help-0

[mossy jetty]

which one

[whole shell]

you dont need to do any

do the

[mossy jetty]

??

[whole shell]

second derivative

for that equation

[mossy jetty]

how do u do it?

[whole shell]

how to do the second derivative?

[mossy jetty]

wait nvm

i thought u said i don't need to do the 2nd derivative

[whole shell]

no i meant

you dont need the answer for a

[mossy jetty]

i gpt (2lnx - 3 )/ x^3

[whole shell]

now

we need to set the second derivative = to 0

and solve for x

[mossy jetty]

ye i did that

e^3/2

but idk where to go after

[whole shell]

that should be it

well you need to plug in e^(3/2) into the y

to find y

[mossy jetty]

the original f?

[whole shell]

yh

[mossy jetty]

i got (lne^3/2) /e^3/2, but idk how to simplify

[whole shell]

start with the ln(e^(3/2))

its an easy one

to simplify

[mossy jetty]

1.5...?

[whole shell]

yh

[mossy jetty]

1.5/e^3/2

is it final or can i simplify even more

[whole shell]

well

you can write

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

[ocean seal]

doctor99268

[mossy jetty]

ahhh right

thanks so much man

[lone heart]

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[fresh fulcrum]

have quick question I have a factor 'A' which is part of a bigger number 'B'
A = 3^3 * 13^1 * 29^2
B = 3^3 * 5^a * 7^b * 11^c * 13^1 * 17^d * 19^e * 23^f * 29^2

So for B as you can see I know the bases but many of the exponents I don't

How can I figure out the exponents of B ?

Thanks

[alpine sable]

You seem to be missing some context here. What is the original question you are trying to solve?

[raven haven]

,tex \factoid original

[fresh fulcrum]

This is all the information I have been given.

Given a number B = 3^3 * 5^a * 7^b * 11^c * 13^1 * 17^d * 19^e * 23^f * 29^2
and one of it's factors A = 3^3 * 13^1 * 29^2

Find the rest of the exponents in B

Sorry there is also this
exponent 3 has to appear exactly 3 times
exponent 2 has to appear exactly 3 times
exponent 1 has to appear exactly 3 times
only these 3 exponents can appear within the exponents of B

Any techniques where I can hone down where each exponent can fit in ?

[alpine sable]

it's still very ambiguous... send a screenshot of the original question

[fresh fulcrum]

That all I got

[blazing bobcat]

There's a lot of answers

There are too few restraints

[fresh fulcrum]

agreed yea I will try and ask if I am missing something thanks !

we are also provided with a website where we can submit our answers (the full number B) and it just tells us closer or further to the answer

Which is making me think there' s probably no way other than trying all possibilities ?

[lone heart]

@fresh fulcrum Has your question been resolved?

[fresh fulcrum]

Is there a methodology then that would help me maybe filter through the possibilities ?

[lone heart]

@fresh fulcrum Has your question been resolved?

[lone heart]

@fresh fulcrum Has your question been resolved?

[lone heart]

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[bold siren]

Hello can anyone help me about this midline theorem?

[bold siren]

I am thinking on number 14, I think the answer is Definition of a Midpoint

[lone heart]

@bold siren Has your question been resolved?

[bold siren]

<@&286206848099549185>

[normal flower]

Gimme few minutes

I am outside

[bold siren]

Oh alright

[normal flower]

What's the 2nd pic about?

You have to prove that too?

Or it's given

Oh okay you have to write about it

[bold siren]

Wait

[bold siren]

Yes

It's the statements that should be given a reason

[normal flower]

Right

[normal flower]

Hey

So yeah

[normal flower]

By proving OTHS as a parallelogram

If you want I will prove it

You will get

OT=HS

1/2HS = OE

[normal flower]

Yeah no

I am just saying unwanted things

You need to prove E as MP

OT=1/2HS

OE=ET

So you can prove E as MP here

OE+OE=OT

2OE=OT

That's all

[lone heart]

@bold siren Has your question been resolved?

[lone heart]

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[full bolt]

(2x^2 +7a^2 -3ax) : (x - 2a)

[lone heart]

@full bolt Has your question been resolved?

[full bolt]

<@&286206848099549185>

[lone heart]

@full bolt Has your question been resolved?

