help-28

[vivid coral]

so 0.689... is the reference angle

the first solution on the interval 0<theta<360 is -0.689205+3060

and the second solution is 180-0.689205

then to find the negative solutions just subtract 360 from both

@torn jolt does this make sense

[full forum]

@torn jolt Has your question been resolved?

[torn jolt]

No

[vivid coral]

do you understand what the principal value solution is

[torn jolt]

no

i tried to draw diagrams

for each quadrant

[full forum]

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[torn jolt]

For A = (3,1) and B = (5,1) I need to find a unit vector of magnitude 3 in the opposite direction of vector AB (which I know is <2,0>) idk how to find the unit vector given a magnitude. Is the oppositie direction <-2,0>? Idk I'm just confused

[hollow geode]

unit vector is a vector with a norm of 1

so normalize the vector, then scale it to have a norm of 3

[torn jolt]

so i just do that and take the unit vector normally?

[hollow geode]

you find the vector, make it a unit vector

then scale it to have a norm of 3

[torn jolt]

i found the vector

it's <2,0>

right

[hollow geode]

yes

[torn jolt]

which is a unit vector

[hollow geode]

it isnt

[torn jolt]

oh

[hollow geode]

[2,0] has norm 2

not 1

[torn jolt]

wait

i see

ok

yeah

i get it

ok

so about the opposite direction thiung

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[lucid wedge]

how do i evaluate the radius of convergence for this power series: \
$\sum_{k=1}^{\infty} a^{k} z^{k^{2}}$?

[glossy valve]

lewis

[light sluice]

a common way its said to find the radius of convergence R is to take $lim_{n\to \infty} \frac{b_n}{b_{n+1}}$

[glossy valve]

bubbles

[light sluice]

but of course thats usually for power series written in the form $a_i z^i$, so for this case I would say use the ratio test and include the $z$ term and find what values make $lim_{n\to \infty} \frac{c_{n+1}}{c_n}<1$

[glossy valve]

bubbles

[light sluice]

where $c_n=a^n z^{n^2}$ in this case

[glossy valve]

bubbles

[light sluice]

Once you find what values of z work, it will probably be an interval, and the radius of convergence is half the length of that interval

For this question you might have multple answers depending on what a is, either they tell you some info about "a" or you gotta split it into cases

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@lucid wedge Has your question been resolved?

[lucid wedge]

sorry, i wasnt here, but how would i apply it to this problem now

can you work through it with me maybe?

[light sluice]

are you given any more information about "a"

[lucid wedge]

yeah, my bad

$a \in \mathbb{C}$

[glossy valve]

lewis

[lucid wedge]

but that's about all

so lets say we try ratio test

[light sluice]

oh shit "a" can be complex

[lucid wedge]

yeah

[light sluice]

okay theres prolly a different approach for this then too that I can't remember rn

[lucid wedge]

but does it matter for ratio test tho?

maybe root test

like lim sup

[light sluice]

yea maybe something like that

i was expecting this to be a problem in the reals, when things are complex, well its a bit different

[lucid wedge]

hmm

[light sluice]

cuz for ex you can't compare 2+i and 5, so you compare like the absolute value of them instead

[lucid wedge]

yeah

[light sluice]

maybe you can still do ratio test but just taking the absolute value, but if theres another test like the root test that works faster then maybe go with that

actually im not sure how the root test would work here

[lucid wedge]

do you not take the absolute value either way?

for ratio test

[light sluice]

oh yea i guess so

okay so lets try that

ofc assuming 'a' isn't 0 or else the radius would just be infinity

what do you get

[lucid wedge]

uhm

$\abs{\frac{a^{n+1} z^{\left({n+1}\right)^2}}{a^n z^{n^2}}}$

[glossy valve]

lewis

[lucid wedge]

right

[light sluice]

yea that looks good

[lucid wedge]

then

we get $\abs{az^{2n+1}}$

[glossy valve]

lewis

[light sluice]

yea

[lucid wedge]

this should < 1

[light sluice]

yes

or rather just focus on isolating the z term

when you set it <1

[lucid wedge]

so

we get $\abs{a} \lim_{n \to \infty} \abs{z^{2n+1}} < 1$

[glossy valve]

lewis

[lucid wedge]

?

