help-19

[idle laurel]

what do you think

[paper kelp]

I think yes

[idle laurel]

no

[paper kelp]

https://tenor.com/view/sad-sad-cat-cat-depressed-depression-gif-13240550249247957481

[idle laurel]

Try to calculate the area of the function x^3 from 0 to 3

And then calculate the are of 6x from 0 to 3

and take the 2nd one from the 1st one

you wont get 6.75

[paper kelp]

It’s -6.75

That is the difference of area

[idle laurel]

yea -6.75 mb

[paper kelp]

It says area cant have both positive and negative values

How can I tell if it does or doesn’t

Without graphing it

Is there a way

Or does negative answer = difference of area

??

[odd edge]

@paper kelp Has your question been resolved?

Channel closed

Closed by @paper kelp

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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

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

[tardy furnace]

Help with this. Am I doing this right?

[tardy furnace]

.close

[odd edge]

Channel closed

Closed by @tardy furnace

Use .reopen if this was a mistake.

[odd edge]

Available help channel!

Send your question here to claim the channel.

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

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

[full yarrow]

had a question: how many points are required to strictly define an exponential curve?

[full yarrow]

can you do so with only 3 points?

[mystic saffron]

two points

is all you need

[full yarrow]

right

how do you then find it's asymptote?

since

taking a log-log plot

[mystic saffron]

wait, is the base known or not?

[full yarrow]

an exponential should result in some form of straight line

[mystic saffron]

do you know if it is base e for example

[full yarrow]

base unknown

no

for context, i'm working on a numerical solver for the basic poisson equation (fluid mechanics)

i'm trying to reduce error, and i have 3 points that I know definitely converge to a correct answer

they form a straight line on a log-log plot (does the base matter in this case? i happen to be using base e) edit: shouldn't matter on second thought

and i'm trying to find the point which they converge to

[odd edge]

@full yarrow Has your question been resolved?

[odd edge]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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

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

[subtle sleet]

Can someone walk me through this problem?

The things I've written down are what I know so far

[mystic saffron]

yeah assuming it's sinusoidal it will have an amplitude of 2000

we have to exclude the negatives though of course so you would need to take the absolute value

something like $2000\abs{\m\cos x}$ as a preliminary version is a good start

[mystic saffron]

then you have to adjust the period for the fluctuations

what do you think so far? @subtle sleet

[subtle sleet]

yes that makes sense, so right now we're unsure of how much fluctuation would occur

[mystic saffron]

yeah ok

[subtle sleet]

also to note i've forgtten the notation for how to do transformations on functions

[mystic saffron]

[0.6\textwidth]
so the period of a sinusoidal wave is represented by $\f{2\pi}{\abs B}$ in $A\m\cos{Bx + C} + K$

[mystic saffron]

thats fine

so like

how much should the period be from what you wrote?

[subtle sleet]

entire time this is happening is over 21 days?

[mystic saffron]

yeah

so like

[
\f{2\pi}B = 21
]

[mystic saffron]

solve for B

[subtle sleet]

B = 2π/21

What does the B exactly stand for?

[mystic saffron]

read this

[subtle sleet]

sorry still slightly confused

[mystic saffron]

if cos(3x) then B = 3

does that help

[subtle sleet]

ummm sorry again i do not understand, do you mind like explaining this expression?

[mystic saffron]

it's just the general shape of any cos

like

ANY cos function is of that shape

3cos(4x + 23) - 5

for example

thats just meant to describe the general shape of a cos function

im using it to explain how to find the period of a cos function

[subtle sleet]

ok

[subtle sleet]

ok i understand now that

[mystic saffron]

great

[mystic saffron]

so using this what is ur cos

[subtle sleet]

B = 0.299 and that we multiply with x stretching the graph?

[mystic saffron]

no

dont approximate it

but yeah the graph stretches with the multiplication

,w plot 2000|cos(2pi/21 x)| from -50 to 50

[clever fjord]

Results provided by WolframAlpha

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

Requested by qylooo

[subtle sleet]

so cos (2π/21*x)

[mystic saffron]

yeah

that should be fine

do you understand the process

[subtle sleet]

yes

oh so like one more thing i should state the domain then right?

D:[0,21]?

[mystic saffron]

hmmm

maybe you should say for t > 0 but idk about 21

they never mention it stops at 21

it just fluctuates

although

wait

[subtle sleet]

oh i see

[mystic saffron]

this is not correct completely still

the period is a bit skewed because of the uh

absolute value

[subtle sleet]

yeah

[mystic saffron]

so the thing is

,w plot |cos(x)| from -20 to 20

[clever fjord]

Results provided by WolframAlpha

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

Requested by qylooo

[mystic saffron]

the abs(cos(x)) function has a periodicity of pi

instead of 2pi with the normal case

[mystic saffron]

so here we replace 2pi witj pi

and we get like

,w plot 2000|cos(pi/21 x)| from -50 to 50

[clever fjord]

Results provided by WolframAlpha

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

Requested by qylooo

[mystic saffron]

which now is accurate

[subtle sleet]

yes

with the 2000 in the front, thats the range of the function?

[mystic saffron]

amplitude

is what you call it

[subtle sleet]

yeah thats the word

[mystic saffron]

but yeah it defines the range as well

multiply it by a number and that's how big the thing extends to

[subtle sleet]

and you calculate amplitiude by max-min/ by something?

[mystic saffron]

no

i didnt do anything

they just said its maximum is 2000

so i used that

[subtle sleet]

I had this in my notes

[mystic saffron]

yeah

but because we are considering abs(cos(x)) instead of normal cos(x) in reality you calculate it as

A = max - min

because half the thing gets cut off (the negative portion)

max is 2000 and minimum is 0

so 2000

[subtle sleet]

hmmmm

[odd edge]

@subtle sleet Has your question been resolved?

