precalculus

[slender river]

what

you can seperate products too right?

the right bit would be 2log_2(y) + (1/2)log_2(z)

so in total it should be $$\log_2 (x+1) - [2\log_2 (y) + \frac{1}{2}\log_2 (z)]$$

aw cmon

so in total it should be $$\log_2 (x+1) - [2\log_2 (y) + \frac{1}{2}\log_2 (z)]$$

[slender river]

there

you can even make everything base e using change of base formula too haha

[wise umbra]

00f

i just dont get logs for some reason, dont make sense to me, i might watch some khan xd

also I have another problem

=tex \log _b\left(\frac{\sqrt{x}y}{z^3w}\right)

[wise umbra]

and would i get

[granite stirrup]

Rendering failed. Check your code. You can edit your existing message if needed.

[wise umbra]

=tex \log _b\left(\sqrt{x}y\right)-\left(z^3w\right)

[fallen cloud]

that (z^3 * w) should also be in the logarithm of base b

[wise umbra]

OH yeah i forgt

but adding that in would make it correct, right/.

yeah i remember that it would, thanks!

So how would i do something like this

=tex 81^{3x-4}=\frac{1}{243}

[vapid oxide]

can someone make a log function that goes from (0,square root of 2) to (100, 34 power of 34)

would be very much appreciated

[spring thunder]

$$f : x \mapsto \sqrt{2}e^{\frac{\ln\left(\frac{34^{34}}{\sqrt{2}}\right)}{100}x}$$ hehe

[spring thunder]

@vapid oxide

[vapid oxide]

oh ok

thanks mate

also this is for configuring android screen brightness cause google changed the brightness slider from linear scale to log scale

hmm

not 0,sqrt2

is k

[spring thunder]

"also this is for configuring android screen brightness cause google changed the brightness slider from linear scale to log scale" dem

[viscid thistle]

does anyone get this problem
tan(sin^-1 4/5 + tan ^-1 5/12

$$f:
tan(sin^-1 4/5 + tan ^-1 5/12

$$f: tan(sin^-1 4/5 + tan ^-1 5/12

$$ tan(sin^-1 4/5 + tan ^-1 5/12

=tex tan(sin^-1 4/5 + tan ^-1 5/12

[fallen cloud]

well

you know the tan sum formula?

[viscid thistle]

uh yes, I believe so

[fallen cloud]

then use it here, with arcsin(14/5) and arctan(15/12)

[viscid thistle]

ah

[wise umbra]

How would someone go about solving a problem like this?

[viscid thistle]

tex = sin (2a) sin a = squareroot 6 /3

= tex sin(2a) sin a = sqrt 6/ 3

[viscid thistle]

how does one solve this

[wise umbra]

idek LOL

[viscid thistle]

lol

[gaunt gate]

hey guys
how would I find the ln 1/radical(e)
wait wtf I cant post a picture of it?

[solar abyss]

ln ( 1/ sqrt(e) ) = ln ( e^(-0.5) ) = -0.5

@gaunt gate

[gaunt gate]

how do I get that?

[solar abyss]

u gotta use ... (hang on im typing)

$$ log_{e} e^x = x $$

[solar abyss]

$$ btw log_{e} is ln $$

[solar abyss]

$$ log_{e} = ln $$

[solar abyss]

also u gotta understand that 1/sqrt(e) is equal to e^(-0.5)

[gaunt gate]

oh jeez

its taking all my last 3 brain cells have got to try to understand that

I know about log_e being the same as ln

but im completly lost on how you got -.5

[solar abyss]

ok so 1/sqrt(e) = 1/e^(0.5) agree?

[gaunt gate]

ohh yeah 1/2 yup

[solar abyss]

yep. 0.5 is same as 1/2. so do u understand the entire thing?

[gaunt gate]

ohhh yeah

I can use the rules

to make it ln 1 - ln e^1/2

ln of 1 is zero so 0 - .5 is .5

thanks

[solar abyss]

yup you could do it that way too

np

[gaunt gate]

I got kinda mixed up a bit since you used .5 and our teachers here despise decimals and everything they stand for

[solar abyss]

woops my bad

haha

[gaunt gate]

no worries lmao thanks for the help!

[wise umbra]

Heya! How would I solve the equation for this problem? :

=tex 3^{x+1}=5^x

[patent beacon]

Take the log of both sides:
(x + 1)log(3) = xlog(5)

Now this is linear in x. So, solve the normal way by isolating x:
xlog(3) - xlog(5) = -log(3)

x(log(3) + log(5)) = -log(3)

x = -log(3) / (log(3) + log(5))

[wise umbra]

sorry i was afk.

ok

thanks! :)

[floral tide]

daily duck problem for u guys

[solar abyss]

quack

[viscid thistle]

hey can I please get helo

what is sin (a/2) when given sin a = 4/5

[fringe stream]

$$\sin\left(\frac{a}{2}\right) = \pm\sqrt{\frac{1 - \cos a}{2}}$$

$$\sin\left(\frac{a}{2}\right) = \pm\sqrt{\frac{1 - \cos a}{2}}$$

[hot falcon]

@viscid thistle find cos(a) (sin^2a + cos^2a = 1) and then use the formula from the Math bot..

[somber plaza]

@hot falcon am easier way would be to think of it geometrically and realise that it’s a 3-4-5 triangle

[fallen cloud]

x^x, once upon a time i knew, that time is no longer here

[gritty blaze]

Not a story, not a joke, #chill .

