help-0

[whole shell]

are you saying this mathmatically, or because of the website you are solving the question on

because mathmatically you can pick any 2 points to find the slope

but if your website only takes it from a specific position, well its not like we can know what that is

what you had here is 100% correct

[lone heart]

@narrow gale Has your question been resolved?

[lone heart]

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[fringe yacht]

Hey! How to solve the system:

[fringe yacht]

$v_0 = v_1 + 2v_2$

[ocean seal]

sentinel

[fringe yacht]

$v_0^2 = v_1^2 + 2v_2^2$

[ocean seal]

sentinel

[fringe yacht]

Tried many things, no clue

[whole shell]

im confused

what do you want

as in

what is the goal

[fringe yacht]

Those are two equations of a system of equations

I want v1 and v2

In terms of the others

And I can't get past a very hairy messy equation, while the answers, include extremely simple ones

[whole shell]

so v0 is a constant?

[fringe yacht]

yeah

[whole shell]

well rearrange for v1 in the firstt equatinn

then sub that into the second one

and solve the quadratic

[fringe yacht]

Oooooh yeah right

I didn't think about that

Thanks

[lone heart]

@fringe yacht Has your question been resolved?

[lone heart]

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[vivid basin]

how do you derive that

the relationship isn't linear

it's called unit circle for a reason haha

so sin(a) is the y coordinate right?

so imagine going from sin(0 deg) to sin(1 deg)

what happens to the y coordinate?

yes

now imaging going from sin(90) to sin(91)
what happens to the y coordinate

yes

but is the increase equal to the decrease?

exactly
so you can't say sin(90° + alpha) = 1 - sin(alpha)

yeah and the increase is faster from sin(0) to sin(1) because it's going up almost vertically

yeah

when you claim sin(90° + alpha) = 1 - sin(alpha)
you are saying the increase/decrease is the same no matter what

but it depends on where you are

yeah you could say that I guess
basically just be careful in visualizing it

[lone heart]

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[drowsy sedge]

Hey everyone, have this practice problem and my first instinct was that it diverged, so I got it right but then apart of me was like "hmm, what if I just take the limit as n went to infinity the only thing affected is -1^n which goes to -1.. is it -8?"

[alpine sable]

try and write out the first 4 terms of the sequence

(your instinct is correct)

[drowsy sedge]

yeah I see its gonna flip flop

so its why I put diverged

but im more concerned on why I cant just take the limit

oh OOPS

I misread it

hahha I thought it was -1^n

not (-1)^n

[alpine sable]

ah yeah lol

[drowsy sedge]

ty

[alpine sable]

np

[drowsy sedge]

.close

[lone heart]

Channel closed

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Use .reopen if this was a mistake.

[drowsy sedge]

.reopen

[lone heart]

✅

[drowsy sedge]

ima now work on proving it diverges

well

is just simply saying its not monotonic sufficent

how do you typically prove convergence/divergence for sequences

the only way I know is either just throwing in the limit

but I guess thats not really a proof

or if it converges it has to be monotonic and bounded

[alpine sable]

no it's not, eg take $a_n= \frac{(-1)^n}{n}\to0$

[ocean seal]

Toby

[alpine sable]

do you know about subsequences?

[drowsy sedge]

neigh

wwait

sorta

I think I heard it

this stuff is new to me

[alpine sable]

do you know the result "if two subsequences converge to different values, then the original sequence doesn't converge"

[drowsy sedge]

it sounds familiar yeah

okay well

that makes sense

because the first subsequence goes to -8 then the next one to - 7

[alpine sable]

-8 and -6

[drowsy sedge]

ye misstype

[alpine sable]

but yeah, different values

[drowsy sedge]

oh okay

so thats all I would have to say?

[alpine sable]

yeah, I would say quoting the result is enough

[drowsy sedge]

one other thing

there is a method

by taking the absoloute value of the sequence right

and if its not 0 then it diverges?

[alpine sable]

are you thinking of a result for series instead of sequences? (something with a sum)

[drowsy sedge]

hmm, no I have in my notes

it is

(-1)^n(n)/(n+1)

and the prof took the abs value of it

got n/(n+1) and through l'hoptials

got 1 and then said it diverged and flips between things close to 1 and close to -1

and I dont really get it

[alpine sable]

$\frac{(-1)^n n}{n+1}$

[ocean seal]

Toby

[drowsy sedge]

yes

[alpine sable]

if the absolute value goes to 0, then it converges

the converse is not true

[drowsy sedge]

teah that I agree with

but how did my prof know it flipped between 1 and -1

[alpine sable]

I guess he split the limit up into two parts: (-1)^n diverges, and n/(n+1) goes to 1

[drowsy sedge]

hmmm

lemme see here

I did not know you could do that

But I suppose that makes sense

[alpine sable]

you have to be careful when you do that

[drowsy sedge]

how so?