[light sluice]

yea exactly! and you can divide out that 'a' term

[lucid wedge]

so $\lim_{n \to \infty} \abs{z^{2n+1}} < \frac{1}{\abs{a}}$

[glossy valve]

lewis

[light sluice]

so then you're looking for what values of z make this work

note $|z^{2n+1}|=|z|^{2n+1}$

[glossy valve]

bubbles

[light sluice]

and that |z| is a real number

[lucid wedge]

can we move to #calculus, im discussing there, too, right now

sorry

[light sluice]

can we finish this first you're almost done

[lucid wedge]

okay

[light sluice]

just wanna keep it in the same thread for this

[lucid wedge]

what about the limit

what happens to it

[light sluice]

its still there

[lucid wedge]

so we have $\lim_{n \to \infty} \abs{z}^{2n+1} < \frac{1}{\abs{a}}$

[glossy valve]

lewis

[light sluice]

yea! so what values of |z| make this work

[lucid wedge]

not quite sure

on how to approach this

[light sluice]

Let's say a is 2 for instance

like pretend the right side is 1/2

ok lets do a quick recap about real numbers, 1 taken to higher powers is always 1 right? and numbers greater than 1 taken to higher powers start to approach infinity right?

what about real numbers between 0 and 1

[lucid wedge]

theyd converge to 0

[light sluice]

yea exactly!

and |z| is going to be a nonnegative real number, what does it have to be for higher powers to be less than 1/|a| ?

[lucid wedge]

less or equal 1

[light sluice]

exactly

wait

so like i think here it depends slightly

two cases for this problem: if $|a|<1$, then $1/|a| >1$ and so the answer is $|z|\leq 1$, because even if $|z|$ is 1 it works

the second case would be if $|a| \geq 1$, then $1/|a| \leq 1$, and your answer would be $|z|<1$.

[glossy valve]

bubbles

bubbles

[lucid wedge]

i would say that we need to consider $\abs{a} = 1$ separately, no?

[glossy valve]

lewis

[lucid wedge]

shouldnt it be $|z| > 1$

[glossy valve]

lewis

[light sluice]

you can if you want like do three cases, but you'll see its the same as one of the other cases so no need

[light sluice]

no

[lucid wedge]

oh wait, yeha, my bad

[light sluice]

essentially asking what values of z make $\lim_{n \to \infty} \abs{z}^{2n+1} < \frac{1}{\abs{a}}\leq 1$

[glossy valve]

bubbles

[light sluice]

actually since the question just asks the radius of convergence i guess the answer would just be 1

[lucid wedge]

right

yea

[light sluice]

like whether $|z|<1$ or $|z| \leq 1$

[glossy valve]

bubbles

[light sluice]

do you see why that is

[lucid wedge]

not rlly

[light sluice]

do you know the complex plane like graphing stuff on there

[lucid wedge]

yeah

[light sluice]

do you know what the graph of $|z|<1$ would be

[glossy valve]

bubbles

[lucid wedge]

circle

[light sluice]

technically a disk but yea

[lucid wedge]

but

yeah

[light sluice]

itd be like this but filled in

[lucid wedge]

that's what i meant i guess

[light sluice]

so the radius of that circle is 1

[lucid wedge]

yup

[light sluice]

thats the radius of convergence

radius of the collection of points that make the series converge

[lucid wedge]

yea

[light sluice]

does that make sense

[lucid wedge]

it does

[light sluice]

okay cool

[lucid wedge]

but i dont see why there is still the $\leq 1$

[glossy valve]

lewis

[lucid wedge]

aren't we supposed to show that the limit is merely $< \frac{1}{\abs{a}}$

[glossy valve]

lewis

[light sluice]

it depends on $|a|$ my guy

[glossy valve]

bubbles

[light sluice]

lets say $|a|=1/3$

[glossy valve]

bubbles

[light sluice]

then $1/|a|=3$

[glossy valve]

bubbles

[lucid wedge]

yea

[light sluice]

so then its asking what values of $|z|$ make $lim |z| ^{2n+1}<3$

[glossy valve]

bubbles

[lucid wedge]

yeah

okay, got it

[light sluice]

if $|z|=1$ then the limit is 1 which is less than 3

[glossy valve]

bubbles

[light sluice]

okay bet

[lucid wedge]

but not for any other values |z| > 1, right

[light sluice]

nope

because that would go to infinity

[lucid wedge]

okay, gotchu

yeah

so technically, its just breaking it down into different sections eventually

[light sluice]

yea for this question

technically there would be two answers to this question, like in the original problem if a is 0 then the radius of convergence is infinity

[lucid wedge]

so we always have a different radius of convergence depending on our a

[lucid wedge]

yeah

[light sluice]

kinda like depending on whether a is nonzero or zero

two possible radius of convergence's

[lucid wedge]

what was the case for |a| > 1 again

this would mean 1/|a| < 1

so only for |z| < 1, right?

so r = 0

basically?

