help-13

[crimson sedge]

the circular part?

[livid hound]

you do know what a cone is right?

[crimson sedge]

yeah

[livid hound]

are you familiar with party hats?

[crimson sedge]

look i may not know this but ive atleast eaten icecream

[crimson sedge]

yes

[livid hound]

the base of a cone is a circle
and the other part is referred to as the curved/lateral part

[crimson sedge]

oh ok

[livid hound]

(you already know the area of the base, so to determine the total area, you'd need to know that other part)

[crimson sedge]

the area of the other part?

[livid hound]

the area of the face/part that isn't the circular base

[crimson sedge]

ok

then?

[livid hound]

wdym then

[crimson sedge]

how do we find the area of that

[livid hound]

did you

perhaps you should first look up on surface area of a cone,
or actually lateral/curved area of a cone would be more helpful
and state any parts (if any) that you don't understand

[crimson sedge]

i tried but i couldnt understand shit

[livid hound]

link what you're reading

and

and state any parts (if any) that you don't understand

[crimson sedge]

https://www.cuemath.com/measurement/surface-area-of-cone/

wait do i use the Pythagoras theorem for this

[livid hound]

pythag would be part of the calculations

[crimson sedge]

25 + 144 = 169

which is 13

[livid hound]

sqrt(169) is 13

that will be the slant height

[crimson sedge]

and thats pi1213

[livid hound]

pi * r * l = pi * 12 * 13
gives you the curved surface area

[crimson sedge]

156*pi

[livid hound]

yes, and the total area
would be
curved area + area of base

[crimson sedge]

156+144

damn thanks man

.close

[cedar kiln]

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[oblique lynx]

I am solving $$\int_{-1}^{2}|cos(\frac{\pi x}{2})|dx$$ and this is my solution $$\int_{-1}^{2}cos(\frac{\pi x}{2})dx =$$ $$= \left[\frac{2}{\pi}sin\frac{\pi x}{2}\right]_{-1}^2$$, is the answer -0,6366... correct? And also, is it equivalent to $\frac{6}{\pi}$?

[wraith dagger]

marejak023

[crimson delta]

6/pi is positive

so that can't be the same

you can't just ignore the absolute value like that

[oblique lynx]

oh right.. im dumb

[crimson delta]

the integrand is nonnegative so the value of the integral also has to be nonnegative

[oblique lynx]

well and what should i do with the abs? I was using the integral-calculator website and I achieved the same result

[crimson delta]

check where cos(pi x/2) switches signs

and then split up the interval into several ones each over those integrals

then depending on whether cos(pi x/2) is positive or negative there, flip the sign

then calculate each integral and add up

[cedar kiln]

@oblique lynx Has your question been resolved?

[oblique lynx]

tried to sketch it on paper, so the sign should be flipped from -pi/2 to pi, if thats correct

[crimson delta]

that would be for a normal cos(x) curve

here its cos(pi x/2)

wait I misread. that's not even correct for cos(x)

[oblique lynx]

well i was plugin in the values

wel the cos flips sign from pi/2 to 3pi/2

[cedar kiln]

@oblique lynx Has your question been resolved?

[dire geode]

,w plot cos(pi x / 2) for -1 < x < 2

[wraith dagger]

Results provided by WolframAlpha

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

Requested by riemann#2529

[dire geode]

adapt your knowledge to cos(pi x / 2) for -1 <= x <= 2

[cedar kiln]

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[shrewd gull]

So like how would I determine how much money I would have if I saved $90 , $95, $100, $120 & $150 for 3 months

[dusk finch]

What do you mean?

[shrewd gull]

I wanna know how much money I would have if I save those amounts of money for 3 months

I should’ve never skipped maths class but oh well

[dusk finch]

If you saved eg. 90$ for 3 months? You would have 90$ :]

[livid hound]

what's the original wording of the question

[shrewd gull]

oh

oops

[livid hound]

are you paraphrasing

[dusk finch]

I am pretty sure they're not :p

[livid hound]

are you translating

[shrewd gull]

If I saved those amounts every week for that much months

[shrewd gull]

nope I just speak broken English so my English is just terrible

[dusk finch]

How many weeks do 3 months have?

It may differ

[shrewd gull]

4 weeks per 3 months ? 🥴

[dusk finch]

It will be either 12 or 13

[dire geode]

12 months in a year, 52 weeks in a year, 13 weeks in 3 months

[dusk finch]

probably 13 unless February is included

So like 1st week you go to bank and save 90$. Another week you go to bank and again save 90$?

[shrewd gull]

yes

[dusk finch]

Okay, so isn't it just 90$x13?

[shrewd gull]

oh is that the sum? Ty

what does the * mean 💀

[dusk finch]

Look, that would be 90+90+90+90+90+90+90+90+90+90+90+90+90, which is 90x13

It's multiplication. 5*4=20. This symbol is used mainly on computer, on paper it usually reffers to differenct concept.

[livid hound]

• is plain text symbol for multiplication

[cedar kiln]

@shrewd gull Has your question been resolved?

[cedar kiln]

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[hushed ore]

this is a self study assesment and im really struggling with understanding it

@uncut veldt

@lusty birch

<@&286206848099549185>

[white field]

you should first roughly graph the function to get better idea

are you fine with graphing it?

[hushed ore]

im already done graphing it i just have a hard time with the lim thing i still dont understand it

[white field]

see,

with the 'a' part the limit will be 2 as it can be easily observed

you agree with it?

