help-0

[grizzled hull]

wait do u think im only trying to find the tan value?

[woeful pulsar]

it looks like you are trying to find everything

like sin cos cosec sec tan cot

[grizzled hull]

ye

im confused on how to find it

[woeful pulsar]

Use trigonometric identitiez

[summer gust]

"Registrants at a large convention are offered 6 sightseeing tours on each of 3 days. In how many ways can a person arrange to go on a sightseeing tour planned by this convention?"

Is this just 18, or am I looking at this wrong.

[woeful pulsar]

6 ways for first day 6 for second so 36 for first two

[summer gust]

why do you multiply them and not add them? also, it's 3 days, not 2

[woeful pulsar]

It should be easy to extend to 3

[summer gust]

yea, mb, didnt see you said for first two lol

but why is it multiplied and not added

[woeful pulsar]

Because after each day one tour you can pick any day 2 tour

[summer gust]

hmm

i guess i was under the assumption theyd only go on one tour

[lime stirrup]

how do you usually determine when to use vertical or horizontal strips?

[woeful pulsar]

If you are making a graphics card, usually horizontal

[lime stirrup]

hmm i meant in calculus sorry

[woeful pulsar]

If you mean integrals, depends which one is easier

[lime stirrup]

yes how do i know which one is easier

[woeful pulsar]

Try both

[calm kiln]

This free?

Is the answer correct

[glossy nymph]

No

Substitute π/6 in place of x

[calm kiln]

huh?

[glossy nymph]

You have to put π/6 instead of x in f(x)

Then calculate the value

[calm kiln]

dont I just multiply sec2x and pi/6

[glossy nymph]

No that's not how it works

[drowsy garden]

a test has 10 multiple choice questions each with four possible choices and only one right answer a student decides to use a spinner with 4 equivalent sectors on it to randomly choose which answer to pick for each question. what is the likelihood the student gets no more than 2 correct

[calm kiln]

wtf

[glossy nymph]

You were given f(x)

You have to find f(π/6)

So replace x by π/6 and find value

[glossy nymph]

Don't you see the channel is already in use

[calm kiln]

so that?

without the x

[glossy nymph]

Nu nu

X was inside sec right, 2x was an input for sec ()

So put it there, not outside

In functions, you give an input (x) and recieve an output [f(x)]. X is a placeholder variable and you substitute that for whatever value you want to put in the function

[candid wedge]

f(x) = sec(2x)
So f(π/6) = sec(2π/6)

[calm kiln]

I still dont get it

[candid wedge]

f(a) would be sec(2*a)

[indigo jetty]

$sec 2x$ is $sec (2x)$, not $(sec 2)x$

[candid wedge]

f(y) would be sec(2*y)

That way

[ocean seal]

Ken G

[calm kiln]

oh I see

I dont put the 2 outside

I put it inside

[candid wedge]

Yes

[calm kiln]

ok ty

[candid wedge]

It's sec(2x) like ken said

[calm kiln]

so the answer is sec(2pi/6)

[indigo jetty]

the 6 is in the brackets

[indigo jetty]

simplify the fraction

[calm kiln]

2?

[indigo jetty]

how do you simplify $\frac{2}{6}$?

[ocean seal]

Ken G

[calm kiln]

its 2pi

[ionic jewel]

how the heck do you simplify 2/6 to 2pi

oh

[calm kiln]

I got 2

[calm kiln]

this to 2

[indigo jetty]

so in other words, you're writing the exact value of sec(2pi/6)?

[ionic jewel]

thats right but i feel like you just plugged it into a calculator

well i guess you didnt need to simplify in that case anyways lmao

[indigo jetty]

You have to be concise when answering our questions, not just put some random number

[calm kiln]

wdym

I just plugged it into a cal

[ionic jewel]

is that what they want?

i guess it is

[calm kiln]

yea

Is this correct?

[ionic jewel]

,w tan(39 degrees) = x/72

[ocean seal]

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[calm kiln]

thanks

[flint holly]

Can anyone show me how to do this

<@&286206848099549185>

[ionic jewel]

$x^{-n} = \frac{1}{x^n}$

[ocean seal]

bunny

[ionic jewel]

switch both negative exponents to this form (to make them positive) then reduce from there

[flint holly]

how do I switch it to positive?

[ionic jewel]

the formula i just wrote

alternatively you can just think of it as "flipping" it over the division sign

so in yours you can just flip the fraction and make them both positive

y^2/x^5

[flint holly]

oh ok thats pretty simple

is it the same for this equations?

[ionic jewel]

distribute the ^2 to everything in the fraction then flip the negative exponent terms

[flint holly]

oh ok I'll try that one sec

I got 16y^-4/x^9

I know its wrong

how do I get rid of the 16

[ionic jewel]

okay let me go through the whole problem

@flint holly what exponent is the x to?

[flint holly]

-3

sorry its blurry

[ionic jewel]

Original problem:
$${(\frac{x^{-3}}{4y^{-2}})}^2$$
Distribute the squared
$$\frac{x^{-6}}{16y^{-4}}$$
"Flip" the negative exponents
$$\frac{y^4}{16x^6}$$
ta-da

[ocean seal]

bunny

[flint holly]

oh ok

so you don't bring the 16 up with y

[ionic jewel]

the 16 does not have a negative exponent

the only reason it goes up is to get rid of the negative in the exponent

[flint holly]

ohhhhh ok that makes sense

thanks

[alpine sable]

Hello, I need a bit of help with Linear Algebra. I need help with Wronskian.

I am trying to solve W(cosh(7x),sinh(7x))

[alpine sable]

hello

[alpine sable]

Lost xOx

<@&286206848099549185>

[shrewd sable]

When you do the first line of the determinant, why did you do 7xcos(h) rather than cosh(7x)?

