help-13

[digital cliff]

you just need to know how to write 1/8 as an exponent of 2

[wise lily]

wait like a powered number of 2?

1/8^2?

or 2^1/8

[digital cliff]

neither

writing 4 as an exponent of 2 would be 2^2 for example

writing 16 would be 2^4

etc

[wise lily]

oh

so then 1/8 would be 2^x

[digital cliff]

i mean

sure

but what is x

[wise lily]

I have no idea

Im trying to think of how to figure this out

could you guide me through the steps

[digital cliff]

what is 8 as an exponent of 2

[wise lily]

64

[digital cliff]

no

thats 8^2

not what i asked

[wise lily]

oh

WHat does EXPONENT MEANNN

Just say power

please

or

[digital cliff]

i gave example

exponent, power, indice, same thing

[wise lily]

2^3

[digital cliff]

yeah

now use this

what is 1/8 as a power of 2

[wise lily]

uh im not sure

but like

the same ig?

wait a minute

2^-3

[digital cliff]

yeah

[wise lily]

=1/8

[digital cliff]

so whats this

= to

[wise lily]

-3

[digital cliff]

there you go

[wise lily]

https://tenor.com/view/dj-khaled-meme-surprise-shock-gif-21311476

i just learned something

[digital cliff]

https://tenor.com/view/bless-yee-with-knowledge-travis-gif-24097608

[wise lily]

i have like 3 hours til my 4th quater final

I still gota learn the rest of the topic

do you perhaps know what to do when you get something like 2^x=7

in logarithms

[digital cliff]

take the log of both sides

base 2 would probably be the most efficient

but any base is fine

[wise lily]

how would you 'take the log'

so like put it in log form?

[digital cliff]

if a=b, then f(a)=f(b) for whatever function

so if a=b

then log(a)=log(b)

thats taking logs of both sides

[wise lily]

oh

gime a sec

leme write this down

okay

[digital cliff]

it would do you well to memorise the first second third fifth and sixth of these

the 4th isnt as important to know comparatively

but it would be good to know it if you can

[wise lily]

i know that loga a=1

and loga1=0

thats obvious

this is like index laws

i just realized

[digital cliff]

well, yeah

this is the definition of a log

so their rules naturally relate

[wise lily]

ah so you are making the index the subject?

[digital cliff]

if you want to see it that way, sure

[wise lily]

I appreciate your help so far

But i believe i would benefit some help at school

i need to sit down with someone

and go through this

thank you for helping me!!

.close

[cedar kiln]

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[hallow oyster]

Hello, nice to meet you. I would be very grateful if you could help me with this problem because I am having difficulty solving it.

Let us assume that legislation on the application of sewage sludge on land limits the increase of heavy metals to less than 5% (relative) within 100 years. Further, assume for simplicity that erosion of soil, eluviation, leaching, uptake by plants, etc. can be neglected. How much sewage sludge can be applied to land? Discuss the example of zinc: Zn concentration in sewage sludge is 1500 mg per kg dry matter; Zn concentration in soil is 30 mg/kg. Is there enough agricultural soil to spread all sewage sludge?

What I have been able to deduce is that:
0.05*30=1.5mg/kg
30+1.5=31.5 mg/kg
But now I'm not so sure if that's the case.

[violet flume]

okay, so as in, you cannot increase the current concentration by more than 5% whats existing?

is the dried sludge being added meant to add to the material?

so if you add a kg of dewatered sludge then you count that as an additional kg of soil in calculating the concentration?

[hallow oyster]

That's the problem I have. Given the lack of non-relevant data (according to the teacher) I must continue with the numbers given only.

[violet flume]

okay. Lets assume that it does, if thats okay?

[hallow oyster]

Ok

[violet flume]

this seems like a solution-mixture problem

like, if youre mixing two different concentrations of an acid, or something

[hallow oyster]

Understand

[violet flume]

<@&268886789983436800>

wait one sec they will delete and we can continue

maybe

[violet flume]

so what you want to do is to express the concentration of metals in the soil in terms of how much sludge you added

say like, say I mix a kg of soil, and a kg of sludge, can you find the concentration of that mixture?

[hallow oyster]

That's one of the questions I have.

The other thing I want to know is there enough agricultural soil to spread all sewage sludge?

[violet flume]

Okay, lets go through the math of the first one

The way you will calculate the concentration of the mixture is take the kg of soil, times the concentration, and add to it the kg of sludge, times the concentration. Then, you divide by the total mass of the mixture

$\text{new concentration} = \frac{ \text{mass of soil} \times \text{concentration in soil} + \text{mass of sludge} \times \text{concentration in sludge} }{ \text{mass of soil} + \text{mass of sludge} }$

[wraith dagger]

jan Niku

[violet flume]

could you do this problem now?

[hallow oyster]

I take into account that the mass is 1?

[violet flume]

yes

1 kg of each

[hallow oyster]

The result is 765 mg/kg

[violet flume]

okay, now calculate the percent increase

$\text{Percent Increase} = \frac{ \text{New Conc.} - \text{Old Conc.} }{ \text{ Old Conc. } } \times 100$

[wraith dagger]

jan Niku

[hallow oyster]

Which one do you mean by old conc?

1500 or 30?

[violet flume]

So, the old concentration was just soil.

[hallow oyster]

Oh, sorry

[violet flume]

Were framing the problem like, we had a kg of soil, and then we added a kg of sludge to it.