[nimble oxide]

Hey, who here understands how to simplify trigonometric identities?

[fallen cloud]

me

wutcha need?

[nimble oxide]

I am completely ... confused .... on When the denominator has a +/-1

My teacher kind of helped me by starting it and I.. think I just foiled wrong
. But for the denominator I literally got 1

[fallen cloud]

the denominator should be 1-cos^2 (x)

[nimble oxide]

But yeah I realized I added the last terms

Instead of multiplying

Lol

[fallen cloud]

you know the identity of s^2 + c^2 = 1, (shortening sin to s and cosine to c

[nimble oxide]

But how do o find out the numerator...

[fallen cloud]

well

lets stay on the denominator for now

s^2 + c^2 = 1, hence s^2 = 1 - c^2

which you can use to replace the bottom

[nimble oxide]

Jugjhhhhhh

I hate this unit so much

[vast trellis]

I was told to use the Cramer’s rule to solve for x y and z but I noticed that the first two equations are almost opposites of each other. What can I do to make this easier or can I even make it easier

I feel like instead of making 3 different matrices and solving for each one (which I did and I know it’s wrong) there’s a shortcut

Can I combine the -2x and 5x equations together and solve by a 2 x 2 matrix?

[hexed ermine]

Well notice if you add the first two equations youll get a false result

0=3

so you can say that the soe has no solutions

[dim charm]

What’s a good way to find the number of solutions of sin(8x) + sin(12x) = 0 on the interval (0,2pi]

[fallen cloud]

um

set sin(8x) = sin(12x)

[dim charm]

U mean sin(8x) = -sin(12x)

@fallen cloud

[fallen cloud]

yeah

[dim charm]

Ok, then what

[fallen cloud]

you could expand them... but

[dim charm]

Um

Rather not

[fallen cloud]

i recommend mutliplying the domain of the left by 4 and the right side's domain by 4

[dim charm]

?

How does that help

[fallen cloud]

so you get sin(2x) = -sin(3x), where x is from 0 to 8pi,

but the values are the same every 2pi, so we will just have 4*the number of solutions that 0 to 2pi would have with the function sin(2x) = -sin(3x)

then you can expand...

[viscid thistle]

OOF

[gaunt gate]

yo

so um

I need help with #61

Im unsure as to how i would calculate it

[hexed ermine]

A=Pe^(rt)

[gaunt gate]

but P isnt given

[hexed ermine]

Yes it is

12000

[gaunt gate]

oh fuk you're right

[hexed ermine]

Y

A

[gaunt gate]

I missread that as A

so I use A=pe^rt for all of them?

just replacing t with the number right

[hexed ermine]

Yes

[gaunt gate]

thanks

[flint lichen]

Could someone help me find two periods for 3sin(2x)?

[hexed ermine]

Two periods?

To evaluate the period of a sine functions you do 2pi/b

In this cases it's just 2pi/2 or just pi

There is no "two" periods

[flint lichen]

Maybe I don’t fully understand what a period is then, may you please elaborate?

[hexed ermine]

A period is the length of one cycle of the function

A regular sin(x) graph has a cycle of 2pi

After that it does the same thing

After every 2pi, the graph repeats over and over

When you have sin(bx), if |b|>1, the period is less due to the horizontal compression of the function

[flint lichen]

That actually makes a lot of sense, thanks!

[hexed ermine]

No problem

[vast trellis]

I’m having so much trouble with this

[spring thunder]

waht are you stuck on? @vast trellis

[vast trellis]

Finding the inverse @spring thunder using the coefficient matrix. I know the matrix is

1 1 1
4 3 -1
3 -1 -1

But where do I go from there

[spring thunder]

are you allowed a calc for this ? (i guess not though)

[west bramble]

The best way is probably to use row operations

[west bramble]

Here is the example worked through using row operations to find the inverse matrix

[nocturne lake]

Alright. here are my assumptions:

trigFunction(x)=t
arcTrigFunction(t)=x

sin = Y value on the unit circle
cos = X value on the unit circle
tan = sin/cos = slope of the line on the unit circle

I was given:

sin(arccos(1/10))

Here is what I did to solve it:

I constructed a triangle with a length of 1 and a hypotonus of 10.
Using the pythagorean theorem, I found the triangle I constructed has a height of sqrt(99) = 3 sqrt(11)

The answer I gave was 3 sqrt(11)
The correct answer was (3 sqrt(11)/10

I would love a hand finding my mistake, thanks!

[hexed ermine]

Well what is sin defined by

Opposite/hypotenuse

You found out what the opposite was, now you need to find what sin of that angle is,

And you know opposite and hypotenuse

Which is 3sqrt(11)/10

You forgot to bring the 10 into play when it's the hypotenuse

@nocturne lake

[nocturne lake]

Awesome. Tried another one with different values.

cos(arcsin(5/11))
I found the adj. was 4sqrt(6)
Because cos is defined by adj/hyp the answer is (4sqrt(6))/11

Thanks a bunch!

[hexed ermine]

Yep!

[calm cloud]

how do i find the initial value? P(0)

[fringe copper]

Guys I think my teacher went nuts

We had a math exam

He asked 12 questions with at least 2 sections

And gave 50 mins

Now can someone tell me isn’t this regarded

Isn’t this stupid***

[opal lotus]

What do you mean

Too little time you mean?

