help-23

[fossil jewel]

yeah

no wait

3/2 x

[lone arch]

Ok, but then there is a -x on the left still

[fossil jewel]

gotta add that x

[lone arch]

Yeah

Exactly

[fossil jewel]

.

[lone arch]

Then $- \frac 2 3 x + y + \frac 2 3 x = -4 + \frac 2 3 x$ and so $y = - 4 + \frac 2 3 x$

[flat frigate]

Kepe

[obsidian ginkgo]

|| Do it again on pen and paper after you are done doing it here ||

[fossil jewel]

yeah

[lone arch]

So we added 2/3 x on both sides.

Yep

[fossil jewel]

Now how do i graph it?

[lone arch]

One possibility would be to pick any two points. This will be a straight line so you can just connect those two points and you are done

So pick for example x = 0 and x = 3

[fossil jewel]

Ok

[lone arch]

Draw in the two points, connect and you are done

[fossil jewel]

Wait

what about Y

[lone arch]

Well, I'm saying find the y value corresponding to x = 0 and x = 3, then draw in the points

Just like you did before

[fossil jewel]

Ok

I'm confused

-1, 0, 1

Can i use those?

[lone arch]

Sure

[fossil jewel]

wiat a minute

[lone arch]

I just suggested 3 so you get a nice value

[fossil jewel]

0 and 3

(0, -1)

and (3, 1)

[lone arch]

You mean (0, -4)

[flat frigate]

Kepe

[fossil jewel]

Ok

y = -4 + 2/3x

2/3 can be graphed, right?

[lone arch]

What do you mean?

[fossil jewel]

wait

[lone arch]

Do you agree with this?

[fossil jewel]

OHHHHH

i'm an idiot

i'm such an idiot

y = -4 + 2/3x can be graphed as (-4, 0)'

and THEN

From (-4, 0), you go up 2 and over 3

[lone arch]

Yes, one possibility

But (0, -4) it should be

Alternatively, just graph any two points

[fossil jewel]

Ok that's how i was tought how to do it

[lone arch]

And connect them

[fossil jewel]

Thank you

[lone arch]

np

[fossil jewel]

I might be back later

to annoy you further for more help

[lone arch]

You can close and open a new channel then, since if you keep it open, it will go down the channel list and you'll have to wait longer for someone to respond later

[fossil jewel]

Ok

Bye for now 👋

[safe radish]

Channel closed

Closed by @fossil jewel

Use .reopen if this was a mistake.

[lone arch]

Someone else it'll most likely be, I will be gone for now. Bye!

[fossil jewel]

Bye!

[safe radish]

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.

[abstract halo]

hello

i put -2.5 on the graph

and then pi/2 right?

because you divide 2pi/4

which gets you pi/2

but when i put it on here

its wrong

or when i put it like this its wrong

[visual kraken]

This one has more of the right idea, but it has a couple issues still

Can you tell me when sin(x) = 0?

[abstract halo]

it only has vertical lines

so it touches 0

[visual kraken]

I'm not sure what you mean, are you confusing sin and tan?

[abstract halo]

it looks like this

[visual kraken]

Oooh I see, desmos is interpreting that as "Put a line at every value of x where sin(x) = 0"

Can you just put in sin(x), no equal sign, and look for where the curve crosses the x-axis?

It will be at all the places the graph you just made has a verticle line

[abstract halo]

crosses the x axis?

[visual kraken]

Yeah

At all those points the curve crosses the x axis

So sin(0) = 0, and also sin(pi) = 0

So, if f(x) = -2.5sin(4x), can you try to evaluate f(0) for me?

Try to do it without a calculator, but if you get stuck you can use one

[abstract halo]

uhhh well if f(0) then wouldnt it be 2.5sin (4x)?

i mean its a point no?

[abstract halo]

.

would this also apply to this question

[visual kraken]

Yes it would, but f(0) = -2.5sin(4*0), so can you evaluate -2.5sin(4*0) for me?

[abstract halo]

i only know how to evaluate this (4 x 0)

i think you put 2pi/4 = 2pi/2

but that would be pi?

[visual kraken]

Hmm, well -2.5sin(4x0) = -2.5sin(0) yeah?

[visual kraken]

And up here I pointed out that sin(0) = 0

So -2.5sin(0) = -2.5 x 0 = 0

Does that make sense?

[abstract halo]

yes

[visual kraken]

Do you see how that relates to this graph?

Or rather, how it contradicts that graph?