[hushed ore]

yeahh

[white field]

good, then what part specifically are you struggling with?

'a', 'b;, 'c',.... which one?

or do you have doubt in each one?

[hushed ore]

what im stuggling is i dont understand what i should do with those my teacher doesnt explain it properly

[white field]

I'm sorryy, I didn't get your point

Is it like- you got it when I explained you 'a' part but you didn't get it when your teacher did

or you are asking how to formally write answer with explanation

[hushed ore]

oh its like the class ended early so my teacher didnt get to teach us those part he just said to search and learn it ourselves

[white field]

ohh

so should I explain 'b' and other parts too?

[hushed ore]

yesss if its okay with you

[white field]

sure

As you can see in 'b', if you approach from right side, the limit would be 3, right?

so 3 is the correct answer

Now if you can see the the right hand and left hand limits aren't same so answer for 'c' would be undefined

are you getting it?

[hushed ore]

yesyes

"undefined" and "does not exist" is just the same right?

[white field]

maybe not

sorry for that

I was wrong, I guess

call it "does not exist" for now

Now for 'd' part you can see definition of function to get g(-2) = 2

for 'e' and 'f' part you can again do the same thing to get 3 and 2 respectively as answers

and again for 'g' limit doesn't exist

and finally g(2) = 1

is it all clear??

[hushed ore]

i still dont fully get it but thank you

[white field]

what part did you not get?

or maybe it's getting hard for you to understand it on a chat

you should probably seek your teacher's help

[cedar kiln]

@hushed ore Has your question been resolved?

[north stump]

for the limits that have a "-" superscript (for example x -> -2⁻) imagine a car driving along the graph, from the left, approaching the value at which x tends to (in this case -2), but not touching it, and stopping just by... which value would the car give? I think that is kind of the idea of a limit (this is how I like to imagine it)

in this sense, what matters for establishing a limit is what happens "around" the value, rather than IN the value itself

[cedar kiln]

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[north stump]

for instance, for a graph like this, when x -> 3⁻, we have f(x) = 1, as the car approaches the value 3 but never "falls"

[cedar kiln]

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[bright sorrel]

could someone just check this?

[bright sorrel]

by my calculations, pi over 12 should be negative

it's 1/3-1/2 = -1/6

divided by 2

=-1/12

[soft owl]

yes

could you show us the whole question ?

[bright sorrel]

moment

it's a trigonometric equation

@soft owl

beginning is underlined

so definitely a mistake by the authors there

[soft owl]

yep

[bright sorrel]

thank you

.close

[cedar kiln]

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[bright sorrel]

.reopen

[cedar kiln]

✅

[soft owl]

but if :
sin(4x + pi/3) + sin(pi/2 - 2x) = 0
doesn't mean by necessary that :
sin(4x + pi/3) = 0
sin(pi/2 - 2x) = 0
isn't ?

[bright sorrel]

well you might be right, but I checked with the answers in the textbook, and it turns out there's really a mistake there

since that's just from a website that's 3-rd party solving my textbook's problems

thank you though

have a good one, @soft owl

[soft owl]

anytime

[bright sorrel]

.close

[cedar kiln]

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[soft owl]

you too

[cedar kiln]

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[torpid urchin]

does anyone know what the F here is, i am kind of confused

is it just a third primitive statement?

or is it possibly saying something like when that statement is true ^ false

[worn patio]

It could be a boolean function

[torpid urchin]

i don’t think we have learned what those are

the only notation for F we know is just representing false

[cedar kiln]

@torpid urchin Has your question been resolved?

[cedar kiln]

@torpid urchin Has your question been resolved?

[cedar kiln]

@torpid urchin Has your question been resolved?

[cedar kiln]

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[umbral adder]

<@&286206848099549185>

bruh

[cedar kiln]

@umbral adder Has your question been resolved?

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[dusky pine]

A public health researcher examines the medical records of a group of 937 men who died in 1999 and discovers that 210 of the men died from causes related to heart disease. Moreover, 312 of the 937 men had at least one parent who suffered from heart disease, and of these 312 men, 102 died from causes related to heart disease. Suppose A is the event where a selected man from this group died of causes related to heart diseased, and B is the event where at least one parent suffered from heart disease.

Construct a venn diagram to represent the given scenario.

A is the 210 or 102?

[cedar kiln]

@dusky pine Has your question been resolved?

[cedar kiln]

@dusky pine Has your question been resolved?

[cedar kiln]

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[hidden nacelle]

assistance on c

[obsidian coral]

Part b should help with part C

[hidden nacelle]

90?

[obsidian coral]

Yep

[hidden nacelle]

ty

.close

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[crimson sedge]

how do i figure this out??

[obsidian coral]

Do you know SOH CAH TOA?

[grand forge]

Multiple ways

[crimson sedge]

yep

[obsidian coral]

What trig function should you use?

[crimson sedge]

cos?

[obsidian coral]

In perspective of the given angle, 50, what side is B?

Adj, opp, or hyp?

[crimson sedge]

o

[obsidian coral]

And what about the side that is 80?

[crimson sedge]

hyp

[obsidian coral]

So what trig function should you use?

[crimson sedge]

sin?

[obsidian coral]

In SOH CAH TOA, which one uses opp and hyp?

[crimson sedge]

sin

[obsidian coral]

So can you make the equation based on that info?

