help-38

[merry zodiac]

Are we checking first onto

[left oriole]

you could

[merry zodiac]

I didn't understand

How do we check on one and into by differntiation

I only can do differentiation

y=2+cosx

[left oriole]

well 2 + cos(x) is always positive

do you agree?

[merry zodiac]

Ohh yes

[left oriole]

what does that imply?

[merry zodiac]

Minimum 1 to 3

Uf dy/dx is positive means then fubction is always increasing

[left oriole]

yes

and if a function is increasing, what can you say about it being one to one or not?

[merry zodiac]

I can say that it is one one and onto

In whole domain

[left oriole]

well increasing doesn't imply onto

take f(x) = arctan(x) for example

[merry zodiac]

🙄🙄

[left oriole]

but it does imply one to one

[merry zodiac]

Is it not increasing?

[left oriole]

arctan(x) is increasing but it is not onto

it never exceeds pi/2

,w plot arctan(x) from x=-100 to x=100

[solid kiln]

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[merry zodiac]

So it will be onto in its range?

(-π/2 π/2)

[left oriole]

yes it is onto (-pi/2, pi/2)

[merry zodiac]

I gyess yes

[left oriole]

but not onto R

a function is always onto its range

[merry zodiac]

So how will we check for onto?

For our giving function

[left oriole]

see how the function behaves when x->infinity and x->-infinity

[merry zodiac]

We will find its range?

[left oriole]

and use continuity

and the intermediate value theorem

[merry zodiac]

Should i put infinity in differentiable finction of our main function

[left oriole]

i don't know what that is

[merry zodiac]

I meant should I out (infinity or munus infinity) in 2+cosx

Ohh i got it i got it

We will chcek its limit at x tends to infinity

It is infinity

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[upbeat cargo]

does anyone know if there is a specific way for me to know when i should split the x^3 the way my teacher did

like I wouldnt think to turn x^3 into x^2 * x and then make the x part of dv

[ionic pendant]

basically you want 'u' to be the x^something term because taking the derivative will reduce the power (which will make the next integral simpler). splitting off the x is just what's needed in order to integrate dv (since it needs a substitution)

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[last ore]

.help

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[last ore]

.help rotate

[trim jolt]

No command called "rotate" found.

[last ore]

,help rotate

[solid kiln]

`rotate` command documentation. (Aliases `rcw`, `rccw`.)

Usage

,rotate [amount]
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,rccw [amount]

Description

Rotates the last image (within the last 10 messages) by amount degrees, or 90 if not specified.
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[last ore]

,rotate

[last ore]

,close

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[worthy dove]

my answer is 3

is that right?

[marble wharf]

your answer is just some random unfinished scribbles. how does that lead you to there being 3 solutions for a

[spring hull]

If AM = GM then what can you say about the terms?

[worthy dove]

idk i just use the AM GM formula to solve the equation

[marble wharf]

well you used AM GM, then you rearranged a bit and then you stopped in the middle of doing the next step

and suddenly claim that you are done

[worthy dove]

i dont know what is the next step actually

[marble wharf]

ok so now at least we got from "my answer is 3" to "well I dont actually know how to continue"

[marble wharf]

think about this

[worthy dove]

if a=b

so whats the right answer?

im sorry

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@worthy dove Has your question been resolved?

[marble wharf]

what do you mean with that

do you actually mean the numbers a,b in the problem or do you mean something else

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[vernal warren]

Show that tangent at any point P of a parabola makes equal angles with the line PF and the line through P parallel to the axis of the parabola being focus

[vernal warren]

can someone help me understand what do they want in this?

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[rough goblet]

@celest trail ^^

[orchid wagon]

i assume F is the focii of the parabola?

[vernal warren]

yes

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[wraith hinge]

hi, im trying to solve this complex issue involving the quadratic formula, basically i am writing an excel document to automate the procedure but i am stuck with how my lecture is solving the quadratic formula. I would like to get quadratic coefficients A,B and C

[wraith hinge]

i have simplified to equation, i made dNA = x for simplicity

so far i have A = bw/2

i dont even know if this is possible

[eager comet]

by automate the procedure do you mean anything more than having inputs for coefficients a, b and c and then two outputs, one for each answer?

because if you dont can you not just do
=(-[b-cell]+SQRT(([b cell])^(2)-4[a cell][c cell])/2*[a cell]) with appropriate stars for multiplication that im too lazy to add against discord's formatting

and another for the - output of +-

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@wraith hinge Has your question been resolved?

