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[vapid steppe]

g=function of x

[safe tartan]

ah

[vapid steppe]

and a and b are also functions

.close

[lone heart]

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[cinder sundial]

Do N and N’ have same magnitude

[ocean whale]

Angles are different so no

[hidden pier]

it shouldn't because the pull of gravity that is causing that normal force is different in each case

[cinder sundial]

I would like to explain that greater inclination would have greater centripetal force

[ocean whale]

Why is centripetal force coming into play? It's not moving in a circular motion, it's on an incline

[cinder sundial]

That’s one of my favorite, the sushi

[hidden pier]

what

[cinder sundial]

It is like a nascar race but in section

[cinder sundial]

Your avatar

Should I call it “nigiri”

[hidden pier]

oh ty

[cinder sundial]

I suppose these two terms have different meanings

[hidden pier]

but it's only moving down

there's no rotation here anywhere is there?

[cinder sundial]

There is, imagine a circular track

That we often see in nascar races

And the picture depicts the track in section

[hidden pier]

if i take a triangular block right now and slide my keys down its side is there centripetal force?

i dont see like a force arrow suggesting that this is like nascar

[cinder sundial]

Sorry

I should explain the picture at the beginning

But the triangular block is the track in section

[hidden pier]

what is the "track in section"

[cinder sundial]

That’s my fingers

[hidden pier]

yea

[cinder sundial]

If you cut them “in section”

They all forms a shape of circle

[hidden pier]

oh right

a cross section

[cinder sundial]

That is my finger in section

[cinder sundial]

Yes exactly

[hidden pier]

so like of this

[ocean whale]

Is everything the same in both cases, only the angle changes?

[cinder sundial]

Yes

[cinder sundial]

Yes

[ocean whale]

Like friction is the same?

[cinder sundial]

Yes

[hidden pier]

surely you wouldn't tell me that this also has N'' equal right?

if angle truly doesn't matter

[ocean whale]

@hidden pier The argument btw

[hidden pier]

oh whoops i didnt see that

i just saw N and N' having the same magnitude mb

[cinder sundial]

It is kinda hard to explain the phenomenon, if the relations between forces in the scenario remain unknown

[hidden pier]

to prove that you can't just have force arrows of gravity and normal force, you need the force arrow that's created by centripetal force don't you?

the rotational movement generates a force against the track

[cinder sundial]

I thought N_x and (N_x)’ are the centripetal forces?

<@&286206848099549185>

[lone heart]

@cinder sundial Has your question been resolved?

[lone heart]

@cinder sundial Has your question been resolved?

[lone heart]

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[humble oak]

Can someone check my sketch of B

I am just not sure because the absolute values are throwing me off

[lone heart]

@humble oak Has your question been resolved?

[noble bear]

wth is this broski 😭

looks complicated asf

although im 16

[lone heart]

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[signal talon]

Hi I’m working on an assignment for homework and I am stuck. I’m in college trigonometry and I don’t know how to figure out how to do the tables. Attached are the pictures I have of the notes from class, and the picture of the homework problem website

[lone heart]

@signal talon Has your question been resolved?

[lone heart]

@signal talon Has your question been resolved?

[lone heart]

@signal talon Has your question been resolved?

[hushed locust]

i would look at the definition of an odd and even function

[signal talon]

I get how it works when I’m given a parent function I just don’t know what to do for a table of points

Like if I did f(2) = 8, is f(-2) = -8? But that doesn’t make sense how it’s even if it’s just being reflected/multiplied by -1

[hushed locust]

if f(x) is odd then f(-x) = -f(x)

[signal talon]

Wait so this is just describing odd not even

?

if it was even I would get 8 not -8 then right

[hushed locust]

well if you know that f(x) is even, then f(-x) = f(x) by the definition, and that applies for all x: f(-5) = f(5) for example

[signal talon]

So all negatives become positives ?

I mean all negative x’s

Because the f of x will be the same if it’s negative or not

[hushed locust]

well for example if you know f(6) then f(-6) must be equal to that

[signal talon]

You are confusing me. Is what I am saying correct or incorrect

[signal talon]

Wait so since the table gives me f(2) = 8 for example, that means f(-2) will also = 8?

[hushed locust]

yes, because f(-2) = f(2)

[signal talon]

Okay I think I get it now

Thanks

[orchid zenith]

*3(xy)*67)=/xy/*2/3

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@signal talon Has your question been resolved?

[lone heart]

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[finite turtle]

n^2+n<=2

[finite turtle]

n^2+n-2>=0

(n+2)(n-1)>=0

[quasi vector]

why did the inequality sign change?

[finite turtle]

why u think i came here 🙂

idk

[charred jewel]

you only change the inequality sign if you're multiplying or dividing a negative

it doesnt change with addition and subtraction

[finite turtle]

can u just solve for n for me n^2+n<=2 im rly confused

i mean ik the awnser is [-2,1]

but how do i get there

[charred jewel]

did you think the inequality sign should change here

[quasi vector]

!nosols

[lone heart]

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.

[solar storm]

yes this. When adding or subtracting both sides of the inequality, the direction doesn't change. It only does when multiplying/dividing a negative.

[finite turtle]

i mean i believe this is 9th grade math and im just trying to understand it (im 8th grade)

so u cannot change the > thing right?

from > to <

[solar storm]

yes. Only change direction if multiplying or dividing negatives.

let's say we have 4 > 2, if you transpose 2 to the opposite side it becomes 4 - 2 > 0, which is 2 > 0. It wouldn't make sense if 2 < 0.