[crimson sedge]

how do i choose which trig function

do i use the one w the pronumeral

[crimson sedge]

no’

[obsidian coral]

perspective of the given angle

[obsidian coral]

You know it's $sin(\theta) = \frac{opp}{hyp}$

[wraith dagger]

dldh06

[obsidian coral]

Fill in what you know

[crimson sedge]

ok

5/80

[obsidian coral]

Where is 5 from?

[crimson sedge]

misclick

b

it’s b

[obsidian coral]

And what about the $sin(\theta)$ part?

[wraith dagger]

dldh06

[obsidian coral]

What do you plug in?

What's theta

[crimson sedge]

50

i think

[obsidian coral]

So the equation is?

[crimson sedge]

uhh

im so dumb ffs

[obsidian coral]

It's this with the stuff you just plugged in

[crimson sedge]

80sin50 ?

[obsidian coral]

You plugged in theta, opp, and hyp

I asked for the equation after you plugged in the stuff

$sin(\theta) = \frac{opp}{hyp}$

[wraith dagger]

dldh06

[obsidian coral]

You know theta, opp, and hyp, plug in those givens

[crimson sedge]

sin50 = b/80

[obsidian coral]

Now the problem asks how would you solve for b, so set the equation equal to b

[crimson sedge]

u multiply both sides by 80 to cancel out the 80 on the left?

so 80sin50?

[obsidian coral]

Yes

[crimson sedge]

tysm

i have another question if u dont mind

[obsidian coral]

Ask

[crimson sedge]

b was a complete gues

[obsidian coral]

Given $tan(\theta)$, what is the ratio for tan?

[wraith dagger]

dldh06

[crimson sedge]

yeah idk where to start with teh questiomn

do u mean like o/a

[obsidian coral]

Yes

[crimson sedge]

yep

i labelled them

a/b

[obsidian coral]

So if tan theta = a/b what is a?

And what is b?

[crimson sedge]

idk

[obsidian coral]

Use tan theta = 1/2

[crimson sedge]

1?

[obsidian coral]

1 for what?

[crimson sedge]

a

[obsidian coral]

Then b is?

[crimson sedge]

2

[obsidian coral]

So if a = 1 and b = 2. can you figure out the proper answer now?

[crimson sedge]

i’ll try hold on

it’s d

b = 2a

[obsidian coral]

Yes

[crimson sedge]

damn this worksheet is hard

im 13 turning 14 this year is is bad that idk how to do these

[obsidian coral]

All this is applications of SOH CAH TOA

[crimson sedge]

wait is it c

bc i think it uses sin

[obsidian coral]

Yes

[crimson sedge]

im so smart

[crimson sedge]

could u answer this pls

be honest

[obsidian coral]

I didn't answer that because that sentence was hard to understand

[crimson sedge]

i am 13, is it bad that i dont know how to do these types of questions

i am turning 14 this year

[obsidian coral]

No, it's not bad, because everyone learns at different rates

[crimson sedge]

ok, im taking a 5 min break (pomodoro) should i close this and open a new one soon

[obsidian coral]

You can close and open when you need to

[crimson sedge]

imma keep this open and come back in 5min

[crimson sedge]

im back

.close

[cedar kiln]

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[little oyster]

No clue what i'm doing wrong here. I'm on part A. I'm integrating over the interval [0,3]

factoring 2pi out, over 0,3, then taking the top function minus the bottom function with respect to y

integrating normally and not getting an answer that makes sense (negative, pi somehow factored out) etc.

should I be integrating from -1 to 3?

<@&286206848099549185>

plz

[cedar kiln]

@little oyster Has your question been resolved?

[cedar kiln]

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[lunar maple]

hello

[lunar maple]

i need help with a trigonometry problem

i need to find how long the line BD is

hello ?

can someone help me ?

<@&286206848099549185>

hello ?

[cedar kiln]

Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.

[lunar maple]

ok

[cosmic steppe]

!status

[cedar kiln]

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

[lunar maple]

1

[half forge]

Let's say BD = x

[lunar maple]

ok

[half forge]

Can you express AD using x and tan35°?

[lunar maple]

i'll try

idk

[half forge]

tan35° = AD/BD

Do you understand that?

[lunar maple]

/ is divided, right ?

tan35 is 88.363

[dire geode]

,calc tan(35 deg)

[wraith dagger]

Result:

0.70020753820971

[lunar maple]

oh, i did tan-1

nvm

[half forge]

Well tangent means opposite divided by adjecent

[lunar maple]

the length, not the angle, right ?

opposite of the angle, and adjecent of the angle

[dire geode]

both AD and BD refer to lengths

[lunar maple]

ok

how do i use the angles and the length of AC to find BD ?

if i use tan, then i have to use the opposite of A

which i dont know

[tired portal]

tan (35°) = AD/BD
AD = BD•tan (35°)

tan (22°) = DC/BD
DC = BD•tan (22°)

AD + DC = AC = 80m

[lunar maple]

i still dont know what to do, tbh

[dire geode]

try not to do the whole problem for people

[lunar maple]

its ok

[dire geode]

it's better to give hints and have them do computations

[lunar maple]

just tell me step by step, what i have to do

[lunar maple]

i am kind of in a hurry, so hints would take a lot longer than i have time to study

[tired portal]

👍 sry, wont do again

[lunar maple]

no no, its ok

[obsidian coral]

Hints help you learn

You then get to apply those helps and solve it yourself

[lunar maple]

ik

[obsidian coral]

Because if someone just gives you the process, you're just going to memorize it

[lunar maple]

but there is a test TOMORROW, and my grades are really bad

[lunar maple]

at this point, i'll take memorizing

[swift sky]

Which will, over long term, lead to not understand the concept, which means you won't know how to solve a similar problem given slightly different constructs.

