help-23

[opal tartan]

try to match the coefficient using differentiation or integration or by multiplying with x^r if that doesn't match

[mossy ridge]

Alright thanks a lot!!!

I will try to

Omfg i cannot get 26 as well

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[quick crater]

,rccw

[quick crater]

,rccw

[quick crater]

AB=6

[versed wave]

what does the question ask?

[quick crater]

it asks for the bigger circle's radiua

[versed wave]

!xy

[safe radish]

Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.

[versed wave]

screenshot your instruction, and translate it

[quick crater]

,rccw

[quick crater]

"the image shown on the side is made out of square ABCD and semicircle with diameter CD, the side length of ABCD is 6cm, then find the bigger circles radius on the image"

qait dont i just pythag

bruh ok nvm

.close

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[quick crater]

.reopen

[safe radish]

✅

[quick crater]

,rccw

[quick crater]

how bout tbis, it wants me to find the area of ABCD

[lean otter]

use pythagoras theorem

[quick crater]

oh and do i just use heron's?

[quick crater]

oh yea

162 right

[lean otter]

hollon lemme check

[quick crater]

how bout this it wanrs me to find the diameter of the semicircle

,rccw

[quick crater]

like say the radius is r, and i drew a line thats parallel that intersects a, and ill call that point x, so 160=2r+x, and x is just $\sqrt{4x^2-6400}$

[flat frigate]

Skill_Issue

[lean otter]

i think ACD cannot use pythagoras to find,,, howd you get 162cm^2?

[quick crater]

$$80=r+\sqrt{r^2-1600}$$
$$80-r=\sqrt{r^2-1600}$$
$$r^2-160r+6400=r^2-1600$$
$$r^2-160r+6400=r^2-1600$$
r=50

[flat frigate]

Skill_Issue

[quick crater]

diametsr is 100 right

[quick crater]

,rccw

[lean otter]

ah yea then that should work, i was thinking of something else but that didnt seem correct

[quick crater]

how bout this?

[lean otter]

looks good to me

[quick crater]

the teacher said it was wrong? was my teacher wrong then?

[lean otter]

lemme try something

did they give the height of the semi circle?

[quick crater]

wdym

[lean otter]

oh wait i forgor nevermind

gimmie a moment ya

[quick crater]

oh yeah it was cofrect

[lean otter]

á?

[quick crater]

it was 100

[lean otter]

oh yea cause

[quick crater]

anyways thanks for your time

cya

[lean otter]

the length youre finding was diametre lmao

[lean otter]

ur wlc

[quick crater]

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[covert kiln]

yo i got the biggest math exam of my life in 2 days and i barely understand lmao any help w/this?

[topaz tree]

can you say MABN is a trapezium?

[covert kiln]

i guess?

[topaz tree]

prove it then

[covert kiln]

i think i should focus on trinagles?

[topaz tree]

yes

[quick crater]

just extend mn till it intersects with the bottom section, then use simmilar triangles (i think)

[covert kiln]

i made 2 trinagles?

do i have to prove they r similair?

[quick crater]

what

[topaz tree]

there is also a theorem for this known as trapezium intercept theorem
Any line drawn parallel to the parallel sides of a trapezium divides the non-parallel sides proportionally.

[covert kiln]

didnt take that yet i think

[quick crater]

excuse my horrible drawing, lets call the intersection point O

[covert kiln]

cant i say angle AMN = MNB = 90 degrees (MN is tangent of both smeicircles)?

so AM is 4cm

AM = RQ = BL = 4 they are

so then

trinagle mpr and mln r similair

[quick crater]

you can try to find AO using the fact that AOM is simmilar to BOM, and you can use it again to find QP since OQ is just AO+4

[covert kiln]

common angle?

and parallel lines?

[covert kiln]

oh

OH SHIT WAIT

PR/NL = MR/ML

PR/4 = 4/12

or, PR/4 = 1/3

so, PR = 4/3cm

PQ = RQ + PR = 4+ 4/3

PQ = 16/3cm (length of perpendicular line is 16/3cm)

is this correct???

[quick crater]

what is R

[covert kiln]

right

this

[quick crater]

lemme try my method

[covert kiln]

okok

[quick crater]

i got the same

[covert kiln]

nice!

can u epxlain it to me

ur method

[quick crater]

alright, AO/BO=4/8=1/2
BO is just AO+12
we can tell that AO=12
AO/AM=QO/QP
QO is just AO+4, so 16
12/4=16/QP
QP=16/3

[covert kiln]

ohhh

ur method is easier imo

thanks man

🙏

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[crude shell]

hi i am currently studying pre-calculus and i see these questions that asks me to derive the given formula. i suck at them and i wonder whether i will see these derive or proof questions a lot

[crude shell]

i dont know whether derive mean prove but anyways

here is the question

like i got the first one partly correct which is 12.1(a) but couldnt exactly prove b

for 12.2 i got nothing like how am i supposed to show them and how is prob. 12.1 related to that equation

i know how to find the area of triangle btw i just suck at these derive or prove type of questions in all chapters

[long shore]

what did you do for this

i dont understand, 12.2 basically shows you how its done?

using the sine rule

,tex $ \frac{b}{\sin(B)} = \frac{c}{sin(C)}

[flat frigate]

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

[safe radish]

@crude shell Has your question been resolved?

