=25 and the square root of 25 is 5 so 5t^22/5

.help

<@&286206848099549185>

[small cloud]

the 5 means the fifth root

a fractional power basically tells you to take the root of the order of the denominator and then raise the answer to the numerator or you can do it the other way around

for example,

$8^{\frac{2}{3}}$

[warm shale]

mcacutt

[small cloud]

would mean cube root 8 and then raise it to the power 2

or you could square 8 and then cube root the answer

you get the same result

so thinking of it in this way

$8^{\frac{2}{3}}=\sqrt[3]{8^2}$

[warm shale]

mcacutt

[small cloud]

or more generally

$x^{\frac{a}{b}}=\sqrt[b]{x^a}$

[warm shale]

mcacutt

[small cloud]

hope that helps

[keen dove]

That helps so much!!! Thank you!!!

[small cloud]

No problem. It's one of what we call the power laws, if you need to brush up just look up power laws, they aren't too complicated 🙂

[keen dove]

Okay I definitely will!!

[keen dove]

So 50 to the 5th would make it 10, correct?

[small cloud]

no

because the fifth root of 50 isn't 10

you're looking for a number which multiplied by itself 5 times gives 50 (NxNxNxNxN=50) But that isn't what the question wants you to do anyway

So the question is

$\sqrt[5]{50t^{22}}$

[warm shale]

mcacutt

[small cloud]

what you're expected to do here is write it in the alternative form i described above

ie

$50^{\frac{1}{5}}t^{\frac{22}{5}}$

You see how I got to that based on what I explained before?

[keen dove]

Uhmm not exactly tbh, where did the 55 come from?

[small cloud]

my bad sorry

[unique solstice]

Wouldn't you factor tree it

[keen dove]

OK so thats the simplified version then?

Because of that original formula you shared

[unique solstice]

Don't forget the ^1/5 too

If you're doing that

[small cloud]

I mean... theoretically yes but it seems like there's another way to simplify it further and I think what papabread said about the factor tree might be the way to go. Give me a minute to actually write stuff down and I'll let you know unless you wanna have a go papabread?

[unique solstice]

We can both try ig

[keen dove]

Okay take your time! Ive got to step outside r4eally quick before I can reply brb]

[small cloud]

ah got you

[warm shale]

mcacutt

[small cloud]

Every way I can see of simplifying it is just ugly

[unique solstice]

I'm not sure if this is what they want but what I initially think of is just

$t^4 \sqrt[5]{50t^2}$

[warm shale]

PapaBread

[keen dove]

Okay back!

[unique solstice]

50 doesn't simplify nicely but t^22 can be split

I think

[small cloud]

yes, that looks right

thats what I got

[unique solstice]

Reasonable

[keen dove]

Okay thank you both so much!!

[obtuse pebble]

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[dark carbon]

i got 3/2 for question 1

and sqrt of 14 for question 2

just need to fact check it

should be right tho

[obtuse pebble]

@dark carbon Has your question been resolved?

[dark carbon]

close

[obtuse pebble]

@dark carbon Has your question been resolved?

[obtuse pebble]

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[timid silo]

no

[short spruce]

slight problem, that was 2 weeks ago

[obtuse pebble]

@timid silo Has your question been resolved?

[scarlet gale]

@timid silo Here's a decent introduction. You can also learn Fermat's little theorem and Euler's theorem after that.

https://brilliant.org/wiki/modular-arithmetic/

[obtuse pebble]

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[graceful drift]

Okay so I haven't done problems like this since I was a kid.
I remember it as being much easier (literally took me like half an hour before I thought of rewriting the left hand side like that), so I'm wondering if I'm even doing this right? I kind of feel like I'm "going the long way around" so to speak
Also, since every term has an X in it, it should also have a root at x=0, right? How do I show this in my calculations?