[wraith hinge]

basically all the inputs, bw, bf df Arc c art d will change each time but it would be useful to be able to make a genreal formula to solve for dNA because the formula wont change

so i imagine the coefficents A= Bw/2, and then B and C in Ax^2 to Bx + C = 0. i just need to know what B and C are in this case

its all good likely to hard to do, thankyou for trying

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[little egret]

why is this wrong

[little egret]

for part b

[dull temple]

3bry21

[vernal warren]

i would consider red blue and green cubes as 1 entity and find how many ways i can arrange them (the 1 entity and 3 other cubes)

[split chasm]

those three colours don't have to be at the start

also your g looks like a y

[little egret]

ITS HARD OK

IM ON A MOUSE

[little egret]

oh

so do i multiply by 4

[dull temple]

sure, that would work

[little egret]

3bry21 32bry1 321bry

bry321

3! x 4!?

[dull temple]

yeah

[little egret]

i swear these questions always switch up on me

[dull temple]

that's the point

[little egret]

if i fail this test...

can u comfort me..............

[lost jay]

🧐

[trail ingot]

[proven hound]

👀

[dull temple]

[hallow crane]

[little egret]

wait guys

[trail ingot]

[little egret]

WTF IS INCLUSION EXCLUSION PRINCIPLE

[hallow crane]

the set circle things

[little egret]

HUH HUH HUH

I NEVER LEARNT THAT

wait can u gimmie an example

[trail ingot]

[hallow crane]

You never learnt these?

[little egret]

WTF IS THAT

OMD

I AM FAILING

[trail ingot]

[proven hound]

Good luck(you need it.)

[little egret]

i havent even started pigeon hole principle

my test is tomorrow

.....

[hallow crane]

Have you at least seen this?

[little egret]

should i wake up at 4 am and study

[little egret]

oh yes

in like year6

[little egret]

thanks...........

[hallow crane]

the other one is this but just for three sets ig lol

[little egret]

wait can u check my past test

i dont see any questions

for

inclusion exclusion

lemme send it

can u read dat>

?

oh probs not

[hallow crane]

There was no inclusion exclusion there

[little egret]

wait theres more pages

[little egret]

is that it?

[hallow crane]

It could be yeah

[little egret]

oh what

i didnt use the venn diagrams

i just used normal logic

[hallow crane]

[little egret]

is there a faster way to do it then?

[hallow crane]

what is your normal logic?

[little egret]

wait so dis is how i did it

[hallow crane]

btw hi layla

[little egret]

wait

so this is how im doing it rn

but it takes

a very long tiume

[dull temple]

do you mean +2 at the end

[little egret]

oh ya

[dull temple]

anyway it looks like you do understand it, you just don't know it by name

[little egret]

is dere a faster way?

i can use my classpad

and my casio

i only get 30 minutes for this test

[dull temple]

calculator would help you with the arithmetic

[full dock]

hi

[little egret]

hi

[little egret]

oh

wait so the way i did

it

is the only way i can do it...

??

[hallow crane]

Yeah but this is just inclusion exclusion right

It's just like bashing the formula

[little egret]

NAURRRRRRRRRRRRRRRRRRRRRR

[hallow crane]

,w floor(150/3) + floor(150/4) + floor(150/5) - floor(150/12) - floor(150/20) - floor(150/15) + floor(150/60)

[little egret]

WHAT THE HECKKKKKKKKK

[solid kiln]

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Requested by kannaaaaaaaaaaaaaaaaaaaaaaa

[full dock]

cries in aussie

[hallow crane]

Lol

[dull temple]

it's probably the way I'd do it yeah

[little egret]

the moment they introduce venn diagrams to me again in math

im done for

IM FINISHED

[hallow crane]

But i think you have the idea

[little egret]

OKI thx :D

wait

are those like

the only inclusion exclusion

questions

or are there different types

[hallow crane]

Mhm, that's the only one i saw at least

[little egret]

OKOK THX

.close

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[full dock]

hii

[little egret]

hi

[full dock]

im trying to figure out why my DC motor wont work 😭 screw physics

[little egret]

whats a dc motor...

GUESS WHAT

I GOT 2ND IN MY PHYSICS TEST

WITH 72%

[full dock]

boooo not even 100% dissapointed!

