help-10

[royal basin]

it's 33/m = sin(35°) not m/33 = sin(35°) as you did.

[robust sleet]

^

[tepid depot]

ohhh that makes sense

ty for help

.close

[obtuse pebble]

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[tepid depot]

.reopen

[obtuse pebble]

✅

[tepid depot]

wait

what would the answer to the question be though

nvm i got it

.close

[obtuse pebble]

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[gritty light]

can someone help me with physics

[robust sleet]

post your question

for higher chance of help ask it in a physics server in #old-network

[obtuse pebble]

@gritty light Has your question been resolved?

[obtuse pebble]

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[little cloak]

Hi I have a problem I am stuck with.
I want to construct a sequence of 1 and 0 in the form
of 110110110110 or vise versa.
To construct this, I can use a sequence of 1 and 0 with
the same number of 1 and 0 between the change.
So something like 111000111 or 101010101.
I can also use other sequences of 1 and 0 that I constructed with
initial sequences.

[little cloak]

With construct I mean the result I get when I do a AND or OR or XOR operation on two sequences to get a new one

[obtuse pebble]

@little cloak Has your question been resolved?

[little cloak]

Is anything wrong with my question?

<@&286206848099549185>

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[obtuse pebble]

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[hasty plover]

Here's the problem : (6x⁴+7y³+3) _ (-7x³+4y²-3)

[hasty plover]

Which one of us is right

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[rocky cosmos]

y = x^2 - a, a>0, and y = 1, limits an area that rotates about the y-axis. Determine the constant a so that the volume of the rotating body becomes 9π ÷ 2 volume units.

[obtuse pebble]

@rocky cosmos Has your question been resolved?

[robust sleet]

The volume of a solid rotated about the y-axis can be calculated by V = π∫dc[f(y)]²dy.

$$V = \pi \int_{c}^{d} [f(y)]^2 dy$$

[warm shale]

$\frac{\tau \alpha lo}{gist}$

[robust sleet]

And you know what V is

[rocky cosmos]

@robust sleet

[warm shale]

AuHasard

[rocky cosmos]

$\int^{?}_{?} x^{2}-a\ dx=\frac{9\pi }{2}$

like that? 😬

[robust sleet]

yes

[warm shale]

AuHasard

[robust sleet]

,w plot y=x²-a

https://www.desmos.com/calculator?lang=nl

you just need to find the boundaries now

[rocky cosmos]

how do i find the boundaries

[robust sleet]

here a visual help

[rocky cosmos]

one sec

i can't see it

[robust sleet]

would y=1 be d or c

[robust sleet]

you forgot 2 stuff at left hand side (the integral)

pi, and the function to the second power

and actually

you need to solve for x

its not f(x) but f(y)

[rocky cosmos]

one sec

$x=\pm \sqrt{y+a}$

right?

[rocky cosmos]

i don't know

[robust sleet]

+-sqrt(y+a)

lets choose positive one

[warm shale]

AuHasard

[rocky cosmos]

how do we determine the upper or lower bound?

[robust sleet]

for which value y will x be zero

[rocky cosmos]

i don't know

[robust sleet]

y=sqrt(x-a) (an example)

when will y be zero?

[rocky cosmos]

when x = a

[robust sleet]

yes

[rocky cosmos]

so ±a?

[robust sleet]

no

[robust sleet]

u just need to solve y+a=0

[rocky cosmos]

y = -a

$\frac{9\pi }{2} =\pi \int^{a}_{-a} [(\pm \sqrt{y+a} )^{2}-a]^{2}\ dy$

[warm shale]

AuHasard

[rocky cosmos]

is this right? 😔

[robust sleet]

$\pi \int_{-a}^{1} [{\sqrt{y+a}]^2dy$

[warm shale]

$\frac{\tau \alpha lo}{gist}$
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[rocky cosmos]

i have a question

[robust sleet]

yes

[rocky cosmos]

okay everything is clear, i just don't get how we get 1 in the upper bound 😄

[robust sleet]

y=1

1>-a

[rocky cosmos]

okay thanks

let me know if this is correct

$$\frac{9\pi }{2} =\pi \int^{1}{-a} [\sqrt{y+a} ]^{2}\ dy$$
$$= \pi \int^{1}{-a} y+a\ dy=\pi [\frac{y^{2}}{2} +ay]^{1}_{-a}=\frac{1^{2}\pi }{2} +a-(\frac{-a^{2}\pi }{2} -a^{2})$$

[warm shale]

AuHasard

[rocky cosmos]

$$\frac{1^{2}\pi }{2} +a-(\frac{-a^{2}\pi }{2} -a^{2})=\frac{\pi }{2} +a+\frac{a^{2}\pi }{2} +a^{2}=\frac{9\pi }{2}$$

[warm shale]

AuHasard

[robust sleet]

$\frac{\pi *(a²+2a+1)}{2}$

[warm shale]

$\frac{\tau \alpha lo}{gist}$

[rocky cosmos]

how you get that?