It's really a matter of short term gain for long term loss, or short term loss for long term gain

[lunar maple]

i will properly learn it after the test

[tired portal]

b4 would be cool tho

[lunar maple]

i dont have time for it tho

[tired portal]

😳

[lunar maple]

i wish i did

[obsidian coral]

Or properly learn now so it doesn't hurt you in the future when you start cramming

[lunar maple]

i cant do it properly now, i SWEAR i will later

but rn, i need to memorize as much as i can

this is the FINAL test

i'll either fail, or pass

and probably fail

[obsidian coral]

Bad idea

[lunar maple]

its all i have rn

[tired portal]

imo, memorising this wont do any good, u need to develop the skill so u can apply it to every question

[lunar maple]

if i memorize the way it works, and try to apply it

[obsidian coral]

Still don't suggest memorizing

[lunar maple]

ok

[obsidian coral]

Under pressure, you will forget everything

[lunar maple]

i dont know anything to forget

how tf did i get here, never would have guessed that i would be this close to failing

anyway, thx

i'll just go

[cedar kiln]

@lunar maple Has your question been resolved?

[cedar kiln]

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[rigid helm]

Alex can box thirty books in 2 minutes, James can box thirty books in 3 minutes, and Mayra can box thirty books in 5 minutes. How many minutes does it take all three of them, working together with no loss of productivity, to box 100 books?

[rigid helm]

May I get a hint on solving this and know what topic this is on?

[crimson sedge]

alex can box 15 books a minute

[rigid helm]

I'm pretty new to these types of problems

[crimson sedge]

james cna box 10 books a minute

marya can box 6 books a minute

all together they can box 31 book s aminute

[rigid helm]

Ohh ok

But what topic is this on?

Inverse proportions?

[crimson sedge]

no

just logic

[frosty ocean]

Time and work

Very basic stuff

[rigid helm]

Oh ok, thanks!

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[spark rune]

do opposite rays always share the same point

[spark rune]

in the middle

hello

[zenith sail]

Yes, opposite rays share the same endpoint, and continue on in opposite directions

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[crimson sedge]

what happened here

[flint plinth]

,rotate

[flint plinth]

,w plot sin(x)

[wraith dagger]

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[flint plinth]

,w plot abs(sin(x))

[wraith dagger]

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[flint plinth]

notice that the period of |sin(x)| is half of the period of sin(x)

this is because the absolute value makes the negative parts positive

and each positive hump is a period

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[scarlet ginkgo]

What rule is being applied here?

$f(x) = x^2 \sec x \$

$f'(x) = 2x \sec^2 x \tan x$

[wraith dagger]

Willow

[scarlet ginkgo]

yes?

[dire geode]

,w diff x^2sec(x)

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[dire geode]

Product rule and power rule

[scarlet ginkgo]

What is my sign to use the chain rule?

[dire geode]

My bad, no chain rule here

[scarlet ginkgo]

same question:
#help-13 message

[dire geode]

function composition

[scarlet ginkgo]

meaning specifically?

or examples?

[dire geode]

https://tutorial.math.lamar.edu/classes/calci/chainrule.aspx

Do all examples 2

[flint plinth]

if you want to have fun, you can use the chain rule for functions of 2 variables to derive the product and quotient rules

[scarlet ginkgo]

I'm about to do all of example 2, but I must stop and say Outstanding explanation of the Chain Rule parts in that link!

could have saved me a ton of time going there first

[dire geode]

Glad to hear

[scarlet ginkgo]

I wonder why the answer was re-written?

[dire geode]

No preference. Both are equivalent

[scarlet ginkgo]

Therefore, the outside function is the exponential function and the inside function is its exponent.

For example c, e and its exponent aren't separated so I don't see how this works here.

[dire geode]

This one?

[scarlet ginkgo]

yes, i read that

[dire geode]

outer function is e^w and inner function is w^4 -3w^2+9

[dire geode]

Do you know
$\frac{d}{dw} e^w=?$

[wraith dagger]

riemann

[scarlet ginkgo]

oh. so, that's how to separate the two

no, I haven't heard of this before

[dire geode]

Hmmm. That's probably something to worry about another time then

[scarlet ginkgo]

i know e is a specific value though

scientific notation, i think

[dire geode]

The organization of this chapter assumes you know most derivatives already: trig, log, exponential, polynomials

[scarlet ginkgo]

ok. i will continue now that I know this:
#help-13 message

[dire geode]

Skip that example and re-read it as soon as you learn this

,w diff e^x

Spoilers

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[scarlet ginkgo]

,w diff ln

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[scarlet ginkgo]

for example d, I thought it would be $\frac{1}{x} \cdot (x^{-4} + x^4) (-4x^{-5} + 4x^3})$

[wraith dagger]

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

[scarlet ginkgo]

but I guess log does not work like sin and must have it's value computed first

I'll have to return to these examples since I must get hw done

the substitution in the last few examples aren't clear

but let me return to the original problem here:

#help-13 message

now, i see what you mean by "no chain rule here"

the variables all occur by themselves with no operator separating them

therefore the product rule and power rule apply

[tropic oxide]

on the one hand i have an itch to mention the higher-order product rule, on the other that'd probably only sow confusion

[cedar kiln]

@scarlet ginkgo Has your question been resolved?