[fringe copper]

Yeah

Too little time

How can you do 20 questions in 50 mins

Which also has some graphing questions by the way

@opal lotus

[opal lotus]

i dunno depends on the questions, also i know some teachers who like to purposely make the tests hard so its easier to see how much they need to curve

[vast drum]

I'm confused on a question.

55=60/1+5e^-0.6x

This is what I have so far, am I on the right track?

ln55=ln60-ln(1+5^-0.6x)

[royal gull]

Can someone explain me the proof that there can't be more than 1 limit of any sequence?

I saw a proof that used triangle inequality but didnt quite get it on my lectures

[lofty slate]

@royal gull what do you mean by series

like a sequence?

[royal gull]

sequence* sry

[lofty slate]

uh i dont remember it but im pretty sure this would be a #calculus question

[royal gull]

Ok, will ask there, thanks

[vast trellis]

Question. So let’s say you have the equation

Would this count as there being an infinite amount of solutions? If so, would would be the set? 4,-4?

[hexed ermine]

Mhm

If you multiply the second equation by -1 you will see that it's the same as the first line making it have the same equation for a line i.e. the same

Or if you were to add the equations you'd get 0=0 giving you a linear dependent system

[vast trellis]

So would I just put (0,0)?

[hexed ermine]

Or I should say consistent dependent

No

Youd put infinitely many solutions

[slender river]

they're the same line

thus this "set" you mean is not really bounded

wot n ternation

what does that top part say about y.. arbitrary?

[vast trellis]

Arbitrary: based on random choice or personal whim, rather than any reason or system.

[slender river]

oof idk that notation

er rather how they want it

sorry

[vast trellis]

It’s fine

[hexed ermine]

Hmm

Try getting an ordered pair with a relation to y for x

[vast trellis]

It’s one of those homework’s that you get x amount of questions, you turn it in all at once and then you get your results. I can redo the whole thing I just don’t want to get a question wrong and have to redo the whole homework

[slender river]

yeah mathxl is sketchy i dont really like it (not just for that reason)

[hexed ermine]

x=(2+4y)/3 correct

[vast trellis]

? I didn’t get the equation for each one I just got them to cancel out

[hexed ermine]

Put ((2+4y)/3, y) as the solution set

[vast trellis]

Ok. I’ll try. Thanks

[vast trellis]

Should I just use the elimination method

[viscid thistle]

@vast trellis make a matrix first

Then do gaussian elimination on it

[hexed ermine]

Yeah I am just now seeing this

[viscid thistle]

Remember to add a column for the rhs

[hexed ermine]

Do what he said, or use your desired method of solving a system

[viscid thistle]

@hexed ermine it says "solve using matrix"

In problem statement

So any form of matrix simplification works

[hexed ermine]

Yeah you can use cramers rule and such you dont need to use gaussjordan or gaussian elimination

But I agree, I would use RREF

[viscid thistle]

👍

[viscid thistle]

How does 5 become 5^2?

[hexed ermine]

You mean 2^5

They used the log rule

log_a(b)=c is the same as a^c=b

[viscid thistle]

Yeah

Thank you

Also why why does log base 2 disappear in the next step?

[vapid oxide]

does 3d graphing go in here or in #calculus

[olive meteor]

How to turn 5/3 radians into terms of pi?

[hexed ermine]

*pi/180

[vast trellis]

Why I hate math word problems

[severe verge]

lol

there are ways to make good math word problems

but all these seem so low effort tbh

[olive meteor]

@hexed ermine so 1/2 radians would be pi/360 in terms of pi?

[severe verge]

so forced

[viscid thistle]

How do i got about solving this?

[vast trellis]

Is this logs?

[viscid thistle]

Yes

[vast trellis]

Ahh...I remember logs...it was like 2 months ago. I think I know but let me check my notes just in case

[viscid thistle]

Cool thanks

Im really stuck on this one lol

I think have to write out something like y=ka^x

With y being the richter level

K being the constant

A being the growth factor

And x being the amount

[vast trellis]

So in this case, they’re saying that the base is 10 and your x is 5.2

Sorry I had to do something lol

[viscid thistle]

Okag np

[vast trellis]

I’m like back and forth /:

[viscid thistle]

Its cool

[hexed ermine]

You are finding x I believe

y=10^x where y represents an increase of a unit, and x is the level

2=10^x, log(2)=x

==log(2)

[granite stirrup]

log(2)/log(10) = 0.301029995663981

[hexed ermine]

==.301+5.2

[granite stirrup]

5501/1000 = 5.501

[viscid thistle]

Ohhhhh

Thanks so much

The words just disnt register in my head

[hexed ermine]

This means that an earthquake that is twice as strong results in a 5.5 level earthquake

[viscid thistle]

Thanks alot

Is that how the richter scale actually works btw?

[hexed ermine]

You are comparing it to 5.2 so you want to negate that till the end, y=10^x only represents the Richter level from the intensity

Yep!

[viscid thistle]

Thats pretty cool

[hexed ermine]

Anyways yeah, if you wanted to find a level for an earthquake that is triple the strength you do log(3)

And add that to whatever scale you have

[viscid thistle]

Cool

Now i know how the richter scale works

[hexed ermine]

Hehe

Btw nice profile picture

[viscid thistle]

Thanks, i cant even remember what meme i got it from

Its been so long

[vast trellis]

Thanks pjs I had to go do something irl rip

Still kanda afk

[viscid thistle]

Thanks for trying to help though

[hexed ermine]

👍

[violet kelp]

=tex 2

[solid reef]

#13?