[light sluice]

no r=1 in that case

if $|z|<1$ then $lim |z|^{2n+1} = 0$

[glossy valve]

bubbles

[light sluice]

and since if $|a|>1$, $0< 1/|a| <1$

[glossy valve]

bubbles

[light sluice]

and since in this case $1/|a|$ is greater than 0, any value of z that makes $|z|<1$ works

[glossy valve]

bubbles

[lucid wedge]

isnt that what i said

[light sluice]

oh yea you did say that my bad

not sure how you got r=0 then

like its very much not 0

like z=1/2 works

[lucid wedge]

wait, could you expand in why it's r = 1

[light sluice]

if you graph $|z|<1$ its a disk of radius 1

[glossy valve]

bubbles

[light sluice]

theres no boundary but still the radius is 1

i get this might be a little confusing to think about but think of it as the length of a line segment, even if you remove the end points it has the same length

a point has length zero, and its the same with the boundary of a disk, it has length zero so removing the boundary wouldn't change the radius, which is a length

[lucid wedge]

yeah, i see it, i think

[light sluice]

okay awesome

[lucid wedge]

tysm tho

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[fossil stump]

The area of a rectangle is base times height

This help?

$A = bh$

[glossy valve]

Shen

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[ruby idol]

"A company donates an amount for the typhoon victims of Super Typhoon Vanity in Africa. The
amount is to be divided equally among the affected families. Name 2 quantities that affect the amount of aid
each family receives."

(1) Number of the affected families and (2) total amount of aid to be given to the families. Is this correct?

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@ruby idol Has your question been resolved?

[ruby idol]

<@&286206848099549185>

[ruby idol]

.close

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[hollow geode]

you dont need multiple channels

[floral berry]

Oh i can use one?

Lk##ok

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@floral berry Has your question been resolved?

[floral berry]

<@&286206848099549185>

<@&286206848099549185>

[floral berry]

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[dense flare]

Hello

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[dense flare]

.close

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[fathom saddle]

Consider a u-sub

u = ln(x)

[ocean lark]

I don't think that's very efficient here. don't you end up with int 8u/e^u and have to do ibp? If you're doing ibp anyway you don't need to u-sub.

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[dry relic]

There are 15 children in a class.
9 of the children have brothers
10 of the children have sisters.

How many children have both sisters and a brothers?

[dry relic]

I've tried solving this by writing some type of equation:
9b + 10s = 15

b stands for brothers and s stands for sisters
i don't really know if I've done the right equation nor how to make an equation to solve this

[plush egret]

not enough information to say for sure

you can bound it

like, it could be 9

because you could have 5 students without any siblings at all

it could also be 6

i think

no, 4

it could be as low as 4

if every child has a sibling

then only 4 have both a brother and a sister

[dry relic]

i thought there was some sort of formula for finding this out

like writing an equation or whatever

but the answers were infact true

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[lilac adder]

Hi, how do I estimate a linear trend line in a given form given a set of data? Full question attached (a, b and c).

[lilac adder]

Data sample:

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[lilac adder]

Not many statisticians I guess haha. <@&286206848099549185> anyone here, perhaps?

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[sweet ingot]

Start with converting t in your data as they say its defined.

What is e_t? But anyway you just use your software to find the best fit for the model given

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[summer gorge]

what are all the possible 2 hot combinations for a dimension N?

[summer gorge]

So if you have dimension 5, the combiations are [1, 1, 0, 0, 0], [1, 0, 1, 0, 0] etc...

struggling to find the max number of distinct combinations

[hollow geode]

#❓how-to-get-help

[frozen umbra]

Whoops sorry

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[sleek sapphire]

Help

[sleek sapphire]

Can someone help?

Is b Not 30?

And is c 150?

And is a 75?

[ornate matrix]

No

The angles opposite to the equal sides are equal.

[sleek sapphire]

So b is 75?

[ornate matrix]

Yes

[sleek sapphire]

Then a is 30?

[ornate matrix]

Yes

[sleek sapphire]

And c is 75

?

[ornate matrix]

You said b=75

C=180-b=180-75

[sleek sapphire]

Sorry 105?

[ornate matrix]

Yep

[sleek sapphire]

Ok ty for this one i don’t understand

[ornate matrix]

What do you need to find, "x"?

[sleek sapphire]

Yes

[ornate matrix]

You know alternate interior angles? x and 42 are one of them

[sleek sapphire]

Like the letters?

Z?

[sleek sapphire]

So x is 42?

[ornate matrix]

Yes!

[sleek sapphire]

Oh okk

[ornate matrix]

That 141 was unrelated

[sleek sapphire]

Yeah TH

Ty

For this one can u help me get started? Or understand a)?

[ornate matrix]

Well, according to the diagram, AF is bisected...

[sleek sapphire]

Ok how would I find the lengths?