[odd edge]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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

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

[velvet juniper]

how do you take the dot product if you don't have the angle between them?

[forest sky]

you can compute the dot product from the components

so if you have 2 vectors
(a, b, c) and (x, y, z) then the dot product is ax + by + cz

[velvet juniper]

ohh I see thank you

.close

[odd edge]

Channel closed

Closed by @velvet juniper

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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

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

[zinc wigeon]

Guys, when he gets rid of the logarithm, how did he do it? What does he mean by raise 2 to each side?

[lyric marlin]

In other words, the definition of logarithm base 2 of x is as the number you need to take 2 to the power of to get x

So $2^{\log_2(25-x)}=25-x$ by definition

[clever fjord]

Edward II

[odd edge]

@zinc wigeon Has your question been resolved?

[odd edge]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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

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

[feral bone]

I need a hint on how to do

\begin{align*}
\int e^{\sqrt{x}} , dx
\end{align*}

Substitution probably is the way, but I can't find the one. If we put $\sqrt{x}$ under the differential, we will have to multiply the expression by $2\sqrt{x}$ to counteract the $$(\sqrt{x})'=\frac{1}{2\sqrt{x}}$$

[clever fjord]

Sweet Tea 🧋

[feral bone]

So it becomes

$$
2 \int \sqrt{x} \cdot e^{\sqrt{x}} , d(\sqrt{x})
$$

[clever fjord]

Sweet Tea 🧋

[feral bone]

I.e. $$2 \int t e^t , dt$$

[clever fjord]

Sweet Tea 🧋

[feral bone]

hmmmm, just a sec

[old berry]

Hello my friend

[neat oxide]

use integration by parts

[old berry]

What is your question

Oh found it

[feral bone]

,w (2 e^(sqrt(x))(sqrt(x)-1))'

[clever fjord]

Results provided by WolframAlpha

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

Requested by sweet.tea3

[feral bone]

oh yea

got it

.close

[odd edge]

Channel closed

Closed by @feral bone

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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

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

[forest thicket]

Somebody help pls

[forest thicket]

I need quick help

I don’t have time for learning atm

Anyone smart enough

[south plume]

1/2 * height * base area

[forest thicket]

Do you know if the other ones are correct

[south plume]

yes

wait

no, wrong base area

[wooden python]

why quick

are you in a test

[south plume]

lol

[forest thicket]

Retaking it

[forest thicket]

Do you know what it is

[wooden python]

think you might be supposed to do this on your own

[forest thicket]

There’s options in the photo

[wooden python]

<@&268886789983436800>

[amber schooner]

yea and retakes still count as tests lol

[odd edge]

@forest thicket Has your question been resolved?

Channel closed

Closed by @forest thicket

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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

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

[olive needle]

Going through an old textbook and working out all of the math problems, I encountered this particular problem that I cannot seem to get the correct answer to. The answer in green is the answer in the back of the textbook. The text in red is how I originally approached the problem incorrectly. The text in blue is how I tried to reason how out how to approach the problem. The text in black is my work solving the problem which still resulted in an incorrect solution. Could someone point out what I'm doing incorrectly.

[cerulean geode]

Is there a reason you have 16 - y as opposed to a second y in your integrand?

That seems to be the only difference

[olive needle]

The 16-y is how I accounted for the distance to move each volume of liquid.

From y=0, the distance would be 16-0 = 16.

[cerulean geode]

I think you may be right

[olive needle]

At y=16, the distance would be 16-16 = 0.

[cerulean geode]

I think that reasoning is right

I think 16-y here instead of y is correct, since you're pumping the water from wherever its height is in the tank to the top (y = 16)

[stark coyote]

well we are pumping water out of the tank. that means the distance should be 0 for y=0 shouldn't it?

unless there's a spout length i didnt see

[olive needle]

The question states that I am pumping water to the top of the tank.

[stark coyote]

if its full though, wouldn't the water already be at the top and take less work?

oh i see whats going on

we are pumping from the bottom

[olive needle]

The difference between my solution and the answer in the back of the book is a factor of 625/4 which seems too coincidental with F_v_1 = 625pi that I got in the text in blue.

,calc 21446605.85 * 4/625

[clever fjord]

Result:

1.3725827744e+5

[olive needle]

Which is the answer in green.

[stark coyote]

if we are pumping from the bottom at all times, why would the height we move change?

16-y seems off to me

[olive needle]

These types of early calculus problems generally aren't concerned with "reality". 🙂

They just want to know how you would calculate moving the entire volume of water.

But you are correct. In reality you would calculate the water pressure at the bottom at any given time and how it affected pumping water to the top.

[odd edge]

@olive needle Has your question been resolved?

Channel closed

Closed by @olive needle

Use .reopen if this was a mistake.

[olive needle]

.reopen

[odd edge]

✅

[odd edge]

@olive needle Has your question been resolved?

[odd edge]

@olive needle Has your question been resolved?

[odd edge]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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

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

[mystic saffron]

hey so I wanted to calculate which are my two lowest and most negatively impacting grades

[mystic saffron]

but I don't know how to do it

[green elm]

compute (numerical score x % of total grade) for each exam or score or whatever

whichever two are smallest are the ones

[odd edge]

@mystic saffron Has your question been resolved?

[odd edge]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[odd edge]

Available help channel!

Send your question here to claim the channel.

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

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

[outer saffron]

is there any formula for a finite set to know how many equivalent relations and clasees?
suppose set is given {4,5,6}

[outer saffron]

or I have to go through general way?