[hallow oyster]

My fault

[violet flume]

No worries.

This is just a toy problem to make sure you feel okay on the math.

Then we can generalize it to approach your problem.

[hallow oyster]

24.5

[violet flume]

this sounds way too low

should be $\frac{ 765 - 15 }{ 15 } \times 100$ i think?

[wraith dagger]

jan Niku

[hallow oyster]

Wait

24.5*100= 2450

I forgot to multiply

[violet flume]

oh, sorry, i also calculated wrong

the concentration in the soil is actually 30, not 15

$\frac{ 765 - 30 }{ 30 } \times 100$

[wraith dagger]

jan Niku

[hallow oyster]

That's 2450

[violet flume]

yea that sounds better

So, to summarize

If we start with 1 kg of soil, and we add 1 kg of sludge, we increase the metal concentration by 2450%.

Lets approach the problem differently. Here is the concentration formula

[wraith dagger]

jan Niku

[violet flume]

(it will be a function of x)

[hallow oyster]

Well...you lost me. I have the same data as before, except that 1kg is now X

I could iterate countless times...

[violet flume]

lemme list out for this problem:

Mass of soil: 1 kg
Mass of sludge: x kg
conc. in soil: 30 mg/kg
conc. in sludge: 1500 mg/kg
new conc.: Unknown

So we need to substitute this information into the formula.

We will have an x in some places, and that's fine.

[hallow oyster]

I understand that

[violet flume]

I'm not sure what you mean here

what we should end up with is a fraction with numbers, and x in some places

[hallow oyster]

new conc= (1kg * 30mg/kg + x * 1500mg/kg) / (1kg + x)

[violet flume]

yea

so lets write it $\frac{30+1500x}{1+x}$

[wraith dagger]

jan Niku

[violet flume]

im not sure how much you want to keep track of units.

[hallow oyster]

there's no need

[violet flume]

luckily, youve done some of the math for the next part up here

you know that a 5% increase in the soil concentration means there is 31.5 mg/kg

this is the maximum that is allowable

[hallow oyster]

Yes

[violet flume]

so we can solve here

$31.5 = \frac{30+1500x}{1+x}$

[wraith dagger]

jan Niku

[violet flume]

are you allowed to use calculators? I mean is it necessary you solve this by hand?

[hallow oyster]

Yes. There's no problem with that

[violet flume]

,w calc 31.5 = (30+1500x)/(1+x)

[wraith dagger]

Results provided by WolframAlpha

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

Requested by janniku

[violet flume]

wow thats smaller than i thought it would be

[hearty arch]

1468.5x=1.5 or something like that

[violet flume]

so, to each kg of soil, we can add 0.001022 kg of sludge

roughly

How much sludge do you have?

,calc 1/0.00102145

[wraith dagger]

Result:

979.0004405502

[violet flume]

for each kg of sludge you will need roughly 979 kg of soil

[hallow oyster]

Okay, that's a lot.

[violet flume]

yea

[hallow oyster]

But not far from reality

[violet flume]

Guess it depends how much sludge you are producing

your problem gives a lot of extra information I wonder if you are supposed to somehow use, but its not enough to fully address the issue.

[hallow oyster]

No. That's all the information

[violet flume]

For example, it says this limit is for every 100 years, so somewhere you maybe have access to a kg/year rate for sludge?

[hallow oyster]

It's confusing in parts, nothing more.

[violet flume]

ah

,w how much does a cubic meter of soil weigh

[hallow oyster]

If I work with software, I might apply that term

[violet flume]

hmm im not sure the bot can help with this

ah i guess our weight is roughly 1 cubic metre of soil

thats convenient

[violet flume]

yea its hard to know exactly what to do here without more information, sorry

you could start approximating stuff. it's not clear to me how you want to move forward.

[hallow oyster]

It is convenient because the problem does not provide more important information.

[violet flume]

they say a m^3 of soil is 950-1200 kg

I don't work in water treatment so I have no idea how to estimate how much solids are generated per year.

[hallow oyster]

This is funny because the teacher gave me this second question for the same problem: b) Discuss the importance of setting appropriate temporal and spatial limits and their influence on the results and conclusions.

[violet flume]

I wonder if you approximate things, you may get some insane number

[hallow oyster]

In the absence of such information, I can only assume that it is 1

[violet flume]

well i googled

lemme see

[hallow oyster]

That's what I thought, I would have infinite results until I got closer to the desired one.

[violet flume]

they say about a 250 grams per cubic meter of water treated

whats a good estimate population lol

a thousand people make 80 cubic meters of wastewater every day is a reasonable estimate

so thats 20 kg of solids per thousand people

thats already...

nearly 20,000 cubic meters of soil

thats a pretty big area.

20 square kilometers, a meter deep

for each thousand people, per day

but my math could be really wrong

[hallow oyster]

I'm not sure about that

[violet flume]

its a lot of estimation

[hallow oyster]

I know. Bot it seems like a pretty reliable data, even if you just calculated it

[violet flume]

IDK im not sure what else to do with the problem other than to make estimates, and get to some crazy number, and then address your other question this way

the limit does not seem attainable

[hallow oyster]

Maybe that's why the professor asked that second question. Given the lack of knowledge of these values, I will never know if it works with the soil of an entire country or a small house.