[ornate matrix]

Which halves are they referring to when they say from (a)?

[sleek sapphire]

I believe the ones with 2 lines

Like A to F

[ornate matrix]

Yes. So the two halves are basically AD and DF

[sleek sapphire]

Yes

[ornate matrix]

We know what length AF is

[sleek sapphire]

13?

[ornate matrix]

Yes

So halving that should give lengths of AD and DF!

[sleek sapphire]

Ok 6.5

Thanks you

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[fleet rampart]

soo how did the x turns out if its infinity?

im really confused at this part

[cold gate]

occupied

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[mint quartz]

<@&286206848099549185> A group of realtors estimates that 23% of all homes purchased last year were considered investment properties.If a sample of 800 homes sold last year is obtained

1. What is the probability that at most 25% homes are going to be used as investment property? So far all I know is P(p-hat <= 0.25)

2. What is the probability that at least 21.9% of homes are going to be used as investment property? I know that P(p-hat >= 0.219)

3. What is the probability that between 21.9% and 25% homes are going to be used as investment property? I know that P(0.219 < p-hat < 0.25)

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[rocky steppe]

"Find the maximum value of:
C = 3x + 4y

subject to the following constraints:

x > 2
x < 5
y > 1
y < 6

[covert wing]

Hi

Is the constraint >= and <= or just > and <

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[ornate matrix]

Because if those were strict inequalities, maximum would not exist

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[balmy frost]

Discrete math, induction

Hi! I'm in need of help with an induction

[balmy frost]

Usually I show that with n=1, the induction base works and then I go to induction step with n=k and then n = k+1

Where do I input n=1 or how am I supposed to solve it?

[sweet ingot]

Why is it written in word or whatever this is

But since b_k=b_{k-1}+2b_{k-2} you need 2 base cases

k=0 and k=1

[balmy frost]

the word case there is irrelevant on the image

Saying in case

So do I show that its true for k=0 and k=1, and then proceed to input what?

[sweet ingot]

That is your base case

Then assume true and prove k+1

[sweet ingot]

(I’m just saying math in Word is ugly (or whatever program that is))

[balmy frost]

if I try to prove for k+1, what will be on the left side of = and whats on the right side?

[sweet ingot]

What do you think?

[balmy frost]

I assume this is on the right

with k replaced by k+1

[sweet ingot]

Si

[balmy frost]

and on the left b_(k−1)+2b_(k−2) with k repalced by k+1

I'm quite sure my step's left side is wrong

Perhaps you can confirm?

[sweet ingot]

You want to show the equality at the end

Just replace k with k+1

[balmy frost]

replace in b(k−1)+2b(k−2) ?

I do know it needs to be equal in the end, I'm trying to figure out if both sides are correct before I proceed

[sweet ingot]

No, you want to prove b_k=…

So replace k with k+1 in that

And prove it

[balmy frost]

Understood. Case closed. Thanks. Much love.

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[quartz harbor]

Could someone help me with a Fourier Series problem?

[somber gale]

dont ask to ask, just ask the question

[tiny ivy]

too advanced for the normal help channels i’d say

you’d be better off in #odes-and-pdes

@quartz harbor

[quartz harbor]

I asked there but no one is answering

[tiny ivy]

well then i hope you get an answer eventually

it would help if you posted the problem

[quartz harbor]

yeah I was doing that sorry

[tiny ivy]

oh wow you still haven’t gotten this question answered? i remember this from earlier

[quartz harbor]

yeah😅

[somber gale]

idk how to do this but in theory i should know in 2 weeks cuz i have an exam on it

[quartz harbor]

Oh😂

[tiny ivy]

well you know what to do in 2 weeks if you don’t have the answer

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[wooden knoll]

,,\frac{d}{dx}\int _{-5}^{x^2}:cos\left(t^3\right)dt

[glossy valve]

epiphonically

[wooden knoll]

how do i do this

is is cos(x^6)6x^5

or cos(x^6)2x?

[hollow geode]

this

Just chain rule

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[marble knoll]

When changing the index of a sum in a power series, aren't you supposed to pull out the values and tack them on separately? I can't remember. Is it this or this (indicated in brackets)

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[marble knoll]

<@&286206848099549185> which one is the right method?

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[marble knoll]

😐

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[marble knoll]

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[wet robin]

how do I even approach this problem?

Use the point to plane formula?

D = (p0p1 * n)/ magnitude(n)?

but I don't have a point on the plane to work with

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[fathom saddle]

You can get any point on the plane

Sub in your choice of x,y, get a z

[jaunty chasm]

I like where this is going

If you can get the surface normal you could take
((1,0,-2)-(point chosen)) dot normal

[wet robin]

ahh yeah that works

thanks!