[robust sleet]

pi is multiplied by everything

its going to be a second degree equation so there will be two solutions

[rocky cosmos]

$$\frac{\pi }{2} +a+\frac{a^{2}\pi }{2} +a^{2}=\boxed {\frac{{}\pi +2a+a^{2}\pi +2a^{2}}{2}} =\frac{9\pi }{2}$$

why do i not get the same solution

[robust sleet]

you didnt multiply a by pi

[warm shale]

AuHasard

[rocky cosmos]

i think i see where i did wrong

$$= \pi \int^{1}{-a} y+a\ dy=\pi [\frac{y^{2}}{2} +ay]^{1}_{-a}=\frac{1^{2}\pi }{2} +\boxed{a}-(\frac{-a^{2}\pi }{2} -\boxed{a^{2}})$$

[robust sleet]

$\pi * ((\frac{1}{2} + a) -\frac{a²}{2} +a²)$

[rocky cosmos]

and here

[warm shale]

AuHasard

$\frac{\tau \alpha lo}{gist}$

[rocky cosmos]

haha wyd

where's the y?

oh nvm

[robust sleet]

u arent multiplying the second terms by pi

[rocky cosmos]

do you mean i should do that, or are you making an observation

[robust sleet]

u should do that lol

[rocky cosmos]

i see

i will re-do it

[robust sleet]

a*(b+c) isnt ab+c

[rocky cosmos]

$$\pi \int^{1}{-a} y+a\ dy=\pi [\frac{y^{2}}{2} +ay]^{1}{-a}=\frac{\pi }{2} +\frac{2\pi }{2} -(\frac{(-a)^{2}\pi }{2} -a(-a))=\frac{9\pi }{2}$$

[warm shale]

AuHasard

[rocky cosmos]

$$\frac{\pi }{2} +\frac{2\pi }{2} -\frac{(a)^{2}\pi }{2} -a^{2})=\frac{9\pi }{2}$$

[warm shale]

AuHasard

[robust sleet]

+a²*

you can just verify your result with an integral calculator

[rocky cosmos]

$$\frac{\pi }{2} +\frac{2\pi }{2} -(\frac{(-a)^{2}\pi }{2} -a(-a))=\frac{\pi }{2} +\frac{2\pi }{2} -\frac{a^{2}\pi }{2} -a^{2}$$

[warm shale]

AuHasard

[rocky cosmos]

is this wrong?

[robust sleet]

+a ² not -a²

for last term

-a(-a)=a²

[rocky cosmos]

so this is a^2π/2, right? and multiplied by - we get - a^2π/2

[robust sleet]

thats right

only -a² is wrong

[rocky cosmos]

then, we have -a(-a) which is a^2, and then the - before the bracket multiplied by that gives us -a^2

$$-(-a(-a))=-a^{2}$$

[warm shale]

AuHasard

[robust sleet]

why

[rocky cosmos]

-a(-a) = a^2
-(-a(-a)) = -a^2

[robust sleet]

-(a*(-a))

[rocky cosmos]

hmm

[robust sleet]

where does the other negative come from

[rocky cosmos]

i'll have to re-check

$$\pi [\frac{y^{2}}{2} +ay]^{1}_{-a}$$

[warm shale]

AuHasard

[rocky cosmos]

so the -a comes from y = -a, right?

[robust sleet]

yes

[rocky cosmos]

hence

-(-a(-a)) = -a^2

what do you think?

[robust sleet]

what

[rocky cosmos]

okay i will show the full solution maybe it's more clearer what's wrong

[robust sleet]

F(1)-F(-a)

-F(-a)=-a(a*(-a)

its just -a(a*(-a) you just magically add an another negative

[rocky cosmos]

$$\frac{9\pi }{2} =\pi \int^{1}{-a} \sqrt{y+a}^{2} dy=\pi [\frac{y^{2}}{2} +ay]^{1}{-a}$$

[warm shale]

AuHasard

[rocky cosmos]

good so far right

$$\pi [\frac{y^{2}}{2} +ay]^{1}_{-a}=\pi [(\frac{1^{2}}{2} +a)-(\frac{(-a)^{2}}{2} \boxed{+a(-a)}]$$

[robust sleet]

see

[warm shale]

AuHasard

[rocky cosmos]

is this good?

[robust sleet]

-(+a(-a))

yes

[rocky cosmos]

okay thank you for your patience

i will now see what we get

$$\pi [(\frac{1^{2}}{2} +a)-(\frac{(-a)^{2}}{2} +a(-a)]=\frac{\pi +2a\pi -2a^{2}\pi +2a^{2}\pi }{2}$$
$$=\frac{\pi (2a-2a^{2}+2a^{2})}{2} =\frac{2a\pi }{2} =a\pi$$

[warm shale]

AuHasard

[rocky cosmos]

and this should equal 9π/2

[robust sleet]

this is correct answer

[rocky cosmos]

$$a\pi =\frac{9\pi }{2} \Rightarrow a=\frac{\frac{9\pi }{2} }{\pi } =\frac{9}{2}$$

[warm shale]

AuHasard

[robust sleet]

just recheck what u did wrong

solutions are ||-4|| and ||2||

[rocky cosmos]

this is what i get

$$\pi [(\frac{1^{2}}{2} +a)-(\frac{(-a)^{2}}{2} +a(-a)]=\frac{\pi +2a\pi -a^{2}\pi +2a^{2}\pi }{2}$$

[warm shale]

AuHasard

[rocky cosmos]

which part is wrong?

[robust sleet]

thats correct now

[rocky cosmos]

$$\frac{\pi +2a\pi -a^{2}\pi +2a^{2}\pi }{2} =\frac{\pi (1+2a-a^{2}+2a^{2})}{2} =\frac{\pi (1+2a+a^{2})}{2}$$
$$ =\frac{9\pi }{2}$$

[warm shale]

AuHasard

[robust sleet]

yeah

[rocky cosmos]

$$\pi (1+2a+a^{2})=9\pi$$
$$1+2a+a^{2}=9$$
$$a^{2}+2a-8=0$$
$$a^{2}+2a-8=0\ ; a=-1\pm \sqrt{\left( \frac{2}{2} \right) +8}$$
$$a_{1}=2,\ a_{2}=-4$$

[warm shale]

AuHasard

[robust sleet]

yes

u can verify it by putting the values in a

in the integral

,w integral of ypi+2pi from -2 to 1

[warm shale]

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[rocky cosmos]

is this correct?

