precalculus

[snow flame]

I'm 15, going into 10th grade.

[dense mango]

American curriculum never fails to astonish me

[summer ruin]

learn the unit circle

once you learn angles from first quarter all others can be easily derived if needed

[dense mango]

Or you can always draw a 30, 60, 90 triangle and figure it out yourself

[snow flame]

It's weird.

[dense mango]

I started trig in 11th grade

And leveled up to trig equations in 12th

[snow flame]

Oh, nice.

I started a little bit of trigonometry in 9th grade.

Except I'm starting more complex trigonometry and trigonometric equations in the summer of 9th grade.

[snow flame]

Yeah, that's what I'm trying to do.

[dense mango]

My teacher never showed me the unit circle tbh

She just gave us a table with values of trig function for 30 60 and 90 degrees and had the students memorize it

[snow flame]

I think I am going to do both.

Thanks @dense mango and @thorn kestrel.

Appreciate your help.

[dense mango]

[charred frigate]

wtf. that's not an american thing, that's just a bad teacher thing

[tribal mason]

hey can someone help me figure out what type of calc my summer school homework falls under

like idk if it's pre cal or calc 1 or something

[untold spindle]

What does it contain?

And also does it not say?

[tribal mason]

Not exactly

I’m doing a summer course but it’s not teaching me basics just running through questions

So I’m trying to find out what it is and where I can learn it myself online for free

Here’s some of the work I’ve gotten so far

[untold spindle]

From what I know, this looks like precalc. But if your summer school is "running through the basics" then I believe this is the Calc 1 course

[tribal mason]

I mean idk if it’s basics or not cause I haven’t done calc before

[slim steppe]

Khan Academy, Organic Chemistry, NancyPi, Albert.io are good

[tribal mason]

But tysmm

[tribal mason]

Ty this is super helpful

[slim steppe]

This is what albert.io looks like

[tribal mason]

I’ve never used that before but it looks like there’s a lot which is good

Is it all free ?

[slim steppe]

It's free if your school is somehow connected to it

But I think it requires some subscription

[tribal mason]

Oh ugh

Is that like an American site ?

[slim steppe]

Khan Academy is free though

[tribal mason]

Tyty

[slim steppe]

Yeah

[tribal mason]

I just hope it covers everything somewhat

[tribal mason]

Aw then it won’t work for me

It looked good too that sucks

[slim steppe]

You can always buy yourself a big ass book that covers all the topics

[tribal mason]

I was already looking thru my local library catalogues a while back loll

But I find that textbooks specifically don’t rlly explain it in like an understandable way

I get confused a lot when there r lots of letters and it’s all like over complicated in a sense

[slim steppe]

Yeah, I get that

I've always preferred printing out actual tests from the past

[tribal mason]

I’d do that if I knew how to do the tests in the first place

[west falcon]

its free for me

just create a google account

seems like an IXL esk thing

[tribal mason]

I tried doing it with my school account but it blocked it

I’ll try with another account or something

[tribal mason]

What’s that ?

[west falcon]

don't use a school account

just a google private account should be fine

[west falcon]

IXL isn't free

but its very similar

it ranges from K-12, to College level stuff math

[tribal mason]

I’ll try that then ty

[tribal mason]

Aw I’m looking for something free

[dense mango]

When did I say it's an american thing tho

[charred frigate]

sort of here but I get if that isn't what you meant

[dense mango]

Yeah I wasn't talking about the unit circle here

[dense mango]

,rotate

[dense mango]

For what values of a, b, c function f(x) is continuous

I'm getting some weird results...

[dense mango]

Nvm I managed to solve it

[spare pilot]

Hi

Can someone help me with this problem

[bright bay]

sure @aer

@spare pilot

ok to start u need to find a and b

for the formula of the elipse

x2a2+y2b2=1

do you know how to @spare pilot

[spare pilot]

yeah

[bright bay]

what did u get for a

[spare pilot]

Oh! I thought you meant the formula. I haven't found a yet.

Do i use law of cosines?

[bright bay]

oh ok

[spare pilot]

because i know that here √b^2+c^2

=a

but I dont know how to find b

if I cant find a

[bright bay]

give me a second iam trying to find a way to tell u without giving the answer

cuz i was told i shouldnt

[spare pilot]

okie

[bright bay]

ok look

there is no way to be more not hidden solution sooo ye

[spare pilot]

oh

[bright bay]

ok ill stop trying to find an indirect way to say it and just do

this is stupid my wifi went off @spare pilot

[spare pilot]

Yep! Im here lol

[bright bay]

can u join a call and i would explain it outside so i wont get banned lol

[spare pilot]

okay

Sorry, I'm also new to Discord so I don't know how to join a call 😢

[bright bay]

anyways this is it

[spare pilot]

👍

[bronze spoke]

What are the best resources for studying multivariable calculus?

[snow whale]

https://www.khanacademy.org/math/multivariable-calculus
i dont know how good khan academy's course is but it should help

[solid elm]

what are the basic properties of logaritihms?

also how do you use the texit bot?

[untold spindle]

there is also some information in #resources

[willow bear]

wym by "subtract the arctan"?

[versed temple]

i'll give you an example

take the equation sinˆ2x+4sinx.cosx+2cosˆ2x=1

[solar olive]

did u mean like, sin(x)^2 + 4 sin(x) cos(x) + 2 cos(x)^2 = 1

[versed temple]

yes

[solar olive]

and u want to solve for x ?

[versed temple]

yes

[solar olive]

well uh

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

0 = 4 cos(x) sin(x) + cos(x)^2

that might help, idk

[versed temple]

yes but where does the arctan in the final answer came from?

[willow bear]

... i was wondering what you meant by "subtracting" the arctan.

do you have a worked example where that's done

[versed temple]

yes, give me a minute

[willow bear]

your example reduces to cos^2(x) + 4 cos(x)sin(x) = 0 btw
which factors to cos(x)(cos(x)+4sin(x)) = 0, from which you get two families of solutions

[solar olive]

idk why but my brain died and stopped at that lol

amazing

0 = cos(x)(cos(x) + 4sin(x))

cos(x) = 0 or cos(x) = -4 sin(x) (this is where the arctan comes)

1 = -4 tan(x)
tan(x) = -1/4
x = arctan(-1/4)

[versed temple]

oh, i got it

thank you ann and impractical

[solar olive]

np

[willow bear]

again tho

"subtracting the arctan"

still kind of sounds sus to me

[solar olive]

he probably meant the other solution

x = -arctan(1/4)
x = pi - arctan(1/4)

its from the fact that tan(x + pi) = tan(x)

[wispy forge]

So is half of precalc just algebra?? I’m halfway through my class and it’s just stuff I learned in college algebra

[versed temple]

mostly algebra, trigonometry and polynomials

[wispy forge]

Okay thanks. I’m really confused lol

[charred frigate]

yeah i mean where i went to community college there was college algebra, trig, and then precalc. to take calc 1 you had to take either college algebra + trig or precalc. and precalc was just college algebra + trig combined into one class.