[full dock]

jk good job lol

[little egret]

THATS GOOD WAHT

I WAS 1 MARK AWAY FROM MAXIMUM

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[foggy wharf]

<@&286206848099549185>

[worn crow]

right?

[craggy kite]

what theorem is cg = ef?

[foggy wharf]

thank you so much

[worn crow]

cg and ef is parallel

[foggy wharf]

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[wraith hinge]

hi, does anybody know how to convert %w/v to grams?

[wraith hinge]

percent weight by volume

[tepid rock]

w/v % is for concentration, gram is a unit for mass. You're not quoting your question correctly. You should do that.

[wraith hinge]

okay thanks

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[crude kayak]

hello everyone! I have a question that I feel is simple, but I'm having a hard time grasping the answer.

suppose I want to know how many non-decreasing sequences of integers of length r there are. eg, aaa, abc, aab are valid, but bca is not.

I understand the answer is given by (26 - r + 1)c(r) - but I cannot yet grasp why. the closest explanation I found was here https://www.quora.com/How-many-non-decreasing-sequences-of-length-r-can-be-formed-from-1-2-3-n-Is-it-nCr-2r-1-C-r-1

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[crude kayak]

.close

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[viral locust]

So I have this infinite summation I've been trying to work out

It's the sum as k goes from 0 to infinity of (-1)ᵏ/((k!)(2k+1)) x^(2k+1)

At first I thought it was really similar to the maclaurin series for sin(x) which is ths sum as k goes from 0 to infinity of (-1)ᵏ/(2k+1)! x^(2k+1), but when I rearrange it in a way that's similar, (-1)ᵏ/(2k+1)! (2k)!/k! x^(2k+1), I know have that factorial fraction term that I don't know how to extract from the equation

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[wraith hinge]

If 10²x = 25, then 10-x is equal to?

[wraith hinge]

I'm trying to understand this question for three days already

[rough goblet]

okay we know that $10^{2x} = 25$

[solid kiln]

ren

[wraith hinge]

Okay

[rough goblet]

which means that $(10^x)^2 = 5^2$

[solid kiln]

ren

[rough goblet]

correct?

[wraith hinge]

Correct

[rough goblet]

can u see the manipulation here

that you need to perform

assuming that x is a real number, of course

[wraith hinge]

Like cutting both 2 expoent

And making 10x=5?

[rough goblet]

u mean 10^x = 5? yes

and also *exponent

[wraith hinge]

Thanks

So

If 10^x= 5

Then 10^-x = -5

[rough goblet]

no

no

no

they're asking for 10^-x

which is NOT -10^x

[wraith hinge]

Ohh

So 10^-x = -5

Right?

@rough goblet , my teacher wrote the answer as 1/5

Why ?

[rough goblet]

don't ping me

[rough goblet]

no!

of course not

@wraith hinge basic exponent rules

[wraith hinge]

I know that 10^-x = 1/10

[rough goblet]

hang on.

[rough goblet]

no, not exactly

but close-ish

[rough goblet]

there's a list of exponent rules here... somewhere...

can't find it

[sudden basalt]

I have a guess of what it is but I am unsure would it be unhelpful if I guessed❓

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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.

[rough goblet]

oops

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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.

[rough goblet]

mb mb

[sudden basalt]

I have done negative exponents in the past

[rough goblet]

good

but don't give out the answer

[sudden basalt]

I am not positive if what i have is correct

[rough goblet]

@wraith hinge basically, $a^{-x} = {\left(\frac 1a \right)}^x$

[rough goblet]

but it might be... so don't for now

[sudden basalt]

👍

I thought the denominator would be a^x❓

[solid kiln]

ren

[rough goblet]

that's the same thing

that's just 1^x / a^x = 1 / a^x

[wraith hinge]

10^-x 😦 1/10)^x

But what about the - 5

[rough goblet]

??