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[prisma flame]

help

how do i find the force of the question mark

the orange is pivot

(this is not for class, this is for calculating force in robotics but i have only basic physics knowledge)

would i need more additional info? like the angle between the bars

[jaunty chasm]

You'd prob want the distance perpendicular to the force

So you can calculate the torque

[prisma flame]

u mean id use the t=rFsintheta

?

[jaunty chasm]

Like this

Then t=fd

[prisma flame]

oh

thats it?

[jaunty chasm]

Then you'd have to un-calculate the torque to the other side

To get a force at a distance

[prisma flame]

ic

ill look into this more

thx tho

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[jaunty chasm]

Np

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[torn jolt]

both r diff btw

[jaunty chasm]

Where do you get stuck

[torn jolt]

everything.

[north forum]

well

[jaunty chasm]

Do you know what slope and y intercepts are

[north forum]

the y-intercept happens when t=0

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[torn jolt]

no but wtv

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[torn jolt]

🤨

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[torn jolt]

can someone help me with a genera math question?

[torn jolt]

if something is written like [6,12] with brackets instead of parenthesis, does that mean both of those numbers are x values?

[north forum]

is this interval notation?

[torn jolt]

yes

this is for my calculus homework with rolles theorem

[north forum]

if they have brackets like that, the numbers 6 and 12 are included in the interval

(6,12) = interval between 6 and 12, 6 and 12 are both not in the interval
[6,12) = interval between 6 and 12, 6 is in the interval but 12 isn't

(6,12] = interval between 6 and 12, 12 is in the interval but 6 isn't

[6,12] = interval between 6 and 12, both 6 and 12 are in the interval

[torn jolt]

ohhh that makes a lot of sense

thank you so much

im doing this question

this is rolles theorem right?

i got the x intercepts which are (0, 0) and (4,0)

so ill need an interval i think to show f'(x)=0

is it [0,4]

<@&286206848099549185>

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[regal forge]

how is LHS <= RHS

RHS is larger than LHS by 1/36

[ocean lark]

which inequality are you asking about? The base case 1<7/6? a) that's not a difference of 1/36, and b, the rhs being larger than the lhs proves that LHS<=RHS

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[regal forge]

@ocean lark i am talking about 8 (a)

and I'n referring to the LHS^2 <= RHS^2 part

[ocean lark]

Oh. Well, you're right that the RHS^2 is larger than the LHS^2 by 1/36! that could be written as LHS^2<=RHS^2, which implies LHS<RHS, which is what you want...

[regal forge]

so this is proof is incorrect?

[ocean lark]

No. Its correct. They wish to prove that LHS<=RHS, and they do so.

[regal forge]

oh right yeah

thanks . close

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[turbid jewel]

how do i intergrate y = 5 and y = x^2 + 1 between x = -2 and x = 2? I know the method for intergration but idk about the between part

[ashen elk]

idea:

that integral approach with y=5 is kind of silly IMO, you can get the area just by making a rectangle

[turbid jewel]

yea, i get that im just unsure how to intergrate to get the area of green

[turbid jewel]

ohhh

i thought i had to substitute x but i didnt know i had to subtract them

thx

[ashen elk]

it's fine. all you need to know is how to use definite integrals after you know, doing the integral LOL

[turbid jewel]

how do i close this lool

[ashen elk]

type .close

should do the trick

[turbid jewel]

thx

[ashen elk]

npnp

[turbid jewel]

.closes

shit

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[spare wedge]

Hey there!

[spare wedge]

I was just wondering if you had access to the resources in edexcel online pearson !

the teacher one

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[tiny ivy]

@spare wedge please close this channel, this isn’t related to a math question

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@spare wedge Has your question been resolved?

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@spare wedge Has your question been resolved?

[somber gale]

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[covert nacelle]

May I ask what is the formula for 1?

[torn gust]

angle is proportional to area, so it's angle/2pi = area/pi*r^2

[covert nacelle]

okayy

how about number 2

[torn gust]

same formula

[covert nacelle]

ohh okayyy thanks

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[fossil stump]

Where is my mistake?

[fossil stump]

(Ordinary Differential Equations)

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@fossil stump Has your question been resolved?

[terse karma]

Shouldn't you be using cos for q and q"

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[stoic escarp]

Hey, I don't know what I'm doing here. I'm stuck and I genuinely have no idea what to do, I need explaining

[stoic escarp]

Please @ me whenever anyone checks this

[knotty adder]

Ummmm I'm not a helper @stoic escarp but it looks like you just graph the lines.

