help-42

[waxen talon]

Could someone help with a)?

Thanks

[potent igloo]

Sandwich theorem

[rapid axle]

calling squeeze theorem sandwich theorem seems illegal

[midnight current]

my teacher calls is smush theorem

[potent igloo]

For 🥪 theorem, it's good to first infer what the limit will be. That will help you decide your bounds.

[calm coral]

@waxen talon Has your question been resolved?

[calm coral]

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.

[drifting vortex]

How does the y values between 0 and 1/2 give u two solutions

Surely it’s just 1 solution

[calm coral]

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

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

[drifting vortex]

Isn’t there two solutions between 1/2 and 1 and one solution between 0 and 1/2?

[calm coral]

@drifting vortex Has your question been resolved?

[drifting vortex]

<@&286206848099549185>

[latent steeple]

What are they

[drifting vortex]

wdym

.close

[calm coral]

Channel closed

Closed by @drifting vortex

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.

[latent steeple]

!status

[calm coral]

What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

[tall laurel]

1

[latent steeple]

How do you convert f(x) to 3f(x)

[tall laurel]

vertical stretch by a factor of 3?

[latent steeple]

Well yeah but in this you are just multiplying f(x) by 3

[tall laurel]

oh ok

so i just multiply everything by 3?

[latent steeple]

So the same input x would produce 3 times the output

[tall laurel]

oh

so

[latent steeple]

Only the outputs

[tall laurel]

it would be for example

-5 and 12 for the first one?

[latent steeple]

Ye

[tall laurel]

oh alright

thanks man

.close

[calm coral]

Channel closed

Closed by @tall laurel

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.

[glacial pecan]

Can I get help with understanding and doing this Im struggling with trigonometric graphs

[pure kayak]

what have you looked at so far

[glacial pecan]

Like what I understand from looking at the graph or what have I used to try and learn

[pure kayak]

the first i guess, have any transformations stood out to you?
or have you noticed anything?

[glacial pecan]

I know it has a range of [-2,2] lol idk if dats any useful

[pure kayak]

it is, thats telling of a vertical stretch

[glacial pecan]

it tells me that its coordinates is at (pi/3,0)

its a sin graph?

[pure kayak]

it is a sin yeah, just transformed

[glacial pecan]

idk how to find the period tho

when its a graph

[pure kayak]

you know one zero is pi/3, when is the next one?

[glacial pecan]

like when im given the equation ik how to point out the period

[pure kayak]

from one zero to the next would be half the period

[glacial pecan]

wym one zero

[pure kayak]

one root

x intercepts

sin(x) has 0's at x=0 and x=pi
pi is half the period, then the period is 2pi

apply a similar line of thought, or get it directly by noting one small division of the x axis is pi/3

[glacial pecan]

so pi/3+pi/3 to get the half or what

[pure kayak]

no

one root is at pi/3, when is the next one?

[glacial pecan]

idk how to calculate that

is that pi/3+3pi

[pure kayak]

you dont need to calculate

[pure kayak]

yes it is

so from one root to the other is 3pi

which is half the period

so the period is 6pi

[glacial pecan]

this is just 3pi?

i thought cuz it like

touched

[pure kayak]

no its 3pi+pi/3

[glacial pecan]

there

oh

[pure kayak]

but from pi/3 to 3pi+pi/3 is 3pi

you can see the period here too
from -3pi+pi/3 to 3pi+pi/3 is the period

which is 6pi

[glacial pecan]

3pi+pi/3 = 6pi?...🥲

[pure kayak]

nono

[pure kayak]

is this the one youre looking at?

[pure kayak]

or this one?

[glacial pecan]

that one

would the equation look something like this

[pure kayak]

alrighty
what im saying is, one a sine graph, each root is separated by pi, half the period

here each root is separated by 3pi, so 3pi is half the period

[pure kayak]

it will

[glacial pecan]

can you show me what the root is...

[pure kayak]

do you know what im meaning when i say root?

[glacial pecan]

im a little lost

[pure kayak]

lets look at this

,w graph sin(x) from 0 to 2pi

[potent lotus]

Results provided by WolframAlpha

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

Requested by aldrnari_

[pure kayak]

from one 0 to the other, you have a separation of pi, right

half the period

[glacial pecan]

this is half the period

[pure kayak]

it is, yeah

[glacial pecan]

right

ok

the whole period is 2pi

[pure kayak]

it is

[glacial pecan]

half of 2pi is pi?

[pure kayak]

also yes

[glacial pecan]

is pi/2 where it starts

[pure kayak]

are you talking about the graph you were given now?