[finite turtle]

alr ty

so i got (n+2)(n-1)<=0/ n+2=0 > n=-2/n-1=0 > n=1 => n=[-2,1] n(is in sign like an euro yk dont have it at keyboard)Z

is this good?

wait no

now is it good?

[charred jewel]

yeah

[lone heart]

@finite turtle Has your question been resolved?

[lone heart]

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[peak bramble]

can anyone help me with b)?

[lone heart]

@peak bramble Has your question been resolved?

[lone heart]

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[tender anchor]

I did 500 * sin130deg/sin120deg and got 447.27 where am i going wrong?

[lone heart]

@tender anchor Has your question been resolved?

[cloud nacelle]

sin130 / sin120?

[lone heart]

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[tender anchor]

.reopen

[lone heart]

✅

[lone heart]

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[grave verge]

5x-4/6 = 4x+1- 3x+10/2

[dire yacht]

ЬИ

[coral thorn]

!status

[lone heart]

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

[dire yacht]

.reopen

[grave verge]

Idk anything abt it

I just know variable gonna end up to lhs rest rhs

[dire yacht]

create

[grave verge]

1

[dire yacht]

3

[grave verge]

I know the answer tho

[vale wigeon]

ты сюда спамить пришел или что?

[grave verge]

Just don't know solution

[vale wigeon]

so you know nothing at all about solving linear equations in one variable?

[grave verge]

I get confused in variables

[vale wigeon]

btw there's a separate issue

you typed the original equation badly

it is impossible to tell what is supposed to go in the fractions and what isn't

can you write the equation on paper and send us a photo

[grave verge]

I mean fraction, i get confused in fraction

Sorry am lagging that's why slow responses

[vale wigeon]

can you write the equation on paper and send us a photo

[grave verge]

The weird looking thing is x

[vale wigeon]

why write this weird looking thing and not x then

anyway ok

(5x-4)/6 = 4x+1 - (3x+10)/2

is how you should write that in plain text

[grave verge]

Ooo ok

[vale wigeon]

so ok

we need to see how much you know

[grave verge]

Can I devived the /6 and -4 with 2 (in the lhs)

[vale wigeon]

...

idk what exactly you're going for, but probably not.

you said you got confused with the fractions

so how about i give you an equation with similar structure but which doesn't have any fractions,
and you try to do it and show us your working?

[grave verge]

Sure

[vale wigeon]

ok right

7x+1 = -23x-11 + 8x

no

this smells like bullshit

[grave verge]

7x+23x-8x = 30+4

[vale wigeon]

idk like, you just threw two terms out the window lol

[grave verge]

22x = 34

x = 34/22

I won't slove more further

17/11

[vale wigeon]

you cannot just ignore those...

[vale wigeon]

how did 30+4 happen?

augh internet lag

ok well you did something even i can't follow so im gonna say this is not gonna be helpful for op.

FUCK WHY ARE MY MESSAGES NOT SENDING AGAIN

FINALLY

@grave verge how did 30+4 happen?

it sounds like you imagined some numbers in my equation which were not there

or maybe mixing my example and the original

[grave verge]

What did I do

Ye I mixed

Amma do whole again

[vale wigeon]

WELL DON'T MIX

@atomic stratus sorry you are just kinda getting in the way here

[grave verge]

7x +23x -8x = -11-1

22x = -12?

[vale wigeon]

im not

im trying to see what he can do

with a different example equation

which doesn't contain the thing op says confuses him

[grave verge]

Just solve the question for me so I can go rest tbh (I am requesting but idk how to make the sentence sound kind)

[vale wigeon]

and THEN ill explain to him how to tackle that

[vale wigeon]

!noans

[lone heart]

The purpose of this server is to help you learn, not to hand out answers. Do not ask someone to give you the answer directly.

[grave verge]

Oh I see

Sorry

[vale wigeon]

ok yeah that sounds right

aight

so you know your way around those

now let's come back to the original

(5x-4)/6 = 4x+1 - (3x+10)/2

[grave verge]

I don't understand what to do with fractions

[vale wigeon]

and i was about to type something to tell you just that.

[grave verge]

Do they get reciprocal? The denominator gets multiplied or what

[vale wigeon]

your best first move here will be to multiply both sides of the equation by a number. of course not any number will help you.

you want to choose the number so that it will cancel out all the denominators when you multiply through by it.

[grave verge]

2

[vale wigeon]

in other words you want a common multiple (not necessarily the LCM, but it is nice if you do the LCM) of all denominators involved

[grave verge]

2 will cancel all of them out, kaboom

[vale wigeon]

in your case the denominators are 6 and 2 so you will want 6.

[vale wigeon]

no.

2 won't cancel out 6.

[grave verge]

Oh lcm I thought hcf

Than 6

[vale wigeon]

when you multiply both sides by 6, you get:

[grave verge]

Then*

1 and 4

I mean 3

1 and 3

[vale wigeon]

5x - 4 = 6(4x+1) - 3(3x+10)

do you understand how this happened or should i write it in more detail

[grave verge]

Where did the /2 go

[vale wigeon]

ok let me write this in more detail then

one moment

im on my phone so i might take a couple minutes...