[alpine sable]

(its probably easier to work with subsequences)

[alpine sable]

(-1)^n diverges, 1/n goes to 0, but the product converges to 0

[drowsy sedge]

mmm right

man how would u know when to do it then

[alpine sable]

if the second thing doesnt go to 0, then you are fine

[alpine sable]

usually, when I see (-1)^n, I would split it into two subsequences: when n is even and when n is odd

[drowsy sedge]

ahh right I get it

so then you know what two numbers it flips between

[alpine sable]

yeah

[drowsy sedge]

makes sense

[alpine sable]

and if the two numbers are different, then it doesnt converge

[drowsy sedge]

but then why do you take the absolute value whats the point

[alpine sable]

idk lol

[drowsy sedge]

do u have to?

u have to do it and if it goes to 0 then it convergess

ah okay I think im starting to understand

the absoloute value meta for convergence of a function

we can call it a function even tho its not

ah okay ye I get it now ty

ima leave this open for a wee bit working on a tricky one now

[alpine sable]

yeah, thats right

because even if it flips between negative and positive, everything still goes to 0

[drowsy sedge]

what

the abs value of it goes to 0

but not original right

[alpine sable]

the red line is zero

[drowsy sedge]

yee

hmm

[alpine sable]

if we take absolute values, everything becomes positive

but it still goes to 0

[drowsy sedge]

im confused why we take the absolute value

it shall remain a mystery

this one is hard

I wanted to use hoptials rule but I looked up the derivative of n!

and idk what the hell it is

[alpine sable]

lol yeah, dont

try showing that a_n is unbounded

[drowsy sedge]

has no upper or lower limit?

[alpine sable]

no upper limit

a lower limit is 0

[drowsy sedge]

yeee

so diverges

yay

hahaha

[alpine sable]

yeah, if you show that its unbounded above, it doesnt converge

[drowsy sedge]

Is there an example of one bounded by above

[alpine sable]

wdym?

a_n=0 is bounded above :p

[drowsy sedge]

i see

well I meant like

a more complicated example

of one bounded above and below

[alpine sable]

$a_n=\frac{1+3n}{n}$

[ocean seal]

Toby

[alpine sable]

is bounded above by 4 and below by 3

[drowsy sedge]

thats a good example

[alpine sable]

thx :D

[drowsy sedge]

I mean if I were to use LH rule on it

I get 3

so is that where it converges to

[alpine sable]

yeah

(it's also (1/n)+3 in disguise)

(and we know that 1/n goes to 0)

[drowsy sedge]

yep

ok but that confuses me

well actually nvm it does not 1 second

ok yee so it converges to 3

is bounded above by 1 and below by 3

i see I see

I have a few more in here

ima grind out

[alpine sable]

yup! :)

[drowsy sedge]

What is a partial sum

[alpine sable]

any context?

[drowsy sedge]

wait nvm

[alpine sable]

(its where you have a finite sum, and you keep adding more terms)

$S_n=\sum_{i=1}^n a_i$

[ocean seal]

Toby

[alpine sable]

a_i is a sequence, S_n is the partial sums of the sequence

[drowsy sedge]

hmmm I see

this is telescoping i presume right

it just seems like it does

[alpine sable]

yup

🔭

[drowsy sedge]

Im not very good at telescoping sums

thats just the only sum we went over a bit in class for series that converge

[alpine sable]

let a_n be the thing inside the sum (arccos - arccos....)

[drowsy sedge]

thats the only thing I know for converging series that and geometric

[alpine sable]

try and write out a_1 + a_2 + a_3 and look for cancellations

[drowsy sedge]

im not sure what arccos(1/3) is

I never memorized the unit circle

is that even on it

[alpine sable]

dont worry about what it actually is

just see that a_1 has -arccos(1/3) and a_2 has +arrcos(1/3)

so they cancel

you should see that the middle terms all cancel

and you are left with a start and end

[drowsy sedge]

it turns out

its just arccos(1/2)?

hmmm

its not

[alpine sable]

a_1+a_2+a_3 = arccos(1/2) - arccos(1/5)

[drowsy sedge]

wut

[alpine sable]

are you talking about the final answer?

[drowsy sedge]

ye

[alpine sable]

,calc cos^-1(0)

[ocean seal]

The following error occured while calculating:
Error: Unexpected type of argument in function pow (expected: number or Complex or BigNumber or Fraction or Unit or Array or Matrix or string or boolean, actual: function, index: 0)

[alpine sable]

um

,w arccos(0)

[ocean seal]

Results provided by WolframAlpha

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

Requested by Toby#2275

[alpine sable]

not quite

[drowsy sedge]

how did u get that

[alpine sable]

do you have a formula for partial sums?

[drowsy sedge]

neigh

[alpine sable]

try and find out what $\sum_{i=1}^n a_i$ is

[ocean seal]

Toby

[alpine sable]

for n=3, its this

[drowsy sedge]

1 + 2 +3

[alpine sable]

but what is it for an arbitrary n?

a_i is the arccos(1/(i+1))-arccos(1/(i+2)) thing

[drowsy sedge]

for any arbitrary n its just

[drowsy sedge]

that lul

[alpine sable]

yeah

but try and get rid of the sum symbol

since its telescoping, the inside terms disappear

[drowsy sedge]

mmmmmmmmmmmmmm

right

but mine goes to infinity

so I need to find

arccos(infinity?)