[violet flume]

i mean im seeing figures like

1 kg of solids per every cubic meter of wastewater

[hallow oyster]

Still, thank you very much for your help. I was really going crazy with that problem.

[violet flume]

it just seems so unattainable

yea, no problem, good luck.

[hallow oyster]

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[wraith dagger]

QuasiStar 超新星

QuasiStar 超新星

QuasiStar 超新星

QuasiStar 超新星

QuasiStar 超新星

QuasiStar 超新星

[cedar kiln]

@wicked swan Has your question been resolved?

[cedar kiln]

@wicked swan Has your question been resolved?

[cedar kiln]

@wicked swan Has your question been resolved?

[gusty forum]

it isn’t wrong and in fact you are about 0.01% away from showing it’s true

cancel out all the garbage and consider when the sins of two angles are equal (aside from the obvious case of sin(x) vs sin(x+360k) for integer k)

[wraith dagger]

QuasiStar 超新星

[cedar kiln]

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[ivory finch]

what does it mean negative orientation

[ivory finch]

i know it affects the sign

but idk how to tell if it's + or - orientation

[cedar kiln]

@ivory finch Has your question been resolved?

[raw gulch]

simply saying when you walk on your curve, in opposite direction than parameter arises, then you have opposite paramtrisation, it also occurs when you walk clockwise

[ivory finch]

how do we know whatr parameterization direction is

tbh

[raw gulch]

assume you have the same parametryc equaiton of yoru cycloid, and you compute linera integral of the second kidn, you know, in vectori field, then if t belogns to , assume [0, 2Pi] , you can put t = 0 and see where you are located on yoru curve

[ivory finch]

hard to visualize the coorinates

[raw gulch]

enxt you put 2 Pi and you aslo visiualsie it

but cycioid is trivial

[ivory finch]

o

so best thing is just to plugin easy numbers

like 0

pi

2pi

[raw gulch]

yes

[ivory finch]

pi/2

3pi/2

[raw gulch]

there is no formula if you mayeb wanted to find

yes they are regular one

enough often to take

beginign and end

maye bif you wud use Bernosuli lemniskata

or

cardiod

you cud take more vlaues

but cyclid is easy

if curve is so caled Jordan curve, clsoed one

then if you walk clockwise, then orientatin is negative

but anticlockwise positive

in future, maybe, you wil find it useful in complex analysis, mayeb in next semester

[ivory finch]

so basically in fact

if i am given the graph

without the arrows

i can actually just test for a few points

which will reveeal which weay i am going?

i have confirmed it

now the issue is

[raw gulch]

orintation is clockwise

=

[ivory finch]

how do i know if my answer become + or -?

[raw gulch]

negative orientation

you see it ?

clockwise

[ivory finch]

is that just somethin to memorize

[raw gulch]

yes

[ivory finch]

if orientation clockwise

my answer multiply (-)?

[raw gulch]

= negative orient

so if oyu want to get area

you mjst set minus before integral

you can here, also integrate on [2pi, 0]

then you walk anticlowise

and ti wil be positive

plz practise it

yes correct

[ivory finch]

so basically

wheneever i am given problem like this

i just memorize this rule?

[raw gulch]

nods

[ivory finch]

clockwise = multiply my final answer by negative 1

couunterclockwisea = keep answer same

[raw gulch]

right

[ivory finch]

ok so it seems like i am good on this

but ther eis one more case where it is came process

but with normal vectors

[raw gulch]

sometimes it is said, we will move in accordance with the parameterization, then you write plsu, and if it is said, we will move in the opposite direction to the parameterization, you put a minus sign

beucase not every curve must be Jordan line

[ivory finch]

i know how to do this problem

the only thing that i am confused on is to set answr positive or negativ ebased on normal vector pointing somewhere

[raw gulch]

in this case, you put plus

[ivory finch]

brb5

[raw gulch]

For closed surfaces, we usually assume that the positive side is the external side.

Double-sided surfaces include, among others, graphs of functions such as: z = f(x,y), x = g(y,z) , y=h(x,z) and then we usually take the upper part of such surfaces as the positive side

[cedar kiln]

@ivory finch Has your question been resolved?

[cedar kiln]

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[west ravine]

What did I do wrong here?

[clear berry]

You reflected from the origin for some reason

0 is always 0, then 1, 2, 3=0 right

This would continue in the negative direction also

Notice that -3 is clearly 0 so -2 would be 1 and -1 would be 2

@west ravine

Does this make sense?

[west ravine]

ohh ok i see

thank you !! @clear berry

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[crimson sedge]

Im confused on how to approach this (ignore the answer selection)

[runic garnet]

Fundamental thm of calculus

Are u familiar

@crimson sedge

[crimson sedge]

Yeah im not sure how to take the antiderivative tho

[runic garnet]

No need to

[crimson sedge]

Ok let me try it out

[crimson sedge]

wait im confused what to do with the ln(x)

[runic garnet]

$\frac d{dx} \int_c^{f(x)} g(t) dt = g(f(x)) \cdot f’(x)$

[wraith dagger]

Stephen

[crimson sedge]

Oh tysm

[runic garnet]

Do u get it now

[crimson sedge]

Yeah

Thx

[runic garnet]

Np

What answer u got

[crimson sedge]

E

[runic garnet]

Ye

[crimson sedge]

Tysmm didnt know that formula existed lmao

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[cedar kiln]

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[west vault]

<@&286206848099549185>

[west vault]

I'm stuck on reading something

It's my work

[royal loom]

!15mins

[cedar kiln]

Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.