[austere matrix]

k

sin(cos^-1(3/5)-sin^-1(5/13))

is my problem

=tex \sin(\arccos{\frac{3}{5}}-\arcsin{\frac{5/13}})

[granite stirrup]

Rendering failed. Check your code. You can edit your existing message if needed.

[austere matrix]

woops

=tex \sin(\arccos(\frac{3}{5})-\arcsin(\frac{5/13}))

[austere matrix]

ok sorry jesus

=tex \sin(\arccos \frac{3}{5} -\arcsin(\frac{5/13})

[austere matrix]

close enough

can anyone help me here? i'm absolutely lost

[earnest finch]

Sorry my next unit in precalc is literally trig but I am not there yet

[limber bone]

no body likes trig anyways

[finite iris]

trig is pretty o:

[rocky bison]

@austere matrix

still stuck

?

[buoyant knot]

@austere matrix hint: addition formulae

[scenic eagle]

Power of an earthquake is given by Richters scale with Richters number R. If E is energy measured in Joules, then the Richter number is given by R (E) = 0.67 * log(E) - 2.9

This is a common log.

a) Find the Richter number to an energy of 4.4*10^15 J.
b) An earthquake was measured 5.4 on the Richters scale. Find the earthquake's energy.
c) Another earthquake was measured 9.5 on the Richters scale. How many times bigger was the energy of this earthquake compared to the first earthquake?

I did A like this in Geogebra, is this correct?

because http://www.convertalot.com/earthquake_power__calculator.html gives me a different answer and I'm concerned.

[spring thunder]

Your site uses a "real" seismographic formula (more precise i mean), just follow the approximation the exercise gives you @scenic eagle

[scenic eagle]

alright thx

[stone atlas]

derivatives help you find the instantaneous rate of change at a given point right?

[viscid thistle]

yes

[mighty trellis]

hey guys

i need help with synthetic division

i just have a quick question

[viscid thistle]

whats the question

[sullen shoal]

Solved

[viscid thistle]

o

https://cdn.discordapp.com/attachments/504663833932202003/505185050199982081/unknown.png

Need an help frens

b=1/4?

a=1 confirm

(-6,-2)

I did b wrong but how da hell the verticies wrong

<@&286206848099549185>

-7 smaller than -5

[slender river]

hmm

idk thats kind of weird

[viscid thistle]

Only option is to put them in wrong backwards and hope is correct

[slender river]

perhaps

[viscid thistle]

fuck me of course it doesn't tell me i used a period

fucking shitty software

@slender river

[slender river]

oh shit i didnt even notice

i thought it was like poor quality lol

oof

that's so sad

[viscid thistle]

feelsbad cuz sent to professor and shows im dumb

[slender river]

oof

does he/she do partial credit

like

you have the numbres correct

just keyboard being domb

dis y i dont really like online math hw programs/websites

can't account for formatting errors unless they only make the blanks for numbers and numbers only which is also annoying

[turbid barn]

Hey

What's a good list of topics I should know before calculus

[patent beacon]

Each of the elementary functions
-polynomials/rationals/radicals
-trig and trig identities
-exponentials and logarithms

Understand domains of functions, continuity of functions, how to compose functions

Be up on your algebra. Know how to manipulate rational functions. Putting everything over one denominator is a common trick

[turbid barn]

Thanks!

[slender river]

especially with algebra you want to be comfortable with working and manipulating loads of terms because stuff like implicit differentiation becomes very ugly very fast

[hoary yoke]

@twilit willow hello

[twilit willow]

Hallu

The options were given (2x+1)(1-x)^2

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

[limber bone]

dy/dx * dx/du = dy/du

[twilit willow]

Chains rule right?

[limber bone]

y

dy/dx * dx/du = dy/du

know this

then u can answer ur prob

[hoary yoke]

Yep

[twilit willow]

Is it the rearrangement of chain's rule?

Never mind it isn't

Okayy lemme try it out

[hoary yoke]

Or you can do harder

And seperate x

[limber bone]

then sub in

[hoary yoke]

Then put that u thing in y

Yup

[twilit willow]

Wait so fast

[limber bone]

never mind this way

its harder

dy/dx * dx/du = dy/du

what if

u have du/dx?

what do u do

[twilit willow]

Find the derivative right?

[limber bone]

you found the deriv

and u have

du/dx

and dy/dx

how can u find dy/du?

[twilit willow]

Mutiply them togethjer

Multiply them*

[limber bone]

du/dx * dy /dx ?

are u sure

[twilit willow]

its dx/du not du/d

x

okay

hmmmm

[limber bone]

show me

the 2

functions

[twilit willow]

y=x^2+x

and 1/(1-x)

[limber bone]

ok so

why

what

what = 1/1-x?

u?

[twilit willow]

yes

sorry

[limber bone]

y = x^2 + x

[twilit willow]

u=1/(1-x)

[limber bone]

ok

what do u have when u differenciate with respect to x

for the first function

[twilit willow]

2x+1

[hoary yoke]

Dy/dx=2x+1

Correc4

[limber bone]

so u have dy/dx

ok

what happens when u diff the other 1

?

[twilit willow]

and we need dx/du

you get (1-x)^-2

[limber bone]

what do u get

ye what is it

[hoary yoke]

Marwan

No

You will get du/dx

[limber bone]

yes

?

did i say something wrong

or what

[hoary yoke]

You need dy/du

Not dydu/dx^2

[limber bone]

u cant multiply them

ye thats

i know this thats why

i asked him the question

what if
u have du/dx?
what do u do

[twilit willow]

Do I have to switch them?