[crude shell]

let me share

i found c sin A = h

[crude shell]

oh could be right i tried doing something for that one like this

i found x negative though lmao

therefore it is completely incorrect

but like i remember following a way similar to this while we were finding the area of triangles like these in the second picture.

also uhm its weird but we did not see Heron's formula nor absinC over 2

or (a^2sinBsinC)/2*sinA

we only did base x height thing

[long shore]

maybe just search up area of triangle proofs

theres not always 1 way to prove something sometimes theres multiple

ive got a bad headache and im pretty tired so i dont think i can help u atm bc my brain isnt working but if you’re still stuck in the morning (like 14hrs) dm me and ill help u

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@crude shell Has your question been resolved?

[crude shell]

Oh okay thanks anyways i appreciate it

[crude shell]

hello😕

trying to make sure the channel doesnt get closed due to timeout lol**

<@&286206848099549185>

[crude shell]

hello?

[rancid nymph]

yepp

[lean otter]

a derivation isnt a proof

its more of a show

you just show how u can make that formula

[rancid nymph]

what is your question....????

[lean otter]

absinC is part 12.1, its showing you how its derived

“area = 1/2 bh, h=asinC, area = 1/2 abSinC”

then for the second part, it wants you to derive an equation without the use of b, so you find some identity for b and plug that in instead of b

[safe radish]

@crude shell Has your question been resolved?

[crude shell]

isnt it the same

[lean otter]

not exactly

[crude shell]

How

[crude shell]

But it shows like how is it not proof

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[opaque forge]

does anybody know o formula for this or how it should be rezolved ?

[lean patio]

For what

[opaque forge]

at b

[lean patio]

Split the integral since its a sum

[opaque forge]

i go to sleep

is egnof math for today

thx

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[lean patio]

Why

[opaque forge]

i was looking for 20 minuts for a formula to do this

and i forgot the simplest one

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[gleaming plinth]

@scenic dove hey again, hopefully I'm not bothering you. I forgot to ask something else on the same topic.
If we talk about PMFs, am I right to say that the top one is a PMF and trhe bottom one isn't?

[gleaming plinth]

in case if follows the same logc as the CDF

and if it's not, this time it's not equal to 1-PMF though, right?

This one was the case of getting EXACTLY k successes, so I used the PMF

[scenic dove]

Yeah I would agree with that. The top function describes all possible outcomes of a stochastic experiment so that its probabilities sum to 1

The bottom one describes a bunch of different experiments

[gleaming plinth]

makes sense. on the other hand, this is the revised graph for the CDF, and the other function. Should be correct this time

[scenic dove]

1-PMF doesn't have much to do with the questions at hand now, no; intuitively, the value of 1 - PMF(k,n,p) describes the probability of getting any outcome that's not exactly equal to k successes

[gleaming plinth]

okay, so in this case it's yet another function. gotcha

and this is my last scenario: the probability of getting AT LEAST k successes, which I originally thought was also a kind of CDF. Do these ones have a name at all?

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[clever hill]

(16.6 * x) + (14.2 * x) + (11.7 * x) + (5.6 * x) + (5.3 * x) + (4.7 * x) + (3.3 * x) + (3.2 * x) + (2 * x) + (1.5 * x) = 100

[clever hill]

how would i solve for x here?

my first thought was to minus the (16.6 * x) but

then im not sure waht to do with it on the other side lol

Ohhh i see, i never looked at it like that interesting

alr so lemme try that rq

so thats 68.1 * x = 100

x = 100 / 68.1

Alright! thanks for the help, at first this question looked much tougher lol

alr gonna close now

.close

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[weak saddle]

Question No 9

[weak saddle]

Combining Like Terms

[fresh owl]

you've named it, time to do it

which terms do you see that are the same in Q9

[weak saddle]

x3y2 and x2y

[thin narwhal]

It would probably be better if you highlight the like terms

Surely you know how to identify them since you already did Q1-8

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[muted pasture]

Help

[muted pasture]

I need help with Simple Interest Formula

I haven't done math in years and I'm sort of going to have to learn shit from the ground up

[red delta]

How?

[muted pasture]

I just can't understand it there's so many different questions it's not just one thing

I don't understand math is so stressful.