[abstract halo]

would i have to put a point in 0?

since -2.5sin(0)

[visual kraken]

Yeah at (0,0)

I should note that having the graph go up to 2.5 and down to -2.5 like that graph does is correct

[abstract halo]

i think what throws me off is this

like where do i put the point where all my x-axis numbers are at

i know where 1.5 is at

but i was taught that 2pi/2 - that you simplify it

not multiply it and get 4

like what? where did you get pi/4

i thought it would just be pi

[visual kraken]

Okay okay I see where you're confused, this is a totally fair misunderstanding

So, -1.5sin(x) will be -1.5 when x = pi/2 yeah?

[abstract halo]

yes

[visual kraken]

Well then -1.5sin(2x) will be -1.5 when 2x = pi/2

Which is the same as x = (pi/2)/2 = pi/4

[abstract halo]

oh

but i thought you simplified it

my prof wrote this and i took it as, oh she made it more simple!

[visual kraken]

Yeah that's a correct thing to do, I think you might be having a misunderstanding about arithmetic stuff

Can you pull up desmos for me again?

[abstract halo]

yes

[visual kraken]

Make a variable called a and put in the curve sin(ax), then experiment with different values of a

You'll see as a gets bigger the waves will get shorter, and as a gets smaller the waves will get longer

Out of curiosity, are you familiar with how a + f(x + b) changes the curve drawn by f(x)?

Like, 2 + f(x) will move the curve drawn by f(x) up by 2, but f(x + 2) will move the curve left by 2 instead of right?

[abstract halo]

im somewhat familar with a+f (x+b)

i know 2 is the period?

[abstract halo]

yeah

i know about this

[visual kraken]

Right, so multiplication works similarily. 2*f(x) will make the curve double in height, but f(2x) will make it halve in length

Since it only takes 2x half as long to reach the same values as just x

Does that make sense at all?

[abstract halo]

so if there was (2x+4) it would be longer?

[visual kraken]

I don't believe so, if I'm understanding you right

Hmm, okay let's go back to the sin wave stuff

So -1.5sin(pi/2) will equal -1.5 right?

[abstract halo]

yes

[visual kraken]

So what will -1.5sin(2 * (pi/4)) be?

[abstract halo]

i think so...

wouldnt it be pi/4 alone?

[visual kraken]

Well if f(x) = -1.5sin(2x) then f(pi/4) = -1.5sin(2 * pi/4)

[abstract halo]

oh theyre the same thing

yes

[visual kraken]

Can you evaluate it for me?

[abstract halo]

2 x pi/4 = pi/2

2 goes into 4 once by itself and gives you pi/2?

im confused ):

[visual kraken]

Yeah, so -1.5sin(2 * pi/4) = -1.5sin(pi/2) = -1.5

Does that make sense at all?

[abstract halo]

yes

they are the same

[visual kraken]

Do you kind of understand how this graph makes sense now?

[abstract halo]

yes

[visual kraken]

Cool!

[visual kraken]

Can you try this one again now?

[abstract halo]

i cant

it doesnt allow me to do that question but i asked for a different one

and i figured it out a while ago

[visual kraken]

Okay then, do you still need/want help?

[abstract halo]

no

you did more than enough help

thank you NotABot (:

I appreciate your time.

[visual kraken]

Glad to hear it! 😄

No problem, I'm happy to help

[abstract halo]

Im gonna close it now

[visual kraken]

Alright, see ya later

[abstract halo]

Thank you NotABot (:

.close

[safe radish]

Channel closed

Closed by @abstract halo

Use .reopen if this was a mistake.

[safe radish]

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.

[trim swan]

Have you given it a shot?

They're basically just asking you to do the substitution you identified in the first part

@fierce silo

[safe radish]

@fierce silo Has your question been resolved?

[safe radish]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[fierce silo]

.reopen

[safe radish]

✅

[fierce silo]

So I just find the derivative of what I identified as u?

[trim swan]

well that's part of it

You need to substitute u for what you identified as u in the original integral

and also differentiate it to find an expression for du

@fierce silo

[fierce silo]

whatdoes that mean

would it just become 14x/2?

[trim swan]

Well you have $\int \frac{x}{(7x^2+8)^5} dx$

[flat frigate]

tatpoj

[trim swan]

If you take $u = 7x^2 + 8$, do you see that you could rewrite your integral as $\int \frac{x}{u^5}dx$ ?

[flat frigate]

tatpoj

[fierce silo]

yes

[trim swan]

but then you also need to replace the "x dx" with something in terms of u and du

so that's where you would take the derivative

if u = 7x^2+8, what is du/dx?

[fierce silo]

derivitive of x/u^5?

[trim swan]

not quite, can you answer this?

[fierce silo]

im not sure

[trim swan]

just the derivative

[fierce silo]

oh okay so it is 14x/2?