[wispy forge]

But here they are saying I need algebra then pre calc then cal 1

[mild swan]

This seems right

I went algebra 2 -> precalc -> calculus

[wispy forge]

I’m curious as to why I don’t need a dedicated trig class

[buoyant aurora]

is the "analysis" unit in alg 2 ever used in pre calc

like margin of error and inferences

[charred frigate]

its different between schools. in high school it was alg 1->geometry->alg 2->precalc->calc 1

[molten topaz]

Can anyone recommend me some good material for exercises about functions? (Sorry for my bad english)

[bright bay]

hey @molten topaz

use this link finish the entire course and you should be good on functions

https://www.khanacademy.org/math/algebra

or if you dont want to there is one part in it about functions only but i prefer u do the course

[dusty gale]

Does anyone get this problem?

[chilly thorn]

So you need a domain such as f is 1 to 1

like [2;8]

[dusty gale]

Can you explain in more detail @chilly thorn

[viscid thistle]

Find the range of all x values which will produce unique f(x) values

i.e. one-to-one

[dusty gale]

I still don’t get it

[viscid thistle]

Ok we‘ll break it up cos I get why what I said is confusing

You know what a one-to-one function is right?

[dusty gale]

Yes

An X value can only make one unique y value

And no other X value can share the same y value

[viscid thistle]

Ok good

[dusty gale]

It will still be a function but it wouldn’t be one to one

[viscid thistle]

The graph of the function displayed is a many-to-one function

You get that?

[dusty gale]

Yep

[viscid thistle]

Ok cool

The reason we can’t have a many to one function is because if we take the inverse, we get a many to one function, which contradicts the definition of a function

i.e. value x to value y

You can’t have multiple x give the same y

[dusty gale]

What I’m struggling on is knowing what points to put to make it one to one just from looking at the graph

[viscid thistle]

make an imaginary line of symmetry

you take the right side inclusive and you get a set of points which provides a one-to-one function and a one-to-one inverse function

wait could you send a screenshot of the possible answers

[dusty gale]

It’s not the same question but it’s the same concept

[viscid thistle]

ok so

for a function to have an inverse that works, the domain has to be restricted

i.e. you have to find all values for which both functions are one-to-one

for this second example you have provided, you can see that it is clearly a many-to-one function because both x=4 and x=-4 give y=2

so you want to find the ranges of all values of x such that all values of y are unique

you still here?

[dusty gale]

Yeah

[viscid thistle]

yeah so if you make a line of symmetry on the function

you see you have two separate 'sections' for which all values of x correspond to different values of y

and those are the intervals you are looking for

hope this is good enough and if you have any more questions just ask

[viscid thistle]

could someone help me with the difference between vertical/horizontal stretches/shrinks i've been failing on this for half my honors algebra II lmao

[viscid thistle]

see heres the problem

[viscid thistle]

math!

these don't explain the difference

i have a general idea of what they are, but not the difference between them

[viscid thistle]

if u read the entire 300 pages of the first 2 pdf

u will know

aha yes

but i didn't come to the discord to be directed to read 600 pages of textbook

i came to be directed to the answer

so if you can't explain it don't even bother 🙂

[viscid thistle]

sorry ma'am or sir or whatever u identify as.

just don't identify as a math genius until u cant solve this:

[viscid thistle]

i am not a math genius that's why i'm asking for help

[dense mango]

bro stop posting it everywhere

this doesn't even belong in this channel

we all know youre trolling

[viscid thistle]

sorry ma'am

or sir

[dusty gale]

Hello everyone, normally I know how to do this but since it’s a -10 on the outside, I don’t know how to decompose it. Please help

[summer ruin]

this is just trivially checking the given options

[dusty gale]

Ok guys so I got those questions right

It was 2 and 5 although I don’t know why it was 5

Next up is this tough sucker. Just like the other one is it telling me to pick 2 choices which I don’t understand.

[summer ruin]

again you can just check

[dusty gale]

How do I check?

[wispy forge]

Bruh my prof has us doing over 200 equations just for participation/hw today I am dying

[dusty gale]

I finally get how to do a inverse function now

It was literally so simple

[wispy forge]

Proud of you

[viscid thistle]

can someone help with this

[digital pendant]

You just have to perform the given operation and simplify

[jolly robin]

Can someone nudge me in the right direction for 121?

I changed the left side to 1 + sin2x over cos2x

But can’t simply further

[opal tree]

Worse case scenario, just change everything into terms of sine and cosine whose argument is just "x"

[dusty gale]

You’re favorite person is back with a new question. I absolutely don’t get this. Someone help

[jolly robin]

Last option

If you see the graph turn flat at one point it’s the third power

When they mean multiplicity they mean this f(x) = (x - k)^3

In this case the graph is

F(x) = (x+1)^3(x-2)

[deep cypress]

This is definitely a long shot but if anybody could solve these it would really be a godsend. I’m so stuck and confused

[void temple]

Do it in a help channel

helpers are more advanced than you think lol

For first one|| express in terms of sin x, cos x||

For second||equate and express in terms of sin x||

If you are still stuck ping me two hours later

[jolly robin]

@void temple can you help with mine?

[void temple]

(I have lessons)

[void temple]

pls don’t ping individual users

[jolly robin]

121 and 129

[void temple]

but which channel

[jolly robin]

Sorry sir

[void temple]

121. Start from the RHS, multiply by cos x+sin x on numerator and denominator. This is because (cos-sin)(cos+sin)=cos^2x-sin^2x=cos2x in denominator which is also the denominator of tan2x+sec2x=(sin2x+1)/(cos2x)

[jolly robin]

I see

I’ve been trying to do it from the left

[void temple]

129. Multiply both sides by cos^2(x/2)

[void temple]

That probably works too but for me it’s more natural

To start from the RHS

[jolly robin]

Alright

Thanks

[void temple]

Wait I meant num and denim

Denominator

Not both sides

Sorry

[jolly robin]

Yeah I solved it

Thanks for the hint

[dusty gale]

Yo people I am back again with once another question

-2 isn’t flat it’s more like straight down

And the 4 is on the line

[jolly robin]

Ok so

Same concept

But different zeroes

4 is turning flat again

And -2 is just multiplicity by one

Typically if it goes straight through the zero and into a new quadrant/side

It’ll be multiplicity of 1

[opal vault]

nice face reveal

send more pls

[dusty gale]

I’m no model

[opal vault]

last option

[dusty gale]

I’m just a guy who ask math questions

People this is not a drill I need help once again. Thank you

[willow bear]

@dusty gale do you still need help with this?

also gonna transcribe the problem for my own sake

The volume of a cone with radius equal to height can be found via the formula V = (1/3)πr^3.

If a cone has a volume of 100 in^3, what is its radius? Round your answer to the nearest- [CUT OFF].