[alpine sable]

no

[drowsy sedge]

o

so its not the first term minus the last term?

ooooooooooooooh WAIT I GET IT

its

arccos(1/2) - arccos(1/n+2) as n approaches inf

[alpine sable]

yup 👍

nice work!

[drowsy sedge]

:D

aight lemme calculate this john

im writtign all this info down

sorry might take a sec

[alpine sable]

np

[drowsy sedge]

wait

so its pi/3 - pi/2?

that seems wrong

[alpine sable]

,w arccos(1/2)-arccos(0)

[ocean seal]

Results provided by WolframAlpha

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

Requested by Toby#2275

[alpine sable]

its correct

😀

[drowsy sedge]

it said -pi/6 was wrong

what could it be??

[alpine sable]

maybe try $\frac{-1}6\pi$

[ocean seal]

Toby

[alpine sable]

oh wait

[drowsy sedge]

well thats dumb

[alpine sable]

its asking for s_n

[alpine sable]

which is the formula for partial sums here

[drowsy sedge]

oh LMAOOOO

[alpine sable]

we went one step too far lol

[drowsy sedge]

we try again

this one I got 😎

[granite needle]

it says to ask my question here but its being used

[alpine sable]

choose one of the ones under available

[granite needle]

thank you

sorry for disturbing you guys

[drowsy sedge]

nw

ok lemme cook

[drowsy sedge]

wait why is there no limit in there?

shoulden't it be lim as n approaches inf for that?

[alpine sable]

yeah

[drowsy sedge]

mmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmm

[alpine sable]

but the first question it asks for s_n

and the second question it asks for the limit of s_n to infinity

[drowsy sedge]

ah okay

wait

well

nv,

wait its not -pi/6 again?

what it should be -pi/6 is it buggin

ah nvm there was a mistyped . there

[alpine sable]

looks good

[drowsy sedge]

alrighty last question

its a geometric one

so it should be a chiller

this does not seem to be a chiller

[alpine sable]

use the geometric series formula

[drowsy sedge]

the formula?

[drowsy sedge]

ohhh hmmm right

but we also have a^n

but its -1^n so i guess it does not really matter

what happens if it was like -2^n

[alpine sable]

put the (-1)^n into (x-3)^n

[alpine sable]

and a=1 in this formula

[drowsy sedge]

how do we know what the series converges for

[alpine sable]

for |r|<1

[drowsy sedge]

diverges for |r| > 1 right

[alpine sable]

first find out what r is here

[alpine sable]

|r| ≥ 1

[drowsy sedge]

ohh okay

how do I fugure out what R is

its like -(x-3) right

i mean that kidna gets us nowhere

unless it does

[alpine sable]

yes

you want |-(x-3)|<1

solve for x

[drowsy sedge]

ah okay this is chill lol

ty!!

[alpine sable]

yw :D

[drowsy sedge]

is it okay if I DM u if I have more questions later?

[alpine sable]

probably best to open a channel just in case im not here, and for latex

but you can dm me to tell me to look at your channel if im online

[drowsy sedge]

awesome!

[lone heart]

@drowsy sedge Has your question been resolved?

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[vestal venture]

Help please

[fallen verge]

whats your question

[vestal venture]

I don't know what the intervals for the numerator and denominators of this equation are

Don't know how to find them

[fallen verge]

when is a squareroot function coninuous?

start with just normal sqrtx

[vestal venture]

Substitute x for 4

Numerator would be 12 + sqrt4^2

Denominator would be sqrt12 + 16

Man I'm lost af

[gusty gorge]

probably should try to answer garlicbreadfries's question

[vestal venture]

At zero

[gusty hazel]

Correct me if I'm wrong but the issue is that this limit has multiple values due to the square root functions

[gusty gorge]

you're wrong

[fallen verge]

square root function is positive

[vestal venture]

R+=[0,∞)

[fallen verge]

the difference between x^2=4 and x=sqrt4 is one has one value, the other has two

[vestal venture]

The square root acting on the real numbers is continuous everywhere on the interval (0,∞)

[gusty gorge]

so would you say that the entire thing within the limit is continuous around x = 4?

[vestal venture]

Yes

[gusty gorge]

what do you know about continuous functions and limits?

in particular, what do you know about the limit of a continuous function?

[vestal venture]

Second week into Calc after a 4 year break 🙂

[gusty gorge]

in other words, if I say something like: f(x) = x+1 if x is not equal to 4, otherwise f(x) = 10 if x = 4

is that function continuous at x=4?