[red delta]

Simple interest is the percentage (rate)of the original amount(principal) over time

[red delta]

To be paid alongside the principal

I =principalxratextime/100

[muted pasture]

What if it doesn't tell me the rate

[red delta]

Make rate stand alone in the above formula

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[somber cape]

I am kind of confused on the story he is giving with vector projection from 1:20:00 to 1:30:00
https://www.youtube.com/watch?v=TKlGMRghcDs&list=PLDesaqWTN6ESk16YRmzuJ8f6-rnuy0Ry7&index=3

[somber cape]

I understand the concept I believe

but I'm confused with how much of v is w, wouldn't all of v be in v in an ideal situation. I'm assuming he's taking into account gravity and so what would gravity be in this case? I'm kind of confused on how the w vector exists, because I was thinking in space, if your pulling something along a vector v then it would travel in that direction only

yeah I think my question is just how can some of v be in w if that makes sense

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[patent flame]

i for iota?

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[tender plover]

Solve the initial value problem of radioactive decay by separating the variables. Where N(t) is the concentration at time t and N0 is the concentration at the beginning

[tender plover]

I know how to get the general solution which is ln(N) = -kt +c

But idk how to solve it. In my booklet there is a solution for this equation but i cant just throw the solution down

[peak estuary]

when you say "I know how to get the solution" then what do you mean by "idk how to solve it"

[tender plover]

like then i need to put in N(0) = N0 but i have no idea how to do so

and the solutions are so confusing

[gusty trench]

so you got ln(N) = -kt + c

and you know from N(0) = N0 that when t = 0, N = N0

[gusty trench]

you can't just substitute those values into this to solve for c?

[tender plover]

.close

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[sacred mountain]

Does anyone know how to do this without a calculator?

[empty gyro]

Find the ratio between successive elements, then use that for the next term

That's how a geometric sequence works

[sacred mountain]

Ye ik but I tried to see how much it times by for the next terms but the r is 4.472135955, and your not meant to use a calculator l

So that doesn’t make sense

And if you treated root5 as an x it still doesn’t make sense how 10 is on its own

Or 200

[empty gyro]

$\frac{1}{\sqrt{n}}=\frac{\sqrt{n}}{n}$

[flat frigate]

SWR

[sacred mountain]

?

I don’t get it

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[halcyon valley]

This just follows from the definition of conditional probability right?

P(A & B | C) = P(A | B & C) ∗ P(B | C)

[halcyon valley]

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[charred cedar]

hello

[charred cedar]

can Anyone explain to me how did we know that it is conservative fron the first glance ??

is it bcz of the circle on the integral ?

btw this is calculus 2 multivariable vector field

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[charred cedar]

<@&286206848099549185>

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[left willow]

they just worked it out after stating it

its a conservative field if curl F= 0

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[quaint aspen]

I just started this topic and am confused

Can some pls explain wht the circle is center at the origin

How do we determine where we draw the base of the object

[crisp mortar]

what topic are you learning

[quaint aspen]

Volume as the integral of cross sectional area

@crisp mortar

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[lilac relic]

how do you work out standard deviation for a set of values? In this situation I'm doing an experiment and have some data

[silent token]

There's a formula, have you seen it?

[lilac relic]

I don't understand it

I'm at a low level of math

[silent token]

Do you understand sigma notation?

[lilac relic]

no

at least I don't think I do

[silent token]

I'll just put it into words then

[lilac relic]

It's something about dividing the data by the average several times

I've done it before but I can't remember

[silent token]

For each individual value, find it's difference with the mean and square it
Then add all those squared vales together and divide by one less than the amount of data points
Square root the entire thing and voila
Standard deviation

[silent token]

You really shouldn't be dividing by the average at any point

[lilac relic]

I've clearly been misinformed then

[silent token]

You do subtract from the average
But never divide

[lilac relic]

right

[silent token]

Alternatively, of this isn't like a hw problem
Plug it into a spreadsheet/calculator and let that do the work

[lilac relic]

this is my data

I'm just checking my answers more or less

ah right

[silent token]

The first one at least doesn't seem right

[lilac relic]

ok

give me a moment to work it out and I'll get back to you

[silent token]

Third one also seems off

[lilac relic]

what do you mean by 'divide by one less than the amount of data points'

would I divide by 2 in this situation?

since I have 3 trials in total

@silent token

[silent token]

Yes

[lilac relic]

all righty

yeah I got a completely different answer

I didn't do it right the first time

0.147 for the first one

that look right?

I don't think so

I think my mind is starting to degrade from lack of sleep

It's a great deal worse than my last lot of data

@silent token

[silent token]

Generally looks more accurate

[lilac relic]

huh

what's a bad number for standard deviation?

[silent token]

I mean your standard deviations seem right

[lilac relic]

is it like coeffecient of determination where the range is between 0 and 1

[silent token]

In hindsight
Can I ask why you're looking for the standard deviation?

[silent token]

No, it's a measure of spread

[lilac relic]

right

what would be bad values for standard deviation?

[lilac relic]

yea

[silent token]

Put really poorly, it's kinda like the average distance of everything from the mean

[lilac relic]

It's something to talk about in my evaluation of my internal

I've doing a investigation into the effect temperature has on peroxidase

[silent token]

The standard deviation of three points is just kinda not as useful as the actual three points?