[limber bone]

y

[hoary yoke]

u=1/(1-x)multiply both sides by 1-x

[twilit willow]

Yea

So then I will get -1

[hoary yoke]

=>u(1-x)=1

[twilit willow]

For dx/du

Sorry I did

du/dx

[hoary yoke]

1-x=1/u

[limber bone]

-x=1/u+1

[hoary yoke]

X=1-1/u

[limber bone]

x=-1/u-1

sub in that for the first function

and differenciate

instead of chain rule

[hoary yoke]

Marwan...

[limber bone]

?

[hoary yoke]

x=1-1/u

[limber bone]

oh ye sry

lol

[hoary yoke]

Now plug that x for y=x^2+x

Y=(1-1/u)^2-1/u+1

Dy/du=2(1-1/u)/u^2+1/u^2

[twilit willow]

OHhhh

okay

Got it

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

Right?

Thanks guys

I understand it now!

[half spruce]

Is this the right subchat for this?

got to 2*(7^x)-3*(2^x)-43*(1/7)(2^x)(sqrt(7^x))>0

[limber bone]

u want to simplify?

[half spruce]

my friend simplified it dividing by (2^x) but I honestly have no clue how he got to that 😄

so consider this one solved I guess

[limber bone]

thats an ugly one

gl

lol

[remote musk]

@half spruce have you studied log or ln functions?

[neon vale]

any ideas?

[patent beacon]

@neon vale
What's wrong with x - (1 + 2i) as a factor?

[neon vale]

Nvm got it @patent beacon ty

But I do need help again

[patent beacon]

What's up?

[neon vale]

@patent beacon idk how to use the zeros to figure out the function

[patent beacon]

= a(x + 3)(x - 1)(x - 3)

Then you need f(0) = -3 to find a

[stone atlas]

i think you should also keep in mind that since it goes from quadrant 2 to quadrant 4, the a value is going to be negative

[neon vale]

I still don’t get it

What even is a

[neon vale]

Nvm got it

[earnest finch]

I'm doing logs and exponentials rn

Trig next unit :'(((

[hexed ermine]

If you need help let me know

[timid willow]

yo guys
i got a question
find the vertex form
of an equation with root 9+i
and passes through 1,-5
how do i solve

@hexed ermine

[blazing raven]

er first what kind of shape is it?

[hexed ermine]

If 9+i is a root, 9-i is also a root

[turbid barn]

this also applies to sqrt(n)-m and sqrt(n)+m because polynomials can't have terms with non whole number coefficients.

[plush peak]

Hey

Im trying to find out if a function is pair or impair

If I give the x values like 3 and -3

and it comes out to the same answer in both cases

its pair right?

[spring thunder]

(Français?)

[turbid barn]

Yeah. So a function like x^2 is even (in English it's even/uneven)

Spanish also has par/impar

[spring thunder]

Well if that property is true for any x yup

[plush peak]

For example

I have

1-root(1-x^2)

I gave it a value of 3 and then -3 and both of them came out to be 1-root(1-9)

[spring thunder]

3 isn't in the domain of that function tho, if you only consider real outputs

[plush peak]

what would be the vertical asymptote for 16/x^2+4?

[hexed ermine]

Nothing

It would be imaginary asymptotes

[plush peak]

I placed the function on desmos and it gave me a weird graph

So I got confused

[turbid barn]

Yeah why does it do this

Oh it's because it has no asymptotes if you add a number to x^2

[hexed ermine]

A vertical asymptote is where its undefined

i.e. the denominator is 0

setting x^2+4=0, you get imaginary x values so in the reals, there are no asymptotes

[fickle moat]

For number 11
I found amp = -5/3
For period the cos formula is 2pie/B
But then how do i find period?

I got 24

But

Is this correct way to find period?

<@&286206848099549185>

[hexed ermine]

2pi/(pi/12)

[fickle moat]

24¿

[gaunt gate]

imma sound really dumb but

whats x/-2x

[viscid thistle]

-1/2 for x =/ 0

[gaunt gate]

im lost

im really dumb btw so you'll have to explain again lmao

[viscid thistle]

In your pfp, it's a shinobi but who? His or her face us stretched out

[gaunt gate]

Itachi

[viscid thistle]

I see it now...

Itachi-sama

[fallen cloud]

itchy-sama hm

i wonder

[gaunt gate]

I also have a picture of Light

thats similar

its in chill

[austere matrix]

...

[viscid thistle]

Light

[solid reef]

15?

[viscid thistle]

maybe substitute?

[serene heath]

@solid reef write your circle equation in the form $$x^2+y^2+ax+by+c=0$$

now you have 3 unknowns and 3 points to plug in

find the values of a,b and c and rearrange into required form

[viscid thistle]

what does "one-one mean for logarthimics

[thick raptor]

one input → one output

[earnest finch]

Doing logs here too

NEXT UNIT TRIG 😢

[viscid thistle]

[patent beacon]

All functions are one-input → one-output.

The important thing about one-to-one functions is that each input gets its own output

log100 = 2
Since logs are one-to-one, I know that 2 is the only input that has an output of 100

[thick raptor]

uh

oh yeah that's gud

[viscid thistle]

yo

where's the set theory channel?