[celest sun]

When you go from x^3 (x^2 - 4x - 32) = 0 [note you say 32x here, which is a typo] to x^2 - 4x -32 = 0, you should instead say

x = 0 or x^2 - 4x - 32 = 0

That's where the x = 0 comes from

You just threw away the x^3

[graceful drift]

That's true.. I was actually a bit unsure about that one. Just figured 0/x^3 = 0, but it did feel sort of wrong.
I'm still not sure I understand how you get x = 0 or .. from that

i guess... other than it's obvious that 0^3(...) = 0.. still kind of feel like I'm missing a step there (and it doesn't solve the whole problem of just throwing it out afterwards)

[warm shale]

Amnesia

[graceful drift]

so the "or" comes from the fact that you have an expression with 2 factors that equals zero. you could move either one of them on the other side of the equal sign, and still have zero on both sides?

or in other words: if either of those 2 factors equal zero, then so will their product

fuck, I think I butchered that explanation. English isn't my strong suite either.
I think I get it. somewhat at least.
Thanks

[short spruce]

zero product property, yeah

[graceful drift]

Thanks!

.close

[obtuse pebble]

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[grim orchid]

help

[grim orchid]

the middle part says "and"

i gotta find a

<@&286206848099549185>

[short spruce]

don’t ping helpers right away

where are you stuck

[grim orchid]

here

[grim orchid]

^

[short spruce]

just use inverse trig?

[grim orchid]

show me how

[short spruce]

$\sin(a)=b \implies \sin^{-1}(b)=a$

[warm shale]

a disappointing son

[grim orchid]

and what is this?

[short spruce]

inverse trig?

[grim orchid]

how do i solve with that?

[obtuse pebble]

@grim orchid Has your question been resolved?

[broken kindle]

They likely just want you to put inverse sin of 3/5 into your calculator

[marsh juniper]

To move sin to the other side of the equation, you have to take the inverse. So sin^-1. To plug it in your calculator, most likely you have to use your 2nd function button

[obtuse pebble]

@grim orchid Has your question been resolved?

[obtuse pebble]

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[fallen thorn]

https://cdn.discordapp.com/attachments/903430333888884736/915685732419502140/Screen_Shot_2021-12-01_at_11.png

In this model, the only way a renting household can leave the renting group is by transitioning to the evicted group. Similarly, the only way an evicted household can leave the evicted group is by transitioning to the renting group. It is helpful to represent this scenario with a flow diagram in Figure 1.

Please help with at least number one, thanks

[obtuse pebble]

@fallen thorn Has your question been resolved?

[obtuse pebble]

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[rare forge]

<@&286206848099549185>

help

<@&286206848099549185>

.close

[obtuse pebble]

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[tepid trench]

what is 100 divided by 0?

[tepid trench]

pls tell

wht

is

it

[weary sail]

undefined

[tepid trench]

ohh

oki

Image

[weary sail]

.close

@tepid trench you should close the room using .close since u're done with ti

[tepid trench]

.close

[obtuse pebble]

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[tepid trench]

oki

[weary sail]

oki

[obtuse pebble]

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[fast horizon]

hey could someone quickly explain how you would get the answer of this:

(2 - sqrt x)^2

[timid silo]

u really coulda not have put this into a calculator

[timid silo]

square of a sqrt is just the number inside the sqrt

bc it's inverses

[fast horizon]

hm okay

but im just confused how you would get

[sick aurora]

you expand

[fast horizon]

how does it become 4sqrtx?

[sick aurora]

im not realy sure

[tepid trench]

Lol I don't even think about it, lol

[timid silo]

bc

(a+b)^2 is a^2 + 2ab + b^2

4sqrt x is the 2 ab

[fast horizon]

ohhh

why the fk did my teacher not tell us about that equation

and our chapter test is tomorrow

like what

[sick aurora]

oh yeah perfect square formula i forgot

[fast horizon]

ok thanks guys!

.close

[obtuse pebble]

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[stiff palm]

how the hell is b 6

i thought the value of B would be the top number 2

idk what im overlooking

<@&286206848099549185>

[obtuse pebble]

@stiff palm Has your question been resolved?

[obtuse pebble]

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[eager blade]

$f(x)=(x-1) e^{x}+1$

[warm shale]

Professor T

[eager blade]

How to calculate the range of this function?

[stone spoke]

do you know calculus?

[eager blade]

Somewhat

[stone spoke]

do you know how to find maxima and minima?

[eager blade]

Yes

[stone spoke]

so what would the minimum be for the function?