[sharp oak]

Every equivalence relation is the same as a partition of the set

So for example,
{4},{5,6}
is a partition and an equivalence relation

[crisp wadi]

Sterling's numbers of second kind count partitions of fixed size of a finite set

It does not have a closed form unfortunately

[sharp oak]

https://en.m.wikipedia.org/wiki/Partition_of_a_set

[crisp wadi]

Like Kaynex said, there exists a one-to-one correspondence between equivalence relation of a set and its partitions

And it will be better to count the partitions of {4, 5, 6}

[outer saffron]

yes it will be

i count them and make partion

and i always tried the formula

thank you

.clse

.close

[odd edge]

Channel closed

Closed by @outer saffron

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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

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

[olive ledge]

$(sin^2(x))^2 \leq sin^2(x)$

[clever fjord]

ColdTee

[olive ledge]

Is this true for all values of x

[sharp oak]

Note that if 0 ≤ u ≤ 1,
u² ≤ u

sin²(x) is between 0 and 1

[olive ledge]

So this will be true for all values of x right

[sharp oak]

.

[olive ledge]

$0 \leq \sin^2(x) \leq 1 \
(\sin^2(x))^2 \leq \sin^2(x)$

[clever fjord]

ColdTee

[olive ledge]

Is this correct

[sharp oak]

Yes it's true for all x

[olive ledge]

That's what I was confused about since whatever value of x sin^2(x) will lie in [0,1] is that right

[odd edge]

@olive ledge Has your question been resolved?

[odd edge]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[odd edge]

Available help channel!

Send your question here to claim the channel.

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

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

[cold musk]

I dont understand how to start this question

And why there are diff pronumerals

[odd edge]

@cold musk Has your question been resolved?

[cold musk]

<@&286206848099549185>

Hellooo??

[jolly narwhal]

Hey

Do you know geometric sequences?

[cold musk]

Yep

[jolly narwhal]

Ok so I see two ways to solve that

[cold musk]

Mhm

[jolly narwhal]

You started this with a proof by induction right?

[cold musk]

Yep

[jolly narwhal]

But your proof should have been done on un+1=2^n-1 ...

You prove that left side of equality is equal to second side

[cold musk]

yep but idk why it switches from r to n

[jolly narwhal]

It's just letters dont be bothered by it

[cold musk]

okay

[jolly narwhal]

The important thing is that they are integers

[cold musk]

Mhm

[jolly narwhal]

Ok so start again

[cold musk]

Is that step right or-?

[jolly narwhal]

That's right, though I would have written this in two parts. First the left hand side with u1 +1 (barely nothing to do) and the second with 2^(1-1) (u1+1) = 1 x (u1+1)= u1+1

[cold musk]

But isnt the lhs subbing r and the other subbing n

And before it i said i was subbing just n for 1 or do i say r equals 1 for the other

[jolly narwhal]

I dont understand what you mean

[cold musk]

Is n = r+1?

Like how do they connect

[jolly narwhal]

r=n

[cold musk]

Ohh

[jolly narwhal]

Substitute it by n

It's just a letter 🙂

Could have been m, p, or whatever

provided it is a natural number

[cold musk]

But the left equation ends up being uh U2=2U1+1

Like u cant go further than that

[jolly narwhal]

But as I said you must do a proof by induction on the second highlighted equality assuming the first highlighted equality is true.

[jolly narwhal]

You dont need that equation for now

[cold musk]

So i dont sub 1 for the left equation?

[jolly narwhal]

You will need it in the second part of induction

[cold musk]

Because for induction when u prove the base case doesnt it have to be true and then u assume further and then the plus one

[jolly narwhal]

Dont need that equation haha trust me

[cold musk]

ah okay

[jolly narwhal]

Is there latex here?

[cold musk]

So the next part i assume true for P(k)?

and then i rewrite it with k instead of r and n

[jolly narwhal]

Your P(n) is actually $u_{n+1}=2^{n+1}(u_1+1)$

[clever fjord]

tresbienmonsieur

[cold musk]

Yeah i wrote that first sentence

[jolly narwhal]

In your base case you must prove that the left side of equality is equal to right side

Then second part is your assume that for some k P(k) is true

So $u_{k+1}=2^{k+1}(u_1+1)$

[clever fjord]

tresbienmonsieur

[jolly narwhal]

Is true

[cold musk]

I dont rlly get what u mean do u mind writing the first few lines so i hv an idea?

[cold musk]

Ohhh okay lemme tweak

Mhm

[jolly narwhal]

So do you agree with what I said?

[jolly narwhal]

Im just trying to make clear everythings so we are on the same page

[cold musk]

So ur saying that the left side is equal to the right side

[jolly narwhal]

Thats what you must prove yes

[cold musk]

But isnt the rhs power k+1 not k-1

I meant other way around sorry

[jolly narwhal]

You must prove P(k+1) is true now $u_{k+2}=2^{k+2}(u_1+1)$

[clever fjord]

tresbienmonsieur

[cold musk]

But i thought it would be minus 1 for the other part

Bc if u sub n as 1

Im at this part

What was the other way with the geometric sequences?

[jolly narwhal]

P(1) is not good you must not use the equaton with r

Just the equation with n

Because its P(n)

The induction must be done with the equation containing n

Do you see what I mean? How did I lose you 😅

[jolly narwhal]

Im so sorry I must have brought confusions to you the rhs is 2^k and not k+1 since it was k-1

[odd edge]

@cold musk Has your question been resolved?

[odd edge]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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

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

[tidal barn]

Can there be a square matrix A, that has only right inverse?

[tidal barn]

eg.: AX=In but XA doesnt equal In

i dont thin kso

but why?

<@&286206848099549185>

I got it, since A is square and has right inverse, it implies that no rows are 0 in row echolen form of A, since A is square, all colums of A are basis columns, therefore A has left inverse.

[odd edge]

@tidal barn Has your question been resolved?