Rather, I'd be more interested in the correlation coefficient of the temp vs the height

[lilac relic]

it's all greek to me at this point

[silent token]

My advice
Don't calculate by hand
Just plug in into Excel or something and tell the computer to do it

Gimme a sec to pull up Google sheets

[lilac relic]

Maybe I should do that since you'll have to go into the trouble of taking all my data into a sheet

and I'm not too sure if I'm actually allowed to be sharing this information but it probably doesn't matter

[silent token]

In hindsight
It's not really linear, so the r^2 isn't of too much help

[lilac relic]

that's interesting

[silent token]

Although you can make a convincing argument for it not being linear

[lilac relic]

yes

[lilac relic]

so wait does this show the standard deviation?

[silent token]

No, the r^2 is the correlation coefficient

[lilac relic]

I'm a fool

I've had the value for ages already

[silent token]

There's a function for it

[lilac relic]

oh

IMAO

[lilac relic]

I got confused

[silent token]

Next time, let the spread sheet do the work

Not worth calculating by hand

[lilac relic]

ok

thank you for doing that

I'm using the r^2 to talk about realibilty too

with future values

[silent token]

Weather the standard deviation is good honestly depends on the context

Is your data being 1 stdev off acceptable?

Although, with only 3 data points each
A visual representation may be a more compelling argument than the standard deviation

[lilac relic]

oh yes, very acceptable

[lilac relic]

right

[silent token]

Then it's probably a decent standard deviation

[lilac relic]

so you think I should the add standard deviation to a graph?

is that possible actually

[silent token]

Probably possible

Maybe not on Google sheets

[lilac relic]

I used google sheets to do my current graph

[silent token]

Oh wait maybe

[lilac relic]

also what do you mean by 1 stdv?

1 standard deviation

is there multiple?

[silent token]

I just mean 1 times your standard deviation

[lilac relic]

right

@silent token

sorry that was a silly question, sorry for the ping

[silent token]

?

Very cursed, but possible

[lilac relic]

lol

[silent token]

Use Excel instead
They've probably done it better

Don't think it's possible to get the individual points in too though

Actually
It is possible

But an entirely new level of cursed

[lilac relic]

lol right

what are bad numbers for stdv?

numbers which would be a sign of inaccurate data or the like

there is none according to researchgate

Interesting

all right thank you for your great help

I'm gonna close the channel now

.close

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[cerulean crane]

Try drawing a picture that includes Q

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[astral brook]

i was just going over a review sheet my geo teacher gave us for our exam and i understand how to plug in for the two equations (y=mx+b and y-y1=m(x-x1) ) but im confused what the difference between the two formulas is because theyre both for equation of a line? like when would one be used and the other one not?

[idle pulsar]

That is general equation of line, but the second formula is most commonly rewritten in this way:
m = (y - y1)/(x - x1)
We use it to find the slope of the line connecting two different points.
But if you have the slope and the point already, you can construct the line using first formula.
Usually, you won't have the slope but two points. So you find slope from second formula, then plug in first formula and find equation of line

[finite yacht]

Also, the first one gives you directly the value of y as a function of x (y = something), and the second one tells you directly that (x_1,y_1) is a point of the line

That is what they are mainly used for

[astral brook]

OHHH that makes sense

thank u both sm i was panicking LOL

[idle pulsar]

Your welcome ❤️
If there's anything else you need help with you can ask, and if not you can close the channel using ".close"

[astral brook]

thank u!!

.close

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[white yew]

is d correct

[lime dust]

What do you mean d? I only see a, b and c

[white yew]

sorry i meant c

[thin bridge]

missing ()

[white yew]

where

(3(x+h))^(1/2)-(3x)^(1/2)/h

[thin bridge]

around what's supposed to be the numerator of your fraction

[white yew]

(3(x+h))^(1/2)-(3x)^(1/2))/h

?

[thin bridge]

still missing a ( at the start

[white yew]

((3(x+h))^(1/2)-(3x)^(1/2)/h

?

[thin bridge]

now you're missing a ) at the end

[white yew]

((3(x+h))^(1/2)-(3x)^(1/2))/h

[thin bridge]

yes,
though they may want you to rationalise the numerator (which will result in cancelling that factor of h)

[white yew]

how would you do that

3/ ((3(x+h))^(1/2)-(3x)^(1/2))

?

is this correct

[thin bridge]

not quite, heck your signs

[white yew]

can you write it? Im not sure what to change

[thin bridge]

how did you get what you wrote

[white yew]

multiply both the numerator and the denominator by the conjugate of the numerator

[thin bridge]

yes, that's what you're supposed to do

but here your denominator isn't the conjugate

[white yew]

is this not what i wrote?