[shut pewter]

I found a similar problem on the internet

And I also tried doing it on yours, I've got 0 for a

[shadow gate]

What is the question though

[shut pewter]

I think u need to find a so that x-2a can be factored out

I tried doing sum and product of roots but can't find it that way so I searched for factoring polynomials with unknown coefficient and I found this

When I always try product and sum rule, I'll always got an i or a square root of -1 which I don't think is the goal

[lone heart]

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[lone heart]

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[worthy falcon]

test corrections help

[quasi vector]

what do you mean "test corrections"

do you have to solve the question

[worthy falcon]

yea i did bad on a test and in order to re do then i must correct my errors in a printed out version

[quasi vector]

so you have to solve the question right

[worthy falcon]

yes

[quasi vector]

notice $224 = 32 \times 7 = 2^5 \times 7$

[ocean seal]

kheerii

[worthy falcon]

i don’t understand

sorry

[worthy falcon]

also the long line is a misprint

it’s suppose to be like this

[quasi vector]

$\sqrt[n]{a\times b} = \sqrt[n]{a} \times \sqrt[n]{b}$

[ocean seal]

kheerii

[worthy falcon]

i believe i’ve solved it

is this correct?

[quasi vector]

yes

[worthy falcon]

ok thank you so much

i have another question would i have to open up another channel

like doing the steps before or can i just ask it

[quasi vector]

you can just ask it

[worthy falcon]

it says “solve and leave answer in reduced form do not put your answer in decimal form”

[quasi vector]

$\frac{a^b}{a^c} = a^{(b-c)}$

[ocean seal]

kheerii

[worthy falcon]

would a^b be 18x^1/3 and a^c be 27x^4/3?

[quasi vector]

well

you can deal with the numbers separately

[worthy falcon]

how so?

[quasi vector]

$\frac{18x^{\frac1{3}}y^{\frac{5}{4}}}{27x^{\frac{4}{3}}y^{\frac1{2}}} = \frac{18}{27} \times \frac{x^{\frac1{3}}}{x^{\frac{4}{3}}} \times \frac{y^{\frac{5}{3}}}{y^{\frac1{2}}}$

and you can deal with each fraction separately

[worthy falcon]

question where does the last x come from in the last fraction to the far right

[quasi vector]

that should be a y

my bad

[ocean seal]

kheerii

[worthy falcon]

like this?

[quasi vector]

is that not the previous question

[worthy falcon]

oh wrong image

this one

[quasi vector]

well

what about the y's

[worthy falcon]

ah

there i have no idea

[quasi vector]

I wrote it down for you

what is the issue

[worthy falcon]

i wouldn’t need to do anything with those y’all

?

would they stay the same?

[quasi vector]

yes

you have to use the property I mentioned beforehand

[quasi vector]

.

for the last two fractions

[worthy falcon]

ahh alright then one sec

would i subtract the numerator or the denominator

or both

[quasi vector]

what?

[worthy falcon]

for the y’s

to subtract

[worthy falcon]

what exactly would i need to subtract here

[quasi vector]

well

if you just consider $\frac{x^{\frac1{3}}}{x^{\frac{4}{3}}}$

[ocean seal]

kheerii

[quasi vector]

here your a is x, b is 1/3 and c is 4/3

[young phoenix]

a little help

[quasi vector]

!help

[lone heart]

Please read #❓how-to-get-help

[quasi vector]

this channel is taken

can't believe how many times I have to say this

[worthy falcon]

would i subtract the top?

[lone heart]

@worthy falcon Has your question been resolved?

[normal flower]

Wait

What answer did you get?

And which question

[lone heart]

@worthy falcon Has your question been resolved?

[lone heart]

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[chilly dove]

Can anyone help me solve C and D? The tax rate is 5%

[clear stump]

nah dont feel like it but cool pfp

[chilly dove]

damn

i see you guys reacting please help me

[ocean hawk]

What have you tried? what is your first guess?

[chilly dove]

nothing cuz idk what to do

[vale wigeon]

@chilly dove have you worked with percentages before

in any capacity whatsoever

[chilly dove]

yea

but only with values like those 2 idk what to do

[vale wigeon]

... ?

okay let's try to backtrack maybe

when we say "the sales tax rate is 5%", do you know what that means?

[chilly dove]

yea

[vale wigeon]

ok

explain in your own words what that phrase means

[chilly dove]

so 5% tax rate means that 5% of the marked price will be ruduced to a new selling price

[vale wigeon]

"ruduced"?

[chilly dove]

what other word then

[ocean hawk]

If I have a product that is marked as $100, and you know sales tax is 5%, how much do you end up paying at the register?

[vale wigeon]

i don't know what you meant by "ruduced". maybe it is a word that i am somehow unfamiliar with.

[chilly dove]

reduced

[vale wigeon]

oh.

so it was a misspelling.