[trim swan]

Actually just 14x

You just multiply by the exponent, and then decrease the exponent by 1

[fierce silo]

ugh i keep getting it confused with the other thing

[trim swan]

integrating, yeah, it takes a little while to get it sorted in your head when you're first learning it

[fierce silo]

okay but yes 14x makes sense and we get rid of the Constant

[trim swan]

yeah so du/dx = 14x

which we can write as du = 14x dx

[fierce silo]

okay

[trim swan]

and in your integral you have x dx

[trim swan]

so you can divide this by 14 and get (1/14)du = x dx

and substitute that into your integral as well, so you only have u, and not x

[fierce silo]

im a little confused we have 1/14du = x dx but how do we just get rid of x do we just find the derivitive of x

[trim swan]

the 1/14 just comes from

du/dx = 14x
du = 14x dx (multiplied both sides by dx)
(1/14)du = x dx (divided both sides by 14)

This is how you get rid of the x in the numerator of your integral

replace x dx with (1/14) du

[fierce silo]

ok so it woukd be (1/14du)/7x^2+8?

or do we keep the ^5

[trim swan]

keep the ^5, it didn't go anywhere

and remember 7x^2+8 is u

You need to only have u, no x

[fierce silo]

Did I do it wrong or is the syntax error the issue idk how to get rid of that

[trim swan]

You've got the right idea but

Well, the du shouldn't be in the denominator of that fraction

but actually for this problem, you shouldn't have the du at all

because they provided it already

They're just asking you for the f(u) part, the du is already there

so $\frac{\frac{1}{14}}{u^5}$ or $\frac{1}{14u^5}$ is what you want

[flat frigate]

tatpoj

[fierce silo]

arent those diffeent tho

are do they = the same

[trim swan]

these are equivalent

$\frac{\frac{1}{14}}{u^5} = \frac{1}{14} \cdot \frac{1}{u^5} = \frac{1}{14u^5}$

[flat frigate]

tatpoj

[fierce silo]

thank you for explaining that

.close

[safe radish]

Channel closed

Closed by @fierce silo

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.

[devout steeple]

i don't know how you would start this

[devout steeple]

solving for x

[glass carbon]

substitution

[ocean crypt]

Write everything in base 3

[glass carbon]

or the thing above

[devout steeple]

how would i do that

[narrow ridge]

Let $y=3^x$ as Modus suggested (substitution)

[flat frigate]

w

[ocean crypt]

on the left, write 7 as 3 raised to the base 3 logarithm of 7

And then highlight 3^x

[devout steeple]

hmm idk what to do after this

[ocean crypt]

You also have the other 3^x

You should do something like this

$3^x*(....)$

[flat frigate]

BobTheBuilder

Potatomonke

[ocean crypt]

On the left at the end of the simplifications you should find $3^{x+2}$

[flat frigate]

BobTheBuilder

[devout steeple]

everything is in base3

[ocean crypt]

Why did a 3^x disappear?

Wait

But what do you mean by 7(3^x)?

If you mean multiplication, above the last thing you wrote we are missing 3^x which multiplies the first factor

[devout steeple]

yeah it is just multiplication

[ocean crypt]

So this

[devout steeple]

this is right but i just dont understand how we got there

is there a rule for simplifying 3^x + 3^x + 3^x

this question is making me mad 😭

[lime dust]

Don’t you like 3(3^x)?

Althougj u dont have that

In left side u have 9(3^x)

[devout steeple]

oh yeah i see that now

[lime dust]

And in right he side

[devout steeple]

how would 9(3^x) simplify to 3^(x+2)

[lime dust]

You are multiplying one 9(3^x)

So you can divide both sides by 9(3^x)

Having 1 = 9^x(27(3^x))

Now equation is mich shorter

I have to leave now, u can finish this for sure

[devout steeple]

okie this is making more sense

9^x(27(3^x)) = 1
27(27^x) = 1
i guess that simplifies to 27^(x+1) = 1

so x = -1

yeah thats right

i hate algebra

thank you @lime dust

.close

[safe radish]

Channel closed

Closed by @devout steeple

Use .reopen if this was a mistake.

[safe radish]

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.

[dull heron]

Can someone give a starting point as to where i can begin, i marked everything out but i dont know what to prove

<@&286206848099549185>

[woven nova]

!15min

[safe radish]

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

@dull heron Has your question been resolved?

[summer crow]

,rotate

[summer crow]

@dull heron
Hint 1: notice that both AED and EBC are triangles, and the sum of angles of each triangle is 180 degree.
Hint 2: define an arbitrary angle, e.g. let the angle AED be $\theta$, and try work out the angle BEC, and thus ECB in terms of $\theta$

[flat frigate]

lgkoo

[dull heron]

I dont know where to go from there though

[summer crow]

let $\angle AED = \theta$

[flat frigate]

lgkoo

[summer crow]

and $\angle DEC = 90$ degree

[flat frigate]

lgkoo

[summer crow]

so what should $\angle BEC$ be?