[thin bridge]

no

[white yew]

oh wait the sign is differnet

3/ ((3(x+h))^(1/2)+(3x)^(1/2))

[thin bridge]

hence why I told you to check your signs, as it resembled/looked close to the correct result

[white yew]

thank you

does this look correct?

.closed

.closed

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[warm crest]

im doing some practice problems for a quiz in a few days and i have cant seem to figure out what trig identity lets you do this?

[icy lance]

tan=sin/cos

thats it really

[warm crest]

oh

wouldnt cos^9x become cos^7x then?

[icy lance]

its tan^3

not tan^2

sin^3/cos^3

[warm crest]

i did not know i had to apply powers to that, gotta redo some other problems :'D

thx for the help and later

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[torn juniper]

does this converge? i know that the general term converges to 0 but i dont know which convergence test works for this series

[idle pulsar]

Take limit test, with respect to 1/n

Then solve the
sqrt(n^2+1) - sqrt(n^2-n) as n goes to infinity

You can use conjugation for it

You will get -1/2

[torn juniper]

doesnt this converge to 0?

[torn juniper]

and which test is that?

[idle pulsar]

Limit Comparison Test?

https://tutorial.math.lamar.edu/classes/calcII/seriescomptest.aspx

[torn juniper]

yeah sorry i just study it in a diffenet language

[idle pulsar]

It's fine I get you

[torn juniper]

so you are saying its smaller n times of the same term?

[idle pulsar]

Oh wait, I think limit test won't help here tho, since limit converges, but what we took is divergent

Okay mb, I think we can still use limit test

[idle pulsar]

yes

So diverges

But now I'm a bit doubtful of myself, let's see if someone else can check as well

[idle pulsar]

I have sign mistake here btw, it becomes +1/2

[torn juniper]

doesnt the test say that if you find a "bigger" series that converges then the series converges aswell?

[idle pulsar]

Okay so I think I remember things now

[torn juniper]

oh i dont think we can use it, since the general term of the new series doesnt converge to 0 it diverges and it not applicabke for the test

[idle pulsar]

Here are cases:
If series converges, if denominator is divergent so is numerator
If series converges, if denominator is convergent so is numerator
If series diverges, if denominator is divergent, so is numerator

[idle pulsar]

No exactly because it doesn't converge to 0 we can use it

Imagine your denominator is very big

Meaning it diverges

But still, you don't get 0, but you have a value

So your numerator must be even bigger than your denominator or have same rate of bigness (which is the case for us here, since it converges to a value less than 1 but bigger than 0) if you want your limit test to converge

If your numerator had less bigness (less order of n for example) then series would have converged to 0

But it didn't converge to 0

If value is between 1 and 0, then bigness (order) of numerator and denominator is same, just denominator is a little bit bigger

If value is more than 1, then bigness (order) of numerator and denominator is same, just numerator is a little bit bigger

Sorry if it's a little confusing, the messages might not be as clear

But basically in a formulatic way:
If limit test converges to bigger than 0 less than infinity, divergence and convergence of numerator and denominator is same
If limit test diverges to infinity, then if denominator is divergent then numerator would be divergent. If denominator is convergent, we can't understand anything

[keen finch]

Hey I am practicing math, and I know I need to multiply the denominators of the numerators.
But why I should multiply?
I know the first reason is because the answer would be 0.
But why I need to multiply the numerators and denominators by 3x, how do I determinate the numbers I should multiply?
It can be a dumb question, but I would be grateful for knowing , Thanks

[torn juniper]

but what are our numerator and denominator? we used the an < bn limit test

[idle pulsar]

You need to get a new help channel #❓how-to-get-help

[keen finch]

Ok thanks

[idle pulsar]

No we didn't say an < bn. That's direct comparison test.
We said lim(n->infinity) an/bn
Where an is your series and bn is 1/n
Numerator is an and denominator is bn

[torn juniper]

okay that makes way more sense

ty

thats what i was missing

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[delicate trellis]

I dont understand how to do this question

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@delicate trellis Has your question been resolved?

[delicate trellis]

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[bitter steppe]

so uh in the answer sheet

he put the vectors in rows

i put it in columns

i reached echelon

and it's the same number of basis vectors

but the actual vector is different

im wondering if im still correct or not

[median vigil]

with one of them you will find the dimension of and a basis for the row space, and one will find the dimension of and a basis for the column space

they are the same vector space and will have the same dimension, but you will not get the same basis

the row approach will give the "simplest" basis, whereas the column approach will give a basis of the original vectors

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@bitter steppe Has your question been resolved?

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[pastel plover]

I have no clue lol I tried

[icy lance]

youre writing velocity having ft as a unit?

also it should at least be negative, i havent checked the number

[hoary wind]

Number is good at least

Sidenote, never seen acceleration due to g written in feet per second squared

I hope I never do again

[pastel plover]

thank u ... ops... it is -139

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[river needle]

any help?

[flat frigate]

hoax

hoax

[river needle]

AB = 48m
BC = 64.3m

[safe radish]

@river needle Has your question been resolved?