[eager blade]

0

Will it be correct to conclude that since the function is continuous at 0 and the minimum is 0, the range of the function is [0, infinity]

?

[stone spoke]

yep

but remember that these are only relative maxima

so you should check endpoints (in this case they don't matter)

[obtuse pebble]

@eager blade Has your question been resolved?

[obtuse pebble]

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[timid silo]

Could someone please help me?

[high lily]

what have you tried

[timid silo]

Yes

Many times

[junior magnet]

look

area = height x base

over 2

u have the length of the base

and then area

calculate the height

[timid silo]

Mhm

[junior magnet]

and since it's an isosceles triangle

the height can be a bisector... median

all of that

so u can't bring the length of BD

or DC

if u take DC

You'll have ADC a right triangle

with vertex D

now

u have DC and AD

use phythagorean's theorem

to bring the AC

do u understand?

@timid silo

[timid silo]

Yeah I tried the pytha Theron

*theorem

But it kept giving me

[junior magnet]

what grade are u in btw

[timid silo]

7

[junior magnet]

ah i see

so what did it give u

[timid silo]

Like

6

3

2

[junior magnet]

oh

seems like u have some problem with calculations

lemme try and solve it on a paper

3 min okay?

is this a hw?

[timid silo]

Ok! And no

This isn’t hw

[junior magnet]

studying for test maybe?

[timid silo]

Nope

Extra practice

[junior magnet]

great job

as a 7th grader

[timid silo]

Thank you

[junior magnet]

that's amazing

back then i was lazy hahaha

I'll solve it wait

[timid silo]

Ok lol

[strong delta]

I think the area formula will give the height. As they give the area and the base only missing the height

[junior magnet]

it's 15

[timid silo]

That’s correct but how😭

[junior magnet]

would u like me to send u my..

solve

[strong delta]

A= h×b/2

[junior magnet]

i already explained that to him

can i dm u?

[timid silo]

Uh me?

[junior magnet]

ye send u my solve

[timid silo]

Ok

Sure

[obtuse pebble]

@timid silo Has your question been resolved?

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[weary sail]

no clue lmao

[grave hamlet]

As a guess I’d say first parameterize in cylindrical coordinates and then convert

[weary sail]

hmm

alrirght

i'll give it a shot

[grave hamlet]

But I mean the idea is to just encode the distance to the x axis and angle in those second and third coords

Distance is given by your original function and angle by the rotation

So using t as an angle say it shouldn’t be too hard to get it to work with some trig

[weary sail]

@grave hamlet how do u know that the third coord is the angle again?

i thought cyl coord was radius, angle, z

[grave hamlet]

I never said third coord was angle

[weary sail]

my b i mustve misunderstood

[grave hamlet]

I’m saying in Cartesian coordinates your second and third coord can be used to encode radius and angle through cylindrical conversions

Since s already gives you the distance along the x axis which would be your “z” in cylindrical

[weary sail]

oh i see

its like

flipped

or not flipped

but orientated so

gotcha

hmm ok

[grave hamlet]

Think about it this way: take plane slices along the x axis and oarameterize the corresponding circle: the two coordinates used will be your second and third coordinate for r(s,t)

[weary sail]

@grave hamlet got it!

thanks

i concentrated so hard reading your sentences i thought i was going to get a nosebleed

it clicked eventually though

i suppose on a conceptual level, i don't understand why we'd use cylindrical coordinates here

actually i think i get that too

[grave hamlet]

Because surfaces of revolution have axial symmetry

Anything that has axial symmetry is probably a good candidate for cylindrical coordinates

Also you should close the channel @weary sail

.close

Right I suppose it’s natural I don’t have the permissions lol

[obtuse pebble]

@weary sail Has your question been resolved?

[obtuse pebble]

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[limber panther]

why the highlighted set has no elements ?

[limber panther]

please mention me

[final python]

because - 2 cannot be bigger than 2

[final python]

bump

[limber panther]

why not all Z elements except numbers between -2 and 2 ?

not homework i'am self-taught

[final python]

wait show

the question

[obtuse pebble]

@limber panther Has your question been resolved?

[limber panther]

ok no proplem thank

.close

[obtuse pebble]

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[timid silo]

there is a property written in my notes way back earlier which I didn't get once I revised it today