[royal loom]

You haven’t even posted a question yet

Don’t tag the helpers

Post your question if you have one

[west vault]

Oh my bad

I was reading the instruction

[crimson delta]

lets ping helpers and then read how this server works

[west vault]

I have a question about place value chart

[west vault]

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[wraith obsidian]

Let V be the portion of a sphere with radius a lying in the first octant. Show that
triple integral
xyz dV

[wraith obsidian]

having a hard time coming up with limits for spherical coordinates of this triple integral

my idea was

r = 0 to 1

theta goes from 0 to pi/2

and phi goes from 0 to pi/2

[hollow trail]

the angular limits seem fine, but the problem states the sphere has radius a

[wraith obsidian]

i meant 0 to a sorry

but its not giving me right answer

int [//math:z^5*(siny)^2cosysinx*cosx//] [//math:dz dy dx//] , z=[//math:0//]..[//math:a//], y=[//math:0//]..[//math:pi/2//], x=[//math:0//]..[//math:pi/2//]

well i put the integral 0 to a and 0 to pi/2 for others

and i get a^6/36

but my question says show that is a^6/48

and i put the integral in wolfram alpha to make sure i integrated correctly

[cedar kiln]

@wraith obsidian Has your question been resolved?

[cedar kiln]

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[dawn ingot]

I’m trying to solve this question for finding the minimum diameter of a steel shaft when subjected to the following:

[dawn ingot]

However I’m getting the wrong answer when I do it with calculus. I likely made a stupid mistake somewhere along the way because it's 2am and im tired

The radius should be 5.54mm according to my class notes where we did it this way:

The difference I see from a cursory glance is that one of my constants is 2/pi vs 2pi but I don’t know how to get 2/pi

[cedar kiln]

@dawn ingot Has your question been resolved?

[cedar kiln]

@dawn ingot Has your question been resolved?

[cedar kiln]

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[slender wasp]

i need to prove that the equation $x^3+3x=sinx+2$ has only one sol in the interval (0,1).
Let $f\left(x\right)=x^3+3x-sinx-2$ and with bolzano's intermediate value theorem i showed that it has at least one sol on (0,1)
Say we have 2 sols x1,x2 with x1 <x2 and by using rolle's theorem on the interval (x1,x2) we come to the conclusion that f'(c) = 0 $f'\left(c\right)=3x^2+3-cosx$ which is not true because i have seen it on desmos but dont know how to prove it here

[wraith dagger]

Striker

[opal basin]

So you need to prove that $f'(c) = 3x^2 + 3 - \cos(x) \neq 0$?

[wraith dagger]

Jelle

[cedar kiln]

@slender wasp Has your question been resolved?

[slender wasp]

yes

[opal basin]

Well -cos(x) >= -1

and then look at the quadratic

f'(c) will always be bigger than 0

[slender wasp]

ok thank you

.close

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[lone mulch]

what does this arrow mean next to q and r

[raw gulch]

to jest implikacja,też 🙂

[lone mulch]

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[turbid spoke]

this graph is cycle?

[turbid spoke]

Is that graph cyclical?

[cedar kiln]

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[coral pagoda]

The sum of the first three terms of the Oseh arithmetic progression was 21. If the first two terms of this arithmetic progression are reduced by 1 and the third term is increased by 2, these numbers will be a geometric progression.
Find the sum of the first eight terms of the geometric progression.

.help

[cedar kiln]

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[coral pagoda]

.help <The sum of the first three terms of the Oseh arithmetic progression was 21. If the first two terms of this arithmetic progression are reduced by 1 and the third term is increased by 2, these numbers will be a geometric progression.
Find the sum of the first eight terms of the geometric progression.>

[cedar kiln]

No command called "<The" found.

[coral pagoda]

.help

[cedar kiln]

Commands:

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@noble dust Has your question been resolved?

[noble dust]

I’m not sure this is what I’m looking for since this is related to series rather than progression

[cedar kiln]

To ask for mathematics help on this server, please open your own help channel or help thread. See #❓how-to-get-help for instructions.

[ancient lodge]

Do yk the formula for taylor's inequality

This is essentially straight substitution

[noble dust]

So do I just keep throwing in different values for N until I find something that sticks or something

[ancient lodge]

What do you have rn

[noble dust]

((e^0.1)/(n+1)!)*0.1^n+1

[ancient lodge]

Yeah ignore what I said earlier

This is just trial and error

[noble dust]

Ok great

Glad to know that much at least lol

I just thought it would be stupid if I just trial and errored my way into the answer R4

And I was wondering if there was another way to do it

Thanks for the help though

[ancient lodge]

I mean I’d just narrow it down based on orders of magnitude if

[noble dust]

I think I can get it now. Thanks

[cedar kiln]

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[native shell]

Prove that f:D->R is not integratable in D

[native shell]

This is what I have, no clue if it's correct

I know I need two riemann sums , one for [0,2) and another for 2 (somehow) and to prove their limits are different

[cedar kiln]

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@native shell Has your question been resolved?

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@native shell Has your question been resolved?

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[near hinge]

How do you conclude this term from the archimedian property

[cedar kiln]

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[near hinge]

.close

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[worldly wagon]

pls help

its my last question!