[junior smelt]

Taking your word for this one: what's the angle that AB makes with the "north" from A?

[i.e. what's the bearing of B from A?]

[river needle]

thats what im tryna figure

the bearing of b from a

if i find that angle

i think the rest is a piece of cake

[junior smelt]

well, you have the bearing of A from B, riggghttttttt

[river needle]

yea it's alr given as 195 deg

[junior smelt]

Which then should get you the bearing of B from A, then, right(?)

[river needle]

no idea

like how?

[junior smelt]

draw a picture

[river needle]

u want me to whip up ms paint?

[junior smelt]

If you have the bearing of [X] to [Y], then you (should) "instantly" know the bearing of [Y] to [X]

[junior smelt]

Well, you could

But, like, anyways, you should be able to spot a "Z" angle if you sketch it out

[river needle]

well tbf idk how to find the bearing of y from x given the bearing of x from y

[river needle]

lol i was about to say that

i was bout to say "unless you want me to do something with parallel lines or anything"

[junior smelt]

Yep, basically that (with the "north-south line" )

[river needle]

it should be 15 deg

[junior smelt]

Yep

[river needle]

aight i think i got it now

so angle CAN should be 56.5 - 15 = 41.5 deg

90-41.5 = 48.5

270+48.5 = 318.5

which is the correct answer in the grading scheme

[junior smelt]

(you could've just done 360 - 41.5 too, btw )

[river needle]

however i'd like to understand why my original approach was incorrect

[junior smelt]

What was your original approach?

[river needle]

so originally, my approach to find the bearing of B from A was to

use the fact that the sum of interior angles is equal to 180

so angle NAB + angle TBA = 180

i calculated angle TBA to be 90+85 = 175 deg

but that gives us the other angle being equal to 5 deg, so.....

[junior smelt]

(and I'm not sure you have a valid triangle there, esp as the angle TBA is actually 90 [see they've marked it as a right angle], and the third angle for the triangle you're considering isn't there?)

[river needle]

lemme open up paint

sorry if the drawing looks bad, but hopefully it's understandable

but basically T should be the north of B, no?

[junior smelt]

T is vertically up, not north of B

it's "above" B

[river needle]

oh ig thay makes sense

im mistaking 3 dimensional shit for 2 dimensional shit

[junior smelt]

Yeeeeaaa, pretty difficult to visualise it tbf

[river needle]

yea but anyways

tysm once again

ur the best

[junior smelt]

No worries and awwww

[river needle]

got my math exam in 8h

[junior smelt]

Ouch best of luck for it, hope it goes well!

[river needle]

hope so 😭

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[west cradle]

hey guys, how do I find the interval in which the function is increasing?

[buoyant shadow]

first of all, can you tell me what is the interval in which the function is increasing?

[pure agate]

I think that's the question they wanted help with. 🤔

[west cradle]

no I’m sorry idek I’m so brain dead rn 😭

[west cradle]

yeah 😭😭

[buoyant shadow]

like you're super tired?

[west cradle]

yes lol it’s almost 5 am and I’ve been awake since 9 am yesterday 😞😞

[buoyant shadow]

thank you

[west cradle]

wait so how do I solve it boss

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[grizzled ridge]

i dont get where to start

thats the answer key

and the example isnt helping

[rancid sand]

Do you know about cross method?

umm

[grizzled ridge]

im blank rn

[rancid sand]

So what cross method does, is first finding out the factor of the constant term

for example 6x^2 - 7x + 1

1 = 1 * 1 = -1 * -1

and 6x^2 = 6x * x = -6x * -x

and you try

[rancid sand]

just like that way

cross multiplication, then sum it up, to see whether the answer is same as the coefficient of x

if ys, then the quadratic equation can be factorized, if not, vice versa

[grizzled ridge]

ty

lowkey helped i got the answer

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[hardy meadow]

The last four people on a sold-out flight enter the airplane one-by-one. All four people have reserved seats. The first of the four just choose a random seat to sit in. Each subsequent person sits in the correct seat if available, or a random seat or not. What is the probability that the last person sits in the correct seat?

[hard crest]

haha i love this problem

[hardy meadow]

I tried using a tree diagram, but it just turned out too complicated for me too easily comprehend

[hard crest]

hmm what if you reduced the problem? what if there were only two people on the flight?

[hardy meadow]

I tried considering that after I saw a reddit post about it, but I can't really understand how to apply it to this

They said no matter the number of people it'll always be 1/2, but how exactly?

[gusty trench]

when there's two people, the first person has a 50% chance of choosing the correct seat and a 50% chance of choosing the incorrect seat. if they chose the correct seat, the other person would also be in the correct seat, and if they didn't choose the correct seat, the other person would also have an incorrect seat. do you see how there's a 1/2 chance here?

if you drew this as a tree diagram, there would be two branches with 1/2 chance each for the first person's choice, then for the branch corresponding to the first person choosing the correct seat, the second person would have a 100% chance of choosing their correct seat, while for the branch corresponding to the first person choosing the incorrect seat, the second person would have a 0% chance of choosing their correct seat.

so multiplying the probabilities, there is a 1/2 * 1 + 1/2 * 0 = 1/2 chance that the second person gets their correct seat here

do you see how you might extend this reasoning to three or four people?