[glacial pecan]

no the one ur showing

[pure kayak]

pi/2 is where the sin(x) is 1

[pure kayak]

im not sure what you mean by 'where it starts'

[glacial pecan]

the period

oh the period starts at 0

[pure kayak]

the period can be measured from any point

im just choosing the zeros

because we can read them from the axis

[glacial pecan]

ok

now what is a root

[pure kayak]

when i say root, im referring to x-intercepts

where y is 0

[glacial pecan]

oh so ur saying its going by pi/3

[pure kayak]

pi/3 is a root, yeah

then look to the next root

the change in x between them would be half the period

[glacial pecan]

where would 2pi/3 be

would it be this line

[pure kayak]

2pi/3 would be the bit directly to the right of the dot

[pure kayak]

yeah

[glacial pecan]

oh okay

i see how the first period is 3pi+pi/3 now

or

i mean

hald

half

[pure kayak]

half is 3pi

not 3pi+pi/3

[glacial pecan]

oh

[pure kayak]

first root is at pi/3
second is at 3pi+pi/3
the change in x between them is 3pi

so 3pi is half the period

[glacial pecan]

oh second root as in when it passes through the x-axis again

[pure kayak]

yeah

[glacial pecan]

ok

and since half is 3pi to find the whole period u multiplied it by 2

the amplitude is 2 right\

the period is 6pi

[pure kayak]

indeed

[glacial pecan]

what should i find next

[pure kayak]

so far you have Asin(1/3 (x+C))+D

whats A

[glacial pecan]

2?

[pure kayak]

and D, those should be straightforward

[pure kayak]

yeah

[glacial pecan]

-2?

d

[pure kayak]

why do you think D (vertical shift) is (-2)?

[glacial pecan]

cuz the lowest it goes down is -2?

[frosty olive]

oh mind if i try to help?

[pure kayak]

youre confusing the stretch and the shift

[pure kayak]

feel free

[frosty olive]

@glacial pecan do you know the general equation of a sine equation?

like with constants A, B, C, D

if you dont understand i can just say it

[glacial pecan]

oh vertically shifts to the right? like from where sine originally is?

[pure kayak]

vertical is up and down shift

[frosty olive]

vertical shift means it shifts up or down. if it shifts right then it is a horizontal shift

[glacial pecan]

oops

[frosty olive]

no its okay

but yes

[glacial pecan]

it goes down -2?

[frosty olive]

uh there actually isnt a vertical shift

[glacial pecan]

oh

[frosty olive]

there are multiple things you should identify

[glacial pecan]

oh

[frosty olive]

first

[glacial pecan]

wait

[pure kayak]

the stretch changed the range to [-2,2] but there is no shifting going on

[frosty olive]

what is the midline?

[glacial pecan]

its cuz it stays on the miudline

this line

holdf up

[frosty olive]

all sine graphs have a midline

what is the midline of your graph?

like y = ?

[frosty olive]

yes

[glacial pecan]

?

[frosty olive]

that is on the x-axis, right?

[glacial pecan]

yeah

[frosty olive]

so the midline is not above nor below the x-axis

[glacial pecan]

true

[frosty olive]

meaning there isnt a vertical shift

[glacial pecan]

so no vertical shift

got it

[frosty olive]

a vertical shift shifts the midline up or down

if the midline is at the x-axis

then that means there never was a vertical shift

remember a shift moves the graph and a stretch/shrink distorts the graph

[glacial pecan]

what i was saying is the vertical stretch?

[frosty olive]

yes there is a vertical stretch

now lets move on to the next aspect

what is the amplitude of the graph?

[glacial pecan]

the highest point right

[frosty olive]

close

how high above the midline the highest point is

[glacial pecan]

2

[frosty olive]

in our case, yes, it is the highest point

yes that is correct

[frosty olive]

that is the amplitude

[glacial pecan]

i have a question

[frosty olive]

yeah?

[glacial pecan]

if the midline was at -1

would the amplitude be 3?

[frosty olive]

well if the highest point was still at 2 then yes the amplitude would be 3

[glacial pecan]

ok

[frosty olive]

because 2 is 3 higher than -1

do you understand?