Also how do your derivatives suddenly have an h variable?

[alpine sable]

Hi help me please

[gray isle]

is the ^g supposed to indicate gradians?

and what's the desired unit of the final answe?

[alpine sable]

Whats 2 + 1

Hmmm...

I'm still lost

I just put my derivatives in that order because it looks less confusing to me

[alpine sable]

sexagesimals

[gray isle]

that references degrees °, minutes ', seconds "

which g is not used for

(unless you replied to the wrong thing and didn't tell me or confirm what g is supposed to be)

[thin surge]

No

You know it if the question gives it to you

Or you find it by finding range

[gray isle]

parentheses/brackets (in context) can be used to represent an interval

here [-4,1] represents the interval between +4 and 1 including both -4 and 1

[alpine sable]

How do i solve this

[thin surge]

So here you cannot put 7 like x can not be equal to 7

[thin surge]

Take sine of 52 deg

Which is perpendicular/hypotenuse

[magic lichen]

@misty pebble it’s not asking for endpoints. It is stating the entire interval of inputs for which the function is defined (the functions domain). In the second case, it includes everything between 0 and 7, but not 7 itself

[alpine sable]

What do i do after sine 52

[thin surge]

Sine52= perp/hyptoneuse

Then calculate hypotenuse from it which will give you X

@alpine sable

Yesss

[alpine sable]

Is my perpendicular 6.5?

[thin surge]

Yes

[alpine sable]

Okay let me solve it and tell you x

[thin surge]

Okay

[alpine sable]

Is it 5.12 cm?

[thin surge]

Noo

[alpine sable]

How do i do it then

[thin surge]

Sine52 is 0.788

[alpine sable]

Yes

[thin surge]

So you calculate.6.5/0.788

[alpine sable]

Oh ok

8.24?

[alpine sable]

?

[thin surge]

Yessss

[magic lichen]

Open dot corresponds to )

[alpine sable]

Does anyone know the rule for bearings how to solve them

[magic lichen]

Closed dot to ]. It’s just a graphical notation and a textual notation of the same concept. Any function maps some set of numbers to another set of numbers. The input set is called domain and the output set is called range. The combination of the function itself and the domain it is defined on will generate the range

Functions are just tools we define and use and we are allowed to tell the function what numbers it is allowed to exist on (domain) sometimes we want to represent every number in an interval but might not want to include the endpoint(s) of the interval in the allowed inputs

There are bounds but not necessarily strict endpoints. Since you can fit an infinitude of numbers between 6.999999999999 and 7, it would be impossible to write that as a closed interval with [0, 6.999999999999999]. The decimal would go forever

Yes, [] means endpoints are in the domain. You still need to evaluate the function at those inputs to obtain the corresponding values in the range though

They are considered endpoints. The important thing is that anything in the domain can be evaluated by the function. For the solution of the second one, notice that the range includes f(7) = 28 as an open boundary. That’s because 7 isn’t in the domain so 28 isn’t in the range, but it is a bound in the range such that f(6.999999999999) approaches 28

When really the last value in the range is 27.9999999999999

Make sense?

I can’t specify exactly the highest value in the range because I would have to keep typing 9 after the decimal. Mathematicians are lazy so this is the easier way to write it while meaning the same thing

[alpine sable]

How do i solve this?

[misty pebble]

I think I was going wrong by looking at the first one, which had both endpoints at 0 on the y

[magic lichen]

Except one will have a closed dot and the other an open dot

[misty pebble]

So I assumed that was the difference

Thank you for the help

I seriously appreciate it

[magic lichen]

Sure!

For the first one, the endpoints of the domain don’t produce the endpoints of the range. Instead you just take the lowest and highest value produced by the function when evaluated for all points in the domain. Same is true for the second one but those happen to correspond to then endpoints of the domain

I assume it’s asking the same thing. From the picture alone it’s not asking anything but I assume the textbook or assignment is just lazy

[misty pebble]

I mean is that the same info? Like just giving you the function and then the domain that it works in

[magic lichen]

Yup

[misty pebble]

They both ask for intercepts and turning point, I should have included that

Well thank you

[magic lichen]

Just different notation for the same thing

[misty pebble]

I can stress how thankful I am

can't

[magic lichen]

No worries

[alpine sable]

Hi guys

Can someone help me with my homework

[bold token]

show it

[bold token]

isnt that volume?

[alpine sable]

Yeah volume of a cone

But I don’t know how to do it

But what’s the answer

[bold token]

jsut plug in the givens

divide 2 the diameter, to get the radius

[alpine sable]

I don’t know how to do that

I’m stupid

[bold token]

15.6/

2

you get the radius

now you complete the values h, and r

[alpine sable]

Bruh I’m stupid

[bold token]

then you plug it on the formula

[alpine sable]

Ima just ask someone for answers

[bold token]

radius is half the diameter

[alpine sable]

This server is so fucking ass

I just need the answers

[bold token]

what

[runic citrus]

im just tryning for fun

could someone help?

<@&286206848099549185>

[bold token]

you're out of luck

[runic citrus]

hey man

can u help?

[bold token]

I don't understand that

[runic citrus]

oh ok nvm

[ionic jewel]

don't have paper near me but does turning it all into sin and cos then combining help at all?

might end up with some double/half angle identity or whatnot and be able to go from there

[runic citrus]

i did get that idea

do i turn cot2 into cos/sin?

[acoustic shadow]

Joe mama so fat we need longitudes and latitudes to locate her

[ionic jewel]

cot = cos/sin

so cos^2/sin^2

[runic citrus]

cos2/sin2 then

yep

cosec to 1/sin?