[robust sleet]

does it looks like its wrong lol?

[rocky cosmos]

,calc 9pi/2

[warm shale]

Result:

14.137166941154

[rocky cosmos]

okay nice

,w integral of ypi+2pi from -4 to 1

[robust sleet]

4*

[warm shale]

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[rocky cosmos]

hmmmmm

what's wrong here

[robust sleet]

https://www.desmos.com/calculator?lang=nl

[rocky cosmos]

does that mean a=-4 is not relevant here

[robust sleet]

a=2 is only solution

[rocky cosmos]

okay thanks

[robust sleet]

bacause a=-4 (the minimum) of the graph is above y=1

https://www.desmos.com/calculator/7fgkzwthyi

[rocky cosmos]

-4 is above 1?

oh right

-(-4)

since a = -4

[robust sleet]

if u get two solutions u need to verify them by plutting it in the integral and see which one is right

[rocky cosmos]

like done here? except a = 4?

[robust sleet]

?

a is - 4

[rocky cosmos]

yeah sorry a = -4

[robust sleet]

if u plug in 2 u get right answer, for - 4 u don't so answer is 2

[rocky cosmos]

is it $\int^{1}{4}$ or $\int^{4}{1}$

[warm shale]

AuHasard

[robust sleet]

doesn't matter

[rocky cosmos]

okay thanks i don't have anymore questions

.close

[obtuse pebble]

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[karmic roost]

Steven is going for his first car when he turns 18, he puts $900 into a simple interest savings account that ears 8.2 percent per year.

A) Set up an equation that represents Steven’s situation as an arithmetic sequence, where tn is the amount in the account after n months.

B) Use your equation from part A to determine the amount in stevens account after each of the 5 months.

C) Calculate the amount in the savings account at the end of 20 months

D) At the interest rate, how many months will it take steven to save $1200

[karmic roost]

ok so

for A

im not too sure but ive put in prt/100 =tn

<@&286206848099549185>

<@&286206848099549185>

yes please

ok so

hol dup

?

like that

that does not look right

???

<@&286206848099549185>

???

.close

[obtuse pebble]

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[grand breach]

@late grove bro use the sin method

bro you dont know sins?

bro no one else solving this im doing it

bro you cant di pythagorus in those

bro dm me these questions imma solve it

[stone lake]

does sin = opposite/hypotenuse ring any bells?

not a problem, I am just trying to see how much needs to be explained

[acoustic bronze]

have u worked with trig functions before?

[grand breach]

nah he has not

[obtuse pebble]

@late grove Has your question been resolved?

[stone lake]

https://www.mathsisfun.com/algebra/trigonometry.html this might help, sorry I had to go for a bit

[patent owl]

have you read through the link sent by jaydamani?

[grand breach]

bro we need answers i have done em but i need to confirm my answers

[hollow plank]

What is the answer you want to check?

[grand breach]

the first pic

this one

[hollow plank]

Yes and what's the answer you got?

[grand breach]

0.53

is it correct or not

[hollow plank]

,wolf cos(32)*14

[grand breach]

well we got someting like 0.52991926 but we rounded off

[warm shale]

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[hollow plank]

11.87 is what you want

[grand breach]

what

[hollow plank]

0.5 is wrong

[grand breach]

then how you got 11.87

[hollow plank]

cos(32)*14

[grand breach]

we need to apply the thing to 10 of these questions

[patent owl]

rounded to the nearest tenth haha

[hollow plank]

cos(32)=x/14

[grand breach]

so we just do cos(angle given)*the side given?

[patent owl]

not for all the questions of course

[grand breach]

so the answer is 10 or 11.90?

[grand breach]

@late grove do this

[patent owl]

well what do you get when you round this to the nearest tenth?

[grand breach]

i get 10 but idk if we supposed to do that to the decimal

[patent owl]

rounding to the nearest tenth is equivalent to saying rounding to 1 decimal place

[grand breach]

so its 10

[patent owl]

that's 1 significant figure

[grand breach]

so the answer is 11.9

[patent owl]

yep

[grand breach]

@late grove

,wolf cos(54)*2

[warm shale]

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[grand breach]

,wolf cos(54)*22

[warm shale]

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[grand breach]

@patent owl @hollow plank so the answer to second one is 13

[patent owl]

no it is not

[grand breach]

then what it is?

@patent owl

[patent owl]

this is a very helpful site, read this and maybe it'll help you

[grand breach]

k and which grade you at?

[patent owl]

that's irrelevant

[grand breach]

above 10th grade or not?

i wanna know

pls tell

@patent owl

nvm he is not telling

[warm shale]

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Requested by Kuratchi#9553

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Upgrade to WolframAlpha Pro!

Requested by Kuratchi#9553

Results provided by WolframAlpha

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Upgrade to WolframAlpha Pro!

Requested by Kuratchi#9553

Results provided by WolframAlpha

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Upgrade to WolframAlpha Pro!

Requested by Kuratchi#9553

Results provided by WolframAlpha

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Requested by Kuratchi#9553

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[obtuse pebble]

@late grove Has your question been resolved?

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[languid bramble]

for dv/dt = a, is it correct to call it "change in velocity" or "change in velocity over time"?

[misty cave]

change in velocity over time

[pine sail]

Latter.

[misty cave]

change in velocity is just dv

[languid bramble]

tyty, makes much more sense now

[misty cave]

actually its more accurate to write Δv right

but yea

[languid bramble]

got it, thanks

.close

[obtuse pebble]

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[grizzled mantle]

This is a half-remembered exercise posted on #geometry-and-trigonometry yesterday

I tried doing it but couldn't figure it out

Any ideas?

[stone lake]

What did you try so far?