[glacial pecan]

yes

[frosty olive]

ok so lets continue

its time

i showed you the form of a sine equation

it is as follows

y = Asin(Bx - C) + D

A is our amplitude

or rather

[glacial pecan]

its the same for cosine right

[frosty olive]

the positive version of A is our amplitude

[frosty olive]

bingo

so in our case

we can make A = 2

since amplitude is 2

so now we have y = 2sin(Bx - C) + D

D is the vertical shift

we already determined there to be no vertical shift

so D is 0

[glacial pecan]

the period is 6pi?

oops

[frosty olive]

if D was, say, 3, then we would have a vertical shift up

[glacial pecan]

6

[frosty olive]

um let me check the graph

[glacial pecan]

me and the other person went over it

[frosty olive]

close

the wavelength is 6pi

the period

is 2pi/wavelength

wavelength is just how much length it takes to repeat again

wait

err im sorry

im wrong

you are right

the period is 6pi

my bad

[glacial pecan]

lol its okay

[frosty olive]

yes

lets bring back our equation so far

y = 2sin(Bx - C)

[glacial pecan]

would it be 6pix

[frosty olive]

the constant B is just 2pi divided by the wavelength

[glacial pecan]

or 6c

7x

oh

2pi/6pi?

[frosty olive]

so B would actually be 1/3

2pi/6pi

the period is 6pi right?

[glacial pecan]

yes

[frosty olive]

so we do

2pi/6pi

= 1/3

[glacial pecan]

ok

[frosty olive]

yes

[glacial pecan]

i see

[frosty olive]

so B = 1/3

now we have

y = 2sin(1/3x - C)

now C can get a little confusing

ima use some latex

[pure kayak]

id write it as 1/3(x-C) to make it easier

[glacial pecan]

i was watching the organic chemistry teacher

[frosty olive]

i am going to factor out the 1/3 from the C as well

[glacial pecan]

and wrote this down

[frosty olive]

yes exactly

[frosty olive]

yes precisely

um i mean

i learned to write it as Asin(Bx - C) + D

not plus C

but its your choice

either way what is our phase shift

how much further to the right are we than we are supposed to be?

[glacial pecan]

pi/3?

[frosty olive]

yes yes yes

smart

[potent lotus]

! extremum

[frosty olive]

right?

[glacial pecan]

yes

[frosty olive]

and we know B

what is B?

just so you remember

[glacial pecan]

1/3

[frosty olive]

yes

good

so solve for C

and what do you get?

take your time its fine

@glacial pecan hey what do you major in?

[glacial pecan]

currently still figuring it out but im on the like computer and it path but wit how im struggling wit math i might just have to figure sum else out😭

[frosty olive]

i see

college seems very scary

i dont want to go to college but i know i will have to one day

ok back to hte problem

[glacial pecan]

Yeah I just struggle with math I always have

[frosty olive]

no its cool

the only thing i am good at is math 💀 im bad at everything else i do

[glacial pecan]

lol

[frosty olive]

ok so

we know

that

[glacial pecan]

I learn math better when its someone explaining it to me

[frosty olive]

well then

youre in luck 😄

$\dfrac{-C}{B} = \dfrac{\pi}{3}$, right?

[potent lotus]

! extremum

[glacial pecan]

yea

[frosty olive]

they are both the phase shift

and so

we know B = 1/3

so solve for C

what do you get?

[glacial pecan]

how do i write this out is c pi/3

[frosty olive]

uh not quite

multiply both sides by B to start

so you get $-C = \dfrac{B\pi}{3}$

[potent lotus]

! extremum

[frosty olive]

then substitute in B = 1/3

since we already found that

[glacial pecan]

i put this into the calculator and got pi/9..

[frosty olive]

oo

there is a minus sign

note that it says -C

not +C

[glacial pecan]

-pi/9

[frosty olive]

so we actually get $-\pi/9$

yes

[potent lotus]

! extremum

[frosty olive]

so now we found C

lets write out our full equation

we get

$2\sin(x/3 - \pi/9)$, i think

i forgot parentheses

[potent lotus]

! extremum

[frosty olive]

like this

[glacial pecan]

i see

[frosty olive]

i believe that should be the answer?

[glacial pecan]

im still iffy on how im getting the c

[frosty olive]

did you understand?

ok

you know how to find phase shift right?

[glacial pecan]

like the formula thing

bx+c=0

[frosty olive]

what?

[glacial pecan]

to find phase shift

[frosty olive]

i mean you dont have to use a formula

it gets intuitive after a bit

the phase shift is just how much right the graph is shifted

in our graph

the graph was shifted a little bit to the right

pi/3 to the right, in fact

[glacial pecan]

yes

[frosty olive]

so our phase shift is pi/3

then all we have to do

is multiple by B

take the phase shift

and multiply it by our already found B value

we get $1/3 * \pi/3$

[potent lotus]

! extremum

[glacial pecan]

the period * the shift = phase shift?