[sudden basalt]

I think you are forgetting the x

[rough goblet]

not 1/10

,w rules of exponentiation

omfg

jesus chr7st

[wraith hinge]

10^-x 😦 1/10)^x

[rough goblet]

u mean 10^-x = (1/10)^x? yes

[wraith hinge]

Yeah, i dont know where the emoji is coming from

[rough goblet]

is alr

[wraith hinge]

What about the 5

Why is 1/5 at the teacher paper

[rough goblet]

and that's just 1^x / 10^x. however, 1^x = 1, so it's just 1/(10^x)

[rough goblet]

jesus chr7st bro chill im typing

[rough goblet]

here

@wraith hinge

@wraith hinge

[wraith hinge]

Hey, I still don't get the 1/5 part but i need to go to a appointment I did with my classmates to make a teacher assigment

But thanks, I got most part of It

[rough goblet]

ohkay

!cond

oops

!done

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[rough goblet]

.close

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[slender seal]

Hello , i have a theory question! Does a constant function have the Darboux Property since it doesnt create an Interval? A constant function is Rieman Integrable , which should mean that it has the Darboux Property...buuut... the image of the function is just a point...

[left oriole]

you can think of a point as an interval of length 0

(closed interval)

[slender seal]

Oh...

so it does have the darboux property?

[left oriole]

sure any continuous function has the darboux property

[slender seal]

And please excuse my awful englisj

[slender seal]

Alright! Thank you! Have a nice day!

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[flat wing]

How do I answer question 5

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[near coral]

Im so lost, I tried to find the relationship between the values so its like u->eta(c,tx), heta(c,t,x)

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[near coral]

<@&286206848099549185>

[undone valley]

this looks DISGUSTING

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[pliant bloom]

How do you complete the square if the LC is greater than 1

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[digital bison]

factor it out

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[warm dune]

i dont really understand this question

i know about definite integrals and how to solve them but i don't really understand what

7<=f(c)<=10 for -3<=x<=7 part means

[burnt mulch]

The function is between 7 and 10 for all x from -3 to 7

You’re just using this tho

[warm dune]

ohh okk so would it be like 70<=integral(idk how to type it)<=100

[burnt mulch]

Yeah

[warm dune]

ok awesome thank you

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[winter apex]

Determine the general solution to the differential equation

Im stuck here

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[molten comet]

Hello

[molten comet]

What's the difference between tangent line equation and linear approximation?

[digital bison]

a linear approximation is a very fancy tangent line

[molten comet]

Why do both have different equations?

[digital bison]

they're the same. Linear approximation is just written differently to serve the specific purpose of approximating a value.

[molten comet]

How did they go from here to there?

[digital bison]

those are identical except for the first terms, z_0 and f(x_0, y_0)
and your f(x,y) = z, so they've just replaced z_0 with the function notation to be consistent.

[molten comet]

Ohh you're right

Tysm!

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[wraith hinge]

what have you tried

[fair meteor]

and idk how they got the arcsin

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[worldly quartz]

In the nation of Onedirectionia certain pairs of cities are connected by one-way roads. Each road connects exactly two cities (roads are allowed to intersect, e.g., through bridges), and each pair of cities has at most one road between them. Additionally, each city has exactly two roads leading out of it and exactly two roads leading into it.

We want to close half of the roads in Onedirectionia in such a way that each city has exactly one road leading out of it and exactly one road leading into it. Show that the number of ways to do this is a power of 2 greater than 1 (i.e., of the form 2^n for some integer n ≥ 1). Hint:(i have been trying to use edge covers and vertex covers as well as perfect matchings)

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[grand sable]

im trying to find hypotenuse

[grand sable]

the base and 2 and height is 6

oh whoops my bad

i got it

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[pearl field]

How do I do this?

[delicate belfry]

$\int\limits_a^b=\int\limits_b^a$

[solid kiln]

Good

[austere cedar]

I think they meant to put a negative.
If you swap the bounds on an integral, you get the negative of the original

@pearl field
How far have you gotten?

[pearl field]

No where

[austere cedar]

Make sure to have your integral properties nearby

[pearl field]

I got it

-33/2

@austere cedar right?

[austere cedar]

,w integral of 1/4 + 4x between 3 and 1

[solid kiln]

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[austere cedar]

Yeah I like it

[pearl field]

Ok thanks

Can you help me with this one too?

[austere cedar]

Sure what's up?

[austere cedar]

,w graph e^x between 0 and 2

[solid kiln]

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[austere cedar]

,w graph e^(x - 3) between 3 and 5

[solid kiln]

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[austere cedar]

They be looking a little similar

[pearl field]

Pretty much the same

[austere cedar]

The thing you want to notice is that the second one is just the first, but shifted right by 3 units.

However, the integral bounds are also shifted with the function

So this is describing the same area

[pearl field]

Wait so how do I answer this?