🥺

<@&286206848099549185>

[woven quail]

B is one

[crimson sedge]

Which ones do u think it is

[worldly wagon]

ty

[umbral dew]

!15m

[cedar kiln]

Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.

[umbral dew]

also

mr

!nosols

[cedar kiln]

As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.

[woven quail]

Oh sorry

I'm new to this server

[umbral dew]

np

[worldly wagon]

i think A

[crimson sedge]

Why A

[worldly wagon]

because if i cut it it wont make a cube

[crimson sedge]

<@&268886789983436800>

[worldly wagon]

?????

[woven quail]

I apologize but isn't the question which ones make a cube?

[worldly wagon]

no

[crystal raptor]

What's up?

[crimson sedge]

Inapp pic here, was edited

[rugged palm]

wait, you first have the cube, then you cut it

[crimson sedge]

Can check logs

[worldly wagon]

yeah

[crimson sedge]

Basically think of it as a piece of paper

[worldly wagon]

k

[woven quail]

Like orgami

[worldly wagon]

k

[crimson sedge]

Of you look at all 4 of those as pieces of paper, which ones can you fold back into a cube

They do

[worldly wagon]

D and B

[crimson sedge]

With the discord addon

[woven quail]

Yeah

[worldly wagon]

ur so smart🙄

[crimson sedge]

!nosols

[cedar kiln]

As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.

[crimson sedge]

He asked the question

[worldly wagon]

since when was i teacher?#

[crimson sedge]

Lmao

Mb

[worldly wagon]

bruh

lol

the bot bassically gave me answer

😂

ok

ima cut now

thanks fr help

discword57 u dint help

send innapropriate pictures somewhere else

and be more mature

.close

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[spice spoke]

How many voters must be asked in order to predict the election result of a party with a probability of 90% and with a maximum error of 1%?

Any idea how to solve it?

[crimson delta]

<@&268886789983436800>

[cedar kiln]

@spice spoke Has your question been resolved?

[spice spoke]

Is it solvable?

[cedar kiln]

@spice spoke Has your question been resolved?

[cedar kiln]

@spice spoke Has your question been resolved?

[bold kettle]

You have to use the last part of the formula for confidence intervals with proportions, which is the margin of error. The problem says that the desired margin of error is 1% or 0.01. The value for z should be the value that goes with a 90% confidence interval. And for p-hat, unless more information is given, you typically do p-hat=0.5 (which is assuming the worst-case scenario in terms of variance). Now it's an algebra problem to solve for n

[spice spoke]

thank you

[cedar kiln]

@spice spoke Has your question been resolved?

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[coral python]

really need help to review derivatives, primarily optimization.
i forgotten the whole question but it was something like this,
suppose that the profit of a company dependds on three variables (x,y,z) and is given by the equation P=9(100z)+4(100y)+100x? If the company produces their product according to the function Z=5-1/x-1/y, determine maximum profit.

[coral python]

,help

[wraith dagger]

A brief description and guide on how to use me was sent to your DMs!
Please use ,list to see a list of all my commands, and ,help cmd to get detailed help on a command!

[coral python]

,tex

[wraith dagger]

Please give me something to compile, for example latex ,tex The solutions to \(x^2 = 1\) are \(x = \pm 1\).See ,help and ,help tex for detailed usage and further examples!

Nov 22, 2023, 3:01 AM

[coral python]

,tex suppose that the profit of a company depends on three variables (x,y,z) and is given by the equation
P=9(100z)+4(100y)+100x
If the company produces their product according to the function
Z=5-1/x-1/y
, determine maximum profit.

[wraith dagger]

norman

[gusty forum]

what prevents you from achieving infinite profit by blowing up x and/or y?

[cedar kiln]

@coral python Has your question been resolved?

[coral python]

i really don't understand how to answer the question

[gusty forum]

it’s a nonsensical question because you can easily achieve infinite profit
so either the question writer wanted you to answer infinity or the question was copied wrong

[coral python]

oh, the choices to the answer is
7200
72 000
27 000
2700

[coral python]

also i wrote the equation wrong sorry:
P = 9(100z) - 4(100x) - 100y

z = 5 - 1/x - 1/y

[cedar kiln]

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[gusty forum]

uh, well you don’t even need to optimize for anything

[coral python]

oh, how do i apporach it

[gusty forum]

just rearrange

then only one of the answers is satisfiable

[cedar kiln]

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[coral python]

okay, thank you for your help.

[coral python]

.close

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[cedar kiln]

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[marsh pond]

I don't understand W_2

is it C for both?

[royal loom]

are you allowed to choose multiple boxes?

What does it mean for something to be a basis of a vector space?

a set of linearly independent vectors, that span the space

right?

so if you fail either criteria

being dependent, or not spanning the space

[floral arrow]

It says answer**(s)**

[royal loom]

they're both reasons you're not a basis

[marsh pond]

so for W_2 it's A and B?

[marsh pond]

for W_2 it's A and B, right?

[royal loom]

No need to tag both of us

[marsh pond]

oops sorry

[royal loom]

I think you can verify that yourself

there's a zero vector

so it is certainly dependent

and there are only 2 other vectors

[marsh pond]

well, i'm pretty sure W_2 is not C

[royal loom]

at most they can span R2

[marsh pond]

so the only other option is A and B

[royal loom]

but deduce it without just eliminating option C haha, it isn't too complicated

you're nearly there

[marsh pond]

A and B it is

it's my last attempt, so I gotta make it count

finger's crossed

[royal loom]

should work

[marsh pond]

tyvm

.close

[cedar kiln]

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[royal loom]

np

[cedar kiln]

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[drifting fable]

what do you think

[crimson obsidian]

Vacuum word is confusing

[drifting fable]

the meaning of vacuum?