[flat frigate]

lgkoo

[dull heron]

angle bec = 90*

wait no

beta

[summer crow]

beta?

[dull heron]

idk what its called

[summer crow]

we don't want to define more arbitrary angles

one is enough

just do all remaning angles in terms of theta

[dull heron]

theta is what i meant mb

[summer crow]

why would BEC be theta?

[dull heron]

angle bec?

[summer crow]

yes

[dull heron]

so they are both equal to 90 degrees split?

[summer crow]

why?

what do you know about total angles on a horizontal line?

[dull heron]

equal to 180

[summer crow]

right

so what should AED + DEC + BEC, which is theta + 90 + BEC equal to?

[dull heron]

180

[summer crow]

now can you work out BEC in terms of theta

[dull heron]

but how does it prove?

[summer crow]

just do it

I'm trying to guide you step by step here since the hints didn't help

[dull heron]

this is my working currenrly

[summer crow]

everything is right, except BEC is not theta

if theta + 90 + BEC = 180, can you, by re-arranging the equation, find BEC in terms of theta

[dull heron]

so 180-90 - theta = BEC

[summer crow]

correct, so simplifying that a bit more, BEC = 90-theta

now

the total angles inside a triangle add up to?

[dull heron]

180

[summer crow]

correct, using this hint, can you figure out what to do to find the angle ECB in terms of theta?

[dull heron]

Theta

[summer crow]

that's right

but remember we defined AED to be theta as well at the beginning

and we've shown that ECB is also theta

thus AED = ECB as required.

[dull heron]

alr thanks

[summer crow]

np

[safe radish]

@dull heron Has your question been resolved?

[safe radish]

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.

[lean otter]

can anyone help me with algebra 2 please

[gusty trench]

well hello again

[safe radish]

@lean otter Has your question been resolved?

[lean otter]

hioi

hiii*

@gusty trench

[median skiff]

Sure

[lean otter]

thank you!

[median skiff]

Well, in this manner, a
quadratic correlation graph
represents a relationship between two variables where one variable changes as the square of the other.
shaped like a U or an upside-down U and
As the x value increases, the y value initially increases, reaches a maximum or minimum point (depending on the direction of the parabola), and then starts to decrease again

[safe radish]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[lean otter]

.reopen

[safe radish]

✅

[lean otter]

@median skiff I am confused

[median skiff]

On what exactly?

[lean otter]

all of that

[granite idol]

What specifically, though

[median skiff]

That's what I'm sayin

[safe radish]

@lean otter Has your question been resolved?

[safe radish]

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.

[fleet mortar]

hey guys, I need help converting r=8cos4 θ into a rectangular equation. my final answer can’t contain √x^2 +y^2 and also to be fully simplified and expanded, AND i have to show all steps 😭

[fleet mortar]

ive made it this far correctly i’m pretty sure

but every attempt i’ve made so far solving it doesn’t line up with the original polar equation

so im wondering if there’s an alternative way

[safe radish]

@fleet mortar Has your question been resolved?

[granite idol]

can't you just solve for r, change that to sqrt(x^2 + y^2), and square both sides?

[exotic bolt]

Ye it doesn’t make sense why you can’t have x^2 +y^2

Idk

[fleet mortar]

i can’t keep the square root of x^2 + y^2

so everytime i try and get rid of it my answer comes out incorrect

[granite idol]

what's the original question?

do you have a picture?

[fleet mortar]

you can see my attempts 😭

[granite idol]

where does it say you can't have sqrt(x^2 + y^2)

[fleet mortar]

it’s on my rubric

lemme show you rq

[granite idol]

sorry, I don't know then. your work is right though

[fleet mortar]

thanks for trying atleast!

[granite idol]

her end result is correct (same as what Wolfram Alpha shows, too)

[fleet mortar]

does wolfram alpha show the final answer by any chance?

and you’re saying the work up until the bottom of my work page is right too?

if so then i probably just made a mistake expanding!

[granite idol]

,w convert r=8cos(4theta) to rectangular coordinates

[flat frigate]

Results provided by WolframAlpha

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

Requested by cwatson

[fleet mortar]

i think i can try working from here

thank you so much!

oh and can it show steps

[granite idol]

you need to pay I think

[fleet mortar]

damn

that’s okay my work lines up with this answer

thanks again!

.close

[safe radish]

Channel closed

Closed by @fleet mortar

Use .reopen if this was a mistake.

[safe radish]

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.