[chilly dove]

you sound like an ai

but yea

[vale wigeon]

maybe that's because i am in somewhat of a not-the-best mental state

[chilly dove]

105 dollars

[vale wigeon]

i do tend to be like that at times

[chilly dove]

wait i think ik what happend

i got tax mixed up with discount

[vale wigeon]

lmao

complete opposites aren't they

[chilly dove]

C marked price should be 100 right

[vale wigeon]

anyway, i think a better phrasing would be: the sales tax is equal to 5% of the pre tax price. that plus the sales tax make up the marked price

[vale wigeon]

no, 100 is the pre tax price

[chilly dove]

yea

marked is pre tax

nvm

[vale wigeon]

no

pre tax is the middle col

[lone heart]

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[crude steeple]

I’m a little stuck on the second part 😔

[molten mesa]

I need help for Statistics

[crude steeple]

Bruh

My channel

[molten mesa]

Oh sorry

[crude steeple]

Lmao

Ur good

[molten mesa]

How do I get my own channel im kinda new here

😅

[crude steeple]

Lol if u go to the channel list the section above this one has help channels with numbers, just put ur question in there and it’ll rename to be ur channel

[molten mesa]

Thanks

[crude steeple]

Yw

Ima resend my question

Stuck on second part

.close

[lone heart]

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[sage hornet]

.open

.ask

[lone heart]

@quasi holly Has your question been resolved?

[lone heart]

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[worthy falcon]

help

[kind patio]

what are you solving for here

or are you just simplifying

[worthy falcon]

question asks “solve and leave answer in reduced form and do not put your answer in decimal form”

[kind patio]

doesn’t say solve for anything?

[worthy falcon]

it just says what i quoted here

<@&286206848099549185>

[normal flower]

Ok wait

[worthy falcon]

alright

[normal flower]

You just want answer?

Or

Steps?

[worthy falcon]

both would be great

[normal flower]

I can't type good in text

But lemme try my best for you

[worthy falcon]

alright thank you

[normal flower]

$3^2 * 2$

[ocean seal]

Buddy

[normal flower]

Okay

It works

Lemme try

$(3^2 * 2 * x^1/3 * y^5/4) / (3^3 * x^4/3 * y*1/2$

Ahh

Dang it

[worthy falcon]

would i turn the 18x into 2x and 27x into 3x?

[normal flower]

$(3^2 * 2 * x^(1/3) * y^(5/4)) / (3^3 * x^(4/3) * y*(1/2)$

[ocean seal]

Buddy

[normal flower]

No no

18 = 3^2 * 2

That is

$3^2 * 2$

[ocean seal]

Buddy

[normal flower]

I have no clue on how to use the exponent thing

That's just sad

It's just sad for me

Gimme a minute

[worthy falcon]

alright

[normal flower]

Okay I solved it

5^3/4 is in exponent btw

I don't know how to use the steps lol

[worthy falcon]

where does the 5 come from?

[normal flower]

Wait

[normal flower]

Oh shit it's y

😂

Lemme just re write

[worthy falcon]

ah ok

so does y^5/4 and y^1/2 just becomes y^3/4 together?

[normal flower]

$1/3 * 2 * 1/x * y^(3/4)$

[ocean seal]

Buddy

[normal flower]

Yes

(5/4)-(1/2)

[worthy falcon]

what about 18x^1/3 and 27x^4/3

like this?

[celest minnow]

yes but no x under the line

[worthy falcon]

this is an example of the type of question it is

that one’s much more simple tho

[worthy falcon]

so this just without the x’s?

[celest minnow]

yes

[worthy falcon]

also question, how did the -2/3 become a negative

[celest minnow]

.

[worthy falcon]

where did the negative come from

[ocean hawk]

What's the original problem?

[worthy falcon]

^

here

[worthy falcon]

and this is what it asks

[ocean hawk]

Should be $x^{-1}$

[ocean seal]

cwatson

[celest minnow]

sorry i made mistake the power of x is -1

1/3- 4/3

[worthy falcon]

like this?

[ocean hawk]

No

[celest minnow]

no

[ocean hawk]

$\frac{2}{3} x^{-1} y^{\frac{3}{4}}$

[ocean seal]

cwatson

[worthy falcon]

ahhh ok

[ocean hawk]

Do you see how that all was obtained?

[worthy falcon]

yea thank you

can i ask one more question

<@&286206848099549185>

for the top ones how would i know wether it’s a exponential growth or decay

i remember my teacher told us a short cut but i don’t remember it

[lone heart]

@worthy falcon Has your question been resolved?

[lone heart]

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[meager rover]

can someone please help me understand this

[tacit arch]

be more specific

[meager rover]

how did they get the variance and the mean on the first slide

[lone heart]

@meager rover Has your question been resolved?

[lone heart]

@meager rover Has your question been resolved?

[meager rover]

.close

[lone heart]

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[tame quest]

hey, sorry, didn't understand this at all, i'll do my best to translate but i just didn't understand what i had to do. top to bottom left to right "To complete the chart you must perform translations. ¡Cheer up!" and then "As inequalities", "As intervals", "Graphically"

[tame quest]

i'd appreciate the help

[surreal meadow]

do you understand the interval notation?