[grizzled mantle]

Well BE = ED, clearly

Tried something with triangles but given we only have length values on one axis it's not of much help

[misty cave]

AE = 1 right?

[grizzled mantle]

Yes

[misty cave]

so you know OA = 6

and OA is radius

now look at OD and OB again

[jagged wyvern]

Have you learnt about the pythagoras' theorem?

Oh sorry

My bad

[misty cave]

dw bro ur good

[grizzled mantle]

I think I might have some mental issues lol every time I go solve a geometry problem I keep trying to remember all the theorems & corollaries but miss the most basic stuff

[misty cave]

fax ur spitting rn this is a common experience

imma just leave this here

[stone lake]

You can solve it using triangles, you just need to see the radius

[grizzled mantle]

yeah I know what a radius is lol I'm just blind

.close

[obtuse pebble]

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[viscid plover]

how can you solve this? substitution wouldnt work here

[stone lake]

Integration by parts

[viscid plover]

so two limts?

[brittle blaze]

No

[viscid plover]

limits*

[brittle blaze]

You’ve never done parts?

[naive owl]

😳

[viscid plover]

is it integrating x and the cos separately

[stone lake]

https://www.khanacademy.org/math/ap-calculus-bc/bc-integration-new/bc-6-11/a/integration-by-parts-review

[viscid plover]

ah right yep must have missed a few lectures thanks

.close

[obtuse pebble]

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[small bloom]

How do you do 21 and 22? Specifically considering 21, from what I have the values I would consider are 0 and then 2 as an NPV

[obtuse pebble]

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[small bloom]

Putting one of the radicals to the other side seems like it would make this more complicated?

[small bloom]

So I’m not sure what steps to take

[brittle blaze]

Where the question?

[small bloom]

It’s showing up above the ‘available channel’ notification for me

Here it is again though! I was struggling with 21 and 22

[tardy epoch]

,rotate

[obtuse pebble]

@small bloom Has your question been resolved?

[jagged wyvern]

What have you tried so far?

[small bloom]

I’ve tried putting the radicals on two different sides

And then cubing it

[jagged wyvern]

Sounds good

[small bloom]

But idk if that was right? Because then one of the zeroes is also an NPV

[jagged wyvern]

NPV?

[small bloom]

Non permissible value, because 2 makes one of the radicals 0 but then makes the denominator on the other radical zero

[jagged wyvern]

Right, so that's a separate case you have to mention. "x != 2"

The original equation couldn't have x = 2 anyway. Cause it was (x-2)^(-1/3) which is the same as 1/(x-2)^(1/3)

[small bloom]

Ohh okay haha I thought that was a sign I’d done something wrong

Thank you!

.close

[obtuse pebble]

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[timid silo]

Uhh, i need help

[timid silo]

Im confused here

My equations are

0 = 16a + 4b + c

-3 = 25a +5b + c

the solution then did -(b)/(2a) = 5

and somehow found out that a = 3, b = -30 and c = 72

[obtuse pebble]

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[quaint coral]

would this just be as simple as converting the y= equation to a parametric equation or is there more to it

[quaint coral]

is it finding the first derivative, and substituting that into the original equation

so x = (the first derivative)

and y= the original equation with x substituted for the first derivative

[tardy epoch]

x is not the first derivative

i think it's saying to use $m = dy/dx = (d/dx)[f(x)] = f'(x)$ and re-write $x^2 / 4 - x - 10$ in terms of $f'(x)$ and $x$

[warm shale]

riemann

[tardy epoch]

this is such a convoluted problem

[obtuse pebble]

@quaint coral Has your question been resolved?

[quaint coral]

@tardy epoch he gave me extra hard problems because i was allowed to take the exam home and use the internet

this one took me 2 whole pages

[tardy epoch]

oh it's an exam?

[quaint coral]

yeah but im allowed to use help from the internet

why do you think the questions are so hard

[tardy epoch]

you're supposed to look yourself, not help from other people

[quaint coral]

well i need direction

i dont need the answer

[tardy epoch]

sorry, against the server rules

#rules message

[quaint coral]

all good

wont post another exam question

[tardy epoch]

shame. interesting problem too. .close to free up the channel

[quaint coral]

.close

[obtuse pebble]

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[candid spindle]

What’s the chance of 144 20 sided dice to roll the same number?

[fickle turret]

(1/20)^144 * 20 = (0.05)^143 ?

[civic zealot]

https://tenor.com/view/dumb-and-dumber-lloyd-theres-a-chance-jim-carrey-gif-11098164

[candid spindle]

😂 thank you thank you

.close

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[timid silo]

Someone help

[obtuse pebble]

@timid silo Has your question been resolved?

[obtuse pebble]

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[tardy epoch]

show your work so someone can find your mistake

[obtuse pebble]

@timid silo Has your question been resolved?

[warm canopy]

@timid silo it's not deleted

[tardy epoch]

look for your history or don't hide channels.

[tardy epoch]

also do this if you want help

[obtuse pebble]

@fast bone Has your question been resolved?

[obtuse pebble]

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[obtuse pebble]

Channel closed

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[unique sandal]

.close

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[keen charm]

Linear, quadratic, or exponential and why?

[dense imp]

Exponential because x is is in the exponent

[hybrid gull]

I think it's a combination (either "neither" or "both")

It's an exponential + polynomial

[obtuse pebble]

@keen charm Has your question been resolved?

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[timid silo]

Help

[timid silo]

<@&286206848099549185> I cant graph relations on my Ti nspire CX

[obtuse pebble]

@timid silo Has your question been resolved?

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[tardy crater]

hey guys

[tardy crater]

just had a brain fart. What is the bottom box supposed to be?