[austere cedar]

I don't believe in giving the answer directly, but feel free to ask about anything I said. It's possible I wasn't clear.

[pearl field]

I'm not sure what the purpose of the first integral is, is the second one doesn't feature the first

@austere cedar

[austere cedar]

It actually is exactly the same

[pearl field]

e^2-1?

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[delicate lance]

how do i start off this problem?

[bright quarry]

what have you tried

what’s the formula for area of a rectangle

and the formula for perimeter

[delicate lance]

area = lw

[delicate lance]

perimeter = 4 x l

[bright quarry]

no

that would be for a square

there’s two sides with length L and 2 sides with length W

[delicate lance]

ohh

[bright quarry]

so what’s the perimeter

[delicate lance]

2w + 2l

[bright quarry]

mhm

so we can set up two equations

what would the perimeter equation be

[delicate lance]

2w + 2l = 440

[bright quarry]

mhm so the whole idea of optimization

is relating the two variables

we want to write one variable

in terms of the other

so how can you write either l or w in terms of the other

which will be used for the area equation

[delicate lance]

w = 220 - l

[bright quarry]

mhm

now use that for A=lw

[delicate lance]

wait does it matter which one i isolate

[bright quarry]

then differentiate to find the maximum

[bright quarry]

nope

they’re dummy variables

you could’ve named them anhthinh

you defined them

[delicate lance]

a = (220-l)(l)

expand them into 220 -l^2

find derivaitve?

set equal to 0

[bright quarry]

yes

220l btw

[delicate lance]

oh yea

[bright quarry]

so what’d you get

[delicate lance]

w = 110

oops

[bright quarry]

l

ok so

w=220-l

and l=110

what’s w

[delicate lance]

110

[bright quarry]

so what kind of rectangle is it

[delicate lance]

a square

[bright quarry]

yup

that’s typical btw

you should expect that

[delicate lance]

i never knew a rectangle could be a square

[nimble stone]

[ripe topaz]

Every Square is a rectangle, but not every rectangle is a square.

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[pearl field]

How do I start?

[bright quarry]

do you know how to find area using definite integrals

[pearl field]

Yeah

[bright quarry]

so what is the issue

maybe try drawing a graph

[pearl field]

It says y=x^2, y=0 why are there two?

[scarlet escarp]

because you want the region bounded by those two heights

try drawing it like knief suggested

[pearl field]

Graph y=x^2?

[bright quarry]

with the boundaries

[pearl field]

How do I graph that on desmos?

[bright quarry]

just type in the equations

y=x^2

x=-1

x=2

y=0 is the x axis

[pearl field]

Oh ok

I got it, thanks

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[umbral shore]

Not homework, but I'm trying to figure out why a numerical approximation doesn't seem to work. This is a function that calculates the upper incomplete gamma function when the parameters a and x are small (-0.5<a<0.5, and x>0 but small). It works fine, except when a gets close to -0.5, the smaller x, the larger the error is. I will post all the relevant info I have. It is not a code issue, it's the math that doesn't work. This is the function: https://github.com/ampl/gsl/blob/master/specfunc/gamma_inc.c#L339

[umbral shore]

I've done a lot of digging, the approximation used is this :

What interests me is the calculation of 1 - x^a/Gamma(a+1), as I said the code is correct, it's the convolution of the series representation of x^a and 1/gamma(a+1), and it works always except in that edge case of a close to -0.5 and small x, i'm confused because it works when a is close to 0.5 for the same x

so I'm really not sure what's going on here, does the series representation of 1/gamma not work for that case?

I've spent a lot of time on this, so I'm not sure my question is clear to somebody hearing it for the first time, don't hesitate if you want clarification!

For instance, for a=-0.45 and x=1e-10, I get 44627.1, it should be 70269.25: for a=0.45 and x=1e-10, I get 1.968066 which is correct.

[trail ingot]

i don’t understand everything you said well enough but have you considered catastrophic cancellation

just throwing it out as an idea, idk what you’re doing enough to suggest that’s what happening

[umbral shore]

Huh, that actually gives me something to think about, very new to numerical methods so I hadn't heard of that, there's subtraction involved so im looking into it from that angle, thanks a bunch. This is a very niche issue so i wasn't expecting someone to pop with the answer haha, thanks a bunch.

[trail ingot]

well again i wouldn’t call it the answer, it’s just a suggestion

might be though

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[wraith hinge]

Hello

[rough goblet]

?

slope fields?