[dusty gale]

No currently I’m struggling on finding inverse functions

But Ty nonetheless

Hello people it’s me again and yes I need help again per usual

Ty

[noble jungle]

i was working on ^^ just a few days ago 😭

such a pain

[dusty gale]

ONG I hate pre calculus

[noble jungle]

real same

[rustic stratus]

Calculus can’t be that bad right?

[dense mango]

[opal vault]

how

did u transcribe it

[opal vault]

bro its terrible

ppl say u should try understanding it but like

its very complicated

[willow bear]

i don't understand what you are asking me

[opal vault]

like whats the function to

like

get the text from the picture

in discord like what command do u do

[willow bear]

there isn't any such command

i did it by hand

[storm lodge]

just read it

its not that bad

[opal vault]

ohhh

i thought it was some bot u added and like auto did it

[opal vault]

but its useful in general

im not talking abt this pic in specific

[echo pelican]

Calculus is your reward for getting through Pre-Calc

[dim goblet]

how to solve this ?

[viscid thistle]

“If f(x) be a real valued function” mf talking in pirate

[hushed sphinx]

subjunctive mood

[echo pelican]

This seems like a Calculus question to me

[dusty talon]

can someone offer a homework service? like x cents per problem solution + explanation? i've a lot of questions and have an exam soon, and really need an explanation on all of this

[untold spindle]

we dont do that, were here to help you with math not do it for you, i suggest you read the rules because paying for math is against them

[dusty talon]

ah ok np

yeah thats what i meant--thats why i like a full explanation

im also here to learn the material

[untold spindle]

still, dont offer money for math

[devout plinth]

Hey anyone available for a quick question. Looking for a domain of this simple square root natural log function

[mellow vigil]

don't ask to ask

[hushed sphinx]

Paying for help is not "against the rules" as such -- but we discourage using the server to set up such transactions because we don't want to be involved in payment disputes ("he took my money but his help made no sense" vs "I spent hours helping and now he won't pay").

[untold spindle]

oh ok. I thought paying for help fell under the same category as paying for someone to do it for you, but I see now.

[late hawk]

can someone help me with this question? the wording of the question gets me bad

[dusty gale]

Pre calc I need y’all help again

The question is to evaluate this

Ok so I got 5 but I really don’t understand why it is 5

[untold spindle]

do you know log properties?

[dense mango]

so there is this "rule" $a^{\log_{a}b}=b$

[obsidian monolith]

iammax420

[dusty gale]

Oh so it’s the inverse

[dusty gale]

I’m back once again how do I solve this

[summer ruin]

take log?

[summer ruin]

use properties of log

[dusty gale]

I’m in a pickle once again

Nvm I got it

[viscid thistle]

May I know how to solve 37. Find a and k

[warped cipher]

What have you tried

@viscid thistle

If you still need help

[viscid thistle]

Tried to find the factor K

But can't find

[warped cipher]

!show

[tender quest]

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

[plush umbra]

I dont know if seperating the denominator is necessary for integration

[warped cipher]

I think this belongs in #calculus

[jaunty crow]

Whts the function of this sinusoid

[warped cipher]

@jaunty crow do you still need help

[jaunty crow]

Yea

[warped cipher]

Ping me when you reply

Anyway do you know how to find midline, amplitude and period?

[jaunty crow]

No

I registered for online precalc courses over the summer

I got the basics but the rest of the course material is extremely vague

[warped cipher]

Well have you watched something related to this

[warped cipher]

https://youtube.com/watch?v=s4cLM0l1gd4

Watch this video and then give it a try

[jaunty crow]

Thnx

I'll check it out

[dim goblet]

how to solve this ?

[dusty gale]

Does anyone know the answer?

And how to solve it

[summer crag]

Does it always mean log₁₀ when unspecified?

[dusty gale]

Yeah

[summer crag]

M = (2/3)log₁₀E/E₀, and M = 5.5 equate it and get E

[dusty gale]

Thank you

[dusty gale]

I kept getting this question wrong

Keep*

[summer crag]

the general form of exp functions is a(b^x)
Now it's given that this exp function is going through the points (2,40) and (3,8).So we get two equations in two variables, solve for the variables a and b and you get your exp function

[dense mango]

can someone tell me how to sketch this function

I kinda got lost

[summer ruin]

hint: 0.2 = 1/5

[dense mango]

I'm stuck, idk what to do next

if not the absolute value, it would be just x^-1

but I'm not sure what to do because of it

[summer ruin]

it would be nice if you could get rid of the 1/5 fraction in the base of log and instead make it a 5

you shouldn't be messing with exponential 5 here because that's not the problem

[dense mango]

hmm

[dense mango]

like this?

[summer ruin]

yes

absolute value kills the minus sign anyway, the rest is just considering cases where log is positive or negative

[dense mango]

ohh right

thanks much

[sweet agate]

can someone help me

solve

D4 i

[untold spindle]

this is better suited for #calculus

[sweet agate]

ok

[flint wave]

Hi guys, sorry to disturb just a short one can someone help me to solve this question. thanks

67
68
69
70
Show that 𝑥 = 1 is a root of
𝑥
3 + 8𝑥2 + 11𝑥 − 20 = 0.
Hence factorise 𝑥
3 + 8𝑥2 + 11𝑥 − 20 fully.
The roots of the equation 𝑘𝑥2 − 3𝑥 + 2 = 0 are
equal.
Calculate the value of k.
Solve the equation 3𝑐𝑜𝑠2𝑥 + 𝑐𝑜𝑠𝑥 = −1
in the interval 0 ≤ 𝑥 ≤ 360.
The diagram shows a right-angled
triangle with sides and angles
marked. What is the value of
𝑐𝑜𝑠2𝑎?
𝐴 = 2𝜋𝑟2 + 6𝜋𝑟.
What is the rate of change of A with repect to r
when 𝑟 = 2?

Thank you and get back to me pls as soon as possible thanks

[sweet agate]

show diagram

[spice stream]

hey guys, sorry to bother but i just cannot figure out row echelon form. could someone break it down for me so it makes sense? tried asking the teacher and she didnt really help much

[median loom]

Do you know the 3 different row operations?

[wispy forge]

We got matrices in precal? I’m in it rn.

[main crystal]

Hi Guys! I need help! Could someone elaborate the answer in an algebraic form or an easier way to do?

Car A departed from Town A and travelled towards Town B. At the same time, Car B started its journey in the direction of Town A from Town B. The two cars passed each other 64 km away from Town B and carried on with their journeys. They made U-turns upon arriving at their destinations so as to return to their own towns. They passed each other again, this time 52 km away from Town A. Find the distance between the two points where they passed each other.

[undone hearth]

HHello frineds

i have precalculus final on monday

@pale anchor

[main crystal]

I need help

Hi Guys! I need help! Could someone elaborate the answer in an algebraic form or an easier way to do?