[crimson obsidian]

Yes

[drifting fable]

it means a space with no air

no molecules or anything

[crimson obsidian]

Without air is also vacuum

[drifting fable]

just nothing

[crimson obsidian]

Yes

[drifting fable]

yes

[crimson obsidian]

And the whole galactic space where stars are there

Is also vacuum

[drifting fable]

yes

[crimson obsidian]

So I don't understand

How to do this question

I know gravity wouldn't depend on vacuum

[drifting fable]

its asking if they have the same net acceleration in a vacuum

[crimson obsidian]

If iron ball and wooden ball have same mass, but that's not mentioned

Only same radius is mentioned

[drifting fable]

if they are in a vacuum, what is the only force acting on them?

[crimson obsidian]

Gravitational force

but isn't it different for different mass objects

In the options I see acceleration due to gravity everywhere

[drifting fable]

yes, the force on either object = m*g

so the force depends on mass

but does the acceleration depend on mass?

[crimson obsidian]

No

Ohh

[drifting fable]

so does that mean they take the sam e time then?

[crimson obsidian]

The small mass m cancels out

[coral jewel]

correct me if im wrong, but im pretty sure if we did this experiment but without vacuum, both balls would still take the same time to reach ground

[crimson obsidian]

Yes!!

[coral jewel]

gravity acceleration doesnt depend on mass

[drifting fable]

yes but if theres atmosphere you introduce friction

[crimson obsidian]

Without vacuum air resistance will be different for 2 objects

[deep wagon]

You'd have to factor in resistance

[supple flume]

https://youtu.be/E43-CfukEgs?si=kBvevsbklvmp1Vgk

[crimson obsidian]

I wonder how they breathe without oxygen in vacuum lol

Spenny

Nvm they do that

[supple flume]

?

[crimson obsidian]

Thanks

I thought they started within without air so it was surprising to see no oxygen mask

[supple flume]

Lmao

That would be some super villain type stuff

[crimson obsidian]

Indeed

Straight out from Marvel universe

[supple flume]

“I have your president in a vacuum which will be sucked of all its air in 4 hours. Solve this to save him”

[crimson obsidian]

Lol

.close

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[coral jewel]

$\sqrt{A} > B$

[wraith dagger]

FungusDesu

[coral jewel]

does that just mean $A > B^2$ or?

[wraith dagger]

FungusDesu

[crimson sedge]

if b is a positive

yes

[coral jewel]

.close

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[marsh horizon]

can anyone help me

[marsh horizon]

can you help me now

plspls

pls

pls

pls

pls

[harsh sky]

bro

[marsh horizon]

ps

[harsh sky]

stop

[marsh horizon]

help me

[harsh sky]

spamming

[marsh horizon]

i have exam tomtow

tomorow

sorry

tho for spamming

[harsh sky]

If no one is helping now, they will later

[marsh horizon]

can you help?

[harsh sky]

I cant sorry

oh I could

actually

yea

[marsh horizon]

tysm

[harsh sky]

ok wait

[marsh horizon]

ok

[harsh sky]

so

88000

is in which range of the table?

[marsh horizon]

45001-120000

[harsh sky]

yes

it says 5092 plus 32.5% of each dollar over 45000

how many is 88000 over 45000

88000-45000

[marsh horizon]

43000

[harsh sky]

yes so our guy Barton

has 43000 over 45000

and

the tax is 5092 plus 32.5% of the money he has over 45000

since he has 43000 dollars over

his tax is 5092 plus 32.5% of 43000

that should be enough to solve

tell me if you dont get it

[marsh horizon]

ok wait here

i will calculate and brb

19067 is that the answer?

[harsh sky]

lemme calculate lol

wait

[marsh horizon]

ok take your time

[harsh sky]

Yes its correct

19067

[marsh horizon]

tysm

ty

!!!!!

[harsh sky]

Np

[marsh horizon]

i have another doubt

brb

[harsh sky]

ok

[cedar kiln]

@marsh horizon Has your question been resolved?

[cedar kiln]

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[marsh horizon]

Hey bro you still there?

[marsh horizon]

can anyone pls help me

Andy drives up a ramp that is at an angle of 32 degrees with the ground. The vertical height of the ramp is 214 cm. Find the distance Andy drives up the ramp. Give your answer to one decimal place.

this is my question

.close

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[covert aurora]

So I have a point at (a, sin(a))
I have s graph y=cos(a)*x + ?
What is ? so that the graph intersects the point

[covert aurora]

.close

[cedar kiln]

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[marsh horizon]

Kiki help me

[cedar kiln]

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[lone plinth]

Can someone solve number 7 for me and show me how you solved it

[fair mortar]

power rule followed by chain rule

[lone plinth]

no I mean like how do I draw the graph not solve the function

I need help with solving the question not the equation

[deep wagon]

You can factor x^2 - 1 as (x+1)(x-1). Then, (x^2 - 1)^3 = ((x+1)(x-1))^3 = (x+1)^3 * (x-1)^3. From this, you can see that the equation has roots at -1 and 1, so you need to check the end conditions for x < -1, -1 < x < 1, and x > 1. This gets that y goes to positive infinity as x goes to + or - infinity, and y is negative for -1 < x < 1. Since the powers of the roots (which is 3) are odd, you know that the function crosses the x-axis at the roots. Knowing all of this, you can sketch the graph

[fair mortar]

wait that is a function of degree 6, you should not be asked graph such graphs by hand

[lone plinth]

ty

[cedar kiln]

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[daring peak]

for part (ii) im not sure how i would do the proof for it

[cursive crystal]

Wait, its called x_n so you need to change that

[daring peak]

ive done this part already

[cursive crystal]

Wait, wasnt that ii)?