[ionic jewel]

cot = cotangent = 1/tan

[ionic jewel]

yes

[acoustic shadow]

What did you try

[runic citrus]

3(1/tan^2x) - 14(1/sinx) - 2 = 0

dont know what to do next

[acoustic shadow]

Why are you converting it to sin and cos

[ionic jewel]

that often helps

[runic citrus]

do i do it to 1/tan then?

[acoustic shadow]

It’ll create a mess

[acoustic shadow]

Yeah but not for this one

[ionic jewel]

ah my suggestion, don't see an obvious way to go otherwise

[acoustic shadow]

Well do you know the basic 3 trig identities

[runic citrus]

correct?

[runic citrus]

yeah

[acoustic shadow]

Write them

[runic citrus]

sin , cos , tan?

[alpine sable]

Can anyone show me step by step how to do this

[runic citrus]

could u pls wait?

[ionic jewel]

ah i see the rest of the problem, definitely shouldn't have missed that

good spotting ^

[runic citrus]

do i multiply 3 with 1/tan^2x?/

?

[ionic jewel]

no

[acoustic shadow]

The identities

[runic citrus]

umm

oh ok

[acoustic shadow]

Sin^2 + cos^2 =1 those

[runic citrus]

ah that

ok yeah

[acoustic shadow]

Write the one with cot

[runic citrus]

cot^2 + 1 = cosec^2

[acoustic shadow]

Can you replace cot^2 in your original q

[acoustic shadow]

Using this

[runic citrus]

dont i need +1 for that

[acoustic shadow]

And then assume cosec as t and it’ll be a quadratic in t

[runic citrus]

oh wait

[acoustic shadow]

Don’t think write it on paper you’ll understand what I’m saying

[runic citrus]

cosec^2 - cot^2 = 1?

[acoustic shadow]

No cot^2=cosec^2-1

[runic citrus]

oh ok

[acoustic shadow]

Now solve it own your own

[runic citrus]

3(cosec^2 x -1) - 14 cosec x- 2 = 0

[acoustic shadow]

Yep

[runic citrus]

thank u so much

[alpine sable]

@acoustic shadow

Can you help me now?

[acoustic shadow]

Write the prime factors of 600

[acoustic shadow]

Do you know how to write prime factors ?

[alpine sable]

No

Can you solve it step by step so i can understand

[acoustic shadow]

🥲🙃

[magic lichen]

Factors are numbers that multiply with each other to equal another number (the product). Prime factors are factors that are also prime numbers. Prime numbers are numbers whose only factors are 1 and itself

[quaint trout]

@alpine sable can you list the first few prime numbers so we can see if you know what they are?

[acoustic shadow]

Pure Definition won’t help them, ig they’re just starting off with the topic

[magic lichen]

Imagine a big tree with a single number at the top (600) and two branches coming out with two factors, say 200 and 3, then go to each of those and keep expanding the tree down until you are left with only primes

Definition is the only way to know what is being asked

[alpine sable]

Oh okay now i get it one i solve it can you see if its right

[magic lichen]

Then by multiplying all of the primes together you will get 600

[subtle nimbus]

I need help with this question ⁉️
Write du incase of u(x) and in case of u(x,y,z)

[ionic jewel]

is this the entire question

[subtle nimbus]

Yes

[ionic jewel]

in that case i have no idea what it's asking sorry

[magic lichen]

There’s some context missing here

[spice cape]

a student takes a test and she attempts 2 questions (multiple choice) each question has 4 options, what is the probability of her getting:2 correct and 0 correct?

[alpine sable]

Is this wrong?

Isnt it x is minus 4cor x is minus 2

[ionic jewel]

multiply independent probabilities

1/4 chance each

(1/4)(1/4) = 1/16

[alpine sable]

Can anyone verify

[spice cape]

wait so for getting 2 correct would also be 1/16 ?

[misty pebble]

A roller coaster is modeled by the function f(x)= 0.001(x-10)(+20)(x-40) What is the height above ground level of the track at x = 50?

[ionic jewel]

you asked for the chance of getting two correct

[misty pebble]

I'm using a graphing calculator to plot this and when I do y cal and enter x=50 it says its not in the domain

[ionic jewel]

not sure what this means

[spice cape]

yeah would that equal 1/16?

[ionic jewel]

yes

[spice cape]

ok what about 0 correct?

[ionic jewel]

is the (+20) supposed to be (x+20)?

[misty pebble]

Yes apologies.

[ionic jewel]

there you go, calc should get it now

i have no idea I'm bad at stats, go to another channel and repost question minti

3/4 chance of getting it wrong the first time

[spice cape]

ok all good

[ionic jewel]

3/4 second time

9/16

probably (tm)

[spice cape]

alright cheers

[misty pebble]

It still gives me the domain error

[ionic jewel]

paste the function here outside a block of text

[misty pebble]

f(x)= 0.001(x-10)(+20)(x-40)

[ionic jewel]

,w f(x)= 0.001(x-10)(x+20)(x-40) where x = 50

[ocean seal]

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[ionic jewel]

there you go

[chrome spade]

https://gyazo.com/03205038ceb0fdc0af19a87dd95a7661

How do I do this questino?

[ionic jewel]

i feel like this is something you have to look up on a table, how many SD above the mean the 80%ile gets you

[chrome spade]

it didnt provide a table tho

[magic lichen]

It’s a standard property of the Gaussian distribution. Look for z-score of 80th percentile https://sphweb.bumc.bu.edu/otlt/mph-modules/bs/bs704_probability/bs704_probability10.html

[chrome spade]

I tried the Z-score formula

i got 167.2cm instead of 167.83

0.8 = (X-156)/14

[magic lichen]

Z-score tells how many standard deviations above/below the mean. Multiply z-score by standard deviation and add to mean

You need the z-score for 0.8, not 0.8 itself in the formula

[chrome spade]

how do I do that lol

[magic lichen]

Otherwise it looks okay. Google z-score of 8th percentile. It’s defined by a formula and is usually precomputed in a table in most statistics textbooks

Check the link I posted for explanation about how it’s used.