[thick raptor]

just use #proofs-and-logic tbh

or #discrete-math if it's not advanced set theory

or one of the other channels if it fits better there

¯_(ツ)_/¯

[viscid thistle]

I see I see

Kk thx

Also

Where does the underlined portion come from

<@&286206848099549185>

[thick raptor]

#❓how-to-get-help rules:
Wait a minimum of 15 minutes after posting before you ping helpers.

[viscid thistle]

ok

[patent beacon]

@viscid thistle
Try taking the line beneath it, and distributing -1/15 in

[viscid thistle]

ah i see

thanks

[sharp sleet]

https://cdn.discordapp.com/attachments/469125935052881930/507007935323308043/a-Q-tran-1381-setA_Online_Assignment_4prob3image1.png

hey guys how do i find the function of this graph?

[viscid thistle]

Oof trig

do yall know any good practice problem websites for precal?

[hallow tide]

f(x)=-sin((1/2)x) transformed 0.5 units left.

[shell salmon]

horizontal translation is -c/b

[hallow tide]

nice

[sharp sleet]

nvm i got it

took me an hour but still

[wise umbra]

Hi I have a trig question :)

A train is traveling at the rate of 40 miles an hour on a curve of two-mile radius. Through what angle does it turn in 22 seconds?

[solar abyss]

ok fren

seems easy i will try

[wise umbra]

lol thanks

i may have worked it out

[solar abyss]

tell me what working u have

[wise umbra]

15.756 degrees?

[steep shell]

yeah doesn't seem too terrible

[wise umbra]

or am i way off

[solar abyss]

@steep shell when r u gonna let the poor goldfish go...

[steep shell]

when it gives me my goddamn money

[wise umbra]

lol

[solar abyss]

[wise umbra]

[solar abyss]

hey so the train is travelling on a circle of radius 2?

[wise umbra]

yes

you see im dumb and dont know how to plug things in

i presume

[steep shell]

arc length should be miles per second * 22 seconds

[solar abyss]

so the obvious next time, i'd imagine, is to figure out what distance the train travelled

[wise umbra]

oh so you divide the 2 miles into 1 but why to the power of 22

[solar abyss]

1 hour has 60 mintues, each minute has 60 seconds, so 60*60 = 3600 seconds

[steep shell]

i mean x 22

[wise umbra]

oh ok

[steep shell]

i've been doing a lot of coding in MatLab and * is used for multipication

[wise umbra]

sorry :oof:

yeah i forget its like 12am and im tired

[steep shell]

all good

[wise umbra]

oh so thats how ou do the hour thing

what would i put for the circumpherence

[solar abyss]

so train travels 40 miles in 3600 seconds, hence 40/3600 miles in 1 second, hence (40/3600)*22 miles in 22 seconds feel me

[wise umbra]

Ohhhhh

[solar abyss]

yes fren

t!dog

[brisk mica]

🐶 | Here is your random dog:

[wise umbra]

OK fren

t!cat

[brisk mica]

🐱 | Here is your random cat:

🐈 #2718140

[wise umbra]

yas

[solar abyss]

so ur final answer should be [ (40/3600)*22 / 2(pi)(2) ] * 360 in degrees fren

[wise umbra]

why u so good fren

[solar abyss]

becuz fren

i studee de meth in uni

[wise umbra]

o fren

i dumbs fren

sophmore in hs

trying to survive the wrath

but thanks

[solar abyss]

np fren

[wise umbra]

de meth 😂

i cant lmao

[solar abyss]

kek

[wise umbra]

[alpine portal]

Don't know why its wrong...??

[spring thunder]

cause your answer is in miles/min

[alpine portal]

Ooh

thx

[spring thunder]

👌

[nimble oxide]

who here can explain the process of Double angle and half- angle identifications to me?

[viscid thistle]

can someone help me build my quadratic equation?
-> "$70 for one hotdog, and i sold 2000 hotdogs, if for every $1 i decrease my hotdog price i sell 50 more"

im assuming 2000 = 70....

but dont know how to translate $1 and 50 doggies

[turbid barn]

Is a hyperbola the inverse function of y=1/x?

[chilly matrix]

Guys

If I know -6 is a zero of a polynomial equation.

How would I find k of f(x)=4x^4 + 3x^3 - kx^2 -x + 16

[thick raptor]

Plug in x=-6

[prime prawn]

If r = ln3 and s = ln5, write ln (0.24) in terms of r and s.

I got to the point of ln2+r-2s

How do youu simplify further?

@viscid thistle Help a fellow pokemon player.

<@&286206848099549185>

[viscid thistle]

Pokemon!

Linguist, I think it's fine like that....

[willow vine]

I need help

discord is fucked right now

aaaaaah

<@&286206848099549185>

youll have to open the link to view it

i think these are like all wrong

log things

[fringe stream]

https://puu.sh/BUSb5/362ff528f7.png

thought embeds were working :/

anyway

[willow vine]

discords broken

am I overthinking it

[fringe stream]

please wait 15 minutes before pinging helpers

[willow vine]

oh

sorry

[fringe stream]

2 and 3 are not right

[willow vine]

all

?

ok so I think

[fringe stream]

d is fine

[willow vine]

if im correct

[fringe stream]

a, b, c are not

[willow vine]

a. should be x

b. should be 1

c should be right for 2

because a^0=1

[fringe stream]

you're right about a and b ^

not c

[willow vine]

wat

whats c then

for 3 a should be right

and b

c should be x

[fringe stream]

$$\log_b 1 = ? \leftrightarrow b^? = 1$$

[fringe stream]

what would ? be then

what's the power you can raise any number (except 0) to, to get 1?