[wraith hinge]

Yes

The equation is

[rough goblet]

hm

[wraith hinge]

So here is what I know so far

So each of those little ticks is the slope of the derivative at that point?

So if it is just a completely flat line, that means the derivative is 0 there

So if I look at I and II, the derivatives on the y-axis are 0

So let me test to see if that is true

Yes

That should be true of our function

So the answer is either I or II

[left oriole]

so far so good

what else makes y' = x(2-y) equal to zero?

[wraith hinge]

It is negative at y=2

So the answer is I

I mean II

Wait

Okay

Final answer is I

I made mistake

Because the slope there is 0

At y=2

[left oriole]

wait

why do you say it is negative at y=2

plug in y=2 into x(2-y), you get exactly 0

[wraith hinge]

I meant to say it is zero at y=2

[left oriole]

ah yes good

[wraith hinge]

Because multiplying anything by 0 is 0

x(2-2)=x(0)=0

[left oriole]

yep

[wraith hinge]

Sorry for confusion

So I think answer is I

[left oriole]

and only graph I has both properties

horizontal lines for y=2 and for x=0

[wraith hinge]

Okay everyone

Thanks for the hlep

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[dusky ocean]

answer below

[young sluice]

do u know how to find all the lengths

i reccomend drawing it out

[dusky ocean]

not allowed on the upcoming test

[young sluice]

u cant draw it out?

[dusky ocean]

nope

[young sluice]

why?

[dusky ocean]

only allowed to use formulas

and drawing it out wasnt the taught method

[young sluice]

no but drawing it out is just a visual aid

ur still using formulas to find the angles

im not saying draw it out and then measure w a protractor

[dusky ocean]

so i take it you dont know how to solve it

[young sluice]

i could solve it in 30 seconds 💀💀

[dusky ocean]

well thats why i posted the question as help

[young sluice]

exactly and im trying to guide u

u want to draw out the shape

first

that will allow you to use ur formulas

[dusky ocean]

i know but its not prohibited on the test

the test is in google classroom meaning we can only type our answers

[young sluice]

ohhh

alright then

find the lengths of AB, BC and AC

first off

thats the first thing u need to do

[dusky ocean]

does it matter if its AC or CA

[young sluice]

nope

its always the same length

[dusky ocean]

for AB i got [3,1]

but how does that turn into 90 degrees

[young sluice]

wait wait ur rushing it

AB should be a length not a coordinate

[young sluice]

we need to find the lengths of each of the sides of the triangle

[dusky ocean]

does the first step require squaring numbers

sorry its 2 in the morning and my brain is all over

[young sluice]

alr r u familar with the distance formula?

[dusky ocean]

x2-x1 and y2-y1 squareroot?

[young sluice]

yes

that

but its (x2-x1)+(y2-y1) squareroot

i want you to use that to find the lengths of all 3 sides of the triangle

[dusky ocean]

sorry to sound lazy but i also need to cover dot product, cross product, and vector projection

can you tell me what steps i must take after finding the lengths?

[young sluice]

alright alright

basically after finding the lengths of all 3 sides

u need to use cos rule to find 1 of the angles

after finding that angle then u can use sin rule to find the 2nd angle

after u have 2 angles u can use 180-angle1-angle 2 to find the 3rd angle

and thats all 3

[dusky ocean]

thank you i appreciate your support

[young sluice]

no worries

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[crystal glen]

i am getting 360 degrees for a triangle instead of 180 degrees, (3 angles adding to 360) does anyone know why that is? i am using the dot product to find the angles between 3 vectors and their respective side lengths

[crystal glen]

between three points ABC

[quick tusk]

Can you show your work?

[void carbon]

well , you could be calc ext angle

and get

360

as total

[crystal glen]

nevermind ive just done something wrong it adds to 370 not 360

i might coem back later i wanan try and figure this out

thanks for the help

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[crystal glen]

.reopen

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✅

[crystal glen]

wait no i had a tipa its exactly 360 degrees

so something weird is up, because i havent made a mathematical mistake

i would prefer not to show my work but i actually just have no idea why its adding to 360 exactly to the decimal

idk nevermind

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[ebon talon]

heya, needed some help with a vectors question.

[void carbon]

go on?