[vestal venture]

Yes, because it falls within the interval

[gusty gorge]

no it is not

because lim x->4 of f(x) = 5, but f(4) = 10

[vestal venture]

Ok

I understand now

lim x->2 of f(x) = 4 is continuous at 2 because f(2) = 4, instead of something weird like f(x) = x + 3 = 5

For example

[gusty gorge]

no

the property of continuous functions is that $\lim\limits_{x \to a} f(x) = f(a)$

[ocean seal]

Saccharine

[gusty gorge]

see if you can parse out what that means

[lone heart]

@vestal venture Has your question been resolved?

[lone heart]

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[full nimbus]

please tell me how you do this, I'm pretty sure this question isn't possible so please do it yourself first before you tell me how to do it

[pine kettle]

@full nimbus

so

its probably going to be a ratio

[full nimbus]

have you done it yourself first to see if its possible

[fallen verge]

use d=rt

[full nimbus]

bro what?

[fallen verge]

distance=rate times time

[full nimbus]

can you like walk me through it step by step

[fallen verge]

what is the distance

in miles

we are going to set up two equations

[clear blade]

Let x be the initial speed and y be the initial time taken

Xy =856

[full nimbus]

yeah

[clear blade]

(x+11)(y-4)= 856

[fallen verge]

bro

[full nimbus]

but u have 2 variables

[full nimbus]

what do you think we do

[clear blade]

We can replace x with 856/y

[fallen verge]

theyre correct

you said step by step though so i was going to explain how to set it up

ill let silver take over, theyre doing fine

[full nimbus]

yeah

[clear blade]

Xy-4x+11y-44= 856

We already have xy = 856

And then replace x with 856/y

It would be easier then replacing x immediately

[graceful perch]

can anyone help, i am doing a quiz with 5 questions left pls!!

[lone heart]

Please stick to your channel.

[graceful perch]

sorry

[full nimbus]

yeah

[lone heart]

@full nimbus Has your question been resolved?

[full nimbus]

.close

[lone heart]

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[eternal fjord]

how do you calculate the area of a parallelogram?

[rustic stratus]

that's a great question

I forgot

[eternal fjord]

ahh fair enough, the area of a parallelogram is just the base times the height

[rustic stratus]

it was that simple

ok

thanks for helping my forgetful brain

[eternal fjord]

no worries - in the future, consider that you can kind of "rearrange" the parallelogram into a rectangle, so you can calculate its area the same way

[rustic stratus]

alright\

[eternal fjord]

sorry for the poor drawing lol

but you get the idea

[rustic stratus]

yeah

thanks

[eternal fjord]

np

[rustic stratus]

so it would be 672

[eternal fjord]

sounds right

[rustic stratus]

so how do I mark this as resolved

[eternal fjord]

type .close

[rustic stratus]

.close

[lone heart]

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[vestal imp]

Hi! Just wanted to get some guidance upon these 2 questions

[vestal imp]

I've tried question 6 multiple times but the signs for the numerator is always different

So I chose the second answer which is correct but not fully correct. For example I got a = (2b+7c-5)/8

[hollow sparrow]

since they want to express a in terms of others variable

you should move anything multiplied by **a ** to the left side and the rest to the right side

and then simplify

[slate jolt]

because theres a mistake in the answer

its yours

the right one

for Q7 the correct answer is actually correct though

[vestal imp]

oh ye (x-3)(x-1) = 0 right

[hollow sparrow]

yep , 3 is the right answer

[vestal imp]

im still confused at 6 lol

[hollow sparrow]

i guess there is a typo in the question

[slate jolt]

the right answer is a = (2b+7c-5)/8

as you found

theres just a typo

[vestal imp]

oh man Q_Q

[hollow sparrow]

:- <

[vestal imp]

Thank you guys so much @slate jolt @hollow sparrow

https://tenor.com/view/love-you-guys-so-much-gif-24332409

.close

[hollow sparrow]

[lone heart]

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[fossil pilot]

Hello, was looking for some assistance regarding this problem.

[fossil pilot]

Am a tad confused since the rotated region is sin(x)

There are no other curves to approximate my answer off of, only the x and y axis

(forgot to add this image)

I keep getting stuck with finding the distance between the vertical line and the region that requires rotation

[lone heart]

@fossil pilot Has your question been resolved?

[tidal crystal]

what are some of your thoughts so far?

and bear with me it's been a long day for me, so i might be a bit slow 😆

[fossil pilot]

Had quite a long day as well, so we're both on the same page 😄

Basically my issue lies trying to plug it into an equation

[tidal crystal]

one thing I do know is that our bounds of integration are going to be from 0 to pi right?