[scarlet ginkgo]

#help-13 message

What happened in the last x^2(....) part?

yes, it was $x^2 \sec x \tan x$

[wraith dagger]

Willow

[scarlet ginkgo]

What I have is:

$2 \sec x + 2x \sec x \tan x + 2x \sec x \tan x + x^2 \sec x \tan x$

[wraith dagger]

Willow

[scarlet ginkgo]

<@&286206848099549185>

[scarlet ginkgo]

<@&286206848099549185>

[cedar kiln]

@scarlet ginkgo Has your question been resolved?

[cerulean sail]

Product rule on $\sec(x)\tan(x)$ I would believe?

[wraith dagger]

chartbit

[scarlet ginkgo]

I thought that's what I did

also, quick question since I'm doing other hw while waiting on assistance for this:

does the exponent 3 go to both the num and denom?

[cerulean sail]

Yep you’d apply it to both, equivalent to $4\frac{(1+t)^{3}}{(t+3)^{3}}$

[wraith dagger]

chartbit

[cerulean sail]

Ah how did you apply it(?)

[scarlet ginkgo]

$2 \sec x + 2x \sec x \tan x + 2x \sec x \tan x + x^2 \sec x \tan x$

[wraith dagger]

Willow

[cerulean sail]

[have poor reception atm 🚂 may reply slowly]

[cerulean sail]

Did you differentiate sec(x)tan(x) on the last bit? You’d need to do that if that’s like the whole expression no?

Looks like everything else you did fine but you’d need to differentiate the sec(x)tan(x), which is their brackets

[scarlet ginkgo]

i'll return to this later

another quick question

^ what's the outside function here?

is it x^2?

[cerulean sail]

What do you mean by outside function, for chain rule?

[scarlet ginkgo]

oh, there is no chain rule here

[cerulean sail]

Just note that (cos(3)) is a constant like any other number there

[tropic oxide]

cos(3) is just a number

[scarlet ginkgo]

this is the product rule

[scarlet ginkgo]

oh, you mean it's a constant?

[tropic oxide]

sure is.

[scarlet ginkgo]

ah, that's what the parens is signifying

[tropic oxide]

i mean, you technically \textbf{can} apply the chain rule here by treating this as the composition of the linear function $t \mapsto \cos(3) \cdot t$ with the function $x \mapsto x^2$... but writing that out will reduce to the linearity rule. or the constant multiple rule, as it might be known in your class.

[scarlet ginkgo]

so, this isn't even the product ruel

[wraith dagger]

Ann

[cerulean sail]

Don’t need it here no

[scarlet ginkgo]

just the plain ole constant multiple rule

[cerulean sail]

(Similar to above, you could, but no need to at all)

[scarlet ginkgo]

What's happening here?

[cerulean sail]

Double angle cos identity

[scarlet ginkgo]

is it this?

[cerulean sail]

No no, there’s $\cos(2a) = \cos^{2}(a) - \sin^{2}(a)$ as an identity

[wraith dagger]

chartbit

[cerulean sail]

(You can use this to get equivalent forms of the double angle cos identity)

They just applied that here by factoring out the 2 (and setting a= 2x)

[scarlet ginkgo]

found it

https://www.onemathematicalcat.org/Math/Precalculus_obj/doubleAngleFormulas.htm

[scarlet ginkgo]

What's this alternate solution?

what rule(s) is this?

[cerulean sail]

That’s double angle identity for sin, first changing the original form using $\sin(2a) = 2\sin(a)\cos(a)$

[wraith dagger]

chartbit

[cerulean sail]

[alright network is getting really bad here :/]

[cerulean sail]

Divide both sides by 2 and set a=2x similarly to beforehand

[cedar kiln]

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[flint shadow]

How do I solve this matrix ? I don't know how to start on this one...

[flint shadow]

I know how to solve n * n matrices but I'm not sure about this one

[dusk finch]

I am not sure about this, but is this thing representing system of 3 equations with 5 variables?

If I was right with my first statement, then first let's name the variables like this.

Now variable B and whole 2nd column can be removed since it's not even present in the system of equations. In whole column, there are just 0s

So you are left with this

You can see that C=4, and E=0, by looking at 2nd and 3rd row of matrix.

Now from the first row, you can reconstruct equation 1A+5D=-5. Which is usolvable.

So your final solution is A is unknown, but there is some relation with D, B is completely unknown, C is 4, D has relation with A but is unknow, and E is 0.

Am I correct charbit? Last time I've encountered linear algebra was like 6 months ago

Okay thanks

[cerulean sail]

Basically I’d say that this step here isn’t needed, but assuming “solve” means there’s a linear equation this represents, yea

[cerulean sail]

Read as a+5d=-5, c=4, e=0

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[summer kayak]

How do I calculate the derivative of absolute value function for some x

[summer kayak]

Differentiate $|x^5-1|$ in the origin?

[wraith dagger]

afeAlway

[tropic oxide]

do you mean at x=0?

the graph of y = |x^5 - 1| does not pass through the origin.

in any case, x^5 - 1 < 0 for x ∈ (-∞, 1), so your function is equal to 1 - x^5 around x=0, and its derivative is the same

[cedar kiln]

@summer kayak Has your question been resolved?

[summer kayak]

so both $x^5-1$ and $1-x^5$ work for x=0?