[ebon talon]

part bs spinnin my head

[void carbon]

break OA and AB into cos and sin components

hint: OA = Lcos(alpha) I cap + Lsin(alpha) J cap

[ebon talon]

alright one sec

L(cosa...sina)+L(cosb...sinb)...???

thats meant to be a vector

[void carbon]

wait

[ebon talon]

Does that look right sorta

[void carbon]

yes

correct

im in 12 grade

and in india they dont write vectors in matrices form

so i was sortta confused

[ebon talon]

ah right right sorry for the confusion

any idea on part b

[void carbon]

umm

so

sum of Y components of our vector must be = c

=1.5 m

[ebon talon]

oh yep got the answer

i found beta to equal arcsin (1.5-sina)

i appreciate you @void carbon

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[latent axle]

25

[latent axle]

Idk where to start

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[warped lodge]

my name is nathan

nath the king natheking

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[dry laurel]

can someone tell me if my first two initial answers are correct? and can you give me the formula for def? i'm confused on that

[craggy kite]

the underlines are an eyesore

[dry laurel]

ikr

[dry laurel]

is the bottom left 8.4?

and the bottom right 63.2?

(rounding to the nearest tenth)

[dry laurel]

or 8?

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[sacred sapphire]

yeah its 7.96 which is like 8

[dry laurel]

ok thanks!

what about the length of b?

is it 63.2

[sacred sapphire]

yeah

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[golden thistle]

What am i meant to do here?

[golden thistle]

I dont think what ive done is rigjt because i only get 1 value

[golden thistle]

Do i take the 2 quadratics away to get x - 4 ?

Then draw a graph for that?

[hallow crane]

think about what changes had to be made to transform:

$x^2 - 6x + 5 \mapsto x^2 - 7x + 9$

[solid kiln]

kanna

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[golden thistle]

So it deceeased by x and increaded by 4?

[golden thistle]

What

[golden thistle]

So 4 - x?

[hallow crane]

correct

,, x^2 - 6x + 5 - x +4 = 0 \implies \boxed{x^2 - 6x + 5 = x - 4}

[solid kiln]

kanna

[hallow crane]

do you see the implications?

This is equivalent to finding the intersection point(s) of the line y = x-4 with the quadratic x^2 - 6x + 5

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[vague pier]

[
2cos^2(\theta) \rightarrow (1+cos(2\theta)))
]

[solid kiln]

rainy

[vague pier]

what trig rule is this

[hard juniper]

Double angle combined with Pythagorean

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[languid pier]

could someone explain this binomial distribution to me?

[languid pier]

ok wait i get it nvm

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[topaz pagoda]

the x is 6

combined by (3x+2x+x)

(2x+10+3x-10+x)

[split chasm]

that doesn't mean that x is 6

[topaz pagoda]

i mean the process

[spiral urchin]

4x seems to be 360

[topaz pagoda]

how do you get the x if the whole number is 0

[split chasm]

what whole number is 0

[spiral urchin]

whole number is 4x -10 + 10

[topaz pagoda]

where did 4x come from

[split chasm]

they did a miscalc

[topaz pagoda]

+10 + -10

[spiral urchin]

(3x-10) + (2x+10) + x

[split chasm]

you're supoosed to apply geometric properties to set up an equation

[topaz pagoda]

like this

[split chasm]

no

set up an equation

that's the expression for the sum of the interior angles of a triangle
do you know the numerical value of such a sum?

[topaz pagoda]

for triangles its 180

[split chasm]

yes

so you'd set that equal to 180

[topaz pagoda]

yes

[split chasm]

then solve that equation for x

[topaz pagoda]

yes

but how do you get the x

[split chasm]

algebra

[topaz pagoda]

steps pls

[split chasm]

write the equation you have
and show what you've managed to simplify so far

[spiral urchin]

steps of what

[topaz pagoda]

wait

[spiral urchin]

4x = 180

x = 180/4

[topaz pagoda]

6x(+10 + -10)

[split chasm]

bad

the insertion of () there implies multiplication between 6x and (+10 + -10) which you don't want

if you wnated to insert ()
they'd be
6x + (10 + -10)

also

the x is 6
is very different from
6x

[topaz pagoda]

6x + 0

[split chasm]

and don't forget you have an equation
so you'd have
6x = 180

[topaz pagoda]

yes

[split chasm]

and from there it's prety much just one step away from getting x

[topaz pagoda]

divide both sides by 6?

[split chasm]

yes

[topaz pagoda]

okayy

x=30?