[patent portal]

Construct a power series of the form (x-a)^n/n^p r^n that has an interval of convergence of -2 ≤ x < 10

[patent portal]

any help with this

not sure where to start

[severe pond]

do you mean

(x-a)^n/((n^p)(r^n))

[patent portal]

yes

[severe pond]

so what would the radius be

[patent portal]

so i take the absolute value and divide by 2 right

6

[severe pond]

mhm so what’s the center

[patent portal]

4

[severe pond]

right so that’s your a

and your r

[patent portal]

p is whats confusing me most i guess

[severe pond]

the n^p is irrelevant

well

i mean for the radius and center

because ratio test

it will always cancel

now you need to check the endpoints

so you have (x-4)^n/((n^p)(6^n))

you know it diverges at 10 yea

so let x=10

and then it’s a p-series

what must p be

to diverge

[patent portal]

greater than 1

oh

[severe pond]

no

[patent portal]

less than one

[severe pond]

or equal to

[patent portal]

yea

[severe pond]

and the -2 will be alternating

so you can choose any 0<p<=1

this makes sense yea

[patent portal]

cause 1/n satisfies ast

[severe pond]

well yea lim n-> inf (an)=0 and an+1<an

for p values in that range

[patent portal]

ok

makes sense

just gotta show all that work

[severe pond]

mhm

[patent portal]

so i should show r and a then how should i show the work for p?

ratio test on the endpoints right

[severe pond]

i don’t think you need ratio test

it’s p series test

for endpoints

just let x=the endpoints

then evaluate the two series

[patent portal]

ok ima right this out and lemmer know if u think its enough

Let me know if there is a better way to show this work

[safe radish]

@patent portal Has your question been resolved?

[safe radish]

@patent portal Has your question been resolved?

Channel closed

Closed by @patent portal

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.

[snow jungle]

5-7 odd

im struggling

plz help

[safe radish]

@snow jungle Has your question been resolved?

[thin bridge]

what have you tried

[safe radish]

@snow jungle Has your question been resolved?

[safe radish]

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.

[trail igloo]

is anyone able to explain what on earth happens when they introduce fg

completely lost me there

[glacial sonnet]

under where it says prop 2.10?

[trail igloo]

yeah

[glacial sonnet]

The first equality, just simplify the RHS and you'll see you end up with fg

then the second equality, s(x) = x^2 so they're just rewriting the 3 terms of the LHS using that composition

Then the apply what they argued in the first paragraph of the proof

[trail igloo]

so if I just expand the 2nd equality it should just be the same aswell?

[glacial sonnet]

yes

[trail igloo]

i know it sounds silly because obviously

[glacial sonnet]

look at what s is

[trail igloo]

although it seems as if its popped out of nowhere

[glacial sonnet]

s(x) = x^2

so

s(f+g) = (f+g)^2

s(f) = f^2, s(g) = g^2

[trail igloo]

oh oh oh

i get you now

i was overthinking it

thanks

[glacial sonnet]

[trail igloo]

.close

[safe radish]

Channel closed

Closed by @trail igloo

Use .reopen if this was a mistake.

[safe radish]

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.

[torn patio]

Is it possible to find the value of alpha in degrees?

[knotty pier]

calculator prolly

[torn patio]

I see

but I don't understand the graphs

Also what is n

[knotty pier]

some integer

[torn patio]

What's the value?

[knotty pier]

n can be any integer

as tanx is periodic

[torn patio]

What does that mean?

[knotty pier]

periodic means

uh idk how to explain

periodic basically means the graph repeats

[torn patio]

happening in regular intervals?

nvm

[knotty pier]

yea

right

[torn patio]

oh

let's go

I still don't know what that means for graphs

[knotty pier]

tht means

value tanx

at x=a and x=a+pi

is same

and so on

so tanx is same for x=a,a+pi,a+2pi,...

[torn patio]

how though

[knotty pier]

its the property of the function

[torn patio]

how can x = a and a+pi

good thing I didn't select mathematics for higher studies

[knotty pier]

maths can be interesting

[torn patio]

Biology ftw

[knotty pier]

that is the property of function

[torn patio]

Idk what any of that means

I will just leave it as tan inverse(1/10)

[knotty pier]

u do not have expanation for tht

[torn patio]

teacher says that is fine

[knotty pier]

mhm

[torn patio]

but I wanted to know the value of degree

[knotty pier]

which class are u in?