[frosty olive]

uh not quite

wait

try to use the formula

B value times phase shift = the negative of C value

so you know how to find the phase shift by looking at the graph

its just how much shifted to the right the graph is

its your horizontal shift

then just multiply it by the B value

[glacial pecan]

ik we wrote this

[frosty olive]

yes

yes good

[glacial pecan]

but how we get the 3 at the bottom

ik 1/3 is the period

[frosty olive]

1/3 isnt the period

6pi is the period

[glacial pecan]

oh

[frosty olive]

our B value is the period

remember that the B value times the period is always equal to 2pi

the B value and the period are two different things

dw i confuse that as well

[glacial pecan]

is 1/3x the period?

or still just the value

of b

[frosty olive]

the period is just how much distance it takes for the graph to repeat again

say i bounced a basketball every three seconds

the period would be 3 seconds

[glacial pecan]

okay

[frosty olive]

this sine graph repeats

[glacial pecan]

it repeats every 6pi?

[frosty olive]

yes

so 6pi is the period

however

we use the formula

2pi divided by the period to get the B value

[glacial pecan]

2pi/b

[frosty olive]

which is why we got 1/3 for the B value

[frosty olive]

yes also the same thing

just rearranged

[glacial pecan]

okay i think i understand

that part

i was confusing b wit equaling the period

[frosty olive]

so you understand B value?

[glacial pecan]

but thats just the b value

[frosty olive]

you are not alone

[frosty olive]

yeah

[glacial pecan]

the period is 6pi

got it

[frosty olive]

B value is just the coefficient of x in the sine equation

yes cool

so you understand A value

[glacial pecan]

2pi/6pi? is how i would use the formula right]

oh

6pi

[frosty olive]

wait where did you get pi/3 from

yes

perfect

so do you understand how to find the B value?

[glacial pecan]

yes

can u go over the c value again tho

[frosty olive]

yes okay

so

in our equation

Asin(Bx + C) + D

C appears inside the sine function

it causes a horizontal shift

do you understand how to find the horizontal shift?

also known as the phase shift

so do you know how to find phase shift?

[glacial pecan]

like it shifts pi/3?

[frosty olive]

yesyes

[glacial pecan]

to the right

[frosty olive]

bingo

so our phase shift is pi/3

[glacial pecan]

yes

[frosty olive]

now we want to find the C value

what we can do

is just multiply the phase shift

by the B value

what was the B value, again?

[glacial pecan]

1/3

[frosty olive]

and the phase shift was pi/3, right?

[glacial pecan]

yes

[frosty olive]

so we multiply the two

[glacial pecan]

this is what were doing right

[frosty olive]

yes

and that gets you $\pi/9$, right?

[potent lotus]

! extremum

[glacial pecan]

okay i think i understand how we got the pi/9 now

yes

[frosty olive]

yes

and we make that negative

we multiply it by -1

to get the C value

so our final equation

is

$2\sin(\dfrac{1}{3}x - \pi/9)$

[potent lotus]

! extremum

[glacial pecan]

hell ye

[frosty olive]

lets gooo

you did great

good job

[glacial pecan]

hopefully i can do it on my own 🙏🏻

[frosty olive]

before you go

i just want to remind you

of some transformation tips

i hope this doesnt confuse you

but listen jsut for a second

when we shift a graph to the right by, say, R units

then the equation changes

it changes in the sense that

every time we write "x", we replace it with "x - R"

so if we had the graph y = x^2

then shifting it right R units

would get you

y = (x - R)^2

@glacial pecan do you understand?

[glacial pecan]

ima be fr ive just been using the fact that everytime the graph goes right its - and left its + without like actually knowing what it means lol

[frosty olive]

yes i can explain that

so if we move the graph right 1 unit (for example)

then that means that every x value increases by 1, right?

[glacial pecan]

yes

[frosty olive]

so the point (3, 2) would become (4, 2)

but if we put in the input "4" to our original function, we wouldnt get 2 out

we would have to put in "3" into our original function to get 2 out

so if our original graph was y = x - 1

one point on this line is (3, 2)

if we shift the graph right by one unit

[glacial pecan]

oh yeah cuz if u plug in the x value 4

[frosty olive]

then now we have the point (4, 2)

[glacial pecan]

it would be 4-1

to get 3,2

[frosty olive]

yesyes

we have to account for the fact

that once we shift the graph right by one unit

all the x values are larger by 1

so we have to resubtract that 1 to make sure we get the correct output

if we have the function f(x) = x - 1

and we shift it right

then the point (3, 2) that was originally on the graph now becomes (4, 2)

but does (4, 2) work for the function f(x) = x - 1?

no!

we have to subtract one from x again in order to get the correct output

so we do

f(x) = (x - 1) - 1

this way

plugging in 4 to our new equation

is the same as plugging in 3 to our old equation

[glacial pecan]

wouldnt the -1 on the outside mean it moves down?