Car A departed from Town A and travelled towards Town B. At the same time, Car B started its journey in the direction of Town A from Town B. The two cars passed each other 64 km away from Town B and carried on with their journeys. They made U-turns upon arriving at their destinations so as to return to their own towns. They passed each other again, this time 52 km away from Town A. Find the distance between the two points where they passed each other.

[analog flower]

@visual widget this might not be useful but dang it i drew it so here you go

[visual widget]

ohh ok. So If i understand correctly, if its in the form ASin(Bx-c)+D, the phase shift is c/b while if its in the form ASin(B(x-c)+d, the phase shift is just c. If im right, is that the only diffrence betweem the two equations?

[analog flower]

yep! that's the only difference

(which you can see if you just distribute the B in one of your eqns)

I find that usually it's in the form sin(Bx - c)

[visual widget]

This helps a lot, thank you so much

[pure radish]

Hello just wanna ask about circles (sorry for the trouble), finding the standard equation of the circle which is
(x -h)^2 + (y -k)^2 = r^2
so here is the question from the text book

at the end it gave the solution for that, here it is

so my question is can i use CB for the distance formula instead?

[summer crag]

yes you can CB = AC = radius of the circle

[pure radish]

oki tysm, so CB is also equal to sqrt of 29/4?

cause i got this when i tried to solve for it

BC=

[summer ruin]

this is the same number

[pure radish]

sorry i didnt understand 😢

[summer ruin]

$\sqrt{\frac{29}{4}} = \frac{\sqrt{29}}{2}$

[obsidian monolith]

Transparent Elemental

[pure radish]

AHHH ic

thank you so much!

[digital pendant]

So I heard awhile ago that there were solutions to higher degree polynomials but that they were infinitely long but I can't find any information about this anywhere. Is it even true?

(not sure where to ask this)

[summer ruin]

https://math.stackexchange.com/questions/1555743/how-do-you-solve-5th-degree-polynomials

sometimes it's not even that the solution is "infinitely long", it's more like it's not useful because we don't get a simple constant at the end - it's a constant hidden under a bunch of elliptic functions or repeated fractions

[frosty sparrow]

how do I do this?

[hushed sphinx]

I can't think of any interpretation that makes that true in a meaningful way.

You can approximate the solutions to a high-degree polynomial equation numerically. That's an iterative process, which could perhaps be described as "infinitely long" if you prioritize shock and awe over actual understanding. 🤣

[hushed sphinx]

Figure out by reading your textbook (or other course material, whatever) what "principal value" means.
It's not a "practice a solution method" exercise, it's a "make sure you understand what the words mean" check.

[west swallow]

guys, how do i solve this?

the degree don't even match

[untold spindle]

what are we supposed to be doing with this? just polynomial division?

[west swallow]

yes\

[untold spindle]

there is no need to use polynomial division yet.

try factoring the numerator and denominator

actually sorry about that i thought things would cancel but i tested it out and they dont

you are kinda on the right track but when subtracting make sure to subtract -12x by -8x because they are like terms

@west swallow

[west swallow]

how m i gonna even do that

if the degree don't match

[untold spindle]

the degrees of -12x and -8x do match..

[west swallow]

can u show me how u did it

would appreicate

[untold spindle]

this is where you are at right now. correct?

(i added 0's for clarification on where the terms go)

[west swallow]

yes

[untold spindle]

do you know what you are supposed to do now?

[west swallow]

after 2x, it would be 2x-5

?

[untold spindle]

that would be correct, can i see your subtraction though?

[west swallow]

i could do this

[untold spindle]

lets stick with the method were already doing. you subtracted correct? may i see?

[west swallow]

hold up im doing it

[untold spindle]

!nosols

[tender quest]

As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.

[west swallow]

??

[untold spindle]

i was asking asferik to show me his work, not you.

[opaque mango]

@west swallow

That’s how u do it

Helping him out

[untold spindle]

your not helping him, your giving him the literal answer

i suggest you delete this so i can show him how to do it

@west swallow have you completed it yet?

[west swallow]

i got this

[untold spindle]

your top part is looking a lil werid, did you mean to put an x there next to the -5?

[west swallow]

yes 5x

[untold spindle]

how did you get 5x?

[west swallow]

cuz i have to match the -5x^2

@untold spindle

[untold spindle]

well how you would go about getting the next term at the top would be to divide the leading term of -5x^2-4x+0 by the leading term of the divisor, x^2+0x-4

so (-5x^2) / (x^2)

[west swallow]

nvm i got it

thanks

[untold spindle]

ok np :)

may i see what you got so i can double check?

[versed temple]

guys, one question. in those m+n.sin(a.x+b) functions, why does the b being positive deslocates the graphic to the left, and the b being negative deslocates the graphic to the right? wouldn't it be the opposite? in my head, the b being positive would have to deslocate the graphic to the right, since it is the positive side of the plane

m, n are integers

and n is obviously different than 0

[wispy forge]

I am beginning trig proofs next week and it looks intimidating. Any advice for me to be able to do this chapter without notes on the test? What things should I focus on remembering?

[uncut mulch]

pythagorean trig identities

that'll pretty much be part of 90% of those types of questions

[wispy forge]

Is there an easier way to condense this? lol

[uncut mulch]

not really

[wispy forge]

jesus

[uncut mulch]

first two sections are definitions

[wispy forge]

Don't take summer classes y'all

[uncut mulch]

3rd is pythag

4th is odd/even properties

5th is complementary properties

[wispy forge]

Well I'm sure I'll be in here a lot

[uncut mulch]

each individual section is quite similar

4,5 aren't that bad if you are familiar with properties of the unit circle

and then there's stuff like compound angle identities
and the most anoying are the stuff with prod to sum and sum to product

[wispy forge]

I am understanding the relations between each function better but the amount of time I have to do all of this is making my brain mush

[uncut mulch]

there's a more detailed list pinned in #geometry-and-trigonometry

[celest glade]

Don't have to remember sec x, csc x, and cot x on the 4th and 5th segment

Basically sec x is just 1/cos x, csc x being 1/sin x, and cot x being 1/tan x

The negative signs should also apply as how sin, cos, and tan applies there

The third segment is used a lot though (especially 1+ tan²x = sec² x) so it's worth remembering

[gaunt sand]

u doing synthetic division wrong g

btw

[spare pilot]

Hello, I am struggling with the third part of this math problem. Can someone help me?

I have solved part a and part b by equating 1000(t) = (4pir^3)/3

And used a similar method for c

[willow bear]

$\frac{4\pi r^3}{3} = 1000t$

[obsidian monolith]

Ann

[willow bear]

yeah that checks out

you can now take the derivative of both sides wrt t here, not forgetting the chain rule on the left

[spare pilot]

Can I solve part c without calculus?

[willow bear]

no of course you can't...

you're asked to find a rate of change

[spare pilot]

Okay, I was just worried because I haven't learned that yet

Thank you!

[wispy forge]

Ty for reaching out. I’m starting early today 🙂

[west walrus]

how to solve?

[summer ruin]

just compute each term?