[odd edge]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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

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

[hearty cape]

.help

[odd edge]

Commands:

• clopen: .close, .reopen
• consensus: .poll
• factoids: .tag
• help: .help
• version: .version

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

[leaden karma]

Prove that in a triangle, $\frac1{a}+\frac1{b}+\frac1{c}\le\frac1{a+b-c}+\frac1{a-b+c}+\frac1{-a+b+c}$

[clever fjord]

kheerii

[leaden karma]

We get $\frac{\sum ab}{abc}\le \frac1{2} \sum \frac1{s-a}$

[clever fjord]

kheerii

[leaden karma]

oh come on man not now

[echo ginkgo]

it's for everybody

nobody can see images rn

[leaden karma]

I know, I thought it got fixed by now

[echo ginkgo]

yeah seems like their fix didn't work or something

[leaden karma]

can you understand what I am trying to say though?

[echo ginkgo]

maybe I should refresh who knows

well I see your question yes, do I have any interesting idea about it not really

[leaden karma]

ok I will keep typing what I've got so far lmao

$\frac{\sum ab}{abc}\le \frac{\sum (s-a)(s-b)}{2(s-a)(s-b)(s-c)}$

[clever fjord]

kheerii

[leaden karma]

the sum on the right hand side numerator becomes $\sum (s-a)(s-b)=\sum s^2 - s\sum (a+b) +\sum ab = \sum ab - s^2$ (since $\sum (a+b)=4s)$

[clever fjord]

kheerii

[leaden karma]

and we have $s^2=\frac{\sum a^2 + 2\sum ab}{9} \ge \frac{\sum ab}{3}$, so the inequality left to prove becomes $\frac{\sum ab}{abc}\le \frac{\sum ab}{3(s-a)(s-b)(s-c)}$

[clever fjord]

kheerii

[odd edge]

@leaden karma Has your question been resolved?

[leaden karma]

<@&286206848099549185>

[scarlet glacier]

bruh 💀

I'm in college

[leaden karma]

After this I get $3(s-a)(s-b)(s-c)\le abc$ or $\frac{3}{4}r\le R$

[clever fjord]

kheerii

[leaden karma]

This is not even close to the optimal inequality (which would be 2r<=R), so I am certain I have made a mistake somewhere

@violet breach can you help now?

oops wrong person

@echo ginkgo

.close

[odd edge]

Channel closed

Closed by @leaden karma

Use .reopen if this was a mistake.

[leaden karma]

.reopen

[odd edge]

✅

[supple mural]

But it still holds

[leaden karma]

Yes, but equality never holds

[supple mural]

Ah

[leaden karma]

while it holds in the original inequality for an equilateral triangle

I should've gotten 2r<=R

[supple mural]

Yeah hmm

[leaden karma]

do you see a problem somewhere?

[supple mural]

Shouldn’t the second expression have denominator 4?

[leaden karma]

You mean $\frac{\sum ab}{abc}\le \frac{\sum ab}{4(s-a)(s-b)(s-c)}$

?

[clever fjord]

kheerii

[supple mural]

No

[leaden karma]

$\frac{\sum ab - s^2}{2}\le \frac{\frac{2}{3} \sum ab}{2}$

[clever fjord]

kheerii

[supple mural]

s^2=…/4

[leaden karma]

no?

[supple mural]

Instead of 9

[leaden karma]

OHH

I considered s to be the AM of a b and c

my bad

thank you so much

[supple mural]

Np

[leaden karma]

god that took too long to figure out

[supple mural]

Silly mistakes are hard to identify in so much alg

[leaden karma]

does that even give me a correct answer though 😓

I think it does

[supple mural]

Hopefully, try it

[leaden karma]

the fraction becomes 1/8

which is correct yes

thanks

.close

[odd edge]

Channel closed

Closed by @leaden karma

Use .reopen if this was a mistake.

[leaden karma]

.reopen

[supple mural]

[odd edge]

✅

[leaden karma]

actually @supple mural Do you know of a proof of 2r<=R?

that doesn't rely on the formula for exradii

[supple mural]

Not off the top of my head

[leaden karma]

hmm

https://www.ias.ac.in/article/fulltext/reso/020/01/0075-0075 this is the only proof I am aware of

but I wish not to use exradii formulas

[supple mural]

Oh I actually do know one

Do you the formula for the distance OI?

[leaden karma]

OI as in circumcenter-incenter?

[supple mural]

Yes

[leaden karma]

yeah, $\sqrt{R^2-r^2}$ right?

[clever fjord]

kheerii

[supple mural]

Not quite

[leaden karma]

wait no

R^2-2Rr

[supple mural]

Yeah

[leaden karma]

hmm but I will have to prove this too

how would the rest of the proof go though?

[supple mural]

And this quantity is never negative

R(R-2r)>0

[leaden karma]

ahhhh right

[supple mural]

R>0

[leaden karma]

simple

[supple mural]

The proof for it iirc comes from power of a point

[leaden karma]

hmm, will look into it, thanks!

.close

[odd edge]

Channel closed

Closed by @leaden karma

Use .reopen if this was a mistake.

[supple mural]

Consider the power of I wrt the Circumcircle

[leaden karma]

yeah that's what I was thinking

should be pretty straightforward

[supple mural]

Yeah

[leaden karma]

maybe even cosine rule might work

[odd edge]

Available help channel!

Send your question here to claim the channel.

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

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

[mystic saffron]

I am confused about this question

[mystic saffron]

I know you need to find a left and right inverse, for the bijection

but in the answers, it defines the function g: [n + 1] -> X u {a}

where g(k) = {f(x) if k < n and a if k = n}

wouldnt it be a if k > n tho?

thats the part that confuses me

because if k = n, then it is still in X since [n] maps to X

I feel like this is not surjective if k = n part

because what would map to n, if k = n then k is {a}

anything else maps to an element less than n

[open onyx]

the answer couldn't decide to use n+1 or <= and >

[late dust]

Looks like an off-by-one error

Also 'f(x)' is wrong

[mystic saffron]

lol yeah sorry f(k)

[mystic saffron]

were my supsicions correct then?