[wraith dagger]

afeAlway

[tropic oxide]

what do you mean by "work"...?

i don't understand your question.

[summer kayak]

I mean if they gave the same answer which they did, for example if it had been x=2 only x^5-1 would have worked but nevermind, I understand it now.

[tropic oxide]

.... ???? what

you are making no sense

[summer kayak]

nevermind

.close

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[coarse jackal]

Hi! I have a question about SageMath/Sage. I know that divisors(x) gives the divisors of x but how does one get for example to 4th divisor of x(If it has that many)? Ex: 4th divisor of 24=4

[cosmic steppe]

As far as I'm concerned, divisor(x) seems to be an operator only used by whatever program you're using

It's probably taking the 4th element from the list of (positive) integer factors of x

Like factors of 24 are {1, 2, 3, 4, 6, 8, 12, 24}

@coarse jackal makes sense?

[coarse jackal]

Uh it prints out a list of all its factors but I don't wish for that here

[gilded elm]

maybe

divisors(x)[3]

seems to be more of a question for #computing-software

[coarse jackal]

Gotcha

That didn't work btw

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[elder elm]

So for problem 3, the relationship would be negative, right?

My work thusfar

[lethal arrow]

Yes

[elder elm]

Is my work also correct?

[lethal arrow]

Yes @elder elm sorry, phone call

[elder elm]

How do we know it is negative? Is it because as one line of x,y ordered pairs incease, the other is decreasing?

[lethal arrow]

I want to phrase it differently. $x$ is the independent variable. As $x$ increases, the $y$ variable decreases. This is most-easily determined by recognizing the coefficient of the $x$ term in your equation. Specifically, you have $y=(-2)x+12$...the $-2$ means the relationship is negative.\

[wraith dagger]

RiemannZeta

[elder elm]

And the same is true for the other part of the table?

the y values for 6, 8, 10, and 12 also decrease as x increases.

[lethal arrow]

Correct

That's because the equation stayed the same.

[elder elm]

last questions

so the answers would be yes

and for the final one, equation-only 2 variables, graph-straight line, and table-constant rate of change

[lethal arrow]

Correct on all of them

[elder elm]

I say yes to question 4 because x is dependent on variable y.

[elder elm]

Thank you Rie.

[lethal arrow]

No problem. For clarification: $x$ is independent. We would say that $y$ is dependent on $x$ (effectively, we get to choose $x$ which forcibly determines the value of $y$...if we choose $y$, we have to then solve for the value of $x$ that gave us that particular $y$ value).

[wraith dagger]

RiemannZeta

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[tawny forge]

<@&286206848099549185> I just wanted to know what the difference between y = f(x) and y = y(x) is or whether they are the same

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[mossy mango]

y=y(x) just means that y depends on x

y=f(x) is usually function notation

[cedar kiln]

@tawny forge Has your question been resolved?

[tawny forge]

how does y depend on y if y is the function?

[mossy mango]

y is not the function, f is the traditional notation for function

y depends on x

[cedar kiln]

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@grim lantern Has your question been resolved?

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[valid lily]

Hello

[valid lily]

Hello

.close

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[hushed spoke]

… hello

[cedar kiln]

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[fossil coral]

Did i get number 5 right?

[fossil coral]

,rotate

[gray blade]

,calc 97/125

[wraith dagger]

Result:

0.776

[fossil coral]

78%

[gray blade]

Yes

[fossil coral]

Ty

!close

,close

.close

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[crimson sedge]

how would one go about solving something like this

n is a positive integer

i feel like there are no solutions

nvm i wrote it down wrong

.close

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[deft spear]

how would i go about this question do i do 15= (3+lamda(i))^2+(2+i)^2 and solve this equation? part (ii)

[deft spear]

.close

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[celest seal]

.close

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[slender dock]

can anyone help me with probabilities

[sullen cliff]

what is it

[slender dock]

1sec@sullen cliff

two boxes contain spheres, box 1 contains 4 red spheres and 5 white spheres; box 2 contains 2 red spheres and 3 white spheres. a sphere is drawn from each of the boxes, find the probability that the spheres: a) are both red b) one is white and the other is red

@sullen cliff

[sullen cliff]

ok

so

the probability of getting a red from the 1st box is 4/9 right, 4 red 9 total

[slender dock]

yes

[sullen cliff]

the other has a probability of 2/5

[slender dock]

yes

so we multiply

[sullen cliff]

yes

[slender dock]

8/45

[sullen cliff]

exactly

for the 2nd part

[slender dock]

yes

[sullen cliff]

one is white and the other is red

[slender dock]

yes

[sullen cliff]

box 1:
red -> 4/9
white -> 5/9

box 2:
red -> 2/5
white -> 3/5

we either have red/red, red/white, white/red or white/white

[slender dock]

yes

[sullen cliff]

red/red -> 8/45
red/white -> 12/45
white/red -> 10/45
white/white -> 15/45

[slender dock]

the row isnt important i think

[sullen cliff]

so if we sum both red/white and white/red

we get 22/45

[slender dock]

yes

[sullen cliff]

yeah so thats it

[slender dock]

wait

i didnt get the last part

[sullen cliff]

well

there are 4 possible outcomes

[slender dock]

yes

[sullen cliff]

with different posibilties each

we need 1 red 1 white

red/red is not what we want

[slender dock]

why is red/red 8/45

[sullen cliff]

.