[willow vine]

umm

idk

[fringe stream]

it would be good for you to revise exponents

[willow vine]

can you help me

I have a test tomorrow

my math teacher talked about this yesterday for 5 minutes

And said its on the test

ok well nvm

well mathway says its 0

[opaque bay]

0^0=1?

[fickle moat]

i have a question
complimentary angle is 90 degree ; pi/2
supplimentary angle is 180 degree ; pi

?

[opaque bay]

ye but geo

[fickle moat]

trig

i am in pre-calc

[opaque bay]

wrong channel

put it in trig

[viscid thistle]

=wolf 0^0

[granite stirrup]

Do more with Wolfram|Alpha pro

Query made by

@true oasis

[crystal current]

i need help finding a formula for this

it's due in 15 min.

long run behavior is implying the degree should be x^4 but theres only 3 zeros wtf?

[lost cipher]

u have the right idea

it's pretty much asking you what the lowest even number is given that it's bigger than or equal to 3

[crystal current]

should i try (x+1)(x-6)(x-7)? and then find a with (0,11)?

[lost cipher]

remember you can have (x+1) to any power or an additional zero (they don't say that those are the only zeroes)

[crystal current]

i tried x(x+1)(x-6)(x-7)+11 but that was wrong lol

[lost cipher]

the reason why that doesn't work is because if you plug in -1, the product becomes zero but the +11 makes it not 0

you want to set it up like this: a(x+1)(x-6)(x-7)

[crystal current]

mkay, but shouldnt the degree be at least 4

because they stated the limit

[lost cipher]

yup so i think you can do a(x+1)^2(x-6)(x-7) or a(x+1)(x-6)^2(x-7)

[lost cipher]

or a(x+1)(x-6)(x-7)^2

or add a new zero

[crystal current]

ill try these quickly i have 9 min

[lost cipher]

and then once you choose one, plug in x=0 to find the value for a

[crystal current]

okay thank you

[lost cipher]

hold on

it's a(x+1)^2(x-6)(x-7)

since it's positive when x=0

meaning that it had to bounce back up at x=-1

(assuming a is positive)

nvm you can choose whatever

[crystal current]

that was right! tyvm @lost cipher

appreciate it

[lost cipher]

np

[viscid thistle]

=tex \lim_{\theta \to 0} \frac{\theta}{\sin(\theta)}

[rocky bison]

You need dat help @viscid thistle

?

[thick raptor]

[rocky bison]

@thick raptor You ready for some hopital

[thick raptor]

[rocky bison]

You lucky he's gone 👀

[serene heath]

out of curiosity, how would you work that limit out?

i know its 1 but my method is iffy

[rocky bison]

Divide top and bottom by theta

[serene heath]

and you cant use l'hopitals right?

[rocky bison]

Then you've got 1/sin(x)/x

=tex \frac{x}{\sin(x)}\equiv\left(\frac{\sin(x)}{x}\right)^{-1}

[rocky bison]

You can use hopital

It's just

Really dumb too

hence the joke

sin(x)/x is then a known limit

Which is commonly given as almost an identity

[serene heath]

sorry could you elaborate

on why its dumb

[thick raptor]

One sec

[rocky bison]

Because it's use in defining the derivative of sin for example

[serene heath]

lol

[rocky bison]

So you're defining the derivative of sin(x)

by differentiating sin(x)

Which is a bit

And hopital is quite often frowned upon tbh

[serene heath]

hmm

[rocky bison]

It's just kinda like a clutch way out

But it does work

[thick raptor]

@serene heath okay so to use L'H, you need to take the derivative of sin(x)

What is the definition of the derivative

[rocky bison]

Here he comes about to repeat what I said

[serene heath]

uhm the slope of the tangent at that point?

[thick raptor]

What is the definition in terms of limits

[serene heath]

oh

the formula thing

[rocky bison]

=tex f'(x)=\lim_{\delta x\to0}\left(\frac{f(x+\delta x)-f(x)}{\delta x}\right)

[thick raptor]

sure that

[serene heath]

yes that

ik that

[viscid thistle]

Change that delta x to h

[thick raptor]

So

To take the derivative of sin(x)

[rocky bison]

nah @viscid thistle

[thick raptor]

we are, by definition doing the above limit

[rocky bison]

Use hopital again 👀

[serene heath]

yes

[thick raptor]

=tex \sin'(x)=\lim_{h\to0}\frac{\sin(x+h)-\sin(x)}h

[rocky bison]

Sin to the power of '

[serene heath]

lol

[thick raptor]

Not only does solving this limit require solving the original problem

[viscid thistle]

[rocky bison]

So to solve this

We just use hopital again

[thick raptor]

but it also requires solving other stuff too

[rocky bison]

Because it's easier

[thick raptor]

[rocky bison]

👀

[serene heath]

ya i kinda get what you mean

but surely thats just being mathematically pedantic

[viscid thistle]

To solve, expand sin(x + h) with trig identity then do other manipulations and vua la

[thick raptor]

@serene heath think of it like this

you ask me to find a limit

I tell you the answer

you ask why

I tell you "because this"

you ask "why that"

I tell you "because answer to your limit is this"

See how I'm avoiding the problem entirely?