[frosty olive]

well that was just the original function

idk why i did that

it was just a random function i chose

the original function was f(x) = x - 1

then shifting it right by one unit

means we replace the x term with (x - 1) in order to account for the fact that the input is now 1 more than it should be

lets say you had a machine that checks your identification with your age

im 14

[glacial pecan]

alright Ima try and do sum more of the trig graphs to see if I understand

[frosty olive]

and next year i will be 15

but the machine still thinks im 14

so next year

when everyone becomes 1 year older

it accounts for this

and subtracts one from their new age and checks it with the age they have stored

so next year

when i go to the machine that checks my age

it sees that i am 15

and thinks, "oh if he is 15 now then he was 14 last year"

and plugs in 14 years old to its identification system

do you understand what im saying?

[glacial pecan]

yeah i think i got it when u was explaining it here

[frosty olive]

ok cool

[glacial pecan]

ima try other problems out now

[frosty olive]

cool

[glacial pecan]

ty for the help

[frosty olive]

no problem

i have to go to sleep

i got the AMC tmrw

its a math competition

what year are you in in college?

[glacial pecan]

2nd

[frosty olive]

my brother is in 2nd year too

[glacial pecan]

math competition crazy

gl wit that

[frosty olive]

thank you

im sort of a math nerd in my school

im only a freshman and im taking precalculus

but then again

its the only thing im good at

good night @glacial pecan

enjoy your trig solving

[glacial pecan]

Yeah these trig graphs got me struggling

[frosty olive]

do you want help?

i could spare like 10 minutes

[glacial pecan]

naw its okay Ill just watch sum more of this video if anything

u broke it down pretty well

[frosty olive]

thank you

enjoy your night

if you are done use .close

[glacial pecan]

.close

[calm coral]

Channel closed

Closed by @glacial pecan

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.

[upper kelp]

The initial condition is at t_0=1/2, but why is the interval (0, inf)?

[upper kelp]

Nvm

Got it

.close

[calm coral]

Channel closed

Closed by @upper 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.

[spring furnace]

How do I solve this type of equation??
"Write a linear function f with the given values"

[main marlin]

you have two points, from those points you can get a slope and then you have the equation of the line for free: $y-y_1=m(x-x_1)$ :)

[potent lotus]

PajamaMamaLlama

[spring furnace]

The points being -2,1? And then how do we solve for slope? M=y2-y1
X2-x1

[calm coral]

@spring furnace Has your question been resolved?

[calm coral]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[calm coral]

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.

[coarse comet]

The solution I get for x is wrong. I believe I messed up the part where I put in log, please explain using log with base of 10.

[potent igloo]

!show

[calm coral]

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

[coarse comet]

i believe i did a mistake on the first line underlined red

[frank gull]

yeah unfortunately you can't do that

is your goal just to isolate x?

[coarse comet]

yes

[frank gull]

the reason being is you have to take log of the whole thing

ok so first thing I would do is add 4^y by both sides

then take the log of both sides

[coarse comet]

let me try it like that

now I’m stuck with this incredibly huge power @frank gull

[frank gull]

,rccw

[frank gull]

without knowing values of y

this is as far as you go, I would consider this the answer

oh wait no you didn' tod the arithmetic right

remember what I said earlier, when you take the log of a side, you have to take the entire thing

So what I would do is this

$3^x - 4^y = 5\\3^x = 5 + 4^y\\log(3^x) = log(5 + 4^y)\\ xlog(3) = log(5 + 4^y)\\ x = \frac{log(5 + 4^y)}{log(3)}$

[potent lotus]

MellowDramaLlama

[frank gull]

that's as far as you can go

[frank gull]

this is what I mean by "taking the log of the entire side"

[coarse comet]

yes i did do that

ok i just realized i didn’t put the full question

one moment

@frank gull this is the full question

i substituted x in the 2nd eqn

forgot to label it so you got confused

can you show how i can get the value of y after substituting x

[leaden thunder]

,rotate

[calm coral]

@coarse comet Has your question been resolved?

[coarse comet]

<@&286206848099549185>

[remote mural]

Add eq 1 and 2

[coarse comet]

alright thanks i missed that one thing

[calm coral]

@coarse comet Has your question been resolved?

Channel closed

Closed by @coarse comet

Use .reopen if this was a mistake.

[calm coral]

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.

[humble steppe]

i dont get this. shouldnt the ansatz form be 1?

[humble steppe]

and then here it says its 2

[stoic oyster]

the ansatz is a constant

[humble steppe]

1/lc is 10 so 10a = 10, a =1

[stoic oyster]

why should it be 1 specifically ?