[slender dock]

oh

[sullen cliff]

chance of red in box 1 * chance of red in box 2

[slender dock]

yeah

[sullen cliff]

red * red
red * white
white * red
red * white

all combinations

[slender dock]

red/white -> 12/45 why

[sullen cliff]

theyre equal to this

because 4/9 * 3/5 is 12/45

chance of the red in box 1 and white in box 2

[slender dock]

oh i get it now

can you help me with a few similar exercices

btw i see youre working on python

do you programm

[sullen cliff]

yeah doing some stuff rn

i could help you later

[slender dock]

can i ask you 1 more exercise though , then we can do more when youre available

@sullen cliff?

[cedar kiln]

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[hot ore]

hallo

[hot ore]

What is the number of families out of 2000 families with 4 kids that have
a) atleast 1 son
b) 2 sons
c) 1 or 2 daughters
d) they have no daughters

how do i do this probability problem?

[cedar kiln]

@hot ore Has your question been resolved?

[hot ore]

anyone?

[cedar kiln]

@hot ore Has your question been resolved?

[slender dock]

@hot ore really feel your struggle, i wish i could at but i suck at this too

[unique nest]

I'm tempted to answer, but it depends whether it's a middle school/ maybe highschool question or a university level one. a k a whether we're considering the chances to have a girl or a boy 50/50. in such a scenario I think I might help

[hot ore]

university

[unique nest]

damn. so I guess the chance for them to have at least 1 son is not 1- (the chance of them having only daughters) = 1- (1/2)^4.
Hope you get an answer

[hot ore]

i gotta learn the basics of probability tbh

imma head on youtube to see if i can find a good course

[dire geode]

.close

[cedar kiln]

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[icy zinc]

with a contrapositive statement, if the antecedent being false, but the consequent being true, is the contrapositive true?

[icy zinc]

Does this just follow the normal rules of conditionals where if the antecedent is false but the consequent is true, the whole conditional is true?

[cedar kiln]

@icy zinc Has your question been resolved?

[cedar kiln]

@icy zinc Has your question been resolved?

[acoustic pivot]

a contrapositive statement is true iff the original statement is true

[cedar kiln]

@icy zinc Has your question been resolved?

[brazen kiln]

Yes, an 'If...Then' statement is an implication and F -> T, (F being false and T being true) will always be true

In case of implication only T->F gives result as F or False

[cedar kiln]

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[marsh furnace]

"Check algebraically that the quadrilateral with vertices at A(-3,-1), B(3,-9), C(5,5), and D(11,-3) is a square"

[marsh furnace]

<@&286206848099549185>

do I just use distance formula and see what all the sides are

https://tenor.com/view/mona-mona-genshin-impact-mona-genshin-genshin-mona-genshin-impact-gif-23478748

[cedar kiln]

@marsh furnace Has your question been resolved?

[sacred grail]

you should check that all the sides are the same length

but that is not enough to guarantee you have a square

[marsh furnace]

so how would I do it?

[sacred grail]

if you have all sides the same length, you could also have a rhombus

what do you need additionally to make it a square?

[marsh furnace]

uhhh

[sacred grail]

what differentiates a square from rhombuses

[marsh furnace]

a square have all 90 degree angles and rhombuses don't

[sacred grail]

indeed

so you should check that the corners are 90 degrees

[marsh furnace]

how?

[sacred grail]

do you know how to check that two lines meet at a right angle?

[marsh furnace]

uhhhhh

i don't remember

[sacred grail]

perhaps something to do with their slopes/gradients?

[marsh furnace]

gradients?

[sacred grail]

slope of a line

sometimes called gradient

[marsh furnace]

https://tenor.com/view/mona-mona-genshin-impact-mona-genshin-genshin-mona-genshin-impact-gif-23478748

[sacred grail]

y = mx + b

the m is the slope

are you familiar with this?

[marsh furnace]

yes

[sacred grail]

and if you have two lines, do you know how to check that they're perpendicular?

[marsh furnace]

https://tenor.com/view/mona-mona-genshin-impact-mona-genshin-genshin-mona-genshin-impact-gif-23478748

[sacred grail]

[marsh furnace]

im so tired i wanna cry 😭

[marsh furnace]

no i don't think so

[sacred grail]

hmm

try checking that all the sides are the same length first ig

[marsh furnace]

how

[sacred grail]

do you know how to use the distance formula?

[marsh furnace]

yes

[sacred grail]

okay so

[marsh furnace]

i was trying to use distance formula and stick in the coords

[sacred grail]

one of the sides is AB

[marsh furnace]

yes

[sacred grail]

the segment joining A(-3,-1) and B(3,-9)

can you calculate it's length?

[marsh furnace]

yes

[sacred grail]

what do you get

[marsh furnace]

just do distance formula for all of it?

[marsh furnace]

10

[sacred grail]

yes

[sacred grail]

lemme check this

[sacred grail]

yes to this

,w distance (-3,-1) to (3,-9)

[wraith dagger]

Results provided by WolframAlpha

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Requested by 夢雪#2250

[sacred grail]

okay it's right

you should do the same for BC, CD, and DA

and ensure that you have the same length for all 4

[marsh furnace]

BC I got 10√2

:/

[sacred grail]

[marsh furnace]

this is already no longer a square

[sacred grail]

,w distance (3,-9) to (5,5)

[marsh furnace]

heck desmos makin it looking like a square

[wraith dagger]

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Requested by 夢雪#2250

[marsh furnace]

man i hate my life

[sacred grail]

okay maybe it isn't ABCD

maybe it's ABDC

[marsh furnace]

ABDC?