[chrome spade]

ok thankyou

[magic lichen]

Coincidentally the z-score for 80th percentile is quite close to 0.8 which is why your answer was close but not exact

https://www.pindling.org/Math/Learning/Statistics/z_scores_table.htm

[severe venture]

I really don't understand the question that much

[spark prawn]

@severe venture Do you still need help?

[severe venture]

Yea

[spark prawn]

So how much of the question do you understand?

Are there specific words that are confusing you?

[severe venture]

I really cant explain I do all my questions in my head

I just cant understand what they mean with consecutive integers and middle integer

[spark prawn]

Consecutive means immediately after

[ionic jewel]

consecutive integers are in a row

[spark prawn]

So 1, 2, and 3 are consecutive integers in a row

Ye

[severe venture]

Ooh okay

I think my answer is correct

[spark prawn]

The one you've highlighted?

[severe venture]

I submitted O_O

[spark prawn]

That's not the correct answer

Ah

[severe venture]

I wanna die

yay

[tawny lion]

B

[unborn merlin]

any calculus experts here

having a tough time with a calculus qn

[wicked ember]

what

[unborn merlin]

can someone pls solve this

[cyan anvil]

1-2x^2+x^4 =0 x=?

[unborn merlin]

no real solns

[cyan anvil]

the answers shows + or -1 but idk steps

[unborn merlin]

+or -1?

thats not possible

[stark lantern]

$(x^2 - 1)^2 = x^4 - 2x^2 + 1$

[ocean seal]

error 404

[stark lantern]

you should be able to obtain the solutions from this

[spark prawn]

I'm not sure how to solve this (after I've made equations for probability in relation to other points)

[woeful pulsar]

answer is 0, because once you reach b the walk ends

and you don't get the chance to move to c

[hardy geyser]

3x + 4y = 7xy yes?

[woeful pulsar]

depends

but probably no

substitute x=1 y=10 to see it be obviously false

[spark prawn]

That would be true if the starting point was c, not a

p(c) = 0
p(b) = 1

[woeful pulsar]

wait

what

[spark prawn]

Hm?

The starting vertex is a from which I need to figure out the probability of reaching vertex b before c

[hardy geyser]

X^3 times Z^4 can’t be multiplied because they powers are different?

[placid zinc]

You can multiply them. Their product is x³z⁴

That doesn't simplify, because x and z aren't the same thing

[hardy geyser]

Xz^7

[placid zinc]

So it depends on the base

[hardy geyser]

XZ^7

[placid zinc]

x³z⁴ ≠ xz⁷

xxxzzzz ≠ xzzzzzzz

[hardy geyser]

yeah that’s what I meant thank you

[plush wagon]

Can you tell me why is 7<X<11

I mean X should be less than both 11 and 7 right?

[placid zinc]

,w graph (x - 11)(x - 7)

[ocean seal]

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[placid zinc]

You care about where that quadratic is below the x-axis

[plush wagon]

Oh I got it thank you

[cosmic agate]

where is the maximum and minimum for this function?

is the maximum 0, 0 or 15?

this is calc 1 btw

high school stuff

[vale wigeon]

(0,0) is a local maximum point, and (15, 0.938) seems to be a local minimum point

this function has no global maximum due to the presence of VAs near which it explodes to +∞ at least once

[cosmic agate]

wait

how is it a maximum

when its lower than the second point?

[vale wigeon]

i said local maximum for a reason.

[cosmic agate]

local?

[vale wigeon]

relative maximum, if you're more accustomed to that terminology.

[cosmic agate]

local to that specific interval?

[vale wigeon]

also are you not able to send an actual screenshot instead of this crude photo?

[cosmic agate]

my computer is weird

[spark prawn]

Windows key + print screen is for screenshots on Windows

[vale wigeon]

x=0 is a maximum point if you consider your function on the interval [-1, 1] for example

you can just press printscreen and it'll copy the screenshot into your clipboard

[cosmic agate]

oh

wait so like when it says local maximum

it means like the maximum point at that speicifc part

because the actual maximum is infinite

[vale wigeon]

cut that last part

[cosmic agate]

whats wrong with the last oart

oh theres no maximum

[vale wigeon]

no, what's wrong is your implication that for local maxima to exist the global maximum must be infinity

[cosmic agate]

because like - x^2

then the maximum could be like 0,0

[vale wigeon]

the 2nd and 4th points highlighted on this graph are local maxima, even though the global maximum exists and is equal to about 6.1 and is achieved at x=0

for the function i just showed

[cosmic agate]

RIGHT

so a question could ask for either global or local maximum/>

and in my function since there is no global maximum or minimum ij ust write the local max and min right

[vale wigeon]

i do not know what the exact wording of your question was so i cannot tell you what you are supposed to write

[cosmic agate]

it just says

find maxmium and minimum

points

[vale wigeon]

"find maxmium and minimum
points"
is that the question verbatim?

no alterations, nothing omitted?

[cosmic agate]

yes

thats

it

i swear to god

[cosmic agate]

if im trying to find critical points of a function

and the numerator is undefined

what do i do?

solve f(x) = 0 for the denominator?

[vale wigeon]

??

[cosmic agate]

if i have this

[vale wigeon]

give me a moment.

[cosmic agate]

x^ = -(32/24)

that is undefined for the numerator

[alpine sable]

Do u want max / min for this ?