[tame quest]

not really

[surreal meadow]

then interval [a,b] represents the values between a and b, inclusive

[tame quest]

i mean, i understand what they represent but i don't know how they translate between each of the other 2

[surreal meadow]

well we have x>2

-2

so we want every value greater than -2

what would be the left value in the interval

you should think of the interval as
[smallest value, largest value]

[tame quest]

uh, -2; +infinity?

[obsidian fossil]

Help

[surreal meadow]

yes

and to be clear, we’d use parentheses

[obsidian fossil]

Ive already done the combination

[surreal meadow]

#❓how-to-get-help

[obsidian fossil]

How do u do the permutation?

[tame quest]

apparently they did it in class, and they just showed me the results, but i don't really understand so i think it'll be better to completely comprehend the things in the graph

[surreal meadow]

well you have the value right

it’d be (-2, infinity)

the interval represents the values
-2 < x < infinity

which is just -2<x, or x > -2

[tame quest]

these were the results, i don't understand the < pointed downwards and the graph

[tame quest]

mhm

[surreal meadow]

the $\land$ means “and”

[ocean seal]

maximo

[tame quest]

oh, makes sense

[surreal meadow]

$\lor$ (which you may run into later) means “or”

[ocean seal]

maximo

[tame quest]

alright, thanks, what about the graphs though?

[surreal meadow]

btw the bottom left answer is incorrect

[surreal meadow]

the graphs should be self explanatory. the shaded areas are the values included, the open circles are not included

they represent the numbers the same way the inequalities and intervals do

[tame quest]

oh, alr

thank you very much.

i understand now

[surreal meadow]

i think it’d be a good exercise for you to fix the bottom left inequality

[tame quest]

alright

i'll try

[surreal meadow]

tambien avisame si preferís que hable en español

[tame quest]

speak in the language you prefer, im good enough at both of them

would the "x" in front of the 1 be the problem or would i be thinking in the wrong way?

[surreal meadow]

well that’s also not ideal

written “correctly” the inequality should be $$x > -1 \land x < 3$$

[ocean seal]

maximo

[surreal meadow]

but there’s still an issue there

[tame quest]

which issue?

[surreal meadow]

i’d like for you to figure it out

look at the graph

[tame quest]

alright

[surreal meadow]

is -1 included?

[tame quest]

yes, i think

[surreal meadow]

it’s not

because it’s an open circle

it’s a hollow circle

[tame quest]

oh, didn't see it because it was so small

[surreal meadow]

how about 3?

is 3 included

[tame quest]

it is, since it has no hollow circle

[surreal meadow]

right

[tame quest]

i think.

[surreal meadow]

so looking at the inequality

[surreal meadow]

this one

what’s missing/wrong?

[tame quest]

would it be x > 0 or x > -0.99 since the areas before -1 are shaded

[surreal meadow]

the idea is that x>-1 excludes -1

-1 is not greater than -1

if we wanted to include $-1$ we’d write $x\ge -1$

[ocean seal]

maximo

[tame quest]

oh, what does the line under > change?

[surreal meadow]

it means “or equal to”

so > with a line means “greater than or equal to”

and < with a line should mean what?

[tame quest]

smaller than or equal to?

[surreal meadow]

yup

now the x>-1 is good

because it excludes the -1

how about the x<3?

[tame quest]

it should have a line under it

since it includes 3

[surreal meadow]

exactly

so you can fix that

one last thing that i noticed

the box right next to that one

is also incorrect

see if you can tell why

[tame quest]

it has no -

[surreal meadow]

yup

that should be all

[tame quest]

alright, thanks for the help again

[surreal meadow]

np

[tame quest]

you did a way better job than my teachers

.close

[lone heart]

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Remember:
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• After 15 minutes, feel free to ping <@&286206848099549185>.
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[alpine sable]

What am I doing wrong here

[wary stream]

$\sqrt{x} * \sqrt{x} \neq x^2$

[ocean seal]

dldh06

[alpine sable]

What is it then

I thought sqrt x becomes x

@wary stream

[wary stream]

No

sqrt(x) doesn't magically become x

Recall your exponent rules

That sqrt(x) = x^(1/2)

So x^(1/2) * x^(1/2)

[alpine sable]

Sqrt x is always x^(1/2)?

[wary stream]

Why would it change to x?

[alpine sable]

Cus like sqrt 1 becomes 1

[wary stream]

What about sqrt(4)?

Is that equal to 4?

[alpine sable]

No

How do u know that x is 1/2?

[wary stream]

I never said that x is 1/2

[alpine sable]

This

[wary stream]

That's not saying x is 1/2

[alpine sable]

Yeah I meant exponent

[wary stream]

Recall your exponent rules

[alpine sable]

Pemdas?