[hardy meadow]

thanks

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[viscid hollow]

Can someone explain why this correct?

[subtle yew]

which part is confusing

[viscid hollow]

Wouldn’t the numerator be ln(x)^2 - 1?

[subtle yew]

why?

[viscid hollow]

Oh wait they factored the -1 out

Ah I get it

Stupid me

Nvm

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[cobalt mason]

Could you please help me with this

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[jovial linden]

Help on this I assume it's 60 km but it looks a bit too obv

[jovial linden]

Btw that's the whole question there's no more other info

[buoyant shadow]

60 makes no sense

there's 0 which is how far you ended up from when you were at 08:00

and there's 120 which comes from 60+60

[jovial linden]

So it's 120 in total?

[buoyant shadow]

i guess you could phrase a question in a way where it's 60, but it would have to be a long sentence

yes i would say 120

[jovial linden]

Ohh okay!!

What about these (just want to review if answers are correct)

ii.) Total time taken for journey:

7.5 hrs

Or

Excluding stationery time: 3.5 hrs

iii.) Average speed of journey:

34.29 units/hour

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[jovial linden]

<@&286206848099549185>

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[dusk stratus]

Why do waves travelling from slow to fast
medium bend away from the normal & vice
versa?

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[charred cedar]

hello

[charred cedar]

this question about polar coordinates

I am having hard time to know what did I exactly do wrong. My ans is different than my teacher's

my teacher explanation

my solution

I'd really appreciate if anyone helped me.. my exam is within hours

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[charred cedar]

<@&286206848099549185>

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[fast gust]

I would like someone to double check my answer. I'm going to explain my thought process.

I think relation t and its inverse are a function because each input must have exactly one corresponding output (x, y).

X values 0, 2, 4, 6 corresponds to exactly each y value -10, -1, 4, and 8. Therefore relation t is a function

To find the inverse, the x and y values must be swapped. Looking at the y and x values of each inverse relation, each y value corresponds to exactly one corresponding x value. This makes the inverse of relation t also a function.

[paper flume]

yeah you're right

[fast gust]

ok thanks

1. x= (7-8f^-1(x))^2

2. ±root x = 7 -8f^-1(x)

±root x - 7 = -8f^-1(x)

f^-1(x)=±root x - 7 over -8

3. inverse is f^-1(x)= ± root x minus 7 over -8

I'm not sure if C or A is the correct answer because my work shows that my final answer is written differently from the answer choices

Wait nvm

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[mental dove]

What's the difference between MVT an IVT?

[glacial sonnet]

one's an M and one's an I

[mental dove]

hmm

like isnt IVT a more general thing?

(Im new to functions)

[mental dove]

like we were taught that if f(a) x f(b) < 0 then the function has a root in between these numbers

hence it intersects the x axis atleast once

and called this the IVT

[glacial sonnet]

the difference is that mvt guarantees a value of the derivative

and ivt guarantees a value of the original function

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@mental dove Has your question been resolved?

[mental dove]

oh

can you explain with an example?

[glacial sonnet]

this one

you have two points, (a, f(a)) and (b, f(b))

the average slope between the two points is (f(b) - f(a)) / (b - a)

[mental dove]

yes

[glacial sonnet]

MVT says somewhere inside [a, b], theres a point c where the derivative of f at c is equal to that average slope

then for the same two points (a, f(a)), and (b, f(b)), with f(a) < f(b)

then within the interval of the range [f(a), f(b)], if you want some value y from that range, IVT says you can find some x value in [a, b] with f(x) = y

[mental dove]

oh

alright

thanks

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[bright oar]

Hello, I need help with this problem. Tbh, I don't even know what the question means so I haven't tried anything. Thanks in advance

[bright oar]

Maybe I should find f(t) first?

[crisp mortar]

yes

i think you should

[bright oar]

But how?

[crisp mortar]

i got no clues for that
does Q1 and Q2 has something to connect with?

[bright oar]

Here's Q1 and Q2. Maybe it helps

[shell bane]

Wait

[bright oar]

Btw, the answer for Q1 is π/2 and Q2 is π²/4

[shell bane]

Imma doing

Will send in a mjnute

[crisp mortar]

hmm i recommend
rewrite it

[bright oar]

I intend to do that when I first see the question lol

[snow onyx]

how d oi study maths

[crisp mortar]

meth helps

[snow onyx]

tinks bro

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@bright oar Has your question been resolved?

[lean otter]

Take this integration in question as some constant "c"

Then what will be the new function?

I mean how would f(x) look like?