[vale wigeon]

you did not find the second derivative properly.

you did not find the second derivative properly.

[cosmic agate]

?

[vale wigeon]

you have f'(x) = -8x/(x^2 - 4)^2, yes?

[cosmic agate]

yes

[vale wigeon]

wait, ok, let me double-check

,w d/dx (-8x/(x^2-4)^2)

[ocean seal]

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[vale wigeon]

okay, so my point about you messing up the derivative stands, even if you did not mess it up as much as i thought you had

anyway, your second derivative simply does not have any zeros.

[cosmic agate]

how did i mess it up

no

[cosmic agate]

i meant to write

8

not 8x

its 8/(x^2 -4) ^ 2

not 8x

[vale wigeon]

oh wait you have a minus sign there

then you did not mess up

you did not show your process at all however

so like, maybe do something about that

[cosmic agate]

i dont care if i lose a mark about that

its such a pain in the ass

ijust need to hand it in

[vale wigeon]

anyway, whatever

f''(x) = 0 has no solutions

you have no inflection points

[cosmic agate]

...

oh

[cosmic agate]

wait but here

at 0,0 is a turning point

at a turning point isnt the derivative equal to 0

[vale wigeon]

but we are not talking about the first derivative

we are talking about the second derivative

and we are not talking about turning points

[cosmic agate]

why do we have to find the second derivative instead of the first?

[vale wigeon]

we are talking about inflection points

...

who said you "have to" do anything

you wanted to analyze this function for concavity, did you not?

[cosmic agate]

in regards to the question

[cosmic agate]

intervals of concavity yeah

[peak niche]

Can someone help with a question from a test i just did? Everyone got a different answer and i want to know what the right answer is

[vale wigeon]

you don't need to reply-ping me at every single message

@peak niche channel busy please move

[cosmic agate]

sorry

[peak niche]

Where should i go

[cosmic agate]

right points of inflection are diferent from max and min points right

[alpine sable]

Come to chanel 4 @peak niche

[vale wigeon]

one of the other 9 questions channels that does not have a convo going on in it right now @peak niche

[vale wigeon]

of course they are

sometimes a point may be both

[cosmic agate]

what are points of infelction

...

haha

[vale wigeon]

they are the points where your graph goes from concave up to concave down or vice versa

but anyway you need the second derivative in order to find these

since f''(x) = 0 is a necessary condition for being an inflection point

[cosmic agate]

right and i got the second derivative and on this graph there is no graph from concave up to down right

it just goes up or down

because of the vertical asymptope

[vale wigeon]

no

your graph is concave up on (-∞, -2) and on (2, +∞), and it is concave down on (-2, 2)

as can be seen from the signs of f''(x) on those intervals

[cosmic agate]

right

but there is no point where it transitions from concave up to concave down right

[vale wigeon]

yes, there are no inflection points

as it happens, both concavity changes occur across a vertical asymptote in your case.

[cosmic agate]

right

thanx for helping me

I know I ask alot of basic shit

but i work like 60 hours a week and i dont have alot of time to study

[vale wigeon]

sheesh

wait how old even are you

[cosmic agate]

20

[vale wigeon]

oh

i was wondering why you would have a job that takes 60 hours a week

[cosmic agate]

i work 3 part time jobs to make sure i have enough money to move out

i am apply to a school that is across the country

and i need to send some money to my parents too

[vale wigeon]

christ

[cosmic agate]

yeah

if i stay in my hometown i will hang myself or something

everyone else does like heroin or works in a steel mill

and all the girls sell mlm shit

just existing here makes me want to die a college acceptance is a golden ticket to freedom

sorry to ask, what is the difference between the intervals of increasing and decreasing

and intervals of concavity

are they the same thing?

[vale wigeon]

no, they are not the same thing.

in fact a function can have any combination of increase/decrease and concave up/concave down on a given interval

concavity is about the placement of your function's graph relative to chords connecting points on it

[cosmic agate]

my friend said that they are the same thing and he used the same logic to find intervals of increasing and decreasing to interals of concavity

but since concavity uses 2nd derivative

he is wrong af right

[vale wigeon]

your friend is right only about the mechanical part

for most functions, yes, concavity is directly controlled by the sign of the second derivative

but conceptually it is a different thing altogether

it would be good if you and your friend tried not to fall into the plug-and-chug mindset that makes people into meat-wrapped calculators in math class

[celest void]

Hmm is this channel vacant?

[vale wigeon]

probably not

[celest void]

Aw

[vale wigeon]

unless joe bidome has no more follow-ups

[cosmic agate]

im fine

for now lmao

[celest void]

Yay which means It's vacant ig

[vale wigeon]

okay post your question here then

[celest void]

Hmm could someone help me with this theorem which goes something like "if a vector set is linearly independent, then its maximal and independent subset is the whole set itself'

I don't necessarily understand what this means

[vale wigeon]

its a bit of a tautological statement

if you have a set S of vectors and you know that S is linearly independent then every subset of S is linearly independent too

and thus among the linearly independent subsets of S there is only one that is maximal, ie not contained in any other: S itself

[celest void]

So maximal and independent subset is basically a set that's contained in itself?

I know how to compute by using the rank of vectors or something but i don't get what it actually is

[quick surge]

how do i do this
if this channel is busy please tell me

[vale wigeon]

no

maximal is a notion from order theory

but roughly: if you have a family of sets, a maximal set is a set which is not contained in any other set from the family.