[naive owl]

If they’re supposed to be the same ur missing a negative

[tardy crater]

let me test it

[dreamy scroll]

they are not the same

[tardy crater]

it wasnt

yeah

[dreamy scroll]

if you have y = ax and you want to solve for x, what do you get

[tardy crater]

y/a = x

[dreamy scroll]

so whats a here

if y is du and x is dx

[tardy crater]

my whole set of numbers

[dreamy scroll]

that whole big ass fraction right

[tardy crater]

ya

lmfao

the only problem tho is that the du is outside the box

[dreamy scroll]

you started with y = ax\

and wrote ay = x

[tardy crater]

so i cant do du/all that

[dreamy scroll]

yeah you can

[tardy crater]

oh?

[dreamy scroll]

because y/a is the same as y x 1/a

[tardy crater]

ohhhhh so i reciprocate -1/etc

[dense imp]

multiply both sides by the denominator of that fraction, itll disappear on one side and show up on the other

(next to the du)

[tardy crater]

ok i see so let me test it

[dense imp]

but not sure what you did earlier in the problem, you may also need to substitute the x in terms of u

[tardy crater]

got it right

now i have this to do

when it says, "when x = etc.", is it telling me to submit the result when i simply plug in the x value?

im a bit confused by this part

[obtuse pebble]

@tardy crater Has your question been resolved?

[obtuse pebble]

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[static jewel]

says wrong

[gilded needle]

did you use the quadratic formula?

[junior fog]

you gotta round to the nearest hundredth

[static jewel]

ya

[twin sapphire]

its right but put it in a calculator

[timid silo]

I think u were meant to write in decimals

[static jewel]

ok

[gilded needle]

agree, sounds like they want a value not involving the square root: "round your answer to the nearest hundredth"

[static jewel]

ya i did that

says wrong

[gilded needle]

what were your answers?

[obsidian isle]

Also you shouldn't have the $\pm$ in your answer

[warm shale]

EndTimes

[timid silo]

Your answers are weird here too, why does the first have a +-, but the second one has a + 💀 this means ur saying x has 3 solutions

[gilded needle]

the second one has +/- as well, he just reversed the order

the answer is right, it's just not in the form that the software wants

[timid silo]

Oh didnt notice that sorry, i dont have glasses on, but doesnt that mean x has 4 answers🗿

[gilded needle]

it might be interpreting it that way!

i'm guessing from the part about rounding to the nearest hundredth that it just wants decimal approximations for the two answers

even though 1 +/- sqrt(6) is more correct imo

[timid silo]

Yes thats what i usually write as well, but sometimes they want us to check for the validity of the answers(not in this question) and thats when the approx sq. root values help a lot

[obtuse pebble]

@static jewel Has your question been resolved?

[obtuse pebble]

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[digital fjord]

can someone please

explain why the highlighed part is 3

i swear its sqrt 25-12

so sqrt 13

[lucid flame]

pretty sure you're right

[glossy ibex]

typo

meant to be 13

[lucid flame]

probably

it obviously can't be sqrt(3) by just imagining it in your head

[digital fjord]

ic

ty

[obtuse pebble]

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[solar flax]

A deck of cards has 52 cards with 13 denominations with 4 different patterns for each one (Spade, Diamond etc).

You draw until you have 4 cards.
What are the odds you get 4 of the same card (4 Jacks, 4 eights etc)?

Im thinking the odds are 0.39% (13/52)^4. Does this seem realistic?

[gilded needle]

aren't you drawing without replacement?

[solar flax]

Yes

Is it then 4/52x3/51 etc?

[dense imp]

why to the ^4? it doesn't matter what card you pick on the first draw

[gilded needle]

well it's unlikely you'll have anything to the 4th power then

[dense imp]

the first card doesnt matter, then on the 2nd draw you have 13/53 to get the same as the first

[gilded needle]

first card can be anything, then the next card has to be one of three (out of 51 remaining)...

[solar flax]

Yes thats right

[dense imp]

so my answer would be $\left(\frac{3}{51}\right)\left(\frac{2}{50}\right)\left(\frac{1}{49}\right)$

[candid sigil]

Shut Up

[gilded needle]

mine would be (3/51)(2/50)(1/49) divided by 3!

[solar flax]

Why 13 then 12 then 11? I want a pair of 4

[dense imp]

oh sorry i misread the question

yah

[solar flax]

Yes this suits how im thinking more

[gilded needle]

?

[solar flax]

Spam bot

[dense imp]

ye for some reason thats what i was thinking oops

[candid sigil]

This

[worn ocean]

52C4 x 13C1

[warm shale]

Sooshon

[worn ocean]

this seems about right in terms of probability

[dense imp]

where does the /3! come from?

[gilded needle]

should be divided by 4!, I guess, since order does not matter?

[gilded needle]

i think i was wrong about 3! and it should be 4! since (3/51)(2/50)(1/49) is the probability of one particular ordering of those 4 cards

and there are 4! orderings

[solar flax]

Order does not matter thats right

[gilded needle]

ah wait it would be multiplication not division

haha my brain is tired

[solar flax]

Yea itd be an absurdily small number

[gilded needle]

4! * (3/51)(2/50)(1/49)

my final attempt 😆

[dense imp]

im not too good with this probability stuff, but why are we bringing order into this? isn't it just simple probablity of 3 sequential events? if we talk about flipping a penny to heads twice in a row its just 1/2 * 1/2 and no talk of ordering comes to the table

oh wait i think i see

since you can get the hearts card first, then another then another etc

[gilded needle]

(3/51)(2/50)(1/49) is the probability of one specific way of drawing 4 of the same denomination, like for example ace of spades, then clubs, then hearts, then diamonds

but ace of clubs, then spades, then hearts, then diamonds is another way to do the same thing

and it has the same probability

and there are 4! different orderings

you have to count them all

[solar flax]

What if we assume the pattern is the same then

There are 4 diamonds of all denominations

[gilded needle]

not sure i understand the question

[gilded needle]

in the coin flip example, suppose you want the probability of 3 heads out of 4 tosses, it's not just (1/2)^3 * (1/2)^1, right?