[humble steppe]

because i thought if you have a constant at the right hand side you would take yp = a

[stoic oyster]

yeah fine

ah ok it's for the value specifically

[humble steppe]

yeah

i got 1

[stoic oyster]

yeah should be 2

if you just plug in the constant in the equation, you get a/c = 10

so a = 10 * .2 = 2

[humble steppe]

uhm i didnt understand this part 😓

[stoic oyster]

replace i by the constant a in the differential equation

I'm using the original expression

[humble steppe]

oh okay

[stoic oyster]

da/dt and d^2a/dt^2 are plain 0

so you're only left with the last term

[humble steppe]

but do you know what i did wrong?

[stoic oyster]

well idk how you got that

seems wrong

[humble steppe]

wait imma send a picture

[humble steppe]

.rotate

[stoic oyster]

still

how do you get that __10__a=10

where does the left 10 come from

[humble steppe]

its from 1/lc

[stoic oyster]

why would you have 1/LC

[stoic oyster]

if you divided everything by L, the RHS is also divided by L you know

[humble steppe]

oh..

im stupid🙂

yeah i got 2 aswell now

thanks again

@stoic oyster

.close

[calm coral]

Channel closed

Closed by @humble 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.

[keen agate]

.close

[calm coral]

Channel closed

Closed by @keen agate

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.

[dawn thicket]

@wooden gyro

[dawn thicket]

this was the question btw

[wooden gyro]

find every dervitive

[dawn thicket]

okay but i want to know is it possible to prove homogenity for w here?

[calm coral]

@dawn thicket Has your question been resolved?

[calm coral]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[calm coral]

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.

[wise reef]

in this question i did on a test i moved the a^-7 up so i could change the -7 into 7 but my teacher put a red circle around both the + and ^7, why?

[chilly lodge]

why do you think you'd have a plus sign there?

[wise reef]

because i didnt see a reason for putting multiplication sign as im just moving the a up

[chilly lodge]

,tex .exp rules

[potent lotus]

B-eard

[chilly lodge]

moreover,

[potent lotus]

B-eard

[wise reef]

i dont get it, am i only allowed to send negative exponents down? and not up?

[chilly lodge]

no, its not like that

[potent lotus]

B-eard

[wise reef]

oh okay but i still dont get why its supposed to be multiplication and why its not ^7

[chilly lodge]

well, it actually should be 7

maybe you did not simplify much

[chilly lodge]

consider this

[wise reef]

why is it multiplication though

[chilly lodge]

well division is just a modification of multiplication

[wise reef]

oh so the way we move it up is by multiplying it and because - * - is + it changes sign?

[calm coral]

@wise reef Has your question been resolved?

[wise reef]

<@&286206848099549185>

[chilly lodge]

well no

See that before bringing it to the numerator, it is already in multiplication

so, the multiplication sign remains and there is no plus sign

[wise reef]

oh okay but how do i know its in multiplication

theres no multiplication sign before it

[chilly lodge]

since it is in division

If two numbers are in division then they are in multiplication aswell

[wise reef]

i dont get it

[wise reef]

is it okay if i just remember that when moving it up or down its always multiplication?

or should i try to understand why

im only in high school

[calm coral]

@wise reef Has your question been resolved?

[calm coral]

@wise reef Has your question been resolved?

[calm coral]

@wise reef Has your question been resolved?

[calm coral]

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.

[vital reef]

can someone please help me fill in the proof

[vital reef]

or explain how to do it

i’m not sure how to solve

[terse flame]

so

what does line 3 mean

[calm coral]

@vital reef Has your question been resolved?

[vital reef]

what do you mean

like

the bottom line?

[terse flame]

no, like

the line that is numbered 3

[vital reef]

BC?

[terse flame]

this guy here

[vital reef]

oh

straight line

[terse flame]

yea

so that's how you explain it

[vital reef]

so if i wrote angle of a straight line always add up to 180

would that be right

[terse flame]

yes

[vital reef]

ok

and for 2

[terse flame]

just like that

you look at 5 and 6 and you can do the same thing

[vital reef]

would i write AB || CD ?

[terse flame]

yea

[vital reef]

okay

wait

[terse flame]

basically this is just getting you to justify your steps of working out

[vital reef]

yes

how do i explain 5

[terse flame]

same idea

it's because AB||CD

[vital reef]

so they have the same measure?