[quick surge]

oh its busy sorry

[celest void]

Ah so wait does maximal in this context mean the same thing as maximal independent subset or is it something like an independent subset in a family of sets like you mentioned

[vale wigeon]

"independent subset" just indicates which family we're talking about maximality in

[celest void]

Wait if you don't mind can you elaborate more on that

I didn't quite get it 😐

I get the maximal definition from what you've mentioned prior though

[celest void]

Oh rereading i actually get it

Ty! ❤️

[jaunty jasper]

Can someone help with part D

What i have tried so far

Pls help

[alpine sable]

Please write tan as sin/ cos and cot as cos/sin and open the bracket

Ull get 2 sin^2+2 cos^2

[humble merlin]

yes it proofs itself after doing that

@jaunty jasper do you get it?

[jaunty jasper]

Yeah im just trying it out

Ty

[cosmic agate]

for the function the y intercept equals 0 right

why is it on the graph crossing it 3 times?

oh no im an idiot

thats the x intercept

[viscid dawn]

Is there a way i can get the formula of 10*11*12*13 .. up to *30 like 10! is 10*9*.. to *1*0?

[tawdry jasper]

Should be 30! / 9! I think

@viscid dawn

[viscid dawn]

Wow

Yeah

Thanks haha

Didn't remember of that

[tawdry jasper]

np

[hushed topaz]

I need help with question B

please

[void yoke]

Gradient probably here means slope. Find an expression with h and numbers that represents the slope between P and Q.

[hushed topaz]

how do I do that lol

@void yoke

[void yoke]

Given two points, find the slope. The points are given as P: (1, 2) and Q: (1 + h, f(1 + h)).

[hushed topaz]

so y2 - y1 / x2 - x1 ??

[void yoke]

watch the parentheses ...

(y2 - y1)/(x2 - x1)

[hushed topaz]

yeah

❤️

[void yoke]

so put it all together?

[hushed topaz]

(2/(1+h^2) - 2)

1 + h - 1

is that right

and then simplify from there

wait

but the squared for the numberator is on the outside of bracket so I messed up

[void yoke]

yep, good catch.

[still crest]

Is this busy?

[hushed topaz]

yes

[still crest]

Alright!

[hushed topaz]

im still writing lol

soz

[still crest]

No worries

[hushed topaz]

ok

so does it become

bruh

[prime mist]

ah shit is this bussy im sorry haha

[hushed topaz]

all g

2- 2(1+h)^2

(1+h)^2

h

@void yoke

[void yoke]

almost. Technically the lower fraction bar needs to be wider than the top one.

[hushed topaz]

yeah true

[void yoke]

anyway, that'd be fine for me but it's up to you to make sure your instructor's formats for answers are followed.

[hushed topaz]

wait

so then what does it simplify to?

@void yoke

[void yoke]

2 🙂

wait no

[hushed topaz]

bc that's the answer

[void yoke]

oh sure looks good to me.

[fickle ridge]

Hi guys

[void yoke]

from your last "text" answer you can finish dividing through by h (it then gets multiplied by the denominator)

[fickle ridge]

how can i solve this

?

[void yoke]

hey um, can you go to another room 🙂

we're still discussing a problem! 🙂

[still crest]

@void yoke if you're working with others I would appreciate to stick to them, ty

[void yoke]

2- 2(1+h)^2

h(1+h)^2

-2h^2 - 4h

h(1+h)^2

[hushed topaz]

wait

but that's diff to answer

when factorised

[void yoke]

@hushed topaz so then I think you got it?

just factor an h from the top and cancel

[hushed topaz]

oh true, yes ok thanks ❤️

[wary stream]

People can go back and forth between helping people, they aren't obligated to just helping a single person at a time

[void yoke]

yep no worries mozzy.

[still crest]

They can let others help too you know

[wary stream]

If there's not many people answer, IE like 2 people helping and all the channels are going off, they can help multiple channels at once, if they know what they're doing

[still crest]

Alright, I don't mind waiting 20 minutes

[half steppe]

hello. I am trying to understand how to do continued fraction expansion, specifically when computing the square root of a number n : https://en.wikipedia.org/wiki/Methods_of_computing_square_roots#Continued_fraction_expansion
I got it right for sqrt(2) and sqrt(3) but I fail at sqrt(7).
this is the correct answer: https://www.wolframalpha.com/input/?i=Convergents[sqrt(7)%2C10] for sqrt(7)
but when i do it myself i get

{2 , 11/4 , 34/11 , 101/34 , 304/101 , 911/304}```

can someone help me understand my mistake?

[fickle ridge]

how can the last question be solved?

[rose glade]

yo some one know how to solve

[alpine sable]

O is the center right

[rose glade]

yes

arc length

[alpine sable]

This means arc AB is a + 50

So a + 50 + 3a + 10 = 360

4a = 300

a = 75

Plug a in

50 + 75 =125

[rose glade]

we always

need collect all a that we know

and make equation

then find yes?

how to find measure of central angle if we know radius and pie

[urban matrix]

i need help on this

[analog terrace]

quick question. how do you read P(S∩D)

[alpine sable]

P(SnD)

[shell widget]

probability that S and D both happen

or occur

[peak niche]

Quick question I'm gonna prepare for A level maths and further maths over the summer a little what topics should I study?