THat's the first step, then you shade in the area of the inequality

[light sonnet]

You don't have to be a helper to help out. Anyone can help. The main rule is just don't give full solutions out. Help the person with what step they are stuck on

[knotty adder]

Oh I see ty

[stoic escarp]

No I know I need to graph the lines

But how

[knotty adder]

If you're more comfortable with y intercept form then you can use that

THese lines are in standard form. The easiest way probably is to set x to zero and see what y is.

That would be one point on your line, and then you do it with y and that gives you your second point

Or like I said you can convert to y-intercept form by solving for y, which basically means subtracting the x term over.

[light sonnet]

Have it in y intercept form, to make it easier
Then you can watch this to understand how to plot it
https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:inequalities-systems-graphs/x2f8bb11595b61c86:graphing-two-variable-inequalities/v/graphing-inequalities

[stoic escarp]

Ty

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[tender roost]

I need help

[knotty adder]

shoot

[tender roost]

How do I solve questions like this.

I have been away from school for a while and have no idea how to do this

Can you read French

I think it might be a dictent thing

Let me translate it

3.a the 0 is the middle point of each circle determin the values of d°, de, e and f

Basically

m I aupposed to find the angle?

90°

But what are the other ones, length

?

3.B) 5. 3.C) 7?

Ok

How would I solve a question like 7.A)

[torn jolt]

hello

Ray drives between towns A and B at an
average speed of 75 km h¡1. Mahmoud
drives the same distance at 80 km h¡1 and
takes 10 minutes less. What is the distance
between A and B?

can you solve this ?

[tender roost]

Uh what

[torn jolt]

:D thank you

[tender roost]

How do I do Pythagorean fromula

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[hollow geode]

integral test probably

[rare gale]

is that the only way is there any way to do it by comparison test or ratio test

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@rare gale Has your question been resolved?

[torn jolt]

@rare gale maybe you can discuss with this person #help-23 message

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[void spade]

optimization 🙂

[gusty hamlet]

perimete should be equal to 1200 ft

find the total perimeter that shoud be an equation of X and Y

then calc the area

sub X or Y

derivative = 0

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[peak holly]

how to find deriv of abs value

[peak holly]

like|x-1|

[jaunty chasm]

If its possible to isolate it you could probably +- both sides

Otherwise Id just piecewise it

[gusty hamlet]

i would do when the value of x + a is negativa

and negative

[peak holly]

is there a value c in the interval [0,4] where |x-1| satisfies the mean value theorem

[sweet ingot]

Solve the equation for c and figure it out

[uncut grotto]

recall that absx=sqrt(x^2)

[peak holly]

so sqrt(x^2-1)

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[torn jolt]

how do I prove (x-5) is a factor of that

[hollow geode]

factor theorem.

[torn jolt]

What's that

[hollow geode]

Google it

[torn jolt]

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[torn jolt]

over here

[torn jolt]

i was able to calculate it when x^x, but when theres three x im lost

[hollow geode]

use your result from y=x^x and do the same process

[torn jolt]

this is for two xs

so it woud be the same answer? except x^x^x in front of the parantheses?

and logx^x i presume

[torn jolt]

am i on the right track?

[sand belfry]

See this:

https://youtu.be/Nx8itxbkXac

instead of x

use, x^x

that should solve this

[torn jolt]

wait wdym

i already did derive an answer with x^x though

just having trouble with x^x^x

[sand belfry]

bro

x^x^x= e^(x^x)*ln(x)

[torn jolt]

bruh how did i not see that

aight thanks sm

[sand belfry]

You may close if you're done @torn jolt

[torn jolt]

.close

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[marble oar]

really need help with this one

[marble oar]

anyone?

[cold orchid]

(a) 6:10=18:(x+6)

(b) y:10=16:12+y

Solve this and you'll get it.

[marble oar]

tyty

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[viral nexus]

given mean, and confidence level 90%, and p for probability of occurence
would the formula for calculating lower bound be : mean - zscoreof90% * sqrt( p(1-p)/sample size) ?

[sweet ingot]

Confidence interval for what distribution and for what parameter?

But anyway no if 90% confidence level that means you want to use 1-alpha/2=1-0.1/2=0.95 quantile as lower and upper

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[viral nexus]

.reopen

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✅

[viral nexus]

Yeah just need to normal inverse .95 to get confi interval for 90% but im more confused about what I should be using for lower and upper bound

For lower bound, I was using
Lower: mean - zscoreof90% * sqrt( p(1-p)/sample size)

Upper: mean + zscoreof90% * sqrt( p(1-p)/sample size)

But I'm starting to think that "mean" doesnt go here

its a exponential distribution

[sweet ingot]

Why you typing 90% again when conf lvl 90%?

[sweet ingot]

.