[solar flax]

A deck of cards has 4 patterns as we know. Can we assume they're all just the same, there's 1 pattern that all 52 cards have

[gilded needle]

because it could be HHHT, HHTH, HTHH, or THHH

[dense imp]

im sticking to my answer

😄

[drifting wraith]

no bungo, you're mixing it up

[gilded needle]

oh, so a different question?

[drifting wraith]

you already handle any order

[gilded needle]

quite possibly.. but where's my mistake?

[solar flax]

Same question but imagine that

[gilded needle]

ah wait you're right

[solar flax]

Yes and we dont care about order, it can be anything

[drifting wraith]

you "started" with (1/51)(1/50)(1/49) then you "improved" it to handle all orders

[gilded needle]

the lack of caring about ordering is built into using 13*(4/52)(3/51)(2/50)(1/49) instead of 13*(1/52)(1/51)(1/50)(1/49) as the calculation

[gilded needle]

you are 100% correct

[solar flax]

Not sure im following

Would the correct one be (1/52)×(1/51)etc

Til 49

And what happened with not caring about the 1st card as all 3 other cards just need to
match the first one

Did not see that 13x

[gilded needle]

if you use 13*(1/52)(1/51)(1/50)(1/49) then that's the probability of drawing 4 of the same value in a particular order. To count all the orders you multiply by 4!, which then gives you 13*(4/52)(3/51)(2/50)(1/49), which equals (3/51)(2/50)(1/49)

[solar flax]

Ah

Yes

Yes that was more obvious than i thought

[dense imp]

btw whats expression for 52 choose 4?

[solar flax]

Choose?

[gilded needle]

(52)(51)(50)(49)/4!?

[dense imp]

i think another way to think of it is 13/ (52 choose 4) since there are 13 possible combinations of 4 suits, out of the total possible way of choosing 4 cards

[scarlet locust]

(1/50C4)*13

[dense imp]

that seems to give the same result

[scarlet locust]

yeah

[solar flax]

Have we agreed with 0.00005?

That's what im getting

And I was wrong with 0.39?

0.39%*

[solar flax]

.?

[gilded needle]

>> (3/51)*(2/50)*(1/49)
ans =
      4.80192076830732e-05

[obtuse pebble]

@solar flax Has your question been resolved?

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[uncut grotto]

How can I solve this <@&286206848099549185>

[stone lake]

<@&268886789983436800>

[uncut grotto]

im struggling and I can't seem to understand anything

even after revising the whole lesson

its still quite confusing

[upbeat plinth]

ty

[uncut grotto]

good job for the heads up

[stone lake]

when you turn the gear by some angle, the chain moves by length of the arc for that angle

[uncut grotto]

yeah ik but I can't seem to find a formila or a way to solve it

I haven't taken this lesson in like 3 weeks

[stone lake]

you mean formula for the arc length?

[uncut grotto]

since I had vacation

[uncut grotto]

yeah for 60 degrees

oh wait

I think I got it

isnt it 2pir*(60/360)

[stone lake]

yes

[uncut grotto]

thats the answer

daym

thanks man

what a silly misunderstanding from my end lmao

.close

[obtuse pebble]

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[outer obsidian]

so for me i feel kinda stupid for this. but i am playing a game where i can get buffs. but i want to calculate it.

[outer obsidian]

so what happens is this i get a perk that gives me 90% damage reduction

another one that gives me 40% and another one that gives me 50%

but it doesnt go over a 100 so with the damage of 90 and 50% only it would be 95% damage reduction

then i also get the 40% on top of that

but how do i calculate something like this? i forgot how to do it

and i plan to add more things to it to change damage reduction higher with other abilities

but in the end how do i calculate my end result of the % damage reduction with all those factors of random % that increase it

i hope i expained it well enough 🙂

[royal basin]

so damage reduction perks stack multiplicatively?

[outer obsidian]

prob thats the name i coudnt remember it

[royal basin]

well 90% reduction and 50% reduction stacking to 95% damage reduction sounds multiplicative to me

0.1 * 0.5 = 0.05

your 40%, 50% and 90% reduction perks are essentially multipliers of 0.6, 0.5 and 0.1 respectively, applied to all incoming damage

,calc 0.6 * 0.5 * 0.1

[warm shale]

Result:

0.03

[royal basin]

the damage ends up being exactly 3% of whatever it'd be unreduced

[outer obsidian]

i see so what is left is what i calc

[royal basin]

for a total reduction of 97% if you so wish

[outer obsidian]

from 100-90 is 10 left to calculate over that 50

and then what is left over that 40

i think i get it

,calc 0.60.50.1 * 0.79

[warm shale]

Result:

0.0237

[outer obsidian]

ah yea i get it now thx man

.close

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[rugged vine]

i dont understand

btw its not 6 its 4 square

[dense imp]

what's the net of a cube?

[rugged vine]

6 square faces

<@&286206848099549185>

help

.close

[obtuse pebble]

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[brisk violet]

am i correct?

[bleak nest]

What are you even trying to answer?

[brisk violet]

cos(225)
sin(225)
without using calc

[bleak nest]

Can't you just check it with a calc?

[royal basin]

without using calc

[brisk violet]

i get decimal with calc

[royal basin]

is this your answer?

this is correct.