[wary stream]

That's order of operations

[alpine sable]

I have no idea what exponent rule is then

[wary stream]

Those

[alpine sable]

I’ve never seen those in my life

[wary stream]

Those come up a lot when dealing with exponents/roots

[alpine sable]

My teacher showed me it like this

[wary stream]

Okay, and?
The exponent rules is to show why I said this $\sqrt{x} * \sqrt{x} \neq x^2$

[ocean seal]

dldh06

[wary stream]

Recall your exponent rules
That sqrt(x) = x^(1/2)
So x^(1/2) * x^(1/2)

$\sqrt{x} * \sqrt{x} = x^{1/2} * x^{1/2}$

[ocean seal]

dldh06

[lone heart]

@alpine sable Has your question been resolved?

[lone heart]

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[plucky hull]

The ones I selected are wrong. Can someone assist me?

[surreal meadow]

why did you select the first one?

[plucky hull]

cuz know that P(1) is true cuz its given in the information. assuming that P(k) is true for some integer k≥1, we can apply the condition P(k)→P(k+1) to conclude that P(k+1) is also true. since k+1 is also a natural number, we can repeat the process and conclude that P(n) is true for all n∈N.

[surreal meadow]

suppose that k was 3

the we have P(1) is true, and P(3) -> P(4)

that doesn’t tell us anything about the truth of P(2), P(3), P(4),…

all we know is P(1) is true

[plucky hull]

oh i see

so was that my only incorrect answer?

[surreal meadow]

no

[plucky hull]

which ones were wrong then?

besides the first one

[surreal meadow]

i feel like you should take a look again

[plucky hull]

ok i will. im almost done again, can i check w you again to see if im correct?

[surreal meadow]

sure

[plucky hull]

yes? no?

[surreal meadow]

you’re missing the last one

also, the third one doesn’t necessarily work

(suppose P(1) is not true)

[plucky hull]

ohh interesting

[surreal meadow]

seeing why the last one works should be easy

[plucky hull]

so just the second fifth and seventh one?

and yea i see now

[surreal meadow]

2,4,7

oh

2,5,7 sorry

7 is like a more restrictive version of 5

but they turn out to be the same thing

[plucky hull]

i see

thank u

[lone heart]

@plucky hull Has your question been resolved?

[lone heart]

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[vapid steppe]

how to fix negative z and w value

[serene junco]

I don't think your equations are correct

or the way you've assigned the variables

ham, turkey, and roast beef are all "meat"

[vapid steppe]

Why

[vapid steppe]

Where

[serene junco]

Read through the question again.

You're given the price per pound of ham, turkey, roast beef, and cheese

And asked how many pounds of each you should buy

[vapid steppe]

roast beef is the meat right

[serene junco]

this is what I meant

[vapid steppe]

oh so what should i do

[vapid steppe]

i thought you meant like i used the same variable for all of them

[serene junco]

Oh, no you should still have four variables

but they should be for ham, turkey, roast beef, and cheese

Try writing your equations again using those

[vapid steppe]

i would change meat to roast beef?

[serene junco]

yeah

but the equations are going to have to change too

[vapid steppe]

so the first equation should be x+y+z+w=12

[serene junco]

yeah

[vapid steppe]

x+z+w=2y

[serene junco]

good

I think the other two are okay

[vapid steppe]

Oh

[serene junco]

I didn't solve the system but theoretically (?) you shouldn't get any negative values

[vapid steppe]

i got x=2,y=4,z=3,w=3

[serene junco]

That looks good to me 👍

[vapid steppe]

Ty bro

.close

[lone heart]

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[vapid steppe]

(x²)^(x²)=5
solve for the exact value

[vapid steppe]

Do i use lambert function

[west girder]

yes

letting x^2=u will make it clearer

[vapid steppe]

so like i take ln of both sides

[west girder]

yea

[vapid steppe]

x²ln(x²)=ln(5)

[west girder]

now x^2=e^(ln(x^2)) and it should be clear how to finish

[vapid steppe]

oh right

e^(ln[x²])ln(x²)=ln(5)

ln(x²)=W(ln(5))

,w √[e^(productlog(ln(5))]

[ocean seal]

Results provided by WolframAlpha

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

Requested by Jash#2503

[vapid steppe]

.close

[lone heart]

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[next blade]

i have an equation but im not sure what im supposed to show at the end

[next blade]

i have ad - bc +b - d = 0

[tacit arch]

!show

[lone heart]

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

[tacit arch]

I think you're done. Anything else is just algebraic manipulation

[next blade]

ok hopefully thats correct then

.close

[lone heart]

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[junior condor]

Trying to show d), here, F is the family of functions $f_i$ that are made continuous by the weak topology on X

[ocean seal]

CatGPT

[junior condor]

Take $x,y\in X$. Then, there exists some $f_i$ such that $f_i(x)\neq f_i(y)$. Y is $T_0$, so there exists some open neighborhood O around $f(x)$ not containing $f(y)$.