[bright oar]

x+c/π?

[lean otter]

Yes

Now write c= assumed function

[lean otter]

And put this at the place of f(t)

I mean

Write c = the integration

[lean otter]

AND put this at the place of f(t)

Are you getting what I'm saying?

[bright oar]

Not really, did you mean that I set c equal the integration and replace f(t) with x + c/π?

[lean otter]

Yess

[bright oar]

So c = integral of (t+c/π)sin²t dt?

[lean otter]

Yes

But will be "t" right

As it's f(t)

[bright oar]

Ok, after that just integrate? But how to treat c in the integration? Like a constant?

[lean otter]

Yes

You will find the value of "c" that way

[bright oar]

I see. I got the answer. c is π²/2, so f(x) = x+π/2, right?

[lean otter]

Yes

You can check the answer

[bright oar]

So, the idea here is that f(t) is just f(x), right? If I understand that that's what the question means in the first place. Thanks a lot

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[lean otter]

Heres the questiobs

[lean otter]

they dont make any sense

yeah

[solar hazel]

hi hyzae

[lean otter]

i dont understand

AI helped me get those ones correct

the science teacher wants us to draw a line and then plot the points

not exactly

ill get an eraser

measure the distance from A-B, B-C, and add them together?

ah

ah

so for question 1

Find the displacement from position 1 (P¹) to positon 2 (P²) where P¹ = +45cm and P² = +33cm

i would subtract P² from P¹

ah

can u give me an example of how i should do it

ah

what about for the ones that have the position (N, E, S, W)?

for this, Id get 12cm displacement

so visualizing helps

ah

so i would still subtract?

ok

yeah

yea

oh

so you'd add them?

ah

thank yoj

ill work through these and ill let u know if theres anything else i dont understand

k

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[lean otter]

hey, sorry, but #8 and #7 are confusing me

[lean otter]

^

yeah

we'll start with 8

oh

[hard egret]

writing in terms of i,j,k would help

im guessing

[lean otter]

ah

oj

oh*

this is confusinh

thanks

ah

k

yeah

ooh

thats what i did too

so id add them together for her distance

and for displacement

that would be how far shes away from her start?

it'd be -16

-14*

ah

so -14 Steps [S]

thx so much!

[solar hazel]

hi hyzae

[lean otter]

ah

ill try 7 next

if u dont hear back from me, i did it without any issues

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[lean otter]

.reopen

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✅

[lean otter]

rip

yeah

its sending

this mobile data sucks

so for distance

i could add them all

but for displacement

but displacement

i think so

yeah

ah

ah

got my work done now

thx

it means alot

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[spice kernel]

check if the integral converges or diverges

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Please don't occupy multiple help channels.

[neat shore]

Can you think of a function you can compare the integrand with?

[spice kernel]

1/(x^2+4)?

[faint seal]

indeed

[spice kernel]

no wait

oh really?

[faint seal]

well

[neat shore]

Almost, the idea is alright.

[spice kernel]

3/that ?

[faint seal]

you need to separate the 2/x^2+4 first

or just compare to 3/x^2+4

[spice kernel]

oh okey

and the idea is that

since 3/x^2+4 converges

the given integral also does

right?

[neat shore]

Exactly. We're using a property called monotonicity.

If f(x) <= g(x) for all x, then so are the integrals.

[faint seal]

how is this monotonicity?

[spice kernel]

thank you so much guys! i have exams tomorrow and these type of questions were the only ones i couldnt solve

[neat shore]

Amazing, good luck! Make sure to practice a few more, just to get the hang of it.

[spice kernel]

will do!

[faint seal]

specifically here we are saying $$\int_1^{\infty} 0 dx < \int_1^{\infty}\frac{e^{-2x}+2}{x^2+4} dx < \int_1^{\infty}\frac{3}{x^2+4} dx$$ since $0<\frac{e^{-2x}+2}{x^2+4} <\frac{3}{x^2+4}\forall x\in [1,\infty)$

[flat frigate]

kheerii

[spice kernel]

got it!

thanks again

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[lethal tundra]

Why is the answer c, and d for the the final questions my professor did it without doing any math I’m confused

[median vigil]

the professor factored the top by difference of squares

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[lethal tundra]

Can someone explain how u do this

[safe radish]

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 was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

[lethal tundra]

1

[tardy mango]

Did you draw a diagram?

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[lean otter]

whats up

[lean otter]

can someone help me i dont know if u can seperate the x or not

[tardy mango]

Hint: $e^{x+2y}=e^x e^{2y}$

[flat frigate]

Civil Service Pigeon

[lean otter]

yes i did that but the problem is i dont know if you can take the x out of the xe part to make the variables fully seperate

[tardy mango]

Wdym? “Take the x out of the xe part”

[lean otter]

nvm i got it thxs bro

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[normal shard]

Can someone explain to me this answer

[normal shard]

.close

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[arctic stone]

-2 is slope