@urban matrix just add up the numbers my guy

Use the radius to find Diameter to find circumfrene which is pi D

And divide by 2 or 4 depending on if its half or quarter of a circle

[autumn fjord]

How do I do this

[urban matrix]

can you explain a little more sorry im not good at this subject

[peak niche]

Ok so the radius of turn 1 is 3 meters

So the diameter of the circle is 6 meters

Circumference is Pi x D which is 6 pi

So turn 1 is a quarter of a circle so that's 1.5 pi

Do that for each turn and add them together then add that to the straight lines

[urban matrix]

alright should i fill in 1.5 on the first side of it

[peak niche]

That's for turn 1

Turn 2,4 and 5 are a quarter too which makes a full circle so thats 6 pi

6, 8 and 9 make a full circle so thats another 6 pi

[urban matrix]

and should i write these on the drawing of the shape or in the first question

[peak niche]

Turn 3 and 7 have radius of 2.25 so diameter is 4.5 which means the full circumference is 4.5 pi

And 3 and 7 make a full circle so add 4.5 pi

So total 16.5 pi

Then add 20,30,8,6,6,12,30

[alpine sable]

are the triangles similar

Water volume: V=550 m3
Top surface area of water: As=171,000 sq mi
temperature: T∞=32-49 °C goes down to 10-22 °C in winter
Water temperature: Tw= 30 ∘C down to 8°C in winter
Relative humidity of water in room air: 15 %

Rain does not exceed 8 inches per year
How much years would it take for that water to dry up, please

[urban matrix]

alright thank you

if i have trouble again can i ask you for help or no

[alpine sable]

yes

[autumn fjord]

<@&286206848099549185>

[alpine sable]

bruh

[peak niche]

@alpine sable 180-90-63 is 27
180-124-27=29
No, one has an angle of 27° and the other is 29°

[alpine sable]

thanks

[peak niche]

Np

[alpine sable]

how to solve angle 1 , 2, and 3

no

angle 1 2 4 5 6 7

[peak niche]

Angle 1 is 180-76

Angle 7 is the same as 76

Angle 5 is the same as angle 1

[alpine sable]

6 is the same

as 76

[peak niche]

Angle 4 = angle 1

Angle 2 = 76

[versed osprey]

Example 6, how did we get 11 and 3 as the two radii

[peak niche]

Angle 6 is 76

Etc etc

[alpine sable]

and 8 is same as 1

[peak niche]

Yes

[alpine sable]

alright thanks

whats the value of x

[peak niche]

Sum of angles in polygon is sides-2 x 180 so 3x180= 270

270-250

[urban matrix]

alright these questions follow up the picture i sent earlier

[peak niche]

Wait

[alpine sable]

20

[peak niche]

My bad

[real sinew]

,calc 3x180

[ocean seal]

The following error occured while calculating:
Error: Undefined symbol x180

[peak niche]

3x180 is 540

[alpine sable]

lol

[peak niche]

I did 3x90

540-250

Then divide by 4

[alpine sable]

72.5?

is the sum of x

[peak niche]

Yeah

@urban matrix 1609 divided by lap length

[alpine sable]

thanks

[urban matrix]

alright 1609 divided by 120

[peak niche]

Then 1609x50 and divide by lap length

And trunkate

(cut off decimal)

Since it says full laps

[urban matrix]

wait do i do 1609 divided by the lap length first or 1609 x 50 divided by lap length

[peak niche]

1609 / lap length is the first question

[urban matrix]

ohhhh alright

[peak niche]

1609 is a mile so 50 mile is 1609x50

Then divide by lap length to find how many laps

Cut off decimal for how many full laps

[urban matrix]

gotcha

for number 2 i got 13.4083333

should i round it

[peak niche]

13

It says how many full laps

0.4 laps isnt a full la

[peak niche]

Lap

[willow bluff]

Can anyone help me?🥺

[peak niche]

@willow bluff 42.72/80x360 is full area

[versed osprey]

Yooo

[peak niche]

Area is pi x r^2

So divide by pi and square root right

[urban matrix]

and number 3 i got 670.416667 and since you said cut off the decimal would it just be 670

[peak niche]

Sorry i thought the other one was the second one

Round the other one to nearest 2dp or something

Make that one 670

@versed osprey I'll see if i can help u

I'm only 15 i came here for help myself but i seem to be capable of helping some people here

[versed osprey]

Yeah ok

Wait nvm

I got it, thanks a lot for responding tho

[peak niche]

Alright nice

[willow bluff]

@peak niche I got 192.24 for the area. How do I get radius?

[real sinew]

Area is pi*r^2

[peak niche]

Divide by pi

[real sinew]

So you can work that equation backwards and solve for r

[peak niche]

Then square root answer

Around 7.723

Oops

7.823

Mistyped

You can check by doing pi x 7.823^2 , divide that by 360 and x by 80 to see if you get 42.72

1/-1 is -1

Uh

Wait lemme wrap my head round this

So -1>x

Waif

Sorry

Wrong sign

Or is it

[livid jolt]

x>-1

[peak niche]

If you make the number bigger then it doesn't work

So -1<x

Because making x equal to or any bigger than -1 and it doesn't work

[versed osprey]

Guys “-r -r” is “-2r” right?

Thanks a lot man

[peak niche]

Yeah

[versed osprey]

Imma head out

[livid jolt]

for positive values of x
-1 < 1/x
multiply both sides with x
-x < 1
multiply both sides with -1
x > -1

and similarly

1/x < 1
1 < x
x > 1

taking intersection u get x > 1

[peak niche]

1/-0.5

Doesnt work

So x smaller than -1 or bigger than 1 right

[peak niche]

@urban matrix 15x8 for the inside rectangle excluding edges

Then do radius X 15 X 2 for top and bottom

Then radius X 8 X 2 for left and right

Then add pi X radius^2 for the four quadrants

Since the 4 quadrants make a full circle

Then basically add all the areas up

[urban matrix]

thanks

[still crest]

Is this busy?

[peak niche]

Nah

[still crest]

I'm having trouble with c

[peak niche]

Yeah sorry I haven't learnt that yet I'm learning it next year

[still crest]

No worries

[peak niche]

@still crest what's the topic called again? Might learn it before next year in the summer

[still crest]

Definite Integrals

This was the last exercise in final exams

[peak niche]

The last question in mine (1 year behind you i think) only 3 of us got the correct answer which i checked with a maths teacher although the tests haven't been handed back yet everyone else got it wrong

There were about 100 people taking the test and there were lots of varied answers

[still crest]

You got it right?