[sacred grail]

the order of the vertices

[marsh furnace]

oh

ok

[sacred grail]

so try BD instead of BC

[marsh furnace]

do I keep the AB?

[sacred grail]

yes

[marsh furnace]

ok

[sacred grail]

that one will be one of the sides

and likely the other one will be BD

then DC

and finally CA

they form the square ABDC

[marsh furnace]

ok

10 😄

[sacred grail]

great

DC?

[marsh furnace]

DC = 10

[sacred grail]

good

last one is CA

[marsh furnace]

10

YAY

DONE ANALYTIC GEO

NOW TIME TO WORRY ABOUT QUAD

THANK YOU

[sacred grail]

you should probably also check that the sides are perpendicular

[marsh furnace]

?

[sacred grail]

because as i said earlier

it's possible to be a rhombus

that all the sides are the same is insufficient to be a square

[marsh furnace]

but all the sides are the same?

oh

[sacred grail]

a rhombus is a shape with all sides equal

[marsh furnace]

ok

how?

[sacred grail]

so as i was saying earlier

it's about the slopes of the lines joining the vertices

[sacred grail]

this equation

https://cdn.discordapp.com/attachments/903430334681608232/1067654593296748634/118663865264242688.png

when the slopes of two lines multiply to -1, they are perpendicular

[marsh furnace]

uh huh

[sacred grail]

you should check that two pairs of lines are perpendicular

[marsh furnace]

what do i sub in hold on

[sacred grail]

actually

i think one pair is enough

you should calculate the slopes of two adjacent sides

[marsh furnace]

adjacent?

im forgetting so many things 💀

[sacred grail]

adjacent means next to each other

,w adjacent

[wraith dagger]

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Requested by 夢雪#2250

[marsh furnace]

ok

my brain is tired 💀

[sacred grail]

then rest

[marsh furnace]

i cant

[sacred grail]

[marsh furnace]

you know what im lazy im just gonna pretend its a square

thanks anyway tho 👍

.close

[cedar kiln]

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[sage forge]

What did you try?

[lavish mulch]

nothing yet

dont know what those means

[sage forge]

OK, a year is x seconds long with x being a large number. You need to calculate what's x/1.000.000 and round it to the nearest integer

[lavish mulch]

year is 12 motnhs

[sage forge]

Yes

And how many days?

[lavish mulch]

365

[sage forge]

How many hours does a year have then?

[lavish mulch]

8766

[sage forge]

It's 8760, but yes

Now how many seconds does a year have then?

[lavish mulch]

uhh

31,536,000 seconds

@sage forge

[sage forge]

Well done !

So do you know the answer now?

[lavish mulch]

how to round to nearest integer?

@sage forge

[sage forge]

What's this devided by a million

[lavish mulch]

31.536

[sage forge]

What's the nearest integer?

[cedar kiln]

@lavish mulch Has your question been resolved?

[cedar kiln]

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[cedar kiln]

@crimson sedge Has your question been resolved?

[cedar kiln]

@crimson sedge Has your question been resolved?

[crimson sedge]

<@&286206848099549185>

[cedar kiln]

@crimson sedge Has your question been resolved?

[cedar kiln]

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[south cobalt]

Can you help? (grade 9 math) please show me step by step :) 💗

[south cobalt]

Please i want to submit this assignment because i took so long 🥹

[brazen kiln]

So we'll use the formula

(n-2) times 180 will be equal to sum of interior angles

So (n-2)180=5220

Try to find n from this equation

It should give you the number of sides

I'm trying to remember how to solve the second part

[south cobalt]

which formula

oh okay let me try to see how mnay sides it has

[brazen kiln]

That's a standard formula

[south cobalt]

yeah i just remembered

so n=31

is it correct @brazen kiln

[brazen kiln]

Yep

[south cobalt]

the second part seems hard

[south cobalt]

yes i got the same thing thankss 💖

[quiet timber]

Excellent! Do you still need help with b?

[cedar kiln]

@south cobalt Has your question been resolved?

[cedar kiln]

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[royal matrix]

In this question isn't 3 a critical point? And thus f'(3) = 0?

[royal matrix]

The answersheet says answer is B not C

[tropic oxide]

f is not differentiable at 3.

[south cobalt]

thank you sooo much 💖

[royal matrix]

So f'(3) = 0?

f'(3) = Doesn't exist

I see

[tropic oxide]

f'(3) does not exist, yes.

"f'(3) = Doesn't exist" is a bit odd.

[royal matrix]

Right

Then still, how is f'(3-) + f'(3+) = -1?

[tropic oxide]

it's the sum of the slopes of your two lines

calculate said slopes

[royal matrix]

You're right

Didn't think of that

One would be -2 and the other 1

We add them together ad get -1

Now it's correct

Thank you very much Ann 🫶

.close

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[dawn jacinth]

why is A) true here? Wouldn't the correlation for (2) be higher?

[zenith sail]

This is like

not really a math question.

This is asking you to know about biology, or physiology, or something like that

A is basically saying 4-year-olds tend to be more similar to each other in terms of height and weight, compared to 18-year-olds, who vary more.

Seems like that's what they're getting at

@dawn jacinth

[dawn jacinth]

it is a statistics question so it is math related

but thank you

.close

[cedar kiln]

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