[late dust]

I'd say so

Do they define enumeration somewhere?

[mystic saffron]

yeah, its a bijection, so i guess [n] and X f: [n] -> X since n is the same cardinality of X

[late dust]

Yeah but maybe by [n] they mean {0, 1, ..., n-1}

[mystic saffron]

i can show you

hmm

it should be 0 tho...

yeah it should be 0 <= k <= n

[late dust]

Well, one of these things is wrong

[mystic saffron]

because 0 in N in my class

i mean it makes sense since a set is finite if there is a bijection from a subset of the natural numbers, which means 0 in [n]

[late dust]

That's irrelevant

[mystic saffron]

what do you suppose?

[late dust]

Wikipedia uses {1, ..., n}
https://en.wikipedia.org/wiki/Enumeration

[mystic saffron]

What would 0 map to then?

[late dust]

I can't say, I'm not your teacher, but I guess it's better to hold the definitions as true and assume the given solution has a typo or something

[mystic saffron]

i mean would the + 1 be to map to 0 by definition of how enumeration is from {1, ..., n}

oh shoo

then you would have to fix the function definition

[late dust]

Well it says "initial segment {1, ..., n}" so in that particular article N does not include 0

[mystic saffron]

to account for that

[open onyx]

asking something that isn't in your domain maps to what in a function
i guess undefined

[mystic saffron]

no, 0 in my class is in N

[open onyx]

oh that's terrible

[mystic saffron]

and if it is undefined, then that function is not valid to use because the domain is undefined

I hate this class dont worry

[open onyx]

but doesn't it impose 1 <= k <= n in your set construction

so 0 isn't in your enumeration anyway

[late dust]

Yes it doesn't matter whether N includes 0 or not, what matters is how they define [n]

They could've said [n] = {k in N | 3 <= k < n+3}, it would still work

(I mean the given solution wouldn't, but it already doesn't)

[mystic saffron]

lets assume its 0 to n

i mean like, if n includes 0, wouldnt that mean that its basically the same idea but you use <= and then > to handle a

[late dust]

That would include n+1 elements

[mystic saffron]

Why?

oh like

if 1 <= n <= n

[late dust]

{0, 1, 2} is three elements

[mystic saffron]

like the wikipedia definition

this is the full answer

[late dust]

So 1 to n, like here

[mystic saffron]

but f(k) implies that 0 is in X right

iim just trying to understand how this is surjective

[late dust]

f(k) doesn't imply anything

[mystic saffron]

its defined tho?

i dont understand

[late dust]

For f(k) to be defined, k must be in the domain of f, which is [n] = {k in N | 1 <= k <= n}

So that just means 1 <= k <= n

[mystic saffron]

i feel like, something here is defined wrong for me

because 0 is a natural number, if n is defined that way, then 0 is never mapped to

and alos [n] -> [n] is bijective

[late dust]

0 doesn't have to be mapped

You can have a bijection between {3, 7655, 32411} and {t, w, g}

No 0 here

[mystic saffron]

yes, but what if 0 in X but 0 not in [n] by the way n is defined

[open onyx]

that's the stupid thing with your course treating 0 as being in N for some insane reason
by construction 0 is not in [n]

[late dust]

It doesn't matter

What elements X contains doesn't matter, only how many elements it contains

It could contain something other than numbers

[mystic saffron]

oh, i understand

i guess this is why n has to start at 1 right

but then what is the size of the empty set...

they said size is defined by f:[n] -> X for some x

[open onyx]

the logical answer

[mystic saffron]

yeah it should be 0, but if n starts at 1, how is that possible

sorry im not trying to be difficult, im genuinely confused

[open onyx]

recall the definition of enumeration

since n = 0 there is no k satisfying 1 <= k <= 0

so what's [n] when n=0?

[mystic saffron]

I guess empty?

[open onyx]

ye, so your f maps from empty set to empty set

[mystic saffron]

I gotcha okay

that makes sense

i still dont think the solution is correct tho?

[late dust]

That may be how to compare sizes (or really "cardinality"), but I don't think that's a good definition of size...

[mystic saffron]

Is there a more clear definition that you think would be helpful?

[late dust]

Yeah, like we said earlier, either the definition or the solution is wrong

[late dust]

Well ok I may be nitpicking but I'd just define the cardinality of the set {k in N | 1 <= k <= n} to be n, and then you can compare that to the cardinality of X by constructing a bijection

See also https://en.wikipedia.org/wiki/Cardinal_number

("Formal definition" in particular, but it's a little complicated)

[mystic saffron]

could you still use the same function definition idea, but like change the signs

so that f(k) = a if k > n

so for the + 1 case

[wind gorge]

Hey y’all I need help with a geometry analytic problem…

[mystic saffron]

@late dust

[late dust]

Not sure what you mean

[mystic saffron]

I want to find a correct bijection

[late dust]

g(k) = {f(k) if k <= n and a if k = n+1}

[mystic saffron]

oh yeah thats what i said

okay

cool

thank you

[late dust]

[mystic saffron]

thank you for helping

could i also ask about part b)

actually nvm

thanks again

.close

[odd edge]

Channel closed

Closed by @quartz reef

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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

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

[mystic saffron]

okay

so

that second last line

$$\leq K\delta\sum(x_i-x_{i-1})$$

[clever fjord]

4C

[mystic saffron]

why is it leq

\begin{left}
\sum K(xi-x{i-1})(xi-x{i-1}) \
\leq\sum \textcolor{red}{ K\delta } (xi-x{i-1})
\leq \textcolor{red}{ K\delta}\sum (xi-x{i-1})
\leq K\delta (1-0)
=K\delta
\end{left}

[clever fjord]

4C
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[mystic saffron]

.close

[odd edge]

Channel closed

Closed by @gleaming cipher

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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

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

[fervent hound]

,plot |x|

[fervent hound]

graphically, why is the derivative at x=0 undefined ??

cause if we take a little nudge in the x direction, the function increases ? so it is defined ?