[terse flame]

i forgot what the name of that property is

but you should look up the names of these properties of parallel lines

[vital reef]

okay

[terse flame]

and use that for these explanations

[vital reef]

are they like

corresponding angles maybe

ok

[terse flame]

oh yea

I think so

it's something along those lines

just make sure the words you are using is what you actually think they are

[vital reef]

okay

and then for six is that like

do i restate the theorum cuz idk about six

[terse flame]

in this case

what are the 3 angles that you are adding

actually

sorry I uh

forgot what the goal for this proof was

anwyay for line 6 i guess

just say that's because of line 3, 4 and 5

and you are done

[vital reef]

okk

thank you

[calm coral]

@vital reef Has your question been resolved?

[calm coral]

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.

[wild marten]

Hi, I apparently made a mistake somewhere in this problem but cannot seam to find it. I marked the incorrect and correct steps, ive redone it a couple times and can not seam to see where I went wrong.

[wild marten]

.close

[calm coral]

Channel closed

Closed by @wild marten

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.

[fair cedar]

Can someone help me with this

[fair cedar]

I already have the answer but idk how to solve

[latent remnant]

do you know the point slope formula

$$m(x-x1)=y-y1$$

[potent lotus]

`

[next hound]

Is that needed? You can just solve for y in each answer and see which has the same slope

[fair cedar]

yes

[calm coral]

@fair cedar Has your question been resolved?

[fair cedar]

how do i do that

[next hound]

which part

if you don't know how to isolate y, look up a basic algebra course
if you dont know what the slope is, when you isolate y, you will get a form that looks like y = mx+b. The slope is m. Two lines are parallel iff their slopes are the same, so you can just coompare to the m of the original line

[fair cedar]

ik what y and slope is

For example

6x + 2y = 15

How do i solve thhis

i never done x + y =

i only done

y = mx+ b

[next hound]

you need to isolate y

[fair cedar]

y is 15?

[next hound]

in this case, subtract 6x from both sides, then divide both sides by 2

[fair cedar]

6x + 2y = 15

is 2 y

or is 15 y

[fair cedar]

Can someone help

[pure kayak]

so whats going on

oh its this one

well, 6x+2y=16

goes to 2y=-6x+16

to then y=-3x+8

[calm coral]

@fair cedar Has your question been resolved?

[calm coral]

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.

[visual cargo]

.

[visual cargo]

ive came across a few different notations

i dont really understand how to approach this

i = 1

and it ends when i = n

[fluid flame]

that’s a little ambiguous with only 2 terms

no additional context anywhere else?

[fluid flame]

ok now it makes perfect sense

[visual cargo]

it says use sigma notation to write the sum

this is what i wrote

sorry, it just says to multiply it by 3/n in front of it

1. is that the correct answer
2. is there a better format to write the answer in

[fluid flame]

yes pulling out constants is generally a good idea and preferred

[visual cargo]

^

is that how you pull out a constant?

[fluid flame]

yes, basically anything that doesn’t depend on the index i
you can also pull the 2 out

[visual cargo]

oh

okay thank you

.close

[calm coral]

Channel closed

Closed by @visual cargo

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.

[queen lynx]

I dont know how to continue

[shadow tendon]

You expanded (x+a)^2 incorrectly

[queen lynx]

how am i supposed to do?

[shadow tendon]

(x+a)^2=(x+a)(x+a). Use distributive property or foil if u prefer that

[queen lynx]

But isnt it complete the square?

[shadow tendon]

Completing the square is a method for finding zeros of a polynomial

Here we are doing something different

[queen lynx]

Like this?

[shadow tendon]

Yeah mostly dont forget the -25 though

[queen lynx]

Ok

but how do i find a and b from this

[shadow tendon]

you need the coefficients for all terms on both sides to be equivalent

You can immediately find what a is right now by comparing one of the terms on the left and one on the right

[queen lynx]

A=7?

[shadow tendon]

Yeah nice. Do a similar thing for the constant terms

[queen lynx]

Oh i get in now

.close

[calm coral]

Channel closed

Closed by @queen lynx

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.

[zealous badger]

hi

[calm coral]

Please don't occupy multiple help channels.

[zealous badger]

I need help with finding the dydxdz bound for

[calm coral]

@zealous badger Has your question been resolved?

[calm coral]

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.

[desert storm]

hi there, so i looked at these graphs and figured out which one goes with which but turns out some of them are wrong and i don't even know which ones. please help

[remote mural]

Not complete question

[desert storm]

wdym?

[remote mural]

I think there must be given some formula for f(x) which is not given

If it's direct f(x) all of them will be straight

Line at some place

[desert storm]

the first picture got all the functions

[remote mural]

Oh ok

[desert storm]

so where did i go wrong?

[remote mural]

What function did you found from the graph

@desert storm

[desert storm]

what?