[fossil pilot]

Yep

And the curve is sin(x)

The area between 0 and pi already satisfies that it is in quadrant 1

[tidal crystal]

yeah, here's my picture, we're rotating around the blue line; the white and purple lines are our bounds of integration

[fossil pilot]

My issue lies trying to figure out how to plug it into an equation that shows the volume of it rotating around the blue line above

The distance from the line to the curve is 1, but im trying to figure out how to write that down

From what i've seen, theres an inner radius and an outer radius that are taken into account to represent two equations, however, im getting confused since theres only one curve, sin(x)

[tidal crystal]

OH

okay, i think i got it

mayyyyyyyybe

wait

[fossil pilot]

Basically, i need to write an expression that represents the volume when that region is rotated around x = -1

[tidal crystal]

okay my thought is that the x=0 line is going to be our inner radius

but i don't think that's true maybe?

wait

[fossil pilot]

I'm getting confused because theres nothing to grab onto

both sides are sin(x)

instead of it being something like y = 2x+5 and y=x^2

[tidal crystal]

that was my thought on the inner and outer radius

but i think that's wrong isn't it?

my other thought is that one side of the sine function is the inner radius, and the other side the outer

[fossil pilot]

Been looking at an example on Khan Academy

They have it so that the y=sqrt(x) line is the outer radius, and the y=x^2 line is the inner radius

And what they're doing is subtracting the equation from the line's value, or distance from the axis

[tidal crystal]

yeah the subtracting based on where the axis is is the (relatively) easy part

okay so he's taking dy's

which like, i guess you could do?

[fossil pilot]

Yep

[tidal crystal]

maybe this if you're doing that

[fossil pilot]

I'm just stuck here because i only have sin(x) to work with

[tidal crystal]

you split sine into half

[fossil pilot]

Indeed, but how do I go about doing that?

I'm on the same page as you here, just stuck in trying to execute my thoughts

[tidal crystal]

we have to rephrase y=sin(x) into x=something with y's right?

[narrow kelp]

Does revolve around x=-1 mean the same as reflect across it?

[tidal crystal]

not quite

[fossil pilot]

It goes in a circle around x = -1

[tidal crystal]

yeah, so it'll end up looking like a very sad half doughnut

[fossil pilot]

^

[tidal crystal]

it feels like we're missing something obvious if we're resorting to dy's

[fossil pilot]

I'm thinking it will turn into x = sin^-1y

[tidal crystal]

especially when everything is so nicely presented in terms of x

[fossil pilot]

Inverse trig

[tidal crystal]

arcsin right?

yeah

[fossil pilot]

yep!

Now that we have that, how do we go about separating the two sides?

Because the curve is the same no matter what

It's x = arcsin y

[tidal crystal]

imma be real i don't think this is making it easier 😆

because then we need to translate our bounds of integration

[fossil pilot]

which leaves us with (pi(-1 - arcsiny)^2 - pi(-1 - arcsiny)^2)

[tidal crystal]

and our axis of rotation

[fossil pilot]

Theres the issue

It comes out to 0

[tidal crystal]

lol

[fossil pilot]

Because its the same function

[tidal crystal]

check out example 2 in here https://math24.net/volume-solid-of-revolution-disks-washers.html

so that's kinda what we knew we needed to do anyway

WAIT

that's about the X axis

not the y...

i'm big smart

[fossil pilot]

Close enough though

I do see whats going on

Just long and confusing

Anyways, i need to head to bed

I do thank you for all of your help!

[tidal crystal]

not sure how much I helped lol

[fossil pilot]

I'll move on this tomorrow, I think I know what i'm doing now

Believe me, you've helped

[tidal crystal]

look up volume of revolutions with trig/sine and that should put you on the right track

[fossil pilot]

Absolutely, will do

Again, thank you!

[tidal crystal]

take care!

[fossil pilot]

.close

[lone heart]

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[cold marsh]

I need help

[cold marsh]

“A right triangle haze side lengths 7, 24, and 25 as shown below. Use these lengths to find cosM sinM and tanM”

[fallen verge]

do you know what sohcahtoa is

[cold marsh]

no

[narrow kelp]

so

M is an angle

Choose M as your starting place

[cold marsh]

Ok

[narrow kelp]

label the hypotenuse, the side opposite, and the side adjacent

hyp = 25

opp = 24

adj = 7

[cold marsh]

ok got it

[narrow kelp]

$sin(\theta) = opp/hyp$

[ocean seal]

CrEpasPmkinPie
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[narrow kelp]

forgot to close parenthesis but hope you understand

[cold marsh]

Oh ok I understand

[narrow kelp]

theta in this case = M

[cold marsh]

I’ll need help with a couple others for my homework is this ok?

[narrow kelp]

sure

[cold marsh]

ok thank you

[narrow kelp]

$cos(\theta) = adj/hyp$

[ocean seal]

CrEpasPmkinPie
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[narrow kelp]

$tan(\theta) = opp/adj$

[ocean seal]