[viral nexus]

95% I mean

I think I just dont understand what 0.28 really means here

[sweet ingot]

for p=0.28

[viral nexus]

But if I have relative freq p, and theory p?

Would I use theory p value instead of this?

[sweet ingot]

You are doing a test for true p value equal to 0.28

All values in the confidence interval you don’t reject the null hypothesis (that true p-value equal to 0.28)

If outside confidence interval you reject

[viral nexus]

im doing a sheet thats like this:

so I dont have the true-p value

[sweet ingot]

You observe a p-value

You can then test if the true p-value could be x

[viral nexus]

wait, the meaning of "true" is like:
If I flip a coin 4 times, 3 times head
my observed p for head is .75
true p is .5 ?

[sweet ingot]

Yes assuming the coin is fair

The true prob is 0.5

[viral nexus]

I see, so lower and upper bound has nothing to do with the observed p

Thx

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[jade sleet]

i dunno where to start :/

[paper parrot]

If it’s hard to see what’s going on, a good first step would be to try letting $t=\sqrt[3]{2z+1}$ and solve for t. This should make it easier to see what you’re doing.

[glossy valve]

lukas traun

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[dusky pelican]

Yeah im super lost lol

[dusky pelican]

The side of a square is 12 ft with possible error of +-0.1

[fathom saddle]

A = s²

dA = 2s ds

[dusky pelican]

Area = side^2

wait what is the d value?

delta?

or not yet

[fathom saddle]

Well, that's where the approximation comes in

We just kinda say dA ≈ ΔA for small changes in A

And this method works for linear approximation

[dusky pelican]

ok so to break it down for my smooth brain

A = s^2

so area is side squared

from there, we do the delta (or error) of area = 2(side) and delta of side

?

or am i overcomplicating

[fathom saddle]

"and" is a weird way to say that haha

They're multiplying, when this approximation is used

dA = (2s)(ds)

We just don't write it like that it kinda looks dumb

[dusky pelican]

oooo

and 12 = s?

[fathom saddle]

So yeah you want dA when s = 12 and ds = 0.1

[dusky pelican]

Ohh so I could just say s is starting length and ds is the error

[fathom saddle]

Ye

Handy method for basic error analysis

[dusky pelican]

ik you said the notation looks dumb lol

but is this the right track

[fathom saddle]

ds is not d×s haha

[dusky pelican]

wait

its just d

or 0.1

[fathom saddle]

ds is the error in s, given as 0.1

ds is one variable here

I know, I know, it's all really strange and yeah numeric calculus is kinda messy like that

[dusky pelican]

lol yeah im just figuring that out

so our error is 2.4

?

[fathom saddle]

Approximately

But ye

[dusky pelican]

oh bet

That makes life so much easier

thank you homie

I appreciate your time

[fathom saddle]

Feel free to ask if you have anything else!

[dusky pelican]

🙏

I might be back later, ill see tho

peace out for now brother

so imma just

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[light sonnet]

End behavior is when x goes to positive infinity and negative infinity

[hollow geode]

it'd be... the other direction for x

[light sonnet]

That should help

[hollow geode]

it'd be whatever happens as x goes to -inf.

[light sonnet]

It gives you the graph

Just look

[hollow geode]

Yes, and?

we just told you how to get the other answer.

[light sonnet]

It could be. Just depends on the graph

[hollow geode]

opposite isnt well defined

[light sonnet]

Use the given graph to determine your answer

[hollow geode]

what's preventing you from just... saying the answers you think it is.

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[torn jolt]

i got 3sin2(x-pi/4)-1 and the graphs looks right in radian mode but in dgeree mode it isn't correct

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[torn jolt]

<@&286206848099549185>

[still pulsar]

why 2x?

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[torn jolt]

bc that's what i got for b, i don't know how else to get the variable for b in the equation (Asinbx-h+k)

[still pulsar]

so when you do 3sin(2*90) - 1 you get 2?

[torn jolt]

what?

no

wdym?

like when you do the calculations for b (360º/180º - which i got as the period value) then b= 2

[still pulsar]

oh wait this is a new question

[torn jolt]

?

[still pulsar]

what exactly is it that's not how you want it?

[torn jolt]

oh sorry i was talking about the equation for the sinusoidal axis

like okay so when i graph 3sin2(x-pi/4)-1 in radian mode it comes out as the correct graph that includes the cooordinates (90º,2) and (180º,-4) however when i can't seem to be able to put it in degree mode bc i think that is what the question is looking for

[still pulsar]

so what do you do when you put it in degree mode?

what do you change?

[torn jolt]

i'm jst not sure how to convert the equation so that it is in degree mode

[still pulsar]

you need to convert what's inside the sin(here) function and turn it into degrees

so in the sin function right now what do you have?