[long tinsel]

because the left hand and right hand derivatives are different at x = 0

[long tinsel]

which direction

[fervent hound]

isn't always from left to right meaning at x=0+epsilon

[long tinsel]

you need to have the left and right hand derivatives be equal for the derivative to be defined

[fervent hound]

i mean the derivative tells us if the value of f increases then f increases/decreases right ?

why do we care about left hand derivative ?

[long tinsel]

that's just how it's defined man

and the derivative does not directly tell us the monotonicity of the function

[clever fjord]

Norbert Baudin

[long tinsel]

the function does not have to be differentiatiable or even continuous to be increasing

[fervent hound]

yeah ik that

[fervent hound]

in this video, the guy defines the derivative as nudging the input x in the direction from left to right only
https://youtu.be/AXqhWeUEtQU?t=645

timestamp 10:40

[late dust]

"nudging the input in some direction"
doesn't specify left to right

[late dust]

That's a representation

[odd edge]

@fervent hound Has your question been resolved?

Channel closed

Closed by @fervent hound

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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

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

[mystic saffron]

Can someone clarify the definition of contably infinite for me

[dense dew]

A simple definition of countable infinity is that it can be mapped with natural numbers

[mystic saffron]

you can count it but it is infinite?

[dense dew]

If we can defined each value of it using natural number or any other defined countable infinity without missing anything from its set.

You can watch the video on how rational number between 0 and 1 are more than natural numbers it will help you build the insight about it.

[odd edge]

@mystic saffron Has your question been resolved?

[mystic saffron]

You can't count, but u can find nth element or map it to some set

[odd edge]

Channel closed

Closed by @quartz reef

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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

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

[digital leaf]

how do I solve it from here

[latent scaffold]

Factor 81^x out on the left side

And solve for that

And take log

[digital leaf]

@latent scaffold how do I do that if I have a plus in the middle

[latent scaffold]

That's why you factor it out of both terms.

81^x is common to both

[digital leaf]

I don't understand what you mean , sorry can you explain it more for me since I dont learn in english

[latent scaffold]

ya + yb = y(a+b)

Do this with your expression on the left side

[latent scaffold]

Yes

Then you can divide both sides by what's in the parentheses

[latent scaffold]

Yes. And now you have 81^x = (something you can calculate)

[digital leaf]

what to do with the right side of the equation

[latent scaffold]

Compute it.

With a calculator

Or simplify it, whichever you prefer

[digital leaf]

am I suppose to it with a calculator at this point in the exam

I'd like to simplify it

[latent scaffold]

Then rewrite all the negative exponents as fractions

[digital leaf]

I will try just give a moment

3^(-2) should be 2/3

correct?

sorry 3^(1/2)

[latent scaffold]

No, 1/3^2

[digital leaf]

oh

[digital leaf]

I dont really know how to solve this without a calculator

[latent scaffold]

First, the 1/3^2 on the numerator is really just multiplying the denominator by 3^2

[digital leaf]

I threw it in a calculator it says 3^(4x) = 3

[latent scaffold]

So you can distribute that in

[digital leaf]

I dont understand this line of text

[digital leaf]

and then how do you continue?

[latent scaffold]

Distribute the 3^2 in the denominator

[digital leaf]

like this?

[latent scaffold]

Yes

[digital leaf]

did you mean this equal that?

[digital leaf]

but the answer shoulsbe x = 1/4

which is what I got in the calculator

oh I forgot this

[latent scaffold]

1+9/27 = 1+1/3 = 4/3

That's the denominator

[digital leaf]

this?

[digital leaf]

and 4/(4/3) = 3 ?

[latent scaffold]

Yes

[digital leaf]

this makes my brain, and thanks 👍

[latent scaffold]

Then you can just compare the exponents on the left and right side of the equation to get x=1/4

[digital leaf]

yep

I wish I didn't need to these kinds of equations for my studies honestly

takes a lot out of me

thanks a lot

.close

[odd edge]

Channel closed

Closed by @digital leaf

Use .reopen if this was a mistake.

[odd edge]

Available help channel!

Send your question here to claim the channel.

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

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

[late wasp]

why can they turn this into a product of two integrals

shouldnt it be int ( (cos th + sin th) int (3r^2) dr ) d th

[nimble blaze]

$\int_2^3 3r^2 \dd{r}$ is a constant

[clever fjord]

ℝαμΩℕωⅤ

[late wasp]

wow

true

ty

[odd edge]

@late wasp Has your question been resolved?

[odd edge]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[odd edge]

Available help channel!

Send your question here to claim the channel.

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

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

[visual hazel]

does anyone know how to factor this? a⁴ + 4a³ - 5

[visual hazel]

according to my book this is the factorization: (a + 1)(a - 1)(a² + 5)

but I don't know how he did to get to that expression

[sick plaza]

the first thought if you're supposed to factor polynomials is to look at (a + 1) and (a - 1)

at least thats what ive been taught when i had to do it

[latent scaffold]

Try to guess easy roots like 1 and -1, it helps a lot.