[uncut mulch]

also not precalc

[dusty gale]

Yep that’s full blown calculus

[slim steppe]

You could factor out e^ax. So that would be e^ax * ( sin(bx) + cos(bx ), then use product rule

[west walrus]

Got it bro

[slim steppe]

I got a

[warm shell]

why does a quadratic function that is always greater than or equal 0 have at most one root?

[untold spindle]

do you mean the quadratic's discriminant?

[warm shell]

no I mean the quadratic itself

then afterwards it was conculded that the discriminant <= 0

[untold spindle]

sorry i dont rlly understand what you are asking, could you elaborate?

quadratics that only have one root take the form of (ax+b)^2 if that is what you mean. (a cannot be 0)

[warm shell]

<u+tv,u+tv> = <u,u> + 2t<u,v> + t^2<v,v>

<u+tv,u+tv> >= 0

<u+tv,u+tv> = <u,u> + 2t<u,v> + t^2<v,v> >= 0

then it was conculded there there was at most one root

then it was conculded that discriminant <= 0

[untold spindle]

ok, i think i see why i didn't understand this is a bit beyond my level, however i did some research and maybe this could help

https://math.stackexchange.com/questions/2077722/quadratic-equations-greater-than-zero-then-we-have-at-most-one-real-root

[whole cipher]

Can someone tell me what rule of exponent to use for this?

[untold spindle]

as in to continue or what rules of exponents were used in the work shown?

[whole cipher]

as in to continue

[untold spindle]

well start by subtracting .03 and .01

[whole cipher]

yeah so e^.02

[untold spindle]

do you know what logs are?

[whole cipher]

not really sure on how to apply log

[untold spindle]

actually wait where did the t go?

[whole cipher]

In 2000 the population of the United States was 280 million and the number of vehicles was 200 million. If the population of the United States was growing at 1% per year, while the number of vehicles was growing at the rate of 3% per year, in what year was there an average of one vehicle per person?
This is the context

This was my original answer

professor wanted it formatted in this picture and to solve using rules of exponenets

she has me lost

[untold spindle]

ok so 280e^(.01t)=200e^(.03t) is what the professor wants you to solve?

[whole cipher]

correct

[untold spindle]

ok, well first of all you didnt address my question

[whole cipher]

buddy i got no clue

[untold spindle]

ok well $\frac{e^{.03t}}{e^{.02t}}=e^{\left(.03t-.02t\right)}$

[obsidian monolith]

Judgemental Snail

[untold spindle]

not $\frac{e^{.03t}}{e^{.02t}}=e^{\left(.03-.02\right)}$

[obsidian monolith]

Judgemental Snail

[whole cipher]

so e^.01t?

[untold spindle]

oh no i mistyped mbmb

[whole cipher]

e^.02t?

[untold spindle]

should be .01

yep

[whole cipher]

so we are at 1.4=e^02t?

[untold spindle]

so e^.02t=1.4

yeah

now do you know how to apply logs in this?

[whole cipher]

unfortunately not

[untold spindle]

ok, well if i gave you the equation 2^x=8 how would you apply logs there?

[whole cipher]

is it just going to be ln(1.4)=ln(e^.02t)?

[untold spindle]

yep

what can you do to the rhs now?

[whole cipher]

rhs?

[untold spindle]

right hand side

[whole cipher]

take the e out?

[untold spindle]

do you know the power rule of logs?

[whole cipher]

no sir

[untold spindle]

,tex .log rules

[obsidian monolith]

Judgemental Snail

[whole cipher]

in this case we use ln because it has e in it right? and not log?

[untold spindle]

yeah

so apply the power rule and tell me what you get

[whole cipher]

t=16.82361183

[untold spindle]

sound about right

[whole cipher]

thanks man I appreciate it

[untold spindle]

no prob :)

[gaunt sand]

u can use ln even if it wasnt e

like 2^0.3t

[modest fox]

Just a quick clarification
in the cosine graph equation -7cos(4(x + π/8))
Is the phase shift a negative due to the negative on the 7cos?

[summer ruin]

it is negative because cos(x-pi) is positive shift and cos(x+pi) is negative shift

[modest fox]

ohh I didnt think to look at it like that, now i completely understand, thank you

[balmy lichen]

Sorry if this is the wrong area to ask this question, but is there another server with higher level math than pre-calc?

[untold spindle]

This server does have higher level math than precalc

Are you not able to see the channels?

[balmy lichen]

I had to change some settings. Thank you!

[untold spindle]

np

[edgy gyro]

BUT ITS A NEGATIVE SIGH FOR POSITIVE SHIFT AND ADDITIONAL SIGN FOR NEGATIVE SHIFT WTF

[gaunt sand]

its like that for a lot of functions

like parabolas

cubics

https://media.discordapp.net/attachments/556765194492182528/848213342374854716/tenor.gif

[warm hedge]

I think that's pretty intuitive tbh

you're not shifting the function, you're shifting the coordinate system

you're shifting x

[modest fox]

how is (0, 0) an x intercept of y=tan(x) on a unit circle if tanx here is 0/0, wouldnt that make it a vertical asymptote since it is undefined?

[summer ruin]

it isn't 0/0

tan(x) = sin(x)/cos(x), cos(0) = 1

[modest fox]

but what about the unit circle definition for tan=y/x , does that not apply in this type of problem?

[summer ruin]

that's exactly the unit circle definition

tan(x) is not y/x, it is sin(x)/cos(x)

[modest fox]

yes, but I thought that when you are speaking in terms of the unit circle, sin= y-coordinate and cos=x-coordinate
thats where i am getting stumped, am I jumping too quickly to assume that tan of the coordinate (0, 0) is 0/0?
am I missing a step or am I just trying to make the question easier than it is

[summer ruin]

you're trying to think that the tan(x)-x axis is exactly the same as sin(x)-cos(x) axis, which they aren't

the fact that cosine represents x-axis on the unit circle doesn't imply that you can treat regular x-axis as something that behaves the same way

since they're different axis that represent different things

[modest fox]

I see now, so I just jumped too quickly and looked at tan(x) and immidiately treated it like it was tan(θ)

[peak delta]

it can only be 2, 5, 1 and 4, 3, 1 if it's a degree of 8 right?

(x+2)^2(x-1)^5(x-4) and (x+2)^4(x-1)^3(x-4)

[indigo plaza]

should i take precalc(H) as a sophomore?

[timber saffron]

what does the (H) mean?

[timber saffron]

but also it depends on how comfortable you are with your earlier math classes. It is certainly doable, especially if you feel like you have a strong grasp on your algebra classes

[jolly sparrow]

Think of adding as making a function hit a zero or more positive point earlier and subtracting as making a function hit a zero or a more positive point later.

Then just extend that line of though to other functions n stuff.

[indigo plaza]

Honors

Thank you for your suggestion

[digital pendant]

Isn't this true for all functions? Like taking f(x+k) for k>0 will push all of the points of the function f(x) back horizontally k units?