[daring peak]

no that was (i), sorry i cut it off a bit

[cursive crystal]

ah nvm, the first thing is just the question, sorry 😄

[daring peak]

i have M as 5/3 but i dont know how to prove it

[cursive crystal]

Well, that shouldnt be that hard, gimme a min

(you didnt do yourself a favor with that M 😄 )

there is a zero missing in the third to last line

but rest of the proof should be correct

[daring peak]

thank you

.close

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[lone plinth]

how do they get this derivate?

[undone epoch]

Quotient rule.

[native heath]

mmm

do you know that?

[lone plinth]

but how when 3x^2 * (x+1) - x^3^(1) /(x+1)^2

[native heath]

uh wha

[lone plinth]

how does that equal what they have as an answer?

oops wait

but still like how do they simplify it to become their answer?

help 🙏

[cedar kiln]

@lone plinth Has your question been resolved?

[cedar kiln]

@lone plinth Has your question been resolved?

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[jovial lake]

The name of a variable in the JAVA programming language is a string of between 1 and 65,535 characters, inclusive, where each character c a n b e an uppercase or a lowercase letter, a dollar sign, an underscore, or a digit, except that the first character must not be a digit.
How many unique variable names could there be in JAVA?

Discrete things

[compact bone]

;)

[gusty forum]

!nosols

[cedar kiln]

As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.

[compact bone]

oh ok

should I delete?

[gusty forum]

i recommend it

[fervent monolith]

what if every variable name was three characters, where each could be an uppercase/lowercase letter, a dollarsign, an underscore, or a digit, except the first character must not be a digit? how many would there be, then?

if this one is too hard, consider the one character variable name case

[cedar kiln]

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[marsh spindle]

I want to calculate and graph the domain

[marsh spindle]

from the arcsin its just -x/2 -2 <= y <= -x/2 +2

but for the logarithm i have a problem

is that correct?

I then get two quadratic functions, and grapgh them properly

or is it not the same?

or since im getting the domain, i have to make another assumption that y+1 > 0, so draw horizontal line at y=-1, and get anything above, right?

[empty kestrel]

That is the way

[marsh spindle]

but desmos is dropping me different answer. When i type x > sqrt(y+1), it just graphs the right side

But when doing it with |y+1|, i get left and right side, above y=-1

[empty kestrel]

After adding the condition y+1>=0, you don’t end up with |y+1| but with just y+1

[marsh spindle]

shouldnt it work either way?

[empty kestrel]

And x>0 needs to be included

[marsh spindle]

stupid question but it needs to be included just cause we got that sqrt on right side?

and at most it can be 0

[empty kestrel]

Yes, doing it formally would be: split the system in two cases, one where x<0, which has no solutions, one where x>0 and only here you can safely square both sides without adding more solutions than those of the original system

x>=0*

[marsh spindle]

yes

alrighty, just wanted to make it clear

thank you

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[marsh spindle]

I have graphed such domain, how do i express it using formula? Like the domain x ∈(-2, 2) for example

[cedar kiln]

@marsh spindle Has your question been resolved?

[novel topaz]

For the third one u can write it as x(x-2)<0 which means the domain x is (0,2)

From there u can get 2 domains of y and take intersection

[lusty flax]

If you want to include the endpoints, use brackets [] if not, then use ()

Infinity always uses ()

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[marsh spindle]

.reopen

[cedar kiln]

✅

[marsh spindle]

thats not what i mean

i want to express the domain Df = {(x, y) ∈ R^2 : "And here conditions"}

or something like that

like is that correct?

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[twilit badger]

dunno how how to solve this

[austere merlin]

What do those symbols represent

[livid dust]

Can you give some more context? those numbers don't have any meaning

[dire geode]

needs more context

[twilit badger]

sorry

geometric sequences

[dire geode]

yea still not enough. you need to define what the variables mean

what's t1, q, n, tn, sn?

[twilit badger]

so a geometric sequence can be defined as tn = tn-1*q

and n is the number which you have

so you could have a sequence for example: 2, 4, 8, 16... with n being 1, 2, 3, 4 and t1 being 2; t2 being 4; t3 being 8; t4 being 16

t4 = 8 * 2

[cedar kiln]

@twilit badger Has your question been resolved?

[dire geode]

where's sn and how does it relate to tn?