[torn patio]

11th

I wanted to know the degree to see the direction of resultant'

[knotty pier]

principal value is when n=0 and for any other n value, u say general

[knotty pier]

oh alr ull be learning tht stuff in trignometric equations chapter

[torn patio]

I don't have mathematics

I didn't opt for it

[knotty pier]

oh

[torn patio]

glad I didn't

[knotty pier]

makes sense

[torn patio]

I have Physics though

[knotty pier]

thts y u dont get it

[torn patio]

I see

Thanks for trying to explain this to me though

.close

[safe radish]

Channel closed

Closed by @torn patio

Use .reopen if this was a mistake.

[safe radish]

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.

[reef quartz]

Can someone please help me with question c

[reef quartz]

it uses the previous parts of Level 2 question 1

[safe radish]

@reef quartz Has your question been resolved?

[safe radish]

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.

[leaden glade]

Find the number of selections of 4 letters from the word S P E C I E S

[leaden glade]

if its selections does it mean i use

perms or combs

[silent bramble]

should be combs

[knotty pier]

selection combinations

[leaden glade]

wait so

would it just be

6c4

[knotty pier]

there are 2S and 2E

[leaden glade]

oops

i missed that one

[knotty pier]

mhm

no wait

actually for selecting

it is 6C4 only

[leaden glade]

wait

[knotty pier]

thts right

[leaden glade]

wait is it

[knotty pier]

yes

if u wanted to shuffle u need to change

u r basically selecting

[leaden glade]

wait i dont rly understnad tho

[knotty pier]

so 6C4

[leaden glade]

how do i account for the

doubles

[knotty pier]

fine take a word like AABB

[leaden glade]

yeahh

[knotty pier]

number of selections of 2 letters is

4C2

[leaden glade]

oh

yes...

[knotty pier]

yep

[leaden glade]

wait

[knotty pier]

but

[leaden glade]

its selections right

[knotty pier]

yes

[leaden glade]

so its how many different ways can i reaarange

wouldnt it be

AB

AA

BB

[knotty pier]

yes

[leaden glade]

isnt that 3

[knotty pier]

im saying

[leaden glade]

oh

sorry

yeah

[knotty pier]

yes 4C2 for selecting

and then

u remove unwanted

[leaden glade]

and then

um

[knotty pier]

AB same as BA

[leaden glade]

how do u remove the

unwanted

[knotty pier]

wait a sec

[leaden glade]

okkokk

[knotty pier]

yea u cant do tht

u gotta consider cases

mb

like

for ur q

[leaden glade]

yeahh

so uh what would i do then

[knotty pier]

SPECIES

[leaden glade]

yep

[silent bramble]

wait but they didnt say different selections

[knotty pier]

u shld consider

[silent bramble]

so u dont need to right

[leaden glade]

so there is 2 doubles

[knotty pier]

4 different

2 diff 2 same

2 same 2 same

[leaden glade]

yeah

[knotty pier]

so 4 diff means

u got S P E C I

choose 4 in how many ways?

[leaden glade]

wait

isnt it

3 diff

oh wait

nvm

im tripping

[knotty pier]

how do u get 3 diff 1 same lol

yea happens

[leaden glade]

wait

wait wdym again

im a bit lost

so its

[knotty pier]

alr

[leaden glade]

PCI

[knotty pier]

lets take simple example

[leaden glade]

that is different

and then u got

2 S

[knotty pier]

mhm

[leaden glade]

wait

2 E

i mean

so its PCI , 2S, 2E

[knotty pier]

yes

so for selecting all different ones

u consider one of those 2

so P C I S E

[leaden glade]

oh...

alr...

[knotty pier]

wait lemme start from beginning

[leaden glade]

okok

[knotty pier]

with a simple example

consider the word ABBCC

[leaden glade]

yep

[knotty pier]

u need to choose 2 letters ok?

[leaden glade]

yep

[knotty pier]

so the possibilities are

[leaden glade]

AB BC BB CC AC

[knotty pier]

both different and both same

[knotty pier]

we are doing it in p and c way

[leaden glade]

oh okok

yes

sure

[knotty pier]

.

ok

so for both diff

u need to choose 2 from

ABC

right?

[leaden glade]

ohh yes

so thats 3c2

[knotty pier]

yes so 3C2 ways

[leaden glade]

yep

[knotty pier]

yep

[leaden glade]

gotchu

[knotty pier]

so now both same

so u can either choose B or C

agreed?

[leaden glade]

um

yes

okok

[knotty pier]

so tht will be 2 ways

BB and CC

[leaden glade]

so thats

2c2

and 2c2

yes?

[knotty pier]

yes

so total will be?

[leaden glade]

3c2 + 2c2 + 2c2

is

5

which is also what i got when i brute forced it

[knotty pier]

u got 5 here yep

[leaden glade]

yeah

[knotty pier]

yes

[leaden glade]

cool

okok

[knotty pier]

so now onto our question

[leaden glade]

yep

[knotty pier]

SPECIES

wht are the possibilities?