[viscid thistle]

does anyone have a good resource for a pre-calc test?

[viscid thistle]

do you know what a linear, squared, and cubic function is and they must sum to 8 degree

they give u the x-intercepts and you check what type of functions they are and add the degrees and those are your multiplicities

[gaunt sand]

i think so, yeah

but then again im not an expert

😅

[void matrix]

someone please confirm $\frac{\sqrt{6}}{3}.$

[obsidian monolith]

FireBlazer

[twin cargo]

Hello everyone, I am looking for a student who knows English well (preferably native). I have a high level of mathematics and I want to learn how to teach lessons in English. I offer you free math lessons if you help me develop my English and teaching skills.

[timber spindle]

Anyone know of any good resources that has a good amount of practice problems for pre calc,trig and calc 1?

[dusty gale]

Khan academy

And it’s this app called practice tests @timber spindle

[viscid thistle]

hi

[dire aspen]

Sus

[solar olive]

when solving t^3 = 3pt + 2q,
t_1 = cbrt(q - sqrt(q^2 - p^3)) + cbrt(q + sqrt(q^2 - p^3))
t_2 = w cbrt(q - sqrt(q^2 - p^3)) + w^2 cbrt(q + sqrt(q^2 - p^3))
t_3 = w^2 cbrt(q - sqrt(q^2 - p^3)) + w cbrt(q + sqrt(q^2 - p^3))
where w = (-1 + i sqrt(3))/2

does anyone know where the w comes from though ?

[untold spindle]

dont troll

[mellow vigil]

10

[uncut mulch]

<@&268886789983436800> (check logs as well if needed)

[wispy forge]

Last test tomorrow then final next week. Hope I can squeeze in this passing grade.

Trig f-ed me up

[gilded spindle]

what tools are you given to solve this

[lucid trench]

hell yeaj

[storm lodge]

omg hi luca

[dusty gale]

I got a quiz and final exam this week

Trig for the final week

[wispy forge]

Good luck 🙂 I'm prepping rn. My final is on Tuesday

Anyone know of a good resource to generate practice tests so I can prep for my final?

[untold spindle]

What is your final going over?

[wispy forge]

Algebra and Trig

I have an exam prep sheet but it's quite small

[untold spindle]

Wolfram alphas problem generator could create algebra problems for you, but I don't think it can create trig ones.

Other than that you can try khan academy tests or Paul's online notes practice problems for trig

[wispy forge]

Thank you 🙂

[untold spindle]

Np :)

[vapid cipher]

(I didn’t know where to put this I’m sorry) I’ve finished up all of algebra 2 and most of trigonometry, and I’m ready to start doing some advanced probability, but the last time I tried to learn it back a few years ago I failed horribly. What’s a good place to easily learn the basics?

[untold spindle]

there is a #probability-statistics channel you can put this question in.

as for your question, you can always try khan academy and see how it suits you.

[vapid cipher]

I apologize for not seeing that sooner. Thank you!

[untold spindle]

no need to apologize, it was no problem

[vapid cipher]

Is there any other site than khan academy though?

(I’m entering 8th grade for context)

[untold spindle]

not that i know of.

[vapid cipher]

Oh well

Either way, thank you :D

[untold spindle]

np :)

[zinc owl]

Can someone help me with this?

[thorny heart]

byjus i think?

[summer ruin]

what do you know about tangents

[zinc owl]

A straight line

[summer ruin]

do you know the equation of a tangent line at a point?

[zinc owl]

y−f(a)=m(x−a)?

[summer ruin]

what's m here

[zinc owl]

1/2

[summer ruin]

no, in general

[zinc owl]

gradient

[summer ruin]

just write what that means mathematically gradient at N being equal to 1/2

[zinc owl]

1/2=(x-3)^1/2?

[summer ruin]

(x-3)^(1/2) is not the gradient of this function

[timber spindle]

How often do we use polar form or polar coordinates in Calc 1. When/what Calc level do we use them the most?

[void matrix]

hi lol

[void matrix]

uhh pencil and paper but i guess a graphing calculator like desmos or smth is allowed

[leaden flint]

I’m having trouble comprehending how to apply phase shift in graphing sinusoids functions. Im currently on the ‘Graphing sinusoidal functions: Phase shift’ area on Khan Academy. Could anyone please teach me how to do it?

[untold spindle]

First, find the midline, amplitude, and period.

@leaden flint

[leaden flint]

I’ve already found those

But I’m having trouble with the phase shift

[untold spindle]

How far is the maximum of this graph, (pi,6), from the maximum of cos(x)?

[leaden flint]

Not sure what you mean by that sorry

[untold spindle]

What is a maximum point of cos(x)?

Or actually, nvm. What is the point of cos(x) when x=0?

Actually this might be a bit confusing srry, I'm a bit bad at explaining sometimes.

Do you know generally what a phase shift is?

[leaden flint]

Ohh I see what you’re asking now

It’s alright

Phase shift is like a horizontal shift, correct?

[untold spindle]

Yeah

[short saddle]

https://physics.stackexchange.com/a/646129/222321 how did they get the exponential formula, why is it -x/4 rather than (2^-x)/4

[scenic coral]

the first one which I'm assuming you mean 2^(-x/4), you can notice that if you increase x by 4, it decreases the exponent by 1, which then means the exponential is halved every 4 fts, while second one you're suggesting is a constant multiple on the exponential equation which would halve every 1 ft instead of 4 fts

[short saddle]

@scenic coral give me more intuit for the second one

why exactly

[scenic coral]

Plug in 0 for x, you would assume that the initial starting is 1, but the second one yields 1/4 which simply does not work

[short saddle]

oh i see

[scenic coral]

Beyond that, I can't understand why this is confusing personally, so I cannot explain it very well

[short saddle]

so how would we generalise dis

[scenic coral]

there is a generalization for this

I'm just gonna use words bc variables seem, not descriptive enough
final = starting * (rate)^(something/interval)

[short saddle]

can i look this up on the internet

[scenic coral]

are you unable to?

[short saddle]

theres nothing on it

ty anway

[scenic coral]

I would recommend learning more about exponential functions, the general form of these functions are fairly easy to derive if you understand the theory

[short saddle]

its actually real good its fine

[short saddle]

how can i confirm i understood tho

that's the real qn

[leaden flint]

Sorry, I still don’t understand

[untold spindle]

hey are you still confused?

[leaden flint]

I know how to do it now but it's pure memorization

[untold spindle]

oh ok im glad to hear

[dapper estuary]

I don’t understand why that step is possible. Please explain the reason for that step. Thanks.

[wispy forge]

Precal final today

[wispy forge]

Do you know what a reference angle is?

So you are solving for the A angle in the left triangle (angle A that is obtuse) by subtracting 46.9 degrees from the flat portion (180 degrees).

The example graph on the left of your page just shows an example of what the triangle you’re solving for would look like on the unit circle.