[serene heath]

yes, youre bein a lazy mathematician

[viscid thistle]

Basically, you answer the why

[serene heath]

i get what you mean

[thick raptor]

Generally speaking, you're not allowed to use "because the answer to the problem is ___"

when solving that problem

that literally makes no sense

[serene heath]

i see

cheers for the explanation

[thick raptor]

If you want explanation of how to actually solve the limit I can give u that

https://i.ytimg.com/vi/vz9_102nL8M/maxresdefault.jpg

It essentially stems from this picture

[viscid thistle]

Khan academy can explain the above picture if you're confused

[thick raptor]

meh imo pretty straight forward

[viscid thistle]

What's an rps

[rocky bison]

t!wiki rps

[brisk mica]

📖 | ** https://en.wikipedia.org/wiki/RPS **

[serene heath]

na its fine i get it

[gaunt rose]

rps looks like a Riemann surface / torus of some kind

nvm don't think its a torus on closer inspection, too small to see though

[viscid thistle]

https://media.discordapp.net/attachments/501177519328722944/507994589052010507/function.PNG?width=914&height=585

Are the values correct? Range is the one I am least confident about

3x/(7x -9) is the inverse

domain is right

$$ f\left(x\right)<\frac{3}{7}\quad \mathrm{or}\quad :f\left(x\right)>\frac{3}{7} $$

[viscid thistle]

range is above

@viscid thistle see above, my comments

I'm so dumb

so its defined for all values except where the denominator would equal zero

[near valve]

yes, so your domain is correct

However, to find the range, you need to look at this inverse function when x approaches positive infinity and when x approaches negative infinity\

that's how you could get the range for this problem

[viscid thistle]

so its going to be (3/7, infinity) (- infinity, 3/7)?

[gaunt rose]

the domain of the function is the range of the inverse

so where the denominator of f(x) = 0

is the point not in the range

[near valve]

@viscid thistle yes, what you just wrote would be the range

[viscid thistle]

Am I supposed to expand the expression on the right and then use the change of base formula?

[earnest finch]

Nah

The fastest way for me to do it is ln on both sides

Then you can use the exponent properties to bring the exponents in front of the lns

Then it just becomes a linear equation from there and you solve for x

[viscid thistle]

so I have 5x(log13)= (x+8)(Log3)

I'm stuck here and dont know how to factor it futher

[near valve]

5x(log13) - x(log3) = 8(log3)

then you can solve for x from there

[viscid thistle]

Got it!

I have a trig question if your down

does this look correct?

[tribal wharf]

looks right

[viscid thistle]

someone told me this "Rotate the whole thing across the x axis -- cos(x - pi/2) = -sin(x). because if you shift cos(x) right by pi/2, the graph doesn’t start going up from (0,0), it should go down

type into google “graph 3cos(x - pi/2)”

[tribal wharf]

uh

whoever told you that was wrong

theyre misunderstanding the way translations work

or no theyre

i dont know what theyre doing but cosx has y=1 at 0

so shift right by pi/2 and the slope is positive because youre approaching that peak at 0

[viscid thistle]

Maybe they had COS mixed up with SIN

I'm not sure why they thought that either

Does this solution look correct to you?

[tribal wharf]

Uhhh

No

2pi isn’t in the interval

0 is though

there’s also probably another solution

since sinx is squared

[hexed ermine]

Convert sin^2(x) to 1-cos^2(x)

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

cos(x)=u

4u=u^2-1+4

4u=u^2+3

u^2-4u+3

Factor the quadratic

(u-3)(u-1)

cos(x)-3=0 ; cos(x)-1=0

cos(x)=3 ; cos(x)=1

cos(x) has range [-1, 1] so 3 is undefined

cos(x)=1 is at 0 and 2pi

but since 2pi is not in the interval just use 0

[viscid thistle]

Thats a really nice explanation

thanks for breaking it all down

[hexed ermine]

No problem

[viscid thistle]

Still digging the farquad picture man

makes me laugh

[hexed ermine]

LOL

I always alternate through my pfps

Some days you will see me as Human Shrek some days as Farquaad

[viscid thistle]

any of the shrek charecters are golden

maybe the gingerbread man

or prince charming

so I guess I could just take this in two parts
and plug the arctan value into the sin function
is the answer -4/5?

[jagged gorge]

how do i find the area of the shaded region?

and is it the same if it's transform onto a different grid?

[viscid thistle]

yes

you need to calculate the integral from 1 to 2 of (y^2-3y+2)

I got 1/6

[jagged gorge]

cool thanks

wait hold on i still don't get it why is it the same if it's transform to a different grid?

[smoky prawn]

Like its basically the same same graph

[viscid thistle]

Does this look correct?

[spring thunder]

seems right ye

[viscid thistle]

pretty sure h*h-1 is wrong

How do we conceptualize multiplying a function by its inverse?

I mean whats the intuition about it

[mellow matrix]

the answer is 2

[spring thunder]

it's not multiplication tho

[mellow matrix]

if you apply its inverse, then apply the original, you get the input back

pretty sure

[viscid thistle]

because the inverse function undoes what the first one does?

[spring thunder]

yus

[viscid thistle]

so no matter what our functions are, we will always get back the input in this scenario?

[spring thunder]

if an inverse function exists yes

[viscid thistle]

ahhh

so they tell use they are one to one

so that we know that is the case

are they other answers ok?

[spring thunder]

yea seems right

[viscid thistle]

sweet

this look right?

I chose the square brackets because its inclusive for 2

[mellow matrix]

yep

[spring thunder]

👌

[viscid thistle]

alright alright alright