CrEpasPmkinPie

$tan(\theta\) = opp/adj$
```Compilation error:```! Missing $ inserted.
<inserted text> 
                $
l.58 \end{document}
                   
I've inserted something that you may have forgotten.
(See the <inserted text> above.)
With luck, this will get me unwedged. But if you
really didn't forget anything, try typing `2' now; then
my insertion and my current dilemma will both disappear.```

[cold marsh]

I figured out the question

[narrow kelp]

woo

[cold marsh]

I have another one

[narrow kelp]

show

[cold marsh]

It’s sending

[narrow kelp]

so x is your theta now

label the sides again

[cold marsh]

Alright done

[narrow kelp]

so now you know your hypotenuse and your adjacent

[cold marsh]

Yes

[narrow kelp]

you could do hyp/adj or adj/hyp

adj/hyp is easier

[cold marsh]

6/11?

[narrow kelp]

close

$cos(\theta) = adj/hyp$

[ocean seal]

CrEpasPmkinPie

[narrow kelp]

$cos(\theta) = 6/11$

[ocean seal]

CrEpasPmkinPie

[cold marsh]

I’m confused

I have to find X

[summer aspen]

They’re 64 cards in total the chance that we dont pick a 7 is 11 out of 12

[narrow kelp]

$cos(x) = 6/11$

[ocean seal]

CrEpasPmkinPie

[narrow kelp]

but cos is a function

cos(x) is just like f(x)

[cold marsh]

So X=6/11?

[narrow kelp]

not quite

the x is locked inside the cos function

[cold marsh]

Ohh

[narrow kelp]

have you done inverse functions?

[cold marsh]

not in a long time

[narrow kelp]

tbh

(I haven't done trig)

so

to get the x out of the cos

you need to

$cos^-1(cos(x))$

[ocean seal]

CrEpasPmkinPie

$cos\^-1(cos(x))$
```Compilation error:```! Please use \mathaccent for accents in math mode.
\MT@orig@add@accent ...gnorespaces \relax \accent 
                                                  #1 #2\egroup \spacefactor ...
l.57 $cos\^-
            1(cos(x))$
I'm changing \accent to \mathaccent here; wish me luck.
(Accents are not the same in formulas as they are in text.)```

[narrow kelp]

oh something weird happened

[cold marsh]

cos^-1

[narrow kelp]

so

yes that

that can also be written as arccos

$arccos(x) = cos^-1(x)$

[ocean seal]

CrEpasPmkinPie

[narrow kelp]

so to get the x out of the cos function

you need to take the arccos of it

$arccos(cos(x)) = x$

[ocean seal]

CrEpasPmkinPie

[narrow kelp]

in general you can just put arc in front of the function for its inverse

so do the same to both sides

$arccos(cos(x)) = arccos(6/11)$

[ocean seal]

CrEpasPmkinPie

[cold marsh]

alright

[narrow kelp]

$x = arccos(6/11)$

[ocean seal]

CrEpasPmkinPie

[narrow kelp]

now evaluate arccos(6/11)

I haven't taken trig so don't ask me how to do that

but calculator or Google or smth

[cold marsh]

Is it 56.9

[narrow kelp]

possibly

if a calculator says so I would trust it

[cold marsh]

alrighty onto the next?

[narrow kelp]

ok

[narrow kelp]

very similar problem

Try the same method with arccos and all that

[cold marsh]

Ok

I have a similar one but with different places

[narrow kelp]

show

[narrow kelp]

hmm

so you want x

you have angle

and you have adj

I would say

take a trig function of 47

that equals opp/adj

tan

[cold marsh]

Ok

Tan47=14 or something right?

[narrow kelp]

$tan(47) = x/14$

[ocean seal]

CrEpasPmkinPie

[narrow kelp]

and tan(47) is actually a number

so use algebra to find x

you would not want to use arctan here

[cold marsh]

I looked it up I think I got it right

what is hyp/adj again?

[narrow kelp]

well

that's sec(x)

hyp/adj = sec

adj/hyp = cos

but it would still work

[cold marsh]

Alright I’m on another one

[narrow kelp]

so replace the ? with x bc that's just better

[cold marsh]

Alright

[narrow kelp]

you know theta

hyp

and want adj

[cold marsh]

Yea

[narrow kelp]

adj/hyp I would say

which is cos

[cold marsh]

Cos74=(x/7)?

[narrow kelp]

yes!!

and then do algebra to it

$cos(74) = x/7$

[ocean seal]

CrEpasPmkinPie

[cold marsh]

Alright got it

Onto the next

Only this and 2 more

[narrow kelp]

show

[narrow kelp]

oof a big one

[cold marsh]

Yea

[narrow kelp]

so lets solve for a first

we know theta

wait

something is weird here

I don't think this is a right triangle

:o

it isnt

[cold marsh]

It’s acute I think

[narrow kelp]

so A is easy

[summer aspen]

They’re 64 cards in total the chance that we dont pick a 7 is 11 out of 12

[narrow kelp]

$180 - (B + C)$

[ocean seal]

CrEpasPmkinPie

[cold marsh]

82

[narrow kelp]

A = 82

[cold marsh]

Alright

[narrow kelp]

Oof

im not sure

[cold marsh]

I know c=17 because of it being parallel

But a is tricky

[narrow kelp]

parallel?

[cold marsh]

b and c

Yea idk I’m lost to

[narrow kelp]

strange

maybe something with feet??