[leaden glade]

so its

choose 4

so um

u can have SPECI

for the all different

[knotty pier]

yes

[leaden glade]

then u can have

2 same 2 diff

[knotty pier]

yes

[leaden glade]

and then 2 same 2 same

[knotty pier]

yes

[leaden glade]

and um for 2same 2diff i have 2 options for that one right

cos it could be like

SS CI or EE CI

[knotty pier]

yes

[leaden glade]

okok

[knotty pier]

and u missed P tho

[leaden glade]

missed p

[knotty pier]

ok so in 2 diff 2 same case

[leaden glade]

yes

[knotty pier]

for 2 same u can either choose

E or S

[leaden glade]

yes

[knotty pier]

assume u chose E

then u can choose rest 2 from?

SPCI agreed?

[leaden glade]

wait

go again this is for

is this for 2 same 2same

[knotty pier]

nop

[leaden glade]

oh

[knotty pier]

2 diff 2 same

[leaden glade]

2same 2 diff

oh ok

[knotty pier]

assume 2 same u chose E

[leaden glade]

yep

[knotty pier]

then u can choose rest 2 from SPCI

[leaden glade]

oh yes

correct

[knotty pier]

assume u chose S then rest 2 u can choose from IPEC

both have 4C2 ways

[leaden glade]

wait

[knotty pier]

mhm

[leaden glade]

chose I ?

wouldnt it be S

[knotty pier]

oops sry

S

yes

[leaden glade]

okok

[knotty pier]

both have 4C2 ie 6 ways

now for both same

[leaden glade]

4c2

[knotty pier]

u choose S and E

so only 1

[leaden glade]

wait its 4c2 cos i have 2 remaingin spots

[knotty pier]

yes

[leaden glade]

and 4 things to choose it from

okok

gotchu

[knotty pier]

ok for same and same only 1

cuz u need four and u have 4

[leaden glade]

oh yes

okok

[knotty pier]

yep add all those up

[leaden glade]

so 4c4

so its

[knotty pier]

yes

[leaden glade]

4c4 + 4c2 + 4c2 + 5c4 ?

[knotty pier]

yes

[leaden glade]

ohhh okok

[knotty pier]

mhm

[leaden glade]

um i got 18

okok

i dont even have the naswers for this but ill tryt o find it

😭😭

but thank u very much

[knotty pier]

no problem!

just go through it again so ull have the clarity

[leaden glade]

okokok

thank u very much

.close

[knotty pier]

npp

[safe radish]

Channel closed

Closed by @leaden glade

Use .reopen if this was a mistake.

[safe radish]

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.

[stoic sage]

I’m not sure how to do this question. Can someone help me.

[eternal carbon]

draw a cubic and try drawing a horizontal line through it

see what happens

[ebon seal]

Can you send previous part as well

[stoic sage]

Yeah I didn’t see it was a part b but I don’t think it has anything to do with part a. (Maybe?)

[summer crow]

no relevance, like mqnic suggested sketch a cubic with two turning points, and think about a horizontal line crossing it

[pure arch]

how does a quadratic have 3 zeroes

[summer crow]

It doesn't that's the point

it has to identical to 0

^and this is the same concept @stoic sage

[stoic sage]

Cubic as in the one with in the one with inflection??

[summer crow]

for part b

[stoic sage]

Or like a polynomial graph with many intersecting points

[summer crow]

this is a cubic

or this sometimes

might be what you mean by inflection point

[stoic sage]

yeah

[summer crow]

but both are cubic

[summer crow]

this is a more special case

[summer crow]

so using this graph @stoic sage can you find a horizontal line y=k that intersect this graph four times?

[stoic sage]

but i only got 3

[summer crow]

exactly

3 max

[stoic sage]

does d = k

[summer crow]

yup

[stoic sage]

but how do i find the values of a b and c

[summer crow]

ok how did you come to this conclusion?

[stoic sage]

because y=k would be a straight line and for the curve, if all x equal 0, y=d so d=k?

[summer crow]

ok

[stoic sage]

oh wait

then a b c equal 0

[summer crow]

why?

[stoic sage]

because they all have to be 0 for k to be equal to d?

is it?

[summer crow]

correct

the way to think about it

is that a cubic can intersect a horizontal line at most 3 times

so it can't be a cubic

so a = 0

then we go down to quadratic

but same logic, where a quadratic intersects a horizontal line at most 2 times

so b = 0

down to linear

same logic

[stoic sage]

oohh

[summer crow]

therefore the only possibility is that the curve is just a flat line

and it is the only line y=k

[stoic sage]

oh okay

[summer crow]

and it intersects itself infinitely many times

[pure arch]

oh so you just equate each coefficient to 0 then

[stoic sage]

Thank you

[summer crow]

indeed

[summer crow]

np

[summer crow]

and d = k

[pure arch]

well i was referring to the first question

part a

but yeah part b follows the same logic

[safe radish]

@stoic sage Has your question been resolved?