[grave verge]

Alr no worries

I hope I remember this stuff till my finals (I have short term memory)

[vale wigeon]

$\frac{5x-4}{6}=4x+1-\frac{3x+10}{2} \ \ 6\cdot \frac{5x-4}{6}=6\paren{4x+1-\frac{3x+10}{2}} \ \ \frac{6(5x-4)}{6}=6(4x+1)-\frac{6(3x+10)}{2} \ \ 5x-4 = 6(4x+1) - 3(3x+10)$

one moment

[ocean seal]

Ann

[vale wigeon]

here

[grave verge]

Why are there 3, 6

Three sixes

3 sixes*

[vale wigeon]

do you think the presence of 3 sixes is bad somehow

i multiplied both sides by 6

then fucked around with the right hand side

distributive law etc

[grave verge]

Will it be rude if I say ill ask my teacher tomorrow

[vale wigeon]

as you wish lmao

[grave verge]

I am sorry :(

[vale wigeon]

there are far ruder ways to say i was not helpful

you're fine

[grave verge]

It's just am dumb

.close ty for your time I am really sorry

[lone heart]

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[brisk fossil]

Not really. Where is the unknown variable? This is an identity because it's a true statement (38 and 14 have the same remainder when you divide them by 12).

Yes, something like that is an equation in a particular ring (Z_420) or, just, a linear congruence.

[ruby current]

a congruence?

[brisk fossil]

But it is already solved, so it not that useful anyway

Like just x=69?

I don't think that's a congruence.

[ruby current]

incongruence maybe? not sure it has a name

it’s the negation of a congruence

[cinder tundra]

≢ is to declare there is not congruence, incongruence is correct

[lone heart]

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[surreal sky]

For the integers a and b, b ≡ a (mod 91) and gcd(a, 91) = 1.

(a) Show that gcd(b, 91) = 1.
(b) Determine a positive number k > 1 such that b^k ≡ a (mod 91).
(c) Determine a^k mod 91 if b = 153.

a) b ≡ a (mod 91) ⇒ 91|b-a expressed b-a = 91k
If we have a number d such that d|b, d|91 ⇒ d|b-a
And now since d|b, d|b-a ⇒ d|a
From this we know d|91, d|a which means that d = gcd(91,a) = 1
Finally, this means that gcd(91,b) = 1

b) Euler's theorem reads mϕ(n) ≡ 1 (mod n) which means that bϕ(91) ≡ 1 (mod 91)
ϕ(91) = ϕ(7 x 13) = (7-1)(13-1) = 72 ← theorem
We now know that b^72 ≡ 1 (mod 91)
We can now multiply b^72 ≡ 1 (mod 91) by a and get
a x b^72 ≡ a (mod 91) ⇔ b^73 ≡ a (mod 91) ← b ≡ a mod (mod 91)
Answer: k = 73

c) b ≡ a (mod 91) ⇔ a ≡ 153 (mod 91) ⇔ a^73 ≡ 153 mod (mod 91) ⇔
a^73^72 ≡ 15372 (mod 91) ⇔ a^72^73 ≡ 1 (mod 91) ⇔ 1^73 ≡ 1 (mod 91)

I am stuck at c, I tried playing around with the numbers but I get 1 ≡ 1 what can i do?

[mortal trellis]

well the basic point of congruence is that a and b are the same thing

so if b^k is a, then a^k is what?

[surreal sky]

so a^73 ≡ 1???

[mortal trellis]

no

[surreal sky]

a ≡ 1?

[mortal trellis]

no a is congruent to b. and b is 153

[surreal sky]

ah so a ≡ 153 too

so 153^73 ≡ 153^73 (mod 91)?

I am confused..

[mortal trellis]

b^k=a. so 153^73=153

where I am too lazy to type congruences and mod

[surreal sky]

Im dumb

I think I get it

therefore answer is simply what you wrote 153^73=153

?

[mortal trellis]

yes

[lone heart]

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[rich walrus]

As precisely as possible, sketch the set of points z ∈ C that satisfy the condition:

[livid sage]

i'd let z = x + yi here

[rich walrus]

yeah I did and then what

[livid sage]

expand and simplify everything

[rich walrus]

you get x^2 +4xy = 8y

[livid sage]

that's right

[rich walrus]

so how do I draw it

[livid sage]

i'd probably solve for y

[rich walrus]

y = x^2/8-4x ?

[livid sage]

yeah

visualizing what that graph looks like now should be easier since it's a rational function

if that's not sufficient, i guess you could make it even easier by doing polynomial division

[rich walrus]

oh okay

yeah sorry my teacher made it all super hard he said the (1-4i) is a rotation and then he used some polar coordinates and removed mixed terms and idk

[livid sage]

lmao

that's funny

[rich walrus]

i suppose it is yeah

thank you

.close

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[smoky vapor]

So I am unsure about my solution to one of the exercises I did. The hint said to use Taylor expansion which I did but I am not sure if i can just simply say "since h approaches 0 all terms with it will equal 0 which means ... = 0". Additionally I would like to know where are my possible mistakes and would like to get a hint how to correct them if possible :)

[brisk fossil]

Do you know little o notation?

[smoky vapor]

You mean in the Taylor expansion? I saw some examples with something similar to O instead of ...

Is this what You meant? That is other example I saw

oh it dissapeard i was trying to understand it haha sorry for late reply

[brisk fossil]

This is just a deitail

I think the main reasoning is correct though

[smoky vapor]

Ah ok so I should just explain it better but otherwise the solution looks correct?

[keen wharf]

hi im new and i have a question so when a twine has a strength of 4 tex, which means 1 km of this thread weighs 4 grams. Calculate the diameter of the thread in mm if the material density is 1.44 g / 2 square centimeters?

[brisk fossil]

The problem is that I don't remember which of the two forms of the Taylor theorem (in Italy, I know the version with Peano's remainder and the other with Lagrange's remainder) I should use because the problem is that f is 3 times differentiable and not 4.