[cold marsh]

I have no idea

I can skip over this one for now

[narrow kelp]

This looks like a harder version of the last question

I have an idea for the previous one now too

[cold marsh]

what’s the idea

[narrow kelp]

so draw a foot from angle A

thats a line perpendicular to a going through A

now you have a right triangle

so now

call that foot h

lemme draw a picture quickly

[cold marsh]

Ok

[narrow kelp]

$a_1 + a_2 = a$

[ocean seal]

CrEpasPmkinPie

[narrow kelp]

h and a are perpendicular

Dang B and C are flipped

But now you have theta and hyp

solve for adj

$cos(52) = \frac{a_1}{17}$

[ocean seal]

CrEpasPmkinPie

[cold marsh]

I can look this up

Or try

[narrow kelp]

$a_1 = 17cos(52)$

[ocean seal]

CrEpasPmkinPie

[narrow kelp]

oh this is a fun problem

[cold marsh]

10.5

Is a

Now I just need c

[narrow kelp]

a or a1

[cold marsh]

a1

[narrow kelp]

so now you have theta hyp and adj

you just need opp now

[cold marsh]

That’s hard

[narrow kelp]

soh cah toa

[cold marsh]

what does that mean

[narrow kelp]

its a mnemonic

soh

sin = opp / hyp

so now you want opp

opp / hyp or opp / adj

$sin(52) = \frac{h}{17}$

[ocean seal]

CrEpasPmkinPie

[narrow kelp]

$tan(52) = \frac{h}{17cos(52)}$

[ocean seal]

CrEpasPmkinPie

[narrow kelp]

$h = 17sin(52)$

[ocean seal]

CrEpasPmkinPie

[narrow kelp]

$cot(46) = \frac{a_2}{17sin(52)}$

[ocean seal]

CrEpasPmkinPie

[narrow kelp]

$a_2 = 17cot(46)sin(52)$

[ocean seal]

CrEpasPmkinPie

[narrow kelp]

$a = 17cos(52) + 17cot(46)sin(52)$

[ocean seal]

CrEpasPmkinPie

[narrow kelp]

$sec(46) = \frac{c}{17cot(46)sin(52)}$

[ocean seal]

CrEpasPmkinPie

[cold marsh]

are you on c?

[narrow kelp]

$c = 17cot(46)sin(52)sec(46)$

[ocean seal]

CrEpasPmkinPie

[narrow kelp]

monstrous

${c = 17cot(46)sin(52)sec(46)} , {a = 17cos(52) + 17cot(46)sin(52)} , {A = 82}$

[ocean seal]

CrEpasPmkinPie

[narrow kelp]

ok bye now I'm gonna go somewhere else

[cold marsh]

That’s nuts

[narrow kelp]

It probably is

[lone heart]

@cold marsh Has your question been resolved?

[lone heart]

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• Show your work, and if possible, explain where you are stuck.
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[wet lagoon]

Hi

[wet lagoon]

How do u add and subtract polynomials

[narrow kelp]

So write the polynomials next to each other

with the add/subtract

mhm

now you combine the like terms

that means they have the same variables and exponents

[wet lagoon]

Wha

18x-12x?

Like thqt

[narrow kelp]

yes

$18x-12x=6x$

[ocean seal]

CrEpasPmkinPie

[wet lagoon]

Wait

Since its positive - negative?

Or positive and positive

How do u know if its a positive oe negative

How do u know if its posi or negative

[lone heart]

@wet lagoon Has your question been resolved?

[lone heart]

@wet lagoon Has your question been resolved?

[lone heart]

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[lone heart]

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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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• Be polite and have a nice day!

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[spare fern]

How do I know when to use each triangle?

[grave cedar]

Yo

What do we need to find

[spare fern]

I just want to know when to use these triangles for finding exact values of trigonometric functions

[grave cedar]

They are different

[spare fern]

Yes but which cos(theta) angles determine which triangle to use?

[vapid shuttle]

these are the 45-45-90 and 30-60-90 triangles

when you have a triangle with the angles 30-60-90 you use that triangle...

and when you have the other, use the other

[flint pecan]

When the reference angle of the given angle is 30° or 60°, you use the first one, and if it's 45° use the second one

[spare fern]

Oh ok

[spare fern]

By reference angle do you mean related acute angle?

[flint pecan]

Yeah

[spare fern]

Alright thanks

.close

[lone heart]

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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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[vernal anchor]

can anyone help me w this thanks

[vapid shuttle]

, rotate

[vapid shuttle]

Do you know how to find the discriminant?

[vernal anchor]

yeah

just getting confused as there are 2 variables

k and x

the discriminant is b^2-4ac but what would the value for 'b' be

[vapid shuttle]

the value for b would be -6k

k I assume would be representing a constant value in this scenario

[vernal anchor]

so a would just be 5?