It’d be less confusing if they didn’t have multiple angles with the same variable lol

[wispy forge]

I got a B on my finalllll

I hate Trig 😄

[scenic coral]

Awesome!

[dapper estuary]

Yes

Got it thanks

[viscid thistle]

me toooo

[timber spindle]

How often do we use polar form or polar coordinates in Calc 1. When/what Calc level do we use them the most?

[warm coral]

mostly in Calc 2

if you follow James Stewart calc series*

[timber spindle]

What do you think in your opinion I should really focus on in order pass pre calc and succeed at calc 1?

[warm coral]

I think most of the students hate the geometry part (trigonometry) rather than the algebraic one. Evaluate yourself and see in which part you are lacking.
Calc 1 is a different thing in a sense as it has many new topics like limits and their precise definitions and simple proofs, etc. Other than that, it's foundation is mostly pre-calc.

If you take my advice then don't just try to "pass" to avoid being failed at pre-calc, try to get above avg if you can because otherwise, Calc 1 will drain you out.

[dusty gale]

Got my final exam for pre calc

This one is make or break

[dusty gale]

As someone who is doing his final exam I would say to definitely study hard I took this course for 6 weeks so it was faster and I didn’t have time to fully concept everything but since you have time study study study and in my opinion trigonometry is the easiest just remember a lot of formulas and try to learn don’t just try to pass actually soak in what your teacher is telling you and do some independent studying on your own time as well and good luck pre calc was a journey

[timber spindle]

Are sequences and series and polar form/coordinates more of a calc 2 things/focus?

[void matrix]

i would say they're more of a intermediate algebra and precalculus topic respectively

[dusk fox]

Anyone know any good resource on pair of straight lines?

[neat spoke]

gravitional pull of the sun

[twilit marsh]

hi does anyone have any knowledge on al khayyams cubic solutions?

[vagrant forge]

I do

[twilit marsh]

Can you help explain it to me

[thorn creek]

i imagine they're in arabic, and a bit hard to translate

[mint forge]

Guys

Can someone teachme power of rule but like integral of n^m√x

Give me some formulas

For example i search the basic formula by integral of 2^2√x

[willow bear]

$2^2 \cdot \sqrt{x}$?

[obsidian monolith]

Ann

[willow bear]

@mint forge

[mint forge]

Yep

[willow bear]

... so just a constant times sqrt(x)?

[mint forge]

$m^n\cdot\sqrt{x}$?

[obsidian monolith]

Akmalkopling

[mint forge]

Yep

You right

[willow bear]

do you know the power rule for integrals in general

$\int x^p \dd{x} = \frac{x^{p+1}}{p+1} + C$

[obsidian monolith]

Ann

[mint forge]

I learned that today

Im grade 11 but highly nerd in calculus

[willow bear]

ok so you did learn the rule that i just posted, yes?

[mint forge]

Yep

[willow bear]

yeah, it still works with p = 1/2.

[mint forge]

Thank you for help

[smoky nexus]

Wait this is #precalculus No one does integrals in precalc

[radiant kite]

how would you solve cosx-1>sinx

ping me if you have an answer

[scenic coral]

cos x - 1 = sin x
cos x - sin x = 1
only happens at cos x = 1 or sin x = -1
(Idk a better way to determine that)
therefore x = 0+2πn, -π/2+2πn
If we sample an x within the interval, let's do x = -π/6, cos -π/6 = sqrt(2)/2 and sin -π/6 = -1/2 we can determine that over the interval, cos -1 is greater than sin

therefore we have the solution set
${(-π/2 + 2πn, 2πn), n\in \mathbb{Z} }$

@radiant kite

[obsidian monolith]

someone1010

[radiant kite]

i put cosx-1 greater than sinx

[scenic coral]

Did I make a mistake?

[radiant kite]

u put equals

[scenic coral]

to solve for intersections

[radiant kite]

im trying to solve an inequality

oh wait nvm

[scenic coral]

Intersections often help come up with bounds for intervals

[radiant kite]

okay thank you!

[storm lodge]

Better way to determine is by taking the trig functions on both sides and squaring

You get that one of them must be 0

as their multiplication ends up being 0

[scenic coral]

cos^2x - 2cos x - 1 = sin^2 x?

Oh wait just (cos x - 1)^2 = (sin x)^2

Nope don't get it

[viscid thistle]

cos^2(x)+1-2cos(x)=sin^2(x) -> 1-cos^2(x)=1+cos^2(x)-2cos(x)-> -cos^2(x)=cos^2(x)-2cos(x) -> 0=-2cos(x)=cos(x) x=kpi where k ∈Z

i think

wait not kpi

(1+k)pi/2

[scenic coral]

cos^2(x)+1-2cos(x)=sin^2(x)
1-cos^2(x)=1+cos^2(x)-2cos(x) (wtf)
-cos^2(x)=cos^2(x)-2cos(x) (how)
0=-2cos(x)=cos(x) x=kpi where k ∈Z (why are there 3 equals)

[viscid thistle]

bruh i messed up my math

well still u get the same result

wait no i didnt

wait i did

[viscid thistle]

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

then i subtracted 1

[scenic coral]

Ah gotucha

[viscid thistle]

also made a mistake x is (1+k)pi/2

[scenic coral]

doesn't check out ?

,w graph cos x - 1 = sin x

[obsidian monolith]

Results provided by WolframAlpha

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

Requested by someone1010

[viscid thistle]

?

wait

[scenic coral]

I don't understand how (1+k)π/2 can possible be correct

[viscid thistle]

on the graph the odd multiples of pi/2 seem to be equal

[scenic coral]

cos^2 x - cos x = 0

[viscid thistle]

but the even ones work too so mustve been wrong or theres just more answers

[scenic coral]

(cos x)(cos x - 1) = 0
this doesn't seem right

[viscid thistle]

or not all evens

[scenic coral]

Nvm that works
except it doesn't wtf

[viscid thistle]

ya cuz the squaring made it the absolute value of each

so whenever its 1 or 0 cosx-1=sinx

whenever cos is 0 or 1

whenever cos is 1, sin is 0, whenever cos is 0, cos is 1

wait tf why did i say that lol

whenever cos is 0, sin is +-1

forgot where i was going with this

well just graph it and ull find the intervals

lol

ah u can find it directly if u square it in the original

the intervals

[twilit marsh]

graph it

[small latch]

Anyone who have doubts in following topics
1 calculus
2 algebra
3 Cordinate geometry
4 vectors
5 trigonometry
6 stats and probability
Wheather related to assignment or tutoring can msg me

[sonic fiber]

Someone help plsplspls

[fleet fossil]

https://tenor.com/view/nick-eh-30-never-back-down-never-give-up-gif-15938629783250590873

[sonic fiber]

Help pls

[viscid thistle]

u still here?

for 5, if a function is concave up it kinda opens up and down if its concave down

use that for 6 aswell

and 7

i suppose just use that fact on all of em lol

also if an interval has a parenthesis at the end or beginning that means it does not include the number next to it and the opposite for brackets