[safe radish]

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.

[eager mica]

chat

[eager mica]

am I correct

or am I cooked

[eternal carbon]

does that say 2 < pi/4

[pure arch]

re you supposed to find possible values of z

[lean otter]

uh yeah the 2 < pi/4 is probably more crucial to address first

[pure arch]

oh i didn't even realise lmao

[safe radish]

@eager mica Has your question been resolved?

[safe radish]

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.

[stoic sage]

im not sure how to do this question, can someone help me

[spice wing]

Hey

I may try to help but im not sure if i can reach the solution , is it okay ?

@stoic sage ?

[stoic sage]

yeah

[pure arch]

does stationary points just mean

points where slope = 0?

[spice wing]

See it says stationary at alpha = á and beta = b stationary

[stoic sage]

well i derivatived it twice and gor to 6x+2a

[spice wing]

So f'(a) = f'(b) = 0

[stoic sage]

whats the f'b and f'a?

[spice wing]

f'(x) = dy/dx

[pure arch]

a should be alpha

i believe

and b should be beta

[spice wing]

Yeah

It is

[spice wing]

Wrote here

[stoic sage]

ooh okay

[spice wing]

f'(x) = 3x² + 2ax + b

Now alpha beta satisfy this equation

[pure arch]

yup

so alpha is one rooot and beta is another root

[spice wing]

Let alpha = u and beta = k okk ?

So 3u² + 2au + b = 0 and 3k²+2ak + b = 0

Point of inflection will be the point where f'(c) and f''(c) both will be 0

Where c is the point of inflection

f''(x) = 6x + 2a

[pure arch]

no no

they're both solutions

to the same equation

essentially

[spice wing]

If f''(x) = 0 , then x = -2a/6

[spice wing]

Yeah im using that

k + u = -2a/3

[spice wing]

And we know this

So if we equate we get f''(x) is 0 at k+u/2

[pure arch]

ye

[spice wing]

That is required to proof

[summer crow]

Here's a hint for you guys: the turning point/vertex of a quadratic is halfway between its roots

[stoic sage]

ooh thank you

[stoic sage]

why does k+u equal -2a/3?

[spice wing]

True because parabolic path

[spice wing]

Sum of roots

[stoic sage]

like why is it a plus

ooh

[spice wing]

Of this eqn

[pure arch]

yeah

but k and u are just alpha and beta

[spice wing]

Yeah

[pure arch]

so alpha + beta = -2a/3 = 2x

since x = -a/3

[spice wing]

from this eqn ^^^

[stoic sage]

is there any other way i can get it without using the sum of roots?

[spice wing]

I think this was the easiest way

[spice wing]

Else you can use the logic as stated by igkoo

But still it would require proof

[stoic sage]

for sum of roots, alpha plus beta equal -b/a. why is -2a/3 the -b/a?

[spice wing]

See this eqn

3x² + 2ax + b = 0

[stoic sage]

yeah

[spice wing]

Alpha beta are roots

So alpha + beta = -2a/3

where 3 is the coefficient of x² and -2a coefficient of x

Ok ?

[stoic sage]

what do you equate it with

[stoic sage]

yea i understand that part now

[spice wing]

If f''(x) = 0 , then x = -2a/6

And k + u = -2a/3

So clearly k + u = 2x from this equations

[stoic sage]

ooh

i get it now thank you

[spice wing]

Welcome!

[safe radish]

@stoic sage Has your question been resolved?

Channel closed

Closed by @stoic sage

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.

[sonic rampart]

how do i solve b) ??

[vagrant ice]

f(2x) means you replace x with 2x every time x appears in the function

So g(x) = f(2x) = 5 (2 sin(3 * 2x) + 4) = 10 sin 6x + 20

[ebon mesa]

huh

[sonic rampart]

ohh

[vagrant ice]

Now the 6x is irrelevant to the range

[sonic rampart]

I made mistake

[vagrant ice]

Yeah so you should remember what the min and max values of sin x are

[sonic rampart]

i didnt mutiply 5 to 4

[vagrant ice]

And then sub in

[vagrant ice]

ahhhh

ok

[sonic rampart]

yesyes

thank you very much

[vagrant ice]

npnp

[sonic rampart]

.close

[safe radish]

Channel closed

Closed by @sonic rampart

Use .reopen if this was a mistake.

[safe radish]

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.

[slate violet]

How to find the limit value for this equation?