@keen wharf you should ask the question in one of the free channels

[keen wharf]

ok

[smoky vapor]

Oh hi sorry but I am already using this channel to answer my question. You should ask your question in one of the empty ones (no username after help- number) you can also read #❓how-to-get-help

[smoky vapor]

oh ok I just started learning about it so unfortunately I am unsure

[brisk fossil]

But, as I said, it is just a detail (I was not convinced about the dots after the third derivative)

I am sorry for that, it's just me being a "mathematician"😅

[smoky vapor]

Ok thank you so much for the help! I will try to maybe use O notation instead of ... for clarity. I just wanted to be sure my main reasoning and solution is correct. I dont want to loose too many points

[brisk fossil]

Check the O and o notations

The main reasoning should be correct

[smoky vapor]

Will do! Thank You so much again have a great day/night

will close the channel now

.close

[lone heart]

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[chrome vortex]

,rotate

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[chrome vortex]

.close

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[thorn patio]

hello

[thorn patio]

can someone help me explain why this certain case happens

When divided by 4, every number has remainder either 0, 1, 2, or 3, in other
words every number can be written as 4m + r for some integer m where r
is 0, 1, 2, or 3.

i cant find out why but when r = 3

you cant write any of those numbers as a sum of 2 squares

like x^2 + y^2 = n

if n = 4m + 3 for any m there isnt any way you can write them as a sum of 2 squares

[rose sigil]

what remainders could x^2 leave when divided by 4?

[cinder tundra]

All of them

Which one? I will give counter example

[rose sigil]

3

give me one for 2 while you're at it

[cinder tundra]

Oh sorry my brain collapsed and I thought 49-3 is 44

@
Lol

I retire my word

[lone heart]

@thorn patio Has your question been resolved?

[thorn patio]

0,1,2,3?

[rose sigil]

consider each case where x is 0, 1, 2 or 3 mod 4. what is x^2 mod 4 in each case?

[safe arrow]

x^2 will always be even

[thorn patio]

if x is 0 mod 4 then

[safe arrow]

x is an integer right

[thorn patio]

yeah

[safe arrow]

wait I just realized x^2 is not always even im silly

[thorn patio]

0 mod 4 means just multiple of 4?

[safe arrow]

yes

[thorn patio]

ok so

[thorn patio]

what do you mean by what is x^2 mod 4 in each case?

[rose sigil]

by x^2 mod 4 i meant the remainder x^2 leaves when divided by 4

[thorn patio]

could it not be any of them/

oh ive checked all cases sorry

say n = 4

or 8/12/16 etc

those are cases where its 0 mod 4?

oh no that is for n

[thorn patio]

but either way since any number can be written as 4m + r for some integer m, where r is 0,1,2,3

<@&286206848099549185>

[slate vortex]

Because $n^2 \equiv 0, 1 \pmod 4 \forall n \in \mathbb{Z}$

[ocean seal]

Ari

[slate vortex]

and you can't add those to 3

[thorn patio]

how is n^2 congruent to that

[slate vortex]

Just test it

1^2 = 1
2^2 =2
3^2 = 9
4^2 = 16

all are either 0 or 1 mod 4

[thorn patio]

how is that relevant though

[rose sigil]

.

[thorn patio]

oh so

for x^2 and y^2

for all numbers

[slate vortex]

You said
like x^2 + y^2 = n
if n = 4m + 3 for any m there isnt any way you can write them as a sum of 2 squares
I'm telling, x^2 and y^2 are both either 0 or 1, so they won't add to 3 ever

[thorn patio]

yeah

is that something i should just know?

[thorn patio]

like this rule

[slate vortex]

No but you can do what @rose sigil did and derive it

[rose sigil]

yea for small moduli it’s easy to just exhaust all cases

[thorn patio]

the considering each case?

oh

ohhh so when x is 0 mod 4 then x^2 would also be 0 mod 4?

[rose sigil]

the possible remainders squares can take are called quadratic residues

if you wanna look into it more

[thorn patio]

alright

thank you for your help

👍

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[limpid turret]

Post a screenshot. We don't follow links'

!noans

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The purpose of this server is to help you learn, not to hand out answers. Do not ask someone to give you the answer directly.

[limpid turret]

!nogpt

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Please do not trust ChatGPT or similar AI tools for mathematical tasks, as they often generate output which "sounds correct" but has numerous factual or logical errors. Use of these AI tools to answer other people's help questions is strictly against server rules (see #rules).

[limpid turret]

Then it's time to learn it

what is this a test?

Your 2 hours is probably better spent just doing the work.

Plus, cheating even on an evaluation is bad karma

[covert shuttle]

asking for answers is cheating

goodbye

[worn fox]

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[dull phoenix]

how do you derive Ae^x ?

[dull phoenix]

the derivate e^x is e^x

and e^kx is ke^kx

but what about Ae^x ?

[last spire]

so Ae^x

[rocky atlas]

If A is constant

Otherwise product rule

[dull phoenix]

right I got it

thanks

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[primal galleon]

How to solve this [\lim _{x \rightarrow \infty} \frac{x-\sin x}{x}]

[ocean seal]

dgh

[primal galleon]

This is my solution: To solve the limit (\lim_{x \to \infty} \frac{x - \sin x}{x}), you can simplify the expression by dividing both the numerator and the denominator by (x):

[
\lim_{x \to \infty} \frac{x - \sin x}{x} = \lim_{x \to \infty} \frac{\frac{x}{x} - \frac{\sin x}{x}}{1}
]

Simplify further:

[
= \lim_{x \to \infty} \frac{1 - \frac{\sin x}{x}}{1}
]

Now, as (x) approaches infinity, the term (\frac{\sin x}{x}) approaches 0. Therefore:

[
= \frac{1 - 0}{1} = 1
]

So, (\lim_{x \to \infty} \frac{x - \sin x}{x} = 1).