[brisk violet]

the pink one

ok thanks

.close

[obtuse pebble]

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[modern pebble]

hello everyone!

[modern pebble]

I'm new here! you guys can call me S or Sath

so I just want to know. I'm currently in 10th grade and I like math, the problem is that I can't understand it very well, especially algebra stuff

and I guess I can also say that I'm pretty weak in the basics

can someone help me out with
how to study math properly??

[brisk violet]

read your text book

[scarlet locust]

if you think your algebra is weak, I recommend you to go through Khan Academy's course

https://www.khanacademy.org/math/algebra-basics

[brisk violet]

well thats unfortunate, you should had paid more attention in grade 9th cause thats where u learn the basics and the advance stuffs comes in at grade 10th

[modern pebble]

I'm a bit in the basics of math in total

yeah I know. I still have my math textbook from 9th grade tho

[brisk violet]

read throught it

the basics are in grade 9th

[dense imp]

you might want to ask this in the #prealg-and-algebra channel or #discussion channels, these are meant more for "can you help me with with this specific problem" type questions and will close within a few minutes of no messages being sent then be used for other people's problems, so not many people will see your question, if you post something like this in those other channels it'll be more likely that more people might reply to your question other than whatever responses you get right away

[modern pebble]

the first lesson they have taught in 10th grade is polynomials. and I just can't understand it at all

I find some lessons in math pretty tough

[modern pebble]

ohhh okay, thank you for telling me!!

[brisk violet]

oh polynomials

i learnt that in grade 7th

[modern pebble]

ohh I see

[brisk violet]

poly means many and nomials means terms

[modern pebble]

they started polynomilals for me in 9th grade

It was pretty confusing tbh

do you know about the division algorithm??

[brisk violet]

ok wait

[modern pebble]

alright

[brisk violet]

here

this took me a while

but here

remember this first

[modern pebble]

okayyy!

[brisk violet]

understand it?

[modern pebble]

yes! this is the base in polynomials right??

[brisk violet]

i guess

use khan academy

i used khan academy for 2 years already

[modern pebble]

yeah I'm using it!

I use khan academy for science!

woww!

[brisk violet]

guess what

try schoolhouse

[modern pebble]

oh is it a website??

[brisk violet]

its free and the founder of schoolhouse is the same as khan academy

[brisk violet]

yes

they offer free online tutoring

amazing

its (free)

[modern pebble]

oh okay!

[brisk violet]

its free tutor

[modern pebble]

I will definitely try it out!

[brisk violet]

regularly tutor cost money

[brisk violet]

ok

[modern pebble]

thank you so much for helping!

[brisk violet]

np

70% of my math was learnt from khan academy

[modern pebble]

ohhhh I see. I will try my best to get good in the basics

[brisk violet]

ok

[modern pebble]

are you in 12th grade now??

[brisk violet]

oh i dont wanna say any information

but im above grade 10th

[modern pebble]

oh kay!

thanks for helping again!

[brisk violet]

np

[modern pebble]

bye!

[brisk violet]

bye

[modern pebble]

.close

[obtuse pebble]

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[obtuse pebble]

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[meager raptor]

Help

What

No

[fading pollen]

how do i prove its independent of theta

[fading pollen]

wait nvm

.clse

.closew

.close

[obtuse pebble]

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[meager raptor]

Help

[misty cave]

oh both you guys sent a q at the same time

[meager raptor]

Yup

[misty cave]

rip

[meager raptor]

Can u help pls

[misty cave]

yea sure

[meager raptor]

Thx

[lucid flame]

send it in another channel

since this is already closed

[meager raptor]

I'm reopening it

[lucid flame]

only Gwak can .reopen i believe

[obtuse pebble]

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[timid silo]

why does x=√9 equal just 3 but x²= 9 get us ±3??

[dusk turret]

That's a good question.

And you should understand this concept really well.

Do you know what a function is?

[timid silo]

yeah, something that gives us exactly 1 output or for input

relation

[dusk turret]

Correct. Well, the square root is an extremely useful tool to be able to treat as a function.

You can consider it a very useful convention.

If we allow it to have two different values, then it's no longer a function, and that becomes unwieldy.

[dense imp]

9 technically has two square roots, -3 and 3, but the square root function only returns the principal root (aka the positive one)

the important bit is $\sqrt{x^2}=|x|$

[warm shale]

Sooshon

[dense imp]

@timid silo maybe thinking of this idea of square root of a squared variable helps

[timid silo]

so is it a function or not? cuz we are finding the square root of 9 as well in x^2=9 and that gives us 2 outputs

[warm canopy]

there is a difference between $\sqrt{9}$ and finding the solutions to $x^2=9$

[warm shale]

iCaird

[timid silo]

what is it

[warm canopy]

one is a function and the other is an equation you're solving

[warm canopy]

this is why $\pm$ turns up when solving

[warm shale]

iCaird

[timid silo]

ive heard everyone say that if the root sign is already there then theres no negative for it and if you introduce it then theres 2 outputs

but why is it

[warm canopy]

.

[timid silo]

.close

[obtuse pebble]

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[obtuse pebble]

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[hazy marlin]

Hey everyone
question, could I use a riemann sum to define an improper integral ?

[hazy marlin]

$$\int_{1}^{\infty}f=\lim_{b\to\infty}\int_{1}^{b}f=\sum_{i=1}^{n}f(\theta_i)\cdot\Delta x_i$$

[warm shale]

Deus_Vult

[hazy marlin]

where $\Delta x_i=\frac{b-1}{n}$

or is delta X not well define here.. ?

[warm shale]

Deus_Vult

[obtuse pebble]

@hazy marlin Has your question been resolved?