[ocean seal]

CatGPT

[junior condor]

Then, take the preimage of f of O, and im a dead fish dunno where to go

[junior condor]

Here, $f_i$ sends $X\to Y_i$

[ocean seal]

CatGPT

[junior condor]

so if I take preimage $f_i^{-1}(X)$ of O, O contains x but not y

[ocean seal]

CatGPT

[junior condor]

showing that X is also $T_0$?

[ocean seal]

CatGPT

[junior condor]

.close

[lone heart]

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[alpine sable]

Can someone help

[alpine sable]

What would the free body diagram be for something that blows air onto another thing and gains momentum because the air is being pushed back at an angle

[long axle]

Could u send a picture as to what ur referring to

[alpine sable]

Sure

Something like this

I drew two free body diagrams and combined them, but I feel that I did it wrong

[quick peak]

That’s not possible

Like you can’t move with that

[alpine sable]

I know

There’s obviously an electric skateboard under him

But hypothetically if you could, what would the free body diagram be

I have all the other fbds

But I have no idea how to draw that fbd

[quick peak]

It would just cancel out on the umbrella

[quick peak]

Because the air however does go sideways

[tulip lintel]

Can anybody help me with this?

[quick peak]

It could have some some force pointed in the direction of the leaf blower

[alpine sable]

Sure

[tulip lintel]

Thank you🙏

I know they aren’t the same I just don’t know why

[alpine sable]

they’re not the same because sin(x) and sin inverse are inverse operations(obviously) but sin inverse x multiplied by sinx is different because they’re being multiplied by each other and yield different values, while sin(arcsin(x)=x because since the arc sin is in the operation, they can cancel out. But if they’re being multiplied by each other, then they would yield different values

sin(arcsinx)=1

Let x = 1

sin(x)arcsin(x)≈1.5

[tulip lintel]

Ohhhh ok I see, thank you paradox. you a real one for that💯

[alpine sable]

np

[tulip lintel]

May I ask you for a little more help on some simple problems?

[alpine sable]

Sure

[tulip lintel]

Cool alright

[alpine sable]

Ok so

Change the notation

y=5cos3x

Divide both sides by 5

Then take the arccos of both sides

So you should get

3x=arccos(y/5)

Then divide by 3

So you get x=arccos(y/5)/3

[tulip lintel]

Oh ok this is for the inverse right?

[alpine sable]

Yeah

[tulip lintel]

Ok cool

[alpine sable]

Then just substitute y with x and you get f^-1(x)=arccos(x/5)/3

Do you have a graphing calculator

[tulip lintel]

Yessir

[alpine sable]

Ok so graph the inverse

And find where it starts being undefined

[tulip lintel]

Yup tryna get the right window

[alpine sable]

You can use the table too

[alpine sable]

Yep so what do you think the domain is

[tulip lintel]

[-1,1]

[alpine sable]

Can I see your table settings

I mean window

[tulip lintel]

Table?

[alpine sable]

So it starts being undefined at 6

Should be the same with -6 too

[tulip lintel]

Yup

Ok

[alpine sable]

So

-5<=x<=5

[tulip lintel]

Oh ok

I thought it would be [-6,6]

Because it never touches it

In domain form would that be [-5,5]?

[alpine sable]

Yes

[alpine sable]

Try plugging in a value really close to 6

You’ll see that it doesn’t work

When you do calculus this is called limits

It’s undefined there

[tulip lintel]

Oh ok yeah

So [-5,5]

[alpine sable]

Yep

[tulip lintel]

Range would be

[alpine sable]

The calculator is scuffed but the range would be

[tulip lintel]

[0,60]

[alpine sable]

Yeah

That’s right

[tulip lintel]

Yesssirr

Cool

Ok

For what values of x satisfy f(f^-1(x)) = x

[alpine sable]

Yeah this is easy just find where they intersect

It’s like 4.840

[tulip lintel]

Wait what💀

[alpine sable]

Wait

[tulip lintel]

Isnt it pi/3 and 5?

[alpine sable]

Ok so

For the first one

It’s [-5,5]

Everything on that interval

[tulip lintel]

The first satisfy one?

[alpine sable]

And you can verify it

And for the second one it’s [-infinity, +infinity]

But the range is [y, +infinity]

Here I will show you

[tulip lintel]

Ok

[alpine sable]

Plug these into your calculator

And look at the tables

Do you see their domains and ranges?