[ocean seal]

dgh

[primal galleon]

Correct?

[gritty wave]

yes, you'd get the same result if u split the fraction up as x/x - sinx/x instead of dividing by x

[last spire]

Yes

[last spire]

It doesn’t matter

[gritty wave]

thats what i said

[primal galleon]

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[fair dome]

How do I get the equation of this ellipse, that doesn't comprehend the part I signaled in red?

[slender gull]

so the entire ellipse would have been (x/a)^2 + (y/b)^2 = 1
Rewrite y in terms of x and remember you only want negative y outputs.

[fair dome]

Done

What do i have to do now

?

[slender gull]

That's it.

What did you get?

[fair dome]

x^2/16 + y^2/4 = 1

[slender gull]

I just said y in terms of x...

You didn't even do that.

[fair dome]

Oof

Ye im dumb

y = ( sqrt(16-x^2) )/2

Is it right?

[slender gull]

Yeah.

[fair dome]

If I wanted to calculate the part that is signed in red

Wait

[fair dome]

theres a - sign at the begininng

Its wrong

Its just +

[slender gull]

no.

- sign was right.

Now it's wrong without that.

Because y is meant to be =< 0

[fair dome]

No

I want to take the part of the ellipse without the red

[slender gull]

Oh you said NOT the red.

I thought only red.

[fair dome]

So if i wanted to take the red part I would have had just to add the -?

[slender gull]

Yeah.

That's right.

[fair dome]

Alr

Thx a lot man

Thought it was harder but it was just that

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[grand parcel]

how to solve this?

[grand parcel]

the term can be written as

[sour verge]

I think you can rewrite it as $\frac{k+1}{(k+2)!}$

[ocean seal]

Azyrashacorki

[sour verge]

And this can be split

[grand parcel]

how can be split?

[grand parcel]

i had found out this

and now im struggling with the factorial

[sour verge]

write the numerator as $k+2 - 1$

[ocean seal]

Azyrashacorki

[sour verge]

Then split into two fractions on the minus sign

[grand parcel]

i got it

it should work out the solution

[sour verge]

It should telescope I think

[grand parcel]

the limit is 1/2

[grand parcel]

yes it does 1/(k+1)! - 1/(k+2)!

sum is 1/2-1/(n+2)! which approaches 1/2 as n approaches inf

ty

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[sharp moth]

Would apperciate if someone could double check this for me. I think it's 2/0 but that limit doesn't really make sense.

[hushed locust]

find the directions of f(x) and g(x) individually, then find the quotient

make sure it's f(x) [red] / g(x) [blue]

[sharp moth]

is 2/0 correct?

[hushed locust]

no

[sharp moth]

at x = 1 f(x) approaches 2 from the right

[hushed locust]

the limit is towards 0

[sharp moth]

Sorry that's the wrong question

[sharp moth]

This is the limit I am concerned with

[hushed locust]

ok so as g(x) approaches 0, it gets very very small. when we divide by very small numbers, we get very large numbers, e.g. 2/0.00001 = 200 000
So the rule with limits where the denominator (but not the numerator) approaches 0 is that they get arbitrarily large; they don't approach any individual number but we sometimes call "getting very large" in a limit "approaching infinity"

the question is then, what's the sign, since a limit of that form can have approach very large values that are either positive or negative, depending on the sign of the functions on the side you're approching from

[lone heart]

@sharp moth Has your question been resolved?

[sharp moth]

And you would know by graphing the function and determining that graphically, if it is increasing from the left to right it is positive infinity?

[hushed locust]

if both f(x) and g(x) are simultaneously positive or simultaneously negative their quotient must always be positive. but if one is positive and one is negative then their quotient is negative

[sharp moth]

You mean by evaluating them individually, if either of them are the same sign they are positive if different than the infinity sign is negative?

Getting the value for each function after breaking them down into individual limits

[hushed locust]

well if g(x) is approaching 0 then the limit is 0 regardless of whether g is positive or negative

but whether g is positive or negative (i.e. approaches 0 from above or below) would change the sign of the limit

[sharp moth]

Only applicable to the scenario where the denominator is zero after evaluating the two functions limits individually then doing the calculation? Or is it easier with the graph, where you can tell if it’s positive or negative infinity by looking at the slope of the line and seeing if it’s going up or down on the coordinate plane?

[hushed locust]

if you have a limit of the form
f(x)/g(x) where g(x) is approaching 0 and f(x) is not, then that limit approaches either +infinity or -infinity. the sign of the limit must be determined by the sign of the functions (i.e., whether the functions are positive or negative) in the region of interest

the slopes are irrelevant

[sharp moth]

They are both positive so I believe this is positive infinity.

[hushed locust]

that's correct

later you'll need to watch out for situations where g(x) goes from positive on one side to negative on the other, since that would mean the directional limits are different

[sharp moth]

Okay, thank you so much for your help.

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[maiden swift]

Prove

[native cloud]

!status

[lone heart]

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

[maiden swift]

I don't know where to begin

x/2 is throwing me off

and idk what to do with that

[rocky atlas]

Convert all terms to sin and cos...

And use sin2x=2sinxcosx

[maiden swift]

where'd u get sin2x from

[rocky atlas]

Oh you don't know this formula

[maiden swift]

i do

[rocky atlas]

Just further simplify LHS

[maiden swift]

LHS?