[split chasm]

yes

[topaz pagoda]

okay thanks

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[merry zodiac]

All options are correct

[twilit tusk]

I need help

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[merry zodiac]

.close

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[chilly raven]

The work above is for this problem

I'm not sure how to finish out the problem, I am confused as to how I combine the integrals

[lusty delta]

it looks like you’re trying to evaluate the integral

[chilly raven]

yes

I checked the answer key but it isn't very helpful

Just this

Where does the 1/37 come from?

I got it into the form they wanted but I don't understand the coefficient

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[chilly raven]

.close

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[rustic cipher]

How can i do this? (#17)

[rustic cipher]

I’m stuck after getting 12 pi for the circle

I don’t know the triangle part

How do I find the area of the triangle

Help would be appreciated!

[wispy totem]

sinus theorem

yes we have 12πcm² right now

[rustic cipher]

Yes

[wispy totem]

but we need to subtract the area of ​​the triangle from this

[rustic cipher]

Yep

[wispy totem]

ab/2 × sin(alpha)

angle alpha is formed by the intersection of a and b

sides

here alpha is 120°

a and b are equal each other

like 6cm, radius

[rustic cipher]

Okay

I haven’t been taught this formula yet, thanks for telling me about it

How would this formula look with all the numbers plugged in?

36/2 x sin(120)?

[wispy totem]

yes

[rustic cipher]

That’s 49.71

50 to nearest whole, do I use this

Or do I use the decimal

[wispy totem]

okay

[rustic cipher]

Alright

[wispy totem]

use decimal

i'd do this but

[rustic cipher]

12pi- 49.71 is the final answer then right?

[wispy totem]

maybe you should leave it square root

to be more accurate

12π-9√3

wait

49.71 is too big

how

sin120° = √3/2

a = 6cm
b = 6cm
sin(120°) = √3/2

(6cm)×(6cm)×(√3/2)×1/2

= 36√3cm²/4 = 9√3cm²

yes it should be like this

It has a value like 15

but it might be more appropriate to write like this

If approximate value isnt wanted

[rustic cipher]

The answer says 22.1

In decimal form

[wispy totem]

yes

it is true

because 12π ≈ 37.2

the other one is ≈ 15

37.2-15 = 22.2

[rustic cipher]

My teacher said to split the triangle to find the other side of the triangle but I don’t really know how to set it up

Ok i ss

See

[wispy totem]

i explained above

[wispy totem]

.

you probably miscalculated

before

but it's okay actually

[rustic cipher]

I didn’t get a final answer it is ok

Thank you

Give me a second to process the information you said

[rustic cipher]

So when it was this

[rustic cipher]

How did it turn into this

[wispy totem]

it was like that already

look for

sin area formula

if you want

with an image if possible

this would be more helpful

[wispy totem]

on a browser

[rustic cipher]

Where did you get radical 3/2 btw

[wispy totem]

this is a known value of sine

function

[rustic cipher]

Oh ok

[wispy totem]

Comes from the 1-√3-2 triangle

1²+√3² = 2²

opposite = √3 and hypotenuse = 2

for the 60° angle

but sin120° = sin60° as well

so it is valid for sin120° too

[rustic cipher]

Ok ty

That’s all

.close

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[proper gulch]

How would I go about it solving this question? I assume I would differentiate by using implicit differentiation then plug in the x and y values?

[proper gulch]

Would I plug in x and y here?

[ionic pendant]

yes, after you solve for dy/dx

[proper gulch]

I got dy/dx = root 3

if I were to plug it into that equation I get 2 times root 3

but that isnt an answer choice

would the answer just be root 3?

[ionic pendant]

what do you mean by that?

[proper gulch]

so I found dy/dx

[proper gulch]

then plugged it into this

was that step necessary?

[ionic pendant]

if you plug it into the equation it should just make the equation true (0=0), which is a good check that you did things right but not strictly necessary

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[umbral maple]

If I have a vector like AB with an arrow on the top for a normal vector, what does it mean when they give. |AB| with an arrow on top instead

[umbral maple]

also what does the triangle on top mean

wrote them out incase i’m unclear

[ionic pendant]

if you have $\abs{\overrightarrow{AB}}$ then that denotes the length or magnitude of the vector. $\widehat{AB}$ denotes a unit vector (vector of length 1) in the same direction as AB

[solid kiln]

cloud

[umbral maple]

yeah I get it thanks

.close

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