[vapid shuttle]

oh

are you sure you wrote it down correctly? perhaps this is a polynomial of "k"

and then it that case b would be -6x

[vernal anchor]

yeah it should be right

[vapid shuttle]

appears so

[vernal anchor]

ok thanks and quick question how would i go about solving the inequality

[vapid shuttle]

it looks like you would solve for a range of x-values that make it true

[vernal anchor]

actually i think it’s an error i think the first value is supposed to have an x in it

if so would this be correct?

[vapid shuttle]

, rotate

[vapid shuttle]

your first step looks right

so assuming you didn't mess up algebra

should be good

[vernal anchor]

thanks a lot

[vapid shuttle]

np

[vernal anchor]

sorry to ask again but you think you can show me how to solve the ineqaulity

[vapid shuttle]

I bet there's a method of using the discriminant to tell if a quadratic is > 0, but I don't know of it. Personally I was able to graph the equation with a slider for k, and I determined for which k values the equation is > 0

so you could try that, but it probably isn't how you are supposed to do it

perhaps try plugging in a few different values , like 0, 1, 10 for k and determining if the equation will be > 0

[vernal anchor]

i sent the image above it was the first one and it does say the equation is >0

[vapid shuttle]

it says that, but for different values of k that isn't true

your question probably wants you to find the range of k values that make the inequality true

https://www.desmos.com/calculator/jvgppnxbhv

play around with the slider on this and see what you can deduce

[vernal anchor]

thanks a lot

[vapid shuttle]

np

[lone heart]

@vernal anchor Has your question been resolved?

[lone heart]

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• Show your work, and if possible, explain where you are stuck.
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[ashen river]

can someone help me how to get the volume

[vernal anchor]

can someone help w solving this

[pliant cedar]

Please read #❓how-to-get-help

[pliant cedar]

You can multiply the area of the cross section by the width of the solid

[alpine sable]

Use formula:

$V = Bh$

where

B is the area of the trapezoid base

and

h is the distance between each trapezoid base

[ocean seal]

pulse

[alpine sable]

@ashen river

[lone heart]

@ashen river Has your question been resolved?

[lone heart]

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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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[whole shell]

how does - 0 + 4 = -4

how does 4 - 0 = 0

[modern sedge]

-0+4=4-0=4

[scenic falcon]

isnt + - = -

cus opposite is -

[whole shell]

yes

but thats only for the thing itself

[modern sedge]

4+(-3)=4-3=1

[scenic falcon]

wait true

sorry mb

i think i did it too fast

i wil, fix now

done

is it

x = 2

?

[scenic falcon]

wdym

[whole shell]

yh

[scenic falcon]

yaaaaaay

[whole shell]

+-0 + 4 is -0 + 4

its not -0 - 4

[wild trail]

that's true for products

not sums

[pale kestrel]

dont write it like that

use words; looks like nonsense to me

(and youre being confused since ur misusing it)

[scenic falcon]

i did that

i put -0+4

i didnt do -0-4

[whole shell]

yes, so how did you get -4

[scenic falcon]

is it just 4 then

[whole shell]

yh

[scenic falcon]

okay okay

tysm

[lone heart]

@scenic falcon Has your question been resolved?

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[whole shell]

the pattern is

x , (x)(x-1)

[abstract skiff]

?

can u explain a bit further

[desert rune]

damn youre fast man

i was close to seeing x^2

[abstract skiff]

ok

[marsh rapids]

anyone with a decent undergrad level can figure that ok quickly

[marsh rapids]

it's just experience

[abstract skiff]

can someone explain pls

[desert rune]

the pattern is x * (x - 1), so for 10 its 10 * (10 - 1) = 10 * 9 = 90

11 * 10 = 110

[abstract skiff]

ohh

[desert rune]

19 * 18 = 342

[abstract skiff]

I see!

how did u work that out

[desert rune]

ask doctor

[abstract skiff]

I wna know so that I can do this for other questions

doctor

[abstract skiff]

hey

how did u work that out

[whole shell]

90 = 10*9, 110 = 11*10

well the straw that broke the camels back

was

[abstract skiff]

yea ik but how did u work out the pattern

[pale kestrel]

!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.

[pale kestrel]

[whole shell]

seeing 21 -> 420

that was almost too specific

[abstract skiff]

ok

thanks

.close

[lone heart]

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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[lone heart]

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

@old widget Has your question been resolved?

[marsh rapids]

let f = LHS - RHS
Then show f reaches its minimum and that it's positive

[old widget]

<@&286206848099549185>

[pale kestrel]

.

No one will help you otherwise.

[marsh rapids]

I feel ignored

[lone heart]

@old widget Has your question been resolved?

[old widget]

I cant find solutions but I think it's actually not false

[marsh rapids]

just plot it

[astral briar]

i think you have to solve this question without doing that

[marsh rapids]

I know

it was for him to understand what's going on

of course you don't need to plot it

[marsh rapids]

that's why it isn't the solution I offered

[lone heart]

@old widget Has your question been resolved?

[fading cave]

what is the answer please help me I am confused

[old widget]

What

[lone heart]

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#❓how-to-get-help

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Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.