[rocky atlas]

Use sinx=2sin(x/2)cos(x/2)

Left hand side

Left side of equation

[waxen flame]

$\sin(x) = \sin{\left(\frac{x}{2} + \frac{x}{2}\right)}$

[rocky atlas]

$$\sin(x) = \sin{\left(\frac{x}{2} + \frac{x}{2}\right)}$$

[ocean seal]

Calamity

[maiden swift]

im so confused rn

ok so sin x

why did u use the sin 2x rule

[rocky atlas]

To prove this type of equation

[maiden swift]

u can do that?

i thought it had to be exactly sin 2x

[rocky atlas]

I used to convert every terms to sin or cos

[waxen flame]

It's the type of hand wavy magic that is often seen in math proofs.

[rocky atlas]

It's necessary for there to be common angle

[maiden swift]

ok when i started off

this is what i did

[rocky atlas]

Why sec^2

[rocky atlas]

1/cos^2(x/2)

Which cancels with the cos term in numerator which you will see

[maiden swift]

$$1/cos^2(x/2)$$

[ocean seal]

Clutch

[rocky atlas]

You're ultimately getting 2sinx/2cosx/2

[maiden swift]

ok so it only cancels out one of the numerator

[rocky atlas]

Yes

[maiden swift]

so the way i did it was correct right

[maiden swift]

would it be written like this

which would then lead to 2sinx/2*cosx/2

OKKKK i got it

[lone heart]

@maiden swift Has your question been resolved?

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[jolly plaza]

Don't understands part B

[unkempt mica]

did you do part a?

[jolly plaza]

Yes

a1 = 1/4

a2 = 1/4

a3 = 1

these were my answers

[unkempt mica]

cool

try to look further (a_4, a_5, a_6, ...) and see if you can find a pattern

[jolly plaza]

yes

theyre similar

a4= 1/4

a5 =1/4

a6 = 1

so multiples of 3 are = 1

[unkempt mica]

yes they are the same

yes

3k+1 and 3k+2 is 1/4

[jolly plaza]

okay

why is that important tho

[unkempt mica]

because you want to sum those

from 1 to 50

how many multiples of 3 do you have from 1 to 50 ?

[jolly plaza]

dont you just do

50/2 . (2+49)

for that?

you get 1275

[unkempt mica]

what are you doing?

oh

[jolly plaza]

I forgot the name of this

[unkempt mica]

thats for the sum of n from 1 to 50

[unkempt mica]

sum of an arithmetic progression

thats good

[jolly plaza]

there we go

yep

[unkempt mica]

because you can split the sum

so you have $\sum_{n=1}^{50} n + \sum_{n=1}^{50} \cos^2 \left( \frac{n \pi}{3} \right)$

[jolly plaza]

oh

[ocean seal]

LF

[unkempt mica]

the left sum is 50x51/2

thats ok

but for the second sum you need the pattern you just found

it will be 1/4 + 1/4 + 1 + 1/4 + 1/4 + 1 + ...

so you need to figure out how many 1s you will have

[jolly plaza]

we have 16 multiples of 3

and so we have 16 1s

[unkempt mica]

yessir

[jolly plaza]

which means the rest of 34 are 1/4s

[unkempt mica]

yes

[jolly plaza]

so now what do i do

its 4 am and my brains fried but im stuck here

[unkempt mica]

the right sum is 16x1 + 34x(1/4)

and the left sum is 50x51/2

add those up

[jolly plaza]

49/2

+1275

= 2599/2

[unkempt mica]

yes

[jolly plaza]

1299 1/2

[unkempt mica]

https://www.wolframalpha.com/input?i2d=true&i=Sum[\(40)n%2BPower[cos\(40)Divide[n*pi%2C3]\(41)%2C2]\(41)%2C{n%2C1%2C50}]

[jolly plaza]

whats this

[unkempt mica]

to check your answer

[jolly plaza]

woah

thanks a bunch man

appreciate it

see you around take care

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[lost flax]

Did I use the formula right? How do I continue from here?

[lost flax]

Confused cuz n is inf

[alpine sable]

no

[lost flax]

Ooo

Rip

[alpine sable]

that formula only applies to a geometric series that ends at a term

[lost flax]

How do I do it since it’s inf?

[alpine sable]

have you ever seen this formula

[lost flax]

Oh I see

Yes

[alpine sable]

so what would you get if you used this formula

a is the first term btw

[lost flax]

1/ (1/3)?

[alpine sable]

not quite

[lost flax]

Uhhh

[alpine sable]

r is the ratio

what is the ratio

[lost flax]

1-1/3=2/3 ?

[lost flax]

1/3

[alpine sable]

yes that is the denominator

[lost flax]

So 1/(2/3) so 3/2

[alpine sable]

yup

nice

[lost flax]

Okk!

Ty

[alpine sable]

np

^^

[lost flax]

The first term is 1 because anything to the 0 power is 1 right

Wait…

[alpine sable]

yes

[lost flax]

I’m confused about how the a is in both sides

[alpine sable]

(1/3)^0 + (1/3)^1 + (1/3)^2.. etc

[lost flax]

Like what does ar^n mean

[alpine sable]

a (first term 1) r (ratio)

[lost flax]

Could it ever be not 1?? Cuz like n=0

[alpine sable]

n is just the power

[alpine sable]

you mean the first term?

[lost flax]

Like wouldn’t the first term always be 1

Yes

[alpine sable]

when n starts at 1

instead of 0

first term would be 1/3

so it would be(1/3)/(1 - 1/3)

[lost flax]

ohhh

okay

got it

thx!