[remote mural]

Like what f(x) something you must have found from question graph

[desert storm]

so basically f(x) is the original graph and below are different functions and i just need to determine which function goes along with each graph

[remote mural]

Which standard

Question is this

[desert storm]

uni

[remote mural]

University

?

[desert storm]

yea

[remote mural]

use @ helpers

[desert storm]

<@&286206848099549185> help plz

[light pasture]

A B and F are wrong
2f(x) is a vertical stretch when F is a vertical squeeze and a movement
B is a vertical stretch while f(2x) is a horizontal squeeze
A is horsantal squeeze while 1/2f(x-1) is a vertical squeeze and a movement

Other than A B and F all is good

[desert storm]

THANK YOUU

.close

[calm coral]

Channel closed

Closed by @desert storm

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.

[timber fog]

Whr did they get the green highlight from

[timber fog]

Do I just need to satisfy the =0 with random numbers?

[thorny stump]

It's the cross product between (3,7,1) and (2,2,3)

@timber fog

If the plane contains the line and the origin, then it also contains any vector between the origin and a point on the line

[timber fog]

Oww

[timber fog]

Thanks for the explanation!

.close

[calm coral]

Channel closed

Closed by @timber fog

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.

[topaz raft]

Use Riemann 4 sums to show that

19/20 <= ln(3) <= 77/60

So I’ve found my 4 sub intervals which are t_0 = 1

t_1 = 3/2

t_2 = 2

t_3 = 5/2

t_4 =3.

But how do I compute a left hand sum? I know my delta t will be (b-a)/n

[oblique current]

I sent you like two websites explaining how to do this

[topaz raft]

i didnt get it lol

at least the a+i stuff

[calm coral]

@topaz raft Has your question been resolved?

Channel closed

Closed by @topaz raft

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.

[calm coral]

Channel closed

Channel closed due to the original message being deleted.
If you did not intend to do this, please open a new help channel,
as this action is irreversible, and this channel may abruptly lock.

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.

[gaunt lichen]

i dont understand why arcsin of sin2x is pi-2x

[warm turtle]

what was the question?

[gaunt lichen]

I'm doing part b

I multiplied both sides by root2/4

so I can use the values sin(pi/12) and cos(pi/12)

<@&286206848099549185>

[chilly lodge]

well, sin(x)=sin(pi-x)

[gaunt lichen]

oh

[gaunt lichen]

so it would be sin(2x) = sin(pi-2x)

?

[calm coral]

@gaunt lichen Has your question been resolved?

Channel closed

Closed by @gaunt lichen

Use .reopen if this was a mistake.

[calm coral]

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.

[main spade]

i am

very confused about b

[jolly charm]

b directly comes from a

they have made it confusing

think about definition of congruence

[main spade]

I proved a)

but i dont know im getting super confused

like id ont know wh y

i have tried this multiple times and i keep getting it wrong

[jolly charm]

ok let me explain

x0 is congruent to x1 modulo b

now let's say if someone doesn't understand congruent modulo how will you say to that person what this above expression means exactly in layman's terms?

[main spade]

like when you do x0 mod b then it has a remainder of x1

[jolly charm]

ok.. that is fine.. it's more like if you divide x0 by b you get x1 as remainder

[split grail]

guys

sorry to interupt

but can someone explain the occupid and non occupied channels

[jolly charm]

you can't questions in occupied channels

you need to open in non-occupied

[jolly charm]

now can you write an equation using euclid's division lemma?

[main spade]

x1 = x0 + kb?

[jolly charm]

well not exactly but this is true as well

since x0 is congruent to x1 modulo b
we can also say x1 is congruent to x0 modulo b

which leads x1 = x0 + kb

[main spade]

yes then you can sub in right?

[jolly charm]

now do this for the y counterparts..but keep in mind k won't be same in that case

[main spade]

for a(x0 + kb) + by1 = c

well for y its y1 = y0 - ka?

[jolly charm]

no

[main spade]

oh

[jolly charm]

you have to prove that

[main spade]

ive donet his so far

[jolly charm]

when you are assuming k in x1 = x0 + kb..you have to prove the same k apears in y1 = y0 - ka

see in a) you did a(x1-x0) + b(y1-y0) = 0
use this

as I mentioned use x1 = x0+kb and some similar relation between y1 and y0 and then substitute

did you get it?

[main spade]

like y1 = y0-ak?

[jolly charm]

no

see

try to understand

you have x1 is congruent to x0 modulo b

and y1 is congruent to y0 modulo a

now from this you can conclude 2 expressions:-
x1 = x0 + kb where k is an integer