[viscid thistle]

its its concave up it can still be decreasing and if its concave down it can still be increasing

[viscid thistle]

anyone here got a good video from algebra 2 to precalc

[warped cipher]

Khan academy

[viscid thistle]

I finished that

[warped cipher]

maybe if you just go to the yt and search for algebra 2 playlist

you can find some good videos like "The Organic Chemistry Tutor"

[viscid thistle]

Bet

[viscid thistle]

yea hes good

[radiant kite]

help

[lucid trench]

so when you see an inverse trigonometric expression, what can we assume?

in this case, what can we assume with cotangent

[solar olive]

arccot((1 - cos(x))/sin(x))

[solar olive]

when simplified, the radical inside turns into (1 + abs(cos(x)))/sin(x)

but since pi/2 < x < pi, its -cos(x)

anyways, (1 - cos(x))/sin(x) = tan(x/2)

so 1/cot(x/2)

so arccot(1/cot(x/2))

= arctan(cot(x/2))

[solar olive]

also

arctan(cot(x)) = mod(-x, pi) - pi/2

so uh

yeah

i wouldnt go as far as that though

but uh, the final answer is (pi - x)/2

[drowsy lantern]

hey

help karo

[timber spindle]

Is -1^0, -1 or +1?

[thorn creek]

no

x^0 is 1 for all x (except possibly 0)

[tough mango]

@thorn creek can u help me

[thorn creek]

probably not

[tough mango]

sad

[thorn creek]

cursed

[glacial flint]

so school starts in 2 days and I'm gunna be a juiner in math but I skipped from 7th grade math so this is a whole new thing for me any advice?

[stable shoal]

They let you skip ahead 4 years?

[glacial flint]

holy shoot that problem has triggered me for so long

[stable shoal]

wtf

[glacial flint]

I did it all on khan acady over 2 years but yea kinna

I did it by myself and told them so they let it count for all middle school classes

[glacial flint]

but like actualy how is this gunna go I know high school is a big deal

[versed ledge]

I actually had the same issue; I got homeschooled and the homeschooling program taught me practically nothing.

[glacial flint]

I know the math just I have no idea about how the school setting will work

[versed ledge]

I don't know the math that well, but I can learn it frankly easily, I'd hope and guess.

Knock on wood, though

[red crane]

Solve for Fa in terms of m, g, and theta. I cannot use T in my response. T sin(angle) =Fa and T cos(angle)=mg

[hallow lodge]

i need help with this

[spring stirrup]

No. x^x Goes to 1 when x Goes to 0. But 0^0 is undefined.

[spring stirrup]

(y+1)^2+(x+2)^2=10

Its equation of a circle

[hallow lodge]

my answer's the same ty bro

🔥

[hallow lodge]

wait is it actually?

isnt it a hyperbola?

opposite signs

[junior plover]

it is indeed a hyperbola

[junior plover]

incorrect equation

[hallow lodge]

mathway's answer is this

why is it over 2 rather than over 10?

[obsidian monolith]

Dissrupt

[junior plover]

do you agree with this?

just manipulated the original equation

[hallow lodge]

i just want the standard form of the equation

[junior plover]

do you agree with what i wrote?

can you write the original equation like that?

[hallow lodge]

no

arent we suppose to transpose it to the right

mb bro im not that smart

[junior plover]

i am asking is it correct? you can subtract and add the constant terms and check

it returns to the original one

i am trying to form perfect squares of y and x terms

[hallow lodge]

so whats the standard equation

[obsidian monolith]

Dissrupt

[hallow lodge]

@junior plover but doesnt the constant have to be exactly 1?

[summer ruin]

just divide by 2

[hallow lodge]

oh right

oh wait I get it now

ty

oh wait i dont

Why do they turn into negative?

@summer ruin

the b/2^2

[summer ruin]

because of this

[hallow lodge]

i think i get it now

oh yeah i def get it now

I didnt realize the x was a negative

how to get the standard form of this?

[summer ruin]

it's the same procedure as always

complete the square

[hallow lodge]

how do u do it with fractions

[summer ruin]

same as with any other numbers?

or just get rid of fractions

[solar olive]

what if uh. expand (ax-b)^2 + (py-q)^2 = r^2 and compare coefficient to get a b p q r

a^2x^2 - 2 a b x + b^2 + p^2 y^2 - 2 p q y + q^2 - r^ 2 = 0
a= 1/2
p=sqrt(3/2)

-1/2 = -2ab
-1/2 = -2(1/2) b
b = 1/2

-3 = -2pq
3 = 2 sqrt (3/2) q
3 = sqrt (6) q
3/sqrt(6) = q

3/4= b^2 + q^2 - r^2
3/4 = 1/4+9/6-r^2

[summer ruin]

seems like a lot of work for such a simple problem

[spring stirrup]

Oh then sorry I tried to solve it in like 10 seconds, bc no paper

[junior plover]

np, happens

[spring stirrup]

When you consider function 0^x it seems that 0^0 should be 0, if you consider x^0 it seems that 0^0 should be 1, so its undefined

[scenic coral]

0^0 is undefined

Unless it's useful for it to be defined

context dependent

[alpine bramble]

need help

[alpine bramble]

i need equation for the function

[thorn creek]

the singularity tells you where the denominator is zero so you can set the denominator to zero at the pole and solve for the parameters in the denominator (c and d)

once you have the denominator, you can use the spots where the graph crosses the x and y axes to solve for the other two parameters (a and b)

[dry sparrow]

can somebody help me with ths? ive been on it for 1.5 hrs now it may be easier than i thought but to me this is drivng me crazy

need help

[summer ruin]

what part

[topaz haven]

If a polynomial has an even degree function, must the symmetry also be even, or can an even degree function also have odd symmetry?

[summer crag]

It may not be either as well

4x^4 + 3x^3 for instance is neither even nor odd

But yeah it cannot be odd

[thorn creek]

there are functions that are both eeven and odd

polynomial functions, even

[summer crag]

Example ?

[thorn creek]

f(x) = 0

[summer crag]

Ohh yeah

Is that the only function though ?

[thorn creek]

only continuous function

i won't guarantee that aren't noncontinuous functions that are both odd and even. i don't know of any but i also don't know of any proof that there aren't

it's fairly easy to prove that there is only one polynomial funciton that is both even and odd, and that functioni s the constant zero function

[summer crag]

cosntant function ?

[thorn creek]

f(x) = 1 is even but not odd

because to be odd f(-x) = -f(x) and that's not true for f(x) = 1

[summer crag]

Yeah

[thorn creek]

nor can it be true for any constant function other than the zero function

so yes, it is possible for a function to be both even and odd

odd polynomails will always have a root at 0

this means that (x-0) will always be a factor, which itselff means that the constant term of every odd polynomial is zero

[autumn quarry]

hey guys, im in my senior year and i need to do a summer assigment before i enter the my pre cal class and i have a test on the first day, what do u guys recommend i do to learn