.close

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[wet vector]

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[radiant oasis]

I’m having trouble starting 55

[lone heart]

@radiant oasis Has your question been resolved?

[lone heart]

@radiant oasis Has your question been resolved?

[radiant oasis]

<@&286206848099549185>

[dense stratus]

check your derivative

[radiant oasis]

...?

[dense stratus]

take the derivative wrt t

basically solve for a local max

[radiant oasis]

how?

[dense stratus]

find where the derivative of h is zero

[radiant oasis]

i figured it out

sorry

thank you though

.close

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[light hinge]

I tried solving this inequality and only got 9/35 is less than or equal to x

When it's supposed to look like this

What am I missing?

[feral hemlock]

Is it no sol or I'm gay

Is it no sol

[light hinge]

Er it's just rewriting it to get to this point

Maybe I'm not sure

Oops

Wrong question

.close

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[buoyant inlet]

Can someone help me with part b?

[buoyant saddle]

so u just go back to ur formulas

ur looking for d

and ur given t1

and the sum

as well as the total number of terms which is n

but u don’t know tn

so whcih formula will u use

[buoyant inlet]

Okay sorry so

I used the sn = n/2(t1 + tn)

No wait-

I used the Sn = n/2 (2t1 + (n-1) d)

[buoyant saddle]

yes

that one

solve for d

so ((2S/n)-(2t1))/(n-1)

@buoyant inlet

[buoyant inlet]

OH

Hm

[buoyant saddle]

does this make sense

unfortunately i will probably need a calculator

with these numbers

[buoyant inlet]

I am not used to changing the formula that way, I usually just isolate the d before

Yeah

I did that too

But the answer is -17 and I got like something in thousands

[buoyant saddle]

-17?

[buoyant inlet]

mhm

[buoyant saddle]

yea

i got that

[buoyant inlet]

Oh

Lemme do it again

[buoyant inlet]

Nice! I got it too

I think my work is too messy which makes me get the wrong answers mostly

tyyy

[buoyant saddle]

gang

[buoyant saddle]

makes sense

[buoyant inlet]

Ty

.close

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[buoyant inlet]

Not sure how I’ll find anything with only Sum value

[noble notch]

You can use simultaneous equations to solve for first term (a) and difference (d)

[buoyant inlet]

How-?

[noble notch]

You have the formula for the sum of n terms

S=(n/2)(2a+(n-1)d)

You can apply this to S5 and S6

[buoyant inlet]

Oh that one

Okay

And then system funcations?

[noble notch]

Yeah

just solve for a and d

and then find the 8th term

[buoyant inlet]

Okay ty!

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[unborn geyser]

I’m confused shouldn’t elevation be the hypotenuse? Why is it on the bottom instead?

[buoyant saddle]

elevation is the angle which makes the height

the bottom angle projects the height

as the angle of the bottom changes the height changes

so the elevation changes

if u change the top angle

u change the horizontal

which is the angle of depression

[unborn geyser]

So it will always be on the bottom for all depression and elevation questions?

[buoyant saddle]

pretty much yea

just whatever angle makes the height

99% of the time it’s the bottom

[unborn geyser]

Yeah I don’t get that part

The angle that makes the height is 90?

[timid lark]

Think of your y-value as the distance from the x-axis

Actually, that's where your sin/cos values come from

sin 45 = .7071 precisely because that is the y-value at the point where the line intersects a circle with radius = 1

[gray isle]

angles of elevation/depression are the angles between the line of sight and the horizontal

[timid lark]

aka... your y-value

[gray isle]

bad/vague wording

[timid lark]

So.. check it out

Take a 3/4/5 right triangle... or any right triangle, for that matter, but I like 3/4/5s 😉

The sides are measurements of distance, right?

[unborn geyser]

The 30 degree is the hypotenuse right?

[gray isle]

no

don't conflate angles with sides

[timid lark]

No.. the hypotenuse is always the side opposite of your 90 degree corner

[gray isle]

30° is the angle between the hypotenuse and the horizontal base

[unborn geyser]

I thought elevation means looking from the bottom point of the hypotenuse to top of it

[timid lark]

Whenever you draw a line from the origin and your intent is to make a right triangle, you are drawing the hypotenuse

That's your line of sight... that is not the elevation

[gray isle]

looking from the bottom point of the hypotenuse to top of it
that would be the line of sight
the angle of elevation is the angle formed between that and the horizontal
as represented in the image above

saying hypotenuse is a certain angle is not an accurate description of that

[timid lark]

Your line of sight is always the hypotenuse... the elevation is the distance between the bottom and the top

[unborn geyser]

Ok so I would always be using tangent for these kinds of problem

[timid lark]

And the hypotenuse is always the longest line in a right triangle

[gray isle]

don't conflate elevation with angle of elevation

[timid lark]

Tangent is the relationship between the elevation and your distance from the object

sine is the relationship between the elevation and the hypotenuse
cosine is the relationship between (the distance from you to the object) and the hypotenuse

[unborn geyser]

Ok so I don’t really need to worry about these elevation and depression then cus I would solve them all the same? By using tangent and putting the degree in it

[timid lark]

It depends on which parts of the triangle you're given

You don't use a hammer to drive screws... you don't use tangent if you're given the hypotenuse and one of the other sides... they are specific tools that only work in specific circumstances

[unborn geyser]

Ok I just took a random problem

[timid lark]

I'm looking at your original problem again, and the 800ft is the distance between the observer and the building... it's not the elevation or the hypotenuse... it's the side adjacent to the angle in question - i.e., the angle of elevation

[unborn geyser]

So how would i solve this

[timid lark]

First, identify which side you're given in the problem... that 1.2km... which side is that? Hypotenuse, opposite, or adjacent?