[tulip lintel]

Ok

[alpine sable]

That’s what satisfies it

[tulip lintel]

Oh wow um ok

Yeah

Let me try to get them

[alpine sable]

Sorry if I’m not that good at explaining

[tulip lintel]

It’s all good

So far I have understood everything you said you’re doing great at explaining

Ok so yeah

Second one is -infinite, infinity

[alpine sable]

Yeah

[tulip lintel]

And the first one is -5,5

[alpine sable]

Yes

[tulip lintel]

Ok

Well I think I pretty much get the gist of it

Cool

Can you help me with this

[alpine sable]

Dude did your teacher want it in degrees or radians

[tulip lintel]

Radians

Lol

I got it tho

I think

[alpine sable]

You have to convert to radians then

[tulip lintel]

I put 60 as pi/3

[alpine sable]

We just did everything in degrees

Yea

[tulip lintel]

Yeah it’s all good the domains and range are good

[alpine sable]

The first one is a ratio

I think

[tulip lintel]

Damn

I got it wrong

[alpine sable]

Wait I’m checking

Yeah it’s a rario

ratio*

[tulip lintel]

Oh ok cool cool fixed that

[alpine sable]

It’s because it represents the ratio of the adjacent to the hypotenuse

The second one is an angle

Because you’re using the inverse

[tulip lintel]

Ohh ok

So depending on whether it’s in or out it is a ratio or angle?

Like inveese

[alpine sable]

Yeah

[tulip lintel]

Inverse

Ok coo

[alpine sable]

I’m pretty sure you remember from the soh cah toa days

That’s a good way to remember it

[tulip lintel]

Yeah (ptsd)

[alpine sable]

😂

[tulip lintel]

😂

[alpine sable]

Is there anything else you need help with

[tulip lintel]

Mann this has been smooth asf brother

[alpine sable]

Thanks bro

[tulip lintel]

You have helped me so damn much

[alpine sable]

No problem man, anytime

[tulip lintel]

More People like you need to exist

You guys are a light in absolute darkness

But yeah can I get help on just a few more problems

[alpine sable]

Of course

[tulip lintel]

Ok so i’ve already answered

But they’re most definitely incorrect

So feel free to humble me rq

[alpine sable]

Ok this one is right

[tulip lintel]

Damn it won’t let me see the image

Is it the tan one?

[alpine sable]

Yes

[tulip lintel]

Ok

Cool

[alpine sable]

Ok for the secant one

Yeah it’s right

Do you have to show work

That’s the only thing I was going to say

[tulip lintel]

Um no I don’t think so

But if I needed to how would I?

[alpine sable]

You have to recognize that secant is the reciprocal of cosine

[tulip lintel]

Oh ok

So domain= [0,pi]

[alpine sable]

Yes

[tulip lintel]

DAMNNNN

LETS FOO

GOO

wait

Is that the answer?

[alpine sable]

No but that’s the domain of secant

[tulip lintel]

😭

[alpine sable]

And if you recognize that then you can find the values of x

If you need to show work

[tulip lintel]

[-1,1]

[alpine sable]

The range

[tulip lintel]

This the range?

[alpine sable]

Yes

Of secant

[tulip lintel]

Oh

But we’re looking for domain right

[alpine sable]

Secant has a range of (-infinity,-1] U [1, infinity], knowing this, we can determine that x will take any value in this range, and that the cos must be between -1, and 1

So if that’s the case

Then we can say that the values that satisfy sec(arcsec(x) is what you said

So you got it rifht

[tulip lintel]

Ohhh shoot

I did

[alpine sable]

And arccot has horizontal asymptotes so yea

[tulip lintel]

So would it be that everything satisfies the statement except what is in the middle of -1,1

V

?

Not sure if I answered correctly

I put any values in (-inf, -1] U [1,inf)

[alpine sable]

Yeah

X cannot be between -1 and 1

It’s going to be undefined

And you can verify it as well

[tulip lintel]

Ohh ok

Cool

Got that one

[alpine sable]

When evaluating arcsecx , there is no angle with a secant between -1 and 1 so that’s why

Say arccotx has horizontal asymptotes at 0 and pi

[tulip lintel]

Ohh ok

Man

So I just gotta memorize all of these domains and ranges huh?

[alpine sable]

You don’t really have to memorize them, you can use reasoning to find them

It will expand your understanding too

[tulip lintel]

How so?

I mean

I got the inv and regular ones down

I just don’t understand the inverse ones

Sec, cot, csc

[alpine sable]

So

The inverse

Is literally just a reflection

[tulip lintel]

Oh

Wait so is

Arcsin and csc the same?