[twilit badger]

sn is the sum of a n amount in the sequence

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[frank bronze]

i don't think i found the derivative right

[glass sky]

you didnt do the diff of e^root x right

[frank bronze]

uh

[glass sky]

what did you do in the third step

like can you name the rule

[frank bronze]

nested chain rule

chain rule 2 times

[glass sky]

why two?

when you do it the second time you are essentially here dealing with root x differentiation with respect to x you dont need to do it another time

for a function f(g(x) ) , you must use chain rule to differentiate it
it goes like this
f'(x) g'(x)

[frank bronze]

well because there are 3 layers to this equation, 2 differnt exponets

[glass sky]

hm consider this

f(x) = e^root x
f'(x) = d(e^root x ) / dx
let root x be t
f'(x ) = d(e^t) / dx
multiplying it by dt/dt

f'(x) = { d(e^t ) / dt } { dt/dx }

check if you are following

[frank bronze]

f'(x) = d(e^root x ) / dx

dont follwo along with that

we are dividing by dx?

[glass sky]

no thats the notation for derivative...

differentiation of e^root x with respect to x

how was chain rule defined when you learnt it....?

[frank bronze]

wait hold on, side question

true or false

[gilded anvil]

that is correct

different notation for the same thing

[frank bronze]

but say that the derivative of the second term has another exponet

[glass sky]

ah give me a sec i will modify my explanation into this notation

[frank bronze]

then it would be nested

[glass sky]

are you aware of this derivativenotation?

dy/dx

[frank bronze]

yes

[glass sky]

oh then this shouldnt be a problem

check?

[frank bronze]

welll, i agree with what you did yes, but you did it with U substitution, which is not wrong, im just tryna find out why i did mine wrong.

[glass sky]

u substitution?

ma'am this is how chain rule is defined

[glass sky]

sadly e^root x and (e^x )^1/2 are two different things

e^root x != root of e^x

you getting my point?

[frank bronze]

i agree

[glass sky]

so yeah^

can you retry?

[frank bronze]

i agreed with that statement but im not sure how it applies here. im still confused. this is what im getting

[glass sky]

not quite

what is diff of e^u

[glass sky]

power rule is used for diff of x^ a , where a is a constant

[cedar kiln]

@frank bronze Has your question been resolved?

[frank bronze]

well its just e to the power of u

[cedar kiln]

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[frank bronze]

.close'

.close

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[cedar kiln]

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[wraith dagger]

Normed

[wet fossil]

.close

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[plucky cloak]

So basiclly i need to find the purple area from this figure:

Then, first i did find the circle area (πr²) r being 7
It gave me a result of 49π cm²

Then i got the area of the half circle.
(Did the same than the normal circle but divided into 2)
Result: 24.5π cm²

Then i got the rectangle area. (b x h)
(i got the h by doing: 7 x 3)
Result: 294cm²

Now to find the purple area we need to do: (Normal circle area + half circle area) - rectangle area.

it is: (24.5π + 49π) - 294.
How can i do that operation if you cant sustract π with a real number???

[deep wagon]

The area of the purple region would be rectangle area - (Normal circle area + half circle area). Which is 294 - (24.5π + 49π)

[plucky cloak]

Yeah, you are right, but anyway how do i sustract 294 - 73.5π

[deep wagon]

Do you want an exact solution or approximate? If exact, then 294 - 73.5π is your answer

[plucky cloak]

Thanks, the instrucctions are to leave π indicated.

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[blissful thorn]

Im trying to find the intervals where it is positive and negative

Im supposed to do it without a calculator thats whats confusing me

[cedar kiln]

@blissful thorn Has your question been resolved?

[blissful thorn]

<@&286206848099549185>

[civic eagle]

test the intervals

plug in a value of your choice to f'(x) for the intervals (0, e/154) and (e/154, inf)

[blissful thorn]

I know but my question is more on like lets say i choose 50 how would i do the calculations without a calculator

[civic eagle]

you only need to determine if its positive or negative

like, if we choose x = 0.01, which falls into the first interval, then we just need to figure if 1 - ln(1.54) is positive or negative

we know lnx is less than 1 when x < e

[blissful thorn]

Missing piece to my puzzle😭

Thanks

.close

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[coral pilot]

hi, i've solved this one but it was wrong :( there is a right answer, so if you know, how to solve it and get this one answer, i'd be grateful!

[gritty viper]

Do you know partial fractions

[coral pilot]

well, i'm really bad at solving them

[gritty viper]

!show

[cedar kiln]

Show your work, and if possible, explain where you are stuck.

[coral pilot]

my work is in the trash bin 💗

NOT THE REACTION.... HELP.

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[dire geode]

The redo it and show it

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[atomic pecan]

where is the best place to get problems in functions ?

[atomic pecan]

practice problems

[past dawn]

which functoins

khanacademy, deltamath

ixl

[atomic pecan]

interesting , okay will check them out

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[lofty kernel]

How to do mathematical induction here

1+3+3^2+... 3^n-1 = (3^n - 1)/2

(in the first term, 3^n-1, -1 is also included in the exponent with n, however, not in the second term, 3^n - 1.)

This was my working so far

verified with n=1 and n=2

step 2: n=k

1+3+3^2... 3^k-1 = (3^k - 1)/2

step 3: n = k+1

1+3+3^2....3^k-1 + 3^(k+1)-1 = (3^(k+1) - 1)/2

(3^k - 1)/2 + 3^k = (3^(k+1) - 1)/2

now i dont know to progress and equate these

[cedar kiln]

@lofty kernel Has your question been resolved?

[thin roost]

your done after that

[lofty kernel]

in a solution i hvae no idea how they got 2.3

or 3.3 whatever

[thin roost]

ahuh

?

i dont see any eqn marked as 2.3 or 3.3

yeah there are right

so "." as in multiplication

alr