If not then I guess you can resort to Rational Root Theorem

[visual hazel]

what I am having trouble seeing is what amount to add and subtract to make the right perfect square trinomial appear and then make a common factor or a difference of squares appear

[visual hazel]

should be able to do it just using common factor, common factor in groups, difference of squares, etc

[cinder elk]

I would first look at the powers, it tells you how many "a's" you would need in total, in this case its four so the possibilities are:
(a +- ?)(a +- ?)(a +- ?)(a +- ?),
(a +- ?)(a +- )(a^2 +- ?),
(a^2 +- ?)(a^2 +- ?),
(a +- ?)(a^3 +- ?)

sorry, the degree of the function

the next is to look at the next powers after the degree, which is just 3, which is not possible in:
(a +- ?)(a^3 +- ?) or
(a^2 +- )(a^2 +- )

so you know the function would look like:
(a +- ?)(a +- ?)(a +- ?)(a +- ?) or
(a +- ?)(a +- )(a^2 +- ?)

then you look at the numbers and go from there

[visual hazel]

hmm, why is not possible in that cases?

[cinder elk]

factor them out and see

it might be possible in the first one, nvm

but a^2 and a^2

it isn't

(a^4 + ?a^2 + ?a^2 + ?)

I guess there are 3 possibilities

[visual hazel]

it's possible

[cinder elk]

oh, so I was right the first time?

[visual hazel]

not possible

[cinder elk]

yeah, now try the other two that are possibile solutions

[visual hazel]

i keep having this problem

i tried a few numbers but got nowhere

[cinder elk]

I mean as they said, look at -1 and +1 first, if you get 0 then you know the (x +- ?) will be the +1 or -1

the basic (x +- ?) will be roots of the function

[visual hazel]

a⁴ + 2a² + 1 - 1 - 2a² + 4a³ - 5

[cinder elk]

?

[visual hazel]

(a² + 1)² + 4a³ - 2a² - 6

I had thought about doing that but nothing

[cinder elk]

what are you doing here?

[visual hazel]

trying to make (a² + 1)² appear

[cinder elk]

oh

It kind of looks like you pulled some numbers out of thin air

[visual hazel]

I just added and subtracted an amount to make the trinomial appear, but I didn't come up with anything interesting

I am really confused, I don't know what to do

[cinder elk]

I wouldn't look for (a^? +- ?)^2

just look for (a^? +- ?)

[cinder elk]

I just plugged this function and the original function into desmos, they aren't equal?

also, the rational root test might be beneficial for you

https://www.chilimath.com/lessons/intermediate-algebra/rational-roots-test/

[cinder elk]

as they stated

[odd edge]

@visual hazel Has your question been resolved?

[odd edge]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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

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

[mystic saffron]

I'm trying to understand something related to units when multiplying that I've always taken as given but never much given it thought:

Say like we have here: 30 degrees * pi radians / 180 degrees = 30pi/180 radians.

I understand the math behind how this works but I can quite understand why the degrees cancel out?

[mystic saffron]

The degrees cancel eachother out. why? I get why the number math here works but the units of measurements cancel out why?

<@&286206848099549185>

🙏

Seriously sorry for the ping.

[wraith ginkgo]

imagine you have a number x, and then you multiply that number by its multiplicative inverse, i.e 1/x. the x's cancel out

its sort of the same concept

but with units

[visual hazel]

∘ / ∘ = 1

[mystic saffron]

x/1 * 1/x = x/x = 1 but like, in the example with degrees, because degrees / degrees = 1 then 1* radian is radian?

[wraith ginkgo]

yes exactly

treat units like how you deal with numbers

[mystic saffron]

Ah cool, thanks! I had to figure this out today lol

.close

[odd edge]

Channel closed

Closed by @latent scaffold

Use .reopen if this was a mistake.

[mystic saffron]

Appreciate the help.

[wraith ginkgo]

np

[odd edge]

Available help channel!

Send your question here to claim the channel.

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

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

[visual hazel]

I just had to go do something, I know the rational root theorem and I know how to use it but I am looking to understand and use other forms of factorization

[odd edge]

@visual hazel Has your question been resolved?

[nimble blaze]

they're not practical for this question

[cinder elk]

I am still wondering why the book says the other function was equivalent though

[cinder elk]

This

[nimble blaze]

you could attempt to introduce expressions to complete squares / form groups, but it's not easy to spot what will be helpful here

based on what was written book is incorrect

,W expand (x-1)(x+1)(x^2 +5)

[clever fjord]

Results provided by WolframAlpha

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

Requested by ramonov

[nimble blaze]

ah...ic

that's different from the expression presented to us

and is more reasonable to factor without having to apply rational root theorem / long division

@visual hazel

did you make a typo

[visual hazel]

that's right, the book has a typing error

I am going to try now

a⁴ - 1 + 4a² - 4

(a⁴ - 1) + (4a² - 4)

(a² + 1)(a² - 1) + 4(a² - 1)

(a² - 1)(a² + 1 + 4)

(a - 1)(a + 1)(a² + 5)

now yes :)))))

thanks

.close

[odd edge]

Channel closed

Closed by @visual hazel

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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

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

[sweet steppe]

h

[sweet steppe]

need help

i have no idea what to do, apparently 0.18 is wrong

tried the slope formula

[quasi sparrow]

,rotate

[sweet steppe]

i think i might of had the wrong

mode on my calculator

[quasi sparrow]

that should be close to the answer

[sweet steppe]

but still help

[quasi sparrow]

if you're in the right mode

[quasi sparrow]

probably missing parentheses

use an online calculator

[sweet steppe]

now this

so im guessing it is 0.19

since i changed the mode

[quasi sparrow]

still probably missing parentheses

[sweet steppe]

but this formula is correct

right ?

[quasi sparrow]

yes

[sweet steppe]

okay thank you

so its just a mistyping error on my part

[odd edge]

@sweet steppe Has your question been resolved?