[alpine sable]

An inverse trig function is x=siny

Or whatever

[tulip lintel]

Oh ok

Alright

Well

Back to the question at hand

[alpine sable]

Csc is the reciprocal of sine

Arcsin is x=siny

So no

[tulip lintel]

Ohhhh ok there is a difference

[alpine sable]

Here

Hopefully this makes it clear

That red line is arcsin

If there were no restrictions, thats what arcsin would look like

[tulip lintel]

Ohh wtf

[alpine sable]

It would look like the blue waves

[tulip lintel]

Yeah

[alpine sable]

On the yaxis

When you want to graph an inverse

Do this

2nd function, prgm, drawinv, alpha, y=, yvar, and the corresponding y

If you’re allowed to use your calculator this can help a lot

Make sure to also graph the actual inverse trig function too

So you can see where the restrictions begin

[tulip lintel]

Ohhh that’s cool

I just tried it

It highlighted the center point

[alpine sable]

Yeah it’s sick

[tulip lintel]

Which is the restriction

That’s dope

Thank you for that

[alpine sable]

No problem

[tulip lintel]

Oh yeah can I get help with that last cot problem

[alpine sable]

Idk if you can graph arccotx but it’s going to be (-infinity, infinity)

So like you said

All real numbers

[tulip lintel]

Oh all of them

[alpine sable]

Yeah I also made a mistake I had to use desmos

It’s defined at pi and 0

[tulip lintel]

Wait

So it’s all real numbers except those two?

[alpine sable]

Desmos is telling me it’s defined at pi and 0

But arccotx never touches 0

Or pi

So I think this

It can never equal to pi

Or to 0

But it’s defined at pi and 0

So x can equal to pi and zero

[alpine sable]

It’s just xer

[tulip lintel]

Xer?????

[alpine sable]

X is an element of the real numbers

It’s an easier way of saying what you said

All real numbers

So arccotx has two horizontal asymptotes

Pi and 0

Do you need more help

[tulip lintel]

Oh ok

I think I get it

It’s still in between (-inf,inf)

So it doesn’t matter

X is in the middle

Because it indicates the real numbers as you mentioned

[alpine sable]

Yes

But arccotx can never have solutions for pi and 0

It can’t equal to them

At least in the real number system

[tulip lintel]

Ok cool I think I get it

Well

This is it

You have helped me finish my assignment

Thank you so very much

I appreciate this very greatly

[alpine sable]

No problem, good luck bro

[tulip lintel]

Thank you bro

I’ll be back soon💀

Another day another struggle😂

[alpine sable]

💀 feel free to ping me when you need help and I’ll get back to you when I can

But you don’t have to wait for me

Other people are available too

[lone heart]

@alpine sable Has your question been resolved?

[lone heart]

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[daring ferry]

Two passenger trains left the station at the same time and traveled in opposite directions. One traveled at the rate of 50 km/h and the other at 45 km/h. After few many hours are the trains 315 km apart?

[daring ferry]

please help

[vapid shuttle]

how fast are the trains moving away from eachother?

[daring ferry]

50 km and 45 km

this is so hard T-T

[vapid shuttle]

one train is traveling 50km/h in one direction

the other is going 45km/h in the opposite direction

so how fast are they traveling away from eachother?

[daring ferry]

i think 315 km

IDK PLEASE

[vapid shuttle]

why would you say 315km ?

try thinking about it, instead of just saying the first number you see on your screen

if me and you are walking down a sidewalk

say we start at the same place

but I go 5 mph

and you go 10 mph

how much faster are you going than me?

[daring ferry]

5

[vapid shuttle]

okay

so would you say you are going away from me at 5mph? yes or no?

[daring ferry]

yes

[vapid shuttle]

what if

I stay in the same place

and you go 5mph away from me

then you are going 5mph away from me

but what if I start going

say 1mph the other way

then how fast are we going apart now?

obviously we are going apart faster

because I started moving away

instead of staying still

but how much faster?

[daring ferry]

wait

hmmmmmmmmmmm

[daring ferry]

is this 10 mph ?? because u repeated the message

[vapid shuttle]

Here's what I meant to say

[daring ferry]

Okay

[vapid shuttle]

if we are at the same place, and you start going 5mph in one direction, and I go 1 mph in the other direction, then how fast are we going apart?

and I gave you the hint that

if I stayed still, we would be going apart at 5mph

but me moving away, instead of staying still makes us go apart faster

but how much faster?

[daring ferry]

4???

[vapid shuttle]

you think we are going apart, 4mph faster than 5mph?

why?

[daring ferry]

i dont know dude

wait

[vapid shuttle]

well try not guessing

I'll be able to help you best if you don't just guess

I am trying to lead you in the direction of understanding the question

guessing doesn't help that

[daring ferry]

it makes me more confused

[vapid shuttle]

what does?

[daring ferry]

.

[vapid shuttle]

how is a simpler example making you more confused?

We can restart though if you'd like me to try going about this in a different way again

[daring ferry]

im trying to understand too

[vapid shuttle]

I'll try rewording it one more time