Draw a diagram if you need to

[unborn geyser]

Like this?

[timid lark]

A little tiny, but that'll work!

So which side is that?

[unborn geyser]

I got 1.2sin49degree18=height

Is that correct

[unborn geyser]

Opposite

[lone heart]

@unborn geyser Has your question been resolved?

[lone heart]

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[strong wedge]

#help-7｜zen1thxyz message

[lone heart]

Please don't occupy multiple help channels.

[tacit arch]

!1c

[lone heart]

Please stick to your channel.

[strong wedge]

No 1 helping

[tacit arch]

doesn't matter

[tacit arch]

read

[lone heart]

Helpers are just people volunteering their time to help you. Be polite and patient.

[strong wedge]

I understand

Sry @lone heart

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@strong wedge Has your question been resolved?

[lone heart]

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[waxen sequoia]

Does binomial distribution mean a fixed number of trials?

[waxen sequoia]

<@&286206848099549185> test is in 4 hours

Help asap

[tacit arch]

!15m

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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.

@waxen sequoia Has your question been resolved?

[topaz leaf]

yup (sorry for ping reply just wanted to make sure you did well on your test)

[waxen sequoia]

How do you do this

@topaz leaf

[topaz leaf]

just to make sure the standard deviation is 4 right

[lone heart]

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[topaz leaf]

.reopen

[waxen sequoia]

Yh

4

[topaz leaf]

okok

[waxen sequoia]

And mean is 25

[topaz leaf]

and i assume calculators are allowed

[waxen sequoia]

Normal distribution

Yh

[topaz leaf]

ok

one sec

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[topaz leaf]

imma reclaim this channel for @waxen sequoia

[waxen sequoia]

Ty

[topaz leaf]

ok so

we know that P(x<12) = 0.000577 and P(x<a) = 0.200577

which means that P(x>a) = 1 - P(x<a) = 0.799423

wait lemme work this out first and make sure im not doing something wrong

[waxen sequoia]

Hold on

I think I understand it now

Thanks

[topaz leaf]

yeah ok

good luck on your test

.close

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[north elk]

hello! so um, on a ti-84, is it possible to change the xlist from L1 to L2 and the ylist from L2 to L1

[north elk]

i incorrectly formatted the x and y on switched lists and id prefer to not have to reenter bc its 50+ digits each of atleast 5 numbers

but if theres no other way i understand

[ocean whale]

On stat plot, right?

[north elk]

the lsrl thing yep

so i have Xlist: L1
and
Ylist: L2

is there anyway to change it to

Xlist: L2

and Ylist: L1

if not i understand but if u know a way please tell me so i dont waste sm time its so late XD

and thanks for the help!

[ocean whale]

You're on this, screen, right?

[north elk]

no

[ocean whale]

First, you're trying to plot the data set, correct?

[north elk]

so I'm on this screen

unfortunately I made a grave error, inputting all my x values on L2 and all my y values on L1

[ocean whale]

Cursor on the L1

[north elk]

is there any way for me to switch the two so it still "comes" out right

[ocean whale]

Then 2nd, 2

[north elk]

oh my gosh thank you

Soooo much lol

[ocean whale]

Then cursor on the ylist, 2nd, 1

[north elk]

I really appreciate this, that worked like a freaking charm

[ocean whale]

Notice how it has those lists are the shift(2nd button) values there

[north elk]

Have a great day/night, thanks for being part of a community that helps strangers on the internet

[north elk]

I see now 👍

[lone heart]

If you are done with this channel, please mark your problem as solved by typing .close

[north elk]

wait

one more thing

the b is negative but the slope is positive

[ocean whale]

Slope shown on what?

[north elk]

well, the graph is positive when I inputted it on a separate program for this project I'm doing (google spreadsheets)

what is the possible reason of this, such as incorrect data?

[ocean whale]

Can you plot that data on the ti?

[north elk]

i did- to clarify, my L1 is the y value, L2 is the x value (and of course i switched them to calculate correctly)

there is a positive correlation- the higher my x the higher my y

is it negative because the x is always higher then the y? i am so confused now-

ah nevermind i'm sorry, i confused slope negative/positive with the y intercept

have a good day!

.close

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[hasty basin]

If anyone is able to read what I did, could they tell me what I did wrong? I have no idea what I’m doing wrong here

[noble frost]

try differentiating (400-y²)^1/2 again

[hasty basin]

ooh ok gotcha thanks

i have no idea if what i have is the right answer, do you know of any way for me to check?

.close

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[frosty pumice]

I have never solved a second order differential equation before.

[lone heart]

@frosty pumice Has your question been resolved?

[hearty quartz]

You just integrate and apply conditions. integrate again and apply conditions. This is an IVP.

[frosty pumice]

How?

[hearty quartz]

Just do it

You know how to integrate right?

[frosty pumice]

Yes. A bit.

[frosty pumice]

Can you show me how please?

[frosty pumice]

This one is not dy/dx with x or y but it is d2y/dx2 with dy/dx. I have no idea how to do it.

[hearty quartz]

Just to check theta is a constant?

[frosty pumice]

Yes.

[hearty quartz]

So we know dv/dt = -kv correct

nevermind, is u also a constant?

[frosty pumice]

Yes.

[hearty quartz]

So we dv/dt = -kucos(theta)

[frosty pumice]

What? How?

[hearty quartz]

Integrating both sides will give v = -kucos(theta)t + C

[hearty quartz]

So dv/dt by definition equal a