Channel closed

Closed by @sweet steppe

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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

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

[mystic saffron]

How do I simplify $\tan^2x-\sec^2x$

[clever fjord]

Matt

[mystic saffron]

I know that tan=sin/cos and sec = 1/cos

[vapid quartz]

pythagorean identities

[mystic saffron]

so it should look like $(\frac{\sin(\theta)}{\cos(\theta)})^2-(\frac{1}{\cos(\theta)})^2$

[clever fjord]

Matt

[mystic saffron]

but idk how to simplify from there

[vapid quartz]

distribute the squares through the parentheses

[mystic saffron]

ok so then itll look like $(\frac{\sin(\theta)^2}{\cos(\theta)^2})-(\frac{1^2}{\cos(\theta)^2})$

[clever fjord]

Matt

[lusty garden]

,tex First, we know that $\tan^2 x = \sec^2 x - 1$ from the Pythagorean identity for tangent.

[clever fjord]

Lia 👅

[pastel orbit]

combine denominators

and then use pythagorean

[mystic saffron]

$\frac{\sin(\theta)^2-1}{cos(\theta)^2}$

[clever fjord]

Matt

[mystic saffron]

how do i use the pythagorean identities for this

[pastel orbit]

cos^2(x) + sin^2(x) = 1

so 1 - sin^2(x) = cos^2(x)

[mystic saffron]

i know this identity but

[mystic saffron]

how did you end up with this

[pastel orbit]

i moved sin^2(x) to the other side?

[mystic saffron]

ok

but how is that gonna help me solve the problem

[pastel orbit]

look at your numerator

it's -(1 - sin^2(x))

[mystic saffron]

ok ty

.close

[odd edge]

Channel closed

Closed by @tall river

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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

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

[haughty prairie]

can anyone help me finish this up

[runic cypress]

is the first system inconsistent or consistent

[haughty prairie]

im not sure

[runic cypress]

you said they were dependent

what does it mean for them to be dependent?

[haughty prairie]

isnt it with the same slope & y interc

[odd edge]

@haughty prairie Has your question been resolved?

[odd edge]

@haughty prairie Has your question been resolved?

[haughty prairie]

anyone??

[dark kraken]

I think you still need to classify the top and bottom as consistent or not

[haughty prairie]

yea i solved it already but now im wondering if this is right

[green elm]

options 1 and 3 don't even make sense
option 2 is correct, can you explain why?

[odd edge]

@haughty prairie Has your question been resolved?

Channel closed

Closed by @haughty prairie

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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

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

[high tusk]

Let's say we have an exponential function, $y^x$. At the point (0,1), we have a tangent with the gradient 1. How would we calculate the value of y?

[clever fjord]

sin city ☆

[nocturne belfry]

youre not using the most intuitive letters here

can we switch it?

$f(x)=y=a^x$

[clever fjord]

jan Niku

[high tusk]

sure

we could

[nocturne belfry]

so whats $f'(x)$

[clever fjord]

jan Niku

[high tusk]

it would be

$xa^(x-1)$

[clever fjord]

sin city ☆

[nocturne belfry]

,w derivative a^x

[clever fjord]

Results provided by WolframAlpha

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

Requested by janniku

[nocturne belfry]

👀

[high tusk]

oh shit

right

anyways yes continuing

[nocturne belfry]

okay

[high tusk]

we know here that the value of x would be zero

[nocturne belfry]

yes

[high tusk]

so we substitute that in

[nocturne belfry]

and its equAL To what?

[high tusk]

log(0)??

idk

uh

a^x= 1

[amber schooner]

it’s log a

[nocturne belfry]

well they say it has a gradient of 1 right

[amber schooner]

a is a constant

a^0

[high tusk]

thats

negative infinity

[nocturne belfry]

so, what gives the gradient at some point

the derivative

[high tusk]

yes

[nocturne belfry]

specifically the information tells you that $f'(0)=1$

[clever fjord]

jan Niku

[high tusk]

,w a^(0)log(a)

[clever fjord]

Results provided by WolframAlpha

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

Requested by waitara

[high tusk]

oop

[nocturne belfry]

use exponent properties

you dont need a calculator for this one

[high tusk]

hold on

[nocturne belfry]

whats our formula for f'(x)?

[high tusk]

its

1/a

isn't it

the derivative

[nocturne belfry]

what? no

[high tusk]

huh

oh

[nocturne belfry]

$f(x)=a^x$

[clever fjord]

jan Niku

[nocturne belfry]

what is $f'(x)$

[clever fjord]

jan Niku

[high tusk]

$a^xlog(a)$

[clever fjord]

sin city ☆

[high tusk]

thats the derivative, right

[nocturne belfry]

okay, $f'(x) = a^x \log (a)$

[clever fjord]

jan Niku

[high tusk]

yes

[nocturne belfry]

and we know $f'(0)=1$

[clever fjord]

jan Niku

[high tusk]

mhm

$1=a^0log(a)$

[clever fjord]

sin city ☆

[high tusk]

correct?

[amber schooner]

mhm

[high tusk]

which becomes

[nocturne belfry]

simplify

[amber schooner]

is the slope 1?

[high tusk]

$log(a)=1$

[clever fjord]

sin city ☆

[nocturne belfry]

okay

interpret the equation

what does this mean about a?

[high tusk]

a= e

[amber schooner]

this log is ln tho

[high tusk]

the euler function

[amber schooner]

yea

[high tusk]

I GOT THE PROOF

[nocturne belfry]

yes

[high tusk]

THANKS POOKIES

MWAH

:)))

.close

[odd edge]

Channel closed

Closed by @high tusk

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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

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

[vale sand]

Can someboady explain to me how to calculate angles in non right traingles?

[nimble blaze]

depending on what info you have
sine rule and cos rule would be useful

[vale sand]

Uh okay

example

to my best understanding

c is 7

b is 5

a is 3

what is C angle

the diagram looks like c is x and a is y and b is r

[sharp oak]

Cosine law would get you this

[vale sand]

doesnt cosine law only apply to the first part