[torn jolt]

so that would be 3sin2(x-45)-1

?

but i tried to graph it in degree mode and it still didn't make the intended graph

i'm just not sure as to why

[still pulsar]

really? what was wrong about it?

[torn jolt]

it didn't gve the coordinates 90º,2 and 180º,-4

ok nvm

i figured it out

i had the domain wack

[still pulsar]

ah

[torn jolt]

thx for the help though 🙂

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[torn jolt]

how can I select the variable cells.

[torn jolt]

in excel with open solver.

those yellow cells are variable cells.

nvm, just control select.

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[torn jolt]

y = 2sin(2x + pi/3) -3
how do i factor the brackets

[meager dew]

it's in a trig function, you don't

[torn jolt]

my teacher says i need to factor (2x + pi/3)

isolate x no coefficient

[meager dew]

are you looking for transformations?

[torn jolt]

im trying to graph it yes

[meager dew]

so you have 2x + pi/3 and you want a(x+h)

[torn jolt]

yeah

[meager dew]

so what do you think you should do about that

[torn jolt]

divide by 2

[meager dew]

well you can't just "divide by two"

you need to factor the two out

[torn jolt]

by dividing?

[meager dew]

well yeah, but the two is factored out

so you still gotta write that

[torn jolt]

(x + pi/3)

[meager dew]

as i said, you need to factor the two, not just divide by two

and you didn't even divide everything by two

(pi/3)/2 is not pi/3

[torn jolt]

i dont know what it is

[meager dew]

??

[torn jolt]

well

would it be pi/6

[meager dew]

yes

[torn jolt]

okay can i ask another question

my teacher says that it is easier to convert scale, period and phase shift to have the same denominators

is this true?

[meager dew]

not imo but it's intuition

[torn jolt]

im not sure if i dont know how to do it without converting

but its a huge problem

because it can make your scales really big

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[torn jolt]

sec and csc both have porabola shapes right

[meager dew]

a bunch of parabolas, yeah

[torn jolt]

wait

so

if i have

y=2csc(1/3x-pi/2) + 4

my graph doesnt touch my x axis

for the sin version

so how do i find my aysmpototes

why is tan (-570) sqrt(3)/3

[meager dew]

reference angle of 30 degrees

[torn jolt]

does 2sqrt(3)/2 just simplify to sqrt(3)

and would this just ben tan pi/3

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[cyan vessel]

I don't really understand my homework

<@&286206848099549185>

[honest oxide]

Can you pinpoint which part confuses you?

[cyan vessel]

The whole thing

🥲

[honest oxide]

A quadratic relation has an optimal value which is positive
, refers to the location of the vertex

meaning, the highest or lowest point of the parabola has a positive y value

[cyan vessel]

Ohhhh

[honest oxide]

Draw a coordinate system and mark it as some dot

I assume the "has no x-intercepts" part is clear?

[cyan vessel]

Yes

OHHH

Okay i get it now

Sorry im awful at word problems

Okay I’ll draw the sketch

Thanks :D

[honest oxide]

Np

[cyan vessel]

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[winged bronze]

can someone explain how he got -3/8 instead of 9/8?

[winged bronze]

using the formula seems to have worked for the first 2 numbers but the third one looks completely different from mine

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@winged bronze Has your question been resolved?

[winged bronze]

The only explanation I can think of is that, because the roots are evenly spaced, that for an even root like 4, the remaining roots have to be reflections in y?

so when adding 2pi.k you let k = 1,2,-1,-2?

[plush lantern]

$\frac{9\pi}{8} = \frac{9\pi -16\pi}{8} = \frac{-7\pi}{8}$

[glossy valve]

glittersparkles

[plush lantern]

Your answers are equivalent mod 2pi

[winged bronze]

mod 2pi?

im not sure what that means, sorry

could you explain ?

[plush lantern]

ie modulo 2pi this is nerd speak for $n \cong n+2\pi m$ for all $n \in [0,2\pi)$ and $m\in\mathbb{Z}$

[glossy valve]

glittersparkles

[plush lantern]

Basically we make 2pi =0

So although your answers look different, they are the same angles

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[meager dew]

<@&268886789983436800>

[floral spear]

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[meager bobcat]

Quick question

[meager bobcat]

What would be in this empty numerator?

[light sonnet]

,rotate

[meager bobcat]

Segment area i think

You know what i can figure it out on my own

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[meager bobcat]

.reopen

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✅

[meager bobcat]

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[sweet veldt]

what does this mean ?

[sweet ingot]

The function f \circ g of z

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[sweet veldt]

sorry but that does not make sense either

[sweet ingot]

Its the same meaning as f(x) like you have normally seen