[wary vigil]

if b goes to infinity then delta x does too

unless n also goes to infinity

[tardy epoch]

your number of terms just needs to grow faster than the width of the interval

https://math.stackexchange.com/questions/2340272/riemann-sums-of-improper-integrals

[obtuse pebble]

@hazy marlin Has your question been resolved?

[hazy marlin]

yea N goes to infinity which is implied by the riemann integal, I should've denoted it

[wary vigil]

i think riemann gave a good answer

it makes sense to me at least 😄

[hazy marlin]

I wonder
will that apply to any integrable function f, or only specific ones ?

[tardy epoch]

i don't know of any general patterns. i wouldn't be surprised if n^2 didn't work for some functions

[obtuse pebble]

@hazy marlin Has your question been resolved?

[obtuse pebble]

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[night flame]

hi

[night flame]

if x = 30

y = 10

what's the answer of (x/y) + (x/y)

i think it's 6

[covert magnet]

yep

[night flame]

ok

goodbye

.close

[obtuse pebble]

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[main cargo]

B

part b

i thought

.close

[obtuse pebble]

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[strong vale]

bruh, go sleep xD how many questions have you done today

[obtuse pebble]

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[unborn brook]

I know the common denominator is 14 but I’m having trouble with the numerator

[nocturne sun]

$$\frac{z + 3}{14} - \frac{8z}{14}$$
do you agree? since you said you know the common denominator is 14

[warm shale]

Doggo

[unborn brook]

but how did you get the 8

[nocturne sun]

multiply top and bottom by 2 to go from 7 to 14

so $2 \cdot 4z = 8z$

[warm shale]

Doggo

[unborn brook]

then combine like terms?

[nocturne sun]

yeah

[unborn brook]

Thank youuu (:

.close

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[main cargo]

this is just causing me pain

because

its just painful

ive got an expression rn with cost and sint

i know what i need to do

normally what i do is this:

differentiate one of them, i differentiated dx/dt this time

then i sub the other equation into it

then i sub the original equation into it

but like

its just a mess of sin's and cos's i cant make the correct substitution

and uh

somethings wrong with the mark scheme lol

[strong vale]

So, you have been given what $\frac{dx}{dt}$ is

[warm shale]

azeem321

[strong vale]

differentiate this again

to find $\frac{d^2x}{dt^2}$

[warm shale]

azeem321

[strong vale]

and carry out the addition given in the problem to show that it equals 4sint

[main cargo]

yep thats the problem

i cant carry out the addition

ive triedl ike

10 times

i cant sub the right things in to get sint

[strong vale]

ok what's d^2x/dt^2

[main cargo]

because

d^2x/dt^2 = dx/dt - dy/dt + cosht

that cosht is a massive problem

[strong vale]

cosht?

[main cargo]

soz

[strong vale]

cos t

[main cargo]

i mean cost

[strong vale]

yh

ok

so you have dx/dt - dy/dt + cos t

now carry out the addition

[main cargo]

normally i now sub stuff in

idk what addition is

normally i sub in the other differential equation

when doing systems

[strong vale]

$\frac{d^2x}{dt^2} + 3\frac{dx}{dt}$

[warm shale]

azeem321

[strong vale]

You want to show that this equals 4sin(t)

[main cargo]

+2x

[strong vale]

You have been given dx/dt

and you just worked out d^2x/dt^2

so add them like above

[main cargo]

uh

uh

ur not supposed to use the thing u show

i dont think im allowed to do that

mark scheme also says substitute

can we do it with substitution rather than addition?

you know what

[strong vale]

There are many ways to do it. But the question asks you to show that $\frac{d^2x}{dt^2} + 3\frac{dx}{dt} + 2x = 4\sin{t}$. An acceptable method should be to find $x''(t)$ and sub this in

[main cargo]

i think i just cracked it anyway

[warm shale]

azeem321

[main cargo]

when subbing this into here

you get -cost

which cancels the other cost

somehow

the 10 times ive done it, ive made that same mistake

WAIT

no

its ok

it works

[strong vale]

ah this looks messy

[strong vale]

what do you mean

subbing that into there

[main cargo]

subbing the photo into the d^2x/dt^2

then you sub the original dx/dt back in to the new expression

and B O O M

got it

🙂

[strong vale]

yeah

[dense imp]

did you get helped here? too long to read over the whole convo : )

[main cargo]

nah its all good now

thanks !

.close

[obtuse pebble]

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[obtuse pebble]

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[scarlet breach]

I've been able to do the iterative steps to verify that there are no separating equilibria in this scenario.

However, when checking for pooling equilibria, I am being stumped by the fact that the expected utility for player 2 for either response is equal. I have no idea how to proceed from there? All examples I can find has an obvious preferred response for player two, which then allows you to check if any deviations from player 1 from the equilibrium path would be profitable.

Am I missing something really obvious?

[obtuse pebble]

@scarlet breach Has your question been resolved?

[scarlet breach]

<@&286206848099549185>

[obtuse pebble]

@scarlet breach Has your question been resolved?

[obtuse pebble]

@scarlet breach Has your question been resolved?

[obtuse pebble]

Channel closed

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[obtuse pebble]

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[frozen wadi]

how to find period

4pi over what

[crystal moss]

the period is 4pi, do you meant the horizontal stretch value? (like the b in sin bx?)

[frozen wadi]

the formula is like 4pi/b

how to find b

[crystal moss]

for period?!

ok so 2pi/|b|=period (in this case 4pi)

[frozen wadi]

and how do i know if it sine or cosine???

[crystal moss]

not 4pi/b, 2pi is 360, 4pi is 720 (in deg)

[crystal moss]

sin and cosine can be reversed, does your question specify what type?

if not just go with the visually closer one

[frozen wadi]

it asking me what type it is