[peak niche]

Yea

[still crest]

Congrats!

[peak niche]

Thank god

It wasn't hard imo but my logical process is on point most of the time

[still crest]

Let me send the problem again so it doesn't get buried

I'm having trouble with c)

[strong furnace]

Sup. What have you tried?

[peak niche]

I don't even know how you'd write sin^2019 on a calculator

[strong furnace]

(Sin(x-2))^2019

[still crest]

I got scared by the big numbers so little to say, I only made some thoughts that we could substitute the x-2 with something

[strong furnace]

They want you to use what you proved in b

Can you connect the integral with lhs of b

[stark creek]

Bruh, I have a headache from that lmao

[peak niche]

If in doubt, the answer is 3

Don't take that seriously

[still crest]

Let us work the problem

[strong furnace]

You see the result from part b ?

[still crest]

Yes

2ab

[strong furnace]

Now what is b in this case?

What is 2a?

[still crest]

4

[strong furnace]

What about b

[still crest]

I'm not sure

[urban matrix]

wait oscar was i supposed to add all the areas up for number 5

or was that for number 4

[peak niche]

Quick question I know this is above my level but what is the function where it says f(2a-x)

[strong furnace]

b would be f(x)+f(2a-x) right?

[still crest]

How do we get that?

[strong furnace]

It's the same function but with input 2a-x instead of x so if you replace x by 2a-x you should get that

This

[still crest]

2b = what you said

[strong furnace]

It doesn't matter because it's just a constant multiplied but no I did not :/

[still crest]

I didn't mean you said it

I meant that the exercise tells us that f(x) + f(2a-x) = 2b

[strong furnace]

Lol

True true

My bad

[still crest]

I don't know how do we get f(x) + f(2a-x) = b

Oh okay

[strong furnace]

It is 2b

But you have to just get this 2b

[still crest]

I can't find a way to correlate b and c part

[strong furnace]

Ok let's do it one by one

2a=4 right?

[still crest]

Yes

[strong furnace]

Now 2a-x=4-x

[still crest]

Right

[strong furnace]

Now write down f(x)

And write down f(2a-x) = f(4-x)

[still crest]

I did

[strong furnace]

If you add them what will happen?

[still crest]

Add these?

[strong furnace]

f(4-x) and f(x)

Add these

[still crest]

Oh wait

We had 2ab

So now it should be hmm

2b?

[strong furnace]

Ok my bad

I missed something that I had in my mind

I just didn't tell you lol

f(x) is the integrand in part c

(sin(x-2))^2019.(x-2)^2018+3=f(x)

[still crest]

and substitute 4-x in

[strong furnace]

Now write down f(4-x) for this

[still crest]

f(4-x) = sin^2019(2-x) * (2-x)^2018 +3

Some typos, it's fixed now

[strong furnace]

You see how the thing inside the bracket is coming out to be -(x-2)?

[still crest]

Yep

[strong furnace]

Can we use some properties to convert it into just (x-2)?

[still crest]

I know that it works with cos(-x)=cos(x)

Does it work with sin?

[strong furnace]

Does it?

[still crest]

I'm not sure

[strong furnace]

You know sin(a-b) right?

[still crest]

Yes

[strong furnace]

Treat sin(-x) as sin(0-x)

[still crest]

Is it -sin(x)?

[strong furnace]

Yes

[still crest]

sin(-x)=-sin(x)

Ohh

And it's +

Because we do the same to the other one

-(x-2)^2018

[strong furnace]

But does the negative come out?

Look at the power

[still crest]

Oh right

It's even

english problems

So we can just swap it

And it won't change

Right?

[strong furnace]

So you get -(that expression)+3 for f(4-x) now I think you can add them like part b says to get your result?

[wise jewel]

Can someone please tell me how the hell my teacher solved this??????

[still crest]

This is busy

[wise jewel]

?

[still crest]

ty

@strong furnace haven't done this in a while

So we have f(4-x) = -sin^2019(x-2) * (x-2)^2018 + 3

[strong furnace]

Lol

[still crest]

Right?

[strong furnace]

Yeah

And this if f(2a-x)

[peak niche]

Damn u two still on the same question...

[still crest]

I can add f(x) + f(4-x)?

[strong furnace]

Yeah

[still crest]

Let me try this

[harsh bone]

Yo

[still crest]

We get 6

[strong furnace]

For 2b

[still crest]

f(x) + f(4-x) = 6

[strong furnace]

And a was 2

[still crest]

That's 3

[strong furnace]

So the result is ?

[still crest]

3

[strong furnace]

The result was 2ab,

[still crest]

I meant b is 3

So that's 12

2ab

[strong furnace]

Yes

And that should be the value of your integral

[still crest]

Okay I got it

[still crest]

Thank you!

[peak niche]

@still crest bruh i said 3 at the start lol

[still crest]

That wasn't the answer though

[peak niche]

Oh i thought u were solving for the letters or something i have no clue what an integral is

[strong furnace]

Should be

[still crest]

Integral answer is 12

[harsh bone]

Help me pls

[strong furnace]

And that's what we got

[peak niche]

Oh cause like 2a is 4 and b is 3

[still crest]

Yep

[harsh bone]

Pls

[stiff quiver]

Please stop spamming.

[still crest]

Yo kid, no one is obligated to help you

[harsh bone]

I’m no

[still crest]

Stop spamming

[harsh bone]

I never said

I’m not

[peak niche]

Straight outta year 7

[still crest]

You are

[stiff quiver]

lowkey

I'm in year 7 😦

[peak niche]

I have 1 more week of tests then I can drop 6 subjects

[harsh bone]